%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW300+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 : n017.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 18:06:51 EDT 2024 % Result : Theorem 14.79s 14.65s % Output : CNFRefutation 14.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.13 % Problem : SWW300+1 : TPTP v8.2.0. Released v5.2.0. % 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n017.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 07:47:39 EDT 2024 % 0.13/0.34 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 14.39/14.50 %------------------------------------------- % 14.39/14.50 % File :CSE---1.7 % 14.39/14.50 % Problem :theBenchmark % 14.39/14.50 % Transform :cnf % 14.39/14.50 % Format :tptp:raw % 14.39/14.50 % Command :java -jar mcs_scs.jar %d %s % 14.39/14.50 % 14.39/14.50 % Result :Theorem 0.540000s % 14.39/14.50 % Output :CNFRefutation 0.540000s % 14.39/14.50 %------------------------------------------- % 14.39/14.51 %------------------------------------------------------------------------------ % 14.39/14.51 % File : SWW300+1 : TPTP v8.2.0. Released v5.2.0. % 14.39/14.51 % Domain : Software Verification % 14.39/14.51 % Problem : Hoare's Logic with Procedures 434814, 5000 axioms selected % 14.39/14.51 % Version : Especial. % 14.39/14.51 % English : % 14.39/14.51 % 14.39/14.51 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 14.39/14.51 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 14.39/14.51 % Source : [Bla11] % 14.39/14.51 % Names : hoare_434814.5000.p [Bla11] % 14.39/14.51 % 14.39/14.51 % Status : Theorem % 14.39/14.51 % Rating : 0.42 v8.2.0, 0.44 v8.1.0, 0.42 v7.5.0, 0.41 v7.4.0, 0.53 v7.3.0, 0.52 v7.2.0, 0.48 v7.1.0, 0.57 v6.4.0, 0.54 v6.2.0, 0.64 v6.1.0, 0.70 v6.0.0, 0.57 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0 % 14.39/14.51 % Syntax : Number of formulae : 5242 (1665 unt; 0 def) % 14.39/14.51 % Number of atoms : 12783 (4408 equ) % 14.39/14.51 % Maximal formula atoms : 13 ( 2 avg) % 14.39/14.51 % Number of connectives : 8527 ( 986 ~; 151 |; 705 &) % 14.39/14.51 % ( 908 <=>;5777 =>; 0 <=; 0 <~>) % 14.39/14.51 % Maximal formula depth : 22 ( 6 avg) % 14.39/14.51 % Maximal term depth : 19 ( 2 avg) % 14.39/14.51 % Number of predicates : 152 ( 151 usr; 1 prp; 0-6 aty) % 14.39/14.51 % Number of functors : 375 ( 375 usr; 45 con; 0-7 aty) % 14.39/14.51 % Number of variables : 16569 (16411 !; 158 ?) % 14.39/14.51 % SPC : FOF_THM_RFO_SEQ % 14.39/14.51 % 14.39/14.51 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 14.39/14.51 % 2011-03-01 11:31:01 % 14.39/14.51 %------------------------------------------------------------------------------ % 14.39/14.51 %----Relevant facts (4982) % 14.39/14.51 fof(fact_ext,axiom, % 14.39/14.51 ! [V_g_2,V_f_2] : % 14.39/14.51 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 14.39/14.51 => V_f_2 = V_g_2 ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_equal__triple__def,axiom, % 14.39/14.51 ! [V_y_2,V_x_2,T_b] : % 14.39/14.51 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(T_b)),V_x_2),V_y_2)) % 14.39/14.51 <=> V_x_2 = V_y_2 ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_Rep__triple__inject,axiom, % 14.39/14.51 ! [V_y_2,V_x_2,T_b] : % 14.39/14.51 ( hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2) = hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_y_2) % 14.39/14.51 <=> V_x_2 = V_y_2 ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_equal,axiom, % 14.39/14.51 ! [T_b] : % 14.39/14.51 ( class_HOL_Oequal(T_b) % 14.39/14.51 => c_HOL_Oequal__class_Oequal(T_b) = c_fequal ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_equal__refl,axiom, % 14.39/14.51 ! [V_x,T_a] : % 14.39/14.51 ( class_HOL_Oequal(T_a) % 14.39/14.51 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_equal__eq,axiom, % 14.39/14.51 ! [V_y_2,V_x_2,T_b] : % 14.39/14.51 ( class_HOL_Oequal(T_b) % 14.39/14.51 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2)) % 14.39/14.51 <=> V_x_2 = V_y_2 ) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_eq__equal,axiom, % 14.39/14.51 ! [T_b] : % 14.39/14.51 ( class_HOL_Oequal(T_b) % 14.39/14.51 => c_fequal = c_HOL_Oequal__class_Oequal(T_b) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_Rep__triple__inverse,axiom, % 14.39/14.51 ! [V_x_2,T_b] : hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2)) = V_x_2 ). % 14.39/14.51 % 14.39/14.51 fof(fact_Rep__triple,axiom, % 14.39/14.51 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ). % 14.39/14.51 % 14.39/14.51 fof(fact_type__definition__triple,axiom, % 14.39/14.51 ! [T_b] : c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(T_b),tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool),c_Hoare__Mirabelle_ORep__triple(T_b),c_Hoare__Mirabelle_OAbs__triple(T_b),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))) ). % 14.39/14.51 % 14.39/14.51 fof(fact_Abs__triple__inverse,axiom, % 14.39/14.51 ! [V_y_2,T_b] : % 14.39/14.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) % 14.39/14.51 => hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2)) = V_y_2 ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_Abs__triple__inject,axiom, % 14.39/14.51 ! [V_y_2,V_x_2,T_b] : % 14.39/14.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_x_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) % 14.39/14.51 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) % 14.39/14.51 => ( hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_x_2) = hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2) % 14.39/14.51 <=> V_x_2 = V_y_2 ) ) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_equalityCE,axiom, % 14.39/14.51 ! [V_ca_2,T_b,V_B_2,V_A_2] : % 14.39/14.51 ( V_A_2 = V_B_2 % 14.39/14.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.39/14.51 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) % 14.39/14.51 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.39/14.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_type__definition_OAbs__inject,axiom, % 14.39/14.51 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.51 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.51 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 14.39/14.51 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 14.39/14.51 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 14.39/14.51 <=> V_x_2 = V_y_2 ) ) ) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_type__definition_OAbs__inverse,axiom, % 14.39/14.51 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.51 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.51 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 14.39/14.51 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_type__definition_ORep,axiom, % 14.39/14.51 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.51 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.51 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_Abs__triple__induct,axiom, % 14.39/14.51 ! [V_x_2,V_Pa_2,T_b] : % 14.39/14.51 ( ! [B_y] : % 14.39/14.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),B_y),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) % 14.39/14.51 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),B_y))) ) % 14.39/14.51 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_Abs__triple__cases,axiom, % 14.39/14.51 ! [T_b,V_x_2] : % 14.39/14.51 ~ ! [B_y] : % 14.39/14.51 ( V_x_2 = hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),B_y) % 14.39/14.51 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),B_y),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ) ). % 14.39/14.51 % 14.39/14.51 fof(fact_Rep__triple__induct,axiom, % 14.39/14.51 ! [V_Pa_2,V_y_2,T_b] : % 14.39/14.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) % 14.39/14.52 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),B_x))) % 14.39/14.52 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Rep__triple__cases,axiom, % 14.39/14.52 ! [V_y_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) % 14.39/14.52 => ~ ! [B_x] : V_y_2 != hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),B_x) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_type__definition_ORep__inject,axiom, % 14.39/14.52 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.52 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.52 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 14.39/14.52 <=> V_x_2 = V_y_2 ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_type__definition_ORep__inverse,axiom, % 14.39/14.52 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.52 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.52 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Collect__def,axiom, % 14.39/14.52 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ). % 14.39/14.52 % 14.39/14.52 fof(fact_eq__mem__trans,axiom, % 14.39/14.52 ! [V_A_2,T_b,V_b_2,V_a_2] : % 14.39/14.52 ( V_a_2 = V_b_2 % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_mem__def,axiom, % 14.39/14.52 ! [V_A_2,V_x_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.52 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_eqset__imp__iff,axiom, % 14.39/14.52 ! [V_x_2,T_b,V_B_2,V_A_2] : % 14.39/14.52 ( V_A_2 = V_B_2 % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.52 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_eqelem__imp__iff,axiom, % 14.39/14.52 ! [V_A_2,T_b,V_y_2,V_x_2] : % 14.39/14.52 ( V_x_2 = V_y_2 % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.52 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_eq__mem,axiom, % 14.39/14.52 ! [V_y_2,V_x_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) % 14.39/14.52 <=> V_x_2 = V_y_2 ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_type__definition_OAbs__cases,axiom, % 14.39/14.52 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.52 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.52 => ~ ! [B_y] : % 14.39/14.52 ( V_x_2 = hAPP(V_Abs_2,B_y) % 14.39/14.52 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_type__definition_OAbs__induct,axiom, % 14.39/14.52 ! [V_x_2,V_Pa_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.52 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.52 => ( ! [B_y] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) % 14.39/14.52 => hBOOL(hAPP(V_Pa_2,hAPP(V_Abs_2,B_y))) ) % 14.39/14.52 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_type__definition_ORep__induct,axiom, % 14.39/14.52 ! [V_Pa_2,V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.52 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 14.39/14.52 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(V_Rep_2,B_x))) % 14.39/14.52 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_type__definition_ORep__cases,axiom, % 14.39/14.52 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.39/14.52 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 14.39/14.52 => ~ ! [B_x] : V_y_2 != hAPP(V_Rep_2,B_x) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_induct__false__def,axiom, % 14.39/14.52 ~ c_HOL_Oinduct__false ). % 14.39/14.52 % 14.39/14.52 fof(fact_ord_OatMost__iff,axiom, % 14.39/14.52 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) % 14.39/14.52 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_ord_OatLeast__iff,axiom, % 14.39/14.52 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) % 14.39/14.52 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_ord_OlessThan__iff,axiom, % 14.39/14.52 ! [V_k_2,V_less_2,V_i_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) % 14.39/14.52 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_ord_OgreaterThan__iff,axiom, % 14.39/14.52 ! [V_k_2,V_less_2,V_i_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) % 14.39/14.52 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_ord_OatLeastAtMost__iff,axiom, % 14.39/14.52 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2))) % 14.39/14.52 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 14.39/14.52 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 14.39/14.52 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2))) % 14.39/14.52 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 14.39/14.52 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 14.39/14.52 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 14.39/14.52 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 14.39/14.52 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_ord_OatLeastLessThan__iff,axiom, % 14.39/14.52 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 14.39/14.52 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 14.39/14.52 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_ballE,axiom, % 14.39/14.52 ! [V_x_2,V_Pa_2,V_A_2,T_b] : % 14.39/14.52 ( ! [B_x] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.39/14.52 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.39/14.52 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_bexE,axiom, % 14.39/14.52 ! [V_Pa_2,V_A_2,T_b] : % 14.39/14.52 ( ? [B_x] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.52 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.39/14.52 => ~ ! [B_x] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.52 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_bexI,axiom, % 14.39/14.52 ! [V_A_2,T_b,V_x_2,V_Pa_2] : % 14.39/14.52 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.52 => ? [B_x] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.52 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_InterE,axiom, % 14.39/14.52 ! [V_X_2,V_C_2,V_A_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_InterD,axiom, % 14.39/14.52 ! [V_X_2,V_C_2,V_A_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_UnionI,axiom, % 14.39/14.52 ! [V_A_2,V_C_2,V_X_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_emptyE,axiom, % 14.39/14.52 ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.39/14.52 % 14.39/14.52 fof(fact_UNIV__I,axiom, % 14.39/14.52 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.39/14.52 % 14.39/14.52 fof(fact_subsetD,axiom, % 14.39/14.52 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_equalityI,axiom, % 14.39/14.52 ! [V_B_2,V_A_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.39/14.52 => V_A_2 = V_B_2 ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_top1I,axiom, % 14.39/14.52 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ). % 14.39/14.52 % 14.39/14.52 fof(fact_empty__subsetI,axiom, % 14.39/14.52 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 14.39/14.52 % 14.39/14.52 fof(fact_predicate1D,axiom, % 14.39/14.52 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) % 14.39/14.52 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.39/14.52 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_rev__predicate1D,axiom, % 14.39/14.52 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] : % 14.39/14.52 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) % 14.39/14.52 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Inf__empty,axiom, % 14.39/14.52 ! [T_b] : % 14.39/14.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.52 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Inter__empty,axiom, % 14.39/14.52 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Inf__UNIV,axiom, % 14.39/14.52 ! [T_b] : % 14.39/14.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.52 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Inter__UNIV,axiom, % 14.39/14.52 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Sup__empty,axiom, % 14.39/14.52 ! [T_b] : % 14.39/14.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.52 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Union__empty,axiom, % 14.39/14.52 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Sup__UNIV,axiom, % 14.39/14.52 ! [T_b] : % 14.39/14.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.52 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Union__UNIV,axiom, % 14.39/14.52 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.39/14.52 % 14.39/14.52 fof(fact_le__Inf__iff,axiom, % 14.39/14.52 ! [V_A_2,V_b_2,T_b] : % 14.39/14.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) % 14.39/14.52 <=> ! [B_x] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Sup__le__iff,axiom, % 14.39/14.52 ! [V_b_2,V_A_2,T_b] : % 14.39/14.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2)) % 14.39/14.52 <=> ! [B_x] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Union__mono,axiom, % 14.39/14.52 ! [V_B_2,V_A_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_Inter__anti__mono,axiom, % 14.39/14.52 ! [V_A_2,V_B_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) % 14.39/14.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_equalityE,axiom, % 14.39/14.52 ! [T_b,V_B_2,V_A_2] : % 14.39/14.52 ( V_A_2 = V_B_2 % 14.39/14.52 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.52 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 14.39/14.52 % 14.39/14.52 fof(fact_subset__trans,axiom, % 14.39/14.52 ! [V_C_2,V_B_2,V_A_2,T_b] : % 14.39/14.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_equalityD2,axiom, % 14.39/14.53 ! [T_b,V_B_2,V_A_2] : % 14.39/14.53 ( V_A_2 = V_B_2 % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_equalityD1,axiom, % 14.39/14.53 ! [T_b,V_B_2,V_A_2] : % 14.39/14.53 ( V_A_2 = V_B_2 % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_set__eq__subset,axiom, % 14.39/14.53 ! [T_b,V_B_2,V_A_2] : % 14.39/14.53 ( V_A_2 = V_B_2 % 14.39/14.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_subset__empty,axiom, % 14.39/14.53 ! [V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.39/14.53 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_subset__refl,axiom, % 14.39/14.53 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 14.39/14.53 % 14.39/14.53 fof(fact_subset__UNIV,axiom, % 14.39/14.53 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.39/14.53 % 14.39/14.53 fof(fact_UNIV__not__empty,axiom, % 14.39/14.53 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Union__upper,axiom, % 14.39/14.53 ! [V_A_2,V_B_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Sup__upper,axiom, % 14.39/14.53 ! [V_A_2,V_x_2,T_b] : % 14.39/14.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Inter__lower,axiom, % 14.39/14.53 ! [V_A_2,V_B_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Inf__lower,axiom, % 14.39/14.53 ! [V_A_2,V_x_2,T_b] : % 14.39/14.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_in__mono,axiom, % 14.39/14.53 ! [V_x_2,V_B_2,V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_set__rev__mp,axiom, % 14.39/14.53 ! [V_B_2,V_A_2,V_x_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_set__mp,axiom, % 14.39/14.53 ! [V_x_2,V_B_2,V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_all__not__in__conv,axiom, % 14.39/14.53 ! [V_A_2,T_b] : % 14.39/14.53 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.53 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_ex__in__conv,axiom, % 14.39/14.53 ! [V_A_2,T_b] : % 14.39/14.53 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.53 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_empty__iff,axiom, % 14.39/14.53 ! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.39/14.53 % 14.39/14.53 fof(fact_equals0D,axiom, % 14.39/14.53 ! [V_a_2,T_b,V_A_2] : % 14.39/14.53 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.39/14.53 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_empty__Collect__eq,axiom, % 14.39/14.53 ! [V_Pa_2,T_b] : % 14.39/14.53 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) % 14.39/14.53 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Collect__empty__eq,axiom, % 14.39/14.53 ! [V_Pa_2,T_b] : % 14.39/14.53 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.39/14.53 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_order__refl,axiom, % 14.39/14.53 ! [V_x,T_a] : % 14.39/14.53 ( class_Orderings_Opreorder(T_a) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_top__apply,axiom, % 14.39/14.53 ! [V_x_2,T_c,T_b] : % 14.39/14.53 ( class_Orderings_Otop(T_b) % 14.39/14.53 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_bot__apply,axiom, % 14.39/14.53 ! [V_x_2,T_c,T_b] : % 14.39/14.53 ( class_Orderings_Obot(T_b) % 14.39/14.53 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_iso__tuple__UNIV__I,axiom, % 14.39/14.53 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.39/14.53 % 14.39/14.53 fof(fact_top__greatest,axiom, % 14.39/14.53 ! [V_x,T_a] : % 14.39/14.53 ( class_Orderings_Otop(T_a) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_le__fun__def,axiom, % 14.39/14.53 ! [V_g_2,V_f_2,T_b,T_c] : % 14.39/14.53 ( class_Orderings_Oord(T_c) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 14.39/14.53 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_le__funD,axiom, % 14.39/14.53 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 14.39/14.53 ( class_Orderings_Oord(T_c) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_le__funE,axiom, % 14.39/14.53 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 14.39/14.53 ( class_Orderings_Oord(T_c) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_bot__least,axiom, % 14.39/14.53 ! [V_x,T_a] : % 14.39/14.53 ( class_Orderings_Obot(T_a) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_InterI,axiom, % 14.39/14.53 ! [V_A_2,V_C_2,T_b] : % 14.39/14.53 ( ! [B_X] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) ) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_UnionE,axiom, % 14.39/14.53 ! [V_C_2,V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 14.39/14.53 => ~ ! [B_X] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) % 14.39/14.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Inter__greatest,axiom, % 14.39/14.53 ! [V_C_2,V_A_2,T_b] : % 14.39/14.53 ( ! [B_X] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),B_X)) ) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_linorder__le__cases,axiom, % 14.39/14.53 ! [V_y,V_x,T_a] : % 14.39/14.53 ( class_Orderings_Olinorder(T_a) % 14.39/14.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_xt1_I6_J,axiom, % 14.39/14.53 ! [V_z,V_x,V_y,T_a] : % 14.39/14.53 ( class_Orderings_Oorder(T_a) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_xt1_I5_J,axiom, % 14.39/14.53 ! [V_x,V_y,T_a] : % 14.39/14.53 ( class_Orderings_Oorder(T_a) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.39/14.53 => V_x = V_y ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_order__trans,axiom, % 14.39/14.53 ! [V_z,V_y,V_x,T_a] : % 14.39/14.53 ( class_Orderings_Opreorder(T_a) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_order__antisym,axiom, % 14.39/14.53 ! [V_y,V_x,T_a] : % 14.39/14.53 ( class_Orderings_Oorder(T_a) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.39/14.53 => V_x = V_y ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_xt1_I4_J,axiom, % 14.39/14.53 ! [V_c,V_a,V_b,T_a] : % 14.39/14.53 ( class_Orderings_Oorder(T_a) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 14.39/14.53 => ( V_b = V_c % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_ord__le__eq__trans,axiom, % 14.39/14.53 ! [V_c,V_b,V_a,T_a] : % 14.39/14.53 ( class_Orderings_Oord(T_a) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.39/14.53 => ( V_b = V_c % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_xt1_I3_J,axiom, % 14.39/14.53 ! [V_c,V_b,V_a,T_a] : % 14.39/14.53 ( class_Orderings_Oorder(T_a) % 14.39/14.53 => ( V_a = V_b % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_ord__eq__le__trans,axiom, % 14.39/14.53 ! [V_c,V_b,V_a,T_a] : % 14.39/14.53 ( class_Orderings_Oord(T_a) % 14.39/14.53 => ( V_a = V_b % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_order__antisym__conv,axiom, % 14.39/14.53 ! [V_x_2,V_y_2,T_b] : % 14.39/14.53 ( class_Orderings_Oorder(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.39/14.53 <=> V_x_2 = V_y_2 ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_order__eq__refl,axiom, % 14.39/14.53 ! [V_y,V_x,T_a] : % 14.39/14.53 ( class_Orderings_Opreorder(T_a) % 14.39/14.53 => ( V_x = V_y % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_order__eq__iff,axiom, % 14.39/14.53 ! [V_y_2,V_x_2,T_b] : % 14.39/14.53 ( class_Orderings_Oorder(T_b) % 14.39/14.53 => ( V_x_2 = V_y_2 % 14.39/14.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.39/14.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_linorder__linear,axiom, % 14.39/14.53 ! [V_y,V_x,T_a] : % 14.39/14.53 ( class_Orderings_Olinorder(T_a) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.39/14.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Powp__mono,axiom, % 14.39/14.53 ! [V_B_2,V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Inter__subset,axiom, % 14.39/14.53 ! [V_B_2,V_A_2,T_b] : % 14.39/14.53 ( ! [B_X] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) ) % 14.39/14.53 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Union__least,axiom, % 14.39/14.53 ! [V_C_2,V_A_2,T_b] : % 14.39/14.53 ( ! [B_X] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_C_2)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Inf__greatest,axiom, % 14.39/14.53 ! [V_z_2,V_A_2,T_b] : % 14.39/14.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.53 => ( ! [B_x] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),B_x)) ) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Sup__least,axiom, % 14.39/14.53 ! [V_z_2,V_A_2,T_b] : % 14.39/14.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.39/14.53 => ( ! [B_x] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_z_2)) ) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_z_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_subsetI,axiom, % 14.39/14.53 ! [V_B_2,V_A_2,T_b] : % 14.39/14.53 ( ! [B_x] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) ) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_greaterThan__subset__iff,axiom, % 14.39/14.53 ! [V_y_2,V_x_2,T_b] : % 14.39/14.53 ( class_Orderings_Olinorder(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2))) % 14.39/14.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Pow__UNIV,axiom, % 14.39/14.53 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 14.39/14.53 % 14.39/14.53 fof(fact_PowI,axiom, % 14.39/14.53 ! [V_B_2,V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_atMost__subset__iff,axiom, % 14.39/14.53 ! [V_y_2,V_x_2,T_b] : % 14.39/14.53 ( class_Orderings_Oorder(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2))) % 14.39/14.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_atLeast__subset__iff,axiom, % 14.39/14.53 ! [V_y_2,V_x_2,T_b] : % 14.39/14.53 ( class_Orderings_Oorder(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2))) % 14.39/14.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_greaterThan__eq__iff,axiom, % 14.39/14.53 ! [V_y_2,V_x_2,T_b] : % 14.39/14.53 ( class_Orderings_Olinorder(T_b) % 14.39/14.53 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) % 14.39/14.53 <=> V_x_2 = V_y_2 ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_atLeast__eq__iff,axiom, % 14.39/14.53 ! [V_y_2,V_x_2,T_b] : % 14.39/14.53 ( class_Orderings_Olinorder(T_b) % 14.39/14.53 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) % 14.39/14.53 <=> V_x_2 = V_y_2 ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_atMost__eq__iff,axiom, % 14.39/14.53 ! [V_y_2,V_x_2,T_b] : % 14.39/14.53 ( class_Orderings_Olinorder(T_b) % 14.39/14.53 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) % 14.39/14.53 <=> V_x_2 = V_y_2 ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Pow__top,axiom, % 14.39/14.53 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Union__Pow__eq,axiom, % 14.39/14.53 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2 ). % 14.39/14.53 % 14.39/14.53 fof(fact_Pow__not__empty,axiom, % 14.39/14.53 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Pow__bottom,axiom, % 14.39/14.53 ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))) ). % 14.39/14.53 % 14.39/14.53 fof(fact_PowD,axiom, % 14.39/14.53 ! [V_B_2,V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Pow__iff,axiom, % 14.39/14.53 ! [V_B_2,V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 14.39/14.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Pow__mono,axiom, % 14.39/14.53 ! [V_B_2,V_A_2,T_b] : % 14.39/14.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_atMost__iff,axiom, % 14.39/14.53 ! [V_k_2,V_i_2,T_b] : % 14.39/14.53 ( class_Orderings_Oord(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) % 14.39/14.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_atLeast__iff,axiom, % 14.39/14.53 ! [V_k_2,V_i_2,T_b] : % 14.39/14.53 ( class_Orderings_Oord(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) % 14.39/14.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_subset__Pow__Union,axiom, % 14.39/14.53 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))) ). % 14.39/14.53 % 14.39/14.53 fof(fact_Pow__empty,axiom, % 14.39/14.53 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ). % 14.39/14.53 % 14.39/14.53 fof(fact_lessThan__subset__iff,axiom, % 14.39/14.53 ! [V_y_2,V_x_2,T_b] : % 14.39/14.53 ( class_Orderings_Olinorder(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2))) % 14.39/14.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_INF__subset,axiom, % 14.39/14.53 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 14.39/14.53 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_SUP__subset,axiom, % 14.39/14.53 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 14.39/14.53 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.39/14.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_greaterThanLessThan__empty,axiom, % 14.39/14.53 ! [V_k_2,V_l_2,T_b] : % 14.39/14.53 ( class_Orderings_Oorder(T_b) % 14.39/14.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 14.39/14.53 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.39/14.53 % 14.39/14.53 fof(fact_greaterThanAtMost__empty,axiom, % 14.39/14.53 ! [V_k_2,V_l_2,T_b] : % 14.39/14.54 ( class_Orderings_Oorder(T_b) % 14.39/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 14.39/14.54 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.39/14.54 % 14.39/14.54 fof(fact_Collect__mono,axiom, % 14.39/14.54 ! [T_b,V_Qa_2,V_Pa_2] : % 14.39/14.54 ( ! [B_x] : % 14.39/14.54 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.39/14.54 => hBOOL(hAPP(V_Qa_2,B_x)) ) % 14.39/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ). % 14.39/14.54 % 14.39/14.54 fof(fact_UNIV__eq__I,axiom, % 14.39/14.54 ! [V_A_2,T_b] : % 14.39/14.54 ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.39/14.54 => c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = V_A_2 ) ). % 14.39/14.54 % 14.39/14.54 fof(fact_UNIV__witness,axiom, % 14.39/14.54 ! [T_b] : % 14.39/14.54 ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.39/14.54 % 14.39/14.54 fof(fact_le__funI,axiom, % 14.39/14.54 ! [T_b,V_g_2,V_f_2,T_c] : % 14.39/14.54 ( class_Orderings_Oord(T_c) % 14.39/14.54 => ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) % 14.39/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ). % 14.39/14.54 % 14.39/14.54 fof(fact_equals0I,axiom, % 14.39/14.54 ! [V_A_2,T_b] : % 14.39/14.54 ( ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 14.39/14.54 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.39/14.54 % 14.39/14.54 fof(fact_insertCI,axiom, % 14.39/14.54 ! [V_b_2,V_B_2,V_a_2,T_b] : % 14.39/14.54 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 14.39/14.54 => V_a_2 = V_b_2 ) % 14.39/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 14.39/14.54 % 14.39/14.54 fof(fact_insertE,axiom, % 14.39/14.54 ! [V_A_2,V_b_2,V_a_2,T_b] : % 14.39/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) % 14.39/14.54 => ( V_a_2 != V_b_2 % 14.39/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 14.39/14.54 % 14.39/14.54 fof(fact_insert__absorb2,axiom, % 14.39/14.54 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ). % 14.39/14.54 % 14.39/14.54 fof(fact_insert__commute,axiom, % 14.39/14.54 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ). % 14.39/14.54 % 14.39/14.54 fof(fact_insert__code,axiom, % 14.39/14.54 ! [V_x_2,V_A_2,V_y_2,T_b] : % 14.39/14.54 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) % 14.39/14.54 <=> ( V_y_2 = V_x_2 % 14.55/14.54 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_lessThan__eq__iff,axiom, % 14.55/14.54 ! [V_y_2,V_x_2,T_b] : % 14.55/14.54 ( class_Orderings_Olinorder(T_b) % 14.55/14.54 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) % 14.55/14.54 <=> V_x_2 = V_y_2 ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__absorb,axiom, % 14.55/14.54 ! [V_A_2,V_a_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insertI2,axiom, % 14.55/14.54 ! [V_b_2,V_B_2,V_a_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__ident,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_x_2,T_b] : % 14.55/14.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 14.55/14.54 => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2) % 14.55/14.54 <=> V_A_2 = V_B_2 ) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__iff,axiom, % 14.55/14.54 ! [V_A_2,V_b_2,V_a_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) % 14.55/14.54 <=> ( V_a_2 = V_b_2 % 14.55/14.54 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insertI1,axiom, % 14.55/14.54 ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_empty__not__insert,axiom, % 14.55/14.54 ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__not__empty,axiom, % 14.55/14.54 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_doubleton__eq__iff,axiom, % 14.55/14.54 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.54 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.55/14.54 <=> ( ( V_a_2 = V_ca_2 % 14.55/14.54 & V_b_2 = V_d_2 ) % 14.55/14.54 | ( V_a_2 = V_d_2 % 14.55/14.54 & V_b_2 = V_ca_2 ) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_singleton__inject,axiom, % 14.55/14.54 ! [V_b_2,V_a_2,T_b] : % 14.55/14.54 ( 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_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 14.55/14.54 => V_a_2 = V_b_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_subset__insertI,axiom, % 14.55/14.54 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_subset__insertI2,axiom, % 14.55/14.54 ! [V_b_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__mono,axiom, % 14.55/14.54 ! [V_a_2,V_D_2,V_C_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_singleton__iff,axiom, % 14.55/14.54 ! [V_a_2,V_b_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),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))))) % 14.55/14.54 <=> V_b_2 = V_a_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_singletonE,axiom, % 14.55/14.54 ! [V_a_2,V_b_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),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))))) % 14.55/14.54 => V_b_2 = V_a_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__subset,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_x_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) % 14.55/14.54 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 14.55/14.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_subset__insert,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_x_2,T_b] : % 14.55/14.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 14.55/14.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_subset__singletonD,axiom, % 14.55/14.54 ! [V_x_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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))))) % 14.55/14.54 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.54 | 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))) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Sup__singleton,axiom, % 14.55/14.54 ! [V_a_2,T_b] : % 14.55/14.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.54 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Inf__singleton,axiom, % 14.55/14.54 ! [V_a_2,T_b] : % 14.55/14.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.54 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_the__elem__eq,axiom, % 14.55/14.54 ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_ivl__disj__un_I1_J,axiom, % 14.55/14.54 ! [V_l_2,T_b] : % 14.55/14.54 ( class_Orderings_Olinorder(T_b) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_atMost__Int__atLeast,axiom, % 14.55/14.54 ! [V_n_2,T_b] : % 14.55/14.54 ( class_Orderings_Oorder(T_b) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_ivl__disj__un_I2_J,axiom, % 14.55/14.54 ! [V_u_2,T_b] : % 14.55/14.54 ( class_Orderings_Olinorder(T_b) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_diff__single__insert,axiom, % 14.55/14.54 ! [V_B_2,V_x_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_subset__insert__iff,axiom, % 14.55/14.54 ! [V_B_2,V_x_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 14.55/14.54 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2)) ) % 14.55/14.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__eq__Inter,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__eq__Union,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_ivl__disj__int_I5_J,axiom, % 14.55/14.54 ! [V_u_2,V_l_2,T_b] : % 14.55/14.54 ( class_Orderings_Oorder(T_b) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_ivl__disj__int_I6_J,axiom, % 14.55/14.54 ! [V_u_2,V_l_2,T_b] : % 14.55/14.54 ( class_Orderings_Oorder(T_b) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_ivl__disj__un_I11_J,axiom, % 14.55/14.54 ! [V_u_2,V_l_2,T_b] : % 14.55/14.54 ( class_Orderings_Olinorder(T_b) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_sup1CI,axiom, % 14.55/14.54 ! [T_b,V_A_2,V_x_2,V_B_2] : % 14.55/14.54 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 14.55/14.54 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 14.55/14.54 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_sup1E,axiom, % 14.55/14.54 ! [V_x_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 14.55/14.54 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 14.55/14.54 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_inf1E,axiom, % 14.55/14.54 ! [V_x_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 14.55/14.54 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 14.55/14.54 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_inf1I,axiom, % 14.55/14.54 ! [T_b,V_B_2,V_x_2,V_A_2] : % 14.55/14.54 ( hBOOL(hAPP(V_A_2,V_x_2)) % 14.55/14.54 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_UnE,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_UnCI,axiom, % 14.55/14.54 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 14.55/14.54 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_IntI,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_IntE,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_DiffI,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_DiffE,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_inf1D2,axiom, % 14.55/14.54 ! [V_x_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 14.55/14.54 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_inf1D1,axiom, % 14.55/14.54 ! [V_x_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 14.55/14.54 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_sup1I2,axiom, % 14.55/14.54 ! [V_A_2,T_b,V_x_2,V_B_2] : % 14.55/14.54 ( hBOOL(hAPP(V_B_2,V_x_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_sup1I1,axiom, % 14.55/14.54 ! [V_B_2,T_b,V_x_2,V_A_2] : % 14.55/14.54 ( hBOOL(hAPP(V_A_2,V_x_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Int__crazy,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__Int2,axiom, % 14.55/14.54 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Diff__Int,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),V_B_2)) = V_A_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_ball__Un,axiom, % 14.55/14.54 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( ! [B_x] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.55/14.54 <=> ( ! [B_x] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.54 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.55/14.54 & ! [B_x] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_bex__Un,axiom, % 14.55/14.54 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( ? [B_x] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.55/14.54 <=> ( ? [B_x] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.54 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.55/14.54 | ? [B_x] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 14.55/14.54 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Int__distrib2,axiom, % 14.55/14.54 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__Un__distrib2,axiom, % 14.55/14.54 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__Int__distrib2,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Diff,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__assoc,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__assoc,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__Diff,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Diff__cancel2,axiom, % 14.55/14.54 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__idemp,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Int__distrib,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__Int__distrib,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_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_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__Un__distrib,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__Un,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__Int,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__left__commute,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__left__commute,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__left__absorb,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_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_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Diff__cancel,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__left__absorb,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_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_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__commute,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : 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_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__commute,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : 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_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__absorb,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__absorb,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__triv,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : % 14.55/14.54 ( 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)) % 14.55/14.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__disjoint,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__partition,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__subset__conv,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 14.55/14.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Int__assoc__eq,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.55/14.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Union__Un__distrib,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Pow__Int__eq,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),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(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Inter__Un__distrib,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Union__Int__subset,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Inter__Un__subset,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__iff,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_DiffD1,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_DiffD2,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__iff,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_UnI1,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_UnI2,axiom, % 14.55/14.54 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__iff,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.54 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_IntD1,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_IntD2,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__cancel,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__empty,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_empty__Diff,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__empty,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hAPP(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)) % 14.55/14.54 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.54 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__empty__right,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__empty__left,axiom, % 14.55/14.54 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_disjoint__iff__not__equal,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : % 14.55/14.54 ( 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)) % 14.55/14.54 <=> ! [B_x] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.54 => ! [B_xa] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) % 14.55/14.54 => B_x != B_xa ) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__empty__right,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_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)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__empty__left,axiom, % 14.55/14.54 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_double__diff,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.55/14.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__mono,axiom, % 14.55/14.54 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__subset,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__insert__left,axiom, % 14.55/14.54 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__insert__right,axiom, % 14.55/14.54 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__inter__insert,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__mono,axiom, % 14.55/14.54 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__least,axiom, % 14.55/14.54 ! [V_B_2,V_C_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,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_C_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__absorb2,axiom, % 14.55/14.54 ! [V_A_2,V_B_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__absorb1,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_subset__Un__eq,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.54 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__upper2,axiom, % 14.55/14.54 ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__upper1,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__UNIV__right,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__UNIV__left,axiom, % 14.55/14.54 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__mono,axiom, % 14.55/14.54 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__greatest,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_C_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) % 14.55/14.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__absorb1,axiom, % 14.55/14.54 ! [V_A_2,V_B_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__absorb2,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__lower2,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__lower1,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__UNIV__right,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__UNIV__left,axiom, % 14.55/14.54 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 14.55/14.54 % 14.55/14.54 fof(fact_Un__Pow__subset,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__Diff1,axiom, % 14.55/14.54 ! [V_A_2,V_B_2,V_x_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 14.55/14.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__Diff__if,axiom, % 14.55/14.54 ! [V_A_2,V_B_2,V_x_2,T_b] : % 14.55/14.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 14.55/14.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) % 14.55/14.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 14.55/14.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__Diff__single,axiom, % 14.55/14.54 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__insert2,axiom, % 14.55/14.54 ! [V_B_2,V_a_2,V_A_2,T_b] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__insert,axiom, % 14.55/14.54 ! [V_B_2,V_a_2,V_A_2,T_b] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_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)))) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__insert__left__if1,axiom, % 14.55/14.54 ! [V_B_2,V_C_2,V_a_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__insert__right__if1,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_a_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__insert__left__if0,axiom, % 14.55/14.54 ! [V_B_2,V_C_2,V_a_2,T_b] : % 14.55/14.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__insert__right__if0,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_a_2,T_b] : % 14.55/14.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__insert__left,axiom, % 14.55/14.54 ! [V_B_2,V_C_2,V_a_2,T_b] : % 14.55/14.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 14.55/14.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Int__insert__right,axiom, % 14.55/14.54 ! [V_B_2,V_A_2,V_a_2,T_b] : % 14.55/14.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 14.55/14.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__UNIV,axiom, % 14.55/14.54 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Sup__insert,axiom, % 14.55/14.54 ! [V_A_2,V_a_2,T_b] : % 14.55/14.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.54 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__is__Un,axiom, % 14.55/14.54 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Inf__insert,axiom, % 14.55/14.54 ! [V_A_2,V_a_2,T_b] : % 14.55/14.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.54 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Union__disjoint,axiom, % 14.55/14.54 ! [V_A_2,V_C_2,T_b] : % 14.55/14.54 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.54 <=> ! [B_x] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_ivl__disj__un_I20_J,axiom, % 14.55/14.54 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.54 ( class_Orderings_Olinorder(T_b) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 14.55/14.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_ivl__disj__int_I14_J,axiom, % 14.55/14.54 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.54 ( class_Orderings_Oorder(T_b) % 14.55/14.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Union__insert,axiom, % 14.55/14.54 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Inter__insert,axiom, % 14.55/14.54 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 14.55/14.54 % 14.55/14.54 fof(fact_Diff__insert__absorb,axiom, % 14.55/14.54 ! [V_A_2,V_x_2,T_b] : % 14.55/14.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),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)))) = V_A_2 ) ). % 14.55/14.54 % 14.55/14.54 fof(fact_insert__Diff,axiom, % 14.55/14.54 ! [V_A_2,V_a_2,T_b] : % 14.55/14.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.54 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_Sup__binary,axiom, % 14.55/14.55 ! [V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.55 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_Inf__binary,axiom, % 14.55/14.55 ! [V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.55 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_single__Diff__lessThan,axiom, % 14.55/14.55 ! [V_k_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I9_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I3_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I1_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I10_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_distrib__sup__le,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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)))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_distrib__inf__le,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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)))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_minus__apply,axiom, % 14.55/14.55 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 14.55/14.55 ( class_Groups_Ominus(T_b) % 14.55/14.55 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__apply,axiom, % 14.55/14.55 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 14.55/14.55 ( class_Lattices_Olattice(T_b) % 14.55/14.55 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__apply,axiom, % 14.55/14.55 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 14.55/14.55 ( class_Lattices_Olattice(T_b) % 14.55/14.55 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__top__left,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__top(T_a) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__top__right,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__top(T_a) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__eq__top__iff,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__top(T_b) % 14.55/14.55 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) % 14.55/14.55 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b) % 14.55/14.55 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__top__left,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__top(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__top__right,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__top(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__absorb,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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 ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__assoc,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__aci_I6_J,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup_Oassoc,axiom, % 14.55/14.55 ! [V_c,V_b,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__left__commute,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__aci_I7_J,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup_Oleft__commute,axiom, % 14.55/14.55 ! [V_c,V_a,V_b,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__left__idem,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__aci_I8_J,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup_Oleft__idem,axiom, % 14.55/14.55 ! [V_b,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__commute,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__aci_I5_J,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup_Ocommute,axiom, % 14.55/14.55 ! [V_b,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__idem,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup_Oidem,axiom, % 14.55/14.55 ! [V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__assoc,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__aci_I2_J,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf_Oassoc,axiom, % 14.55/14.55 ! [V_c,V_b,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__left__commute,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__aci_I3_J,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf_Oleft__commute,axiom, % 14.55/14.55 ! [V_c,V_a,V_b,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__left__idem,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__aci_I4_J,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf_Oleft__idem,axiom, % 14.55/14.55 ! [V_b,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__commute,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__aci_I1_J,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf_Ocommute,axiom, % 14.55/14.55 ! [V_b,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__idem,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf_Oidem,axiom, % 14.55/14.55 ! [V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__supE,axiom, % 14.55/14.55 ! [V_x,V_b,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( 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)) % 14.55/14.55 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__mono,axiom, % 14.55/14.55 ! [V_d,V_b,V_c,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 14.55/14.55 => 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))) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__least,axiom, % 14.55/14.55 ! [V_z,V_x,V_y,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 14.55/14.55 => 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)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__supI,axiom, % 14.55/14.55 ! [V_b,V_x,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 14.55/14.55 => 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)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__absorb1,axiom, % 14.55/14.55 ! [V_x,V_y,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__absorb2,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__supI2,axiom, % 14.55/14.55 ! [V_a,V_b,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 14.55/14.55 => 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))) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__supI1,axiom, % 14.55/14.55 ! [V_b,V_a,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 14.55/14.55 => 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))) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__sup__iff,axiom, % 14.55/14.55 ! [V_z_2,V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2)) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 14.55/14.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__iff__sup,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__ge2,axiom, % 14.55/14.55 ! [V_x,V_y,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__ord_I4_J,axiom, % 14.55/14.55 ! [V_x,V_y,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__ge1,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => 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))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__ord_I3_J,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__infE,axiom, % 14.55/14.55 ! [V_b,V_a,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( 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))) % 14.55/14.55 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__mono,axiom, % 14.55/14.55 ! [V_d,V_b,V_c,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 14.55/14.55 => 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))) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__greatest,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 14.55/14.55 => 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))) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__infI,axiom, % 14.55/14.55 ! [V_b,V_a,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 14.55/14.55 => 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))) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__absorb2,axiom, % 14.55/14.55 ! [V_x,V_y,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__absorb1,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__infI2,axiom, % 14.55/14.55 ! [V_a,V_x,V_b,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 14.55/14.55 => 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)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__infI1,axiom, % 14.55/14.55 ! [V_b,V_x,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 14.55/14.55 => 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)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__inf__iff,axiom, % 14.55/14.55 ! [V_z_2,V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2))) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_le__iff__inf,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__le2,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__ord_I2_J,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__le1,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__ord_I1_J,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__eq__bot__iff,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__bot(T_b) % 14.55/14.55 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) % 14.55/14.55 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b) % 14.55/14.55 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__bot__right,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__bot(T_a) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__bot__left,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__bot(T_a) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__bot__right,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__bot(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__bot__left,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Obounded__lattice__bot(T_a) % 14.55/14.55 => 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) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__inf__distrib2,axiom, % 14.55/14.55 ! [V_x,V_z,V_y,T_a] : % 14.55/14.55 ( class_Lattices_Odistrib__lattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__distrib2,axiom, % 14.55/14.55 ! [V_x,V_z,V_y,T_a] : % 14.55/14.55 ( class_Lattices_Odistrib__lattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__inf__distrib1,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Odistrib__lattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_inf__sup__distrib1,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Odistrib__lattice(T_a) % 14.55/14.55 => 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)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_sup__inf__absorb,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Olattice(T_a) % 14.55/14.55 => 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 ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_diff__eq__diff__less__eq,axiom, % 14.55/14.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.55 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 14.55/14.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I5_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I4_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I13_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_psubset__insert__iff,axiom, % 14.55/14.55 ! [V_B_2,V_x_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 14.55/14.55 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 14.55/14.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 14.55/14.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2)) ) % 14.55/14.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I10_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_Int__Collect__mono,axiom, % 14.55/14.55 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 => ( ! [B_x] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.55 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.55/14.55 => hBOOL(hAPP(V_Qa_2,B_x)) ) ) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Qa_2)))) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 14.55/14.55 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.55 => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_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)))),V_y_2) % 14.55/14.55 => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I12_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_insert__partition,axiom, % 14.55/14.55 ! [V_F_2,V_x_2,T_b] : % 14.55/14.55 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) % 14.55/14.55 => ( ! [B_x] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) % 14.55/14.55 => ! [B_xa] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) % 14.55/14.55 => ( B_x != B_xa % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_atLeastatMost__psubset__iff,axiom, % 14.55/14.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2))) % 14.55/14.55 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 14.55/14.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 14.55/14.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) % 14.55/14.55 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) % 14.55/14.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) ) % 14.55/14.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__cases,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Olinorder(T_a) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => ( V_x != V_y % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__asym,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_xt1_I10_J,axiom, % 14.55/14.55 ! [V_z,V_x,V_y,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__trans,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_xt1_I2_J,axiom, % 14.55/14.55 ! [V_c,V_a,V_b,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 14.55/14.55 => ( V_b = V_c % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ord__less__eq__trans,axiom, % 14.55/14.55 ! [V_c,V_b,V_a,T_a] : % 14.55/14.55 ( class_Orderings_Oord(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.55 => ( V_b = V_c % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_xt1_I1_J,axiom, % 14.55/14.55 ! [V_c,V_b,V_a,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( V_a = V_b % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ord__eq__less__trans,axiom, % 14.55/14.55 ! [V_c,V_b,V_a,T_a] : % 14.55/14.55 ( class_Orderings_Oord(T_a) % 14.55/14.55 => ( V_a = V_b % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_xt1_I9_J,axiom, % 14.55/14.55 ! [V_a,V_b,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__asym_H,axiom, % 14.55/14.55 ! [V_b,V_a,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__imp__not__eq2,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => V_y != V_x ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__imp__not__eq,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => V_x != V_y ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__imp__not__less,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__not__sym,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_less__imp__neq,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => V_x != V_y ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__neqE,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Olinorder(T_a) % 14.55/14.55 => ( V_x != V_y % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__antisym__conv3,axiom, % 14.55/14.55 ! [V_x_2,V_y_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> V_x_2 = V_y_2 ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__less__linear,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Olinorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 | V_x = V_y % 14.55/14.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_not__less__iff__gr__or__eq,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 14.55/14.55 | V_x_2 = V_y_2 ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__neq__iff,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( V_x_2 != V_y_2 % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__irrefl,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_psubset__trans,axiom, % 14.55/14.55 ! [V_C_2,V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_atLeastatMost__empty,axiom, % 14.55/14.55 ! [V_a_2,V_b_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) % 14.55/14.55 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_lessThan__strict__subset__iff,axiom, % 14.55/14.55 ! [V_n_2,V_m_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2))) % 14.55/14.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_diff__eq__diff__less,axiom, % 14.55/14.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.55 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 14.55/14.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 14.55/14.55 ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2) ). % 14.55/14.55 % 14.55/14.55 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 14.55/14.55 ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2) ). % 14.55/14.55 % 14.55/14.55 fof(fact_less__fun__def,axiom, % 14.55/14.55 ! [V_g_2,V_f_2,T_b,T_c] : % 14.55/14.55 ( class_Orderings_Oord(T_c) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 14.55/14.55 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__not__less,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__not__le,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__le__less__linear,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Olinorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__le,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 & V_x_2 != V_y_2 ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_less__le__not__le,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Opreorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__le__less,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 | V_x_2 = V_y_2 ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_leI,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Olinorder(T_a) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_not__leE,axiom, % 14.55/14.55 ! [V_x,V_y,T_a] : % 14.55/14.55 ( class_Orderings_Olinorder(T_a) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__antisym__conv1,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> V_x_2 = V_y_2 ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__neq__le__trans,axiom, % 14.55/14.55 ! [V_b,V_a,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( V_a != V_b % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_xt1_I12_J,axiom, % 14.55/14.55 ! [V_b,V_a,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( V_a != V_b % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_leD,axiom, % 14.55/14.55 ! [V_x,V_y,T_a] : % 14.55/14.55 ( class_Orderings_Olinorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.55/14.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__imp__le,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_linorder__antisym__conv2,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.55/14.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 14.55/14.55 <=> V_x_2 = V_y_2 ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__le__imp__less__or__eq,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 | V_x = V_y ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__le__neq__trans,axiom, % 14.55/14.55 ! [V_b,V_a,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.55 => ( V_a != V_b % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_xt1_I11_J,axiom, % 14.55/14.55 ! [V_a,V_b,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 14.55/14.55 => ( V_a != V_b % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__less__le__trans,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_xt1_I7_J,axiom, % 14.55/14.55 ! [V_z,V_x,V_y,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_order__le__less__trans,axiom, % 14.55/14.55 ! [V_z,V_y,V_x,T_a] : % 14.55/14.55 ( class_Orderings_Opreorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_xt1_I8_J,axiom, % 14.55/14.55 ! [V_z,V_x,V_y,T_a] : % 14.55/14.55 ( class_Orderings_Oorder(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_psubsetD,axiom, % 14.55/14.55 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_not__psubset__empty,axiom, % 14.55/14.55 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.55/14.55 % 14.55/14.55 fof(fact_less__supI1,axiom, % 14.55/14.55 ! [V_b,V_a,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 14.55/14.55 => 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))) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_less__supI2,axiom, % 14.55/14.55 ! [V_a,V_b,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__sup(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 14.55/14.55 => 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))) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_less__infI1,axiom, % 14.55/14.55 ! [V_b,V_x,V_a,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 14.55/14.55 => 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)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_less__infI2,axiom, % 14.55/14.55 ! [V_a,V_x,V_b,T_a] : % 14.55/14.55 ( class_Lattices_Osemilattice__inf(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 14.55/14.55 => 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)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_subset__psubset__trans,axiom, % 14.55/14.55 ! [V_C_2,V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_psubset__subset__trans,axiom, % 14.55/14.55 ! [V_C_2,V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_psubset__imp__subset,axiom, % 14.55/14.55 ! [V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_subset__iff__psubset__eq,axiom, % 14.55/14.55 ! [V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 | V_A_2 = V_B_2 ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_psubset__eq,axiom, % 14.55/14.55 ! [V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 & V_A_2 != V_B_2 ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_less__Sup__iff,axiom, % 14.55/14.55 ! [V_S_2,V_a_2,T_b] : % 14.55/14.55 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.55 & class_Orderings_Olinorder(T_b) ) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) % 14.55/14.55 <=> ? [B_x] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 14.55/14.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_Inf__less__iff,axiom, % 14.55/14.55 ! [V_a_2,V_S_2,T_b] : % 14.55/14.55 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.55 & class_Orderings_Olinorder(T_b) ) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) % 14.55/14.55 <=> ? [B_x] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 14.55/14.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_lessThan__iff,axiom, % 14.55/14.55 ! [V_k_2,V_i_2,T_b] : % 14.55/14.55 ( class_Orderings_Oord(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) % 14.55/14.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I19_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_greaterThanAtMost__empty__iff,axiom, % 14.55/14.55 ! [V_l_2,V_k_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 14.55/14.55 ! [V_l_2,V_k_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) % 14.55/14.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_greaterThan__iff,axiom, % 14.55/14.55 ! [V_k_2,V_i_2,T_b] : % 14.55/14.55 ( class_Orderings_Oord(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) % 14.55/14.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_atLeastatMost__empty__iff,axiom, % 14.55/14.55 ! [V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_atLeastatMost__empty__iff2,axiom, % 14.55/14.55 ! [V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) % 14.55/14.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_atLeastatMost__subset__iff,axiom, % 14.55/14.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2))) % 14.55/14.55 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 14.55/14.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 14.55/14.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_atLeastAtMost__singleton_H,axiom, % 14.55/14.55 ! [V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( V_a_2 = V_b_2 % 14.55/14.55 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_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))) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_atLeastAtMost__singleton__iff,axiom, % 14.55/14.55 ! [V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 14.55/14.55 <=> ( V_a_2 = V_b_2 % 14.55/14.55 & V_b_2 = V_ca_2 ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_atLeastAtMost__singleton,axiom, % 14.55/14.55 ! [V_a_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_diff__eq__diff__eq,axiom, % 14.55/14.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Groups_Oab__group__add(T_b) % 14.55/14.55 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 14.55/14.55 => ( V_a_2 = V_b_2 % 14.55/14.55 <=> V_ca_2 = V_d_2 ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I22_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I4_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I16_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I13_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I12_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I7_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I16_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I7_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 14.55/14.55 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] : % 14.55/14.55 ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 14.55/14.55 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.55 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 14.55/14.55 | ? [B_x,B_y] : % 14.55/14.55 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 14.55/14.55 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) % 14.55/14.55 & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I18_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I3_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I6_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I15_J,axiom, % 14.55/14.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_Diff1__fold__graph,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.55 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_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))))),V_y_2)) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.55 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_psubset__imp__ex__mem,axiom, % 14.55/14.55 ! [V_B_2,V_A_2,T_b] : % 14.55/14.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.55 => ? [B_b] : hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__int_I8_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Oorder(T_b) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_compl__unique,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.55 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 14.55/14.55 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 14.55/14.55 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ivl__disj__un_I14_J,axiom, % 14.55/14.55 ! [V_u_2,V_l_2,T_b] : % 14.55/14.55 ( class_Orderings_Olinorder(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 14.55/14.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_ComplI,axiom, % 14.55/14.55 ! [V_A_2,V_ca_2,T_b] : % 14.55/14.55 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.55/14.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_minus__minus,axiom, % 14.55/14.55 ! [V_a,T_a] : % 14.55/14.55 ( class_Groups_Ogroup__add(T_a) % 14.55/14.55 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_equation__minus__iff,axiom, % 14.55/14.55 ! [V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Groups_Ogroup__add(T_b) % 14.55/14.55 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 14.55/14.55 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_minus__equation__iff,axiom, % 14.55/14.55 ! [V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Groups_Ogroup__add(T_b) % 14.55/14.55 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2 % 14.55/14.55 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_neg__equal__iff__equal,axiom, % 14.55/14.55 ! [V_b_2,V_a_2,T_b] : % 14.55/14.55 ( class_Groups_Ogroup__add(T_b) % 14.55/14.55 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 14.55/14.55 <=> V_a_2 = V_b_2 ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_double__compl,axiom, % 14.55/14.55 ! [V_x,T_a] : % 14.55/14.55 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.55 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_uminus__apply,axiom, % 14.55/14.55 ! [V_x_2,V_A_2,T_c,T_b] : % 14.55/14.55 ( class_Groups_Ouminus(T_b) % 14.55/14.55 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_compl__eq__compl__iff,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Lattices_Oboolean__algebra(T_b) % 14.55/14.55 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) % 14.55/14.55 <=> V_x_2 = V_y_2 ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_compl__mono,axiom, % 14.55/14.55 ! [V_y,V_x,T_a] : % 14.55/14.55 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.55 => 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))) ) ) ). % 14.55/14.55 % 14.55/14.55 fof(fact_compl__le__compl__iff,axiom, % 14.55/14.55 ! [V_y_2,V_x_2,T_b] : % 14.55/14.55 ( class_Lattices_Oboolean__algebra(T_b) % 14.55/14.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) % 14.55/14.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_le__imp__neg__le,axiom, % 14.55/14.56 ! [V_b,V_a,T_a] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_a) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.56 => 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))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_neg__le__iff__le,axiom, % 14.55/14.56 ! [V_a_2,V_b_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 14.55/14.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_minus__le__iff,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) % 14.55/14.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_le__minus__iff,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) % 14.55/14.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_neg__less__iff__less,axiom, % 14.55/14.56 ! [V_a_2,V_b_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 14.55/14.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_minus__less__iff,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) % 14.55/14.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_less__minus__iff,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) % 14.55/14.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ComplE,axiom, % 14.55/14.56 ! [V_A_2,V_ca_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 14.55/14.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ComplD,axiom, % 14.55/14.56 ! [V_A_2,V_ca_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 14.55/14.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__iff,axiom, % 14.55/14.56 ! [V_A_2,V_ca_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 14.55/14.56 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_minus__diff__eq,axiom, % 14.55/14.56 ! [V_b,V_a,T_a] : % 14.55/14.56 ( class_Groups_Oab__group__add(T_a) % 14.55/14.56 => 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) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__subset__Compl__iff,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2))) % 14.55/14.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__anti__mono,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_atLeastLessThan__eq__iff,axiom, % 14.55/14.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 14.55/14.56 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 14.55/14.56 <=> ( V_a_2 = V_ca_2 % 14.55/14.56 & V_b_2 = V_d_2 ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 14.55/14.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 14.55/14.56 => V_a_2 = V_ca_2 ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 14.55/14.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 14.55/14.56 => V_b_2 = V_d_2 ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_empty__fold__graphE,axiom, % 14.55/14.56 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) % 14.55/14.56 => V_x_2 = V_z_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__graph_OemptyI,axiom, % 14.55/14.56 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__graph_Oequations_I1_J,axiom, % 14.55/14.56 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_compl__inf__bot,axiom, % 14.55/14.56 ! [V_x,T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => 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) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_inf__compl__bot,axiom, % 14.55/14.56 ! [V_x,T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => 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) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_diff__eq,axiom, % 14.55/14.56 ! [V_y,V_x,T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => 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)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_compl__top__eq,axiom, % 14.55/14.56 ! [T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_compl__bot__eq,axiom, % 14.55/14.56 ! [T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_compl__sup,axiom, % 14.55/14.56 ! [V_y,V_x,T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => 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)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_compl__inf,axiom, % 14.55/14.56 ! [V_y,V_x,T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => 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)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_compl__sup__top,axiom, % 14.55/14.56 ! [V_x,T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => 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) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_sup__compl__top,axiom, % 14.55/14.56 ! [V_x,T_a] : % 14.55/14.56 ( class_Lattices_Oboolean__algebra(T_a) % 14.55/14.56 => 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) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_subset__Compl__self__eq,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( 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)),V_A_2))) % 14.55/14.56 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__empty__eq,axiom, % 14.55/14.56 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__UNIV__eq,axiom, % 14.55/14.56 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__disjoint,axiom, % 14.55/14.56 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__disjoint2,axiom, % 14.55/14.56 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__partition,axiom, % 14.55/14.56 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__partition2,axiom, % 14.55/14.56 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__Int,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__Un,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__eq__Diff__UNIV,axiom, % 14.55/14.56 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_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_A_2) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__Diff__eq,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Diff__eq,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Diff__Compl,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__atLeast,axiom, % 14.55/14.56 ! [V_k_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__lessThan,axiom, % 14.55/14.56 ! [V_k_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_atLeastLessThan__empty,axiom, % 14.55/14.56 ! [V_a_2,V_b_2,T_b] : % 14.55/14.56 ( class_Orderings_Oorder(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) % 14.55/14.56 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_atLeastLessThan__empty__iff2,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Orderings_Oorder(T_b) % 14.55/14.56 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) % 14.55/14.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_atLeastLessThan__empty__iff,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Orderings_Oorder(T_b) % 14.55/14.56 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__atMost,axiom, % 14.55/14.56 ! [V_k_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__greaterThan,axiom, % 14.55/14.56 ! [V_k_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_atLeastLessThan__subset__iff,axiom, % 14.55/14.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2))) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) % 14.55/14.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 14.55/14.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ivl__disj__un_I17_J,axiom, % 14.55/14.56 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__graph_OinsertI,axiom, % 14.55/14.56 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 14.55/14.56 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ivl__diff,axiom, % 14.55/14.56 ! [V_m_2,V_n_2,V_i_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2)) % 14.55/14.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ivl__disj__int_I11_J,axiom, % 14.55/14.56 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.56 ( class_Orderings_Oorder(T_b) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_disjoint__eq__subset__Compl,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( 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)) % 14.55/14.56 <=> 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)),V_B_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ivl__disj__un_I21_J,axiom, % 14.55/14.56 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ivl__disj__int_I15_J,axiom, % 14.55/14.56 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.56 ( class_Orderings_Oorder(T_b) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ivl__disj__un_I8_J,axiom, % 14.55/14.56 ! [V_u_2,V_l_2,T_b] : % 14.55/14.56 ( class_Orderings_Olinorder(T_b) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ivl__disj__int_I2_J,axiom, % 14.55/14.56 ! [V_u_2,V_l_2,T_b] : % 14.55/14.56 ( class_Orderings_Oorder(T_b) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ivl__disj__int_I9_J,axiom, % 14.55/14.56 ! [V_u_2,V_m_2,V_l_2,T_b] : % 14.55/14.56 ( class_Orderings_Oorder(T_b) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1Set_Ointros,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__graph__permute__diff,axiom, % 14.55/14.56 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] : % 14.55/14.56 ( class_Groups_Oab__semigroup__mult(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one_Osingleton,axiom, % 14.55/14.56 ! [V_x_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.56 => hAPP(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)))) = V_x_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1Set__sing,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,V_f_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(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)))),V_b_2)) % 14.55/14.56 <=> V_a_2 = V_b_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_nonempty__iff,axiom, % 14.55/14.56 ! [T_b,V_A_2] : % 14.55/14.56 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 <=> ? [B_x,B_B] : % 14.55/14.56 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B) % 14.55/14.56 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Pow__insert,axiom, % 14.55/14.56 ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 14.55/14.56 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.56 => ? [B_y_H] : % 14.55/14.56 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 14.55/14.56 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Oidem,axiom, % 14.55/14.56 ! [V_x,T_a] : % 14.55/14.56 ( class_Lattices_Olattice(T_a) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Oidem,axiom, % 14.55/14.56 ! [V_x,T_a] : % 14.55/14.56 ( class_Lattices_Olattice(T_a) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_linorder__neqE__linordered__idom,axiom, % 14.55/14.56 ! [V_y,V_x,T_a] : % 14.55/14.56 ( class_Rings_Olinordered__idom(T_a) % 14.55/14.56 => ( V_x != V_y % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__eqI,axiom, % 14.55/14.56 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] : % 14.55/14.56 ( V_b_2 = hAPP(V_f_2,V_x_2) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_double__complement,axiom, % 14.55/14.56 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 14.55/14.56 % 14.55/14.56 fof(fact_Compl__eq__Compl__iff,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( 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_b,tc_HOL_Obool)),V_B_2) % 14.55/14.56 <=> V_A_2 = V_B_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__Pow__surj,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : % 14.55/14.56 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 % 14.55/14.56 => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_mult__left__idem,axiom, % 14.55/14.56 ! [V_b,V_a,T_a] : % 14.55/14.56 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 14.55/14.56 => 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) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_mult__idem,axiom, % 14.55/14.56 ! [V_x,T_a] : % 14.55/14.56 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 14.55/14.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_times_Oidem,axiom, % 14.55/14.56 ! [V_a,T_a] : % 14.55/14.56 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 14.55/14.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 14.55/14.56 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.56 => 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)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 14.55/14.56 ! [V_c,V_b,V_a,T_a] : % 14.55/14.56 ( class_Groups_Oab__semigroup__mult(T_a) % 14.55/14.56 => 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)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm,axiom, % 14.55/14.56 ! [T_b] : % 14.55/14.56 ( class_Groups_Oab__semigroup__mult(T_b) % 14.55/14.56 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_minus__mult__right,axiom, % 14.55/14.56 ! [V_b,V_a,T_a] : % 14.55/14.56 ( class_Rings_Oring(T_a) % 14.55/14.56 => 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)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_minus__mult__left,axiom, % 14.55/14.56 ! [V_b,V_a,T_a] : % 14.55/14.56 ( class_Rings_Oring(T_a) % 14.55/14.56 => 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) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_minus__mult__commute,axiom, % 14.55/14.56 ! [V_b,V_a,T_a] : % 14.55/14.56 ( class_Rings_Oring(T_a) % 14.55/14.56 => 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)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_minus__mult__minus,axiom, % 14.55/14.56 ! [V_b,V_a,T_a] : % 14.55/14.56 ( class_Rings_Oring(T_a) % 14.55/14.56 => 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) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_square__eq__iff,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,T_b] : % 14.55/14.56 ( class_Rings_Oidom(T_b) % 14.55/14.56 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2) % 14.55/14.56 <=> ( V_a_2 = V_b_2 % 14.55/14.56 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__iff,axiom, % 14.55/14.56 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 14.55/14.56 <=> ? [B_x] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.55/14.56 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_imageI,axiom, % 14.55/14.56 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_rev__image__eqI,axiom, % 14.55/14.56 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__is__empty,axiom, % 14.55/14.56 ! [V_A_2,V_f_2,T_b,T_c] : % 14.55/14.56 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__empty,axiom, % 14.55/14.56 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_empty__is__image,axiom, % 14.55/14.56 ! [V_A_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) % 14.55/14.56 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__insert,axiom, % 14.55/14.56 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__mono,axiom, % 14.55/14.56 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_subset__image__iff,axiom, % 14.55/14.56 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 14.55/14.56 <=> ? [B_AA] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) % 14.55/14.56 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__Un,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__Pow__mono,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_insert__image,axiom, % 14.55/14.56 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_range__eqI,axiom, % 14.55/14.56 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] : % 14.55/14.56 ( V_b_2 = hAPP(V_f_2,V_x_2) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_rangeI,axiom, % 14.55/14.56 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__Int__subset,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__diff__subset,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__uminus__atLeastAtMost,axiom, % 14.55/14.56 ! [V_y_2,V_x_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_type__definition_OAbs__image,axiom, % 14.55/14.56 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.55/14.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.55/14.56 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_type__definition_ORep__range,axiom, % 14.55/14.56 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 14.55/14.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 14.55/14.56 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 14.55/14.56 => V_y_2 = V_x_2 ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__uminus__greaterThanLessThan,axiom, % 14.55/14.56 ! [V_y_2,V_x_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_empty__fold1SetE,axiom, % 14.55/14.56 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1Set__nonempty,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_f_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) % 14.55/14.56 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__uminus__atLeastLessThan,axiom, % 14.55/14.56 ! [V_y_2,V_x_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__uminus__greaterThanAtMost,axiom, % 14.55/14.56 ! [V_y_2,V_x_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__uminus__lessThan,axiom, % 14.55/14.56 ! [V_x_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__uminus__greaterThan,axiom, % 14.55/14.56 ! [V_x_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__uminus__atLeast,axiom, % 14.55/14.56 ! [V_x_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_image__uminus__atMost,axiom, % 14.55/14.56 ! [V_x_2,T_b] : % 14.55/14.56 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__graph__insert__swap,axiom, % 14.55/14.56 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] : % 14.55/14.56 ( class_Groups_Oab__semigroup__mult(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_surj__Compl__image__subset,axiom, % 14.55/14.56 ! [V_A_2,V_f_2,T_b,T_c] : % 14.55/14.56 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Cantors__paradox,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one_Oremove,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 14.55/14.56 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => 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_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)))))) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_insert__fold1SetE,axiom, % 14.55/14.56 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2)) % 14.55/14.56 => ~ ! [B_a,B_A] : % 14.55/14.56 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1Set_Oequations,axiom, % 14.55/14.56 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2)) % 14.55/14.56 <=> ? [B_a,B_A] : % 14.55/14.56 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 14.55/14.56 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) % 14.55/14.56 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 14.55/14.56 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ~ ! [B_y] : % 14.55/14.56 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 14.55/14.56 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one_Ounion__inter,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( 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)) % 14.55/14.56 => 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)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one_Ounion__disjoint,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( 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)) % 14.55/14.56 => 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)) ) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one_Oinsert__remove,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 14.55/14.56 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),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_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)))))) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite_OemptyI,axiom, % 14.55/14.56 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite_OinsertI,axiom, % 14.55/14.56 ! [V_a_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__imageI,axiom, % 14.55/14.56 ! [V_h_2,T_c,V_F_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Int,axiom, % 14.55/14.56 ! [V_Ga_2,V_F_2,T_b] : % 14.55/14.56 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.55/14.56 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Diff,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Inter,axiom, % 14.55/14.56 ! [V_M_2,T_b] : % 14.55/14.56 ( ? [B_x] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) % 14.55/14.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__UN,axiom, % 14.55/14.56 ! [V_B_2,T_c,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.56 <=> ! [B_x] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Finite__Set_Ofinite(T_b) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__code,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Finite__Set_Ofinite(T_b) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Prod__UNIV,axiom, % 14.55/14.56 ! [T_c,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__option__UNIV,axiom, % 14.55/14.56 ! [T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)))) % 14.55/14.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Plus__UNIV__iff,axiom, % 14.55/14.56 ! [T_c,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)))) % 14.55/14.56 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 14.55/14.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__UnionD,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Pow__iff,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) % 14.55/14.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite_Oequations_I1_J,axiom, % 14.55/14.56 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__insert,axiom, % 14.55/14.56 ! [V_A_2,V_a_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) % 14.55/14.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__fun__UNIVD2,axiom, % 14.55/14.56 ! [T_c,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__subset,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_rev__finite__subset,axiom, % 14.55/14.56 ! [V_A_2,V_B_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__UNIV,axiom, % 14.55/14.56 ! [T_b] : % 14.55/14.56 ( class_Finite__Set_Ofinite(T_b) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__UnI,axiom, % 14.55/14.56 ! [V_Ga_2,V_F_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Un,axiom, % 14.55/14.56 ! [V_Ga_2,V_F_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) % 14.55/14.56 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.55/14.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Diff2,axiom, % 14.55/14.56 ! [V_A_2,V_B_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__graph__imp__finite,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__surj,axiom, % 14.55/14.56 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Diff__insert,axiom, % 14.55/14.56 ! [V_B_2,V_a_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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_a_2),V_B_2)))) % 14.55/14.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__compl,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 14.55/14.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one_Oinsert,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__image__simple_Oremove,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 14.55/14.56 => 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_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.55/14.56 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Oremove,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) % 14.55/14.56 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,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)))))) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Oremove,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) % 14.55/14.56 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,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)))))) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one_Oclosed,axiom, % 14.55/14.56 ! [V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__image,axiom, % 14.55/14.56 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 14.55/14.56 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,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)))))) ) % 14.55/14.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__empty__induct,axiom, % 14.55/14.56 ! [V_Pa_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 14.55/14.56 => ( ! [B_a,B_A] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) % 14.55/14.56 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 14.55/14.56 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) % 14.55/14.56 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one__idem_Ounion__idem,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => 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)) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__triv,axiom, % 14.55/14.56 ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__idem,axiom, % 14.55/14.56 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] : % 14.55/14.56 ( hAPP(V_f_2,V_x_2) = V_y_2 % 14.55/14.56 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__other,axiom, % 14.55/14.56 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 14.55/14.56 ( V_z_2 != V_x_2 % 14.55/14.56 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__twist,axiom, % 14.55/14.56 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] : % 14.55/14.56 ( V_a_2 != V_ca_2 % 14.55/14.56 => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__apply,axiom, % 14.55/14.56 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 14.55/14.56 ( ( V_z_2 = V_x_2 % 14.55/14.56 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) % 14.55/14.56 & ( V_z_2 != V_x_2 % 14.55/14.56 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__same,axiom, % 14.55/14.56 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__upd,axiom, % 14.55/14.56 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__upd__idem__iff,axiom, % 14.55/14.56 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2 % 14.55/14.56 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one__idem_Oidem,axiom, % 14.55/14.56 ! [V_x_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 14.55/14.56 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_ball__UN,axiom, % 14.55/14.56 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] : % 14.55/14.56 ( ! [B_x] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.56 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.55/14.56 <=> ! [B_x] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.55/14.56 => ! [B_xa] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) % 14.55/14.56 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__le__Sup,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__image__simple_Oempty,axiom, % 14.55/14.56 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.56 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Osingleton,axiom, % 14.55/14.56 ! [V_x_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Osingleton,axiom, % 14.55/14.56 ! [V_x_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Oin__idem,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_sup__Inf__absorb,axiom, % 14.55/14.56 ! [V_a_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Oin__idem,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_inf__Sup__absorb,axiom, % 14.55/14.56 ! [V_a_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin__Sup,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin__Inf,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one__idem_Oin__idem,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Oinsert__idem,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Oinsert__idem,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Osubset__idem,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Osubset__idem,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Ounion__idem,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Ounion__idem,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,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__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__image__simple_Oinsert,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 14.55/14.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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)) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__image__simple_Ounion__inter,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.55/14.56 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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)) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Oinsert,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Oinsert,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Oinsert__remove,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 14.55/14.56 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,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)))))) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Oinsert__remove,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 14.55/14.56 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,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)))))) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Ounion__inter,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( 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)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,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__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( 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)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Ounion__inter,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( 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)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( 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)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,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__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 14.55/14.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one__idem_Osubset__idem,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.56 => 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) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Oclosed,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Oclosed,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__Union,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) % 14.55/14.56 => ( ! [B_M] : % 14.55/14.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) ) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_Ohom__commute,axiom, % 14.55/14.56 ! [V_N_2,V_h_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.55/14.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_Ohom__commute,axiom, % 14.55/14.56 ! [V_N_2,V_h_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.55/14.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_finite__subset__induct,axiom, % 14.55/14.56 ! [V_Pa_2,V_A_2,V_F_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.55/14.56 => ( ! [B_a,B_F] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) % 14.55/14.56 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 14.55/14.56 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) ) % 14.55/14.56 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm_Ofold__rec,axiom, % 14.55/14.56 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_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)))))) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1__Un,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Groups_Oab__semigroup__mult(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => ( 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)) % 14.55/14.56 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one__idem_Ohom__commute,axiom, % 14.55/14.56 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( ! [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)) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.55/14.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.56 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__empty,axiom, % 14.55/14.56 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1__eq__fold__idem,axiom, % 14.55/14.56 ! [V_a_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1__eq__fold,axiom, % 14.55/14.56 ! [V_a_2,V_A_2,T_b] : % 14.55/14.56 ( class_Groups_Oab__semigroup__mult(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.56 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 14.55/14.56 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1__singleton__def,axiom, % 14.55/14.56 ! [V_a_2,V_f_2,T_b,V_g_2] : % 14.55/14.56 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) % 14.55/14.56 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold1__singleton,axiom, % 14.55/14.56 ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(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)))) = V_a_2 ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm_Ofold__equality,axiom, % 14.55/14.56 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 14.55/14.56 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one_Oeq__fold,axiom, % 14.55/14.56 ! [V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_union__fold__insert,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__sup__insert,axiom, % 14.55/14.56 ! [V_a_2,V_b_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Osemilattice__sup(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__inf__insert,axiom, % 14.55/14.56 ! [V_a_2,V_b_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Osemilattice__inf(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_sup__Sup__fold__sup,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_inf__Inf__fold__inf,axiom, % 14.55/14.56 ! [V_B_2,V_A_2,T_b] : % 14.55/14.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 14.55/14.56 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 14.55/14.56 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.56 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fin_OF__eq,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Inf__fin_OF__eq,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Olattice(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_sup__le__fold__sup,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Osemilattice__sup(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_fold__inf__le__inf,axiom, % 14.55/14.56 ! [V_b_2,V_a_2,V_A_2,T_b] : % 14.55/14.56 ( class_Lattices_Osemilattice__inf(T_b) % 14.55/14.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ). % 14.55/14.56 % 14.55/14.56 fof(fact_Sup__fold__sup,axiom, % 14.55/14.56 ! [V_A_2,T_b] : % 14.55/14.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_Inf__fold__inf,axiom, % 14.55/14.57 ! [V_A_2,T_b] : % 14.55/14.57 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 14.55/14.57 ! [V_a_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Olattice(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 14.55/14.57 ! [V_a_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Olattice(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 14.55/14.57 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm_Ofold__insert,axiom, % 14.55/14.57 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_folding__one_Oeq__fold_H,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fold1__belowI,axiom, % 14.55/14.57 ! [V_a_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Osemilattice__inf(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_below__fold1__iff,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Osemilattice__inf(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2))) % 14.55/14.57 <=> ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fold1__insert__idem,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 14.55/14.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fold1__Un2,axiom, % 14.55/14.57 ! [V_B_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.57 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Olattice(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Olattice(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 14.55/14.57 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_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)))))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fold1__insert,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( class_Groups_Oab__semigroup__mult(T_b) % 14.55/14.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_semilattice__big_OF__eq,axiom, % 14.55/14.57 ! [V_A_2,V_F_2,V_f_2,T_b] : % 14.55/14.57 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fold1__in,axiom, % 14.55/14.57 ! [V_A_2,T_b] : % 14.55/14.57 ( class_Groups_Oab__semigroup__mult(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.57 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_hom__fold1__commute,axiom, % 14.55/14.57 ! [V_N_2,V_h_2,T_b] : % 14.55/14.57 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 14.55/14.57 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.55/14.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.57 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 14.55/14.57 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.57 => hAPP(V_g_2,B_x) = V_z_2 ) % 14.55/14.57 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 14.55/14.57 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 14.55/14.57 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__diff1__ring,axiom, % 14.55/14.57 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Rings_Oring(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__diff1,axiom, % 14.55/14.57 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Oab__group__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 14.55/14.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod_Oremove,axiom, % 14.55/14.57 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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)))))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 14.55/14.57 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__diff__nat__ivl,axiom, % 14.55/14.57 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 14.55/14.57 ( class_Groups_Oab__group__add(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 14.55/14.57 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm__idem__insert,axiom, % 14.55/14.57 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm__idem,axiom, % 14.55/14.57 ! [T_b] : % 14.55/14.57 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 14.55/14.57 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm__idem__sup,axiom, % 14.55/14.57 ! [T_b] : % 14.55/14.57 ( class_Lattices_Osemilattice__sup(T_b) % 14.55/14.57 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fun__left__comm__idem__inf,axiom, % 14.55/14.57 ! [T_b] : % 14.55/14.57 ( class_Lattices_Osemilattice__inf(T_b) % 14.55/14.57 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__diff__nat,axiom, % 14.55/14.57 ! [V_f_2,V_A_2,V_B_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_Nat_Onat),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,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod_Oinsert,axiom, % 14.55/14.57 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__insert,axiom, % 14.55/14.57 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__Un__Int,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod_Ounion__inter,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__diff1__nat,axiom, % 14.55/14.57 ! [V_f_2,V_A_2,V_a_2,T_b] : % 14.55/14.57 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 14.55/14.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__diff,axiom, % 14.55/14.57 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Oab__group__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod_Oinsert__remove,axiom, % 14.55/14.57 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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)))))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__Un__disjoint,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( 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)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod_Ounion__disjoint,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( 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)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__strict__mono,axiom, % 14.55/14.57 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) ) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,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_A_2))) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__diff1_H,axiom, % 14.55/14.57 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum_Oremove,axiom, % 14.55/14.57 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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)))))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_inf__le__fold__inf,axiom, % 14.55/14.57 ! [V_ca_2,V_b_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Osemilattice__inf(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fold__sup__le__sup,axiom, % 14.55/14.57 ! [V_ca_2,V_b_2,V_A_2,T_b] : % 14.55/14.57 ( class_Lattices_Osemilattice__sup(T_b) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_2))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__ivl__cong,axiom, % 14.55/14.57 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] : % 14.55/14.57 ( ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 & class_Orderings_Oord(T_b) ) % 14.55/14.57 => ( V_a_2 = V_ca_2 % 14.55/14.57 => ( V_b_2 = V_d_2 % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) % 14.55/14.57 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 14.55/14.57 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.55/14.57 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 14.55/14.57 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.57 => 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) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_finite__atLeastLessThan,axiom, % 14.55/14.57 ! [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))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__add__nat__ivl,axiom, % 14.55/14.57 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 14.55/14.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 14.55/14.57 ! [V_N_2] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 14.55/14.57 <=> ? [B_m] : % 14.55/14.57 ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oab__semigroup__add(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__left__cancel,axiom, % 14.55/14.57 ! [V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.57 ( class_Groups_Ocancel__semigroup__add(T_b) % 14.55/14.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2) % 14.55/14.57 <=> V_b_2 = V_ca_2 ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__right__cancel,axiom, % 14.55/14.57 ! [V_ca_2,V_a_2,V_b_2,T_b] : % 14.55/14.57 ( class_Groups_Ocancel__semigroup__add(T_b) % 14.55/14.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2) % 14.55/14.57 <=> V_b_2 = V_ca_2 ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__left__imp__eq,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ocancel__semigroup__add(T_a) % 14.55/14.57 => ( 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) % 14.55/14.57 => V_b = V_c ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__imp__eq,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 14.55/14.57 => ( 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) % 14.55/14.57 => V_b = V_c ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__right__imp__eq,axiom, % 14.55/14.57 ! [V_c,V_a,V_b,T_a] : % 14.55/14.57 ( class_Groups_Ocancel__semigroup__add(T_a) % 14.55/14.57 => ( 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) % 14.55/14.57 => V_b = V_c ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_atLeastLessThan__add__Un,axiom, % 14.55/14.57 ! [V_k_2,V_j_2,V_i_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_folding__image__simple__idem_Oidem,axiom, % 14.55/14.57 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.57 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__le__imp__le__left,axiom, % 14.55/14.57 ! [V_b,V_a,V_c,T_a] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 14.55/14.57 => ( 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))) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__le__imp__le__right,axiom, % 14.55/14.57 ! [V_b,V_c,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 14.55/14.57 => ( 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))) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__mono,axiom, % 14.55/14.57 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 14.55/14.57 => 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))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__left__mono,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__right__mono,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__le__cancel__left,axiom, % 14.55/14.57 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__le__cancel__right,axiom, % 14.55/14.57 ! [V_b_2,V_ca_2,V_a_2,T_b] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__less__imp__less__left,axiom, % 14.55/14.57 ! [V_b,V_a,V_c,T_a] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 14.55/14.57 => ( 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))) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__less__imp__less__right,axiom, % 14.55/14.57 ! [V_b,V_c,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 14.55/14.57 => ( 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))) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__strict__mono,axiom, % 14.55/14.57 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 14.55/14.57 => 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))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__strict__left__mono,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__strict__right__mono,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__less__cancel__left,axiom, % 14.55/14.57 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__less__cancel__right,axiom, % 14.55/14.57 ! [V_b_2,V_ca_2,V_a_2,T_b] : % 14.55/14.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_combine__common__factor,axiom, % 14.55/14.57 ! [V_c,V_b,V_e,V_a,T_a] : % 14.55/14.57 ( class_Rings_Osemiring(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__class_Odistrib,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__diff__cancel,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ogroup__add(T_a) % 14.55/14.57 => 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 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__add__cancel,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ogroup__add(T_a) % 14.55/14.57 => 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 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_minus__add__distrib,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oab__group__add(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_minus__add,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ogroup__add(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__minus__cancel,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ogroup__add(T_a) % 14.55/14.57 => 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 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_minus__add__cancel,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ogroup__add(T_a) % 14.55/14.57 => 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 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__le__less__mono,axiom, % 14.55/14.57 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 14.55/14.57 => 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))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__less__le__mono,axiom, % 14.55/14.57 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 14.55/14.57 => 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))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_eq__add__iff1,axiom, % 14.55/14.57 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] : % 14.55/14.57 ( class_Rings_Oring(T_b) % 14.55/14.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) % 14.55/14.57 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_eq__add__iff2,axiom, % 14.55/14.57 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] : % 14.55/14.57 ( class_Rings_Oring(T_b) % 14.55/14.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) % 14.55/14.57 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__def,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ogroup__add(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_ab__diff__minus,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Oab__group__add(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__minus__eq__add,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Groups_Ogroup__add(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__add__iff1,axiom, % 14.55/14.57 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] : % 14.55/14.57 ( class_Rings_Oordered__ring(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__add__iff2,axiom, % 14.55/14.57 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] : % 14.55/14.57 ( class_Rings_Oordered__ring(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__add__iff1,axiom, % 14.55/14.57 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] : % 14.55/14.57 ( class_Rings_Oordered__ring(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__add__iff2,axiom, % 14.55/14.57 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] : % 14.55/14.57 ( class_Rings_Oordered__ring(T_b) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__Un__nat,axiom, % 14.55/14.57 ! [V_f_2,V_B_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_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_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__insert,axiom, % 14.55/14.57 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum_Oinsert,axiom, % 14.55/14.57 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__Un__Int,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 14.55/14.57 => 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) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.57 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum_Oinsert__remove,axiom, % 14.55/14.57 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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)))))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__Un__disjoint,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( 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)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__Un,axiom, % 14.55/14.57 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Oab__group__add(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 14.55/14.57 ! [V_y,V_x,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__ring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__less__add__iff2,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 14.55/14.57 => ( 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))) % 14.55/14.57 <=> 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__less__add__iff1,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 14.55/14.57 => ( 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))) % 14.55/14.57 <=> 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)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__eq__add__iff2,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 14.55/14.57 => ( 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) % 14.55/14.57 <=> 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) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__diff__add__eq2,axiom, % 14.55/14.57 ! [V_n,V_m,V_u,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__le__add__iff2,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 14.55/14.57 => ( 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))) % 14.55/14.57 <=> 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__eq__add__iff1,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 14.55/14.57 => ( 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) % 14.55/14.57 <=> 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 ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__diff__add__eq1,axiom, % 14.55/14.57 ! [V_n,V_m,V_u,V_i,V_j] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_finite__lessThan,axiom, % 14.55/14.57 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_finite__greaterThanAtMost,axiom, % 14.55/14.57 ! [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))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_finite__greaterThanLessThan,axiom, % 14.55/14.57 ! [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))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_finite__atMost,axiom, % 14.55/14.57 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_finite__atLeastAtMost,axiom, % 14.55/14.57 ! [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))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_left__add__mult__distrib,axiom, % 14.55/14.57 ! [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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_finite__nat__set__iff__bounded,axiom, % 14.55/14.57 ! [V_N_2] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 14.55/14.57 <=> ? [B_m] : % 14.55/14.57 ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_infinite__UNIV__nat,axiom, % 14.55/14.57 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 14.55/14.57 ! [V_c,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 14.55/14.57 ! [V_d,V_c,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 14.55/14.57 ! [V_d,V_c,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 14.55/14.57 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 14.55/14.57 ! [V_b,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 14.55/14.57 ! [V_ry,V_rx,V_lx,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 14.55/14.57 ! [V_ry,V_rx,V_lx,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 14.55/14.57 ! [V_rx,V_ly,V_lx,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 14.55/14.57 ! [V_rx,V_ly,V_lx,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 14.55/14.57 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 14.55/14.57 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 14.55/14.57 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_crossproduct__eq,axiom, % 14.55/14.57 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] : % 14.55/14.57 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 14.55/14.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2)) % 14.55/14.57 <=> ( V_w_2 = V_x_2 % 14.55/14.57 | V_y_2 = V_z_2 ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 14.55/14.57 ! [V_b,V_m,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 14.55/14.57 ! [V_c,V_b,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_crossproduct__noteq,axiom, % 14.55/14.57 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.57 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 14.55/14.57 => ( ( V_a_2 != V_b_2 % 14.55/14.57 & V_ca_2 != V_d_2 ) % 14.55/14.57 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 14.55/14.57 ! [V_z,V_y,V_x,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__le__add__iff1,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 14.55/14.57 => ( 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))) % 14.55/14.57 <=> 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)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__diff__right,axiom, % 14.55/14.57 ! [V_i,V_j,V_k] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__diff__conv,axiom, % 14.55/14.57 ! [V_i_2,V_k_2,V_j_2] : % 14.55/14.57 ( 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)) % 14.55/14.57 <=> 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__add__diff,axiom, % 14.55/14.57 ! [V_m,V_n,V_k] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__add__diff__inverse,axiom, % 14.55/14.57 ! [V_m,V_n] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.55/14.57 => 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 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__diff__assoc,axiom, % 14.55/14.57 ! [V_i,V_j,V_k] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__diff__conv2,axiom, % 14.55/14.57 ! [V_i_2,V_j_2,V_k_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 14.55/14.57 => ( 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))) % 14.55/14.57 <=> 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)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__add__diff__inverse2,axiom, % 14.55/14.57 ! [V_m,V_n] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.55/14.57 => 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 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__imp__diff__is__add,axiom, % 14.55/14.57 ! [V_k_2,V_j_2,V_i_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 14.55/14.57 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 14.55/14.57 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__less__cases,axiom, % 14.55/14.57 ! [V_Pa_2,V_n_2,V_m_2] : % 14.55/14.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 14.55/14.57 => ( ( V_m_2 = V_n_2 % 14.55/14.57 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 14.55/14.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 14.55/14.57 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__not__refl3,axiom, % 14.55/14.57 ! [V_t,V_s] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 14.55/14.57 => V_s != V_t ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__not__refl2,axiom, % 14.55/14.57 ! [V_m,V_n] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 14.55/14.57 => V_m != V_n ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__irrefl__nat,axiom, % 14.55/14.57 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_linorder__neqE__nat,axiom, % 14.55/14.57 ! [V_y,V_x] : % 14.55/14.57 ( V_x != V_y % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__neq__iff,axiom, % 14.55/14.57 ! [V_n_2,V_m_2] : % 14.55/14.57 ( V_m_2 != V_n_2 % 14.55/14.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__not__refl,axiom, % 14.55/14.57 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__add__commute,axiom, % 14.55/14.57 ! [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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__add__left__commute,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__add__assoc,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__add__left__cancel,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.57 ( 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) % 14.55/14.57 <=> V_m_2 = V_n_2 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__add__right__cancel,axiom, % 14.55/14.57 ! [V_n_2,V_k_2,V_m_2] : % 14.55/14.57 ( 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) % 14.55/14.57 <=> V_m_2 = V_n_2 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__antisym,axiom, % 14.55/14.57 ! [V_n,V_m] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.55/14.57 => V_m = V_n ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__trans,axiom, % 14.55/14.57 ! [V_k,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_eq__imp__le,axiom, % 14.55/14.57 ! [V_n,V_m] : % 14.55/14.57 ( V_m = V_n % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__le__linear,axiom, % 14.55/14.57 ! [V_n,V_m] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__refl,axiom, % 14.55/14.57 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__commute,axiom, % 14.55/14.57 ! [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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__mult__commute,axiom, % 14.55/14.57 ! [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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__mult__assoc,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_not__add__less1,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_not__add__less2,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__add__left__cancel__less,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.57 ( 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))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_trans__less__add1,axiom, % 14.55/14.57 ! [V_m,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_trans__less__add2,axiom, % 14.55/14.57 ! [V_m,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__less__mono1,axiom, % 14.55/14.57 ! [V_k,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__less__mono,axiom, % 14.55/14.57 ! [V_l,V_k,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__add__eq__less,axiom, % 14.55/14.57 ! [V_n,V_m,V_l,V_k] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 14.55/14.57 => ( 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) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__lessD1,axiom, % 14.55/14.57 ! [V_k,V_j,V_i] : % 14.55/14.57 ( 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)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__or__eq__imp__le,axiom, % 14.55/14.57 ! [V_n,V_m] : % 14.55/14.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 | V_m = V_n ) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__neq__implies__less,axiom, % 14.55/14.57 ! [V_n,V_m] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 => ( V_m != V_n % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__imp__le__nat,axiom, % 14.55/14.57 ! [V_n,V_m] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__eq__less__or__eq,axiom, % 14.55/14.57 ! [V_n_2,V_m_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 | V_m_2 = V_n_2 ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__less__le,axiom, % 14.55/14.57 ! [V_n_2,V_m_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 & V_m_2 != V_n_2 ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__leE,axiom, % 14.55/14.57 ! [V_n,V_k,V_m] : % 14.55/14.57 ( 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)) % 14.55/14.57 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__leD1,axiom, % 14.55/14.57 ! [V_n,V_k,V_m] : % 14.55/14.57 ( 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)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__leD2,axiom, % 14.55/14.57 ! [V_n,V_k,V_m] : % 14.55/14.57 ( 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)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__le__mono,axiom, % 14.55/14.57 ! [V_l,V_k,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__le__mono1,axiom, % 14.55/14.57 ! [V_k,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_trans__le__add2,axiom, % 14.55/14.57 ! [V_m,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_trans__le__add1,axiom, % 14.55/14.57 ! [V_m,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__add__left__cancel__le,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.57 ( 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))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__iff__add,axiom, % 14.55/14.57 ! [V_n_2,V_m_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.57 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__add1,axiom, % 14.55/14.57 ! [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))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__add2,axiom, % 14.55/14.57 ! [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))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__less__mono2,axiom, % 14.55/14.57 ! [V_l,V_n,V_m] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__imp__diff__less,axiom, % 14.55/14.57 ! [V_n,V_k,V_j] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__cancel2,axiom, % 14.55/14.57 ! [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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__cancel,axiom, % 14.55/14.57 ! [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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__diff__left,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__add__inverse,axiom, % 14.55/14.57 ! [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 ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__add__inverse2,axiom, % 14.55/14.57 ! [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 ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__mult__distrib,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__mult__distrib2,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__diff__iff,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 14.55/14.57 => ( 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))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_Nat_Odiff__diff__eq,axiom, % 14.55/14.57 ! [V_n,V_m,V_k] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 14.55/14.57 => 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) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_eq__diff__iff,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 14.55/14.57 => ( 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) % 14.55/14.57 <=> V_m_2 = V_n_2 ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__diff__cancel,axiom, % 14.55/14.57 ! [V_n,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 14.55/14.57 => 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 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__le__mono,axiom, % 14.55/14.57 ! [V_l,V_n,V_m] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__le__mono2,axiom, % 14.55/14.57 ! [V_l,V_n,V_m] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__le__self,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__square,axiom, % 14.55/14.57 ! [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))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_le__cube,axiom, % 14.55/14.57 ! [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)))) ). % 14.55/14.57 % 14.55/14.57 fof(fact_mult__le__mono1,axiom, % 14.55/14.57 ! [V_k,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_mult__le__mono2,axiom, % 14.55/14.57 ! [V_k,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_mult__le__mono,axiom, % 14.55/14.57 ! [V_l,V_k,V_j,V_i] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__mult__distrib2,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__mult__distrib,axiom, % 14.55/14.57 ! [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)) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__diff__inverse,axiom, % 14.55/14.57 ! [V_n,V_m] : % 14.55/14.57 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.57 => 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 ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__diff__conv,axiom, % 14.55/14.57 ! [V_k_2,V_j_2,V_i_2] : % 14.55/14.57 ( 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))) % 14.55/14.57 <=> 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__diff__iff,axiom, % 14.55/14.57 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 14.55/14.57 => ( 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))) % 14.55/14.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__less__mono,axiom, % 14.55/14.57 ! [V_c,V_b,V_a] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 14.55/14.57 => 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))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__add__assoc2,axiom, % 14.55/14.57 ! [V_i,V_j,V_k] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_add__diff__assoc2,axiom, % 14.55/14.57 ! [V_i,V_j,V_k] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__add__assoc,axiom, % 14.55/14.57 ! [V_i,V_j,V_k] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 14.55/14.57 => 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)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_termination__basic__simps_I4_J,axiom, % 14.55/14.57 ! [V_y,V_z,V_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_termination__basic__simps_I3_J,axiom, % 14.55/14.57 ! [V_z,V_y,V_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_termination__basic__simps_I5_J,axiom, % 14.55/14.57 ! [V_y,V_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_termination__basic__simps_I1_J,axiom, % 14.55/14.57 ! [V_z,V_y,V_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_termination__basic__simps_I2_J,axiom, % 14.55/14.57 ! [V_y,V_z,V_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Diff2__less,axiom, % 14.55/14.57 ! [V_y_2,V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),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))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Diff1__less,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),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)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setsum__ub__add__nat,axiom, % 14.55/14.57 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.57 => ( 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)))) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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)))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__UNIV__unit,axiom, % 14.55/14.57 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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_one__reorient,axiom, % 14.55/14.57 ! [V_x_2,T_b] : % 14.55/14.57 ( class_Groups_Oone(T_b) % 14.55/14.57 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2 % 14.55/14.57 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 14.55/14.57 ! [V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 14.55/14.57 ! [V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_mult_Ocomm__neutral,axiom, % 14.55/14.57 ! [V_a,T_a] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_a) % 14.55/14.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_mult__1__right,axiom, % 14.55/14.57 ! [V_a,T_a] : % 14.55/14.57 ( class_Groups_Omonoid__mult(T_a) % 14.55/14.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_mult__1,axiom, % 14.55/14.57 ! [V_a,T_a] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_a) % 14.55/14.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_mult__1__left,axiom, % 14.55/14.57 ! [V_a,T_a] : % 14.55/14.57 ( class_Groups_Omonoid__mult(T_a) % 14.55/14.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__eq__1__iff,axiom, % 14.55/14.57 ! [V_f_2,V_F_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.55/14.57 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 14.55/14.57 <=> ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 14.55/14.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__mult__1,axiom, % 14.55/14.57 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__1__eq__mult__iff,axiom, % 14.55/14.57 ! [V_n_2,V_m_2] : % 14.55/14.57 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 14.55/14.57 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 14.55/14.57 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__mult__1__right,axiom, % 14.55/14.57 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 14.55/14.57 % 14.55/14.57 fof(fact_nat__mult__eq__1__iff,axiom, % 14.55/14.57 ! [V_n_2,V_m_2] : % 14.55/14.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 14.55/14.57 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 14.55/14.57 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__lessThan,axiom, % 14.55/14.57 ! [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 ). % 14.55/14.57 % 14.55/14.57 fof(fact_card_Oinsert,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),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_b),V_A_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 14.55/14.57 ! [V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 14.55/14.57 => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.55/14.57 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__add__one,axiom, % 14.55/14.57 ! [V_a,T_a] : % 14.55/14.57 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.57 => 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)))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_less__1__mult,axiom, % 14.55/14.57 ! [V_n,V_m,T_a] : % 14.55/14.57 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 14.55/14.57 => 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))) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 14.55/14.57 ! [V_m,V_a,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 14.55/14.57 ! [V_a,V_m,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 14.55/14.57 ! [V_m,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 14.55/14.57 ! [V_x,T_a] : % 14.55/14.57 ( class_Rings_Ocomm__ring__1(T_a) % 14.55/14.57 => 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) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_square__eq__1__iff,axiom, % 14.55/14.57 ! [V_x_2,T_b] : % 14.55/14.57 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 14.55/14.57 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 14.55/14.57 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b) % 14.55/14.57 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_subset__card__intvl__is__intvl,axiom, % 14.55/14.57 ! [V_k_2,V_A_2] : % 14.55/14.57 ( 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))))) % 14.55/14.57 => 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))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__atLeastLessThan,axiom, % 14.55/14.57 ! [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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod_Oempty,axiom, % 14.55/14.57 ! [V_g_2,T_c,T_b] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_b) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__empty,axiom, % 14.55/14.57 ! [V_f_2,T_c,T_b] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_b) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod_Oinfinite,axiom, % 14.55/14.57 ! [V_g_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__infinite,axiom, % 14.55/14.57 ! [V_f_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Diff__insert,axiom, % 14.55/14.57 ! [V_B_2,V_a_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),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_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card_Oinsert__remove,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),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_b),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)))))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__greaterThanAtMost,axiom, % 14.55/14.57 ! [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) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card_Oremove,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),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_b),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)))))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Diff__singleton,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Diff__singleton__if,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 14.55/14.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__insert__le,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__seteq,axiom, % 14.55/14.57 ! [V_A_2,V_B_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 14.55/14.57 => V_A_2 = V_B_2 ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__mono,axiom, % 14.55/14.57 ! [V_A_2,V_B_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__image__le,axiom, % 14.55/14.57 ! [V_f_2,T_c,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_psubset__card__mono,axiom, % 14.55/14.57 ! [V_A_2,V_B_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Un__Int,axiom, % 14.55/14.57 ! [V_B_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card_Ounion__inter,axiom, % 14.55/14.57 ! [V_B_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Diff__subset,axiom, % 14.55/14.57 ! [V_A_2,V_B_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Diff__subset__Int,axiom, % 14.55/14.57 ! [V_B_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_diff__card__le__card__Diff,axiom, % 14.55/14.57 ! [V_A_2,V_B_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => 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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__psubset,axiom, % 14.55/14.57 ! [V_A_2,V_B_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Un__disjoint,axiom, % 14.55/14.57 ! [V_B_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( 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)) % 14.55/14.57 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Diff1__le,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),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)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod_Ounion__inter__neutral,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( 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))) % 14.55/14.57 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__Un__one,axiom, % 14.55/14.57 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( 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_S_2),V_T_2))) % 14.55/14.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fold__Un__disjoint,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.57 => ( 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)) % 14.55/14.57 => hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(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)) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__mono__one__right,axiom, % 14.55/14.57 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 14.55/14.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_setprod__mono__one__left,axiom, % 14.55/14.57 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 14.55/14.57 => ( ! [B_x] : % 14.55/14.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 14.55/14.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 14.55/14.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_card__Suc__Diff1,axiom, % 14.55/14.57 ! [V_x_2,V_A_2,T_b] : % 14.55/14.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.57 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),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)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 14.55/14.57 % 14.55/14.57 fof(fact_fold__image__Un__Int,axiom, % 14.55/14.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_convex__bound__lt,axiom, % 14.55/14.58 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 14.55/14.58 => 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)) ) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__zeroE,axiom, % 14.55/14.58 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le0,axiom, % 14.55/14.58 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__less__Suc,axiom, % 14.55/14.58 ! [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))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__mono,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_lessI,axiom, % 14.55/14.58 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_One__nat__def,axiom, % 14.55/14.58 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 14.55/14.58 ! [V_k_2,V_f_2,T_b] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.58 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__reorient,axiom, % 14.55/14.58 ! [V_x_2,T_b] : % 14.55/14.58 ( class_Groups_Ozero(T_b) % 14.55/14.58 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2 % 14.55/14.58 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeast__Suc__greaterThan,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_greaterThan__Suc,axiom, % 14.55/14.58 ! [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)))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeast__Suc,axiom, % 14.55/14.58 ! [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)))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 14.55/14.58 ! [V_k_2,V_f_2] : % 14.55/14.58 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 14.55/14.58 ! [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))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Zero__not__Suc,axiom, % 14.55/14.58 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat_Osimps_I2_J,axiom, % 14.55/14.58 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 14.55/14.58 % 14.55/14.58 fof(fact_n__not__Suc__n,axiom, % 14.55/14.58 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__not__Zero,axiom, % 14.55/14.58 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat_Osimps_I3_J,axiom, % 14.55/14.58 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__n__not__n,axiom, % 14.55/14.58 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat_Oinject,axiom, % 14.55/14.58 ! [V_nat_H_2,V_nat_2] : % 14.55/14.58 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 14.55/14.58 <=> V_nat_2 = V_nat_H_2 ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Zero__neq__Suc,axiom, % 14.55/14.58 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__neq__Zero,axiom, % 14.55/14.58 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__inject,axiom, % 14.55/14.58 ! [V_y,V_x] : % 14.55/14.58 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 14.55/14.58 => V_x = V_y ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_greaterThan__0,axiom, % 14.55/14.58 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))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__eq__1__iff,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( 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)) % 14.55/14.58 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 14.55/14.58 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__Suc__eq__0__disj,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 14.55/14.58 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 | ? [B_j] : % 14.55/14.58 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__Suc0,axiom, % 14.55/14.58 ! [V_n_2] : % 14.55/14.58 ( 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)))) % 14.55/14.58 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_gr0__conv__Suc,axiom, % 14.55/14.58 ! [V_n_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 14.55/14.58 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_one__is__add,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( 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) % 14.55/14.58 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 14.55/14.58 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.55/14.58 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__is__1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( 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)) % 14.55/14.58 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 14.55/14.58 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.55/14.58 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__pred,axiom, % 14.55/14.58 ! [V_n] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.58 => 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 ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__Suc__less,axiom, % 14.55/14.58 ! [V_i,V_n] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_n__less__m__mult__n,axiom, % 14.55/14.58 ! [V_m,V_n] : % 14.55/14.58 ( 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)) % 14.55/14.58 => ( 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)) % 14.55/14.58 => 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))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_n__less__n__mult__m,axiom, % 14.55/14.58 ! [V_m,V_n] : % 14.55/14.58 ( 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)) % 14.55/14.58 => ( 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)) % 14.55/14.58 => 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))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_one__less__mult,axiom, % 14.55/14.58 ! [V_m,V_n] : % 14.55/14.58 ( 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)) % 14.55/14.58 => ( 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)) % 14.55/14.58 => 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))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_one__le__mult__iff,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> ( 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)) % 14.55/14.58 & 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)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__eq__Suc0__iff,axiom, % 14.55/14.58 ! [V_f_2,V_A_2,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 14.55/14.58 <=> ? [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.58 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 14.55/14.58 & ! [B_xa] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 14.55/14.58 => ( B_x != B_xa % 14.55/14.58 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_not__less__eq,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__Suc__eq,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 14.55/14.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 | V_m_2 = V_n_2 ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__less__eq,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_not__less__less__Suc__eq,axiom, % 14.55/14.58 ! [V_m_2,V_n_2] : % 14.55/14.58 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 14.55/14.58 <=> V_n_2 = V_m_2 ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__antisym,axiom, % 14.55/14.58 ! [V_m,V_n] : % 14.55/14.58 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 14.55/14.58 => V_m = V_n ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__SucI,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__lessI,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__trans__Suc,axiom, % 14.55/14.58 ! [V_k,V_j,V_i] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__SucE,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 14.55/14.58 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => V_m = V_n ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__lessD,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__less__SucD,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__Suc__shift,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__Suc,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__Suc__right,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__n__not__le__n,axiom, % 14.55/14.58 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_not__less__eq__eq,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le__Suc__eq,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 14.55/14.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__le__mono,axiom, % 14.55/14.58 ! [V_m_2,V_n_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le__SucI,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le__SucE,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 14.55/14.58 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__leD,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__Suc__Suc,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__diff__diff,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__mult__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( 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) % 14.55/14.58 <=> V_m_2 = V_n_2 ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__0__left,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Omonoid__add(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__0,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_double__zero__sym,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) % 14.55/14.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__0__right,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Omonoid__add(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add_Ocomm__neutral,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__0__iff,axiom, % 14.55/14.58 ! [V_a_2,V_b_2,T_b] : % 14.55/14.58 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 14.55/14.58 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) % 14.55/14.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_divisors__zero,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Ono__zero__divisors(T_a) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_no__zero__divisors,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Ono__zero__divisors(T_a) % 14.55/14.58 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__eq__0__iff,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Oring__no__zero__divisors(T_b) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__zero__right,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Omult__zero(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__zero__left,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Omult__zero(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_right__minus__eq,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_b) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 <=> V_a_2 = V_b_2 ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_eq__iff__diff__eq__0,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Oab__group__add(T_b) % 14.55/14.58 => ( V_a_2 = V_b_2 % 14.55/14.58 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__self,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__0__right,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_a) % 14.55/14.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_one__neq__zero,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Rings_Ozero__neq__one(T_a) % 14.55/14.58 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__neq__one,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Rings_Ozero__neq__one(T_a) % 14.55/14.58 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_minus__zero,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_a) % 14.55/14.58 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_neg__0__equal__iff__equal,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_b) % 14.55/14.58 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 14.55/14.58 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_equal__neg__zero,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 14.55/14.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_neg__equal__0__iff__equal,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_b) % 14.55/14.58 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_neg__equal__zero,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 % 14.55/14.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_fold__image__empty,axiom, % 14.55/14.58 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ). % 14.55/14.58 % 14.55/14.58 fof(fact_not__less0,axiom, % 14.55/14.58 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_neq0__conv,axiom, % 14.55/14.58 ! [V_n_2] : % 14.55/14.58 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__nat__zero__code,axiom, % 14.55/14.58 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_gr__implies__not0,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_gr0I,axiom, % 14.55/14.58 ! [V_n] : % 14.55/14.58 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__eq__self__zero,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 14.55/14.58 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__is__0,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Nat_Oadd__0__right,axiom, % 14.55/14.58 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 14.55/14.58 % 14.55/14.58 fof(fact_plus__nat_Oadd__0,axiom, % 14.55/14.58 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeastLessThan__singleton,axiom, % 14.55/14.58 ! [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))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_image__Suc__atLeastLessThan,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 14.55/14.58 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le__0__eq,axiom, % 14.55/14.58 ! [V_n_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 14.55/14.58 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__0__eq__0,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_minus__nat_Odiff__0,axiom, % 14.55/14.58 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__self__eq__0,axiom, % 14.55/14.58 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diffs0__imp__equal,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => V_m = V_n ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__cancel2,axiom, % 14.55/14.58 ! [V_n_2,V_k_2,V_m_2] : % 14.55/14.58 ( 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) % 14.55/14.58 <=> ( V_m_2 = V_n_2 % 14.55/14.58 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( 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) % 14.55/14.58 <=> ( V_m_2 = V_n_2 % 14.55/14.58 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__is__0,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__0__right,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__0,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat__mult__eq__cancel__disj,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( 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) % 14.55/14.58 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 | V_m_2 = V_n_2 ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_image__Suc__atLeastAtMost,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_lessThan__Suc,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeastLessThan0,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atMost__Suc,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__atMost,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeast__0,axiom, % 14.55/14.58 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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_lessThan__0,axiom, % 14.55/14.58 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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum_Oeq__fold,axiom, % 14.55/14.58 ! [V_g_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum_OF__eq,axiom, % 14.55/14.58 ! [V_g_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) % 14.55/14.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__diff__1,axiom, % 14.55/14.58 ! [V_n] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.58 => 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 ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atMost__0,axiom, % 14.55/14.58 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))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__op__ivl__Suc,axiom, % 14.55/14.58 ! [V_f_2,V_m_2,V_n_2,T_b] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b) ) % 14.55/14.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__add__Suc1,axiom, % 14.55/14.58 ! [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)))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__add__Suc2,axiom, % 14.55/14.58 ! [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)))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__iff__Suc__add,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__eq__Suc__le,axiom, % 14.55/14.58 ! [V_m_2,V_n_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__Suc__eq__le,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__le__eq,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le__imp__less__Suc,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__leI,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le__less__Suc__eq,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 14.55/14.58 <=> V_n_2 = V_m_2 ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__le__lessD,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__cl__ivl__Suc,axiom, % 14.55/14.58 ! [V_f_2,V_m_2,V_n_2,T_b] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b) ) % 14.55/14.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__less__Suc,axiom, % 14.55/14.58 ! [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))) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__mult__less__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__Suc,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__Suc__right,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__diff__le,axiom, % 14.55/14.58 ! [V_m,V_n] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__mult__le__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__nonneg__nonneg,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__nonneg__eq__0__iff,axiom, % 14.55/14.58 ! [V_y_2,V_x_2,T_b] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__increasing,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__increasing2,axiom, % 14.55/14.58 ! [V_a,V_b,V_c,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__nonpos__nonpos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_split__mult__neg__le,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__cancel__semiring(T_a) % 14.55/14.58 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 14.55/14.58 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 14.55/14.58 => 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))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_split__mult__pos__le,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__ring(T_a) % 14.55/14.58 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 14.55/14.58 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 14.55/14.58 => 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))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__mono,axiom, % 14.55/14.58 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__mono_H,axiom, % 14.55/14.58 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__left__mono__neg,axiom, % 14.55/14.58 ! [V_c,V_a,V_b,T_a] : % 14.55/14.58 ( class_Rings_Oordered__ring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__right__mono__neg,axiom, % 14.55/14.58 ! [V_c,V_a,V_b,T_a] : % 14.55/14.58 ( class_Rings_Oordered__ring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_comm__mult__left__mono,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__comm__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__left__mono,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__right__mono,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__nonpos__nonpos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__ring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__nonpos__nonneg,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__cancel__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__nonneg__nonpos2,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__cancel__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__nonneg__nonpos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__cancel__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__nonneg__nonneg,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Oordered__cancel__semiring(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__le__0__iff,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 14.55/14.58 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__le__mult__iff,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2))) % 14.55/14.58 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 14.55/14.58 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__le__square,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__ring(T_a) % 14.55/14.58 => 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))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_pos__add__strict,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__neg__neg,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__pos__pos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__strict__left__mono__neg,axiom, % 14.55/14.58 ! [V_c,V_a,V_b,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__strict__right__mono__neg,axiom, % 14.55/14.58 ! [V_c,V_a,V_b,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_comm__mult__strict__left__mono,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__strict__left__mono,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__strict__right__mono,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__neg__neg,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__neg__pos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__cancel__left__neg,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__less__mult__pos2,axiom, % 14.55/14.58 ! [V_a,V_b,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( 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))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__less__mult__pos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( 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))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__pos__neg2,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__pos__neg,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__pos__pos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__cancel__left__pos,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__cancel__left__disj,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) % 14.55/14.58 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) % 14.55/14.58 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__cancel__right__disj,axiom, % 14.55/14.58 ! [V_b_2,V_ca_2,V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))) % 14.55/14.58 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) % 14.55/14.58 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_not__square__less__zero,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__ring(T_a) % 14.55/14.58 => ~ 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))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le__iff__diff__le__0,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__iff__diff__less__0,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__scale__eq__noteq,axiom, % 14.55/14.58 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 14.55/14.58 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 14.55/14.58 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => ( ( V_a = V_b % 14.55/14.58 & V_c != V_d ) % 14.55/14.58 => 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)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__le__one,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.58 => 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))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_not__one__le__zero,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.58 => ~ 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))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__less__one,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_not__one__less__zero,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.58 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__Suc__1,axiom, % 14.55/14.58 ! [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 ). % 14.55/14.58 % 14.55/14.58 fof(fact_neg__0__le__iff__le,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_le__minus__self__iff,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_neg__le__0__iff__le,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_minus__le__self__iff,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_neg__0__less__iff__less,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_neg__less__0__iff__less,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Oordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_neg__less__nonneg,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_less__minus__self__iff,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_right__minus,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_eq__neg__iff__add__eq__0,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_b) % 14.55/14.58 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 14.55/14.58 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_left__minus,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_ab__left__minus,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Oab__group__add(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_minus__unique,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_a) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__0,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Groups_Ogroup__add(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeastLessThanSuc,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 => 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)) ) % 14.55/14.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 => 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)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__empty,axiom, % 14.55/14.58 ! [V_f_2,T_c,T_b] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum_Oempty,axiom, % 14.55/14.58 ! [V_g_2,T_c,T_b] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__infinite,axiom, % 14.55/14.58 ! [V_f_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum_Oinfinite,axiom, % 14.55/14.58 ! [V_g_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setprod__pos__nat__iff,axiom, % 14.55/14.58 ! [V_f_2,V_S_2,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.55/14.58 => ( 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_b,tc_Nat_Onat),V_f_2),V_S_2))) % 14.55/14.58 <=> ! [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeastAtMostSuc__conv,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setprod__zero__iff,axiom, % 14.55/14.58 ! [V_f_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( ( class_Rings_Ocomm__semiring__1(T_c) % 14.55/14.58 & class_Rings_Ono__zero__divisors(T_c) ) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) % 14.55/14.58 <=> ? [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.58 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setprod__zero,axiom, % 14.55/14.58 ! [V_f_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Rings_Ocomm__semiring__1(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( ? [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.58 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__atLeastAtMost,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__gr__0,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 14.55/14.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card_Oempty,axiom, % 14.55/14.58 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__infinite,axiom, % 14.55/14.58 ! [V_A_2,T_b] : % 14.55/14.58 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__less,axiom, % 14.55/14.58 ! [V_m,V_n] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 14.55/14.58 => 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)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__less__diff,axiom, % 14.55/14.58 ! [V_m_2,V_n_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat__0__less__mult__iff,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__cancel2,axiom, % 14.55/14.58 ! [V_n_2,V_k_2,V_m_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 14.55/14.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__mono1,axiom, % 14.55/14.58 ! [V_k,V_j,V_i] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 14.55/14.58 => 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))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__mono2,axiom, % 14.55/14.58 ! [V_k,V_j,V_i] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 14.55/14.58 => 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))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat__mult__eq__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 14.55/14.58 => ( 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) % 14.55/14.58 <=> V_m_2 = V_n_2 ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat__mult__less__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 14.55/14.58 => ( 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))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__add__0,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__is__0__eq_H,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__is__0__eq,axiom, % 14.55/14.58 ! [V_n_2,V_m_2] : % 14.55/14.58 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__eq__self__implies__10,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 14.55/14.58 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 14.55/14.58 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__eq__0__iff,axiom, % 14.55/14.58 ! [V_f_2,V_F_2,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.55/14.58 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 <=> ! [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 14.55/14.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_lessThan__Suc__atMost,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeast0LessThan,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 14.55/14.58 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.58 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.58 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__greaterThanLessThan,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeast0AtMost,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__Suc__diff__eq2,axiom, % 14.55/14.58 ! [V_m,V_j,V_k] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__Suc__diff__eq1,axiom, % 14.55/14.58 ! [V_m,V_j,V_k] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__nonpos__neg,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__neg__nonpos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__strict__increasing2,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__strict__increasing,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__nonneg__pos,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__pos__nonneg,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => 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))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__left__le__imp__le,axiom, % 14.55/14.58 ! [V_b,V_a,V_c,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( 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))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__right__le__imp__le,axiom, % 14.55/14.58 ! [V_b,V_c,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( 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))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__imp__less__left,axiom, % 14.55/14.58 ! [V_b,V_a,V_c,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( 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))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__left__less__imp__less,axiom, % 14.55/14.58 ! [V_b,V_a,V_c,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring(T_a) % 14.55/14.58 => ( 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))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__imp__less__right,axiom, % 14.55/14.58 ! [V_b,V_c,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( 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))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__right__less__imp__less,axiom, % 14.55/14.58 ! [V_b,V_c,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring(T_a) % 14.55/14.58 => ( 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))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__le__less__imp__less,axiom, % 14.55/14.58 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__less__le__imp__less,axiom, % 14.55/14.58 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__strict__mono_H,axiom, % 14.55/14.58 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__strict__mono,axiom, % 14.55/14.58 ! [V_d,V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__strict(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.58 => 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))) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__le__cancel__left__neg,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__le__cancel__left__pos,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__left__le__one__le,axiom, % 14.55/14.58 ! [V_y,V_x,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 14.55/14.58 => 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)) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__right__le__one__le,axiom, % 14.55/14.58 ! [V_y,V_x,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 14.55/14.58 => 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)) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_zero__less__two,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.58 => 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)))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__eq__0__iff,axiom, % 14.55/14.58 ! [V_A_2,T_b] : % 14.55/14.58 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.58 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__ge__0__finite,axiom, % 14.55/14.58 ! [V_A_2,T_b] : % 14.55/14.58 ( 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_b),V_A_2))) % 14.55/14.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat__diff__split,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,V_Pa_2] : % 14.55/14.58 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 14.55/14.58 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 14.55/14.58 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 14.55/14.58 & ! [B_d] : % 14.55/14.58 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 14.55/14.58 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat__diff__split__asm,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,V_Pa_2] : % 14.55/14.58 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 14.55/14.58 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 14.55/14.58 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 14.55/14.58 | ? [B_d] : % 14.55/14.58 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 14.55/14.58 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__le__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__le__cancel2,axiom, % 14.55/14.58 ! [V_n_2,V_k_2,V_m_2] : % 14.55/14.58 ( 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))) % 14.55/14.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nat__mult__le__cancel1,axiom, % 14.55/14.58 ! [V_n_2,V_m_2,V_k_2] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 14.55/14.58 => ( 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))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__eq__1__iff,axiom, % 14.55/14.58 ! [V_f_2,V_A_2,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 14.55/14.58 <=> ? [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.58 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 14.55/14.58 & ! [B_xa] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 14.55/14.58 => ( B_x != B_xa % 14.55/14.58 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__insert__if,axiom, % 14.55/14.58 ! [V_x_2,V_A_2,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.58 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) % 14.55/14.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.58 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__insert__disjoint,axiom, % 14.55/14.58 ! [V_x_2,V_A_2,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.55/14.58 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_convex__bound__le,axiom, % 14.55/14.58 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__semiring__1(T_a) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 14.55/14.58 => 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)) ) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__head__upt__Suc,axiom, % 14.55/14.58 ! [V_f_2,V_n_2,V_m_2,T_b] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_fold__image__insert,axiom, % 14.55/14.58 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Oab__semigroup__mult(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.58 => 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(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),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),V_A_2)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__head__Suc,axiom, % 14.55/14.58 ! [V_f_2,V_n_2,V_m_2,T_b] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__gt__0__iff,axiom, % 14.55/14.58 ! [V_A_2,T_b] : % 14.55/14.58 ( 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_b),V_A_2))) % 14.55/14.58 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setprod_OF__eq,axiom, % 14.55/14.58 ! [V_g_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.58 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(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_A_2) ) % 14.55/14.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setprod_Oeq__fold,axiom, % 14.55/14.58 ! [V_g_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(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_A_2) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_finite__UNIV__card__ge__0,axiom, % 14.55/14.58 ! [T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 14.55/14.58 => 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_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__insert,axiom, % 14.55/14.58 ! [V_x_2,V_A_2,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),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)))))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_finite__fun__UNIVD1,axiom, % 14.55/14.58 ! [T_c,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) % 14.55/14.58 => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 14.55/14.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_mult__eq__if,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.55/14.58 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => 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)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__eq__if,axiom, % 14.55/14.58 ! [V_n,V_m] : % 14.55/14.58 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 14.55/14.58 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => 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)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__pred_H,axiom, % 14.55/14.58 ! [V_n] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.58 => 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))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sum__squares__gt__zero__iff,axiom, % 14.55/14.58 ! [V_y_2,V_x_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))) % 14.55/14.58 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_not__sum__squares__lt__zero,axiom, % 14.55/14.58 ! [V_y,V_x,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__ring(T_a) % 14.55/14.58 => ~ 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))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sum__squares__le__zero__iff,axiom, % 14.55/14.58 ! [V_y_2,V_x_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sum__squares__ge__zero,axiom, % 14.55/14.58 ! [V_y,V_x,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__ring(T_a) % 14.55/14.58 => 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)))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_bot__nat__def,axiom, % 14.55/14.58 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sum__squares__eq__zero__iff,axiom, % 14.55/14.58 ! [V_y_2,V_x_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__ring__strict(T_b) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__eq__plus1__left,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Suc__eq__plus1,axiom, % 14.55/14.58 ! [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)) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__Suc__eq__diff__pred,axiom, % 14.55/14.58 ! [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) ). % 14.55/14.58 % 14.55/14.58 fof(fact_ex__nat__less,axiom, % 14.55/14.58 ! [V_Pa_2,V_n_2] : % 14.55/14.58 ( ? [B_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 14.55/14.58 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 14.55/14.58 <=> ? [B_x] : % 14.55/14.58 ( 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))) % 14.55/14.58 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_all__nat__less,axiom, % 14.55/14.58 ! [V_Pa_2,V_n_2] : % 14.55/14.58 ( ! [B_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 14.55/14.58 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 14.55/14.58 <=> ! [B_x] : % 14.55/14.58 ( 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))) % 14.55/14.58 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_ex__nat__less__eq,axiom, % 14.55/14.58 ! [V_Pa_2,V_n_2] : % 14.55/14.58 ( ? [B_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 14.55/14.58 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 14.55/14.58 <=> ? [B_x] : % 14.55/14.58 ( 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))) % 14.55/14.58 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_all__nat__less__eq,axiom, % 14.55/14.58 ! [V_Pa_2,V_n_2] : % 14.55/14.58 ( ! [B_m] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 14.55/14.58 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 14.55/14.58 <=> ! [B_x] : % 14.55/14.58 ( 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))) % 14.55/14.58 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_even__less__0__iff,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_comm__monoid__big_OF__eq,axiom, % 14.55/14.58 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.58 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 14.55/14.58 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.58 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) % 14.55/14.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.58 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card_Ounion__inter__neutral,axiom, % 14.55/14.58 ! [V_B_2,V_A_2,T_b] : % 14.55/14.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.58 => ( ( ? [B_x] : 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))) % 14.55/14.58 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.55/14.58 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_comm__monoid__big_Oinfinite,axiom, % 14.55/14.58 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 14.55/14.58 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 14.55/14.58 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.55/14.58 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_double__eq__0__iff,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__mono2,axiom, % 14.55/14.58 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Oordered__comm__monoid__add(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.58 => ( ! [B_b] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) ) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_fold__image__Un__one,axiom, % 14.55/14.58 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 14.55/14.58 => ( ! [B_x] : % 14.55/14.58 ( 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_S_2),V_T_2))) % 14.55/14.58 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 14.55/14.58 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum_Ounion__inter__neutral,axiom, % 14.55/14.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.58 => ( ! [B_x] : % 14.55/14.58 ( 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))) % 14.55/14.58 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__Un__zero,axiom, % 14.55/14.58 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 14.55/14.58 => ( ! [B_x] : % 14.55/14.58 ( 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_S_2),V_T_2))) % 14.55/14.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__Suc__eq,axiom, % 14.55/14.58 ! [V_k_2,V_A_2,T_b] : % 14.55/14.58 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 14.55/14.58 <=> ? [B_b,B_B] : % 14.55/14.58 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) % 14.55/14.58 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) % 14.55/14.58 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 % 14.55/14.58 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.58 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__mono3,axiom, % 14.55/14.58 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 14.55/14.58 ( ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.58 => ( ! [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__odd__less__0,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__0,axiom, % 14.55/14.58 ! [T_b] : % 14.55/14.58 ( class_Rings_Oring__1(T_b) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__add,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Oring__1(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__mult,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Oring__1(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__diff,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Oring__1(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__1,axiom, % 14.55/14.58 ! [T_b] : % 14.55/14.58 ( class_Rings_Oring__1(T_b) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__minus,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Oring__1(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__double__eq__0__iff,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Int_Oring__char__0(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_Ints__odd__nonzero,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Int_Oring__char__0(T_b) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_card__Plus__conv__if,axiom, % 14.55/14.58 ! [V_B_2,T_c,V_A_2,T_b] : % 14.55/14.58 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 14.55/14.58 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) % 14.55/14.58 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 14.55/14.58 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setprod__diff1,axiom, % 14.55/14.58 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] : % 14.55/14.58 ( class_Fields_Ofield(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.58 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) % 14.55/14.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 14.55/14.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_ex__least__nat__less,axiom, % 14.55/14.58 ! [V_n_2,V_Pa_2] : % 14.55/14.58 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 14.55/14.58 => ( hBOOL(hAPP(V_Pa_2,V_n_2)) % 14.55/14.58 => ? [B_k] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 14.55/14.58 & ! [B_i] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 14.55/14.58 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 14.55/14.58 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__mono__zero__right,axiom, % 14.55/14.58 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 14.55/14.58 => ( ! [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 14.55/14.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_setsum__mono__zero__left,axiom, % 14.55/14.58 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 14.55/14.58 ( class_Groups_Ocomm__monoid__add(T_c) % 14.55/14.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 14.55/14.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 14.55/14.58 => ( ! [B_x] : % 14.55/14.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 14.55/14.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 14.55/14.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sgn__1__neg,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_b) % 14.55/14.58 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) % 14.55/14.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sgn__sgn,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_divide__zero__left,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_divide__zero,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_add__divide__distrib,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_times__divide__eq__right,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_diff__divide__distrib,axiom, % 14.55/14.58 ! [V_c,V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_divide__1,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_minus__divide__left,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => 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) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sgn__0__0,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_b) % 14.55/14.58 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sgn0,axiom, % 14.55/14.58 ! [T_a] : % 14.55/14.58 ( class_Groups_Osgn__if(T_a) % 14.55/14.58 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sgn__times,axiom, % 14.55/14.58 ! [V_b,V_a,T_a] : % 14.55/14.58 ( class_Rings_Olinordered__idom(T_a) % 14.55/14.58 => 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)) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_eq__divide__imp,axiom, % 14.55/14.58 ! [V_b,V_a,V_c,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 14.55/14.58 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_divide__eq__imp,axiom, % 14.55/14.58 ! [V_a,V_b,V_c,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 14.55/14.58 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nonzero__divide__eq__eq,axiom, % 14.55/14.58 ! [V_a_2,V_b_2,V_ca_2,T_b] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_b) % 14.55/14.58 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2 % 14.55/14.58 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nonzero__eq__divide__eq,axiom, % 14.55/14.58 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_b) % 14.55/14.58 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) % 14.55/14.58 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_right__inverse__eq,axiom, % 14.55/14.58 ! [V_a_2,V_b_2,T_b] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_b) % 14.55/14.58 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.58 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b) % 14.55/14.58 <=> V_a_2 = V_b_2 ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_divide__self,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_divide__self__if,axiom, % 14.55/14.58 ! [V_a,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 14.55/14.58 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 14.55/14.58 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nonzero__minus__divide__divide,axiom, % 14.55/14.58 ! [V_a,V_b,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => 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) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_nonzero__minus__divide__right,axiom, % 14.55/14.58 ! [V_a,V_b,T_a] : % 14.55/14.58 ( class_Rings_Odivision__ring(T_a) % 14.55/14.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.58 => 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)) ) ) ). % 14.55/14.58 % 14.55/14.58 fof(fact_sgn__less,axiom, % 14.55/14.58 ! [V_a_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__idom(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_sgn__greater,axiom, % 14.55/14.59 ! [V_a_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__idom(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__Plus__iff,axiom, % 14.55/14.59 ! [V_B_2,V_A_2,T_c,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 14.55/14.59 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__Plus,axiom, % 14.55/14.59 ! [V_B_2,T_c,V_A_2,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.55/14.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__PlusD_I1_J,axiom, % 14.55/14.59 ! [V_B_2,V_A_2,T_c,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 14.55/14.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__PlusD_I2_J,axiom, % 14.55/14.59 ! [V_B_2,V_A_2,T_c,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 14.55/14.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_sgn__pos,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__idom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_sgn__1__pos,axiom, % 14.55/14.59 ! [V_a_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__idom(T_b) % 14.55/14.59 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_card__Plus,axiom, % 14.55/14.59 ! [V_B_2,T_c,V_A_2,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.55/14.59 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_sgn__if,axiom, % 14.55/14.59 ! [V_x,T_a] : % 14.55/14.59 ( class_Groups_Osgn__if(T_a) % 14.55/14.59 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 14.55/14.59 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_sgn__neg,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__idom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__left__mono__neg,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => ( 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))) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__left__mono,axiom, % 14.55/14.59 ! [V_c,V_a,V_b,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.59 => ( 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))) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_neg__divide__le__eq,axiom, % 14.55/14.59 ! [V_a_2,V_b_2,V_ca_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_neg__le__divide__eq,axiom, % 14.55/14.59 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mult__imp__le__div__pos,axiom, % 14.55/14.59 ! [V_x,V_z,V_y,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.59 => ( 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)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mult__imp__div__pos__le,axiom, % 14.55/14.59 ! [V_z,V_x,V_y,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.59 => ( 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))) % 14.55/14.59 => 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)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_times__divide__times__eq,axiom, % 14.55/14.59 ! [V_w,V_z,V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_minus__divide__divide,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_minus__divide__right,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__right__mono__neg,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__right__mono,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__le__0__iff,axiom, % 14.55/14.59 ! [V_b_2,V_a_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 14.55/14.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zero__le__divide__iff,axiom, % 14.55/14.59 ! [V_b_2,V_a_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 14.55/14.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__strict__right__mono__neg,axiom, % 14.55/14.59 ! [V_c,V_a,V_b,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__strict__right__mono,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__neg__neg,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__neg__pos,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__pos__neg,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__pos__pos,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__less__0__iff,axiom, % 14.55/14.59 ! [V_b_2,V_a_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 14.55/14.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zero__less__divide__iff,axiom, % 14.55/14.59 ! [V_b_2,V_a_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 14.55/14.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_eq__divide__eq,axiom, % 14.55/14.59 ! [V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_b) % 14.55/14.59 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) % 14.55/14.59 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) % 14.55/14.59 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__eq__eq,axiom, % 14.55/14.59 ! [V_a_2,V_ca_2,V_b_2,T_b] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_b) % 14.55/14.59 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2 % 14.55/14.59 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) % 14.55/14.59 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mult__divide__mult__cancel__right,axiom, % 14.55/14.59 ! [V_b,V_a,V_c,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mult__divide__mult__cancel__left,axiom, % 14.55/14.59 ! [V_b,V_a,V_c,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_frac__eq__eq,axiom, % 14.55/14.59 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] : % 14.55/14.59 ( class_Fields_Ofield(T_b) % 14.55/14.59 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2) % 14.55/14.59 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__nonneg__pos,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__nonneg__neg,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_frac__less2,axiom, % 14.55/14.59 ! [V_z,V_w,V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 14.55/14.59 => 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))) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_frac__less,axiom, % 14.55/14.59 ! [V_z,V_w,V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 14.55/14.59 => 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))) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_frac__le,axiom, % 14.55/14.59 ! [V_z,V_w,V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 14.55/14.59 => 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))) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__nonpos__pos,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__nonpos__neg,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__strict__left__mono__neg,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 14.55/14.59 => ( 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))) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__strict__left__mono,axiom, % 14.55/14.59 ! [V_c,V_a,V_b,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 14.55/14.59 => ( 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))) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_neg__divide__less__eq,axiom, % 14.55/14.59 ! [V_a_2,V_b_2,V_ca_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_neg__less__divide__eq,axiom, % 14.55/14.59 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mult__imp__less__div__pos,axiom, % 14.55/14.59 ! [V_x,V_z,V_y,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.59 => ( 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)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mult__imp__div__pos__less,axiom, % 14.55/14.59 ! [V_z,V_x,V_y,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.55/14.59 => ( 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))) % 14.55/14.59 => 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)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__divide__less__eq,axiom, % 14.55/14.59 ! [V_a_2,V_b_2,V_ca_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__less__divide__eq,axiom, % 14.55/14.59 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__less__eq,axiom, % 14.55/14.59 ! [V_a_2,V_ca_2,V_b_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__divide__eq,axiom, % 14.55/14.59 ! [V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add__num__frac,axiom, % 14.55/14.59 ! [V_x,V_z,V_y,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add__divide__eq__iff,axiom, % 14.55/14.59 ! [V_y,V_x,V_z,T_a] : % 14.55/14.59 ( class_Fields_Ofield(T_a) % 14.55/14.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add__frac__num,axiom, % 14.55/14.59 ! [V_z,V_x,V_y,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__add__eq__iff,axiom, % 14.55/14.59 ! [V_y,V_x,V_z,T_a] : % 14.55/14.59 ( class_Fields_Ofield(T_a) % 14.55/14.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add__frac__eq,axiom, % 14.55/14.59 ! [V_w,V_x,V_z,V_y,T_a] : % 14.55/14.59 ( class_Fields_Ofield(T_a) % 14.55/14.59 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_diff__frac__eq,axiom, % 14.55/14.59 ! [V_w,V_x,V_z,V_y,T_a] : % 14.55/14.59 ( class_Fields_Ofield(T_a) % 14.55/14.59 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__diff__eq__iff,axiom, % 14.55/14.59 ! [V_y,V_x,V_z,T_a] : % 14.55/14.59 ( class_Fields_Ofield(T_a) % 14.55/14.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_diff__divide__eq__iff,axiom, % 14.55/14.59 ! [V_y,V_x,V_z,T_a] : % 14.55/14.59 ( class_Fields_Ofield(T_a) % 14.55/14.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__half__sum,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.59 => 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))))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_gt__half__sum,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_le__divide__eq,axiom, % 14.55/14.59 ! [V_ca_2,V_b_2,V_a_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__le__eq,axiom, % 14.55/14.59 ! [V_a_2,V_ca_2,V_b_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__le__divide__eq,axiom, % 14.55/14.59 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__divide__le__eq,axiom, % 14.55/14.59 ! [V_a_2,V_b_2,V_ca_2,T_b] : % 14.55/14.59 ( class_Fields_Olinordered__field(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_UNIV__Plus__UNIV,axiom, % 14.55/14.59 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_setprod__Un,axiom, % 14.55/14.59 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 14.55/14.59 ( class_Fields_Ofield(T_c) % 14.55/14.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.55/14.59 => ( ! [B_x] : % 14.55/14.59 ( 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))) % 14.55/14.59 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) ) % 14.55/14.59 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Plus__eq__empty__conv,axiom, % 14.55/14.59 ! [V_B_2,V_A_2,T_c,T_b] : % 14.55/14.59 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) % 14.55/14.59 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.55/14.59 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_field__le__mult__one__interval,axiom, % 14.55/14.59 ! [V_y,V_x,T_a] : % 14.55/14.59 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 14.55/14.59 => ( ! [B_z] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 14.55/14.59 => 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)) ) ) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_setprod__pos__nat,axiom, % 14.55/14.59 ! [V_f_2,V_S_2,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.55/14.59 => ( ! [B_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 14.55/14.59 => 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))) ) % 14.55/14.59 => 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_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_setsum__SucD,axiom, % 14.55/14.59 ! [V_n_2,V_A_2,V_f_2,T_b] : % 14.55/14.59 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) % 14.55/14.59 => ? [B_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.59 & 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_card__partition,axiom, % 14.55/14.59 ! [V_k_2,V_C_2,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) % 14.55/14.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 14.55/14.59 => ( ! [B_c] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) % 14.55/14.59 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 ) % 14.55/14.59 => ( ! [B_c1] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) % 14.55/14.59 => ! [B_c2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) % 14.55/14.59 => ( B_c1 != B_c2 % 14.55/14.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 14.55/14.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_fold__image__1,axiom, % 14.55/14.59 ! [V_f_2,V_S_2,T_b,T_c] : % 14.55/14.59 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.55/14.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.55/14.59 => ( ! [B_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 14.55/14.59 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 14.55/14.59 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_card_Oneutral,axiom, % 14.55/14.59 ! [V_A_2,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.59 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.59 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.55/14.59 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_fold__image__cong,axiom, % 14.55/14.59 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] : % 14.55/14.59 ( class_Groups_Oab__semigroup__mult(T_c) % 14.55/14.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.59 => ( ! [B_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.55/14.59 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 14.55/14.59 => 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),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_expand__Suc,axiom, % 14.55/14.59 ! [V_v] : % 14.55/14.59 ( 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))) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_card__Pow,axiom, % 14.55/14.59 ! [V_A_2,T_b] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.55/14.59 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),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_b),V_A_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_eq__number__of,axiom, % 14.55/14.59 ! [V_y_2,V_x_2,T_b] : % 14.55/14.59 ( ( class_Int_Onumber__ring(T_b) % 14.55/14.59 & class_Int_Oring__char__0(T_b) ) % 14.55/14.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 14.55/14.59 <=> V_x_2 = V_y_2 ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_number__of__reorient,axiom, % 14.55/14.59 ! [V_x_2,V_w_2,T_b] : % 14.55/14.59 ( class_Int_Onumber(T_b) % 14.55/14.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 % 14.55/14.59 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_le__number__of,axiom, % 14.55/14.59 ! [V_y_2,V_x_2,T_b] : % 14.55/14.59 ( ( class_Int_Onumber__ring(T_b) % 14.55/14.59 & class_Rings_Olinordered__idom(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__number__of,axiom, % 14.55/14.59 ! [V_y_2,V_x_2,T_b] : % 14.55/14.59 ( ( class_Int_Onumber__ring(T_b) % 14.55/14.59 & class_Rings_Olinordered__idom(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 14.55/14.59 ! [V_q,V_y,V_x,T_a] : % 14.55/14.59 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_number__of__add,axiom, % 14.55/14.59 ! [V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add__number__of__eq,axiom, % 14.55/14.59 ! [V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add__number__of__left,axiom, % 14.55/14.59 ! [V_z,V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_number__of__mult,axiom, % 14.55/14.59 ! [V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_arith__simps_I32_J,axiom, % 14.55/14.59 ! [V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mult__number__of__left,axiom, % 14.55/14.59 ! [V_z,V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_diff__number__of__eq,axiom, % 14.55/14.59 ! [V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_number__of__diff,axiom, % 14.55/14.59 ! [V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_number__of__minus,axiom, % 14.55/14.59 ! [V_w,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_arith__simps_I30_J,axiom, % 14.55/14.59 ! [V_w,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 14.55/14.59 ! [V_q,V_p,V_x,T_a] : % 14.55/14.59 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 14.55/14.59 ! [V_x,T_a] : % 14.55/14.59 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.59 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_le__number__of__eq__not__less,axiom, % 14.55/14.59 ! [V_w_2,V_v_2,T_b] : % 14.55/14.59 ( ( class_Int_Onumber(T_b) % 14.55/14.59 & class_Orderings_Olinorder(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_left__distrib__number__of,axiom, % 14.55/14.59 ! [V_v,V_b,V_a,T_b] : % 14.55/14.59 ( ( class_Int_Onumber(T_b) % 14.55/14.59 & class_Rings_Osemiring(T_b) ) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_right__distrib__number__of,axiom, % 14.55/14.59 ! [V_c,V_b,V_v,T_b] : % 14.55/14.59 ( ( class_Int_Onumber(T_b) % 14.55/14.59 & class_Rings_Osemiring(T_b) ) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 14.55/14.59 ! [V_q,V_x,T_a] : % 14.55/14.59 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 14.55/14.59 ! [V_q,V_x,T_a] : % 14.55/14.59 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 14.55/14.59 ! [V_q,V_x,T_a] : % 14.55/14.59 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add__number__of__diff1,axiom, % 14.55/14.59 ! [V_c,V_w,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add__number__of__diff2,axiom, % 14.55/14.59 ! [V_w,V_c,V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_right__diff__distrib__number__of,axiom, % 14.55/14.59 ! [V_c,V_b,V_v,T_b] : % 14.55/14.59 ( ( class_Int_Onumber(T_b) % 14.55/14.59 & class_Rings_Oring(T_b) ) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_left__diff__distrib__number__of,axiom, % 14.55/14.59 ! [V_v,V_b,V_a,T_b] : % 14.55/14.59 ( ( class_Int_Onumber(T_b) % 14.55/14.59 & class_Rings_Oring(T_b) ) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 14.55/14.59 ! [V_x,T_a] : % 14.55/14.59 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 14.55/14.59 ! [V_q,V_p,V_x,T_a] : % 14.55/14.59 ( class_Rings_Ocomm__semiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_minus__number__of__mult,axiom, % 14.55/14.59 ! [V_z,V_w,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Ints__power,axiom, % 14.55/14.59 ! [V_n_2,V_a_2,T_b] : % 14.55/14.59 ( class_Rings_Oring__1(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Ints__number__of,axiom, % 14.55/14.59 ! [V_w_2,T_b] : % 14.55/14.59 ( class_Int_Onumber__ring(T_b) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_eq__divide__eq__number__of1,axiom, % 14.55/14.59 ! [V_w_2,V_b_2,V_a_2,T_b] : % 14.55/14.59 ( ( class_Fields_Ofield__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) % 14.55/14.59 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 ) % 14.55/14.59 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_eq__divide__eq__number__of,axiom, % 14.55/14.59 ! [V_ca_2,V_b_2,V_w_2,T_b] : % 14.55/14.59 ( ( class_Fields_Ofield__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) % 14.55/14.59 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_b_2 ) % 14.55/14.59 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__eq__eq__number__of,axiom, % 14.55/14.59 ! [V_w_2,V_ca_2,V_b_2,T_b] : % 14.55/14.59 ( ( class_Fields_Ofield__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) % 14.55/14.59 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) ) % 14.55/14.59 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__eq__eq__number__of1,axiom, % 14.55/14.59 ! [V_a_2,V_w_2,V_b_2,T_b] : % 14.55/14.59 ( ( class_Fields_Ofield__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2 % 14.55/14.59 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) % 14.55/14.59 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__divide__eq__number__of1,axiom, % 14.55/14.59 ! [V_w_2,V_b_2,V_a_2,T_b] : % 14.55/14.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__divide__eq__number__of,axiom, % 14.55/14.59 ! [V_ca_2,V_b_2,V_w_2,T_b] : % 14.55/14.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__less__eq__number__of,axiom, % 14.55/14.59 ! [V_w_2,V_ca_2,V_b_2,T_b] : % 14.55/14.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__less__eq__number__of1,axiom, % 14.55/14.59 ! [V_a_2,V_w_2,V_b_2,T_b] : % 14.55/14.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__eq__if,axiom, % 14.55/14.59 ! [V_p,V_m] : % 14.55/14.59 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 14.55/14.59 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 => 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)))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__le__eq__number__of1,axiom, % 14.55/14.59 ! [V_a_2,V_w_2,V_b_2,T_b] : % 14.55/14.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divide__le__eq__number__of,axiom, % 14.55/14.59 ! [V_w_2,V_ca_2,V_b_2,T_b] : % 14.55/14.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_le__divide__eq__number__of,axiom, % 14.55/14.59 ! [V_ca_2,V_b_2,V_w_2,T_b] : % 14.55/14.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_le__divide__eq__number__of1,axiom, % 14.55/14.59 ! [V_w_2,V_b_2,V_a_2,T_b] : % 14.55/14.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.55/14.59 & class_Int_Onumber(T_b) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__strict__mono,axiom, % 14.55/14.59 ! [V_n,V_b,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__diff,axiom, % 14.55/14.59 ! [V_m,V_n,V_a,T_a] : % 14.55/14.59 ( class_Fields_Ofield(T_a) % 14.55/14.59 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.55/14.59 => 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)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_one__less__power,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__le__imp__le__exp,axiom, % 14.55/14.59 ! [V_n,V_m,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => ( 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))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__increasing__iff,axiom, % 14.55/14.59 ! [V_y_2,V_x_2,V_b_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__decreasing,axiom, % 14.55/14.59 ! [V_a,V_N,V_n,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_minus__numeral__code_I6_J,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_plus__numeral__code_I9_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__number__of__int__code,axiom, % 14.55/14.59 ! [V_l_2,V_k_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_times__numeral__code_I5_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_minus__numeral__code_I5_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__eq__number__of__int__code,axiom, % 14.55/14.59 ! [V_l_2,V_k_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmult__1,axiom, % 14.55/14.59 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmult__1__right,axiom, % 14.55/14.59 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 14.55/14.59 % 14.55/14.59 fof(fact_zle__add1__eq__le,axiom, % 14.55/14.59 ! [V_z_2,V_w_2] : % 14.55/14.59 ( 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)))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_add1__zle__eq,axiom, % 14.55/14.59 ! [V_z_2,V_w_2] : % 14.55/14.59 ( 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)) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zless__imp__add1__zle,axiom, % 14.55/14.59 ! [V_z,V_w] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zless__add1__eq,axiom, % 14.55/14.59 ! [V_z_2,V_w_2] : % 14.55/14.59 ( 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)))) % 14.55/14.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 14.55/14.59 | V_w_2 = V_z_2 ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__left__mono,axiom, % 14.55/14.59 ! [V_k,V_j,V_i] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__zless__mono,axiom, % 14.55/14.59 ! [V_z,V_z_H,V_w,V_w_H] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zless__le,axiom, % 14.55/14.59 ! [V_w_2,V_z_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 14.55/14.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 14.55/14.59 & V_z_2 != V_w_2 ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zle__refl,axiom, % 14.55/14.59 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zle__linear,axiom, % 14.55/14.59 ! [V_w,V_z] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 14.55/14.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zle__trans,axiom, % 14.55/14.59 ! [V_k,V_j,V_i] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zle__antisym,axiom, % 14.55/14.59 ! [V_w,V_z] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 14.55/14.59 => V_z = V_w ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zminus__zminus,axiom, % 14.55/14.59 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmult__zminus,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmult__commute,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmult__assoc,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zless__linear,axiom, % 14.55/14.59 ! [V_y,V_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 14.55/14.59 | V_x = V_y % 14.55/14.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__strict__right__mono,axiom, % 14.55/14.59 ! [V_k,V_j,V_i] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__commute,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__left__commute,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__assoc,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__zmult__distrib,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__zmult__distrib2,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zminus__zadd__distrib,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_diff__int__def__symmetric,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_diff__int__def,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiff__zmult__distrib2,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiff__zmult__distrib,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_equal__int__def,axiom, % 14.55/14.59 ! [V_l_2,V_k_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 14.55/14.59 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zminus__0,axiom, % 14.55/14.59 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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmult__zless__mono2,axiom, % 14.55/14.59 ! [V_k,V_j,V_i] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__bin__lemma,axiom, % 14.55/14.59 ! [V_l_2,V_k_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 14.55/14.59 <=> 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__0,axiom, % 14.55/14.59 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__0__right,axiom, % 14.55/14.59 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__zminus__inverse2,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_odd__nonzero,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_odd__less__0,axiom, % 14.55/14.59 ! [V_z_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_le__imp__0__less,axiom, % 14.55/14.59 ! [V_z] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__one__le__iff__zero__less,axiom, % 14.55/14.59 ! [V_z_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zle__diff1__eq,axiom, % 14.55/14.59 ! [V_z_2,V_w_2] : % 14.55/14.59 ( 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)))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__0__less__1,axiom, % 14.55/14.59 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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__zmult__eq__1__iff,axiom, % 14.55/14.59 ! [V_n_2,V_m_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 14.55/14.59 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 14.55/14.59 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 14.55/14.59 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zsgn__def,axiom, % 14.55/14.59 ! [V_i] : % 14.55/14.59 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.59 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 14.55/14.59 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 14.55/14.59 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 14.55/14.59 => 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)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zpower__zadd__distrib,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zpower__zpower,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_field__power__not__zero,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 14.55/14.59 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__mult__distrib,axiom, % 14.55/14.59 ! [V_n,V_b,V_a,T_a] : % 14.55/14.59 ( class_Groups_Ocomm__monoid__mult(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__commutes,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Groups_Omonoid__mult(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__one,axiom, % 14.55/14.59 ! [V_n,T_a] : % 14.55/14.59 ( class_Groups_Omonoid__mult(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__mult,axiom, % 14.55/14.59 ! [V_n,V_m,V_a,T_a] : % 14.55/14.59 ( class_Groups_Omonoid__mult(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__divide,axiom, % 14.55/14.59 ! [V_n,V_b,V_a,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__one__right,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Groups_Omonoid__mult(T_a) % 14.55/14.59 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zero__le__power,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__mono,axiom, % 14.55/14.59 ! [V_n,V_b,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zero__less__power,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__eq__0__iff,axiom, % 14.55/14.59 ! [V_n_2,V_a_2,T_b] : % 14.55/14.59 ( ( class_Power_Opower(T_b) % 14.55/14.59 & class_Rings_Omult__zero(T_b) % 14.55/14.59 & class_Rings_Ono__zero__divisors(T_b) % 14.55/14.59 & class_Rings_Ozero__neq__one(T_b) ) % 14.55/14.59 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.55/14.59 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_one__le__power,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__0__Suc,axiom, % 14.55/14.59 ! [V_n,T_a] : % 14.55/14.59 ( ( class_Power_Opower(T_a) % 14.55/14.59 & class_Rings_Osemiring__0(T_a) ) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__inject__exp,axiom, % 14.55/14.59 ! [V_n_2,V_m_2,V_a_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) % 14.55/14.59 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) % 14.55/14.59 <=> V_m_2 = V_n_2 ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__Suc2,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Groups_Omonoid__mult(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__Suc,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Power_Opower(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__0,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Power_Opower(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__add,axiom, % 14.55/14.59 ! [V_n,V_m,V_a,T_a] : % 14.55/14.59 ( class_Groups_Omonoid__mult(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_nonzero__power__divide,axiom, % 14.55/14.59 ! [V_n,V_a,V_b,T_a] : % 14.55/14.59 ( class_Fields_Ofield(T_a) % 14.55/14.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__one__over,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__Suc__0,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 14.55/14.59 ! [V_m_2,V_x_2] : % 14.55/14.59 ( 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)) % 14.55/14.59 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_nat__power__less__imp__less,axiom, % 14.55/14.59 ! [V_n,V_m,V_i] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 14.55/14.59 => ( 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))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_nat__zero__less__power__iff,axiom, % 14.55/14.59 ! [V_n_2,V_x_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 14.55/14.59 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__less__imp__less__base,axiom, % 14.55/14.59 ! [V_b,V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( 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))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__le__imp__le__base,axiom, % 14.55/14.59 ! [V_b,V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( 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)))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__inject__base,axiom, % 14.55/14.59 ! [V_b,V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( 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)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.59 => V_a = V_b ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__less__power__Suc,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => 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)))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__gt1__lemma,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => 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)))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__0__left,axiom, % 14.55/14.59 ! [V_n,T_a] : % 14.55/14.59 ( ( class_Power_Opower(T_a) % 14.55/14.59 & class_Rings_Osemiring__0(T_a) ) % 14.55/14.59 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 => 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) ) % 14.55/14.59 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 => 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) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__gt1,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => 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)))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__strict__increasing__iff,axiom, % 14.55/14.59 ! [V_y_2,V_x_2,V_b_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__less__imp__less__exp,axiom, % 14.55/14.59 ! [V_n,V_m,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => ( 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))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__strict__increasing,axiom, % 14.55/14.59 ! [V_a,V_N,V_n,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__increasing,axiom, % 14.55/14.59 ! [V_a,V_N,V_n,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__minus,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Oring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_nat__one__le__power,axiom, % 14.55/14.59 ! [V_n,V_i] : % 14.55/14.59 ( 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)) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__Suc__less,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__eq__imp__eq__base,axiom, % 14.55/14.59 ! [V_b,V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( 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) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.59 => V_a = V_b ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__Suc__less__one,axiom, % 14.55/14.59 ! [V_n,V_a,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__strict__decreasing,axiom, % 14.55/14.59 ! [V_a,V_N,V_n,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_self__quotient__aux1,axiom, % 14.55/14.59 ! [V_q,V_r,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.55/14.59 => ( 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)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_self__quotient__aux2,axiom, % 14.55/14.59 ! [V_q,V_r,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.55/14.59 => ( 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)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_q__pos__lemma,axiom, % 14.55/14.59 ! [V_r_H,V_q_H,V_b_H] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_q__neg__lemma,axiom, % 14.55/14.59 ! [V_r_H,V_q_H,V_b_H] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_unique__quotient__lemma,axiom, % 14.55/14.59 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__mono2__lemma,axiom, % 14.55/14.59 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 14.55/14.59 ( 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) % 14.55/14.59 => ( 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))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__atLeastAtMost__int,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__atLeastLessThan__int,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__greaterThanAtMost__int,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__greaterThanLessThan__int,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_number__of__is__id,axiom, % 14.55/14.59 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 14.55/14.59 % 14.55/14.59 fof(fact_eq__number__of__int__code,axiom, % 14.55/14.59 ! [V_l_2,V_k_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__0__neq__1,axiom, % 14.55/14.59 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 14.55/14.59 % 14.55/14.59 fof(fact_eq__int__refl,axiom, % 14.55/14.59 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__mono2__neg__lemma,axiom, % 14.55/14.59 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 14.55/14.59 ( 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) % 14.55/14.59 => ( 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))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_unique__quotient__lemma__neg,axiom, % 14.55/14.59 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_simp__from__to,axiom, % 14.55/14.59 ! [V_i_2,V_j_2] : % 14.55/14.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 14.55/14.59 => 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)) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 14.55/14.59 ! [V_n,V_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 14.55/14.59 ! [V_y,V_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 14.55/14.59 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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 14.55/14.59 ! [V_y,V_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power__power__power,axiom, % 14.55/14.59 ! [T_b] : % 14.55/14.59 ( class_Power_Opower(T_b) % 14.55/14.59 => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_infinite__UNIV__int,axiom, % 14.55/14.59 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_power_Opower_Opower__0,axiom, % 14.55/14.59 ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 14.55/14.59 % 14.55/14.59 fof(fact_power_Opower_Opower__Suc,axiom, % 14.55/14.59 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,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_b,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 14.55/14.59 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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_aset_I6_J,axiom, % 14.55/14.59 ! [V_A_2,V_t_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ( 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)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 14.55/14.59 => 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)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_bset_I8_J,axiom, % 14.55/14.59 ! [V_B_2,V_t_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ( 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)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_bset_I6_J,axiom, % 14.55/14.59 ! [V_t_2,V_B_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 14.55/14.59 => 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)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_aset_I8_J,axiom, % 14.55/14.59 ! [V_t_2,V_A_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_periodic__finite__ex,axiom, % 14.55/14.59 ! [V_Pa_2,V_d_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 14.55/14.59 => ( ! [B_x,B_k] : % 14.55/14.59 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.55/14.59 <=> hBOOL(hAPP(V_Pa_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)))) ) % 14.55/14.59 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 14.55/14.59 <=> ? [B_x] : % 14.55/14.59 ( 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))) % 14.55/14.59 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_aset_I4_J,axiom, % 14.55/14.59 ! [V_A_2,V_t_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( B_x != V_t_2 % 14.55/14.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_bset_I3_J,axiom, % 14.55/14.59 ! [V_B_2,V_t_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ( 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)) % 14.55/14.59 => ( ! [B_x] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xa] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 14.55/14.59 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 14.55/14.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_aset_I3_J,axiom, % 14.55/14.59 ! [V_A_2,V_t_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ( 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)) % 14.55/14.59 => ( ! [B_x] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xa] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 14.55/14.59 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 14.55/14.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_aset_I5_J,axiom, % 14.55/14.59 ! [V_A_2,V_t_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 14.55/14.59 => 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)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_bset_I7_J,axiom, % 14.55/14.59 ! [V_B_2,V_t_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 14.55/14.59 => 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))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_bset_I4_J,axiom, % 14.55/14.59 ! [V_B_2,V_t_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( B_x != V_t_2 % 14.55/14.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_aset_I7_J,axiom, % 14.55/14.59 ! [V_t_2,V_A_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_bset_I5_J,axiom, % 14.55/14.59 ! [V_t_2,V_B_2,V_D_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( ! [B_xa] : % 14.55/14.59 ( 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))) % 14.55/14.59 => ! [B_xb] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 14.55/14.59 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 14.55/14.59 => 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)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_tsub__def,axiom, % 14.55/14.59 ! [V_x,V_y] : % 14.55/14.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 14.55/14.59 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 14.55/14.59 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__power__div__base,axiom, % 14.55/14.59 ! [V_k,V_m] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 14.55/14.59 => 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)))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_decr__mult__lemma,axiom, % 14.55/14.59 ! [V_k_2,V_Pa_2,V_d_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 14.55/14.59 => ( ! [B_x] : % 14.55/14.59 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.55/14.59 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.55/14.59 => hBOOL(hAPP(V_Pa_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)))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_incr__mult__lemma,axiom, % 14.55/14.59 ! [V_k_2,V_Pa_2,V_d_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 14.55/14.59 => ( ! [B_x] : % 14.55/14.59 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.55/14.59 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 14.55/14.59 => ! [B_x] : % 14.55/14.59 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.55/14.59 => hBOOL(hAPP(V_Pa_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)))) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__number__of__lemma,axiom, % 14.55/14.59 ! [V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => ( ( 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))) % 14.55/14.59 => 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) ) % 14.55/14.59 & ( ~ 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))) % 14.55/14.59 => 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) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_negative__zle,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_negative__zless,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__eq__iff,axiom, % 14.55/14.59 ! [V_n_2,V_m_2,T_b] : % 14.55/14.59 ( class_Nat_Osemiring__char__0(T_b) % 14.55/14.59 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) % 14.55/14.59 <=> V_m_2 = V_n_2 ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__zero,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__zminus__zminus,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__zminus2,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__0,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__by__0,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__by__1,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 14.55/14.59 ! [V_A_2,V_x_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 14.55/14.59 <=> 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 14.55/14.59 ! [V_B_2,V_A_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.59 <=> 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 14.55/14.59 ! [V_y,V_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 14.55/14.59 ! [V_a_2,V_b_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 14.55/14.59 => ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 14.55/14.59 ! [V_a_2,V_b_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__neg__pos__less0,axiom, % 14.55/14.59 ! [V_b,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__self,axiom, % 14.55/14.59 ! [V_a] : % 14.55/14.59 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__0,axiom, % 14.55/14.59 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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__eq__0__conv,axiom, % 14.55/14.59 ! [V_n_2] : % 14.55/14.59 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.59 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 14.55/14.59 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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zero__zle__int,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 14.55/14.59 ! [V_Pa_2] : % 14.55/14.59 ( ? [B_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 14.55/14.59 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.55/14.59 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 14.55/14.59 ! [V_Pa_2] : % 14.55/14.59 ( ! [B_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 14.55/14.59 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.55/14.59 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__less__0__conv,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zless__int,axiom, % 14.55/14.59 ! [V_n_2,V_m_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 14.55/14.59 ! [V_y_2,V_x_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zle__int,axiom, % 14.55/14.59 ! [V_n_2,V_m_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 14.55/14.59 ! [V_y_2,V_x_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__int,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zadd__int__left,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zle__iff__zadd,axiom, % 14.55/14.59 ! [V_z_2,V_w_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 14.55/14.59 <=> ? [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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zero__le__imp__of__nat,axiom, % 14.55/14.59 ! [V_m,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__0__le__iff,axiom, % 14.55/14.59 ! [V_n,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_negative__eq__positive,axiom, % 14.55/14.59 ! [V_m_2,V_n_2] : % 14.55/14.59 ( 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) % 14.55/14.59 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__less__0__iff,axiom, % 14.55/14.59 ! [V_m,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ~ 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_not__int__zless__negative,axiom, % 14.55/14.59 ! [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)))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__mult,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmult__int,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__0,axiom, % 14.55/14.59 ! [T_a] : % 14.55/14.59 ( class_Rings_Osemiring__1(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__less__imp__less,axiom, % 14.55/14.59 ! [V_n,V_m,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( 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))) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_less__imp__of__nat__less,axiom, % 14.55/14.59 ! [V_n,V_m,T_a] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__less__iff,axiom, % 14.55/14.59 ! [V_n_2,V_m_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__1,axiom, % 14.55/14.59 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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 14.55/14.59 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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__le__iff,axiom, % 14.55/14.59 ! [V_n_2,V_m_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__add,axiom, % 14.55/14.59 ! [V_n,V_m,T_a] : % 14.55/14.59 ( class_Rings_Osemiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__mult,axiom, % 14.55/14.59 ! [V_n,V_m,T_a] : % 14.55/14.59 ( class_Rings_Osemiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__mult__mult1__if,axiom, % 14.55/14.59 ! [V_b,V_a,V_c,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) % 14.55/14.59 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__mult__self2__is__id,axiom, % 14.55/14.59 ! [V_a,V_b,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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 ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__mult__self1__is__id,axiom, % 14.55/14.59 ! [V_a,V_b,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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 ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__mult__mult2,axiom, % 14.55/14.59 ! [V_b,V_a,V_c,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__mult__mult1,axiom, % 14.55/14.59 ! [V_b,V_a,V_c,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__self,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__1,axiom, % 14.55/14.59 ! [T_a] : % 14.55/14.59 ( class_Rings_Osemiring__1(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Ints__of__nat,axiom, % 14.55/14.59 ! [V_n_2,T_b] : % 14.55/14.59 ( class_Rings_Oring__1(T_b) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__power,axiom, % 14.55/14.59 ! [V_n,V_m,T_a] : % 14.55/14.59 ( class_Rings_Osemiring__1(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__power,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zpower__int,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 14.55/14.59 ! [V_A_2] : % 14.55/14.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 14.55/14.59 <=> 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 14.55/14.59 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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__eq__0__iff,axiom, % 14.55/14.59 ! [V_k_2,V_i_2] : % 14.55/14.59 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.59 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 14.55/14.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 14.55/14.59 ! [V_a_2,V_b_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 14.55/14.59 => ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 14.55/14.59 ! [V_i_2,V_k_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 14.55/14.59 => ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 14.55/14.59 ! [V_b_2,V_a_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 14.55/14.59 => ( 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))) % 14.55/14.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__mono2,axiom, % 14.55/14.59 ! [V_b,V_b_H,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__nonneg__neg__le0,axiom, % 14.55/14.59 ! [V_b,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__pos__pos__trivial,axiom, % 14.55/14.59 ! [V_b,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 14.55/14.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 14.55/14.59 ! [V_a_2,V_b_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__nonpos__pos__le0,axiom, % 14.55/14.59 ! [V_b,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__mono2__neg,axiom, % 14.55/14.59 ! [V_b,V_b_H,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 14.55/14.59 => 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))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__neg__neg__trivial,axiom, % 14.55/14.59 ! [V_b,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 14.55/14.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__mono1,axiom, % 14.55/14.59 ! [V_b,V_a_H,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__mono1__neg,axiom, % 14.55/14.59 ! [V_b,V_a_H,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__div__less__self,axiom, % 14.55/14.59 ! [V_k,V_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__zmult2__eq,axiom, % 14.55/14.59 ! [V_b,V_a,V_c] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__le__0__conv,axiom, % 14.55/14.59 ! [V_n_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__Suc0__eq__1,axiom, % 14.55/14.59 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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zless__iff__Suc__zadd,axiom, % 14.55/14.59 ! [V_z_2,V_w_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 14.55/14.59 <=> ? [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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__zle__neg,axiom, % 14.55/14.59 ! [V_m_2,V_n_2] : % 14.55/14.59 ( 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)))) % 14.55/14.59 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__Suc,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_negative__zle__0,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiff__int,axiom, % 14.55/14.59 ! [V_m,V_n] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__Suc,axiom, % 14.55/14.59 ! [V_m,T_a] : % 14.55/14.59 ( class_Rings_Osemiring__1(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__diff,axiom, % 14.55/14.59 ! [V_m,V_n,T_a] : % 14.55/14.59 ( class_Rings_Oring__1(T_a) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__mult__self2,axiom, % 14.55/14.59 ! [V_c,V_a,V_b,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__mult__self1,axiom, % 14.55/14.59 ! [V_c,V_a,V_b,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__add__self1,axiom, % 14.55/14.59 ! [V_a,V_b,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__add__self2,axiom, % 14.55/14.59 ! [V_a,V_b,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.55/14.59 => 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)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zero__less__int__conv,axiom, % 14.55/14.59 ! [V_n_2] : % 14.55/14.59 ( 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))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmult__zless__mono2__lemma,axiom, % 14.55/14.59 ! [V_k,V_j,V_i] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_not__zle__0__negative,axiom, % 14.55/14.59 ! [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))))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_negative__zless__0,axiom, % 14.55/14.59 ! [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))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__0__less__iff,axiom, % 14.55/14.59 ! [V_n_2,T_b] : % 14.55/14.59 ( class_Rings_Olinordered__semidom(T_b) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 14.55/14.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_divmod__int__rel__div__eq,axiom, % 14.55/14.59 ! [V_r_1,V_y,V_b_1,V_a_1] : % 14.55/14.59 ( 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) % 14.55/14.59 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 14.55/14.59 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_split__zdiv,axiom, % 14.55/14.59 ! [V_k_2,V_n_2,V_Pa_2] : % 14.55/14.59 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 14.55/14.59 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.59 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.55/14.59 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 14.55/14.59 => ! [B_i] : % 14.55/14.59 ( ? [B_j] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 14.55/14.59 & 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) ) % 14.55/14.59 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 14.55/14.59 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ! [B_i] : % 14.55/14.59 ( ? [B_j] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 & 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) ) % 14.55/14.59 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 14.55/14.59 ! [V_y,V_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiff__int__split,axiom, % 14.55/14.59 ! [V_y_2,V_x_2,V_Pa_2] : % 14.55/14.59 ( hBOOL(hAPP(V_Pa_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)))) % 14.55/14.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 14.55/14.59 => hBOOL(hAPP(V_Pa_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)))) ) % 14.55/14.59 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 14.55/14.59 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_tsub__eq,axiom, % 14.55/14.59 ! [V_x,V_y] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 14.55/14.59 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_z3div__def,axiom, % 14.55/14.59 ! [V_k,V_l] : % 14.55/14.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 14.55/14.59 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_setsum__bounded,axiom, % 14.55/14.59 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] : % 14.55/14.59 ( ( class_Groups_Oordered__ab__semigroup__add(T_c) % 14.55/14.59 & class_Rings_Osemiring__1(T_c) ) % 14.55/14.59 => ( ! [B_i] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) ) % 14.55/14.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__pos__neg__trivial,axiom, % 14.55/14.59 ! [V_b,V_a] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.55/14.59 => ( 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))) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_split__neg__lemma,axiom, % 14.55/14.59 ! [V_n_2,V_Pa_2,V_k_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(V_Pa_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))) % 14.55/14.59 <=> ! [B_i,B_j] : % 14.55/14.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 & 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) ) % 14.55/14.59 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_split__pos__lemma,axiom, % 14.55/14.59 ! [V_n_2,V_Pa_2,V_k_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(V_Pa_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))) % 14.55/14.59 <=> ! [B_i,B_j] : % 14.55/14.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 14.55/14.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 14.55/14.59 & 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) ) % 14.55/14.59 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_of__nat__number__of__eq,axiom, % 14.55/14.59 ! [V_v,T_a] : % 14.55/14.59 ( class_Int_Onumber__ring(T_a) % 14.55/14.59 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.59 => 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) ) % 14.55/14.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.59 => 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) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 14.55/14.59 ! [V_B_2,V_A_2] : % 14.55/14.59 ( V_A_2 = V_B_2 % 14.55/14.59 <=> 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 14.55/14.59 ! [V_y_2,V_x_2] : % 14.55/14.59 ( 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) % 14.55/14.59 <=> V_x_2 = V_y_2 ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 14.55/14.59 ! [V_B_2,V_A_2] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.55/14.59 <=> 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_int__int__eq,axiom, % 14.55/14.59 ! [V_n_2,V_m_2] : % 14.55/14.59 ( 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) % 14.55/14.59 <=> V_m_2 = V_n_2 ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_not__neg__int,axiom, % 14.55/14.59 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__0,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__by__0,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__self,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_neg__number__of__Min,axiom, % 14.55/14.59 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__minus1__right,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mod__trivial,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__add__self2,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__add__self1,axiom, % 14.55/14.59 ! [V_a,V_b,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__add__right__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__add__left__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__add__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__simps_I2_J,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__simps_I1_J,axiom, % 14.55/14.59 ! [V_b,V_c,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__add__cong,axiom, % 14.55/14.59 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 14.55/14.59 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 14.55/14.59 => 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) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__right__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__left__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__mult1,axiom, % 14.55/14.59 ! [V_b,V_a,V_c,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__mult2,axiom, % 14.55/14.59 ! [V_b,V_c,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__simps_I4_J,axiom, % 14.55/14.59 ! [V_b,V_c,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__cong,axiom, % 14.55/14.59 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 14.55/14.59 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 14.55/14.59 => 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) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__diff__cong,axiom, % 14.55/14.59 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 14.55/14.59 ( class_Divides_Oring__div(T_a) % 14.55/14.59 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 14.55/14.59 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 14.55/14.59 => 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) ) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__diff__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Oring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__diff__left__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Oring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__diff__right__eq,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Oring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__minus__cong,axiom, % 14.55/14.59 ! [V_a_H,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Oring__div(T_a) % 14.55/14.59 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__minus__eq,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Oring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__le__dividend,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__le__mono,axiom, % 14.55/14.59 ! [V_k,V_n,V_m] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__mult2__eq,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__self,axiom, % 14.55/14.59 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__zero,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiv__int,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_rel__simps_I24_J,axiom, % 14.55/14.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_rel__simps_I7_J,axiom, % 14.55/14.59 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__zmult1__eq,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__simps_I3_J,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiff__zmod__right,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zdiff__zmod__left,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__zminus2,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__zminus__zminus,axiom, % 14.55/14.59 ! [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)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zminus__zmod,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zpower__zmod,axiom, % 14.55/14.59 ! [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) ). % 14.55/14.59 % 14.55/14.59 fof(fact_eq__int__code_I6_J,axiom, % 14.55/14.59 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 14.55/14.59 % 14.55/14.59 fof(fact_not__neg__0,axiom, % 14.55/14.59 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_not__neg__1,axiom, % 14.55/14.59 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__self1__is__0,axiom, % 14.55/14.59 ! [V_a,V_b,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__self2__is__0,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__self2,axiom, % 14.55/14.59 ! [V_c,V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__mult__self1,axiom, % 14.55/14.59 ! [V_b,V_c,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__by__1,axiom, % 14.55/14.59 ! [V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_mod__div__trivial,axiom, % 14.55/14.59 ! [V_b,V_a,T_a] : % 14.55/14.59 ( class_Divides_Osemiring__div(T_a) % 14.55/14.59 => 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) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__1,axiom, % 14.55/14.59 ! [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 ). % 14.55/14.59 % 14.55/14.59 fof(fact_div__less,axiom, % 14.55/14.59 ! [V_n,V_m] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_nat__mult__div__cancel__disj,axiom, % 14.55/14.59 ! [V_n,V_m,V_k] : % 14.55/14.59 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 => 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) ) % 14.55/14.59 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.59 => 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) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 14.55/14.59 ! [V_y,V_x] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.55/14.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.55/14.59 => 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))) ) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_zmod__le__nonneg__dividend,axiom, % 14.55/14.59 ! [V_k,V_m] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 14.55/14.59 => 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)) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_neg__mod__bound,axiom, % 14.55/14.59 ! [V_a,V_b] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.59 => 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))) ) ). % 14.55/14.59 % 14.55/14.59 fof(fact_pos__mod__bound,axiom, % 14.55/14.59 ! [V_a,V_b] : % 14.55/14.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.55/14.60 => 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)) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__eq__0__iff,axiom, % 14.55/14.60 ! [V_d_2,V_m_2] : % 14.55/14.60 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_bin__less__0__simps_I2_J,axiom, % 14.55/14.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__zminus2__not__zero,axiom, % 14.55/14.60 ! [V_l,V_k] : % 14.55/14.60 ( 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) % 14.55/14.60 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__zminus1__not__zero,axiom, % 14.55/14.60 ! [V_l,V_k] : % 14.55/14.60 ( 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) % 14.55/14.60 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_DIVISION__BY__ZERO,axiom, % 14.55/14.60 ! [V_a] : % 14.55/14.60 ( 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) % 14.55/14.60 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__zdiv__trivial,axiom, % 14.55/14.60 ! [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) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zdiv__zadd1__eq,axiom, % 14.55/14.60 ! [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)) ). % 14.55/14.60 % 14.55/14.60 fof(fact_Int_OMin__def,axiom, % 14.55/14.60 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mult__Min,axiom, % 14.55/14.60 ! [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) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__minus1,axiom, % 14.55/14.60 ! [V_b] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.55/14.60 => 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)) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_not__neg__eq__ge__0,axiom, % 14.55/14.60 ! [V_x_2] : % 14.55/14.60 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 14.55/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_neg__def,axiom, % 14.55/14.60 ! [V_Z_2] : % 14.55/14.60 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 14.55/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_neg__zminus__int,axiom, % 14.55/14.60 ! [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))))) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__mod__equality,axiom, % 14.55/14.60 ! [V_c,V_b,V_a,T_a] : % 14.55/14.60 ( class_Divides_Osemiring__div(T_a) % 14.55/14.60 => 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) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__mod__equality2,axiom, % 14.55/14.60 ! [V_c,V_a,V_b,T_a] : % 14.55/14.60 ( class_Divides_Osemiring__div(T_a) % 14.55/14.60 => 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) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mod__div__equality,axiom, % 14.55/14.60 ! [V_b,V_a,T_a] : % 14.55/14.60 ( class_Divides_Osemiring__div(T_a) % 14.55/14.60 => 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 ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mod__div__equality2,axiom, % 14.55/14.60 ! [V_a,V_b,T_a] : % 14.55/14.60 ( class_Divides_Osemiring__div(T_a) % 14.55/14.60 => 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 ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 14.55/14.60 ! [V_b,V_a,T_a] : % 14.55/14.60 ( class_Divides_Osemiring__div(T_a) % 14.55/14.60 => 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 ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__le__mono2,axiom, % 14.55/14.60 ! [V_k,V_n,V_m] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.55/14.60 => 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))) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_nat__mult__div__cancel1,axiom, % 14.55/14.60 ! [V_n,V_m,V_k] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 14.55/14.60 => 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) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__mult__self1__is__m,axiom, % 14.55/14.60 ! [V_m,V_n] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.60 => 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 ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__mult__self__is__m,axiom, % 14.55/14.60 ! [V_m,V_n] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.60 => 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 ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__less__dividend,axiom, % 14.55/14.60 ! [V_m,V_n] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 14.55/14.60 => 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)) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mult__minus1__right,axiom, % 14.55/14.60 ! [V_z,T_a] : % 14.55/14.60 ( class_Int_Onumber__ring(T_a) % 14.55/14.60 => 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) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mult__minus1,axiom, % 14.55/14.60 ! [V_z,T_a] : % 14.55/14.60 ( class_Int_Onumber__ring(T_a) % 14.55/14.60 => 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) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mod__neg__neg__trivial,axiom, % 14.55/14.60 ! [V_b,V_a] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 14.55/14.60 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_neg__mod__conj,axiom, % 14.55/14.60 ! [V_a,V_b] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.60 => ( 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))) % 14.55/14.60 & 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))) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_neg__mod__sign,axiom, % 14.55/14.60 ! [V_a,V_b] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.60 => 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))) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mod__pos__pos__trivial,axiom, % 14.55/14.60 ! [V_b,V_a] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 14.55/14.60 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_pos__mod__conj,axiom, % 14.55/14.60 ! [V_a,V_b] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.55/14.60 => ( 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))) % 14.55/14.60 & 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)) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_pos__mod__sign,axiom, % 14.55/14.60 ! [V_a,V_b] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.55/14.60 => 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))) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_number__of__Min,axiom, % 14.55/14.60 ! [T_a] : % 14.55/14.60 ( class_Int_Onumber__ring(T_a) % 14.55/14.60 => 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)) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_arith__simps_I31_J,axiom, % 14.55/14.60 ! [T_a] : % 14.55/14.60 ( class_Int_Onumber__ring(T_a) % 14.55/14.60 => 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) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_divide__minus1,axiom, % 14.55/14.60 ! [V_x,T_a] : % 14.55/14.60 ( ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.60 & class_Int_Onumber__ring(T_a) ) % 14.55/14.60 => 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) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__zminus2__eq__if,axiom, % 14.55/14.60 ! [V_b,V_a] : % 14.55/14.60 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => 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) ) % 14.55/14.60 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => 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) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__zminus1__eq__if,axiom, % 14.55/14.60 ! [V_b,V_a] : % 14.55/14.60 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => 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) ) % 14.55/14.60 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => 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)) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__zdiv__equality,axiom, % 14.55/14.60 ! [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)) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zdiv__zmult1__eq,axiom, % 14.55/14.60 ! [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)) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zdiv__zmod__equality,axiom, % 14.55/14.60 ! [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) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zdiv__zmod__equality2,axiom, % 14.55/14.60 ! [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) ). % 14.55/14.60 % 14.55/14.60 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 14.55/14.60 ! [V_n,V_m] : % 14.55/14.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 14.55/14.60 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 14.55/14.60 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmult__eq__1__iff,axiom, % 14.55/14.60 ! [V_n_2,V_m_2] : % 14.55/14.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 14.55/14.60 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 14.55/14.60 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 14.55/14.60 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 14.55/14.60 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmult__div__cancel,axiom, % 14.55/14.60 ! [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)) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__zdiv__equality_H,axiom, % 14.55/14.60 ! [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)) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zdiv__minus1__right,axiom, % 14.55/14.60 ! [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) ). % 14.55/14.60 % 14.55/14.60 fof(fact_neg__imp__number__of__eq__0,axiom, % 14.55/14.60 ! [V_v] : % 14.55/14.60 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_int__nat__number__of,axiom, % 14.55/14.60 ! [V_v] : % 14.55/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => 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) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => 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) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__geq,axiom, % 14.55/14.60 ! [V_m,V_n] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.60 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.60 => 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)) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__if,axiom, % 14.55/14.60 ! [V_m,V_n] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.60 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.55/14.60 => 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)) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_split__div,axiom, % 14.55/14.60 ! [V_k_2,V_n_2,V_Pa_2] : % 14.55/14.60 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 14.55/14.60 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.60 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 14.55/14.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.60 => ! [B_i,B_j] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 14.55/14.60 => ( 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) % 14.55/14.60 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mod__pos__neg__trivial,axiom, % 14.55/14.60 ! [V_b,V_a] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.55/14.60 => ( 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))) % 14.55/14.60 => 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) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_minus1__divide,axiom, % 14.55/14.60 ! [V_x,T_a] : % 14.55/14.60 ( ( class_Fields_Ofield__inverse__zero(T_a) % 14.55/14.60 & class_Int_Onumber__ring(T_a) ) % 14.55/14.60 => 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)) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_div__eq__minus1,axiom, % 14.55/14.60 ! [V_b] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.55/14.60 => 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) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_le__div__geq,axiom, % 14.55/14.60 ! [V_m,V_n] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.55/14.60 => 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)) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_split__div__lemma,axiom, % 14.55/14.60 ! [V_m_2,V_q_2,V_n_2] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 14.55/14.60 => ( ( 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)) % 14.55/14.60 & 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)))) ) % 14.55/14.60 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_split__div_H,axiom, % 14.55/14.60 ! [V_n_2,V_m_2,V_Pa_2] : % 14.55/14.60 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 14.55/14.60 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.55/14.60 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 14.55/14.60 | ? [B_q] : % 14.55/14.60 ( 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)) % 14.55/14.60 & 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)))) % 14.55/14.60 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_eq__nat__number__of,axiom, % 14.55/14.60 ! [V_v_H_2,V_v_2] : % 14.55/14.60 ( 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) % 14.55/14.60 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 14.55/14.60 => 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))) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 14.55/14.60 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 14.55/14.60 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 14.55/14.60 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_nat__number__of__add__left,axiom, % 14.55/14.60 ! [V_k,V_v_H,V_v] : % 14.55/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => 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) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 14.55/14.60 => 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) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 14.55/14.60 => 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) ) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_split__zmod,axiom, % 14.55/14.60 ! [V_k_2,V_n_2,V_Pa_2] : % 14.55/14.60 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 14.55/14.60 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 14.55/14.60 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 14.55/14.60 => ! [B_i,B_j] : % 14.55/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 14.55/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 14.55/14.60 & 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) ) % 14.55/14.60 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 14.55/14.60 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.60 => ! [B_i,B_j] : % 14.55/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 14.55/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.60 & 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) ) % 14.55/14.60 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmult2__lemma__aux3,axiom, % 14.55/14.60 ! [V_q,V_b,V_r,V_c] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 14.55/14.60 => 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))) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmult2__lemma__aux4,axiom, % 14.55/14.60 ! [V_q,V_b,V_r,V_c] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 14.55/14.60 => 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))) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmult2__lemma__aux1,axiom, % 14.55/14.60 ! [V_q,V_r,V_b,V_c] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.60 => 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))) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmult2__lemma__aux2,axiom, % 14.55/14.60 ! [V_q,V_r,V_b,V_c] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.60 => 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))) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_divmod__int__rel__mod__eq,axiom, % 14.55/14.60 ! [V_y,V_q_1,V_b_1,V_a_1] : % 14.55/14.60 ( 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) % 14.55/14.60 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.55/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 14.55/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 14.55/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 14.55/14.60 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zmod__zmult2__eq,axiom, % 14.55/14.60 ! [V_b,V_a,V_c] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 14.55/14.60 => 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)) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zdiv__zminus2__eq__if,axiom, % 14.55/14.60 ! [V_a,V_b] : % 14.55/14.60 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => 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)) ) % 14.55/14.60 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => 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)) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_zdiv__zminus1__eq__if,axiom, % 14.55/14.60 ! [V_a,V_b] : % 14.55/14.60 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => 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)) ) % 14.55/14.60 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.55/14.60 => 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)) ) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_z3mod__def,axiom, % 14.55/14.60 ! [V_k,V_l] : % 14.55/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 14.55/14.60 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 14.55/14.60 => 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)) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_Suc__nat__number__of__add,axiom, % 14.55/14.60 ! [V_n,V_v] : % 14.55/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => 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) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => 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) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_Suc__nat__number__of,axiom, % 14.55/14.60 ! [V_v] : % 14.55/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 14.55/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.55/14.60 => 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)) ) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_image__atLeastZeroLessThan__int,axiom, % 14.55/14.60 ! [V_u_2] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 14.55/14.60 => 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))) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_negD,axiom, % 14.55/14.60 ! [V_x] : % 14.55/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.55/14.60 => ? [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))) ) ). % 14.55/14.60 % 14.55/14.60 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 14.55/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__less,axiom, % 14.79/14.60 ! [V_n,V_m] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.79/14.60 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_div__add1__eq,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__less__eq__dividend,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__mult__distrib,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__mult__distrib2,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__int,axiom, % 14.79/14.60 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 14.79/14.60 % 14.79/14.60 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__mod__distrib,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__0,axiom, % 14.79/14.60 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 14.79/14.60 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__Suc,axiom, % 14.79/14.60 ! [V_n,V_m] : % 14.79/14.60 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 14.79/14.60 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.79/14.60 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__1,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__less__divisor,axiom, % 14.79/14.60 ! [V_m,V_n] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__nat__nat__iff,axiom, % 14.79/14.60 ! [V_z_H_2,V_z_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 14.79/14.60 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 14.79/14.60 <=> V_z_2 = V_z_H_2 ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_ex__nat,axiom, % 14.79/14.60 ! [V_Pa_2] : % 14.79/14.60 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 14.79/14.60 <=> ? [B_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 14.79/14.60 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_all__nat,axiom, % 14.79/14.60 ! [V_Pa_2] : % 14.79/14.60 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 14.79/14.60 <=> ! [B_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 14.79/14.60 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 14.79/14.60 ! [V_y_2,V_x_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 14.79/14.60 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 14.79/14.60 <=> V_x_2 = V_y_2 ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__eq__0__iff,axiom, % 14.79/14.60 ! [V_d_2,V_m_2] : % 14.79/14.60 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.60 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__geq,axiom, % 14.79/14.60 ! [V_n,V_m] : % 14.79/14.60 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__if,axiom, % 14.79/14.60 ! [V_n,V_m] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.79/14.60 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.79/14.60 => 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) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__mult__self3,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__mult2__eq,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_div__mult1__eq,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_le__mod__geq,axiom, % 14.79/14.60 ! [V_m,V_n] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__number__of__def,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__number__of,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_div__mod__equality_H,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__div__cancel,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Divides_Omod__div__equality_H,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 14.79/14.60 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zmod__int,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_neg__nat,axiom, % 14.79/14.60 ! [V_z] : % 14.79/14.60 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 14.79/14.60 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_not__neg__nat,axiom, % 14.79/14.60 ! [V_z] : % 14.79/14.60 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 14.79/14.60 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__int__nat__set__return__embed,axiom, % 14.79/14.60 ! [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 ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__nat__number__of,axiom, % 14.79/14.60 ! [V_v_H,V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.79/14.60 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 14.79/14.60 => 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))) ) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 14.79/14.60 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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__le__0,axiom, % 14.79/14.60 ! [V_z] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__0__iff,axiom, % 14.79/14.60 ! [V_i_2] : % 14.79/14.60 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__mono__iff,axiom, % 14.79/14.60 ! [V_w_2,V_z_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 14.79/14.60 => ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zless__nat__conj,axiom, % 14.79/14.60 ! [V_z_2,V_w_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 14.79/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__le__divisor,axiom, % 14.79/14.60 ! [V_m,V_n] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 14.79/14.60 ! [V_y_2,V_x_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 14.79/14.60 => ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__1,axiom, % 14.79/14.60 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__mult__self4,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_int__nat__eq,axiom, % 14.79/14.60 ! [V_z] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.79/14.60 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.79/14.60 => 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) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_int__eq__iff,axiom, % 14.79/14.60 ! [V_z_2,V_m_2] : % 14.79/14.60 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 14.79/14.60 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 14.79/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__0__le,axiom, % 14.79/14.60 ! [V_z] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.79/14.60 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zless__nat__eq__int__zless,axiom, % 14.79/14.60 ! [V_z_2,V_m_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 14.79/14.60 <=> 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__div__distrib,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__zminus__int,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_one__mod__nat__number__of,axiom, % 14.79/14.60 ! [V_v_H] : % 14.79/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 14.79/14.60 => 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)) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_succ__def,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I2_J,axiom, % 14.79/14.60 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 14.79/14.60 % 14.79/14.60 fof(fact_card__atLeastZeroLessThan__int,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_card__atLeastLessThan__int,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__less__nat__eq,axiom, % 14.79/14.60 ! [V_z_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__less__eq__zless,axiom, % 14.79/14.60 ! [V_z_2,V_w_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 14.79/14.60 => ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 14.79/14.60 ! [V_y_2,V_x_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 14.79/14.60 => ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__eq__iff,axiom, % 14.79/14.60 ! [V_m_2,V_w_2] : % 14.79/14.60 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 14.79/14.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 14.79/14.60 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 14.79/14.60 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__eq__iff2,axiom, % 14.79/14.60 ! [V_w_2,V_m_2] : % 14.79/14.60 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 14.79/14.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 14.79/14.60 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 14.79/14.60 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__le__eq__zle,axiom, % 14.79/14.60 ! [V_z_2,V_w_2] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 14.79/14.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 14.79/14.60 => ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_split__nat,axiom, % 14.79/14.60 ! [V_i_2,V_Pa_2] : % 14.79/14.60 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 14.79/14.60 <=> ( ! [B_n] : % 14.79/14.60 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 14.79/14.60 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 14.79/14.60 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_split__mod,axiom, % 14.79/14.60 ! [V_k_2,V_n_2,V_Pa_2] : % 14.79/14.60 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 14.79/14.60 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.60 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 14.79/14.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.60 => ! [B_i,B_j] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 14.79/14.60 => ( 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) % 14.79/14.60 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__lemma,axiom, % 14.79/14.60 ! [V_q,V_b,V_r,V_c] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__add__distrib,axiom, % 14.79/14.60 ! [V_z_H,V_z] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_int__eq__iff__number__of,axiom, % 14.79/14.60 ! [V_v_2,V_m_2] : % 14.79/14.60 ( 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) % 14.79/14.60 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 14.79/14.60 & 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__mult__distrib,axiom, % 14.79/14.60 ! [V_z_H,V_z] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__diff__distrib,axiom, % 14.79/14.60 ! [V_z,V_z_H] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__times__mod__eq,axiom, % 14.79/14.60 ! [V_m,V_k] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_card__greaterThanAtMost__int,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 14.79/14.60 ! [V_n,V_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__power__eq,axiom, % 14.79/14.60 ! [V_n,V_z] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_one__less__nat__eq,axiom, % 14.79/14.60 ! [V_z_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__less__iff,axiom, % 14.79/14.60 ! [V_m_2,V_w_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 14.79/14.60 <=> 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 14.79/14.60 ! [V_z] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_number__of__succ,axiom, % 14.79/14.60 ! [V_k,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__mult__distrib__neg,axiom, % 14.79/14.60 ! [V_z_H,V_z] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_div__nat__number__of,axiom, % 14.79/14.60 ! [V_v_H,V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_card__atLeastAtMost__int,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_one__div__nat__number__of,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_card__greaterThanLessThan__int,axiom, % 14.79/14.60 ! [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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__nat__number__of__number__of,axiom, % 14.79/14.60 ! [V_w,V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.79/14.60 => 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)) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__nat__number__of,axiom, % 14.79/14.60 ! [V_n,V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__aux__def,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__morphism__nat__int,axiom, % 14.79/14.60 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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 14.79/14.60 ! [V_n_2,V_m_2] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_m_2) % 14.79/14.60 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__of__nat,axiom, % 14.79/14.60 ! [V_k,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => 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)))) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => 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)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 14.79/14.60 ! [V_B_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 14.79/14.60 ! [V_y_2,V_x_2] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x_2) % 14.79/14.60 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__eq__iff,axiom, % 14.79/14.60 ! [V_z_2,V_w_2,T_b] : % 14.79/14.60 ( class_Int_Oring__char__0(T_b) % 14.79/14.60 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 14.79/14.60 <=> V_w_2 = V_z_2 ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 14.79/14.60 ! [V_B_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 14.79/14.60 ! [V_B_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 14.79/14.60 ! [V_x_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 14.79/14.60 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_number__of__eq,axiom, % 14.79/14.60 ! [V_k,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_int__number__of__def,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__int__eq,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 14.79/14.60 ! [V_B_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.60 => ( V_A_2 = V_B_2 % 14.79/14.60 <=> 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) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 14.79/14.60 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x) % 14.79/14.60 => ( c_Nat__Transfer_Ois__nat(V_y) % 14.79/14.60 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 14.79/14.60 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 14.79/14.60 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x) % 14.79/14.60 => ( c_Nat__Transfer_Ois__nat(V_y) % 14.79/14.60 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x) % 14.79/14.60 => ( c_Nat__Transfer_Ois__nat(V_y) % 14.79/14.60 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x) % 14.79/14.60 => ( c_Nat__Transfer_Ois__nat(V_y) % 14.79/14.60 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 14.79/14.60 ! [V_n,V_x] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x) % 14.79/14.60 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 14.79/14.60 ! [V_y,V_x] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x) % 14.79/14.60 => ( c_Nat__Transfer_Ois__nat(V_y) % 14.79/14.60 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 14.79/14.60 ! [V_A_2,V_x_2] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x_2) % 14.79/14.60 => ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 14.79/14.60 <=> 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))) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__eq__0__iff,axiom, % 14.79/14.60 ! [V_z_2,T_b] : % 14.79/14.60 ( class_Int_Oring__char__0(T_b) % 14.79/14.60 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.60 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__0__eq__iff,axiom, % 14.79/14.60 ! [V_z_2,T_b] : % 14.79/14.60 ( class_Int_Oring__char__0(T_b) % 14.79/14.60 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 14.79/14.60 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__0,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 14.79/14.60 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__le__iff,axiom, % 14.79/14.60 ! [V_z_2,V_w_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__less__iff,axiom, % 14.79/14.60 ! [V_z_2,V_w_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__add,axiom, % 14.79/14.60 ! [V_z,V_w,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__number__of__eq,axiom, % 14.79/14.60 ! [V_v,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__mult,axiom, % 14.79/14.60 ! [V_z,V_w,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__1,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__diff,axiom, % 14.79/14.60 ! [V_z,V_w,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__of__nat__eq,axiom, % 14.79/14.60 ! [V_n,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__minus,axiom, % 14.79/14.60 ! [V_z,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Ints__of__int,axiom, % 14.79/14.60 ! [V_z_2,T_b] : % 14.79/14.60 ( class_Rings_Oring__1(T_b) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__power,axiom, % 14.79/14.60 ! [V_n,V_z,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__set__def,axiom, % 14.79/14.60 ! [V_S_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_S_2) % 14.79/14.60 <=> ! [B_x] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_is__nat__def,axiom, % 14.79/14.60 ! [V_x_2] : % 14.79/14.60 ( c_Nat__Transfer_Ois__nat(V_x_2) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__m1,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 14.79/14.60 ! [V_y_2,V_x_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 14.79/14.60 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 14.79/14.60 ! [V_B_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__nat__int__set__return__embed,axiom, % 14.79/14.60 ! [V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => 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 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 14.79/14.60 ! [V_x_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__0__le__iff,axiom, % 14.79/14.60 ! [V_z_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__le__0__iff,axiom, % 14.79/14.60 ! [V_z_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__0__less__iff,axiom, % 14.79/14.60 ! [V_z_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__int__less__0__iff,axiom, % 14.79/14.60 ! [V_z_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__nat__nat,axiom, % 14.79/14.60 ! [V_z,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 14.79/14.60 => 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) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 14.79/14.60 ! [V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 14.79/14.60 <=> 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 14.79/14.60 ! [V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 14.79/14.60 ! [V_B_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.60 <=> 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))) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 14.79/14.60 ! [V_B_2,V_A_2] : % 14.79/14.60 ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.60 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.60 <=> 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))) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__less__imp__eq__int,axiom, % 14.79/14.60 ! [V_k] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 14.79/14.60 => ? [B_n] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 14.79/14.60 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_decr__lemma,axiom, % 14.79/14.60 ! [V_z,V_x,V_d] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_incr__lemma,axiom, % 14.79/14.60 ! [V_x,V_z,V_d] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__1__add__number__of,axiom, % 14.79/14.60 ! [V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__number__of__add__1,axiom, % 14.79/14.60 ! [V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Pls__def,axiom, % 14.79/14.60 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I19_J,axiom, % 14.79/14.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__ge__self,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__le__D1,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__add__abs,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__mult__self,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__mult,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__minus__commute,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__one,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__minus__cancel,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__idempotent,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__zero,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__eq__0,axiom, % 14.79/14.60 ! [V_a_2,T_b] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 14.79/14.60 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.60 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__int__eq,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__divide,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__abs,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__of__nat,axiom, % 14.79/14.60 ! [V_n,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I2_J,axiom, % 14.79/14.60 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__Pls__right,axiom, % 14.79/14.60 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__Pls,axiom, % 14.79/14.60 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__Pls,axiom, % 14.79/14.60 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I1_J,axiom, % 14.79/14.60 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 14.79/14.60 % 14.79/14.60 fof(fact_minus__Pls,axiom, % 14.79/14.60 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I37_J,axiom, % 14.79/14.60 c_Int_OPls != c_Int_OMin ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I40_J,axiom, % 14.79/14.60 c_Int_OMin != c_Int_OPls ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I1_J,axiom, % 14.79/14.60 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__ge__zero,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__le__zero__iff,axiom, % 14.79/14.60 ! [V_a_2,T_b] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.79/14.60 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__of__nonneg,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__of__pos,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__less__abs__iff,axiom, % 14.79/14.60 ! [V_a_2,T_b] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2))) % 14.79/14.60 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__not__less__zero,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => ~ 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__triangle__ineq,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__mult__less,axiom, % 14.79/14.60 ! [V_d,V_b,V_c,V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 14.79/14.60 => 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))) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__triangle__ineq3,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__triangle__ineq2,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__triangle__ineq2__sym,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__le__D2,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__leI,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__le__iff,axiom, % 14.79/14.60 ! [V_b_2,V_a_2,T_b] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) % 14.79/14.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 14.79/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__ge__minus__self,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__less__iff,axiom, % 14.79/14.60 ! [V_b_2,V_a_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) % 14.79/14.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 14.79/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nonzero__abs__divide,axiom, % 14.79/14.60 ! [V_a,V_b,T_a] : % 14.79/14.60 ( class_Fields_Olinordered__field(T_a) % 14.79/14.60 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__power__minus,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__zmult__eq__1,axiom, % 14.79/14.60 ! [V_n,V_m] : % 14.79/14.60 ( 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) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_number__of__Pls,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_semiring__norm_I112_J,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__numeral__0,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__numeral__0__right,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__sgn,axiom, % 14.79/14.60 ! [V_k,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__sgn__abs,axiom, % 14.79/14.60 ! [V_x,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_bin__less__0__simps_I1_J,axiom, % 14.79/14.60 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_semiring__norm_I113_J,axiom, % 14.79/14.60 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__number__of__Pls,axiom, % 14.79/14.60 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__is__num__zero,axiom, % 14.79/14.60 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I23_J,axiom, % 14.79/14.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I20_J,axiom, % 14.79/14.60 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I3_J,axiom, % 14.79/14.60 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I6_J,axiom, % 14.79/14.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__number__of__Pls__Min,axiom, % 14.79/14.60 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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_not__neg__number__of__Pls,axiom, % 14.79/14.60 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I5_J,axiom, % 14.79/14.60 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I2_J,axiom, % 14.79/14.60 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_succ__Min,axiom, % 14.79/14.60 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__mult__pos,axiom, % 14.79/14.60 ! [V_y,V_x,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__eq__mult,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Rings_Oordered__ring__abs(T_a) % 14.79/14.60 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.79/14.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 14.79/14.60 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 14.79/14.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__triangle__ineq4,axiom, % 14.79/14.60 ! [V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__diff__triangle__ineq,axiom, % 14.79/14.60 ! [V_d,V_c,V_b,V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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))))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__of__nonpos,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__minus__le__zero,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__of__neg,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__if,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Oabs__if(T_a) % 14.79/14.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__le__power__abs,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__div__pos,axiom, % 14.79/14.60 ! [V_x,V_y,T_a] : % 14.79/14.60 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__minus__one,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_a) % 14.79/14.60 & class_Rings_Olinordered__idom(T_a) ) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zabs__less__one__iff,axiom, % 14.79/14.60 ! [V_z_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zabs__def,axiom, % 14.79/14.60 ! [V_i] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__abs__mult__distrib,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__le__zpower__abs,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_divide__Numeral0,axiom, % 14.79/14.60 ! [V_x,T_a] : % 14.79/14.60 ( ( class_Fields_Ofield__inverse__zero(T_a) % 14.79/14.60 & class_Int_Onumber__ring(T_a) ) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__number__of__0,axiom, % 14.79/14.60 ! [V_v_2] : % 14.79/14.60 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__0__number__of,axiom, % 14.79/14.60 ! [V_v_2] : % 14.79/14.60 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_number__of2,axiom, % 14.79/14.60 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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__nat__number__of,axiom, % 14.79/14.60 ! [V_v_H_2,V_v_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 14.79/14.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_le__nat__number__of,axiom, % 14.79/14.60 ! [V_v_H_2,V_v_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__number__of,axiom, % 14.79/14.60 ! [V_x,T_a] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_a) % 14.79/14.60 & class_Rings_Olinordered__idom(T_a) ) % 14.79/14.60 => ( ( 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))) % 14.79/14.60 => 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)) ) % 14.79/14.60 & ( ~ 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))) % 14.79/14.60 => 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) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__power__minus__one,axiom, % 14.79/14.60 ! [V_n,T_a] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_a) % 14.79/14.60 & class_Rings_Olinordered__idom(T_a) ) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__less__zpower__abs__iff,axiom, % 14.79/14.60 ! [V_n_2,V_x_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.60 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_le__special_I1_J,axiom, % 14.79/14.60 ! [V_y_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Rings_Olinordered__idom(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_le__special_I3_J,axiom, % 14.79/14.60 ! [V_x_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Rings_Olinordered__idom(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__special_I1_J,axiom, % 14.79/14.60 ! [V_y_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Rings_Olinordered__idom(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__special_I3_J,axiom, % 14.79/14.60 ! [V_x_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Rings_Olinordered__idom(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__0__number__of,axiom, % 14.79/14.60 ! [V_v_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__nat__number__of,axiom, % 14.79/14.60 ! [V_v_H,V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 14.79/14.60 => 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)) ) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__number__of__mult__left,axiom, % 14.79/14.60 ! [V_k,V_v_H,V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__nat__number__of,axiom, % 14.79/14.60 ! [V_v_H,V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__special_I3_J,axiom, % 14.79/14.60 ! [V_x_2,T_b] : % 14.79/14.60 ( class_Int_Onumber__ring(T_b) % 14.79/14.60 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.60 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__special_I1_J,axiom, % 14.79/14.60 ! [V_y_2,T_b] : % 14.79/14.60 ( class_Int_Onumber__ring(T_b) % 14.79/14.60 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 14.79/14.60 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__number__of__diff__1,axiom, % 14.79/14.60 ! [V_v] : % 14.79/14.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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) ) % 14.79/14.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nats__number__of,axiom, % 14.79/14.60 ! [V_w_2,T_b] : % 14.79/14.60 ( class_Int_Onumber__ring(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nitpick_Oint__lcm__def,axiom, % 14.79/14.60 ! [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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_succ__pred,axiom, % 14.79/14.60 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 14.79/14.60 % 14.79/14.60 fof(fact_iszero__def,axiom, % 14.79/14.60 ! [V_z_2,T_b] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_b) % 14.79/14.60 => ( c_Int_Oiszero(T_b,V_z_2) % 14.79/14.60 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_iszero__0,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_a) % 14.79/14.60 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_not__iszero__1,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_a) % 14.79/14.60 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_le__iff__pred__less,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_pred__Pls,axiom, % 14.79/14.60 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 14.79/14.60 % 14.79/14.60 fof(fact_pred__def,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__Min__right,axiom, % 14.79/14.60 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__Min,axiom, % 14.79/14.60 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 14.79/14.60 % 14.79/14.60 fof(fact_iszero__Numeral0,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nats__0,axiom, % 14.79/14.60 ! [T_b] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_b) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nats__add,axiom, % 14.79/14.60 ! [V_b_2,V_a_2,T_b] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nats__mult,axiom, % 14.79/14.60 ! [V_b_2,V_a_2,T_b] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nonzero__number__of__Min,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nats__1,axiom, % 14.79/14.60 ! [T_b] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_b) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__nat__in__Nats,axiom, % 14.79/14.60 ! [V_n_2,T_b] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_b) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_number__of__pred,axiom, % 14.79/14.60 ! [V_w,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_neg__number__of__pred__iff__0,axiom, % 14.79/14.60 ! [V_v_2] : % 14.79/14.60 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 14.79/14.60 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__number__of__eq,axiom, % 14.79/14.60 ! [V_y_2,V_x_2,T_b] : % 14.79/14.60 ( class_Int_Onumber__ring(T_b) % 14.79/14.60 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 14.79/14.60 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__diff__number__of,axiom, % 14.79/14.60 ! [V_m,V_v] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nitpick_Onat__lcm__def,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__special_I4_J,axiom, % 14.79/14.60 ! [V_x_2,T_b] : % 14.79/14.60 ( class_Int_Onumber__ring(T_b) % 14.79/14.60 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 14.79/14.60 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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))))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__special_I2_J,axiom, % 14.79/14.60 ! [V_y_2,T_b] : % 14.79/14.60 ( class_Int_Onumber__ring(T_b) % 14.79/14.60 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 14.79/14.60 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__special_I2_J,axiom, % 14.79/14.60 ! [V_v,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__special_I1_J,axiom, % 14.79/14.60 ! [V_w,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Bit1__Min,axiom, % 14.79/14.60 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I43_J,axiom, % 14.79/14.60 ! [V_l_2] : % 14.79/14.60 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 14.79/14.60 <=> c_Int_OMin = V_l_2 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I47_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 14.79/14.60 <=> V_k_2 = c_Int_OMin ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I51_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 14.79/14.60 <=> V_k_2 = V_l_2 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__int__code_I16_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I17_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I34_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__eq__int__code_I16_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I39_J,axiom, % 14.79/14.60 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I46_J,axiom, % 14.79/14.60 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I16_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_bin__less__0__simps_I4_J,axiom, % 14.79/14.60 ! [V_w_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I22_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I12_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Bit1__def,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I26_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I30_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I13_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I9_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_neg__number__of__Bit1,axiom, % 14.79/14.60 ! [V_w_2] : % 14.79/14.60 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 14.79/14.60 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I4_J,axiom, % 14.79/14.60 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I10_J,axiom, % 14.79/14.60 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_minus__Bit1,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I8_J,axiom, % 14.79/14.60 ! [V_k2_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I12_J,axiom, % 14.79/14.60 ! [V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_iszero__number__of__Bit1,axiom, % 14.79/14.60 ! [V_w,T_a] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_a) % 14.79/14.60 & class_Int_Oring__char__0(T_a) ) % 14.79/14.60 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_succ__Pls,axiom, % 14.79/14.60 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 14.79/14.60 % 14.79/14.60 fof(fact_number__of__Bit1,axiom, % 14.79/14.60 ! [V_w,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__numeral__1,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__numeral__1__right,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_semiring__norm_I110_J,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_numeral__1__eq__1,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I29_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I5_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_divide__Numeral1,axiom, % 14.79/14.60 ! [V_x,T_a] : % 14.79/14.60 ( ( class_Fields_Ofield(T_a) % 14.79/14.60 & class_Int_Onumber__ring(T_a) ) % 14.79/14.60 => 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 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_divide__numeral__1,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( ( class_Fields_Ofield(T_a) % 14.79/14.60 & class_Int_Onumber__ring(T_a) ) % 14.79/14.60 => 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 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_one__is__num__one,axiom, % 14.79/14.60 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Numeral1__eq1__nat,axiom, % 14.79/14.60 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__numeral__1__eq__1,axiom, % 14.79/14.60 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I4_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_minus__Min,axiom, % 14.79/14.60 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 14.79/14.60 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_not__iszero__Numeral1,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_numeral__1__eq__Suc__0,axiom, % 14.79/14.60 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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_numeral__3__eq__3,axiom, % 14.79/14.60 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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power3__eq__cube,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Omonoid__mult(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 14.79/14.60 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))))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc3__eq__add__3,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 14.79/14.60 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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 14.79/14.60 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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_le__special_I2_J,axiom, % 14.79/14.60 ! [V_y_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Rings_Olinordered__idom(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_le__special_I4_J,axiom, % 14.79/14.60 ! [V_x_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Rings_Olinordered__idom(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__special_I2_J,axiom, % 14.79/14.60 ! [V_y_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Rings_Olinordered__idom(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__special_I4_J,axiom, % 14.79/14.60 ! [V_x_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Rings_Olinordered__idom(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__special_I3_J,axiom, % 14.79/14.60 ! [V_v,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__special_I2_J,axiom, % 14.79/14.60 ! [V_w,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__diff__eq__diff__pred,axiom, % 14.79/14.60 ! [V_m,V_n] : % 14.79/14.60 ( 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)) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__gcd_Osimps,axiom, % 14.79/14.60 ! [V_x,V_y] : % 14.79/14.60 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.60 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 14.79/14.60 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__mod__eq__add3__mod,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod__Suc__eq__mod__add3,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__div__eq__add3__div,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_div__Suc__eq__div__add3,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nitpick_Oint__gcd__def,axiom, % 14.79/14.60 ! [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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zmod__number__of__Bit1,axiom, % 14.79/14.60 ! [V_v,V_w] : % 14.79/14.60 ( ( 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))) % 14.79/14.60 => 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)) ) % 14.79/14.60 & ( ~ 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))) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_neg__zmod__mult__2,axiom, % 14.79/14.60 ! [V_b,V_a] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_pos__zdiv__mult__2,axiom, % 14.79/14.60 ! [V_b,V_a] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I50_J,axiom, % 14.79/14.60 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I49_J,axiom, % 14.79/14.60 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I44_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 14.79/14.60 <=> V_k_2 = c_Int_OPls ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I38_J,axiom, % 14.79/14.60 ! [V_l_2] : % 14.79/14.60 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 14.79/14.60 <=> c_Int_OPls = V_l_2 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Bit0__Pls,axiom, % 14.79/14.60 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__eq__int__code_I13_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I31_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I14_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__int__code_I13_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__Bit0__Bit0,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Bit0__def,axiom, % 14.79/14.60 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I48_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 14.79/14.60 <=> V_k_2 = V_l_2 ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I45_J,axiom, % 14.79/14.60 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I42_J,axiom, % 14.79/14.60 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 14.79/14.60 % 14.79/14.60 fof(fact_minus__Bit0,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I7_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__Bit0,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I13_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_bin__less__0__simps_I3_J,axiom, % 14.79/14.60 ! [V_w_2] : % 14.79/14.60 ( 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))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I21_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I27_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I32_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__eq__int__code_I14_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I10_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I4_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__int__code_I15_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I16_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__Bit1__Bit0,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__Bit0__Bit1,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I3_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I10_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I9_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I28_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I8_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zdiv__number__of__Bit0,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_neg__number__of__Bit0,axiom, % 14.79/14.60 ! [V_w_2] : % 14.79/14.60 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 14.79/14.60 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_pred__Bit0,axiom, % 14.79/14.60 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_pred__Bit1,axiom, % 14.79/14.60 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I9_J,axiom, % 14.79/14.60 ! [V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I3_J,axiom, % 14.79/14.60 ! [V_k2_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I15_J,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I14_J,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_pred__Min,axiom, % 14.79/14.60 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I11_J,axiom, % 14.79/14.60 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_eq__int__code_I7_J,axiom, % 14.79/14.60 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_iszero__number__of__Bit0,axiom, % 14.79/14.60 ! [V_w_2,T_b] : % 14.79/14.60 ( ( class_Int_Onumber__ring(T_b) % 14.79/14.60 & class_Int_Oring__char__0(T_b) ) % 14.79/14.60 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) % 14.79/14.60 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_succ__Bit1,axiom, % 14.79/14.60 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_succ__Bit0,axiom, % 14.79/14.60 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 14.79/14.60 % 14.79/14.60 fof(fact_number__of__Bit0,axiom, % 14.79/14.60 ! [V_w,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I15_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__int__code_I14_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I33_J,axiom, % 14.79/14.60 ! [V_l_2,V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__eq__int__code_I15_J,axiom, % 14.79/14.60 ! [V_k2_2,V_k1_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_card__UNIV__bool,axiom, % 14.79/14.60 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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__Bit1,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I25_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_rel__simps_I11_J,axiom, % 14.79/14.60 ! [V_k_2] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I5_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I6_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_diff__bin__simps_I8_J,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__Bit1__Bit1,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_double__number__of__Bit0,axiom, % 14.79/14.60 ! [V_w,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_number__of1,axiom, % 14.79/14.60 ! [V_n] : % 14.79/14.60 ( 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))) % 14.79/14.60 => ( 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)))) % 14.79/14.60 & 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)))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 14.79/14.60 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__2__right,axiom, % 14.79/14.60 ! [V_z,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mult__2,axiom, % 14.79/14.60 ! [V_z,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_one__add__one__is__two,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__power2,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__eq__power2,axiom, % 14.79/14.60 ! [V_a_2,T_b] : % 14.79/14.60 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 14.79/14.60 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b) % 14.79/14.60 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_semiring__norm_I115_J,axiom, % 14.79/14.60 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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_numeral__2__eq__2,axiom, % 14.79/14.60 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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 14.79/14.60 ! [V_x,T_a] : % 14.79/14.60 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__eq__square,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Groups_Omonoid__mult(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 14.79/14.60 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))))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__2__eq__Suc_H,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__2__eq__Suc,axiom, % 14.79/14.60 ! [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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_one__power2,axiom, % 14.79/14.60 ! [T_a] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__minus,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__mult__2__right,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__mult__2,axiom, % 14.79/14.60 ! [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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__even__eq,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Groups_Omonoid__mult(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 14.79/14.60 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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 14.79/14.60 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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__abs,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_abs__power2,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__1__add__1,axiom, % 14.79/14.60 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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod2__Suc__Suc,axiom, % 14.79/14.60 ! [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)))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_div2__Suc__Suc,axiom, % 14.79/14.60 ! [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))))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zmod__number__of__Bit0,axiom, % 14.79/14.60 ! [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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_add__self__div__2,axiom, % 14.79/14.60 ! [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 ). % 14.79/14.60 % 14.79/14.60 fof(fact_half__gt__zero,axiom, % 14.79/14.60 ! [V_r,T_a] : % 14.79/14.60 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 14.79/14.60 & class_Int_Onumber__ring(T_a) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 14.79/14.60 => 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)))))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_half__gt__zero__iff,axiom, % 14.79/14.60 ! [V_r_2,T_b] : % 14.79/14.60 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 14.79/14.60 & class_Int_Onumber__ring(T_b) ) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 14.79/14.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__le__power2,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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)))))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__le__imp__le,axiom, % 14.79/14.60 ! [V_y,V_x,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__semidom(T_a) % 14.79/14.60 => ( 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)))))) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__eq__imp__eq,axiom, % 14.79/14.60 ! [V_y,V_x,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__semidom(T_a) % 14.79/14.60 => ( 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)))) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.79/14.60 => V_x = V_y ) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__less__0,axiom, % 14.79/14.60 ! [V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => ~ 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__less__power2,axiom, % 14.79/14.60 ! [V_a_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 14.79/14.60 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_sum__power2__eq__zero__iff,axiom, % 14.79/14.60 ! [V_y_2,V_x_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),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_b) % 14.79/14.60 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.60 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__eq__square__number__of,axiom, % 14.79/14.60 ! [V_w,T_b] : % 14.79/14.60 ( ( class_Groups_Omonoid__mult(T_b) % 14.79/14.60 & class_Int_Onumber(T_b) ) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_less__2__cases,axiom, % 14.79/14.60 ! [V_n] : % 14.79/14.60 ( 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))))) % 14.79/14.60 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.60 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__2,axiom, % 14.79/14.60 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))) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__eq__1__iff,axiom, % 14.79/14.60 ! [V_a_2,T_b] : % 14.79/14.60 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 14.79/14.60 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b) % 14.79/14.60 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b) % 14.79/14.60 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 14.79/14.60 ! [V_n,V_x,T_a] : % 14.79/14.60 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__minus__even,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__less__imp__less,axiom, % 14.79/14.60 ! [V_y,V_x,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__semidom(T_a) % 14.79/14.60 => ( 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)))))) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_sum__power2__le__zero__iff,axiom, % 14.79/14.60 ! [V_y_2,V_x_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),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_b))) % 14.79/14.60 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.60 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_sum__power2__ge__zero,axiom, % 14.79/14.60 ! [V_y,V_x,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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))))))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_sum__power2__gt__zero__iff,axiom, % 14.79/14.60 ! [V_y_2,V_x_2,T_b] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_b) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 14.79/14.60 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.60 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_not__sum__power2__lt__zero,axiom, % 14.79/14.60 ! [V_y,V_x,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => ~ 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__sum,axiom, % 14.79/14.60 ! [V_y,V_x,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__le__even__power_H,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => 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)))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__odd__eq,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Groups_Omonoid__mult(T_a) % 14.79/14.60 => 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))))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 14.79/14.60 ! [V_n,V_x,T_a] : % 14.79/14.60 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__minus1__even,axiom, % 14.79/14.60 ! [V_n,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zdiv__number__of__Bit1,axiom, % 14.79/14.60 ! [V_v,V_w] : % 14.79/14.60 ( ( 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))) % 14.79/14.60 => 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)) ) % 14.79/14.60 & ( ~ 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))) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_mod2__gr__0,axiom, % 14.79/14.60 ! [V_m_2] : % 14.79/14.60 ( 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)))))) % 14.79/14.60 <=> 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_div__2__gt__zero,axiom, % 14.79/14.60 ! [V_n] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 14.79/14.60 => 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)))))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power2__diff,axiom, % 14.79/14.60 ! [V_y,V_x,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_odd__0__le__power__imp__0__le,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => ( 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))))) % 14.79/14.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_odd__power__less__zero,axiom, % 14.79/14.60 ! [V_n,V_a,T_a] : % 14.79/14.60 ( class_Rings_Olinordered__idom(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__minus1__odd,axiom, % 14.79/14.60 ! [V_n,T_a] : % 14.79/14.60 ( class_Rings_Oring__1(T_a) % 14.79/14.60 => 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)) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__m1__even,axiom, % 14.79/14.60 ! [V_n,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_power__m1__odd,axiom, % 14.79/14.60 ! [V_n,T_a] : % 14.79/14.60 ( class_Int_Onumber__ring(T_a) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_Suc__n__div__2__gt__zero,axiom, % 14.79/14.60 ! [V_n] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.79/14.60 => 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)))))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_of__nat__double,axiom, % 14.79/14.60 ! [V_x,T_a] : % 14.79/14.60 ( class_Rings_Osemiring__1(T_a) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 14.79/14.60 => 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))) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_pos__zmod__mult__2,axiom, % 14.79/14.60 ! [V_b,V_a] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.60 => 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))) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_neg__zdiv__mult__2,axiom, % 14.79/14.60 ! [V_b,V_a] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.60 => 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) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_int__of__code,axiom, % 14.79/14.60 ! [V_k] : % 14.79/14.60 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.60 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 14.79/14.60 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.60 => ( ( 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) % 14.79/14.60 => 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)))))) ) % 14.79/14.60 & ( 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) % 14.79/14.60 => 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)) ) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_one__code__numeral__code,axiom, % 14.79/14.60 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)) ). % 14.79/14.60 % 14.79/14.60 fof(fact_int__val__lemma,axiom, % 14.79/14.60 ! [V_k_2,V_f_2,V_n_2] : % 14.79/14.60 ( ! [B_i] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 14.79/14.60 => 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))) ) % 14.79/14.60 => ( 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)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 14.79/14.60 => ? [B_i] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 14.79/14.60 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat0__intermed__int__val,axiom, % 14.79/14.60 ! [V_k_2,V_f_2,V_n_2] : % 14.79/14.60 ( ! [B_i] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 14.79/14.60 => 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))) ) % 14.79/14.60 => ( 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)) % 14.79/14.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 14.79/14.60 => ? [B_i] : % 14.79/14.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 14.79/14.60 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_code__numeral__zero__minus__one,axiom, % 14.79/14.60 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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_zero__code__numeral__code,axiom, % 14.79/14.60 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) ). % 14.79/14.60 % 14.79/14.60 fof(fact_nat__of__aux__code,axiom, % 14.79/14.60 ! [V_n,V_i] : % 14.79/14.60 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.60 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 14.79/14.60 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.60 => 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)) ) ) ). % 14.79/14.60 % 14.79/14.60 fof(fact_code__numeral_Osize_I1_J,axiom, % 14.79/14.60 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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_code__numeral_Osize_I3_J,axiom, % 14.79/14.61 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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_code__numeral_Osimps_I4_J,axiom, % 14.79/14.61 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 14.79/14.61 % 14.79/14.61 fof(fact_code__numeral_Osize_I4_J,axiom, % 14.79/14.61 ! [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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_code__numeral_Osize_I2_J,axiom, % 14.79/14.61 ! [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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_nat__mod__eq__lemma,axiom, % 14.79/14.61 ! [V_y,V_n,V_x] : % 14.79/14.61 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 14.79/14.61 => ? [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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_mod__induct__0,axiom, % 14.79/14.61 ! [V_i_2,V_Pa_2,V_p_2] : % 14.79/14.61 ( ! [B_i] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 14.79/14.61 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 14.79/14.61 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 14.79/14.61 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 14.79/14.61 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_code__numeral_Oinject,axiom, % 14.79/14.61 ! [V_code__numeral_H_2,V_code__numeral_2] : % 14.79/14.61 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 14.79/14.61 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_code__numeral_Osimps_I3_J,axiom, % 14.79/14.61 ! [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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_code__numeral_Osimps_I2_J,axiom, % 14.79/14.61 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 14.79/14.61 % 14.79/14.61 fof(fact_code__numeral_Osimps_I5_J,axiom, % 14.79/14.61 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Suc__code__numeral__minus__one,axiom, % 14.79/14.61 ! [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 ). % 14.79/14.61 % 14.79/14.61 fof(fact_nat__intermed__int__val,axiom, % 14.79/14.61 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 14.79/14.61 ( ! [B_i] : % 14.79/14.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 14.79/14.61 => 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))) ) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 14.79/14.61 => ? [B_i] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 14.79/14.61 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_log_Osimps,axiom, % 14.79/14.61 ! [V_i,V_b] : % 14.79/14.61 ( ( ( 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))) % 14.79/14.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 14.79/14.61 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 14.79/14.61 & ( ~ ( 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))) % 14.79/14.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 14.79/14.61 => 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))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_mod__div__decomp,axiom, % 14.79/14.61 ! [V_b,V_a,T_a] : % 14.79/14.61 ( class_Divides_Osemiring__div(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__pos,axiom, % 14.79/14.61 ! [V_f_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Rings_Olinordered__semidom(T_c) % 14.79/14.61 => ( ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_minus__shift__def,axiom, % 14.79/14.61 ! [V_r,V_l,V_k] : % 14.79/14.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 14.79/14.61 => 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) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 14.79/14.61 => 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) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_inc__shift__def,axiom, % 14.79/14.61 ! [V_k,V_v] : % 14.79/14.61 ( ( V_v = V_k % 14.79/14.61 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 14.79/14.61 & ( V_v != V_k % 14.79/14.61 => 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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__nonneg,axiom, % 14.79/14.61 ! [V_f_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Rings_Olinordered__semidom(T_c) % 14.79/14.61 => ( ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__induct,axiom, % 14.79/14.61 ! [V_Pa_2,V_F_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.79/14.61 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.61 => ( ! [B_x,B_F] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F)) % 14.79/14.61 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 14.79/14.61 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) ) % 14.79/14.61 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fold1__antimono,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_field__le__epsilon,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Fields_Olinordered__field(T_a) % 14.79/14.61 => ( ! [B_e] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) ) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_subtract__code__numeral__def,axiom, % 14.79/14.61 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.61 % 14.79/14.61 fof(fact_minus__code__numeral__code,axiom, % 14.79/14.61 ! [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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__0R,axiom, % 14.79/14.61 ! [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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__0L,axiom, % 14.79/14.61 ! [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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 14.79/14.61 ! [T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__Suc__Suc,axiom, % 14.79/14.61 ! [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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Oidem,axiom, % 14.79/14.61 ! [V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf_Oidem,axiom, % 14.79/14.61 ! [V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf_Ocommute,axiom, % 14.79/14.61 ! [V_b,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__commute,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 14.79/14.61 ! [V_b,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__left__idem,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 14.79/14.61 ! [V_c,V_a,V_b,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__left__commute,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf_Oassoc,axiom, % 14.79/14.61 ! [V_c,V_b,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__assoc,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_inf__min,axiom, % 14.79/14.61 ! [T_b] : % 14.79/14.61 ( ( class_Lattices_Osemilattice__inf(T_b) % 14.79/14.61 & class_Orderings_Olinorder(T_b) ) % 14.79/14.61 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__diff,axiom, % 14.79/14.61 ! [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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__diff__distrib__left,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Groups_Oordered__ab__group__add(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__infE,axiom, % 14.79/14.61 ! [V_b,V_a,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( 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))) % 14.79/14.61 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 14.79/14.61 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__mono,axiom, % 14.79/14.61 ! [V_d,V_b,V_c,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 14.79/14.61 => 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))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__greatest,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 14.79/14.61 => 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))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__infI,axiom, % 14.79/14.61 ! [V_b,V_a,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 14.79/14.61 => 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))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__absorb2,axiom, % 14.79/14.61 ! [V_x,V_y,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__absorb1,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__infI2,axiom, % 14.79/14.61 ! [V_a,V_x,V_b,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 14.79/14.61 => 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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__infI1,axiom, % 14.79/14.61 ! [V_b,V_x,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 14.79/14.61 => 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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__inf__iff,axiom, % 14.79/14.61 ! [V_z_2,V_y_2,V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2))) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__iff__inf,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.79/14.61 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__le2,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__le1,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__le__iff__disj,axiom, % 14.79/14.61 ! [V_z_2,V_y_2,V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 14.79/14.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__add__distrib__left,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oless__infI2,axiom, % 14.79/14.61 ! [V_a,V_x,V_b,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 14.79/14.61 => 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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oless__infI1,axiom, % 14.79/14.61 ! [V_b,V_x,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 14.79/14.61 => 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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__less__iff__disj,axiom, % 14.79/14.61 ! [V_z_2,V_y_2,V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 14.79/14.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__less__iff__conj,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,V_z_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2))) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__number__of,axiom, % 14.79/14.61 ! [V_v,V_u,T_b] : % 14.79/14.61 ( ( class_Int_Onumber(T_b) % 14.79/14.61 & class_Orderings_Oord(T_b) ) % 14.79/14.61 => ( ( 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))) % 14.79/14.61 => 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) ) % 14.79/14.61 & ( ~ 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))) % 14.79/14.61 => 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) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ofold__inf__insert,axiom, % 14.79/14.61 ! [V_a_2,V_b_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__atLeastAtMostL1,axiom, % 14.79/14.61 ! [V_d_2,V_b_2,V_a_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__atLeastAtMostR1,axiom, % 14.79/14.61 ! [V_d_2,V_ca_2,V_b_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 14.79/14.61 ! [V_b_2,V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ofold1__belowI,axiom, % 14.79/14.61 ! [V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Obelow__fold1__iff,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fold1__below__iff,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) % 14.79/14.61 <=> ? [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fold1__strict__below__iff,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) % 14.79/14.61 <=> ? [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_strict__below__fold1__iff,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__ord__min,axiom, % 14.79/14.61 ! [T_b] : % 14.79/14.61 ( class_Orderings_Oord(T_b) % 14.79/14.61 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Oremove,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) % 14.79/14.61 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,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)))))) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Oremove,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) % 14.79/14.61 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),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)))))) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Oeq__fold_H,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_inf__nat__def,axiom, % 14.79/14.61 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Osingleton,axiom, % 14.79/14.61 ! [V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min__le,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 14.79/14.61 ! [V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min__in,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Oin__idem,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_OF__eq,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min__antimono,axiom, % 14.79/14.61 ! [V_N_2,V_M_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 14.79/14.61 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 14.79/14.61 ! [V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min__insert,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Osubset__idem,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min__Un,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Oeq__fold__idem_H,axiom, % 14.79/14.61 ! [V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 14.79/14.61 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),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)))))) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( 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)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( 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)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Oinsert,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Oinsert__remove,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 14.79/14.61 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,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)))))) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Ounion__inter,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( 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)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Ounion__disjoint,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( 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)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Oclosed,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 14.79/14.61 ! [V_N_2,V_h_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.79/14.61 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min_Ohom__commute,axiom, % 14.79/14.61 ! [V_N_2,V_h_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.79/14.61 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_minus__Max__eq__Min,axiom, % 14.79/14.61 ! [V_S_2,T_b] : % 14.79/14.61 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_minus__Min__eq__Max,axiom, % 14.79/14.61 ! [V_S_2,T_b] : % 14.79/14.61 ( class_Groups_Olinordered__ab__group__add(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 14.79/14.61 ! [V_ca_2,V_b_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Min__eqI,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ! [B_y] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) ) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Osingleton,axiom, % 14.79/14.61 ! [V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max__ge,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max__in,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max__mono,axiom, % 14.79/14.61 ! [V_N_2,V_M_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 14.79/14.61 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Oremove,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) % 14.79/14.61 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,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)))))) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max__eqI,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ! [B_y] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) ) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Oeq__fold_H,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Ounion__inter,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( 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)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__inf__absorb,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__sup__absorb,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__inf__distrib1,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__inf__distrib2,axiom, % 14.79/14.61 ! [V_x,V_z,V_y,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 14.79/14.61 ! [V_x,V_z,V_y,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__0R,axiom, % 14.79/14.61 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__0L,axiom, % 14.79/14.61 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 14.79/14.61 ! [T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__Suc__Suc,axiom, % 14.79/14.61 ! [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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Oidem,axiom, % 14.79/14.61 ! [V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup_Oidem,axiom, % 14.79/14.61 ! [V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup_Ocommute,axiom, % 14.79/14.61 ! [V_b,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__commute,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup_Oleft__idem,axiom, % 14.79/14.61 ! [V_b,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__left__idem,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup_Oleft__commute,axiom, % 14.79/14.61 ! [V_c,V_a,V_b,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__left__commute,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup_Oassoc,axiom, % 14.79/14.61 ! [V_c,V_b,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__assoc,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_sup__max,axiom, % 14.79/14.61 ! [T_b] : % 14.79/14.61 ( ( class_Lattices_Osemilattice__sup(T_b) % 14.79/14.61 & class_Orderings_Olinorder(T_b) ) % 14.79/14.61 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__diff__distrib__left,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Groups_Oordered__ab__group__add(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__supE,axiom, % 14.79/14.61 ! [V_x,V_b,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( 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)) % 14.79/14.61 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 14.79/14.61 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__mono,axiom, % 14.79/14.61 ! [V_d,V_b,V_c,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 14.79/14.61 => 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))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__least,axiom, % 14.79/14.61 ! [V_z,V_x,V_y,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 14.79/14.61 => 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)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__supI,axiom, % 14.79/14.61 ! [V_b,V_x,V_a,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 14.79/14.61 => 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)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__absorb1,axiom, % 14.79/14.61 ! [V_x,V_y,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__absorb2,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__supI2,axiom, % 14.79/14.61 ! [V_a,V_b,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 14.79/14.61 => 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))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__supI1,axiom, % 14.79/14.61 ! [V_b,V_a,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 14.79/14.61 => 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))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__sup__iff,axiom, % 14.79/14.61 ! [V_z_2,V_y_2,V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ole__iff__sup,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.79/14.61 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_le__maxI2,axiom, % 14.79/14.61 ! [V_x,V_y,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_le__maxI1,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_le__max__iff__disj,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,V_z_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) % 14.79/14.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__add__distrib__left,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oless__supI2,axiom, % 14.79/14.61 ! [V_a,V_b,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 14.79/14.61 => 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))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oless__supI1,axiom, % 14.79/14.61 ! [V_b,V_a,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 14.79/14.61 => 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))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__less__iff__conj,axiom, % 14.79/14.61 ! [V_z_2,V_y_2,V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_less__max__iff__disj,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,V_z_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 14.79/14.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__number__of,axiom, % 14.79/14.61 ! [V_v,V_u,T_b] : % 14.79/14.61 ( ( class_Int_Onumber(T_b) % 14.79/14.61 & class_Orderings_Oord(T_b) ) % 14.79/14.61 => ( ( 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))) % 14.79/14.61 => 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) ) % 14.79/14.61 & ( ~ 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))) % 14.79/14.61 => 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) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Odistrib__inf__le,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Odistrib__sup__le,axiom, % 14.79/14.61 ! [V_z,V_y,V_x,T_a] : % 14.79/14.61 ( class_Orderings_Olinorder(T_a) % 14.79/14.61 => 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)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_minus__min__eq__max,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Groups_Olinordered__ab__group__add(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_minus__max__eq__min,axiom, % 14.79/14.61 ! [V_y,V_x,T_a] : % 14.79/14.61 ( class_Groups_Olinordered__ab__group__add(T_a) % 14.79/14.61 => 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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_nat__minus__add__max,axiom, % 14.79/14.61 ! [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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ofold__sup__insert,axiom, % 14.79/14.61 ! [V_a_2,V_b_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Oin__idem,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__atLeastAtMost,axiom, % 14.79/14.61 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__atLeastLessThan,axiom, % 14.79/14.61 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__greaterThanAtMost,axiom, % 14.79/14.61 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__greaterThanLessThan,axiom, % 14.79/14.61 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__atLeastAtMostL2,axiom, % 14.79/14.61 ! [V_ca_2,V_b_2,V_a_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__atLeastAtMostR2,axiom, % 14.79/14.61 ! [V_d_2,V_ca_2,V_a_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_OF__eq,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__le__fold__sup,axiom, % 14.79/14.61 ! [V_b_2,V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max__insert,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Osubset__idem,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Osup__Inf__absorb,axiom, % 14.79/14.61 ! [V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max__Un,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Oeq__fold__idem_H,axiom, % 14.79/14.61 ! [V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Oinsert,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Oinsert__remove,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 14.79/14.61 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,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)))))) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Ounion__disjoint,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( 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)) % 14.79/14.61 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__ord__max,axiom, % 14.79/14.61 ! [T_b] : % 14.79/14.61 ( class_Orderings_Oord(T_b) % 14.79/14.61 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Oclosed,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OInf__le__Sup,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Oremove,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) % 14.79/14.61 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),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)))))) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_sup__nat__def,axiom, % 14.79/14.61 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 14.79/14.61 ! [V_x_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 14.79/14.61 ! [V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 14.79/14.61 ! [V_a_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 14.79/14.61 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),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)))))) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( 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)) % 14.79/14.61 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( 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)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 14.79/14.61 ! [V_N_2,V_h_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.79/14.61 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Max_Ohom__commute,axiom, % 14.79/14.61 ! [V_N_2,V_h_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.79/14.61 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 14.79/14.61 ! [V_ca_2,V_b_2,V_A_2,T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => ( ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_2))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_pair__box_Osize_I1_J,axiom, % 14.79/14.61 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_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(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_arith__series__int,axiom, % 14.79/14.61 ! [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)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 14.79/14.61 ! [V_w] : % 14.79/14.61 ( 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))) % 14.79/14.61 => ( ( 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)))) % 14.79/14.61 => 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))) ) % 14.79/14.61 & ( ~ 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)))) % 14.79/14.61 => 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)))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_nat_Osize_I2_J,axiom, % 14.79/14.61 ! [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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF2__E,axiom, % 14.79/14.61 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 14.79/14.61 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF2__D,axiom, % 14.79/14.61 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF1__E,axiom, % 14.79/14.61 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 14.79/14.61 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF1__D,axiom, % 14.79/14.61 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__D,axiom, % 14.79/14.61 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_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))) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__E,axiom, % 14.79/14.61 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_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))) % 14.79/14.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 14.79/14.61 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUP2__I,axiom, % 14.79/14.61 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__INT,axiom, % 14.79/14.61 ! [V_A_2,T_c,V_I_2,T_b] : % 14.79/14.61 ( ? [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 14.79/14.61 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 14.79/14.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_CollectI,axiom, % 14.79/14.61 ! [T_b,V_a_2,V_Pa_2] : % 14.79/14.61 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__Collect__conjI,axiom, % 14.79/14.61 ! [V_Qa_2,V_Pa_2,T_b] : % 14.79/14.61 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 14.79/14.61 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) % 14.79/14.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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),V_Pa_2)),V_Qa_2)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__I,axiom, % 14.79/14.61 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUP1__I,axiom, % 14.79/14.61 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 14.79/14.61 => hBOOL(hAPP(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_b_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__Collect__less__nat,axiom, % 14.79/14.61 ! [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)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__Collect__le__nat,axiom, % 14.79/14.61 ! [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)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__abs,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__abs__ge__zero,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 14.79/14.61 => 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__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__Collect__subsets,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_insert__def,axiom, % 14.79/14.61 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I2_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I3_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I2_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I3_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__insert,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Collect__imp__eq,axiom, % 14.79/14.61 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_sup__Un__eq,axiom, % 14.79/14.61 ! [V_x_2,V_S_2,V_R_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_sup__Un__eq2,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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)) % 14.79/14.61 <=> 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_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__Un__distrib,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__Un,axiom, % 14.79/14.61 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I7_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I6_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I7_J,axiom, % 14.79/14.61 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Un__INT__distrib,axiom, % 14.79/14.61 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I6_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Un__INT__distrib2,axiom, % 14.79/14.61 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Collect__disj__eq,axiom, % 14.79/14.61 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_sup__fun__def,axiom, % 14.79/14.61 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Lattices_Olattice(T_b) % 14.79/14.61 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Un__Inter,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__absorb,axiom, % 14.79/14.61 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Un__def,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__Un,axiom, % 14.79/14.61 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Union__image__eq,axiom, % 14.79/14.61 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UNION__eq__Union__image,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I1_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I2_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_inf__Int__eq,axiom, % 14.79/14.61 ! [V_x_2,V_S_2,V_R_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__absorb,axiom, % 14.79/14.61 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_inf__Int__eq2,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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)) % 14.79/14.61 <=> 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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__insert,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I2_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I1_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__Union,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__Union2,axiom, % 14.79/14.61 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I5_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I4_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I5_J,axiom, % 14.79/14.61 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__UN__distrib,axiom, % 14.79/14.61 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I4_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__UN__distrib2,axiom, % 14.79/14.61 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__Int__distrib,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Collect__conj__eq,axiom, % 14.79/14.61 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_inf__fun__def,axiom, % 14.79/14.61 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Lattices_Olattice(T_b) % 14.79/14.61 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__Collect,axiom, % 14.79/14.61 ! [V_Pa_2,V_A_2,V_x_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))) % 14.79/14.61 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__def,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 14.79/14.61 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_card__eq__setsum,axiom, % 14.79/14.61 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__UN__finite__eq,axiom, % 14.79/14.61 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),tc_fun(T_b,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_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 14.79/14.61 ! [V_n_2,V_m_2,V_f_2,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_b] : % 14.79/14.61 ( ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 & class_Groups_Ocomm__monoid__mult(T_b) ) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 14.79/14.61 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_nat_Osize_I1_J,axiom, % 14.79/14.61 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.61 % 14.79/14.61 fof(fact_less__eq__Suc__le__raw,axiom, % 14.79/14.61 ! [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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_nat__number__of__Bit0,axiom, % 14.79/14.61 ! [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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_nat__seg__image__imp__finite,axiom, % 14.79/14.61 ! [V_n_2,V_f_2,T_b,V_A_2] : % 14.79/14.61 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,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))) % 14.79/14.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__M__bounded__by__nat,axiom, % 14.79/14.61 ! [V_i_2,V_Pa_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_Pa_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))))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF__less__iff,axiom, % 14.79/14.61 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.61 & class_Orderings_Olinorder(T_b) ) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2)) % 14.79/14.61 <=> ? [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_less__SUP__iff,axiom, % 14.79/14.61 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] : % 14.79/14.61 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.61 & class_Orderings_Olinorder(T_b) ) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2))) % 14.79/14.61 <=> ? [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__addf,axiom, % 14.79/14.61 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),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_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_le__INF__iff,axiom, % 14.79/14.61 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2))) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUP__le__iff,axiom, % 14.79/14.61 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2)) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__subset__iff,axiom, % 14.79/14.61 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__subset__iff,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_pred__subset__eq2,axiom, % 14.79/14.61 ! [V_S_2,V_R_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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))) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__lower,axiom, % 14.79/14.61 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_pred__subset__eq,axiom, % 14.79/14.61 ! [V_S_2,V_R_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__upper,axiom, % 14.79/14.61 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum_Odistrib,axiom, % 14.79/14.61 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF__leI,axiom, % 14.79/14.61 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_le__SUPI,axiom, % 14.79/14.61 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 14.79/14.61 ! [V_Pa_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_Pa_2))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Pow__def,axiom, % 14.79/14.61 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I3_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I3_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I4_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I7_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I6_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I7_J,axiom, % 14.79/14.61 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I6_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fun__diff__def,axiom, % 14.79/14.61 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Ominus(T_b) % 14.79/14.61 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__subtractf,axiom, % 14.79/14.61 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Oab__group__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_set__diff__eq,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_insert__compr,axiom, % 14.79/14.61 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_insert__compr__raw,axiom, % 14.79/14.61 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Collect__conv__if,axiom, % 14.79/14.61 ! [T_b,V_a_2,V_Pa_2] : % 14.79/14.61 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 14.79/14.61 => hAPP(c_Set_OCollect(T_b),hAPP(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,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 14.79/14.61 => hAPP(c_Set_OCollect(T_b),hAPP(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,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Collect__conv__if2,axiom, % 14.79/14.61 ! [T_b,V_a_2,V_Pa_2] : % 14.79/14.61 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 14.79/14.61 => hAPP(c_Set_OCollect(T_b),hAPP(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(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 14.79/14.61 => hAPP(c_Set_OCollect(T_b),hAPP(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(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_singleton__conv,axiom, % 14.79/14.61 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_singleton__conv2,axiom, % 14.79/14.61 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__insert__distrib,axiom, % 14.79/14.61 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__constant__conv,axiom, % 14.79/14.61 ! [V_ca_2,T_c,T_b,V_A_2] : % 14.79/14.61 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_abs__setprod,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Fields_Olinordered__field(T_b) % 14.79/14.61 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_abs__setsum__abs,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 14.79/14.61 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INTER__eq__Inter__image,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Inter__image__eq,axiom, % 14.79/14.61 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__Union,axiom, % 14.79/14.61 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I10_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__UN,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I10_J,axiom, % 14.79/14.61 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__image,axiom, % 14.79/14.61 ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__ident,axiom, % 14.79/14.61 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I10_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I10_J,axiom, % 14.79/14.61 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : 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(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_int__setsum,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__insert__distrib,axiom, % 14.79/14.61 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_bot__empty__eq2,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) % 14.79/14.61 <=> 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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_bot__empty__eq,axiom, % 14.79/14.61 ! [V_x_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__iff,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_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))) % 14.79/14.61 <=> ? [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__iff,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_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))) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_pred__equals__eq,axiom, % 14.79/14.61 ! [V_S_2,V_R_2,T_b] : % 14.79/14.61 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2) % 14.79/14.61 <=> V_R_2 = V_S_2 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_pred__equals__eq2,axiom, % 14.79/14.61 ! [V_S_2,V_R_2,T_c,T_b] : % 14.79/14.61 ( 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_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) % 14.79/14.61 <=> V_R_2 = V_S_2 ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_CollectE,axiom, % 14.79/14.61 ! [V_Pa_2,V_a_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 14.79/14.61 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_CollectD,axiom, % 14.79/14.61 ! [V_Pa_2,V_a_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 14.79/14.61 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_mem__Collect__eq,axiom, % 14.79/14.61 ! [V_Pa_2,V_a_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 14.79/14.61 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Collect__mem__eq,axiom, % 14.79/14.61 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__Collect__disjI,axiom, % 14.79/14.61 ! [V_Qa_2,V_Pa_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),V_Pa_2)),V_Qa_2)))) % 14.79/14.61 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 14.79/14.61 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I5_J,axiom, % 14.79/14.61 ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I5_J,axiom, % 14.79/14.61 ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_insert__Collect,axiom, % 14.79/14.61 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_bot__fun__def,axiom, % 14.79/14.61 ! [V_x_2,T_c,T_b] : % 14.79/14.61 ( class_Orderings_Obot(T_b) % 14.79/14.61 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_empty__def,axiom, % 14.79/14.61 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF__const,axiom, % 14.79/14.61 ! [V_M_2,T_b,V_A_2,T_c] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UNION__empty__conv_I1_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,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) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__empty2,axiom, % 14.79/14.61 ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__constant,axiom, % 14.79/14.61 ! [V_ca_2,T_c,T_b,V_A_2] : % 14.79/14.61 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UNION__empty__conv_I2_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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)) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUP__const,axiom, % 14.79/14.61 ! [V_M_2,T_b,V_A_2,T_c] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.79/14.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__negf,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Oab__group__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__timesf,axiom, % 14.79/14.61 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__mult(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__product,axiom, % 14.79/14.61 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Rings_Osemiring__0(T_b) % 14.79/14.61 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__left__distrib,axiom, % 14.79/14.61 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Rings_Osemiring__0(T_b) % 14.79/14.61 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__right__distrib,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] : % 14.79/14.61 ( class_Rings_Osemiring__0(T_b) % 14.79/14.61 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Collect__neg__eq,axiom, % 14.79/14.61 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fun__Compl__def,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Ouminus(T_b) % 14.79/14.61 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Compl__UN,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,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)) = 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_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Compl__INT,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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_OSUPR(T_c,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_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUPR__apply,axiom, % 14.79/14.61 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.61 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__divide__distrib,axiom, % 14.79/14.61 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Fields_Ofield(T_b) % 14.79/14.61 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 14.79/14.61 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.61 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 14.79/14.61 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Pow__INT__eq,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),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(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Inter__def,axiom, % 14.79/14.61 ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF__commute,axiom, % 14.79/14.61 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INFI__apply,axiom, % 14.79/14.61 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.61 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I8_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I8_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_pair__box_Oinject,axiom, % 14.79/14.61 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.61 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) % 14.79/14.61 <=> ( V_a_2 = V_a_H_2 % 14.79/14.61 & V_b_2 = V_b_H_2 ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 14.79/14.61 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.61 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.79/14.61 => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Union__def,axiom, % 14.79/14.61 ! [V_S_2,T_b] : 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_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUP1__iff,axiom, % 14.79/14.61 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(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_b_2)) % 14.79/14.61 <=> ? [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.61 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__UN__flatten,axiom, % 14.79/14.61 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I9_J,axiom, % 14.79/14.61 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I9_J,axiom, % 14.79/14.61 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I9_J,axiom, % 14.79/14.61 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__extend__simps_I9_J,axiom, % 14.79/14.61 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUP__commute,axiom, % 14.79/14.61 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fun__upd__def,axiom, % 14.79/14.61 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] : % 14.79/14.61 ( ( V_x_2 = V_a_2 % 14.79/14.61 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 ) % 14.79/14.61 & ( V_x_2 != V_a_2 % 14.79/14.61 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__commute,axiom, % 14.79/14.61 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fold__image__def,axiom, % 14.79/14.61 ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I8_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I8_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_int__setprod,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 14.79/14.61 % 14.79/14.61 fof(fact_of__int__setsum,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Rings_Oring__1(T_b) % 14.79/14.61 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_of__int__setprod,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 14.79/14.61 & class_Rings_Oring__1(T_b) ) % 14.79/14.61 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__dividef,axiom, % 14.79/14.61 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Fields_Ofield__inverse__zero(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Compl__eq,axiom, % 14.79/14.61 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod_Odistrib,axiom, % 14.79/14.61 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__extend__simps_I1_J,axiom, % 14.79/14.61 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__singleton,axiom, % 14.79/14.61 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_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)))) = V_A_2 ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__simps_I1_J,axiom, % 14.79/14.61 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__atMost__UNIV,axiom, % 14.79/14.61 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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__constant,axiom, % 14.79/14.61 ! [V_ca_2,T_c,T_b,V_A_2] : % 14.79/14.61 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__empty,axiom, % 14.79/14.61 ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b] : % 14.79/14.61 ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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)) % 14.79/14.61 <=> ! [B_x] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.61 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UNIV__def,axiom, % 14.79/14.61 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__1,axiom, % 14.79/14.61 ! [V_A_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__mult(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__0,axiom, % 14.79/14.61 ! [V_A_2,T_c,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__lessThan__UNIV,axiom, % 14.79/14.61 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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF__INT__eq,axiom, % 14.79/14.61 ! [V_x_2,V_r_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INF__INT__eq2,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUP__UN__eq2,axiom, % 14.79/14.61 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_range__composition,axiom, % 14.79/14.61 ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__atLeast__UNIV,axiom, % 14.79/14.61 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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__range__imageI,axiom, % 14.79/14.61 ! [V_f_2,T_d,V_g_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 14.79/14.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUP__UN__eq,axiom, % 14.79/14.61 ! [V_x_2,V_r_2,T_c,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_finite__Collect__not,axiom, % 14.79/14.61 ! [V_Pa_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)))) % 14.79/14.61 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 14.79/14.61 ! [V_n_2,V_m_2,V_f_2,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_of__nat__setsum,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( class_Rings_Osemiring__1(T_b) % 14.79/14.61 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Int__Inter__image,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,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_c),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)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__le__add__shift,axiom, % 14.79/14.61 ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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_b,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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__Pow__subset,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_of__nat__setprod,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.61 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 14.79/14.61 & class_Rings_Osemiring__1(T_b) ) % 14.79/14.61 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__add__atLeastLessThan,axiom, % 14.79/14.61 ! [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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__add__atLeastAtMost,axiom, % 14.79/14.61 ! [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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__delta_H,axiom, % 14.79/14.61 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__delta,axiom, % 14.79/14.61 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__constant,axiom, % 14.79/14.61 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.61 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__setsum__restrict,axiom, % 14.79/14.61 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_d) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__greaterThan__UNIV,axiom, % 14.79/14.61 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)) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__delta_H,axiom, % 14.79/14.61 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__delta,axiom, % 14.79/14.61 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__eq__UN,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_if__image__distrib,axiom, % 14.79/14.61 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,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_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INT__simps_I4_J,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 14.79/14.61 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.61 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__constant,axiom, % 14.79/14.61 ! [V_A_2,V_y_2,T_c,T_b] : % 14.79/14.61 ( class_Rings_Osemiring__1(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_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_c),V_A_2))),V_y_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_power__number__of__even,axiom, % 14.79/14.61 ! [V_w_2,V_z_2,T_b] : % 14.79/14.61 ( class_Int_Onumber__ring(T_b) % 14.79/14.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fold__image__distrib,axiom, % 14.79/14.61 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_dual__max,axiom, % 14.79/14.61 ! [T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_dual__min,axiom, % 14.79/14.61 ! [T_b] : % 14.79/14.61 ( class_Orderings_Olinorder(T_b) % 14.79/14.61 => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__constant,axiom, % 14.79/14.61 ! [V_y_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_sup__SUPR__fold__sup,axiom, % 14.79/14.61 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_inf__INFI__fold__inf,axiom, % 14.79/14.61 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 14.79/14.61 ! [V_Pa_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_Pa_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_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 14.79/14.61 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_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_Pa_2),c_Int_Onat)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_zpower__number__of__even,axiom, % 14.79/14.61 ! [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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__lessThan__Suc,axiom, % 14.79/14.61 ! [V_n_2,V_f_2,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__atMost__Suc,axiom, % 14.79/14.61 ! [V_n_2,V_f_2,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 14.79/14.61 ! [V_A_2,V_f_2,T_b] : % 14.79/14.61 ( ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 & class_Groups_Ocomm__monoid__mult(T_b) ) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Un__Union__image,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,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_c),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)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__add__int__atLeastLessThan,axiom, % 14.79/14.61 ! [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) ). % 14.79/14.61 % 14.79/14.61 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 14.79/14.61 ! [V_f_2,V_A_2,T_b] : % 14.79/14.61 ( ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 & class_Groups_Ocomm__monoid__mult(T_b) ) % 14.79/14.61 => ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Powp__Pow__eq,axiom, % 14.79/14.61 ! [V_x_2,V_A_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) % 14.79/14.61 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__restrict__set_H,axiom, % 14.79/14.61 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(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_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)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__restrict__set,axiom, % 14.79/14.61 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__image__gen,axiom, % 14.79/14.61 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),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_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__eq__fold__image,axiom, % 14.79/14.61 ! [V_f_2,T_c,V_A_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_power__number__of__even__number__of,axiom, % 14.79/14.61 ! [V_w_2,V_v_2,T_b] : % 14.79/14.61 ( class_Int_Onumber__ring(T_b) % 14.79/14.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_SUPR__fold__sup,axiom, % 14.79/14.61 ! [V_f_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_card_Oeq__fold__g,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_card__def,axiom, % 14.79/14.61 ! [V_A_2,T_b] : % 14.79/14.61 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_fun__left__comm__idem__remove,axiom, % 14.79/14.61 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,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_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),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))))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_INFI__fold__inf,axiom, % 14.79/14.61 ! [V_f_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_diff__nat__eq__if,axiom, % 14.79/14.61 ! [V_z_2,V_z_H_2] : % 14.79/14.61 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 14.79/14.61 => 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) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 14.79/14.61 => 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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_negDivAlg__div__mod,axiom, % 14.79/14.61 ! [V_l,V_k] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 14.79/14.61 => 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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_negDivAlg__minus1,axiom, % 14.79/14.61 ! [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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_card__less__Suc2,axiom, % 14.79/14.61 ! [V_i_2,V_M_2] : % 14.79/14.61 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 14.79/14.61 => 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))))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_card__less,axiom, % 14.79/14.61 ! [V_i_2,V_M_2] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 14.79/14.61 => 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) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_card__less__Suc,axiom, % 14.79/14.61 ! [V_i_2,V_M_2] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 14.79/14.61 => 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))))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_UN__le__eq__Un0,axiom, % 14.79/14.61 ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 14.79/14.61 ! [V_f_2,V_A_2,T_b] : % 14.79/14.61 ( ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 & class_Groups_Ocomm__monoid__mult(T_b) ) % 14.79/14.61 => ( c_Nat__Transfer_Onat__set(V_A_2) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,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)) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_adjust__eq,axiom, % 14.79/14.61 ! [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))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__head,axiom, % 14.79/14.61 ! [V_Pa_2,V_n_2,V_m_2,T_b] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__cases,axiom, % 14.79/14.61 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_Set_OCollect(T_b),V_Pa_2))))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_minus__fold__remove,axiom, % 14.79/14.61 ! [V_B_2,V_A_2,T_b] : % 14.79/14.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.61 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,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_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),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))))),V_B_2),V_A_2) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_Suc__eq__number__of,axiom, % 14.79/14.61 ! [V_v_2,V_n_2] : % 14.79/14.61 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 14.79/14.61 <=> 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))))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_eq__number__of__Suc,axiom, % 14.79/14.61 ! [V_n_2,V_v_2] : % 14.79/14.61 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 14.79/14.61 <=> 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))))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_nat__number__of__Bit1,axiom, % 14.79/14.61 ! [V_w_2] : % 14.79/14.61 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 14.79/14.61 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 14.79/14.61 => 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)))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_geometric__sum,axiom, % 14.79/14.61 ! [V_n_2,V_x_2,T_b] : % 14.79/14.61 ( class_Fields_Ofield(T_b) % 14.79/14.61 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),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_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_gauss__sum,axiom, % 14.79/14.61 ! [V_n_2,T_b] : % 14.79/14.61 ( class_Rings_Ocomm__semiring__1(T_b) % 14.79/14.61 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),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_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setsum__natinterval__difff,axiom, % 14.79/14.61 ! [V_f_2,V_n_2,V_m_2,T_b] : % 14.79/14.61 ( class_Groups_Oab__group__add(T_b) % 14.79/14.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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_b),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)))) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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_b) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_less__Suc__number__of,axiom, % 14.79/14.61 ! [V_v_2,V_n_2] : % 14.79/14.61 ( 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))) % 14.79/14.61 <=> 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))))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_less__number__of__Suc,axiom, % 14.79/14.61 ! [V_n_2,V_v_2] : % 14.79/14.61 ( 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))) % 14.79/14.61 <=> 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)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_le__Suc__number__of,axiom, % 14.79/14.61 ! [V_v_2,V_n_2] : % 14.79/14.61 ( 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))) % 14.79/14.61 <=> 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))))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_le__number__of__Suc,axiom, % 14.79/14.61 ! [V_n_2,V_v_2] : % 14.79/14.61 ( 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))) % 14.79/14.61 <=> 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)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__Suc__number__of,axiom, % 14.79/14.61 ! [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)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_max__number__of__Suc,axiom, % 14.79/14.61 ! [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)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_power__number__of__odd,axiom, % 14.79/14.61 ! [V_z_2,V_w_2,T_b] : % 14.79/14.61 ( class_Int_Onumber__ring(T_b) % 14.79/14.61 => ( ( 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))) % 14.79/14.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) ) % 14.79/14.61 & ( ~ 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))) % 14.79/14.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_setprod__gen__delta,axiom, % 14.79/14.61 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] : % 14.79/14.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 14.79/14.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 14.79/14.61 ! [V_x_2,V_y_2,V_ca_2] : % 14.79/14.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 14.79/14.61 => 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_ca_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_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 14.79/14.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 14.79/14.61 => 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_ca_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))) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 14.79/14.61 => 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_ca_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)) ) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_zpower__number__of__odd,axiom, % 14.79/14.61 ! [V_z_2,V_w_2] : % 14.79/14.61 ( ( 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))) % 14.79/14.61 => 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))) ) % 14.79/14.61 & ( ~ 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))) % 14.79/14.61 => 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) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_arith__series__general,axiom, % 14.79/14.61 ! [V_n_2,V_d_2,V_a_2,T_b] : % 14.79/14.61 ( class_Rings_Ocomm__semiring__1(T_b) % 14.79/14.61 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_negDivAlg_Osimps,axiom, % 14.79/14.61 ! [V_b,V_a] : % 14.79/14.61 ( ( ( 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))) % 14.79/14.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.61 => 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)) ) % 14.79/14.61 & ( ~ ( 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))) % 14.79/14.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.61 => 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))) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__number__of__Suc,axiom, % 14.79/14.61 ! [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)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_min__Suc__number__of,axiom, % 14.79/14.61 ! [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)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_arith__series__nat,axiom, % 14.79/14.61 ! [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)))) ). % 14.79/14.61 % 14.79/14.61 fof(fact_power__number__of__odd__number__of,axiom, % 14.79/14.61 ! [V_v_2,V_w_2,T_b] : % 14.79/14.61 ( class_Int_Onumber__ring(T_b) % 14.79/14.61 => ( ( 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))) % 14.79/14.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) ) % 14.79/14.61 & ( ~ 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))) % 14.79/14.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_negDivAlg__eqn__number__of,axiom, % 14.79/14.61 ! [V_w,V_v] : % 14.79/14.61 ( 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))) % 14.79/14.61 => ( ( 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)))) % 14.79/14.61 => 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))) ) % 14.79/14.61 & ( ~ 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)))) % 14.79/14.61 => 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)))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_negDivAlg__eqn,axiom, % 14.79/14.61 ! [V_a,V_b] : % 14.79/14.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.61 => ( ( 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))) % 14.79/14.61 => 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)) ) % 14.79/14.61 & ( ~ 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))) % 14.79/14.61 => 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))) ) ) ) ). % 14.79/14.61 % 14.79/14.61 fof(fact_diff__nat__number__of,axiom, % 14.79/14.61 ! [V_v_2,V_v_H_2] : % 14.79/14.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 14.79/14.61 => 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) ) % 14.79/14.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 14.79/14.61 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_norm__frac_Osimps,axiom, % 14.79/14.62 ! [V_a_2,V_b_2] : % 14.79/14.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 14.79/14.62 => 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))) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__case__add__eq__if,axiom, % 14.79/14.62 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 14.79/14.62 ! [V_w] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( 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))) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( ~ 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))) % 14.79/14.62 => 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)))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg_Osimps,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.62 => 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) ) % 14.79/14.62 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.62 => 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))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_sup2CI,axiom, % 14.79/14.62 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] : % 14.79/14.62 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_sup2E,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 14.79/14.62 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inf2I,axiom, % 14.79/14.62 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inf2E,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 14.79/14.62 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 14.79/14.62 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_bot2E,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_INF1__iff,axiom, % 14.79/14.62 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 14.79/14.62 <=> ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_INF2__iff,axiom, % 14.79/14.62 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 14.79/14.62 <=> ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_SUP2__iff,axiom, % 14.79/14.62 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 14.79/14.62 <=> ? [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rev__predicate2D,axiom, % 14.79/14.62 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_predicate2D,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_less__by__empty,axiom, % 14.79/14.62 ! [V_B_2,T_b,V_A_2] : % 14.79/14.62 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inf2D1,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inf2D2,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_sup2I2,axiom, % 14.79/14.62 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_sup2I1,axiom, % 14.79/14.62 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__case__0,axiom, % 14.79/14.62 ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__case__Suc,axiom, % 14.79/14.62 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg__0,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__Suc1,axiom, % 14.79/14.62 ! [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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__Suc2,axiom, % 14.79/14.62 ! [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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 14.79/14.62 ! [V_n_2,V_m_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 14.79/14.62 <=> 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)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_diff__Suc,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__Suc2,axiom, % 14.79/14.62 ! [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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__Suc1,axiom, % 14.79/14.62 ! [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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg__div__mod,axiom, % 14.79/14.62 ! [V_l,V_k] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__case__number__of,axiom, % 14.79/14.62 ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg__eqn,axiom, % 14.79/14.62 ! [V_a,V_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 14.79/14.62 => 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) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 14.79/14.62 => 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))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg__eqn__number__of,axiom, % 14.79/14.62 ! [V_w,V_v] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( 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))) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( ~ 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))) % 14.79/14.62 => 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)))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_in__rel__def,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) % 14.79/14.62 <=> 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)),V_R_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__mod__code__numeral__def,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Nitpick_Orefl_H__def,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Nitpick_Orefl_H(T_b,V_r_2) % 14.79/14.62 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_adjust__def,axiom, % 14.79/14.62 ! [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))))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__step,axiom, % 14.79/14.62 ! [V_m,V_n] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__rec__add__eq__if,axiom, % 14.79/14.62 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),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_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__rec__0,axiom, % 14.79/14.62 ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__rec__Suc,axiom, % 14.79/14.62 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b,V_f1_2,V_f2_2),V_nat_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__zero,axiom, % 14.79/14.62 ! [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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__base,axiom, % 14.79/14.62 ! [V_n,V_m] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.79/14.62 => 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) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__div__mod,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__rec__number__of,axiom, % 14.79/14.62 ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__imageI,axiom, % 14.79/14.62 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_of__int__num,axiom, % 14.79/14.62 ! [V_k_2,T_b] : % 14.79/14.62 ( class_Rings_Oring__1(T_b) % 14.79/14.62 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) % 14.79/14.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),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_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),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))))) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 14.79/14.62 ! [V_n_2,T_b] : % 14.79/14.62 ( class_Rings_Osemiring__1(T_b) % 14.79/14.62 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_splitI,axiom, % 14.79/14.62 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_prod__caseI,axiom, % 14.79/14.62 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mem__splitI,axiom, % 14.79/14.62 ! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_splitD,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_splitD_H,axiom, % 14.79/14.62 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_ca_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 14.79/14.62 ! [V_i_2,V_inc_2,T_b] : % 14.79/14.62 ( class_Rings_Osemiring__1(T_b) % 14.79/14.62 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 14.79/14.62 ! [V_i_2,V_n_2,V_inc_2,T_b] : % 14.79/14.62 ( class_Rings_Osemiring__1(T_b) % 14.79/14.62 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__paired__All,axiom, % 14.79/14.62 ! [T_c,T_b,V_Pa_2] : % 14.79/14.62 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 14.79/14.62 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Pair__eq,axiom, % 14.79/14.62 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.62 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) % 14.79/14.62 <=> ( V_a_2 = V_a_H_2 % 14.79/14.62 & V_b_2 = V_b_H_2 ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Pair__inject,axiom, % 14.79/14.62 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 14.79/14.62 ( 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) % 14.79/14.62 => ~ ( V_a = V_a_H % 14.79/14.62 => V_b != V_b_H ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__weak__cong,axiom, % 14.79/14.62 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] : % 14.79/14.62 ( V_p_2 = V_q_2 % 14.79/14.62 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__mod__div,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_prod_Osimps_I2_J,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__conv,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__if,axiom, % 14.79/14.62 ! [V_m_2,V_n_2] : % 14.79/14.62 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 14.79/14.62 => 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) ) % 14.79/14.62 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__eta,axiom, % 14.79/14.62 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__twice,axiom, % 14.79/14.62 ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Nitpick_OFrac__def,axiom, % 14.79/14.62 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)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__def,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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))) ) ) ) ) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => 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))) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__pdivmod,axiom, % 14.79/14.62 ! [V_l_2,V_k_2] : % 14.79/14.62 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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) ) % 14.79/14.62 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)))) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_apsnd__conv,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_negateSnd__def,axiom, % 14.79/14.62 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_negateSnd__eq,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pdivmod__def,axiom, % 14.79/14.62 ! [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))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pdivmod__posDivAlg,axiom, % 14.79/14.62 ! [V_k,V_l] : % 14.79/14.62 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__code,axiom, % 14.79/14.62 ! [V_l_2,V_k_2] : % 14.79/14.62 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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) ) % 14.79/14.62 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)))) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Nitpick_Oprod__def,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),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_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_int__ge__less__than2__def,axiom, % 14.79/14.62 ! [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)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_int__ge__less__than__def,axiom, % 14.79/14.62 ! [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)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 14.79/14.62 ! [V_a,V_r,V_q,V_c,V_b] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 14.79/14.62 => 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)))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 14.79/14.62 ! [V_c,V_r,V_q,V_b,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 14.79/14.62 => 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)))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__box_Osize_I2_J,axiom, % 14.79/14.62 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__rel__unique,axiom, % 14.79/14.62 ! [V_qr_H,V_qr,V_n,V_m] : % 14.79/14.62 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 14.79/14.62 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 14.79/14.62 => V_qr = V_qr_H ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 14.79/14.62 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__eq,axiom, % 14.79/14.62 ! [V_qr,V_n,V_m] : % 14.79/14.62 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 14.79/14.62 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__eq,axiom, % 14.79/14.62 ! [V_r,V_q,V_n,V_m] : % 14.79/14.62 ( 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))) % 14.79/14.62 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__eq,axiom, % 14.79/14.62 ! [V_r,V_q,V_n,V_m] : % 14.79/14.62 ( 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))) % 14.79/14.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__rel,axiom, % 14.79/14.62 ! [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)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__rel__add1__eq,axiom, % 14.79/14.62 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( 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))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 14.79/14.62 => 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)))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__box_Orecs,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__box_Osimps_I2_J,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_negDivAlg_Opsimps,axiom, % 14.79/14.62 ! [V_b_2,V_a_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( ( 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))) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( ~ ( 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))) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.62 => 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))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_accp__downward,axiom, % 14.79/14.62 ! [V_a_2,V_b_2,V_r_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 14.79/14.62 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_accp_Oequations,axiom, % 14.79/14.62 ! [V_a_2,V_r_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 14.79/14.62 <=> ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 14.79/14.62 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_accp_Osimps,axiom, % 14.79/14.62 ! [V_a_2,V_r_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 14.79/14.62 <=> ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 14.79/14.62 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_accp__subset,axiom, % 14.79/14.62 ! [V_R2_2,V_R1_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg_Opsimps,axiom, % 14.79/14.62 ! [V_b_2,V_a_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.62 => 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) ) % 14.79/14.62 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.62 => 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))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_norm__frac_Opsimps,axiom, % 14.79/14.62 ! [V_b_2,V_a_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 14.79/14.62 => 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)) ) % 14.79/14.62 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 14.79/14.62 => 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))) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_negDivAlg_Opinduct,axiom, % 14.79/14.62 ! [V_Pa_2,V_a1_2,V_a0_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ! [B_a,B_b] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( ~ ( 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))) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_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))) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg_Opinduct,axiom, % 14.79/14.62 ! [V_Pa_2,V_a1_2,V_a0_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ! [B_a,B_b] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 14.79/14.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_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))) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__gcd_Opsimps,axiom, % 14.79/14.62 ! [V_y_2,V_x_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.62 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 14.79/14.62 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.62 => 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)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_zmult2__lemma,axiom, % 14.79/14.62 ! [V_c,V_r,V_q,V_b,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 14.79/14.62 => 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)))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__rel__0,axiom, % 14.79/14.62 ! [V_b] : % 14.79/14.62 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_self__remainder,axiom, % 14.79/14.62 ! [V_r,V_q,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_unique__quotient,axiom, % 14.79/14.62 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( 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))) % 14.79/14.62 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => V_q = V_q_H ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_unique__remainder,axiom, % 14.79/14.62 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( 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))) % 14.79/14.62 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => V_r = V_r_H ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__rel__neg,axiom, % 14.79/14.62 ! [V_qr,V_b,V_a] : % 14.79/14.62 ( 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)) % 14.79/14.62 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__correct,axiom, % 14.79/14.62 ! [V_a,V_b] : % 14.79/14.62 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_self__quotient,axiom, % 14.79/14.62 ! [V_r,V_q,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__rel__mod,axiom, % 14.79/14.62 ! [V_r,V_q,V_b,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__rel__div,axiom, % 14.79/14.62 ! [V_r,V_q,V_b,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_negDivAlg__correct,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__rel__div__mod,axiom, % 14.79/14.62 ! [V_a,V_b] : % 14.79/14.62 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_posDivAlg__correct,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_zadd1__lemma,axiom, % 14.79/14.62 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( 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))) % 14.79/14.62 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_zminus1__lemma,axiom, % 14.79/14.62 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => 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))))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__relI,axiom, % 14.79/14.62 ! [V_r,V_q,V_b,V_a] : % 14.79/14.62 ( 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) % 14.79/14.62 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 14.79/14.62 => 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))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_zmult1__lemma,axiom, % 14.79/14.62 ! [V_a,V_r,V_q,V_c,V_b] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 14.79/14.62 => 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)))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__int__rel__def,axiom, % 14.79/14.62 ! [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))))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 14.79/14.62 ! [V_f_2,V_A_2,T_b] : % 14.79/14.62 ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 14.79/14.62 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,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_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__pos__neg__1__number__of,axiom, % 14.79/14.62 ! [V_w] : % 14.79/14.62 ( 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))) % 14.79/14.62 => 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))))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_in__measure,axiom, % 14.79/14.62 ! [V_f_2,V_y_2,V_x_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2))) % 14.79/14.62 <=> 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))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_snd__apsnd,axiom, % 14.79/14.62 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_apsnd__eq__conv,axiom, % 14.79/14.62 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] : % 14.79/14.62 ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2) % 14.79/14.62 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_snd__conv,axiom, % 14.79/14.62 ! [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 ). % 14.79/14.62 % 14.79/14.62 fof(fact_snd__eqD,axiom, % 14.79/14.62 ! [V_a,V_y,V_x,T_a,T_b] : % 14.79/14.62 ( 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 % 14.79/14.62 => V_y = V_a ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_snd__def,axiom, % 14.79/14.62 ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__int__def,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__neg__pos,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__pos__pos,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__pos__pos__1__number__of,axiom, % 14.79/14.62 ! [V_w] : % 14.79/14.62 ( 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))) % 14.79/14.62 => 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))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__pos__neg,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => 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)))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__neg__neg,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => 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)))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 14.79/14.62 ! [V_f_2,V_A_2,T_b] : % 14.79/14.62 ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 14.79/14.62 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,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_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_norm__frac_Opinduct,axiom, % 14.79/14.62 ! [V_Pa_2,V_a1_2,V_a0_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ! [B_a,B_b] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__pos__neg__1__number__of,axiom, % 14.79/14.62 ! [V_w] : % 14.79/14.62 ( 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))) % 14.79/14.62 => 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))))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Pair__fst__snd__eq,axiom, % 14.79/14.62 ! [T_c,T_b,V_t_2,V_s_2] : % 14.79/14.62 ( V_s_2 = V_t_2 % 14.79/14.62 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) % 14.79/14.62 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_prod__eqI,axiom, % 14.79/14.62 ! [V_q,V_p,T_b,T_a] : % 14.79/14.62 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 14.79/14.62 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 14.79/14.62 => V_p = V_q ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_fst__def,axiom, % 14.79/14.62 ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_fst__eqD,axiom, % 14.79/14.62 ! [V_a,V_y,V_x,T_b,T_a] : % 14.79/14.62 ( 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 % 14.79/14.62 => V_x = V_a ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_fst__conv,axiom, % 14.79/14.62 ! [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 ). % 14.79/14.62 % 14.79/14.62 fof(fact_fst__apsnd,axiom, % 14.79/14.62 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__collapse,axiom, % 14.79/14.62 ! [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 ). % 14.79/14.62 % 14.79/14.62 fof(fact_surjective__pairing,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_prod__case__beta,axiom, % 14.79/14.62 ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__int__def,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mod__nat__def,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__comp__eq,axiom, % 14.79/14.62 ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__beta,axiom, % 14.79/14.62 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__def,axiom, % 14.79/14.62 ! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__neg__pos,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__pos__pos,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__pos__pos__1__number__of,axiom, % 14.79/14.62 ! [V_w] : % 14.79/14.62 ( 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))) % 14.79/14.62 => 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))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__pos__neg,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => 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)))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__neg__neg,axiom, % 14.79/14.62 ! [V_b,V_a] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 14.79/14.62 => 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)))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_prod__size__simp,axiom, % 14.79/14.62 ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,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_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_exI__realizer,axiom, % 14.79/14.62 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_conjI__realizer,axiom, % 14.79/14.62 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] : % 14.79/14.62 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 14.79/14.62 => ( hBOOL(hAPP(V_Qa_2,V_q_2)) % 14.79/14.62 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) % 14.79/14.62 & hBOOL(hAPP(V_Qa_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_div__nat__def,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__rel__def,axiom, % 14.79/14.62 ! [V_qr_2,V_n_2,V_m_2] : % 14.79/14.62 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 14.79/14.62 <=> ( 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)) % 14.79/14.62 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.62 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.79/14.62 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 14.79/14.62 => ( 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))) % 14.79/14.62 & 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)) ) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 14.79/14.62 => ( 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))) % 14.79/14.62 & 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))) ) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__def,axiom, % 14.79/14.62 ! [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)))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_UN__finite2__subset,axiom, % 14.79/14.62 ! [V_B_2,V_k_2,V_A_2,T_b] : % 14.79/14.62 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__gcd_Opinduct,axiom, % 14.79/14.62 ! [V_Pa_2,V_a1_2,V_a0_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ! [B_x,B_y] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Rep__Integ__inject,axiom, % 14.79/14.62 ! [V_y_2,V_x_2] : % 14.79/14.62 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 14.79/14.62 <=> V_x_2 = V_y_2 ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_range,axiom, % 14.79/14.62 ! [V_s,V_k] : % 14.79/14.62 ( 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)) % 14.79/14.62 => 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)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_setsum__multicount,axiom, % 14.79/14.62 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 14.79/14.62 => ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) % 14.79/14.62 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 ) % 14.79/14.62 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_c),V_T_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mlex__leq,axiom, % 14.79/14.62 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mlex__less,axiom, % 14.79/14.62 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 14.79/14.62 ( 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))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__psubset__def,axiom, % 14.79/14.62 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_b] : % 14.79/14.62 ( class_Orderings_Olinorder(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.62 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 14.79/14.62 ! [V_x_2,V_A_2,T_b] : % 14.79/14.62 ( class_Orderings_Olinorder(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__Collect__bounded__ex,axiom, % 14.79/14.62 ! [V_Qa_2,T_c,V_Pa_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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),V_Pa_2))),V_Qa_2))))) % 14.79/14.62 <=> ! [B_y] : % 14.79/14.62 ( hBOOL(hAPP(V_Pa_2,B_y)) % 14.79/14.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Qa_2),B_y)))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__image__set,axiom, % 14.79/14.62 ! [V_f_2,T_c,V_Pa_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 14.79/14.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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_b,T_c),tc_fun(T_b,tc_HOL_Obool)),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)),V_f_2)))),V_Pa_2))))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Pow__Compl,axiom, % 14.79/14.62 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_add__Max__commute,axiom, % 14.79/14.62 ! [V_k_2,V_N_2,T_b] : % 14.79/14.62 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.79/14.62 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_add__Min__commute,axiom, % 14.79/14.62 ! [V_k_2,V_N_2,T_b] : % 14.79/14.62 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 14.79/14.62 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_sup__Inf1__distrib,axiom, % 14.79/14.62 ! [V_x_2,V_A_2,T_b] : % 14.79/14.62 ( class_Lattices_Odistrib__lattice(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_sup__Inf2__distrib,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_b] : % 14.79/14.62 ( class_Lattices_Odistrib__lattice(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.62 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inf__Sup1__distrib,axiom, % 14.79/14.62 ! [V_x_2,V_A_2,T_b] : % 14.79/14.62 ( class_Lattices_Odistrib__lattice(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inf__Sup2__distrib,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_b] : % 14.79/14.62 ( class_Lattices_Odistrib__lattice(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.62 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_in__finite__psubset,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b))) % 14.79/14.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.62 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_b] : % 14.79/14.62 ( class_Orderings_Olinorder(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.62 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 14.79/14.62 ! [V_x_2,V_A_2,T_b] : % 14.79/14.62 ( class_Orderings_Olinorder(T_b) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat_Osize_I4_J,axiom, % 14.79/14.62 ! [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))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_prod_Orecs,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_UN__finite2__eq,axiom, % 14.79/14.62 ! [V_B_2,V_k_2,V_A_2,T_b] : % 14.79/14.62 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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) % 14.79/14.62 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat__size,axiom, % 14.79/14.62 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat_Osize_I3_J,axiom, % 14.79/14.62 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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_UN__finite__subset,axiom, % 14.79/14.62 ! [V_C_2,V_A_2,T_b] : % 14.79/14.62 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_setsum__multicount__gen,axiom, % 14.79/14.62 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) % 14.79/14.62 => ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) % 14.79/14.62 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) ) % 14.79/14.62 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_in__lex__prod,axiom, % 14.79/14.62 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2))) % 14.79/14.62 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) % 14.79/14.62 | ( V_a_2 = V_a_H_2 % 14.79/14.62 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_same__fstI,axiom, % 14.79/14.62 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] : % 14.79/14.62 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_setsum__nonneg__0,axiom, % 14.79/14.62 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] : % 14.79/14.62 ( class_Groups_Oordered__ab__group__add(T_c) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 14.79/14.62 => ( ! [B_i] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 14.79/14.62 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 14.79/14.62 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_setsum__nonneg__leq__bound,axiom, % 14.79/14.62 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] : % 14.79/14.62 ( class_Groups_Oordered__ab__group__add(T_c) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 14.79/14.62 => ( ! [B_i] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 14.79/14.62 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_sum__diff__distrib,axiom, % 14.79/14.62 ! [V_n_2,V_Pa_2,V_Qa_2] : % 14.79/14.62 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_2,B_x))) % 14.79/14.62 => 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_Pa_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_Qa_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_Pa_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_apfst__apsnd,axiom, % 14.79/14.62 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_apsnd__apfst,axiom, % 14.79/14.62 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_fst__apfst,axiom, % 14.79/14.62 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_apfst__eq__conv,axiom, % 14.79/14.62 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] : % 14.79/14.62 ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2) % 14.79/14.62 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_apfst__conv,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_snd__apfst,axiom, % 14.79/14.62 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_apsnd__apfst__commute,axiom, % 14.79/14.62 ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__lessI2,axiom, % 14.79/14.62 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__ext__additive,axiom, % 14.79/14.62 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 14.79/14.62 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 14.79/14.62 ( ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.62 & class_Groups_Ocomm__monoid__mult(T_b) ) % 14.79/14.62 => ( V_A_2 = V_B_2 % 14.79/14.62 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.62 => ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 14.79/14.62 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 14.79/14.62 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__lessI1,axiom, % 14.79/14.62 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 14.79/14.62 => 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)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__extp__max__ext__eq,axiom, % 14.79/14.62 ! [V_xa_2,V_x_2,V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__leqI2,axiom, % 14.79/14.62 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_smax__insertI,axiom, % 14.79/14.62 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 14.79/14.62 => ( 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)) % 14.79/14.62 => ( 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)) % 14.79/14.62 => 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)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_smax__emptyI,axiom, % 14.79/14.62 ! [V_Y_2] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 14.79/14.62 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 14.79/14.62 => 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)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__strict__def,axiom, % 14.79/14.62 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__leqI1,axiom, % 14.79/14.62 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 14.79/14.62 => 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)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wmin__insertI,axiom, % 14.79/14.62 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 14.79/14.62 => ( 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)) % 14.79/14.62 => ( 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)) % 14.79/14.62 => 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)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wmax__insertI,axiom, % 14.79/14.62 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 14.79/14.62 => ( 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)) % 14.79/14.62 => ( 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)) % 14.79/14.62 => 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)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_smin__insertI,axiom, % 14.79/14.62 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 14.79/14.62 => ( 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)) % 14.79/14.62 => ( 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)) % 14.79/14.62 => 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)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wmax__emptyI,axiom, % 14.79/14.62 ! [V_X_2] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 14.79/14.62 => 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)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_smin__emptyI,axiom, % 14.79/14.62 ! [V_X_2] : % 14.79/14.62 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 14.79/14.62 => 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)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wmin__emptyI,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__weak__def,axiom, % 14.79/14.62 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)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__weak__def,axiom, % 14.79/14.62 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)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__rpair__set,axiom, % 14.79/14.62 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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__rpair__set,axiom, % 14.79/14.62 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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__strict__def,axiom, % 14.79/14.62 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 14.79/14.62 % 14.79/14.62 fof(fact_less__than__iff,axiom, % 14.79/14.62 ! [V_y_2,V_x_2] : % 14.79/14.62 ( 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)) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_intrel__iff,axiom, % 14.79/14.62 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 14.79/14.62 ( 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)) % 14.79/14.62 <=> 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) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rp__inv__image__rp,axiom, % 14.79/14.62 ! [V_f_2,T_c,V_Pa_2,T_b] : % 14.79/14.62 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 14.79/14.62 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pair__less__def,axiom, % 14.79/14.62 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mlex__prod__def,axiom, % 14.79/14.62 ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rp__inv__image__def,axiom, % 14.79/14.62 ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(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(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(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_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equiv__intrel__iff,axiom, % 14.79/14.62 ! [V_y_2,V_x_2] : % 14.79/14.62 ( 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)))) % 14.79/14.62 <=> 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)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_measure__def,axiom, % 14.79/14.62 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__singleton,axiom, % 14.79/14.62 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__singleton__iff,axiom, % 14.79/14.62 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inv__image__def,axiom, % 14.79/14.62 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),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_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__empty,axiom, % 14.79/14.62 ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__Un,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__UN,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__Int__subset,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__mono,axiom, % 14.79/14.62 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Un__Image,axiom, % 14.79/14.62 ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_in__inv__image,axiom, % 14.79/14.62 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2))) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__INT__subset,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rev__ImageI,axiom, % 14.79/14.62 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__iff,axiom, % 14.79/14.62 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 14.79/14.62 <=> ? [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__eq__UN,axiom, % 14.79/14.62 ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_of__int,axiom, % 14.79/14.62 ! [V_j_2,V_i_2,T_b] : % 14.79/14.62 ( class_Rings_Oring__1(T_b) % 14.79/14.62 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),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_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_One__int__def,axiom, % 14.79/14.62 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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mult,axiom, % 14.79/14.62 ! [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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Rep__Integ__inverse,axiom, % 14.79/14.62 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_minus,axiom, % 14.79/14.62 ! [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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Zero__int__def,axiom, % 14.79/14.62 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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_int__def,axiom, % 14.79/14.62 ! [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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_add,axiom, % 14.79/14.62 ! [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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_nat,axiom, % 14.79/14.62 ! [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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_minus__int__def,axiom, % 14.79/14.62 ! [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))))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_less,axiom, % 14.79/14.62 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 14.79/14.62 ( 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))))))) % 14.79/14.62 <=> 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))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_le,axiom, % 14.79/14.62 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 14.79/14.62 ( 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))))))) % 14.79/14.62 <=> 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))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_irrefl__def,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Relation_Oirrefl(T_b,V_r_2) % 14.79/14.62 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_eq__Abs__Integ,axiom, % 14.79/14.62 ! [V_z_2] : % 14.79/14.62 ~ ! [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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Field__insert,axiom, % 14.79/14.62 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Field__Union,axiom, % 14.79/14.62 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Field__empty,axiom, % 14.79/14.62 ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_mono__Field,axiom, % 14.79/14.62 ! [V_s_2,V_r_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Field__Un,axiom, % 14.79/14.62 ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__Field,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Id__on__def,axiom, % 14.79/14.62 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,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_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotient__def,axiom, % 14.79/14.62 ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,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)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_ImageE,axiom, % 14.79/14.62 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 14.79/14.62 => ~ ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) % 14.79/14.62 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotient__is__empty,axiom, % 14.79/14.62 ! [V_r_2,V_A_2,T_b] : % 14.79/14.62 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 14.79/14.62 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotient__is__empty2,axiom, % 14.79/14.62 ! [V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) % 14.79/14.62 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotient__empty,axiom, % 14.79/14.62 ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Id__on__def_H,axiom, % 14.79/14.62 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),c_fequal))),V_A_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Id__on__empty,axiom, % 14.79/14.62 ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Image__Id__on,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotientI,axiom, % 14.79/14.62 ! [V_r_2,V_A_2,V_x_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Id__on__eqI,axiom, % 14.79/14.62 ! [V_A_2,T_b,V_b_2,V_a_2] : % 14.79/14.62 ( V_a_2 = V_b_2 % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Id__on__iff,axiom, % 14.79/14.62 ! [V_A_2,V_y_2,V_x_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2))) % 14.79/14.62 <=> ( V_x_2 = V_y_2 % 14.79/14.62 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_singleton__quotient,axiom, % 14.79/14.62 ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equiv__class__nondisjoint,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_subset__equiv__class,axiom, % 14.79/14.62 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,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)))))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotientE,axiom, % 14.79/14.62 ! [V_r_2,V_A_2,V_X_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ~ ! [B_x] : % 14.79/14.62 ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.62 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equiv__intrel,axiom, % 14.79/14.62 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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Union__quotient,axiom, % 14.79/14.62 ! [V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equiv__class__self,axiom, % 14.79/14.62 ! [V_a_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,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)))))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotient__disj,axiom, % 14.79/14.62 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( V_X_2 = V_Y_2 % 14.79/14.62 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equiv__class__eq,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.62 => hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotient__eq__iff,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 14.79/14.62 => ( V_X_2 = V_Y_2 % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotient__eqI,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.62 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equiv__class__eq__iff,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.62 <=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_eq__equiv__class__iff,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 14.79/14.62 => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_eq__equiv__class,axiom, % 14.79/14.62 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] : % 14.79/14.62 ( hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.62 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equiv__class__subset,axiom, % 14.79/14.62 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_eq__equiv__class__iff2,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 14.79/14.62 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_UN__equiv__class,axiom, % 14.79/14.62 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.62 => hAPP(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_r_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) = hAPP(V_f_2,V_a_2) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_UN__equiv__class2,axiom, % 14.79/14.62 ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 14.79/14.62 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 14.79/14.62 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) % 14.79/14.62 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equivp__equiv,axiom, % 14.79/14.62 ! [V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 14.79/14.62 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equivp__transp,axiom, % 14.79/14.62 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equivp__symp,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_R_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equivp__reflp,axiom, % 14.79/14.62 ! [V_x_2,V_R_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.62 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_equivp__def,axiom, % 14.79/14.62 ! [V_R_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.62 <=> ! [B_x,B_y] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 14.79/14.62 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_identity__equivp,axiom, % 14.79/14.62 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ). % 14.79/14.62 % 14.79/14.62 fof(fact_congruent2__implies__congruent,axiom, % 14.79/14.62 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) % 14.79/14.62 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.62 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_congruent2D,axiom, % 14.79/14.62 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2)) % 14.79/14.62 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_congruentD,axiom, % 14.79/14.62 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2)) % 14.79/14.62 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_congruent2__implies__congruent__UN,axiom, % 14.79/14.62 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 14.79/14.62 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 14.79/14.62 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) % 14.79/14.62 => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_UN__equiv__class__inject,axiom, % 14.79/14.62 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 14.79/14.62 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 => ! [B_y] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 14.79/14.62 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) ) % 14.79/14.62 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_UN__equiv__class__type2,axiom, % 14.79/14.62 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 14.79/14.62 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 14.79/14.62 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2))) % 14.79/14.62 => ( ! [B_x1] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) % 14.79/14.62 => ! [B_x2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_UN__equiv__class__type,axiom, % 14.79/14.62 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 14.79/14.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.62 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.62 => ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Integ__def,axiom, % 14.79/14.62 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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_card__quotient__disjoint,axiom, % 14.79/14.62 ! [V_r_2,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),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))))),V_r_2),V_A_2) % 14.79/14.62 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Id__onE,axiom, % 14.79/14.62 ! [V_A_2,V_ca_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2))) % 14.79/14.62 => ~ ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__empty,axiom, % 14.79/14.62 ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__uminus,axiom, % 14.79/14.62 ! [V_A_2,T_b] : % 14.79/14.62 ( class_Groups_Oordered__ab__group__add(T_b) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__Un__image__eq__iff,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.62 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) % 14.79/14.62 <=> V_A_2 = V_B_2 ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__id2,axiom, % 14.79/14.62 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_subset__inj__on,axiom, % 14.79/14.62 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__Int,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__diff,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__def,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 <=> ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.62 => ! [B_xa] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 14.79/14.62 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 14.79/14.62 => B_x = B_xa ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__onD,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 14.79/14.62 => V_x_2 = V_y_2 ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__iff,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 14.79/14.62 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 14.79/14.62 <=> V_x_2 = V_y_2 ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__contraD,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( V_x_2 != V_y_2 % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 14.79/14.62 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__imageD,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 14.79/14.62 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) % 14.79/14.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__eq,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 14.79/14.62 <=> V_x_2 = V_y_2 ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_injD,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 14.79/14.62 => V_x_2 = V_y_2 ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__fun,axiom, % 14.79/14.62 ! [T_d,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__image__eq__iff,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) % 14.79/14.62 <=> V_A_2 = V_B_2 ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_card__image,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__strict__subset,axiom, % 14.79/14.62 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_range__ex1__eq,axiom, % 14.79/14.62 ! [V_b_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 14.79/14.62 <=> ? [B_x] : % 14.79/14.62 ( V_b_2 = hAPP(V_f_2,B_x) % 14.79/14.62 & ! [B_y] : % 14.79/14.62 ( V_b_2 = hAPP(V_f_2,B_y) % 14.79/14.62 => B_y = B_x ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__image__mem__iff,axiom, % 14.79/14.62 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__iff__surj,axiom, % 14.79/14.62 ! [V_A_H_2,T_c,T_b,V_A_2] : % 14.79/14.62 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => ( ? [B_f] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) ) % 14.79/14.62 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_endo__inj__surj,axiom, % 14.79/14.62 ! [V_f_2,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2)) % 14.79/14.62 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) % 14.79/14.62 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__surj__inj,axiom, % 14.79/14.62 ! [V_f_2,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2))) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__UNIV__surj__inj,axiom, % 14.79/14.62 ! [V_f_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.62 => ( hAPP(c_Set_Oimage(T_b,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_b,tc_HOL_Obool)) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__UNIV__inj__surj,axiom, % 14.79/14.62 ! [V_f_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.62 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => hAPP(c_Set_Oimage(T_b,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_b,tc_HOL_Obool)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__image__subset__iff,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__image__Int,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.79/14.62 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_image__Int,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__iff__eq__card,axiom, % 14.79/14.62 ! [V_f_2,T_c,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_eq__card__imp__inj__on,axiom, % 14.79/14.62 ! [V_f_2,T_c,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__image__set__diff,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 14.79/14.62 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_image__set__diff,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pigeonhole,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) % 14.79/14.62 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__fun__updI,axiom, % 14.79/14.62 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__singleton,axiom, % 14.79/14.62 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),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))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Rep__Integ,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_card__bij__eq,axiom, % 14.79/14.62 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) % 14.79/14.62 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.79/14.62 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__image__Compl__subset,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__insert,axiom, % 14.79/14.62 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) % 14.79/14.62 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 & ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__Un,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.62 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 14.79/14.62 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_card__inj__on__le,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__iff__card__le,axiom, % 14.79/14.62 ! [V_B_2,T_c,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.79/14.62 => ( ? [B_f] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)) ) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_quotient__diff1,axiom, % 14.79/14.62 ! [V_a_2,V_A_2,V_r_2,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),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))))),V_r_2),V_A_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.62 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_type__definition__Integ,axiom, % 14.79/14.62 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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_image__INT,axiom, % 14.79/14.62 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 14.79/14.62 => ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) % 14.79/14.62 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__inv__into__into,axiom, % 14.79/14.62 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__conv__nat__seg__image,axiom, % 14.79/14.62 ! [V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.62 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,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))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__add__nat,axiom, % 14.79/14.62 ! [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) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__Suc,axiom, % 14.79/14.62 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__of__nat,axiom, % 14.79/14.62 ! [T_b] : % 14.79/14.62 ( class_Nat_Osemiring__char__0(T_b) % 14.79/14.62 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__int,axiom, % 14.79/14.62 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))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_swap__inj__on,axiom, % 14.79/14.62 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,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_A_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__inv__into__f__f,axiom, % 14.79/14.62 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__inv__into__f__eq,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.62 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__inv__f__f,axiom, % 14.79/14.62 ! [V_x_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__inv__into__onto,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__the__inv__into,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__graph,axiom, % 14.79/14.62 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_f__the__inv__into__f,axiom, % 14.79/14.62 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.62 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 14.79/14.62 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 14.79/14.62 ( ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.62 & class_Groups_Ocomm__monoid__mult(T_b) ) % 14.79/14.62 => ( V_A_2 = V_B_2 % 14.79/14.62 => ( c_Nat__Transfer_Onat__set(V_B_2) % 14.79/14.62 => ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 14.79/14.62 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 14.79/14.62 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_accp__acc__eq,axiom, % 14.79/14.62 ! [V_x_2,V_r_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2)) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__comp__def,axiom, % 14.79/14.62 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,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_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__compI,axiom, % 14.79/14.62 ! [V_s_2,V_ca_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_ca_2)),V_s_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__comp__UNION__distrib,axiom, % 14.79/14.62 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__comp__UNION__distrib2,axiom, % 14.79/14.62 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__comp__empty1,axiom, % 14.79/14.62 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__comp__empty2,axiom, % 14.79/14.62 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__comp__distrib,axiom, % 14.79/14.62 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__comp__distrib2,axiom, % 14.79/14.62 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_O__assoc,axiom, % 14.79/14.62 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_rel__comp__mono,axiom, % 14.79/14.62 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_union__comp__emptyR,axiom, % 14.79/14.62 ! [V_C_2,V_B_2,V_A_2,T_b] : % 14.79/14.62 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 14.79/14.62 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_union__comp__emptyL,axiom, % 14.79/14.62 ! [V_B_2,V_C_2,V_A_2,T_b] : % 14.79/14.62 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 14.79/14.62 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 14.79/14.62 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_acc__subset,axiom, % 14.79/14.62 ! [V_R2_2,V_R1_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_acc__downward,axiom, % 14.79/14.62 ! [V_a_2,V_r_2,V_b_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_acc_Osimps,axiom, % 14.79/14.62 ! [V_r_2,V_a_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 14.79/14.62 <=> ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__ext__compat,axiom, % 14.79/14.62 ! [V_S_2,V_R_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__ext__compat,axiom, % 14.79/14.62 ! [V_S_2,V_R_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pred__comp__rel__comp__eq,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,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_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2)) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_reduction__pairI,axiom, % 14.79/14.62 ! [V_S_2,V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_R_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 14.79/14.62 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(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)),V_R_2),V_S_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__extp_Oequations,axiom, % 14.79/14.62 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 14.79/14.62 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 14.79/14.62 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 14.79/14.62 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 & ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 14.79/14.62 => ? [B_xa] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 14.79/14.62 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__less__than,axiom, % 14.79/14.62 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pred__comp_Ointros,axiom, % 14.79/14.62 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__empty,axiom, % 14.79/14.62 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__inv__image,axiom, % 14.79/14.62 ! [V_f_2,T_c,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__lex__prod,axiom, % 14.79/14.62 ! [V_rb_2,T_c,V_ra_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_ra_2) % 14.79/14.62 => ( c_Wellfounded_Owf(T_c,V_rb_2) % 14.79/14.62 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__measure,axiom, % 14.79/14.62 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__comp__self,axiom, % 14.79/14.62 ! [V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_R_2) % 14.79/14.62 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_min__ext__wf,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__finite__psubset,axiom, % 14.79/14.62 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pred__comp_Oequations,axiom, % 14.79/14.62 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2)) % 14.79/14.62 <=> ? [B_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 14.79/14.62 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__subset,axiom, % 14.79/14.62 ! [V_p_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2)) % 14.79/14.62 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__Int2,axiom, % 14.79/14.62 ! [V_r_H_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__Int1,axiom, % 14.79/14.62 ! [V_r_H_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__mlex,axiom, % 14.79/14.62 ! [V_f_2,V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_R_2) % 14.79/14.62 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__pair__less,axiom, % 14.79/14.62 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__ext__wf,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__less,axiom, % 14.79/14.62 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)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__irrefl,axiom, % 14.79/14.62 ! [V_a_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__asym,axiom, % 14.79/14.62 ! [V_x_2,V_a_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2)) % 14.79/14.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__not__sym,axiom, % 14.79/14.62 ! [V_x_2,V_a_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2)) % 14.79/14.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__not__refl,axiom, % 14.79/14.62 ! [V_a_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__int__ge__less__than,axiom, % 14.79/14.62 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__int__ge__less__than2,axiom, % 14.79/14.62 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_acc__wfD,axiom, % 14.79/14.62 ! [V_x_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__acc__iff,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__no__loop,axiom, % 14.79/14.62 ! [V_R_2,T_b] : % 14.79/14.62 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 14.79/14.62 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__union__merge,axiom, % 14.79/14.62 ! [V_S_2,V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) % 14.79/14.62 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 <=> ~ ? [B_f] : % 14.79/14.62 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wfE__pf,axiom, % 14.79/14.62 ! [V_A_2,V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_R_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2))) % 14.79/14.62 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__union__compatible,axiom, % 14.79/14.62 ! [V_S_2,V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_R_2) % 14.79/14.62 => ( c_Wellfounded_Owf(T_b,V_S_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 14.79/14.62 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf,axiom, % 14.79/14.62 ! [T_b] : % 14.79/14.62 ( class_Orderings_Owellorder(T_b) % 14.79/14.62 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_reduction__pair__def,axiom, % 14.79/14.62 ! [V_Pa_2,T_b] : % 14.79/14.62 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 14.79/14.62 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_reduction__pair__lemma,axiom, % 14.79/14.62 ! [V_S_2,V_R_2,V_Pa_2,T_b] : % 14.79/14.62 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) % 14.79/14.62 => ( c_Wellfounded_Owf(T_b,V_S_2) % 14.79/14.62 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__lenlex,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__if__measure,axiom, % 14.79/14.62 ! [T_b,V_g_2,V_f_2,V_Pa_2] : % 14.79/14.62 ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.79/14.62 => 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))) ) % 14.79/14.62 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_max__ext_Ointros,axiom, % 14.79/14.62 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 14.79/14.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 14.79/14.62 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 14.79/14.62 => ? [B_xa] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 14.79/14.62 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_pred__nat__def,axiom, % 14.79/14.62 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))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__lex,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__lexn,axiom, % 14.79/14.62 ! [V_n_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_lex__def,axiom, % 14.79/14.62 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_lexn_Osimps_I1_J,axiom, % 14.79/14.62 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__pred__nat,axiom, % 14.79/14.62 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__same__fst,axiom, % 14.79/14.62 ! [T_b,V_R_2,T_c,V_Pa_2] : % 14.79/14.62 ( ! [B_x] : % 14.79/14.62 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.79/14.62 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) ) % 14.79/14.62 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Nitpick_Ozero__frac__def,axiom, % 14.79/14.62 ! [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))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__on__Inter,axiom, % 14.79/14.62 ! [V_f_2,T_c,T_b,V_S_2] : % 14.79/14.62 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 14.79/14.62 => ( ! [B_A] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) ) % 14.79/14.62 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Nitpick_Oone__frac__def,axiom, % 14.79/14.62 ! [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))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 14.79/14.62 ! [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))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Nitpick_Ofrac__def,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__Collect__split,axiom, % 14.79/14.62 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__elem__def,axiom, % 14.79/14.62 ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_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))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wfP__def,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_OwfP(T_b,V_r_2) % 14.79/14.62 <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wfP__empty,axiom, % 14.79/14.62 ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_RangeI,axiom, % 14.79/14.62 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wfP__accp__iff,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_OwfP(T_b,V_r_2) % 14.79/14.62 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_accp__wfPD,axiom, % 14.79/14.62 ! [V_x_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_OwfP(T_b,V_r_2) % 14.79/14.62 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__eq__trivial,axiom, % 14.79/14.62 ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__sym__eq__trivial,axiom, % 14.79/14.62 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__Id__on,axiom, % 14.79/14.62 ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_wfP__subset,axiom, % 14.79/14.62 ! [V_p_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_OwfP(T_b,V_r_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2)) % 14.79/14.62 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__Diff__subset,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__Union,axiom, % 14.79/14.62 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__empty,axiom, % 14.79/14.62 ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__empty__iff,axiom, % 14.79/14.62 ! [V_r_2,T_b,T_c] : % 14.79/14.62 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__Un__eq,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,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(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__Range,axiom, % 14.79/14.62 ! [V_r_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_snd__eq__Range,axiom, % 14.79/14.62 ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_split__paired__The,axiom, % 14.79/14.62 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_The__split__eq,axiom, % 14.79/14.62 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__iff,axiom, % 14.79/14.62 ! [V_r_2,T_c,V_a_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 14.79/14.62 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_the__inv__into__def,axiom, % 14.79/14.62 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(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_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_fold__def,axiom, % 14.79/14.62 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__insert,axiom, % 14.79/14.62 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_divmod__nat__def,axiom, % 14.79/14.62 ! [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)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Range__Int__subset,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,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(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_fold1__def,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_The__split,axiom, % 14.79/14.62 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__in__rel,axiom, % 14.79/14.62 ! [V_R_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_R_2) % 14.79/14.62 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wfP__wf__eq,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)) % 14.79/14.62 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_RangeP__Range__eq,axiom, % 14.79/14.62 ! [V_x_2,V_r_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,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_r_2)),V_x_2)) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_flat__lub__def,axiom, % 14.79/14.62 ! [V_b_2,V_A_2,T_b] : % 14.79/14.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 14.79/14.62 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 14.79/14.62 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),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_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__vimage__singleton,axiom, % 14.79/14.62 ! [V_a_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_RangeP_Ointros,axiom, % 14.79/14.62 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 14.79/14.62 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimageI,axiom, % 14.79/14.62 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] : % 14.79/14.62 ( hAPP(V_f_2,V_a_2) = V_b_2 % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__empty,axiom, % 14.79/14.62 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__UN,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__Collect__eq,axiom, % 14.79/14.62 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__UNIV,axiom, % 14.79/14.62 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__code,axiom, % 14.79/14.62 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) % 14.79/14.62 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_RangeP_Oequations,axiom, % 14.79/14.62 ! [V_a2_2,V_r_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) % 14.79/14.62 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__Compl,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__Int,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__INT,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__ident,axiom, % 14.79/14.62 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__Diff,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__eq,axiom, % 14.79/14.62 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimageD,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimageI2,axiom, % 14.79/14.62 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__mono,axiom, % 14.79/14.62 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__Un,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_image__vimage__subset,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_surj__image__vimage__eq,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_b,T_c] : % 14.79/14.62 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__def,axiom, % 14.79/14.62 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__Union,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__singleton__eq,axiom, % 14.79/14.62 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 14.79/14.62 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__insert,axiom, % 14.79/14.62 ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__vimageD,axiom, % 14.79/14.62 ! [V_F_2,V_h_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 14.79/14.62 => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_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)) % 14.79/14.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__subsetD,axiom, % 14.79/14.62 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] : % 14.79/14.62 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_image__vimage__eq,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__vimageI,axiom, % 14.79/14.62 ! [V_h_2,T_c,V_F_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 14.79/14.62 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 14.79/14.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_inj__vimage__image__eq,axiom, % 14.79/14.62 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__const,axiom, % 14.79/14.62 ! [T_c,V_A_2,V_ca_2,T_b] : % 14.79/14.62 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.79/14.62 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.79/14.62 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__eq__UN,axiom, % 14.79/14.62 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__subsetI,axiom, % 14.79/14.62 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 14.79/14.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_vimage__if,axiom, % 14.79/14.62 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] : % 14.79/14.62 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 14.79/14.62 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 14.79/14.62 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 14.79/14.62 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 14.79/14.62 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) % 14.79/14.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 14.79/14.62 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_RangeE,axiom, % 14.79/14.62 ! [V_r_2,T_c,V_b_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 14.79/14.62 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wfP__acyclicP,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_OwfP(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__Un,axiom, % 14.79/14.62 ! [V_s_2,V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => ( c_Wellfounded_Owf(T_b,V_s_2) % 14.79/14.62 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_DomainI,axiom, % 14.79/14.62 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__Id__on,axiom, % 14.79/14.62 ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ). % 14.79/14.62 % 14.79/14.62 fof(fact_acyclic__subset,axiom, % 14.79/14.62 ! [V_r_2,V_s_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Oacyclic(T_b,V_s_2) % 14.79/14.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.62 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__acyclic,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__empty,axiom, % 14.79/14.62 ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__empty__iff,axiom, % 14.79/14.62 ! [V_r_2,T_c,T_b] : % 14.79/14.62 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.62 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__mono,axiom, % 14.79/14.62 ! [V_s_2,V_r_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__Un__eq,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),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(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__Domain,axiom, % 14.79/14.62 ! [V_r_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 14.79/14.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_fst__eq__Domain,axiom, % 14.79/14.62 ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__iff,axiom, % 14.79/14.62 ! [V_r_2,T_c,V_a_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 14.79/14.62 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__insert,axiom, % 14.79/14.62 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_wf__iff__acyclic__if__finite,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 14.79/14.62 => ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.62 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_finite__acyclic__wf,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 14.79/14.62 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 14.79/14.62 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__Int__subset,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),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_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__Diff__subset,axiom, % 14.79/14.62 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Field__def,axiom, % 14.79/14.62 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__Union,axiom, % 14.79/14.62 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Domain__Collect__split,axiom, % 14.79/14.62 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ). % 14.79/14.62 % 14.79/14.62 fof(fact_DomainP__Domain__eq,axiom, % 14.79/14.62 ! [V_x_2,V_r_2,T_c,T_b] : % 14.79/14.62 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,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_r_2)),V_x_2)) % 14.79/14.62 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_Nitpick_Owf_H__def,axiom, % 14.79/14.62 ! [V_r_2,T_b] : % 14.79/14.62 ( c_Nitpick_Owf_H(T_b,V_r_2) % 14.79/14.62 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 14.79/14.62 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 14.79/14.62 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_DomainE,axiom, % 14.79/14.62 ! [V_r_2,T_c,V_a_2,T_b] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 14.79/14.62 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ). % 14.79/14.62 % 14.79/14.62 fof(fact_DomainP_Ointros,axiom, % 14.79/14.62 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 14.79/14.62 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 14.79/14.63 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_DomainP_Oequations,axiom, % 14.79/14.63 ! [V_a1_2,V_r_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) % 14.79/14.63 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_image__split__eq__Sigma,axiom, % 14.79/14.63 ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,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_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,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)))))),V_A_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Rep__Integ__cases,axiom, % 14.79/14.63 ! [V_y_2] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 14.79/14.63 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Rep__Integ__induct,axiom, % 14.79/14.63 ! [V_Pa_2,V_y_2] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 14.79/14.63 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_SigmaI,axiom, % 14.79/14.63 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__Union,axiom, % 14.79/14.63 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Times__eq__cancel2,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 14.79/14.63 => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) % 14.79/14.63 <=> V_A_2 = V_B_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__empty1,axiom, % 14.79/14.63 ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_card__cartesian__product,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),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_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setsum__cartesian__product,axiom, % 14.79/14.63 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),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))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__empty2,axiom, % 14.79/14.63 ! [V_A_2,T_c,T_b] : 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),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Times__empty,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_c,T_b] : % 14.79/14.63 ( 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)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) % 14.79/14.63 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Compl__Times__UNIV2,axiom, % 14.79/14.63 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Compl__Times__UNIV1,axiom, % 14.79/14.63 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setprod__cartesian__product,axiom, % 14.79/14.63 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__mult(T_b) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),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))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__Un__distrib1,axiom, % 14.79/14.63 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Times__Un__distrib1,axiom, % 14.79/14.63 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__Un__distrib2,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__comp__subset__Sigma,axiom, % 14.79/14.63 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_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)))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_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_C_2)))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_swap__product,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_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_A_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__cartesian__product,axiom, % 14.79/14.63 ! [V_B_2,T_c,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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)))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_equiv__type,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__Int__distrib2,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Times__Int__distrib1,axiom, % 14.79/14.63 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__Int__distrib1,axiom, % 14.79/14.63 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Id__on__subset__Times,axiom, % 14.79/14.63 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__Diff__distrib2,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Times__Diff__distrib1,axiom, % 14.79/14.63 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__Diff__distrib1,axiom, % 14.79/14.63 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_UNIV__Times__UNIV,axiom, % 14.79/14.63 ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_mem__Sigma__iff,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 14.79/14.63 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_SigmaD1,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_SigmaD2,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_SigmaE2,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 14.79/14.63 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_card__cartesian__product__singleton,axiom, % 14.79/14.63 ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Times__subset__cancel2,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)))) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Image__subset,axiom, % 14.79/14.63 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_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)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__cartesian__productD1,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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)))) % 14.79/14.63 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__cartesian__productD2,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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)))) % 14.79/14.63 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Collect__split,axiom, % 14.79/14.63 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_SetCompr__Sigma__eq,axiom, % 14.79/14.63 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Qa_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_fst__image__times,axiom, % 14.79/14.63 ! [V_A_2,T_c,T_b,V_B_2] : % 14.79/14.63 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.63 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_snd__image__times,axiom, % 14.79/14.63 ! [V_B_2,T_c,T_b,V_A_2] : % 14.79/14.63 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),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))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.63 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),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))) = V_B_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_insert__times__insert,axiom, % 14.79/14.63 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__equiv__class,axiom, % 14.79/14.63 ! [V_X_2,V_r_2,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_UN__Times__distrib,axiom, % 14.79/14.63 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__def,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,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_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),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_fun(tc_prod(T_b,T_c),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_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__quotient,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setsum__mult__setsum__if__inj,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : % 14.79/14.63 ( class_Rings_Osemiring__0(T_d) % 14.79/14.63 => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_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))) % 14.79/14.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),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_d,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(T_b,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_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),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_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),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_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 14.79/14.63 ! [V_A_2,V_I_2,T_c,T_b] : % 14.79/14.63 ? [B_f] : % 14.79/14.63 ( c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_fold__image__Sigma,axiom, % 14.79/14.63 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__mult(T_d) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 14.79/14.63 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_image__id,axiom, % 14.79/14.63 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_inj__on__id,axiom, % 14.79/14.63 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_apfst__id,axiom, % 14.79/14.63 ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_apsnd__id,axiom, % 14.79/14.63 ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_id__apply,axiom, % 14.79/14.63 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 14.79/14.63 % 14.79/14.63 fof(fact_id__def,axiom, % 14.79/14.63 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 14.79/14.63 % 14.79/14.63 fof(fact_vimage__id,axiom, % 14.79/14.63 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_of__int__eq__id,axiom, % 14.79/14.63 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 14.79/14.63 % 14.79/14.63 fof(fact_surj__id,axiom, % 14.79/14.63 ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_split__Pair,axiom, % 14.79/14.63 ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setsum__reindex__id,axiom, % 14.79/14.63 ! [V_B_2,V_f_2,T_b,T_c] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_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_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setprod__reindex__id,axiom, % 14.79/14.63 ! [V_B_2,V_f_2,T_b,T_c] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setprod__Sigma,axiom, % 14.79/14.63 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__mult(T_d) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),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_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setsum__Sigma,axiom, % 14.79/14.63 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_d) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),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_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_card__SigmaI,axiom, % 14.79/14.63 ! [V_B_2,T_c,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 14.79/14.63 => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__SigmaI,axiom, % 14.79/14.63 ! [V_B_2,T_c,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( ! [B_a] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_SigmaE,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 14.79/14.63 => ~ ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) % 14.79/14.63 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair__surj,axiom, % 14.79/14.63 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] : % 14.79/14.63 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) % 14.79/14.63 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair__imageI,axiom, % 14.79/14.63 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_fst__map__pair,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_snd__prod__fun,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair__simp,axiom, % 14.79/14.63 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair__ident,axiom, % 14.79/14.63 ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair_Oidentity,axiom, % 14.79/14.63 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_apfst__def,axiom, % 14.79/14.63 ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_apsnd__def,axiom, % 14.79/14.63 ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair_Oid,axiom, % 14.79/14.63 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair__def,axiom, % 14.79/14.63 ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair__surj__on,axiom, % 14.79/14.63 ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] : % 14.79/14.63 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 14.79/14.63 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 % 14.79/14.63 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wf__map__pair__image,axiom, % 14.79/14.63 ! [V_f_2,T_c,V_r_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.63 => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair__inj__on,axiom, % 14.79/14.63 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.63 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) % 14.79/14.63 => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,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))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_prod__fun__imageE,axiom, % 14.79/14.63 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) % 14.79/14.63 => ~ ! [B_x,B_y] : % 14.79/14.63 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__on__def,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 14.79/14.63 & ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_inj__on__INTER,axiom, % 14.79/14.63 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] : % 14.79/14.63 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 => ( ! [B_i] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) % 14.79/14.63 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) ) % 14.79/14.63 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__on__Id__on,axiom, % 14.79/14.63 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__on__empty,axiom, % 14.79/14.63 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__on__Un,axiom, % 14.79/14.63 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 14.79/14.63 => c_Relation_Orefl__on(T_b,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(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__on__Int,axiom, % 14.79/14.63 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 14.79/14.63 => c_Relation_Orefl__on(T_b,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(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__onD2,axiom, % 14.79/14.63 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__onD1,axiom, % 14.79/14.63 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__onD,axiom, % 14.79/14.63 ! [V_a_2,V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_reflp__def,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( c_Predicate_Oreflp(T_b,V_r_2) % 14.79/14.63 <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__onI,axiom, % 14.79/14.63 ! [V_A_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) % 14.79/14.63 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_pigeonhole__infinite,axiom, % 14.79/14.63 ! [V_f_2,T_c,V_A_2,T_b] : % 14.79/14.63 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.63 => ? [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_reflpE,axiom, % 14.79/14.63 ! [V_x_2,V_r_2,T_b] : % 14.79/14.63 ( c_Predicate_Oreflp(T_b,V_r_2) % 14.79/14.63 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__on__def_H,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 <=> ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) ) % 14.79/14.63 & ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Abs__Integ__induct,axiom, % 14.79/14.63 ! [V_x_2,V_Pa_2] : % 14.79/14.63 ( ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Abs__Integ__cases,axiom, % 14.79/14.63 ! [V_x_2] : % 14.79/14.63 ~ ! [B_y] : % 14.79/14.63 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_INFI__bool__eq,axiom, % 14.79/14.63 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ). % 14.79/14.63 % 14.79/14.63 fof(fact_ball__empty,axiom, % 14.79/14.63 ! [V_Pa_2,T_b,B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Powp__def,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) % 14.79/14.63 <=> ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 14.79/14.63 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Collect__ball__eq,axiom, % 14.79/14.63 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_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_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_congruent__def,axiom, % 14.79/14.63 ! [V_f_2,V_r_2,T_c,T_b] : % 14.79/14.63 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 14.79/14.63 <=> ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),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_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_INTER__def,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_b,T_c] : 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(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Inf__Sup,axiom, % 14.79/14.63 ! [V_A_2,T_b] : % 14.79/14.63 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.63 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sup__Inf,axiom, % 14.79/14.63 ! [V_A_2,T_b] : % 14.79/14.63 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.63 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__UN__I,axiom, % 14.79/14.63 ! [V_B_2,T_c,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( ! [B_a] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_inj__on__diff__nat,axiom, % 14.79/14.63 ! [V_k_2,V_N_2] : % 14.79/14.63 ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 14.79/14.63 => 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) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wfP__SUP,axiom, % 14.79/14.63 ! [T_b,V_r_2,T_c] : % 14.79/14.63 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) % 14.79/14.63 => ( ! [B_i,B_j] : % 14.79/14.63 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 14.79/14.63 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 14.79/14.63 => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Inter__eq,axiom, % 14.79/14.63 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,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_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_mem__splitI2,axiom, % 14.79/14.63 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] : % 14.79/14.63 ( ! [B_a,B_b] : % 14.79/14.63 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_mem__splitE,axiom, % 14.79/14.63 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),V_p_2))) % 14.79/14.63 => ~ ! [B_x,B_y] : % 14.79/14.63 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_vimage__Times,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair_Ocomp,axiom, % 14.79/14.63 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair__compose,axiom, % 14.79/14.63 ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_map__pair_Ocompositionality,axiom, % 14.79/14.63 ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_comp__surj,axiom, % 14.79/14.63 ! [V_g_2,T_d,V_f_2,T_b,T_c] : % 14.79/14.63 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) % 14.79/14.63 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_image__compose,axiom, % 14.79/14.63 ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_comp__inj__on__iff,axiom, % 14.79/14.63 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.63 => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) % 14.79/14.63 <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_comp__inj__on,axiom, % 14.79/14.63 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.63 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) % 14.79/14.63 => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_inj__on__imageI,axiom, % 14.79/14.63 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] : % 14.79/14.63 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2) % 14.79/14.63 => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_inj__on__imageI2,axiom, % 14.79/14.63 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] : % 14.79/14.63 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2) % 14.79/14.63 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_inj__comp,axiom, % 14.79/14.63 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.63 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 14.79/14.63 => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_vimage__compose,axiom, % 14.79/14.63 ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_o__def,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_K__record__comp,axiom, % 14.79/14.63 ! [V_x_2,V_f_2,V_ca_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 14.79/14.63 ! [V_x_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 14.79/14.63 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_o__eq__elim,axiom, % 14.79/14.63 ! [V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] : % 14.79/14.63 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2) % 14.79/14.63 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_o__eq__dest,axiom, % 14.79/14.63 ! [V_v_2,V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] : % 14.79/14.63 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2) % 14.79/14.63 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_o__apply,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_o__assoc,axiom, % 14.79/14.63 ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_o__eq__dest__lhs,axiom, % 14.79/14.63 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] : % 14.79/14.63 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2 % 14.79/14.63 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_comp__cong,axiom, % 14.79/14.63 ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 14.79/14.63 ( 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)) % 14.79/14.63 => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_fun__upd__comp,axiom, % 14.79/14.63 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_apsnd__compose,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_apfst__compose,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_o__id,axiom, % 14.79/14.63 ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_id__o,axiom, % 14.79/14.63 ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_o__eq__id__dest,axiom, % 14.79/14.63 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] : % 14.79/14.63 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_ca_2) % 14.79/14.63 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setsum__reindex,axiom, % 14.79/14.63 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_d) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setprod__reindex,axiom, % 14.79/14.63 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__mult(T_d) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setprod__reindex__cong,axiom, % 14.79/14.63 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__mult(T_d) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.63 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 14.79/14.63 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setsum_Oreindex,axiom, % 14.79/14.63 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setprod_Oreindex,axiom, % 14.79/14.63 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_the__inv__into__comp,axiom, % 14.79/14.63 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) % 14.79/14.63 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)))) % 14.79/14.63 => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_fold__image__reindex,axiom, % 14.79/14.63 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] : % 14.79/14.63 ( class_Groups_Oab__semigroup__mult(T_d) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) % 14.79/14.63 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Oremove,axiom, % 14.79/14.63 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.63 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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)))))),hAPP(V_f_2,V_x_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__image_Oreindex,axiom, % 14.79/14.63 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.79/14.63 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 14.79/14.63 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ounion,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.63 => ( 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)) % 14.79/14.63 => 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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_fst__comp__map__pair,axiom, % 14.79/14.63 ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_UN__o,axiom, % 14.79/14.63 ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ocommute__left__comp,axiom, % 14.79/14.63 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ocommute__comp,axiom, % 14.79/14.63 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 14.79/14.63 ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_snd__comp__map__pair,axiom, % 14.79/14.63 ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__image_Odistrib,axiom, % 14.79/14.63 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.79/14.63 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),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)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_split__comp,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 14.79/14.63 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ocommute__comp_H_H,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ocommute__left__comp_H,axiom, % 14.79/14.63 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ocommute__comp_H,axiom, % 14.79/14.63 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Oempty,axiom, % 14.79/14.63 ! [V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Oeq__fold,axiom, % 14.79/14.63 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__image_Oeq__fold,axiom, % 14.79/14.63 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.79/14.63 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Oinsert,axiom, % 14.79/14.63 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.63 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Ounion__inter,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding_Oinsert__remove,axiom, % 14.79/14.63 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setsum__reindex__nonzero,axiom, % 14.79/14.63 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_d) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 14.79/14.63 => ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) % 14.79/14.63 => ( B_x != B_y % 14.79/14.63 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 14.79/14.63 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__idem_Ounion__idem,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.63 => 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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__idem_Oidem__left__comp,axiom, % 14.79/14.63 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__idem_Oidem__comp,axiom, % 14.79/14.63 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__idem_Oin__comp__idem,axiom, % 14.79/14.63 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.63 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_folding__idem_Oinsert__idem,axiom, % 14.79/14.63 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 14.79/14.63 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 14.79/14.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_strong__setprod__reindex__cong,axiom, % 14.79/14.63 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__mult(T_d) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.63 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) ) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Eps__split,axiom, % 14.79/14.63 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wfI__pf,axiom, % 14.79/14.63 ! [V_R_2,T_b] : % 14.79/14.63 ( ! [B_A] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A))) % 14.79/14.63 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 14.79/14.63 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_tfl__some,axiom, % 14.79/14.63 ! [T_b,B_P] : % 14.79/14.63 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 14.79/14.63 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_someI,axiom, % 14.79/14.63 ! [T_b,V_x_2,V_Pa_2] : % 14.79/14.63 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_some__sym__eq__trivial,axiom, % 14.79/14.63 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_some__eq__trivial,axiom, % 14.79/14.63 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_some__eq__ex,axiom, % 14.79/14.63 ! [T_b,V_Pa_2] : % 14.79/14.63 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) % 14.79/14.63 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_someI__ex,axiom, % 14.79/14.63 ! [T_b,V_Pa_2] : % 14.79/14.63 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_exE__some,axiom, % 14.79/14.63 ! [T_b,V_ca_2,V_Pa_2] : % 14.79/14.63 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 14.79/14.63 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_split__paired__Eps,axiom, % 14.79/14.63 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Eps__split__eq,axiom, % 14.79/14.63 ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Sigma__mono,axiom, % 14.79/14.63 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) ) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_not__acc__down,axiom, % 14.79/14.63 ! [V_R_2,V_x_2,T_b] : % 14.79/14.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) % 14.79/14.63 => ~ ! [B_z] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_acc_OaccI,axiom, % 14.79/14.63 ! [V_r_2,V_x_2,T_b] : % 14.79/14.63 ( ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) ) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_max__ext_Osimps,axiom, % 14.79/14.63 ! [V_R_2,V_a2_2,V_a1_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 14.79/14.63 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 14.79/14.63 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 14.79/14.63 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 & ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 14.79/14.63 => ? [B_xa] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wf__no__infinite__down__chainE,axiom, % 14.79/14.63 ! [V_f_2,V_r_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.63 => ~ ! [B_k] : 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,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_iterate_Osimps,axiom, % 14.79/14.63 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 14.79/14.63 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.63 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) ) % 14.79/14.63 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.63 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,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)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_setsum__reindex__cong,axiom, % 14.79/14.63 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_d) % 14.79/14.63 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.63 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 14.79/14.63 => ( ! [B_a] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 14.79/14.63 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 14.79/14.63 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_scomp__apply,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Pair__scomp,axiom, % 14.79/14.63 ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_scomp__scomp,axiom, % 14.79/14.63 ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_scomp__Pair,axiom, % 14.79/14.63 ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_scomp__def,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_scomp__unfold,axiom, % 14.79/14.63 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_less__eq,axiom, % 14.79/14.63 ! [V_n_2,V_m_2] : % 14.79/14.63 ( 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))) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wf__eq__minimal,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.63 <=> ! [B_Q] : % 14.79/14.63 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 14.79/14.63 => ? [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 14.79/14.63 & ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wf__trancl,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.63 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_less__than__def,axiom, % 14.79/14.63 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 14.79/14.63 % 14.79/14.63 fof(fact_acyclic__def,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 14.79/14.63 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl_Or__into__trancl,axiom, % 14.79/14.63 ! [V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__subset__Field2,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_r__into__trancl_H,axiom, % 14.79/14.63 ! [V_r_2,V_p_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__empty,axiom, % 14.79/14.63 ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__domain,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__range,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__trancl,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_r__r__into__trancl,axiom, % 14.79/14.63 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2)) % 14.79/14.63 => ( 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_ca_2)),V_R_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__into__trancl2,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.63 => ( 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => ( 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_ca_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__trans,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => ( 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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__mono,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,V_p_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__unfold,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__subset__Sigma,axiom, % 14.79/14.63 ! [V_A_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__Int__subset,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__insert,axiom, % 14.79/14.63 ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_reflcl__set__eq,axiom, % 14.79/14.63 ! [V_y_2,V_x_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2)) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_r__into__rtrancl,axiom, % 14.79/14.63 ! [V_r_2,V_p_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl_Ortrancl__refl,axiom, % 14.79/14.63 ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_IdI,axiom, % 14.79/14.63 ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__into__rtrancl,axiom, % 14.79/14.63 ! [V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__rtrancl__absorb,axiom, % 14.79/14.63 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__trancl__absorb,axiom, % 14.79/14.63 ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_reflcl__trancl,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__reflcl,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__unfold__right,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__unfold__left,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__r__diff__Id,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__Int__subset,axiom, % 14.79/14.63 ! [V_r_2,V_s_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_r__comp__rtrancl__eq,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__idemp__self__comp,axiom, % 14.79/14.63 ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__unfold,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__Un__subset,axiom, % 14.79/14.63 ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__reflcl,axiom, % 14.79/14.63 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__Un__rtrancl,axiom, % 14.79/14.63 ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__reflcl__absorb,axiom, % 14.79/14.63 ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__subset__rtrancl,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__subset,axiom, % 14.79/14.63 ! [V_S_2,V_R_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 14.79/14.63 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__mono,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Image__closed__trancl,axiom, % 14.79/14.63 ! [V_X_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2)) % 14.79/14.63 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__rtrancl__UnI,axiom, % 14.79/14.63 ! [V_S_2,V_R_2,V_x_2,T_b] : % 14.79/14.63 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 14.79/14.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) ) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.63 => ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( 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_ca_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__trans,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__idemp,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__empty,axiom, % 14.79/14.63 ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Range__rtrancl,axiom, % 14.79/14.63 ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Domain__rtrancl,axiom, % 14.79/14.63 ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__rtrancl,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Image__Id,axiom, % 14.79/14.63 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_Id__O__R,axiom, % 14.79/14.63 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_R__O__Id,axiom, % 14.79/14.63 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_pair__in__Id__conv,axiom, % 14.79/14.63 ! [V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b))) % 14.79/14.63 <=> V_a_2 = V_b_2 ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__eq__or__trancl,axiom, % 14.79/14.63 ! [V_R_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 14.79/14.63 <=> ( V_x_2 = V_y_2 % 14.79/14.63 | ( V_x_2 != V_y_2 % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__into__trancl2,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.63 => ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtranclD,axiom, % 14.79/14.63 ! [V_R_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 14.79/14.63 => ( V_a_2 = V_b_2 % 14.79/14.63 | ( V_a_2 != V_b_2 % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__into__trancl1,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( 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_ca_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__rtrancl__trancl,axiom, % 14.79/14.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => ( 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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__trancl__trancl,axiom, % 14.79/14.63 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Domain__Id,axiom, % 14.79/14.63 ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Range__Id,axiom, % 14.79/14.63 ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__Id,axiom, % 14.79/14.63 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_pair__leq__def,axiom, % 14.79/14.63 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))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Not__Domain__rtrancl,axiom, % 14.79/14.63 ! [V_y_2,V_R_2,V_x_2,T_b] : % 14.79/14.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 14.79/14.63 <=> V_x_2 = V_y_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_acc__downwards__aux,axiom, % 14.79/14.63 ! [V_r_2,V_a_2,V_b_2,T_b] : % 14.79/14.63 ( 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_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_acc__downwards,axiom, % 14.79/14.63 ! [V_b_2,V_r_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 14.79/14.63 => ( 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_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wf__insert,axiom, % 14.79/14.63 ! [V_r_2,V_x_2,V_y_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) % 14.79/14.63 <=> ( c_Wellfounded_Owf(T_b,V_r_2) % 14.79/14.63 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_acyclic__insert,axiom, % 14.79/14.63 ! [V_r_2,V_x_2,V_y_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) % 14.79/14.63 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 14.79/14.63 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__reflcl,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Id__def,axiom, % 14.79/14.63 ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_irrefl__diff__Id,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_pred__nat__trancl__eq__le,axiom, % 14.79/14.63 ! [V_n_2,V_m_2] : % 14.79/14.63 ( 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))) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__subset__Sigma__aux,axiom, % 14.79/14.63 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 14.79/14.63 => ( V_a_2 = V_b_2 % 14.79/14.63 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_irrefl__tranclI,axiom, % 14.79/14.63 ! [V_x_2,V_r_2,T_b] : % 14.79/14.63 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_sequence__trans,axiom, % 14.79/14.63 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] : % 14.79/14.63 ( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => 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,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_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__converse,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__Id,axiom, % 14.79/14.63 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__INTER,axiom, % 14.79/14.63 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__UNION,axiom, % 14.79/14.63 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__iff,axiom, % 14.79/14.63 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converseI,axiom, % 14.79/14.63 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converseD,axiom, % 14.79/14.63 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__rel__comp,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__Un,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Field__converse,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__inv__image,axiom, % 14.79/14.63 ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__converse,axiom, % 14.79/14.63 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__Int,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__converse,axiom, % 14.79/14.63 ! [V_r_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 14.79/14.63 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__Id__on,axiom, % 14.79/14.63 ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_acyclic__converse,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 14.79/14.63 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__on__converse,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 14.79/14.63 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__converse,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wf__converse__trancl,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 14.79/14.63 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_equiv__comp__eq,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.63 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Range__converse,axiom, % 14.79/14.63 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Domain__converse,axiom, % 14.79/14.63 ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Range__def,axiom, % 14.79/14.63 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__converseD,axiom, % 14.79/14.63 ! [V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__converseI,axiom, % 14.79/14.63 ! [V_r_2,V_x_2,V_y_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__converseD,axiom, % 14.79/14.63 ! [V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__converseI,axiom, % 14.79/14.63 ! [V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Image__subset__eq,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2)) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_refl__on__comp__subset,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_comp__equivI,axiom, % 14.79/14.63 ! [V_A_2,V_r_2,T_b] : % 14.79/14.63 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 % 14.79/14.63 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 % 14.79/14.63 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__acyclic__wf__converse,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 14.79/14.63 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 14.79/14.63 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converse__def,axiom, % 14.79/14.63 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),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_r_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Image__INT__eq,axiom, % 14.79/14.63 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] : % 14.79/14.63 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) % 14.79/14.63 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 14.79/14.63 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_total__on__diff__Id,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) % 14.79/14.63 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_single__valued__Id,axiom, % 14.79/14.63 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_single__valued__rel__comp,axiom, % 14.79/14.63 ! [V_s_2,T_d,V_r_2,T_c,T_b] : % 14.79/14.63 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 14.79/14.63 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 14.79/14.63 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_single__valued__subset,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.63 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 14.79/14.63 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_single__valued__Id__on,axiom, % 14.79/14.63 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_total__on__empty,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_total__on__converse,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 14.79/14.63 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_single__valuedD,axiom, % 14.79/14.63 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] : % 14.79/14.63 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 14.79/14.63 => ( 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)),V_r_2)) % 14.79/14.63 => ( 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_z_2)),V_r_2)) % 14.79/14.63 => V_y_2 = V_z_2 ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_single__valued__def,axiom, % 14.79/14.63 ! [V_r_2,T_c,T_b] : % 14.79/14.63 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 14.79/14.63 <=> ! [B_x,B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) % 14.79/14.63 => ! [B_z] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) % 14.79/14.63 => B_y = B_z ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_total__on__def,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2) % 14.79/14.63 <=> ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.63 => ! [B_xa] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 14.79/14.63 => ( B_x != B_xa % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2)) % 14.79/14.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_single__valued__confluent,axiom, % 14.79/14.63 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 14.79/14.63 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Image__Int__eq,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : % 14.79/14.63 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) % 14.79/14.63 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 14.79/14.63 ! [V_R_2,V_p_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),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_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_acyclicI,axiom, % 14.79/14.63 ! [V_r_2,T_b] : % 14.79/14.63 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 14.79/14.63 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_single__valued__rel__pow,axiom, % 14.79/14.63 ! [V_n_2,V_R_2,T_b] : % 14.79/14.63 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2) % 14.79/14.63 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_funpow__swap1,axiom, % 14.79/14.63 ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_funpow__mult,axiom, % 14.79/14.63 ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_wf__exp,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,T_b] : % 14.79/14.63 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) % 14.79/14.63 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_comp__funpow,axiom, % 14.79/14.63 ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__1,axiom, % 14.79/14.63 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__commute,axiom, % 14.79/14.63 ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__power,axiom, % 14.79/14.63 ! [V_R_2,V_p_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 14.79/14.63 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__imp__rtrancl,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,V_p_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_relpow_Osimps_I2_J,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__add,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),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_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_relpow_Osimps_I1_J,axiom, % 14.79/14.63 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__0__E,axiom, % 14.79/14.63 ! [V_R_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) % 14.79/14.63 => V_x_2 = V_y_2 ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__0__I,axiom, % 14.79/14.63 ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__Suc__I2,axiom, % 14.79/14.63 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__Suc__I,axiom, % 14.79/14.63 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_funpow_Osimps_I2_J,axiom, % 14.79/14.63 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_funpow__add,axiom, % 14.79/14.63 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_funpow_Osimps_I1_J,axiom, % 14.79/14.63 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ). % 14.79/14.63 % 14.79/14.63 fof(fact_trancl__power,axiom, % 14.79/14.63 ! [V_R_2,V_p_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 14.79/14.63 <=> ? [B_n] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 14.79/14.63 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),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_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_funpow__code__def,axiom, % 14.79/14.63 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__E2,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 14.79/14.63 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 => V_x_2 != V_z_2 ) % 14.79/14.63 => ~ ! [B_y,B_m] : % 14.79/14.63 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__E,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 14.79/14.63 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 => V_x_2 != V_z_2 ) % 14.79/14.63 => ~ ! [B_y,B_m] : % 14.79/14.63 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__Un__separatorE,axiom, % 14.79/14.63 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2)))) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) % 14.79/14.63 => ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Qa_2)) % 14.79/14.63 => B_x = B_y ) ) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__Un__separator__converseE,axiom, % 14.79/14.63 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2)))) % 14.79/14.63 => ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) % 14.79/14.63 => ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Qa_2)) % 14.79/14.63 => B_y = B_x ) ) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__Suc__D2,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 14.79/14.63 => ? [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__Suc__E,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 14.79/14.63 => ~ ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__pow__Suc__E2,axiom, % 14.79/14.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 14.79/14.63 => ~ ! [B_y] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_tranclD,axiom, % 14.79/14.63 ! [V_R_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 14.79/14.63 => ? [B_z] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_tranclD2,axiom, % 14.79/14.63 ! [V_R_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 14.79/14.63 => ? [B_z] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_IdE,axiom, % 14.79/14.63 ! [V_p_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) % 14.79/14.63 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_transfer__nat__int__set__cong,axiom, % 14.79/14.63 ! [V_P_Ha_2,V_Pa_2] : % 14.79/14.63 ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 14.79/14.63 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.79/14.63 <=> hBOOL(hAPP(V_P_Ha_2,B_x)) ) ) % 14.79/14.63 => 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_Pa_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_Ha_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_converseE,axiom, % 14.79/14.63 ! [V_r_2,V_yx_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 14.79/14.63 => ~ ! [B_x,B_y] : % 14.79/14.63 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rel__compE,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2))) % 14.79/14.63 => ~ ! [B_x,B_y,B_z] : % 14.79/14.63 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Oplus__frac__def,axiom, % 14.79/14.63 ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),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_b),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_b),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_b),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_b),V_r_2)))))),c_COMBI(tc_Int_Oint))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_internal__split__def,axiom, % 14.79/14.63 ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d) ). % 14.79/14.63 % 14.79/14.63 fof(fact_internal__split__conv,axiom, % 14.79/14.63 ! [V_b_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Otimes__frac__def,axiom, % 14.79/14.63 ! [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))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Oof__frac__def,axiom, % 14.79/14.63 ! [V_q,T_a,T_b] : % 14.79/14.63 ( ( class_Rings_Oinverse(T_b) % 14.79/14.63 & class_Rings_Oring__1(T_b) ) % 14.79/14.63 => 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))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 14.79/14.63 ! [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))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Oless__frac__def,axiom, % 14.79/14.63 ! [V_r_2,V_q_2,T_b] : % 14.79/14.63 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 14.79/14.63 ! [V_r_2,V_q_2,T_b] : % 14.79/14.63 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Odenom__def,axiom, % 14.79/14.63 ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Onum__def,axiom, % 14.79/14.63 ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_bool_Osize_I2_J,axiom, % 14.79/14.63 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.63 % 14.79/14.63 fof(fact_bool_Osize_I1_J,axiom, % 14.79/14.63 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__less__ub,axiom, % 14.79/14.63 ! [V_u_2,V_f_2] : % 14.79/14.63 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 14.79/14.63 => 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)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lenlex__def,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lexn__length,axiom, % 14.79/14.63 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2))) % 14.79/14.63 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 % 14.79/14.63 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_neq__if__length__neq,axiom, % 14.79/14.63 ! [V_ys,V_xs,T_a] : % 14.79/14.63 ( 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) % 14.79/14.63 => V_xs != V_ys ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lenlex__conv,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_length__sublist,axiom, % 14.79/14.63 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,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_b)),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)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lexn_Osimps_I2_J,axiom, % 14.79/14.63 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,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_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_impossible__Cons,axiom, % 14.79/14.63 ! [V_x,V_ys,V_xs,T_a] : % 14.79/14.63 ( 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))) % 14.79/14.63 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_not__Cons__self,axiom, % 14.79/14.63 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 14.79/14.63 % 14.79/14.63 fof(fact_not__Cons__self2,axiom, % 14.79/14.63 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 14.79/14.63 % 14.79/14.63 fof(fact_list_Oinject,axiom, % 14.79/14.63 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] : % 14.79/14.63 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2) % 14.79/14.63 <=> ( V_a_2 = V_a_H_2 % 14.79/14.63 & V_list_2 = V_list_H_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list_Osize_I4_J,axiom, % 14.79/14.63 ! [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))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Cons__in__lex,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2))) % 14.79/14.63 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.63 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) % 14.79/14.63 | ( V_x_2 = V_y_2 % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__Cons__def,axiom, % 14.79/14.63 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),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_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_pick_Osimps,axiom, % 14.79/14.63 ! [V_xs,V_x,T_a,V_i] : % 14.79/14.63 ( ( 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))) % 14.79/14.63 => 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) ) % 14.79/14.63 & ( ~ 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))) % 14.79/14.63 => 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))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_select__weight__cons__zero,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lexord__cons__cons,axiom, % 14.79/14.63 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) % 14.79/14.63 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.63 | ( V_a_2 = V_b_2 % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lexord__lex,axiom, % 14.79/14.63 ! [V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2))) % 14.79/14.63 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 14.79/14.63 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 14.79/14.63 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list_Osize_I2_J,axiom, % 14.79/14.63 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),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_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Cons__acc__listrel1I,axiom, % 14.79/14.63 ! [V_xs_2,V_r_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel1__mono,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel1__converse,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 14.79/14.63 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel1I2,axiom, % 14.79/14.63 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__listrel1__eq__len,axiom, % 14.79/14.63 ! [V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 14.79/14.63 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel1__eq__len,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.63 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__listrel1__converse,axiom, % 14.79/14.63 ! [V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Cons__listrel1__Cons,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.63 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.63 & V_xs_2 = V_ys_2 ) % 14.79/14.63 | ( V_x_2 = V_y_2 % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel1I1,axiom, % 14.79/14.63 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__Cons,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lexord__linear,axiom, % 14.79/14.63 ! [V_y_2,V_x_2,V_r_2,T_b] : % 14.79/14.63 ( ! [B_a,B_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) % 14.79/14.63 | B_a = B_b % 14.79/14.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)) ) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 14.79/14.63 | V_x_2 = V_y_2 % 14.79/14.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__rtrancl__refl,axiom, % 14.79/14.63 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__mono,axiom, % 14.79/14.63 ! [V_s_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__eq__len,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__rtrancl__trans,axiom, % 14.79/14.63 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__reflcl__if__listrel1,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel1__subset__listrel,axiom, % 14.79/14.63 ! [V_r_H_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) % 14.79/14.63 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel_OCons,axiom, % 14.79/14.63 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrelp__listrel__eq,axiom, % 14.79/14.63 ! [V_xa_2,V_x_2,V_r_2,T_b] : % 14.79/14.63 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__Cons1,axiom, % 14.79/14.63 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 => ~ ! [B_y,B_ys] : % 14.79/14.63 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrelp_OCons,axiom, % 14.79/14.63 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 14.79/14.63 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) % 14.79/14.63 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrelp_Oequations_I2_J,axiom, % 14.79/14.63 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] : % 14.79/14.63 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2)) % 14.79/14.63 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 14.79/14.63 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__Cons2,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 => ~ ! [B_x,B_xs] : % 14.79/14.63 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__subset,axiom, % 14.79/14.63 ! [V_A_2,V_r_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lists__UNIV,axiom, % 14.79/14.63 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lists__mono,axiom, % 14.79/14.63 ! [V_B_2,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_equiv__listrel,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.63 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__refl__on,axiom, % 14.79/14.63 ! [V_r_2,V_A_2,T_b] : % 14.79/14.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.63 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Cons__in__lists__iff,axiom, % 14.79/14.63 ! [V_A_2,V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2))) % 14.79/14.63 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lists__accD,axiom, % 14.79/14.63 ! [V_r_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lists__accI,axiom, % 14.79/14.63 ! [V_r_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__iff__nth,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 14.79/14.63 & ! [B_n] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lexord__irreflexive,axiom, % 14.79/14.63 ! [V_y_2,V_r_2,T_b] : % 14.79/14.63 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_infinite__UNIV__listI,axiom, % 14.79/14.63 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__eq__iff__nth__eq,axiom, % 14.79/14.63 ! [T_b,V_ys_2,V_xs_2] : % 14.79/14.63 ( V_xs_2 = V_ys_2 % 14.79/14.63 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 14.79/14.63 & ! [B_i] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__Cons__Suc,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__Cons__0,axiom, % 14.79/14.63 ! [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 ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth_Osimps,axiom, % 14.79/14.63 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__Cons_H,axiom, % 14.79/14.63 ! [V_xs,V_x,T_a,V_n] : % 14.79/14.63 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 14.79/14.63 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 => 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))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__Cons__number__of,axiom, % 14.79/14.63 ! [V_xs,V_x,T_a,V_v] : % 14.79/14.63 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 => 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 ) % 14.79/14.63 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 => 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))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lexord__take__index__conv,axiom, % 14.79/14.63 ! [V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 14.79/14.63 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) % 14.79/14.63 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 ) % 14.79/14.63 | ? [B_i] : % 14.79/14.63 ( 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_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) % 14.79/14.63 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__sublist,axiom, % 14.79/14.63 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),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_b)),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))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__set,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__subset__Cons,axiom, % 14.79/14.63 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__all,axiom, % 14.79/14.63 ! [V_n,V_xs,T_a] : % 14.79/14.63 ( 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)) % 14.79/14.63 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__take__subset__set__take,axiom, % 14.79/14.63 ! [V_xs_2,T_b,V_n_2,V_m_2] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__take__subset,axiom, % 14.79/14.63 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__sublist__subset,axiom, % 14.79/14.63 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__take,axiom, % 14.79/14.63 ! [V_xs,T_a,V_n,V_i] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 14.79/14.63 => 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) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__Suc__Cons,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__ConsD,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,V_y_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) % 14.79/14.63 => ( V_y_2 = V_x_2 % 14.79/14.63 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__set__sublistD,axiom, % 14.79/14.63 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__set__takeD,axiom, % 14.79/14.63 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_notin__set__sublistI,axiom, % 14.79/14.63 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_length__take,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__take,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_List_Oset_Osimps_I2_J,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_sublist__upt__eq__take,axiom, % 14.79/14.63 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_card__length,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_all__set__conv__all__nth,axiom, % 14.79/14.63 ! [V_Pa_2,V_xs_2,T_b] : % 14.79/14.63 ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.63 <=> ! [B_i] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__size__estimation,axiom, % 14.79/14.63 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__size__estimation_H,axiom, % 14.79/14.63 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__lists__conv__set,axiom, % 14.79/14.63 ! [V_A_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 14.79/14.63 <=> ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_length__pos__if__in__set,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => 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_b)),V_xs_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__set__conv__nth,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 <=> ? [B_i] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__mem,axiom, % 14.79/14.63 ! [V_xs_2,T_b,V_n_2] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lists__eq__set,axiom, % 14.79/14.63 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__conv__nth,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),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_b)),V_xs_2))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__lists__length__eq,axiom, % 14.79/14.63 ! [V_n_2,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_finite__lists__length__le,axiom, % 14.79/14.63 ! [V_n_2,V_A_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__iff__zip,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 14.79/14.63 & ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__zip,axiom, % 14.79/14.63 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),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_b,T_c)),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_b,T_c)),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_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__zip,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_length__zip,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_zip__Cons__Cons,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__eq__iff__zip__eq,axiom, % 14.79/14.63 ! [T_b,V_ys_2,V_xs_2] : % 14.79/14.63 ( V_xs_2 = V_ys_2 % 14.79/14.63 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 14.79/14.63 & ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__set__zipE,axiom, % 14.79/14.63 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 14.79/14.63 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 14.79/14.63 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__zip__rightD,axiom, % 14.79/14.63 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 14.79/14.63 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__zip__leftD,axiom, % 14.79/14.63 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 14.79/14.63 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_zip__same,axiom, % 14.79/14.63 ! [V_xs_2,V_b_2,V_a_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2)))) % 14.79/14.63 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 & V_a_2 = V_b_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__zip,axiom, % 14.79/14.63 ! [V_ys,T_b,V_xs,T_a,V_i] : % 14.79/14.63 ( 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))) % 14.79/14.63 => ( 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))) % 14.79/14.63 => 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)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_greaterThanLessThan__upto,axiom, % 14.79/14.63 ! [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)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listsum__setsum__nth,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.63 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),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_b)),V_xs_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 14.79/14.63 ! [V_ns_2] : % 14.79/14.63 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 <=> ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 14.79/14.63 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_atLeastAtMost__upto,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__upto,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_elem__le__listsum__nat,axiom, % 14.79/14.63 ! [V_ns,V_k] : % 14.79/14.63 ( 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))) % 14.79/14.63 => 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))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listsum__simps_I2_J,axiom, % 14.79/14.63 ! [V_xs,V_x,T_a] : % 14.79/14.63 ( class_Groups_Omonoid__add(T_a) % 14.79/14.63 => 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)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_atLeastLessThan__upto,axiom, % 14.79/14.63 ! [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)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_greaterThanAtMost__upto,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nat__list__def,axiom, % 14.79/14.63 ! [V_l_2] : % 14.79/14.63 ( c_List_Onat__list(V_l_2) % 14.79/14.63 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__size__pointwise,axiom, % 14.79/14.63 ! [V_g_2,V_f_2,V_xs_2,T_b] : % 14.79/14.63 ( ! [B_x] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listsum__update__nat,axiom, % 14.79/14.63 ! [V_n,V_ns,V_k] : % 14.79/14.63 ( 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))) % 14.79/14.63 => 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)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_butlast__take,axiom, % 14.79/14.63 ! [V_xs,T_a,V_n] : % 14.79/14.63 ( 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))) % 14.79/14.63 => 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) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__beyond,axiom, % 14.79/14.63 ! [V_x,V_i,V_xs,T_a] : % 14.79/14.63 ( 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)) % 14.79/14.63 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__list__update__neq,axiom, % 14.79/14.63 ! [V_x,V_xs,T_a,V_j,V_i] : % 14.79/14.63 ( V_i != V_j % 14.79/14.63 => 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) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__id,axiom, % 14.79/14.63 ! [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 ). % 14.79/14.63 % 14.79/14.63 fof(fact_butlast__list__update,axiom, % 14.79/14.63 ! [V_x,V_xs,T_a,V_k] : % 14.79/14.63 ( ( 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)) % 14.79/14.63 => 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) ) % 14.79/14.63 & ( 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)) % 14.79/14.63 => 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) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_length__list__update,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_zip__update,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_update__zip,axiom, % 14.79/14.63 ! [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))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__overwrite,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__swap,axiom, % 14.79/14.63 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 14.79/14.63 ( V_i != V_i_H % 14.79/14.63 => 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) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update_Osimps_I2_J,axiom, % 14.79/14.63 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__code_I3_J,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__code_I2_J,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__set__butlastD,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__update__subsetI,axiom, % 14.79/14.63 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2)) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__update__subset__insert,axiom, % 14.79/14.63 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__list__update__eq,axiom, % 14.79/14.63 ! [V_x,V_xs,T_a,V_i] : % 14.79/14.63 ( 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))) % 14.79/14.63 => 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 ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__same__conv,axiom, % 14.79/14.63 ! [V_x_2,V_xs_2,T_b,V_i_2] : % 14.79/14.63 ( 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_xs_2))) % 14.79/14.63 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 14.79/14.63 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__list__update,axiom, % 14.79/14.63 ! [V_x,V_j,V_xs,T_a,V_i] : % 14.79/14.63 ( 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))) % 14.79/14.63 => ( ( V_i = V_j % 14.79/14.63 => 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 ) % 14.79/14.63 & ( V_i != V_j % 14.79/14.63 => 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) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__butlast,axiom, % 14.79/14.63 ! [V_xs,T_a,V_n] : % 14.79/14.63 ( 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))) % 14.79/14.63 => 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) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_length__butlast,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__update__memI,axiom, % 14.79/14.63 ! [V_x_2,V_xs_2,T_b,V_n_2] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_butlast__conv__take,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel1__iff__update,axiom, % 14.79/14.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.63 <=> ? [B_y,B_n] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) % 14.79/14.63 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__list__update,axiom, % 14.79/14.63 ! [V_i_2,V_a_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.63 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 14.79/14.63 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__upto,axiom, % 14.79/14.63 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__take,axiom, % 14.79/14.63 ! [V_i,V_xs,T_a] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.63 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__sublistI,axiom, % 14.79/14.63 ! [V_I_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.63 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__zipI1,axiom, % 14.79/14.63 ! [V_ys,T_b,V_xs,T_a] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.63 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__zipI2,axiom, % 14.79/14.63 ! [V_xs,T_b,V_ys,T_a] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 14.79/14.63 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct_Osimps_I2_J,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) % 14.79/14.63 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__card,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.63 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_card__distinct,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 14.79/14.63 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__eq__iff__index__eq,axiom, % 14.79/14.63 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.63 => ( 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_xs_2))) % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) % 14.79/14.63 <=> V_i_2 = V_j_2 ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__conv__nth,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.63 <=> ! [B_i] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 => ! [B_j] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.63 => ( B_i != B_j % 14.79/14.63 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__listsum__conv__Setsum,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.63 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_Nitpick_Ocard_H__def,axiom, % 14.79/14.63 ! [V_A_2,T_b] : % 14.79/14.63 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) ) % 14.79/14.63 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.63 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_nth__take__lemma,axiom, % 14.79/14.63 ! [V_ys,V_xs,T_a,V_k] : % 14.79/14.63 ( 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))) % 14.79/14.63 => ( 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))) % 14.79/14.63 => ( ! [B_i] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 14.79/14.63 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 14.79/14.63 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__remove1__eq,axiom, % 14.79/14.63 ! [V_x_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.63 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__Cons__number__of,axiom, % 14.79/14.63 ! [V_xs,V_x,T_a,V_v] : % 14.79/14.63 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 => 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) ) % 14.79/14.63 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 => 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)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_lists_ONil,axiom, % 14.79/14.63 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__Nil2,axiom, % 14.79/14.63 ! [V_r_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel__Nil1,axiom, % 14.79/14.63 ! [V_r_2,V_xs_2,T_b] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) % 14.79/14.63 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__butlast,axiom, % 14.79/14.63 ! [T_a,V_xs] : % 14.79/14.63 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.63 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct__remove1,axiom, % 14.79/14.63 ! [V_x,V_xs,T_a] : % 14.79/14.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_distinct_Osimps_I1_J,axiom, % 14.79/14.63 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_butlast_Osimps_I1_J,axiom, % 14.79/14.63 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 14.79/14.63 % 14.79/14.63 fof(fact_butlast_Osimps_I2_J,axiom, % 14.79/14.63 ! [V_x,T_a,V_xs] : % 14.79/14.63 ( ( V_xs = c_List_Olist_ONil(T_a) % 14.79/14.63 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 14.79/14.63 & ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.63 => 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)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list_Osimps_I2_J,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list_Osimps_I3_J,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_remove1_Osimps_I2_J,axiom, % 14.79/14.63 ! [V_xs,T_a,V_y,V_x] : % 14.79/14.63 ( ( V_x = V_y % 14.79/14.63 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 14.79/14.63 & ( V_x != V_y % 14.79/14.63 => 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)) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_upto__empty,axiom, % 14.79/14.63 ! [V_i,V_j] : % 14.79/14.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 14.79/14.63 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__Nil,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__eq__Nil,axiom, % 14.79/14.63 ! [V_xs_2,V_n_2,T_b] : % 14.79/14.63 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 14.79/14.63 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__0,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_sublist__nil,axiom, % 14.79/14.63 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ). % 14.79/14.63 % 14.79/14.63 fof(fact_remove1__commute,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_remove1_Osimps_I1_J,axiom, % 14.79/14.63 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrelp_Oequations_I1_J,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrelp_ONil,axiom, % 14.79/14.63 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_zip__Nil,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_zip_Osimps_I1_J,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listsum__simps_I1_J,axiom, % 14.79/14.63 ! [T_a] : % 14.79/14.63 ( class_Groups_Omonoid__add(T_a) % 14.79/14.63 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_length__0__conv,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list_Osize_I3_J,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_List_Oset_Osimps_I1_J,axiom, % 14.79/14.63 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__empty2,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) % 14.79/14.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__empty,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list_Osize_I1_J,axiom, % 14.79/14.63 ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__code_I1_J,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update_Osimps_I1_J,axiom, % 14.79/14.63 ! [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) ). % 14.79/14.63 % 14.79/14.63 fof(fact_list__update__nonempty,axiom, % 14.79/14.63 ! [V_x_2,V_k_2,V_xs_2,T_b] : % 14.79/14.63 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) % 14.79/14.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_in__set__remove1,axiom, % 14.79/14.63 ! [V_xs_2,T_b,V_b_2,V_a_2] : % 14.79/14.63 ( V_a_2 != V_b_2 % 14.79/14.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2)))) % 14.79/14.63 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_notin__set__remove1,axiom, % 14.79/14.63 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_remove1__idem,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.63 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_sublist__empty,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ). % 14.79/14.63 % 14.79/14.63 fof(fact_set__remove1__subset,axiom, % 14.79/14.63 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_length__greater__0__conv,axiom, % 14.79/14.63 ! [V_xs_2,T_b] : % 14.79/14.63 ( 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_b)),V_xs_2))) % 14.79/14.63 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ). % 14.79/14.63 % 14.79/14.63 fof(fact_take__1__Cons,axiom, % 14.79/14.63 ! [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)) ). % 14.79/14.63 % 14.79/14.63 fof(fact_not__listrel1__Nil,axiom, % 14.79/14.63 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_not__Nil__listrel1,axiom, % 14.79/14.63 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ). % 14.79/14.63 % 14.79/14.63 fof(fact_listrel_ONil,axiom, % 14.79/14.63 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lexord__Nil__right,axiom, % 14.79/14.64 ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Nil2__notin__lex,axiom, % 14.79/14.64 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Nil__notin__lex,axiom, % 14.79/14.64 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__Cons,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upto_Osimps,axiom, % 14.79/14.64 ! [V_j,V_i] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 14.79/14.64 => 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)) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 14.79/14.64 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublist__singleton,axiom, % 14.79/14.64 ! [V_x_2,T_b,V_A_2] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 14.79/14.64 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 14.79/14.64 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lists__empty,axiom, % 14.79/14.64 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__Cons_H,axiom, % 14.79/14.64 ! [V_xs,V_x,T_a,V_n] : % 14.79/14.64 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 => 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) ) % 14.79/14.64 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 => 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)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upto__rec__number__of,axiom, % 14.79/14.64 ! [V_n,V_m] : % 14.79/14.64 ( ( 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))) % 14.79/14.64 => 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))) ) % 14.79/14.64 & ( ~ 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))) % 14.79/14.64 => 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) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listrel__Nil,axiom, % 14.79/14.64 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__Cons__sing__Nil,axiom, % 14.79/14.64 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__remove1,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,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_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upto_Opsimps,axiom, % 14.79/14.64 ! [V_j_2,V_i_2] : % 14.79/14.64 ( 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))) % 14.79/14.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 14.79/14.64 => 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)) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 14.79/14.64 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_select,axiom, % 14.79/14.64 ! [V_s_2,T_b,V_xs_2] : % 14.79/14.64 ( V_xs_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listset_Osimps_I1_J,axiom, % 14.79/14.64 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__Cons1,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list_Osimps_I5_J,axiom, % 14.79/14.64 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list_Osimps_I4_J,axiom, % 14.79/14.64 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ). % 14.79/14.64 % 14.79/14.64 fof(fact_listset_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__Cons,axiom, % 14.79/14.64 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__list__of__set__remove,axiom, % 14.79/14.64 ! [V_x_2,V_A_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.64 => c_List_Olinorder__class_Osorted__list__of__set(T_b,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))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upto_Opinduct,axiom, % 14.79/14.64 ! [V_Pa_2,V_a1_2,V_a0_2] : % 14.79/14.64 ( 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))) % 14.79/14.64 => ( ! [B_i,B_j] : % 14.79/14.64 ( 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))) % 14.79/14.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 14.79/14.64 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) ) % 14.79/14.64 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 14.79/14.64 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__list__of__set__empty,axiom, % 14.79/14.64 ! [T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_anamorph_Osimps,axiom, % 14.79/14.64 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 14.79/14.64 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.64 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) ) % 14.79/14.64 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.64 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,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)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublist__Cons,axiom, % 14.79/14.64 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),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_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,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)))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__eq__Cons__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) % 14.79/14.64 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 14.79/14.64 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) % 14.79/14.64 | ? [B_ys_H] : % 14.79/14.64 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) % 14.79/14.64 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Cons__eq__append__conv,axiom, % 14.79/14.64 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) % 14.79/14.64 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 14.79/14.64 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 ) % 14.79/14.64 | ? [B_ys_H] : % 14.79/14.64 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 % 14.79/14.64 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append1__eq__conv,axiom, % 14.79/14.64 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) % 14.79/14.64 <=> ( V_xs_2 = V_ys_2 % 14.79/14.64 & V_x_2 = V_y_2 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__Cons,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Cons__eq__appendI,axiom, % 14.79/14.64 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 14.79/14.64 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 14.79/14.64 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 14.79/14.64 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__in__lists__conv,axiom, % 14.79/14.64 ! [V_A_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2))) % 14.79/14.64 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 14.79/14.64 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__eq__appendI,axiom, % 14.79/14.64 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 14.79/14.64 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 14.79/14.64 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__same__eq,axiom, % 14.79/14.64 ! [V_zs_2,V_xs_2,V_ys_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2) % 14.79/14.64 <=> V_ys_2 = V_zs_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_same__append__eq,axiom, % 14.79/14.64 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2) % 14.79/14.64 <=> V_ys_2 = V_zs_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__eq__append__conv2,axiom, % 14.79/14.64 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2) % 14.79/14.64 <=> ? [B_us] : % 14.79/14.64 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) % 14.79/14.64 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 ) % 14.79/14.64 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 % 14.79/14.64 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__assoc,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__append,axiom, % 14.79/14.64 ! [V_ys,V_xs,T_a] : % 14.79/14.64 ( class_Groups_Omonoid__add(T_a) % 14.79/14.64 => 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__append,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__append,axiom, % 14.79/14.64 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 14.79/14.64 ( 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) % 14.79/14.64 => ( 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) % 14.79/14.64 => 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)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__append,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__Nil,axiom, % 14.79/14.64 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 14.79/14.64 % 14.79/14.64 fof(fact_Nil__is__append__conv,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 14.79/14.64 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 14.79/14.64 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__Nil2,axiom, % 14.79/14.64 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 14.79/14.64 % 14.79/14.64 fof(fact_self__append__conv,axiom, % 14.79/14.64 ! [V_ys_2,T_b,V_xs_2] : % 14.79/14.64 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 14.79/14.64 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_self__append__conv2,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_ys_2] : % 14.79/14.64 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__is__Nil__conv,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 14.79/14.64 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__self__conv,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 % 14.79/14.64 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__self__conv2,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_eq__Nil__appendI,axiom, % 14.79/14.64 ! [T_a,V_ys,V_xs] : % 14.79/14.64 ( V_xs = V_ys % 14.79/14.64 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_butlast__append,axiom, % 14.79/14.64 ! [V_xs,T_a,V_ys] : % 14.79/14.64 ( ( V_ys = c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 14.79/14.64 & ( V_ys != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__append__length,axiom, % 14.79/14.64 ! [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 ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__append__length__plus,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__append,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__update__append1,axiom, % 14.79/14.64 ! [V_x,V_ys,V_xs,T_a,V_i] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__update__length,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remove1__append,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_in__set__butlast__appendI,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 14.79/14.64 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) ) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_butlast__snoc,axiom, % 14.79/14.64 ! [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 ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__listrel1I,axiom, % 14.79/14.64 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.64 & V_us_2 = V_vs_2 ) % 14.79/14.64 | ( V_xs_2 = V_ys_2 % 14.79/14.64 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lexord__append__leftI,axiom, % 14.79/14.64 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__append,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 14.79/14.64 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 14.79/14.64 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__append,axiom, % 14.79/14.64 ! [V_ys,V_xs,T_a,V_n] : % 14.79/14.64 ( ( 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))) % 14.79/14.64 => 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) ) % 14.79/14.64 & ( ~ 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))) % 14.79/14.64 => 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))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__update__append,axiom, % 14.79/14.64 ! [V_x,V_ys,V_xs,T_a,V_n] : % 14.79/14.64 ( ( 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))) % 14.79/14.64 => 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) ) % 14.79/14.64 & ( ~ 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))) % 14.79/14.64 => 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)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublist__append,axiom, % 14.79/14.64 ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,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_b)),V_l_2)))),V_A_2)))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listrel1I,axiom, % 14.79/14.64 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 14.79/14.64 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2)) % 14.79/14.64 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2)) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lexord__append__left__rightI,axiom, % 14.79/14.64 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__Suc__conv__app__nth,axiom, % 14.79/14.64 ! [V_xs,T_a,V_i] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_snoc__listrel1__snoc__iff,axiom, % 14.79/14.64 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.64 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.64 & V_x_2 = V_y_2 ) % 14.79/14.64 | ( V_xs_2 = V_ys_2 % 14.79/14.64 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listrel1E,axiom, % 14.79/14.64 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 14.79/14.64 => ~ ! [B_x,B_y] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 14.79/14.64 => ! [B_us,B_vs] : % 14.79/14.64 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) % 14.79/14.64 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lexord__append__leftD,axiom, % 14.79/14.64 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) % 14.79/14.64 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2)) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate1__def,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upd__conv__take__nth__drop,axiom, % 14.79/14.64 ! [V_a,V_xs,T_a,V_i] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__take__drop__id,axiom, % 14.79/14.64 ! [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 ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__1__Cons,axiom, % 14.79/14.64 ! [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 ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__Suc__Cons,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__via__drop,axiom, % 14.79/14.64 ! [V_ys,V_y,V_xs,V_n,T_a] : % 14.79/14.64 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 14.79/14.64 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__drop,axiom, % 14.79/14.64 ! [V_i,V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct1__rotate,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) % 14.79/14.64 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_butlast__drop,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__butlast,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__take,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__drop,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__drop,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__0,axiom, % 14.79/14.64 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__zip,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__rotate1,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__drop,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__rotate1,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_in__set__dropD,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__drop__subset,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__Nil,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate1__is__Nil__conv,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__drop__subset__set__drop,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_m_2,V_n_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__eq__Nil,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__all,axiom, % 14.79/14.64 ! [V_n,V_xs,T_a] : % 14.79/14.64 ( 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)) % 14.79/14.64 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__append,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__eq__conv__conj,axiom, % 14.79/14.64 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 % 14.79/14.64 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) % 14.79/14.64 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__Cons,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__Cons_H,axiom, % 14.79/14.64 ! [V_xs,V_x,T_a,V_n] : % 14.79/14.64 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 => 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) ) % 14.79/14.64 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 => 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) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__drop,axiom, % 14.79/14.64 ! [V_xs,T_a,V_i,V_n] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__eq__append__conv__if,axiom, % 14.79/14.64 ! [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_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) % 14.79/14.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) % 14.79/14.64 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) % 14.79/14.64 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) % 14.79/14.64 => ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 % 14.79/14.64 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),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 ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__drop_H,axiom, % 14.79/14.64 ! [V_xs,T_a,V_i] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__simps,axiom, % 14.79/14.64 ! [V_xs,V_x,T_b,T_a] : % 14.79/14.64 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 14.79/14.64 & 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__Cons__number__of,axiom, % 14.79/14.64 ! [V_xs,V_x,T_a,V_v] : % 14.79/14.64 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 => 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) ) % 14.79/14.64 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 => 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) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__add,axiom, % 14.79/14.64 ! [V_xs,T_a,V_j,V_i] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate1__length01,axiom, % 14.79/14.64 ! [V_xs,T_a] : % 14.79/14.64 ( 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))) % 14.79/14.64 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__append1,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__append2,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_id__take__nth__drop,axiom, % 14.79/14.64 ! [V_xs,T_a,V_i] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__hd__drop,axiom, % 14.79/14.64 ! [V_xs,T_a,V_n] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__drop__conv__nth,axiom, % 14.79/14.64 ! [V_n,T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => ( 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))) % 14.79/14.64 => 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) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd_Osimps,axiom, % 14.79/14.64 ! [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 ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__append2,axiom, % 14.79/14.64 ! [V_ys,T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__append,axiom, % 14.79/14.64 ! [V_ys,T_a,V_xs] : % 14.79/14.64 ( ( V_xs = c_List_Olist_ONil(T_a) % 14.79/14.64 => 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) ) % 14.79/14.64 & ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__in__set,axiom, % 14.79/14.64 ! [T_b,V_xs_2] : % 14.79/14.64 ( V_xs_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__conv__nth,axiom, % 14.79/14.64 ! [T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate1__hd__tl,axiom, % 14.79/14.64 ! [T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__rotate__conv__nth,axiom, % 14.79/14.64 ! [V_n,T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__tl,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_tl__drop,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_tl_Osimps_I2_J,axiom, % 14.79/14.64 ! [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 ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__tl,axiom, % 14.79/14.64 ! [V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__rotate,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) % 14.79/14.64 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__rotate,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate0,axiom, % 14.79/14.64 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__add,axiom, % 14.79/14.64 ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__rotate,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__rotate,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_tl_Osimps_I1_J,axiom, % 14.79/14.64 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__is__Nil__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate1__rotate__swap,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__def,axiom, % 14.79/14.64 ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_tl__append2,axiom, % 14.79/14.64 ! [V_ys,T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__tl,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__conv__mod,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__Suc,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__Suc,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_tl__append,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__id,axiom, % 14.79/14.64 ! [V_xs,T_a,V_n] : % 14.79/14.64 ( 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) % 14.79/14.64 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__length01,axiom, % 14.79/14.64 ! [V_n,V_xs,T_a] : % 14.79/14.64 ( 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))) % 14.79/14.64 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__tl,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_tl__take,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__Suc,axiom, % 14.79/14.64 ! [V_n,T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__drop__take,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_fold1__set,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 14.79/14.64 => ( V_xs_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__list__of__set__insert,axiom, % 14.79/14.64 ! [V_x_2,V_A_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.64 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,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)))))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__Nil,axiom, % 14.79/14.64 ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2 ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__not__Nil,axiom, % 14.79/14.64 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remove1__insort,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_start__le__sum,axiom, % 14.79/14.64 ! [V_ns_2,V_n_2,V_m_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__absorb0,axiom, % 14.79/14.64 ! [V_zs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Groups_Omonoid__add(T_b) % 14.79/14.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__key__left__comm,axiom, % 14.79/14.64 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 14.79/14.64 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__assoc,axiom, % 14.79/14.64 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 14.79/14.64 ( class_Groups_Osemigroup__add(T_b) % 14.79/14.64 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__left__comm,axiom, % 14.79/14.64 ! [V_xs_2,V_y_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_fun__left__comm__insort,axiom, % 14.79/14.64 ! [T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__insort,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__insort,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__Cons,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__key_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 14.79/14.64 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 14.79/14.64 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__key_Osimps_I1_J,axiom, % 14.79/14.64 ! [V_x_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__append,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__foldl,axiom, % 14.79/14.64 ! [T_b] : % 14.79/14.64 ( class_Groups_Omonoid__add(T_b) % 14.79/14.64 => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sum__eq__0__conv,axiom, % 14.79/14.64 ! [V_ns_2,V_m_2] : % 14.79/14.64 ( 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) % 14.79/14.64 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 & ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 14.79/14.64 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__insort,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2))) % 14.79/14.64 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 14.79/14.64 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 14.79/14.64 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Sup__set__fold,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.64 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Inf__set__fold,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.64 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Sup__fin__set__fold,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Lattices_Olattice(T_b) % 14.79/14.64 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Inf__fin__set__fold,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Lattices_Olattice(T_b) % 14.79/14.64 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Min__fin__set__fold,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Max__fin__set__fold,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_min__max_OInf__fin__set__fold,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_min__max_OSup__fin__set__fold,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_SUPR__set__fold,axiom, % 14.79/14.64 ! [V_f_2,V_xs_2,T_c,T_b] : % 14.79/14.64 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.64 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_INFI__set__fold,axiom, % 14.79/14.64 ! [V_f_2,V_xs_2,T_c,T_b] : % 14.79/14.64 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.64 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_elem__le__sum,axiom, % 14.79/14.64 ! [V_ns_2,V_n_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__insert__insort__key,axiom, % 14.79/14.64 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)))) % 14.79/14.64 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lexord__append__rightI,axiom, % 14.79/14.64 ! [V_r_2,V_x_2,T_b,V_y_2] : % 14.79/14.64 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__insort__insert,axiom, % 14.79/14.64 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__insert__triv,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__insort__insert,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__insert__key__triv,axiom, % 14.79/14.64 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)))) % 14.79/14.64 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__insert__insort,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lexord__Nil__left,axiom, % 14.79/14.64 ! [V_r_2,V_y_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 14.79/14.64 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__list__update,axiom, % 14.79/14.64 ! [V_x,V_k,T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => ( ( 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)) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 14.79/14.64 & ( 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)) % 14.79/14.64 => 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) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__ConsL,axiom, % 14.79/14.64 ! [V_x,T_a,V_xs] : % 14.79/14.64 ( V_xs = c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__ConsR,axiom, % 14.79/14.64 ! [V_x,T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last_Osimps,axiom, % 14.79/14.64 ! [V_x,T_a,V_xs] : % 14.79/14.64 ( ( V_xs = c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 14.79/14.64 & ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__appendL,axiom, % 14.79/14.64 ! [V_xs,T_a,V_ys] : % 14.79/14.64 ( V_ys = c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__appendR,axiom, % 14.79/14.64 ! [V_xs,T_a,V_ys] : % 14.79/14.64 ( V_ys != c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__append,axiom, % 14.79/14.64 ! [V_xs,T_a,V_ys] : % 14.79/14.64 ( ( V_ys = c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 14.79/14.64 & ( V_ys != c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__in__set,axiom, % 14.79/14.64 ! [T_b,V_as_2] : % 14.79/14.64 ( V_as_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__snoc,axiom, % 14.79/14.64 ! [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 ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__drop,axiom, % 14.79/14.64 ! [V_xs,T_a,V_n] : % 14.79/14.64 ( 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))) % 14.79/14.64 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_snoc__eq__iff__butlast,axiom, % 14.79/14.64 ! [V_ys_2,V_x_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2 % 14.79/14.64 <=> ( V_ys_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 % 14.79/14.64 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__butlast__last__id,axiom, % 14.79/14.64 ! [T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__conv__nth,axiom, % 14.79/14.64 ! [T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lists_Osimps,axiom, % 14.79/14.64 ! [V_A_2,V_a_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) % 14.79/14.64 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 14.79/14.64 | ? [B_a,B_l] : % 14.79/14.64 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) % 14.79/14.64 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 14.79/14.64 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_select__weigth__select,axiom, % 14.79/14.64 ! [T_b,V_xs_2] : % 14.79/14.64 ( V_xs_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_inj__mapI,axiom, % 14.79/14.64 ! [V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.64 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__map,axiom, % 14.79/14.64 ! [V_f_2,T_c,T_b,V_xs_2] : % 14.79/14.64 ( V_xs_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__size__map,axiom, % 14.79/14.64 ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__map,axiom, % 14.79/14.64 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_List_Omap_Ocompositionality,axiom, % 14.79/14.64 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__comp__map,axiom, % 14.79/14.64 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_List_Omap_Ocomp,axiom, % 14.79/14.64 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_List_Omap_Oid,axiom, % 14.79/14.64 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_List_Omap_Oidentity,axiom, % 14.79/14.64 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__map,axiom, % 14.79/14.64 ! [V_f_2,T_c,T_b,V_xs_2] : % 14.79/14.64 ( V_xs_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__append,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__butlast,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__ident,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ). % 14.79/14.64 % 14.79/14.64 fof(fact_inj__map__eq__map,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.64 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) % 14.79/14.64 <=> V_xs_2 = V_ys_2 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__injective,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) % 14.79/14.64 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 14.79/14.64 => V_xs_2 = V_ys_2 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__subtractf,axiom, % 14.79/14.64 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Groups_Oab__group__add(T_b) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__addf,axiom, % 14.79/14.64 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__const__mult,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] : % 14.79/14.64 ( class_Rings_Osemiring__0(T_b) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__mult__const,axiom, % 14.79/14.64 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Rings_Osemiring__0(T_b) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_ca_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__0,axiom, % 14.79/14.64 ! [V_xs_2,T_c,T_b] : % 14.79/14.64 ( class_Groups_Omonoid__add(T_b) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__eq__imp__length__eq,axiom, % 14.79/14.64 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__eq__conv,axiom, % 14.79/14.64 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2) % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 14.79/14.64 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__update,axiom, % 14.79/14.64 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Nil__is__map__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map_Osimps_I1_J,axiom, % 14.79/14.64 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__is__Nil__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__same__conv__map,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__map2,axiom, % 14.79/14.64 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),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_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__zip__map2,axiom, % 14.79/14.64 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,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_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__zip__map,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__map1,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,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_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__map__map,axiom, % 14.79/14.64 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,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_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),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_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__tl,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_inj__on__map__eq__map,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Fun_Oinj__on(T_b,T_c,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))) % 14.79/14.64 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) % 14.79/14.64 <=> V_xs_2 = V_ys_2 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__inj__on,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) % 14.79/14.64 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2))) % 14.79/14.64 => V_xs_2 = V_ys_2 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__map,axiom, % 14.79/14.64 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__fun__upd,axiom, % 14.79/14.64 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] : % 14.79/14.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 14.79/14.64 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 14.79/14.64 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__abs,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_uminus__listsum__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Groups_Oab__group__add(T_b) % 14.79/14.64 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_inj__on__mapI,axiom, % 14.79/14.64 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2))) % 14.79/14.64 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_inj__mapD,axiom, % 14.79/14.64 ! [V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) % 14.79/14.64 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_inj__map,axiom, % 14.79/14.64 ! [V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) % 14.79/14.64 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 14.79/14.64 ! [V_f_2,V_xs_2,T_b,T_c] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__triv,axiom, % 14.79/14.64 ! [V_xs_2,V_r_2,T_c,T_b] : % 14.79/14.64 ( class_Rings_Osemiring__1(T_b) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__map__remove1,axiom, % 14.79/14.64 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Nitpick_Osetsum_H__def,axiom, % 14.79/14.64 ! [V_f_2,V_A_2,T_b,T_c] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.64 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.64 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.64 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_pick__same,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_l_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),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_b),V_xs_2),V_l_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 14.79/14.64 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.64 % 14.79/14.64 fof(fact_times__code__numeral__code,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 14.79/14.64 ! [V_m_2,V_n_2] : % 14.79/14.64 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 14.79/14.64 <=> V_n_2 = V_m_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zero__code__numeral__def,axiom, % 14.79/14.64 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_one__code__numeral__def,axiom, % 14.79/14.64 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_less__code__numeral__code,axiom, % 14.79/14.64 ! [V_m_2,V_n_2] : % 14.79/14.64 ( 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))) % 14.79/14.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_code__numeral_Oof__nat__inject,axiom, % 14.79/14.64 ! [V_y_2,V_x_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 14.79/14.64 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 14.79/14.64 <=> V_x_2 = V_y_2 ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__fst__zip,axiom, % 14.79/14.64 ! [V_ys_2,T_c,V_xs_2,T_b] : % 14.79/14.64 ( 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) % 14.79/14.64 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__snd__zip,axiom, % 14.79/14.64 ! [V_ys_2,T_c,V_xs_2,T_b] : % 14.79/14.64 ( 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) % 14.79/14.64 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_number__of__code__numeral__def,axiom, % 14.79/14.64 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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__map__fst__snd,axiom, % 14.79/14.64 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ). % 14.79/14.64 % 14.79/14.64 fof(fact_plus__code__numeral__code,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_less__eq__code__numeral__code,axiom, % 14.79/14.64 ! [V_m_2,V_n_2] : % 14.79/14.64 ( 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))) % 14.79/14.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_subtract__code__numeral__code,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_pick__member,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_i_2] : % 14.79/14.64 ( 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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__eq__conv,axiom, % 14.79/14.64 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] : % 14.79/14.64 ( 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) % 14.79/14.64 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 % 14.79/14.64 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 % 14.79/14.64 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__size__conv__listsum,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,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_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_code__numeral__not__eq__zero,axiom, % 14.79/14.64 ! [V_i_2] : % 14.79/14.64 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 14.79/14.64 <=> 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 14.79/14.64 ! [V_l_2,V_k_2,V_f_2,T_b] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),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_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 14.79/14.64 ! [V_j_2,V_i_2,V_f_2,T_b] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.64 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),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_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_select__weight__member,axiom, % 14.79/14.64 ! [V_s_2,V_xs_2,T_b] : % 14.79/14.64 ( 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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_select__weight__def,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,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_b,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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_select__def,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,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_b,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_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__mono,axiom, % 14.79/14.64 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] : % 14.79/14.64 ( ( class_Groups_Omonoid__add(T_c) % 14.79/14.64 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 14.79/14.64 => ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_times__code__numeral__def,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nat__of__of__nat,axiom, % 14.79/14.64 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 14.79/14.64 % 14.79/14.64 fof(fact_of__nat__nat__of,axiom, % 14.79/14.64 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 14.79/14.64 % 14.79/14.64 fof(fact_nat__of__inverse,axiom, % 14.79/14.64 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 14.79/14.64 % 14.79/14.64 fof(fact_code__numeral_Onat__of__inject,axiom, % 14.79/14.64 ! [V_y_2,V_x_2] : % 14.79/14.64 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 14.79/14.64 <=> V_x_2 = V_y_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 14.79/14.64 ! [V_l_2,V_k_2] : % 14.79/14.64 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 14.79/14.64 <=> V_k_2 = V_l_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_type__definition__code__numeral,axiom, % 14.79/14.64 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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_less__code__numeral__def,axiom, % 14.79/14.64 ! [V_m_2,V_n_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 14.79/14.64 <=> 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nat__of,axiom, % 14.79/14.64 ! [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)))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nat__of__number,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_int__of__def,axiom, % 14.79/14.64 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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_less__eq__code__numeral__def,axiom, % 14.79/14.64 ! [V_m_2,V_n_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 14.79/14.64 <=> 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nat__of__code,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nat__of__aux__def,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Suc__code__numeral__def,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_minus__code__numeral__def,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_of__nat__inverse,axiom, % 14.79/14.64 ! [V_y_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 14.79/14.64 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_plus__code__numeral__def,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_div__code__numeral__def,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_mod__code__numeral__def,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_code__numeral__decr,axiom, % 14.79/14.64 ! [V_k] : % 14.79/14.64 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_partition__set,axiom, % 14.79/14.64 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) % 14.79/14.64 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_partition__P,axiom, % 14.79/14.64 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) % 14.79/14.64 => ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.64 & ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) % 14.79/14.64 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_partition_Osimps_I1_J,axiom, % 14.79/14.64 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_partition_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lists__Int__eq,axiom, % 14.79/14.64 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_lists__IntI,axiom, % 14.79/14.64 ! [V_B_2,V_A_2,V_l_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2))) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2))) % 14.79/14.64 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsp_ONil,axiom, % 14.79/14.64 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_append__in__listsp__conv,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_A_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 14.79/14.64 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 14.79/14.64 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsp_Oequations_I2_J,axiom, % 14.79/14.64 ! [V_a2_2,V_a1_2,V_A_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2))) % 14.79/14.64 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 14.79/14.64 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsp__infI,axiom, % 14.79/14.64 ! [V_B_2,V_l_2,V_A_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2)) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2)) % 14.79/14.64 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsp__inf__eq,axiom, % 14.79/14.64 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,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(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsp__conj__eq,axiom, % 14.79/14.64 ! [V_x_2,V_B_2,V_A_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(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),V_A_2)),V_B_2)),V_x_2)) % 14.79/14.64 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) % 14.79/14.64 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_in__listsp__conv__set,axiom, % 14.79/14.64 ! [V_xs_2,V_A_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsp_Oequations_I1_J,axiom, % 14.79/14.64 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsp__mono,axiom, % 14.79/14.64 ! [V_B_2,V_A_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsp__lists__eq,axiom, % 14.79/14.64 ! [V_x_2,V_A_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) % 14.79/14.64 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_product_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__def,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 <=> ( 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) % 14.79/14.64 & ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__map1,axiom, % 14.79/14.64 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2) % 14.79/14.64 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__map2,axiom, % 14.79/14.64 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2)) % 14.79/14.64 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__Nil2,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c)) % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__Nil,axiom, % 14.79/14.64 ! [V_ys_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2) % 14.79/14.64 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__lengthD,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__eq,axiom, % 14.79/14.64 ! [T_b,V_ys_2,V_xs_2] : % 14.79/14.64 ( V_xs_2 = V_ys_2 % 14.79/14.64 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__takeI,axiom, % 14.79/14.64 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__Cons,axiom, % 14.79/14.64 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) % 14.79/14.64 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 14.79/14.64 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__append,axiom, % 14.79/14.64 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 14.79/14.64 ( 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) % 14.79/14.64 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2)) % 14.79/14.64 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__appendI,axiom, % 14.79/14.64 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) % 14.79/14.64 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2) % 14.79/14.64 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__dropI,axiom, % 14.79/14.64 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2) % 14.79/14.64 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_product_Osimps_I1_J,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__conv__all__nth,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 <=> ( 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) % 14.79/14.64 & ! [B_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__nthD,axiom, % 14.79/14.64 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 => ( 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_xs_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__nthD2,axiom, % 14.79/14.64 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__update__cong,axiom, % 14.79/14.64 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] : % 14.79/14.64 ( 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_xs_2))) % 14.79/14.64 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 14.79/14.64 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__update__cong2,axiom, % 14.79/14.64 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) % 14.79/14.64 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__product,axiom, % 14.79/14.64 ! [V_ys,T_b,V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_product__list__set,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublists__powset,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__sublists,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublists_Osimps_I1_J,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublists_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__set__sublists,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__n__lists,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_enum__the__def,axiom, % 14.79/14.64 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__n__lists,axiom, % 14.79/14.64 ! [V_n,V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_n__lists_Osimps_I1_J,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_n__lists__Nil,axiom, % 14.79/14.64 ! [T_a,V_n] : % 14.79/14.64 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 => 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))) ) % 14.79/14.64 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__n__lists,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__n__lists__elem,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,V_ys_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)))) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2I,axiom, % 14.79/14.64 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] : % 14.79/14.64 ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2)))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) % 14.79/14.64 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2) % 14.79/14.64 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_all__nth__imp__all__set,axiom, % 14.79/14.64 ! [V_x_2,V_Pa_2,V_xs_2,T_b] : % 14.79/14.64 ( ! [B_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 14.79/14.64 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 14.79/14.64 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__removeAll__inj__on,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__remdups,axiom, % 14.79/14.64 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__remdups__leq,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remdups__id__iff__distinct,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2 % 14.79/14.64 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__removeAll,axiom, % 14.79/14.64 ! [V_x,V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__remdups__id,axiom, % 14.79/14.64 ! [V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__remdups__eq,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 14.79/14.64 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__remdups,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remdups__remdups,axiom, % 14.79/14.64 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 14.79/14.64 % 14.79/14.64 fof(fact_removeAll__append,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_removeAll_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs,T_a,V_y,V_x] : % 14.79/14.64 ( ( V_x = V_y % 14.79/14.64 => 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) ) % 14.79/14.64 & ( V_x != V_y % 14.79/14.64 => 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)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remdups_Osimps_I1_J,axiom, % 14.79/14.64 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remdups__eq__nil__right__iff,axiom, % 14.79/14.64 ! [V_x_2,T_b] : % 14.79/14.64 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2) % 14.79/14.64 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_removeAll_Osimps_I1_J,axiom, % 14.79/14.64 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remdups__eq__nil__iff,axiom, % 14.79/14.64 ! [V_x_2,T_b] : % 14.79/14.64 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remdups__map__remdups,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remove1__remdups,axiom, % 14.79/14.64 ! [V_x,V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_removeAll__id,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__remove1__removeAll,axiom, % 14.79/14.64 ! [V_x,V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remdups_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__remdups__card__conv,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__removeAll__inj,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.64 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__removeAll,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__remdups__concat,axiom, % 14.79/14.64 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat__conv__foldl,axiom, % 14.79/14.64 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__conv__concat,axiom, % 14.79/14.64 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sort__key__simps_I1_J,axiom, % 14.79/14.64 ! [V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__sort,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__sort,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__sort,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2))) % 14.79/14.64 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat_Osimps_I1_J,axiom, % 14.79/14.64 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat_Osimps_I2_J,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Nil__eq__concat__conv,axiom, % 14.79/14.64 ! [V_xss_2,T_b] : % 14.79/14.64 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 14.79/14.64 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat__eq__Nil__conv,axiom, % 14.79/14.64 ! [V_xss_2,T_b] : % 14.79/14.64 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 14.79/14.64 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__concat,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__concat,axiom, % 14.79/14.64 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__concat,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sort__key__simps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat__append,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sort__foldl__insort,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat__eq__concat__iff,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) ) % 14.79/14.64 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2) % 14.79/14.64 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 14.79/14.64 <=> V_xs_2 = V_ys_2 ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat__injective,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 14.79/14.64 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2) % 14.79/14.64 => ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) ) % 14.79/14.64 => V_xs_2 = V_ys_2 ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat__map__singleton,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_n__lists_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose_Osimps_I3_J,axiom, % 14.79/14.64 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__aux__filter__head,axiom, % 14.79/14.64 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__concat,axiom, % 14.79/14.64 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__sort,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__filter,axiom, % 14.79/14.64 ! [V_Pa_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__filter__le,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sum__length__filter__compl,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__id__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__is__subset,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remove1__filter__not,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 14.79/14.64 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__remove1,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__filter,axiom, % 14.79/14.64 ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(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),V_Qa_2)),V_Pa_2)),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__insort__triv,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_partition__filter1,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_partition__filter__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_partition__filter2,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__append,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 14.79/14.64 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose_Osimps_I1_J,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter_Osimps_I1_J,axiom, % 14.79/14.64 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__empty__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__filter__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_removeAll__filter__not__eq,axiom, % 14.79/14.64 ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_removeAll__filter__not,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 14.79/14.64 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_remdups__filter,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose_Osimps_I2_J,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__transpose,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_i_2] : % 14.79/14.64 ( 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_b))),c_List_Otranspose(T_b,V_xs_2)))) % 14.79/14.64 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__map__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__filter,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(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)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__filter__less,axiom, % 14.79/14.64 ! [V_Pa_2,V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__minus__filter__out,axiom, % 14.79/14.64 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),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,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__in__sublist,axiom, % 14.79/14.64 ! [V_s_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__empty,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__filter__conv__card,axiom, % 14.79/14.64 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,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_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__aux__filter__tail,axiom, % 14.79/14.64 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose_Opsimps_I3_J,axiom, % 14.79/14.64 ! [V_xss_2,V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2))) % 14.79/14.64 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose_Opsimps_I2_J,axiom, % 14.79/14.64 ! [V_xss_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2))) % 14.79/14.64 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublist__shift__lemma__Suc,axiom, % 14.79/14.64 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_pick__drop__zero,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),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_b,V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_select__weigth__drop__zero,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),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_b,V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose_Opsimps_I1_J,axiom, % 14.79/14.64 ! [T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b)))) % 14.79/14.64 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__max__length,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : 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))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),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_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__aux__max,axiom, % 14.79/14.64 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),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_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldr__append,axiom, % 14.79/14.64 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldr_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldr_Osimps_I1_J,axiom, % 14.79/14.64 ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2 ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldr__conv__foldl,axiom, % 14.79/14.64 ! [V_a_2,V_xs_2,T_b] : % 14.79/14.64 ( class_Groups_Oab__semigroup__add(T_b) % 14.79/14.64 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldr__map,axiom, % 14.79/14.64 ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__foldr1__lemma,axiom, % 14.79/14.64 ! [V_xs_2,V_a_2,T_b] : % 14.79/14.64 ( class_Groups_Omonoid__add(T_b) % 14.79/14.64 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__foldr1,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Groups_Omonoid__add(T_b) % 14.79/14.64 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__transpose,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,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_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublist__def,axiom, % 14.79/14.64 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2))))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sublist__shift__lemma,axiom, % 14.79/14.64 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2))))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__upt,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_atLeastLessThan__upt,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__0,axiom, % 14.79/14.64 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__eq__Nil__conv,axiom, % 14.79/14.64 ! [V_j_2,V_i_2] : % 14.79/14.64 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 14.79/14.64 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__conv__Nil,axiom, % 14.79/14.64 ! [V_i,V_j] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 14.79/14.64 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__conv__Cons,axiom, % 14.79/14.64 ! [V_j,V_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__rec,axiom, % 14.79/14.64 ! [V_j,V_i] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => 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)) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__add__eq__append,axiom, % 14.79/14.64 ! [V_k,V_j,V_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__Suc,axiom, % 14.79/14.64 ! [V_j,V_i] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => 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))) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__Suc__append,axiom, % 14.79/14.64 ! [V_j,V_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_drop__upt,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__upt,axiom, % 14.79/14.64 ! [V_j,V_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__list__of__set__range,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_take__upt,axiom, % 14.79/14.64 ! [V_n,V_m,V_i] : % 14.79/14.64 ( 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)) % 14.79/14.64 => 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__upt,axiom, % 14.79/14.64 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__upt,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__rec__number__of,axiom, % 14.79/14.64 ! [V_n,V_m] : % 14.79/14.64 ( ( 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))) % 14.79/14.64 => 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))) ) % 14.79/14.64 & ( ~ 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))) % 14.79/14.64 => 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) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_upt__eq__Cons__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 14.79/14.64 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 14.79/14.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 14.79/14.64 & V_i_2 = V_x_2 % 14.79/14.64 & 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 ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__upt,axiom, % 14.79/14.64 ! [V_j,V_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__Suc__upt,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_atLeastAtMost__upt,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_atLeast__upt,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__upt,axiom, % 14.79/14.64 ! [V_j,V_k,V_i] : % 14.79/14.64 ( 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)) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_greaterThanAtMost__upt,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_greaterThanLessThan__upt,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_atMost__upto,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__nth,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ). % 14.79/14.64 % 14.79/14.64 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 14.79/14.64 ! [V_n_2,V_m_2,V_f_2,T_b] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),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_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 14.79/14.64 ! [V_n_2,V_m_2,V_f_2,T_b] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_b) % 14.79/14.64 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__map__upt,axiom, % 14.79/14.64 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] : % 14.79/14.64 ( 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))) % 14.79/14.64 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__rectangle,axiom, % 14.79/14.64 ! [V_n_2,T_b,V_xs_2] : % 14.79/14.64 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 14.79/14.64 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.79/14.64 => ( ! [B_i] : % 14.79/14.64 ( 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_b))),V_xs_2))) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 ) % 14.79/14.64 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),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_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__key__remove1,axiom, % 14.79/14.64 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 14.79/14.64 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 % 14.79/14.64 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted_ONil,axiom, % 14.79/14.64 ! [T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__single,axiom, % 14.79/14.64 ! [V_x,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__upt,axiom, % 14.79/14.64 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__sort,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__insort__insert,axiom, % 14.79/14.64 ! [V_x_2,V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__tl,axiom, % 14.79/14.64 ! [V_xs,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__remove1,axiom, % 14.79/14.64 ! [V_a,V_xs,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__take,axiom, % 14.79/14.64 ! [V_n,V_xs,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__upto,axiom, % 14.79/14.64 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__drop,axiom, % 14.79/14.64 ! [V_n,V_xs,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__insort,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) % 14.79/14.64 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__many,axiom, % 14.79/14.64 ! [V_zs,V_y,V_x,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 14.79/14.64 => 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))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__many__eq,axiom, % 14.79/14.64 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))) % 14.79/14.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 14.79/14.64 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted_Oequations_I1_J,axiom, % 14.79/14.64 ! [T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__butlast,axiom, % 14.79/14.64 ! [V_xs,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__remdups,axiom, % 14.79/14.64 ! [V_l,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__distinct__set__unique,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 14.79/14.64 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 14.79/14.64 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__sort__key,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__insort__insert__key,axiom, % 14.79/14.64 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__map__remove1,axiom, % 14.79/14.64 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__insort__key,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2))) % 14.79/14.64 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__map__same,axiom, % 14.79/14.64 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__filter,axiom, % 14.79/14.64 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__same,axiom, % 14.79/14.64 ! [V_xs_2,V_g_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__Cons,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 14.79/14.64 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.64 & ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__append,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 14.79/14.64 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.64 & c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 14.79/14.64 & ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => ! [B_xa] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__insort,axiom, % 14.79/14.64 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 14.79/14.64 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted_Oequations_I2_J,axiom, % 14.79/14.64 ! [V_a1_2,V_a2_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) % 14.79/14.64 <=> ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) % 14.79/14.64 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__list__of__set,axiom, % 14.79/14.64 ! [V_A_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.64 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 % 14.79/14.64 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) % 14.79/14.64 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insort__remove1,axiom, % 14.79/14.64 ! [V_xs_2,V_a_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.64 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__equals__nth__mono,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.64 <=> ! [B_j] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => ! [B_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__nth__mono,axiom, % 14.79/14.64 ! [V_j,V_i,V_xs,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => ( 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))) % 14.79/14.64 => 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))) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_map__sorted__distinct__set__unique,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( class_Orderings_Olinorder(T_c) % 14.79/14.64 => ( c_Fun_Oinj__on(T_b,T_c,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))) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) % 14.79/14.64 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 14.79/14.64 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__column,axiom, % 14.79/14.64 ! [V_i_2,V_xs_2,T_b] : % 14.79/14.64 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 14.79/14.64 => ( 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_b))),V_xs_2))) % 14.79/14.64 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__nth__transpose__sorted,axiom, % 14.79/14.64 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 14.79/14.64 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 14.79/14.64 => ( 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_b))),c_List_Otranspose(T_b,V_xs_2)))) % 14.79/14.64 => ( 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_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)))) % 14.79/14.64 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_inj__on__rev,axiom, % 14.79/14.64 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__rev,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) % 14.79/14.64 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__append,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__singleton__conv,axiom, % 14.79/14.64 ! [V_x_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) % 14.79/14.64 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_singleton__rev__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2) % 14.79/14.64 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev_Osimps_I1_J,axiom, % 14.79/14.64 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 14.79/14.64 % 14.79/14.64 fof(fact_Nil__is__rev__conv,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__is__Nil__conv,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__concat,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__filter,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__rev,axiom, % 14.79/14.64 ! [V_ys,T_b,V_xs,T_a] : % 14.79/14.64 ( 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) % 14.79/14.64 => 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)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__rev,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__rev1,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2) % 14.79/14.64 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_list__all2__rev,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 14.79/14.64 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2)) % 14.79/14.64 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__is__rev__conv,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) % 14.79/14.64 <=> V_xs_2 = V_ys_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__swap,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 % 14.79/14.64 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__rev__ident,axiom, % 14.79/14.64 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__rev,axiom, % 14.79/14.64 ! [V_xs,T_a] : % 14.79/14.64 ( class_Groups_Ocomm__monoid__add(T_a) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__rev,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldr__foldl,axiom, % 14.79/14.64 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__foldr,axiom, % 14.79/14.64 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev_Osimps_I2_J,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__eq__Cons__iff,axiom, % 14.79/14.64 ! [V_ys_2,V_y_2,V_xs_2,T_b] : % 14.79/14.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 14.79/14.64 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_last__rev,axiom, % 14.79/14.64 ! [T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__rev,axiom, % 14.79/14.64 ! [T_a,V_xs] : % 14.79/14.64 ( V_xs != c_List_Olist_ONil(T_a) % 14.79/14.64 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__transpose,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__foldl__cons,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__take,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__drop,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rotate__rev,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__nth,axiom, % 14.79/14.64 ! [V_xs,T_a,V_n] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_rev__update,axiom, % 14.79/14.64 ! [V_y,V_xs,T_a,V_k] : % 14.79/14.64 ( 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))) % 14.79/14.64 => 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) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__rev__nth__mono,axiom, % 14.79/14.64 ! [V_j,V_i,V_xs,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 14.79/14.64 => ( 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))) % 14.79/14.64 => 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))) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldr__max__sorted,axiom, % 14.79/14.64 ! [V_y_2,V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) % 14.79/14.64 => ( ( V_xs_2 = c_List_Olist_ONil(T_b) % 14.79/14.64 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) % 14.79/14.64 & ( V_xs_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__transpose__sorted,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 14.79/14.64 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 14.79/14.64 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__column__length,axiom, % 14.79/14.64 ! [V_i_2,V_xs_2,T_b] : % 14.79/14.64 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 14.79/14.64 => ( 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_b))),V_xs_2))) % 14.79/14.64 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transpose__transpose,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 14.79/14.64 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(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_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 14.79/14.64 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__takeWhile,axiom, % 14.79/14.64 ! [V_Pa_2,V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__takeWhile__le,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__eq__all__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_set__takeWhileD,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__takeWhile__fst,axiom, % 14.79/14.64 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__takeWhile__snd,axiom, % 14.79/14.64 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile_Osimps_I1_J,axiom, % 14.79/14.64 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 14.79/14.64 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__tail,axiom, % 14.79/14.64 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] : % 14.79/14.64 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__eq__take,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__takeWhile,axiom, % 14.79/14.64 ! [V_Pa_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_return__list__def,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__append1,axiom, % 14.79/14.64 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__nth,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) % 14.79/14.64 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_nth__length__takeWhile,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__not__last,axiom, % 14.79/14.64 ! [T_b,V_xs_2] : % 14.79/14.64 ( V_xs_2 != c_List_Olist_ONil(T_b) % 14.79/14.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 14.79/14.64 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 14.79/14.64 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transfer__nat__int__list__return__embed,axiom, % 14.79/14.64 ! [V_l] : % 14.79/14.64 ( c_List_Onat__list(V_l) % 14.79/14.64 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 14.79/14.64 ! [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))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_embed__list__def,axiom, % 14.79/14.64 ! [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) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__neq__rev,axiom, % 14.79/14.64 ! [V_x_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile__neq__rev,axiom, % 14.79/14.64 ! [V_x_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__dropWhile__id,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2 ). % 14.79/14.64 % 14.79/14.64 fof(fact_hd__dropWhile,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b) % 14.79/14.64 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__dropWhile,axiom, % 14.79/14.64 ! [V_Pa_2,V_xs_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__dropWhile__le,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile__eq__Nil__conv,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b) % 14.79/14.64 <=> ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile_Osimps_I1_J,axiom, % 14.79/14.64 ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile_Osimps_I2_J,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 14.79/14.64 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) ) % 14.79/14.64 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__dropWhile,axiom, % 14.79/14.64 ! [V_Pa_2,V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile__map,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile__append1,axiom, % 14.79/14.64 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.64 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile__eq__Cons__conv,axiom, % 14.79/14.64 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 14.79/14.64 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) % 14.79/14.64 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile__eq__drop,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_dropWhile__nth,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) % 14.79/14.64 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),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_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_listsum__map__filter,axiom, % 14.79/14.64 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] : % 14.79/14.64 ( class_Groups_Omonoid__add(T_c) % 14.79/14.64 => ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => ( ~ hBOOL(hAPP(V_Pa_2,B_x)) % 14.79/14.64 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) % 14.79/14.64 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted__nth__monoI,axiom, % 14.79/14.64 ! [V_xs,T_a] : % 14.79/14.64 ( class_Orderings_Olinorder(T_a) % 14.79/14.64 => ( ! [B_i,B_j] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 14.79/14.64 => ( 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))) % 14.79/14.64 => 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))) ) ) % 14.79/14.64 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__eq__filter,axiom, % 14.79/14.64 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.64 ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) % 14.79/14.64 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.64 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_takeWhile__eq__take__P__nth,axiom, % 14.79/14.64 ! [V_Pa_2,V_xs_2,T_b,V_n_2] : % 14.79/14.64 ( ! [B_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) % 14.79/14.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) % 14.79/14.64 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_length__takeWhile__less__P__nth,axiom, % 14.79/14.64 ! [V_xs_2,T_b,V_Pa_2,V_j_2] : % 14.79/14.64 ( ! [B_i] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 14.79/14.64 => ( 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_b)),V_xs_2))) % 14.79/14.64 => 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_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_sorted_Osimps,axiom, % 14.79/14.64 ! [V_a_2,T_b] : % 14.79/14.64 ( class_Orderings_Olinorder(T_b) % 14.79/14.64 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2) % 14.79/14.64 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 14.79/14.64 | ? [B_xs,B_x] : % 14.79/14.64 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 14.79/14.64 & ! [B_xa] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) % 14.79/14.64 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_List_Oinsert__def,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) % 14.79/14.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_not__in__set__insert,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insert__remdups,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__insert,axiom, % 14.79/14.64 ! [V_x,V_xs,T_a] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_in__set__insert,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_List_Oset__insert,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_insert__Nil,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_concat__map__maps,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) ). % 14.79/14.64 % 14.79/14.64 fof(fact_maps__def,axiom, % 14.79/14.64 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_maps__simps_I2_J,axiom, % 14.79/14.64 ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ). % 14.79/14.64 % 14.79/14.64 fof(fact_maps__simps_I1_J,axiom, % 14.79/14.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_distinct__concat,axiom, % 14.79/14.64 ! [V_xs_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2)) % 14.79/14.64 => ( ! [B_ys] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) ) % 14.79/14.64 => ( ! [B_ys] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => ! [B_zs] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.64 => ( B_ys != B_zs % 14.79/14.64 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 14.79/14.64 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_measures__lesseq,axiom, % 14.79/14.64 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 14.79/14.64 ( 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))) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_wf__measures,axiom, % 14.79/14.64 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_in__measures_I1_J,axiom, % 14.79/14.64 ! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))) ). % 14.79/14.64 % 14.79/14.64 fof(fact_measures__def,axiom, % 14.79/14.64 ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)) ). % 14.79/14.64 % 14.79/14.64 fof(fact_measures__less,axiom, % 14.79/14.64 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 14.79/14.64 ( 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))) % 14.79/14.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_in__measures_I2_J,axiom, % 14.79/14.64 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) % 14.79/14.64 <=> ( 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))) % 14.79/14.64 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 14.79/14.64 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_foldl__apply,axiom, % 14.79/14.64 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] : % 14.79/14.64 ( ! [B_x] : % 14.79/14.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.64 => hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) ) % 14.79/14.64 => hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_order__fun_I2_J,axiom, % 14.79/14.64 ! [V_g_2,V_f_2,T_b,T_c] : % 14.79/14.64 ( ( class_Orderings_Oorder(T_c) % 14.79/14.64 & class_Enum_Oenum(T_b) ) % 14.79/14.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 14.79/14.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 14.79/14.64 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2)))) ) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_enum__ex__prod__def,axiom, % 14.79/14.64 ! [V_Pa_2,T_b,T_c] : % 14.79/14.64 ( ( class_Enum_Oenum(T_c) % 14.79/14.64 & class_Enum_Oenum(T_b) ) % 14.79/14.64 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2)) % 14.79/14.64 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_exists__code,axiom, % 14.79/14.64 ! [V_Pa_2,T_b] : % 14.79/14.64 ( class_Enum_Oenum(T_b) % 14.79/14.64 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 14.79/14.64 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_enum__ex,axiom, % 14.79/14.64 ! [V_Pa_2,T_b] : % 14.79/14.64 ( class_Enum_Oenum(T_b) % 14.79/14.64 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) % 14.79/14.64 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_zip__obtain__same__length,axiom, % 14.79/14.64 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 14.79/14.64 ( ( 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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2)) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2)))) ) % 14.79/14.64 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ). % 14.79/14.64 % 14.79/14.64 fof(fact_pos__not__random__dseq__def,axiom, % 14.79/14.64 ! [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)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dropWhile__append2,axiom, % 14.79/14.65 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 14.79/14.65 ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all2__all__nthI,axiom, % 14.79/14.65 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] : % 14.79/14.65 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2) % 14.79/14.65 => ( ! [B_n] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2))) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) ) % 14.79/14.65 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_finite__sorted__distinct__unique,axiom, % 14.79/14.65 ! [V_A_2,T_b] : % 14.79/14.65 ( class_Orderings_Olinorder(T_b) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.65 => ? [B_x] : % 14.79/14.65 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2 % 14.79/14.65 & c_List_Olinorder__class_Osorted(T_b,B_x) % 14.79/14.65 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x)) % 14.79/14.65 & ! [B_y] : % 14.79/14.65 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2 % 14.79/14.65 & c_List_Olinorder__class_Osorted(T_b,B_y) % 14.79/14.65 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) ) % 14.79/14.65 => B_y = B_x ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_takeWhile__append2,axiom, % 14.79/14.65 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 14.79/14.65 ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_insort__is__Cons,axiom, % 14.79/14.65 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] : % 14.79/14.65 ( class_Orderings_Olinorder(T_c) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 14.79/14.65 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_filter__eq__Cons__iff,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] : % 14.79/14.65 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) % 14.79/14.65 <=> ? [B_us,B_vs] : % 14.79/14.65 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) % 14.79/14.65 & ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 14.79/14.65 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.65 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Cons__eq__filter__iff,axiom, % 14.79/14.65 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 14.79/14.65 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) % 14.79/14.65 <=> ? [B_us,B_vs] : % 14.79/14.65 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) % 14.79/14.65 & ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 14.79/14.65 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.65 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_order__fun_I1_J,axiom, % 14.79/14.65 ! [V_g_2,V_f_2,T_b,T_c] : % 14.79/14.65 ( ( class_Orderings_Oorder(T_c) % 14.79/14.65 & class_Enum_Oenum(T_b) ) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 14.79/14.65 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_enum__all,axiom, % 14.79/14.65 ! [V_Pa_2,T_b] : % 14.79/14.65 ( class_Enum_Oenum(T_b) % 14.79/14.65 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) % 14.79/14.65 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_all__code,axiom, % 14.79/14.65 ! [V_Pa_2,T_b] : % 14.79/14.65 ( class_Enum_Oenum(T_b) % 14.79/14.65 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 14.79/14.65 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_enum__all__prod__def,axiom, % 14.79/14.65 ! [V_Pa_2,T_b,T_c] : % 14.79/14.65 ( ( class_Enum_Oenum(T_c) % 14.79/14.65 & class_Enum_Oenum(T_b) ) % 14.79/14.65 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2)) % 14.79/14.65 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ball__nth,axiom, % 14.79/14.65 ! [V_Pa_2,V_xs_2,T_b,V_n_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sorted_OCons,axiom, % 14.79/14.65 ! [V_x_2,V_xs_2,T_b] : % 14.79/14.65 ( class_Orderings_Olinorder(T_b) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) % 14.79/14.65 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 14.79/14.65 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__length,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 <=> ? [B_n] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_in__set__conv__decomp,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__simps_I2_J,axiom, % 14.79/14.65 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__append,axiom, % 14.79/14.65 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 14.79/14.65 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__iff,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 <=> ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__rev,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 14.79/14.65 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__simps_I1_J,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 14.79/14.65 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.65 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_in__set__conv__decomp__first,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 <=> ? [B_ys] : % 14.79/14.65 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_in__set__conv__decomp__last,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 <=> ? [B_ys,B_zs] : % 14.79/14.65 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__length,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 <=> ! [B_n] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_measure__function__int,axiom, % 14.79/14.65 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))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__simps_I2_J,axiom, % 14.79/14.65 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__append,axiom, % 14.79/14.65 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 14.79/14.65 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_measure__size,axiom, % 14.79/14.65 ! [T_b] : % 14.79/14.65 ( class_Nat_Osize(T_b) % 14.79/14.65 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_is__measure_Ointros,axiom, % 14.79/14.65 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_is__measure_Oequations,axiom, % 14.79/14.65 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_is__measure_Osimps,axiom, % 14.79/14.65 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__iff,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 <=> ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_measure__snd,axiom, % 14.79/14.65 ! [T_c,V_f_2,T_b] : % 14.79/14.65 ( c_FunDef_Ois__measure(T_b,V_f_2) % 14.79/14.65 => c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_measure__fst,axiom, % 14.79/14.65 ! [T_c,V_f_2,T_b] : % 14.79/14.65 ( c_FunDef_Ois__measure(T_b,V_f_2) % 14.79/14.65 => c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__rev,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 14.79/14.65 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__simps_I1_J,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 14.79/14.65 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.65 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Ball__set__list__all,axiom, % 14.79/14.65 ! [V_Pa_2,V_xs_2,T_b] : % 14.79/14.65 ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__iff__raw,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 <=> ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex1__simps_I2_J,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 14.79/14.65 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.65 => c_List_Olist__all(T_b,hAPP(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_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) % 14.79/14.65 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.65 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_transfer__morphism__int__nat,axiom, % 14.79/14.65 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)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex1__simps_I1_J,axiom, % 14.79/14.65 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bool_Osize_I3_J,axiom, % 14.79/14.65 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bool_Osize_I4_J,axiom, % 14.79/14.65 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex1__iff,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 <=> ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) % 14.79/14.65 & ! [B_y] : % 14.79/14.65 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 14.79/14.65 => B_y = B_x ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 14.79/14.65 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 14.79/14.65 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.65 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) ) % 14.79/14.65 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.65 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,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_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 14.79/14.65 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 14.79/14.65 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.65 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) ) % 14.79/14.65 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 14.79/14.65 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,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_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 14.79/14.65 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),hAPP(hAPP(c_COMBC(T_c,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_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 14.79/14.65 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b))),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 14.79/14.65 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Opos__empty__def,axiom, % 14.79/14.65 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 14.79/14.65 % 14.79/14.65 fof(fact_pos__empty__def,axiom, % 14.79/14.65 ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b) ). % 14.79/14.65 % 14.79/14.65 fof(fact_neg__bind__def,axiom, % 14.79/14.65 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),hAPP(hAPP(c_COMBC(T_c,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_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Opos__bind__def,axiom, % 14.79/14.65 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_neg__map__def,axiom, % 14.79/14.65 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,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_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_neg__single__def,axiom, % 14.79/14.65 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_pos__bind__def,axiom, % 14.79/14.65 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b))),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Oneg__single__def,axiom, % 14.79/14.65 ! [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) ). % 14.79/14.65 % 14.79/14.65 fof(fact_pos__map__def,axiom, % 14.79/14.65 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,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_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_pos__single__def,axiom, % 14.79/14.65 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_length__splice,axiom, % 14.79/14.65 ! [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)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_splice_Osimps_I3_J,axiom, % 14.79/14.65 ! [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))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_splice__Nil2,axiom, % 14.79/14.65 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 14.79/14.65 % 14.79/14.65 fof(fact_splice_Osimps_I1_J,axiom, % 14.79/14.65 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 14.79/14.65 % 14.79/14.65 fof(fact_splice_Osimps_I2_J,axiom, % 14.79/14.65 ! [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) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Opos__single__def,axiom, % 14.79/14.65 ! [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) ). % 14.79/14.65 % 14.79/14.65 fof(fact_acyclicP__converse,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2)))) % 14.79/14.65 <=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_converse__meet,axiom, % 14.79/14.65 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_converse__join,axiom, % 14.79/14.65 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_conversep__eq,axiom, % 14.79/14.65 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ). % 14.79/14.65 % 14.79/14.65 fof(fact_conversep__conversep,axiom, % 14.79/14.65 ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2 ). % 14.79/14.65 % 14.79/14.65 fof(fact_conversep__iff,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_conversep_Oequations,axiom, % 14.79/14.65 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2)) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_conversep_Ointros,axiom, % 14.79/14.65 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_conversepD,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_conversep__noteq,axiom, % 14.79/14.65 ! [V_y_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2)) % 14.79/14.65 <=> V_x_2 != V_y_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_converse__pred__comp,axiom, % 14.79/14.65 ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_conversep__converse__eq,axiom, % 14.79/14.65 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,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_r_2)),V_x_2),V_y_2)) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_,axiom, % 14.79/14.65 ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_tl__replicate,axiom, % 14.79/14.65 ! [V_x,T_a,V_n] : % 14.79/14.65 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.65 => 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) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_replicate__length__filter,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_length__replicate,axiom, % 14.79/14.65 ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n ). % 14.79/14.65 % 14.79/14.65 fof(fact_map__replicate__const,axiom, % 14.79/14.65 ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_replicate__app__Cons__same,axiom, % 14.79/14.65 ! [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)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_replicate__Suc,axiom, % 14.79/14.65 ! [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)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_rev__replicate,axiom, % 14.79/14.65 ! [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) ). % 14.79/14.65 % 14.79/14.65 fof(fact_take__replicate,axiom, % 14.79/14.65 ! [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) ). % 14.79/14.65 % 14.79/14.65 fof(fact_hd__replicate,axiom, % 14.79/14.65 ! [V_x,T_a,V_n] : % 14.79/14.65 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.65 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_drop__replicate,axiom, % 14.79/14.65 ! [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) ). % 14.79/14.65 % 14.79/14.65 fof(fact_last__replicate,axiom, % 14.79/14.65 ! [V_x,T_a,V_n] : % 14.79/14.65 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.65 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_zip__replicate,axiom, % 14.79/14.65 ! [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)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Ball__set__replicate,axiom, % 14.79/14.65 ! [V_Pa_2,V_a_2,V_n_2,T_b] : % 14.79/14.65 ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 14.79/14.65 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Bex__set__replicate,axiom, % 14.79/14.65 ! [V_Pa_2,V_a_2,V_n_2,T_b] : % 14.79/14.65 ( ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 14.79/14.65 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_replicate__eq__replicate,axiom, % 14.79/14.65 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] : % 14.79/14.65 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2) % 14.79/14.65 <=> ( V_m_2 = V_n_2 % 14.79/14.65 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.65 => V_x_2 = V_y_2 ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_nth__replicate,axiom, % 14.79/14.65 ! [V_x,T_a,V_n,V_i] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 14.79/14.65 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_append__replicate__commute,axiom, % 14.79/14.65 ! [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)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_replicate__add,axiom, % 14.79/14.65 ! [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)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_filter__replicate,axiom, % 14.79/14.65 ! [V_n_2,T_b,V_x_2,V_Pa_2] : % 14.79/14.65 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.65 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) ) % 14.79/14.65 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 14.79/14.65 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_concat__replicate__trivial,axiom, % 14.79/14.65 ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a) ). % 14.79/14.65 % 14.79/14.65 fof(fact_replicate__empty,axiom, % 14.79/14.65 ! [V_x_2,V_n_2,T_b] : % 14.79/14.65 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b) % 14.79/14.65 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_empty__replicate,axiom, % 14.79/14.65 ! [V_x_2,V_n_2,T_b] : % 14.79/14.65 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2) % 14.79/14.65 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_replicate__0,axiom, % 14.79/14.65 ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a) ). % 14.79/14.65 % 14.79/14.65 fof(fact_map__replicate,axiom, % 14.79/14.65 ! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_in__set__replicate,axiom, % 14.79/14.65 ! [V_y_2,V_n_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2)))) % 14.79/14.65 <=> ( V_x_2 = V_y_2 % 14.79/14.65 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_replicate__append__same,axiom, % 14.79/14.65 ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_map__replicate__trivial,axiom, % 14.79/14.65 ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_set__replicate,axiom, % 14.79/14.65 ! [V_x_2,T_b,V_n_2] : % 14.79/14.65 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.65 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_set__replicate__conv__if,axiom, % 14.79/14.65 ! [V_x_2,T_b,V_n_2] : % 14.79/14.65 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.65 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 14.79/14.65 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.65 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_set__replicate__Suc,axiom, % 14.79/14.65 ! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_small__lazy__list_Osimps,axiom, % 14.79/14.65 ! [V_d_2,T_b] : % 14.79/14.65 ( class_Lazy__Sequence_Osmall__lazy(T_b) % 14.79/14.65 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_eq__comp__r,axiom, % 14.79/14.65 ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2 ). % 14.79/14.65 % 14.79/14.65 fof(fact_small__lazy__prod__def,axiom, % 14.79/14.65 ! [V_d,T_b,T_a] : % 14.79/14.65 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 14.79/14.65 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 14.79/14.65 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Opos__union__def,axiom, % 14.79/14.65 ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 14.79/14.65 ! [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))) ). % 14.79/14.65 % 14.79/14.65 fof(fact__01,axiom, % 14.79/14.65 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Oinject,axiom, % 14.79/14.65 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] : % 14.79/14.65 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2) % 14.79/14.65 <=> ( V_a_2 = V_a_H_2 % 14.79/14.65 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_pos__union__def,axiom, % 14.79/14.65 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 14.79/14.65 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,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_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_small__lazy_H_Osimps,axiom, % 14.79/14.65 ! [V_i,V_d] : % 14.79/14.65 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 14.79/14.65 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 14.79/14.65 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 14.79/14.65 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_small__lazy_H_Opsimps,axiom, % 14.79/14.65 ! [V_i_2,V_d_2] : % 14.79/14.65 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))) % 14.79/14.65 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 14.79/14.65 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 14.79/14.65 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 14.79/14.65 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_small__lazy__int__def,axiom, % 14.79/14.65 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_small__lazy_H_Opinduct,axiom, % 14.79/14.65 ! [V_Pa_2,V_a1_2,V_a0_2] : % 14.79/14.65 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 14.79/14.65 => ( ! [B_d,B_i] : % 14.79/14.65 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))) % 14.79/14.65 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) ) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_size__code,axiom, % 14.79/14.65 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),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_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence__size__code,axiom, % 14.79/14.65 ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),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_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_seq__case,axiom, % 14.79/14.65 ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_yieldn__def,axiom, % 14.79/14.65 ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 14.79/14.65 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_refl__on__INTER,axiom, % 14.79/14.65 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] : % 14.79/14.65 ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 14.79/14.65 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 14.79/14.65 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_List_Omember__def,axiom, % 14.79/14.65 ! [V_x_2,V_xs_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_member__rec_I2_J,axiom, % 14.79/14.65 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_member__set,axiom, % 14.79/14.65 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ). % 14.79/14.65 % 14.79/14.65 fof(fact_member__rec_I1_J,axiom, % 14.79/14.65 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2)) % 14.79/14.65 <=> ( V_x_2 = V_y_2 % 14.79/14.65 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_in__set__member,axiom, % 14.79/14.65 ! [V_xs_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex1__iff__raw,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 <=> ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) % 14.79/14.65 & ! [B_y] : % 14.79/14.65 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 14.79/14.65 => B_y = B_x ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_setsum__UNION__zero,axiom, % 14.79/14.65 ! [V_f_2,V_S_2,T_b,T_c] : % 14.79/14.65 ( class_Groups_Ocomm__monoid__add(T_c) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2)) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2)) % 14.79/14.65 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 14.79/14.65 => ( ! [B_T1] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2)) % 14.79/14.65 => ! [B_T2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2)) % 14.79/14.65 => ( B_T1 != B_T2 % 14.79/14.65 => ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2)) % 14.79/14.65 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) % 14.79/14.65 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_THE__default__def,axiom, % 14.79/14.65 ! [V_d_2,T_b,V_Pa_2] : % 14.79/14.65 ( ( ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.79/14.65 & ! [B_y] : % 14.79/14.65 ( hBOOL(hAPP(V_Pa_2,B_y)) % 14.79/14.65 => B_y = B_x ) ) % 14.79/14.65 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ) % 14.79/14.65 & ( ~ ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(V_Pa_2,B_x)) % 14.79/14.65 & ! [B_y] : % 14.79/14.65 ( hBOOL(hAPP(V_Pa_2,B_y)) % 14.79/14.65 => B_y = B_x ) ) % 14.79/14.65 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_INF2__I,axiom, % 14.79/14.65 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,T_b] : % 14.79/14.65 ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) % 14.79/14.65 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_SUP2__E,axiom, % 14.79/14.65 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 14.79/14.65 => ~ ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.65 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_finite__maxlen,axiom, % 14.79/14.65 ! [V_M_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2)) % 14.79/14.65 => ? [B_n] : % 14.79/14.65 ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Osize_I3_J,axiom, % 14.79/14.65 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Osize_I1_J,axiom, % 14.79/14.65 ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(fact__02,axiom, % 14.79/14.65 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Osimps_I3_J,axiom, % 14.79/14.65 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Osimps_I2_J,axiom, % 14.79/14.65 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Osimps_I4_J,axiom, % 14.79/14.65 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__iff__all__interval__int,axiom, % 14.79/14.65 ! [V_j_2,V_i_2,V_Pa_2] : % 14.79/14.65 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 14.79/14.65 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__iff__not__all__inverval__int,axiom, % 14.79/14.65 ! [V_j_2,V_i_2,V_Pa_2] : % 14.79/14.65 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 14.79/14.65 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_all__interval__int__def,axiom, % 14.79/14.65 ! [V_j_2,V_i_2,V_Pa_2] : % 14.79/14.65 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) % 14.79/14.65 <=> ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_code__numeral_Orecs_I2_J,axiom, % 14.79/14.65 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Random_Osimps,axiom, % 14.79/14.65 ! [V_size_2,V_g_2,T_b,V_nrandom_2] : % 14.79/14.65 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) % 14.79/14.65 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ) % 14.79/14.65 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) % 14.79/14.65 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_code__numeral_Orecs_I1_J,axiom, % 14.79/14.65 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 14.79/14.65 % 14.79/14.65 fof(fact_Random__Sequence_Oempty__def,axiom, % 14.79/14.65 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Random__Sequence_Osingle__def,axiom, % 14.79/14.65 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Random__Sequence_Omap__def,axiom, % 14.79/14.65 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,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_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_exE__realizer,axiom, % 14.79/14.65 ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2))) % 14.79/14.65 => ( ! [B_x,B_y] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) % 14.79/14.65 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 14.79/14.65 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Image__Collect__split,axiom, % 14.79/14.65 ! [V_A_2,V_Pa_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2)))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lexord__trans,axiom, % 14.79/14.65 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) % 14.79/14.65 => ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__less__than,axiom, % 14.79/14.65 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__lex__prod,axiom, % 14.79/14.65 ! [V_R2_2,T_c,V_R1_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_R1_2) % 14.79/14.65 => ( c_Relation_Otrans(T_c,V_R2_2) % 14.79/14.65 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__def,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 <=> ! [B_x,B_y] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 14.79/14.65 => ! [B_z] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_transD,axiom, % 14.79/14.65 ! [V_ca_2,V_b_2,V_a_2,V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.65 => ( 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_ca_2)),V_r_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),V_r_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Union__eq,axiom, % 14.79/14.65 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,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_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__O__subset,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bex__UNIV,axiom, % 14.79/14.65 ! [V_Pa_2,T_b] : % 14.79/14.65 ( ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_finite__Collect__bex,axiom, % 14.79/14.65 ! [V_Qa_2,T_c,V_A_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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_A_2)))),V_Qa_2))))) % 14.79/14.65 <=> ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.65 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Qa_2),B_x)))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__converse,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 14.79/14.65 <=> c_Relation_Otrans(T_b,V_r_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bex__empty,axiom, % 14.79/14.65 ! [V_Pa_2,T_b] : % 14.79/14.65 ~ ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_listrel__trans,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lexord__transI,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__finite__psubset,axiom, % 14.79/14.65 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__Id__on,axiom, % 14.79/14.65 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__trancl,axiom, % 14.79/14.65 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trancl__id,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__Id,axiom, % 14.79/14.65 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__rtrancl,axiom, % 14.79/14.65 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__Int,axiom, % 14.79/14.65 ! [V_s_2,V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => ( c_Relation_Otrans(T_b,V_s_2) % 14.79/14.65 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_SUPR__bool__eq,axiom, % 14.79/14.65 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__reflclI,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__inv__image,axiom, % 14.79/14.65 ! [V_f_2,T_c,V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__iff__raw,axiom, % 14.79/14.65 ! [V_xs_2,V_Pa_2,T_b] : % 14.79/14.65 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 14.79/14.65 <=> ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Bex__set__list__ex,axiom, % 14.79/14.65 ! [V_Pa_2,V_xs_2,T_b] : % 14.79/14.65 ( ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_UN__eq,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_INT__eq,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Sup__apply,axiom, % 14.79/14.65 ! [V_x_2,V_A_2,T_c,T_b] : % 14.79/14.65 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.65 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Sup__fun__def,axiom, % 14.79/14.65 ! [V_x_2,V_A_2,T_c,T_b] : % 14.79/14.65 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.65 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Inf__apply,axiom, % 14.79/14.65 ! [V_x_2,V_A_2,T_c,T_b] : % 14.79/14.65 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.65 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Inf__fun__def,axiom, % 14.79/14.65 ! [V_x_2,V_A_2,T_c,T_b] : % 14.79/14.65 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 14.79/14.65 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_max__extp_Ointros,axiom, % 14.79/14.65 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 14.79/14.65 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 14.79/14.65 => ? [B_xa] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 14.79/14.65 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) % 14.79/14.65 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_transp__def,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Predicate_Otransp(T_b,V_r_2) % 14.79/14.65 <=> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_transpE,axiom, % 14.79/14.65 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 14.79/14.65 ( c_Predicate_Otransp(T_b,V_r_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_equivp__reflp__symp__transp,axiom, % 14.79/14.65 ! [V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.65 <=> ( c_Predicate_Oreflp(T_b,V_R_2) % 14.79/14.65 & c_Predicate_Osymp(T_b,V_R_2) % 14.79/14.65 & c_Predicate_Otransp(T_b,V_R_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_equivpI,axiom, % 14.79/14.65 ! [V_R_2,T_b] : % 14.79/14.65 ( c_Predicate_Oreflp(T_b,V_R_2) % 14.79/14.65 => ( c_Predicate_Osymp(T_b,V_R_2) % 14.79/14.65 => ( c_Predicate_Otransp(T_b,V_R_2) % 14.79/14.65 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sympE,axiom, % 14.79/14.65 ! [V_y_2,V_x_2,V_r_2,T_b] : % 14.79/14.65 ( c_Predicate_Osymp(T_b,V_r_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_equivpE,axiom, % 14.79/14.65 ! [V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.65 => ~ ( c_Predicate_Oreflp(T_b,V_R_2) % 14.79/14.65 => ( c_Predicate_Osymp(T_b,V_R_2) % 14.79/14.65 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_max__extp_Osimps,axiom, % 14.79/14.65 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 14.79/14.65 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 14.79/14.65 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 14.79/14.65 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 14.79/14.65 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.65 & ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 14.79/14.65 => ? [B_xa] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 14.79/14.65 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_trans__diff__Id,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => ( c_Relation_Oantisym(T_b,V_r_2) % 14.79/14.65 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_antisym__subset,axiom, % 14.79/14.65 ! [V_s_2,V_r_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 14.79/14.65 => ( c_Relation_Oantisym(T_b,V_s_2) % 14.79/14.65 => c_Relation_Oantisym(T_b,V_r_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_antisym__Id__on,axiom, % 14.79/14.65 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_antisym__Id,axiom, % 14.79/14.65 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_antisym__empty,axiom, % 14.79/14.65 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_antisym__converse,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 14.79/14.65 <=> c_Relation_Oantisym(T_b,V_r_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_antisymD,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Oantisym(T_b,V_r_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.65 => ( 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_a_2)),V_r_2)) % 14.79/14.65 => V_a_2 = V_b_2 ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_antisym__def,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Oantisym(T_b,V_r_2) % 14.79/14.65 <=> ! [B_x,B_y] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) % 14.79/14.65 => B_x = B_y ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_antisym__reflcl,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) % 14.79/14.65 <=> c_Relation_Oantisym(T_b,V_r_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_acyclic__impl__antisym__rtrancl,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 14.79/14.65 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_fun__lub__def,axiom, % 14.79/14.65 ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__trans__comp__subset,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__def,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 <=> ! [B_x,B_y] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_symD,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 14.79/14.65 => 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_a_2)),V_r_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__converse,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 14.79/14.65 <=> c_Relation_Osym(T_b,V_r_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__conv__converse__eq,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_listrel__sym,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__Id__on,axiom, % 14.79/14.65 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__trancl,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__Un,axiom, % 14.79/14.65 ! [V_s_2,V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => ( c_Relation_Osym(T_b,V_s_2) % 14.79/14.65 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__Id,axiom, % 14.79/14.65 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__rtrancl,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__Int,axiom, % 14.79/14.65 ! [V_s_2,V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => ( c_Relation_Osym(T_b,V_s_2) % 14.79/14.65 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__Un__converse,axiom, % 14.79/14.65 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__inv__image,axiom, % 14.79/14.65 ! [V_f_2,T_c,V_r_2,T_b] : % 14.79/14.65 ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_sym__Int__converse,axiom, % 14.79/14.65 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_equivE,axiom, % 14.79/14.65 ! [V_r_2,V_A_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.65 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.65 => ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_equivI,axiom, % 14.79/14.65 ! [V_r_2,V_A_2,T_b] : % 14.79/14.65 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.65 => ( c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 => ( c_Relation_Otrans(T_b,V_r_2) % 14.79/14.65 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_equiv__def,axiom, % 14.79/14.65 ! [V_r_2,V_A_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 14.79/14.65 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 14.79/14.65 & c_Relation_Osym(T_b,V_r_2) % 14.79/14.65 & c_Relation_Otrans(T_b,V_r_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_symp__def,axiom, % 14.79/14.65 ! [V_r_2,T_b] : % 14.79/14.65 ( c_Predicate_Osymp(T_b,V_r_2) % 14.79/14.65 <=> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_part__equivp__refl__symp__transp,axiom, % 14.79/14.65 ! [V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 14.79/14.65 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 14.79/14.65 & c_Predicate_Osymp(T_b,V_R_2) % 14.79/14.65 & c_Predicate_Otransp(T_b,V_R_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_part__equivpI,axiom, % 14.79/14.65 ! [T_b,V_R_2] : % 14.79/14.65 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 14.79/14.65 => ( c_Predicate_Osymp(T_b,V_R_2) % 14.79/14.65 => ( c_Predicate_Otransp(T_b,V_R_2) % 14.79/14.65 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_equivp__implies__part__equivp,axiom, % 14.79/14.65 ! [V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.65 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_part__equivp__def,axiom, % 14.79/14.65 ! [V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 14.79/14.65 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 14.79/14.65 & ! [B_x,B_y] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 14.79/14.65 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 14.79/14.65 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y)) % 14.79/14.65 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_part__equivp__symp,axiom, % 14.79/14.65 ! [V_y_2,V_x_2,V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_part__equivp__transp,axiom, % 14.79/14.65 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_part__equivpE,axiom, % 14.79/14.65 ! [V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 14.79/14.65 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 14.79/14.65 => ( c_Predicate_Osymp(T_b,V_R_2) % 14.79/14.65 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_part__equivp__typedef,axiom, % 14.79/14.65 ! [V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 14.79/14.65 => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inj__iff,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__o__cancel,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_o__inv__o__cancel,axiom, % 14.79/14.65 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__id,axiom, % 14.79/14.65 ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b) ). % 14.79/14.65 % 14.79/14.65 fof(fact_image__inv__into__cancel,axiom, % 14.79/14.65 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] : % 14.79/14.65 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2)) % 14.79/14.65 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_surj__iff__all,axiom, % 14.79/14.65 ! [V_f_2,T_b,T_c] : % 14.79/14.65 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.65 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_surj__f__inv__f,axiom, % 14.79/14.65 ! [V_y_2,V_f_2,T_b,T_c] : % 14.79/14.65 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.65 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_image__surj__f__inv__f,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_b,T_c] : % 14.79/14.65 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.65 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__into__injective,axiom, % 14.79/14.65 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] : % 14.79/14.65 ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 14.79/14.65 => V_x_2 = V_y_2 ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__into__into,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_f__inv__into__f,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 14.79/14.65 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__into__f__f,axiom, % 14.79/14.65 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.65 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__into__f__eq,axiom, % 14.79/14.65 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 14.79/14.65 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 14.79/14.65 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__f__eq,axiom, % 14.79/14.65 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 14.79/14.65 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__f__f,axiom, % 14.79/14.65 ! [V_x_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__into__def,axiom, % 14.79/14.65 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(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_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__def,axiom, % 14.79/14.65 ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inj__imp__surj__inv,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_image__inv__f__f,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__image__comp,axiom, % 14.79/14.65 ! [V_X_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_surj__imp__inj__inv,axiom, % 14.79/14.65 ! [V_f_2,T_b,T_c] : % 14.79/14.65 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.65 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inj__on__inv__into,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 14.79/14.65 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__into__image__cancel,axiom, % 14.79/14.65 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2)) % 14.79/14.65 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__into__comp,axiom, % 14.79/14.65 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) % 14.79/14.65 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)))) % 14.79/14.65 => hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_surj__iff,axiom, % 14.79/14.65 ! [V_f_2,T_b,T_c] : % 14.79/14.65 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 14.79/14.65 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inj__transfer,axiom, % 14.79/14.65 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => ( ! [B_y] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) ) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_fold__image__UN__disjoint,axiom, % 14.79/14.65 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] : % 14.79/14.65 ( class_Groups_Ocomm__monoid__mult(T_d) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2)) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 14.79/14.65 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 14.79/14.65 => ! [B_xa] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2)) % 14.79/14.65 => ( B_x != B_xa % 14.79/14.65 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) % 14.79/14.65 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_nat__of__induct,axiom, % 14.79/14.65 ! [V_Pa_2,V_y_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 14.79/14.65 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_nat__of__cases,axiom, % 14.79/14.65 ! [V_y_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 14.79/14.65 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_of__nat__induct,axiom, % 14.79/14.65 ! [V_x_2,V_Pa_2] : % 14.79/14.65 ( ! [B_y] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) ) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_of__nat__cases,axiom, % 14.79/14.65 ! [V_x_2] : % 14.79/14.65 ~ ! [B_y] : % 14.79/14.65 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y) % 14.79/14.65 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Orecs_I1_J,axiom, % 14.79/14.65 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ). % 14.79/14.65 % 14.79/14.65 fof(fact_beyond__def,axiom, % 14.79/14.65 ! [V_l,V_k] : % 14.79/14.65 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 14.79/14.65 => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) % 14.79/14.65 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 14.79/14.65 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_beyond__zero,axiom, % 14.79/14.65 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(fact_lazy__sequence_Orecs_I2_J,axiom, % 14.79/14.65 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__image__Collect__eq,axiom, % 14.79/14.65 ! [V_Pa_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_curry__def,axiom, % 14.79/14.65 ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_curryI,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] : % 14.79/14.65 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__id,axiom, % 14.79/14.65 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__imp__bij__inv,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__inv__eq,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inv__into__inv__into__eq,axiom, % 14.79/14.65 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 14.79/14.65 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__inv__into,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 14.79/14.65 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_o__inv__distrib,axiom, % 14.79/14.65 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__image__INT,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__comp__iff2,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2)) % 14.79/14.65 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2) % 14.79/14.65 <=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__comp,axiom, % 14.79/14.65 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 14.79/14.65 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,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_d,tc_HOL_Obool))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__comp__iff,axiom, % 14.79/14.65 ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 14.79/14.65 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2) % 14.79/14.65 <=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__trans,axiom, % 14.79/14.65 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 14.79/14.65 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2) % 14.79/14.65 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_curryE,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) % 14.79/14.65 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_curryD,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) % 14.79/14.65 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_curry__conv,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_finite__vimage__iff,axiom, % 14.79/14.65 ! [V_F_2,V_h_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_h_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))) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 14.79/14.65 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__image__Compl__eq,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__is__inj,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__imp__inj__on,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 14.79/14.65 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__def,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 14.79/14.65 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.65 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inj__on__imp__bij__betw,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.65 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__imp__surj,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 14.79/14.65 => hAPP(c_Set_Oimage(T_b,T_c,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)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__is__surj,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => hAPP(c_Set_Oimage(T_b,T_c,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)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__subset,axiom, % 14.79/14.65 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.79/14.65 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2 % 14.79/14.65 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__id,axiom, % 14.79/14.65 ! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__id__iff,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2) % 14.79/14.65 <=> V_A_2 = V_B_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__finite,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.65 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_BIJ,axiom, % 14.79/14.65 ! [V_B_2,T_c,V_A_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 14.79/14.65 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2) % 14.79/14.65 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__empty1,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 14.79/14.65 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__empty2,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) % 14.79/14.65 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__same__card,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 14.79/14.65 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__the__inv__into,axiom, % 14.79/14.65 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 14.79/14.65 => c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__combine,axiom, % 14.79/14.65 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 14.79/14.65 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2) % 14.79/14.65 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 14.79/14.65 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__betw__Disj__Un,axiom, % 14.79/14.65 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] : % 14.79/14.65 ( 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)) % 14.79/14.65 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 14.79/14.65 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 14.79/14.65 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) % 14.79/14.65 => c_Fun_Obij__betw(T_b,T_c,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_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__def,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 & hAPP(c_Set_Oimage(T_b,T_c,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)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bijI,axiom, % 14.79/14.65 ! [V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 14.79/14.65 => ( hAPP(c_Set_Oimage(T_b,T_c,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)) % 14.79/14.65 => c_Fun_Obij__betw(T_b,T_c,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))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_curry__split,axiom, % 14.79/14.65 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ). % 14.79/14.65 % 14.79/14.65 fof(fact_split__curry,axiom, % 14.79/14.65 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ). % 14.79/14.65 % 14.79/14.65 fof(fact_vimage__subset__eq,axiom, % 14.79/14.65 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bij__vimage__eq__inv__image,axiom, % 14.79/14.65 ! [V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Obij__betw(T_b,T_c,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))) % 14.79/14.65 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_ex__bij__betw__nat__finite__1,axiom, % 14.79/14.65 ! [V_M_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 14.79/14.65 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Cantor__Bernstein,axiom, % 14.79/14.65 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) % 14.79/14.65 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2)) % 14.79/14.65 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_ex__bij__betw__nat__finite,axiom, % 14.79/14.65 ! [V_M_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 14.79/14.65 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_ex__bij__betw__finite__nat,axiom, % 14.79/14.65 ! [V_M_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 14.79/14.65 => ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_refl__on__UNION,axiom, % 14.79/14.65 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] : % 14.79/14.65 ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 14.79/14.65 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 14.79/14.65 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bex__reg__eqv,axiom, % 14.79/14.65 ! [V_Pa_2,V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.65 => ( ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Respects__def,axiom, % 14.79/14.65 ! [V_x_2,V_R_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2)) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_in__respects,axiom, % 14.79/14.65 ! [V_R_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_bex__reg__right,axiom, % 14.79/14.65 ! [V_Pa_2,V_Qa_2,V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(V_Qa_2,B_x)) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 14.79/14.65 => ( ? [B_x1] : hBOOL(hAPP(V_Qa_2,B_x1)) % 14.79/14.65 => ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_babs__reg__eqv,axiom, % 14.79/14.65 ! [V_Pa_2,T_c,V_R_2,T_b] : % 14.79/14.65 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 14.79/14.65 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_Babs__def,axiom, % 14.79/14.65 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2)) % 14.79/14.65 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_wf__weak__decr__stable,axiom, % 14.79/14.65 ! [V_r_2,V_f_2,T_b] : % 14.79/14.65 ( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 14.79/14.65 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) % 14.79/14.65 => ? [B_i] : % 14.79/14.65 ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_INT__anti__mono,axiom, % 14.79/14.65 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_INT__greatest,axiom, % 14.79/14.65 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : % 14.79/14.65 ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) ) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_rtrancl__induct2,axiom, % 14.79/14.65 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) % 14.79/14.65 => ( ! [B_a,B_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 14.79/14.65 => ! [B_aa,B_ba] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) ) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_converse__rtranclE2,axiom, % 14.79/14.65 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 14.79/14.65 => ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2) % 14.79/14.65 => ~ ! [B_a,B_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2)) % 14.79/14.65 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_converse__rtrancl__induct2,axiom, % 14.79/14.65 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) % 14.79/14.65 => ( ! [B_a,B_b,B_aa,B_ba] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) ) % 14.79/14.65 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_congruentI,axiom, % 14.79/14.65 ! [T_c,V_f_2,V_r_2,T_b] : % 14.79/14.65 ( ! [B_y,B_z] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) % 14.79/14.65 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) ) % 14.79/14.65 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_congruent2I_H,axiom, % 14.79/14.65 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] : % 14.79/14.65 ( ! [B_y1,B_z1] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2)) % 14.79/14.65 => ! [B_y2,B_z2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2)) % 14.79/14.65 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) ) % 14.79/14.65 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact__03,axiom, % 14.79/14.65 ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_all__interval__nat__def,axiom, % 14.79/14.65 ! [V_j_2,V_i_2,V_Pa_2] : % 14.79/14.65 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) % 14.79/14.65 <=> ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2))) % 14.79/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact__04,axiom, % 14.79/14.65 ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__all__iff__all__interval__nat,axiom, % 14.79/14.65 ! [V_j_2,V_i_2,V_Pa_2] : % 14.79/14.65 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 14.79/14.65 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_list__ex__iff__not__all__inverval__nat,axiom, % 14.79/14.65 ! [V_j_2,V_i_2,V_Pa_2] : % 14.79/14.65 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 14.79/14.65 <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact__05,axiom, % 14.79/14.65 ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_folding__image_Ocong,axiom, % 14.79/14.65 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 14.79/14.65 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 14.79/14.65 => ( ! [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 14.79/14.65 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 14.79/14.65 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact__06,axiom, % 14.79/14.65 ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact__07,axiom, % 14.79/14.65 ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b) ). % 14.79/14.65 % 14.79/14.65 fof(fact_New__DSequence_Opos__map__def,axiom, % 14.79/14.65 ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_power__dvd__imp__le,axiom, % 14.79/14.65 ! [V_n,V_m,V_i] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Oorder__refl,axiom, % 14.79/14.65 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__0__right,axiom, % 14.79/14.65 ! [V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__1__left,axiom, % 14.79/14.65 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__imp__le,axiom, % 14.79/14.65 ! [V_n,V_k] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_nat__mult__dvd__cancel1,axiom, % 14.79/14.65 ! [V_n_2,V_m_2,V_k_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mult__cancel,axiom, % 14.79/14.65 ! [V_n,V_m,V_k] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_setprod__dvd__setprod__subset,axiom, % 14.79/14.65 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 14.79/14.65 ( ( class_Groups_Ocomm__monoid__mult(T_c) % 14.79/14.65 & class_Rings_Odvd(T_c) ) % 14.79/14.65 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inf__period_I4_J,axiom, % 14.79/14.65 ! [V_t_2,V_D_2,V_d_2,T_b] : % 14.79/14.65 ( ( class_Rings_Ocomm__ring(T_b) % 14.79/14.65 & class_Rings_Odvd(T_b) ) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 14.79/14.65 => ! [B_x,B_k] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_inf__period_I3_J,axiom, % 14.79/14.65 ! [V_t_2,V_D_2,V_d_2,T_b] : % 14.79/14.65 ( ( class_Rings_Ocomm__ring(T_b) % 14.79/14.65 & class_Rings_Odvd(T_b) ) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 14.79/14.65 => ! [B_x,B_k] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__div__eq__mult,axiom, % 14.79/14.65 ! [V_ca_2,V_b_2,V_a_2,T_b] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_b) % 14.79/14.65 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 14.79/14.65 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_ca_2 % 14.79/14.65 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__div__div__eq__mult,axiom, % 14.79/14.65 ! [V_d_2,V_b_2,V_ca_2,V_a_2,T_b] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_b) % 14.79/14.65 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.65 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2)) % 14.79/14.65 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_ca_2) % 14.79/14.65 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_nat__mult__dvd__cancel__disj,axiom, % 14.79/14.65 ! [V_n_2,V_m_2,V_k_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) % 14.79/14.65 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 14.79/14.65 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_div__mult__div__if__dvd,axiom, % 14.79/14.65 ! [V_w,V_z,V_x,V_y,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w)) % 14.79/14.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__div__mult,axiom, % 14.79/14.65 ! [V_c,V_b,V_a,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 14.79/14.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__div__mult__self,axiom, % 14.79/14.65 ! [V_b,V_a,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 14.79/14.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_div__mult__swap,axiom, % 14.79/14.65 ! [V_a,V_b,V_c,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 14.79/14.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mult__div__cancel,axiom, % 14.79/14.65 ! [V_b,V_a,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 14.79/14.65 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mult__right,axiom, % 14.79/14.65 ! [V_c,V_b,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mult__left,axiom, % 14.79/14.65 ! [V_c,V_b,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvdI,axiom, % 14.79/14.65 ! [V_k,V_b,V_a,T_a] : % 14.79/14.65 ( class_Rings_Odvd(T_a) % 14.79/14.65 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_mult__dvd__mono,axiom, % 14.79/14.65 ! [V_d,V_c,V_b,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mult,axiom, % 14.79/14.65 ! [V_b,V_c,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mult2,axiom, % 14.79/14.65 ! [V_c,V_b,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__triv__right,axiom, % 14.79/14.65 ! [V_b,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__triv__left,axiom, % 14.79/14.65 ! [V_b,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mult__cancel__left,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,V_ca_2,T_b] : % 14.79/14.65 ( class_Rings_Oidom(T_b) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) % 14.79/14.65 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.65 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mult__cancel__right,axiom, % 14.79/14.65 ! [V_b_2,V_ca_2,V_a_2,T_b] : % 14.79/14.65 ( class_Rings_Oidom(T_b) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))) % 14.79/14.65 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 14.79/14.65 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_unity__coeff__ex,axiom, % 14.79/14.65 ! [V_l_2,V_Pa_2,T_b] : % 14.79/14.65 ( ( class_Rings_Odvd(T_b) % 14.79/14.65 & class_Rings_Osemiring__0(T_b) ) % 14.79/14.65 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))) % 14.79/14.65 <=> ? [B_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) % 14.79/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_le__imp__power__dvd,axiom, % 14.79/14.65 ! [V_a,V_n,V_m,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__power__le,axiom, % 14.79/14.65 ! [V_m,V_n,V_y,V_x,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_power__le__dvd,axiom, % 14.79/14.65 ! [V_m,V_b,V_n,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_OatLeastatMost__subset__iff,axiom, % 14.79/14.65 ! [V_d_2,V_ca_2,V_b_2,V_a_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2,V_d_2))) % 14.79/14.65 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 14.79/14.65 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) % 14.79/14.65 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__diffD1,axiom, % 14.79/14.65 ! [V_n,V_m,V_k] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__diffD,axiom, % 14.79/14.65 ! [V_n,V_m,V_k] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_OlessThan__iff,axiom, % 14.79/14.65 ! [V_k_2,V_i_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) % 14.79/14.65 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_OgreaterThan__iff,axiom, % 14.79/14.65 ! [V_k_2,V_i_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) % 14.79/14.65 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_OatLeast__iff,axiom, % 14.79/14.65 ! [V_k_2,V_i_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_OatMost__iff,axiom, % 14.79/14.65 ! [V_k_2,V_i_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__1__iff__1,axiom, % 14.79/14.65 ! [V_m_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 14.79/14.65 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_nat__dvd__not__less,axiom, % 14.79/14.65 ! [V_n,V_m] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 14.79/14.65 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_div__power,axiom, % 14.79/14.65 ! [V_n,V_x,V_y,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 14.79/14.65 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__imp__mod__0,axiom, % 14.79/14.65 ! [V_b,V_a,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 14.79/14.65 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__eq__mod__eq__0,axiom, % 14.79/14.65 ! [V_b_2,V_a_2,T_b] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_b) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 14.79/14.65 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mod__iff,axiom, % 14.79/14.65 ! [V_m_2,V_n_2,V_k_2,T_b] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_b) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_mod__mod__cancel,axiom, % 14.79/14.65 ! [V_a,V_b,V_c,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 14.79/14.65 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mod,axiom, % 14.79/14.65 ! [V_n,V_m,V_k,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__mod__imp__dvd,axiom, % 14.79/14.65 ! [V_n,V_m,V_k,T_a] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_one__dvd,axiom, % 14.79/14.65 ! [V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__0__left,axiom, % 14.79/14.65 ! [V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 14.79/14.65 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_div__dvd__div,axiom, % 14.79/14.65 ! [V_ca_2,V_b_2,V_a_2,T_b] : % 14.79/14.65 ( class_Divides_Osemiring__div(T_b) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ca_2),V_a_2))) % 14.79/14.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)) ) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_nat__dvd__1__iff__1,axiom, % 14.79/14.65 ! [V_m_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 14.79/14.65 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__power__same,axiom, % 14.79/14.65 ! [V_n,V_y,V_x,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__refl,axiom, % 14.79/14.65 ! [V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd__trans,axiom, % 14.79/14.65 ! [V_c,V_b,V_a,T_a] : % 14.79/14.65 ( class_Rings_Ocomm__semiring__1(T_a) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Oeq__iff,axiom, % 14.79/14.65 ! [V_y_2,V_x_2] : % 14.79/14.65 ( V_x_2 = V_y_2 % 14.79/14.65 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 14.79/14.65 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Ole__less,axiom, % 14.79/14.65 ! [V_y_2,V_x_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 14.79/14.65 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 14.79/14.65 | V_x_2 = V_y_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Oless__le,axiom, % 14.79/14.65 ! [V_y_2,V_x_2] : % 14.79/14.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 14.79/14.65 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 14.79/14.65 & V_x_2 != V_y_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Oneq__le__trans,axiom, % 14.79/14.65 ! [V_b,V_a] : % 14.79/14.65 ( V_a != V_b % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Oeq__refl,axiom, % 14.79/14.65 ! [V_y,V_x] : % 14.79/14.65 ( V_x = V_y % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Oantisym__conv,axiom, % 14.79/14.65 ! [V_x_2,V_y_2] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 14.79/14.65 <=> V_x_2 = V_y_2 ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Ole__imp__less__or__eq,axiom, % 14.79/14.65 ! [V_y,V_x] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 14.79/14.65 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 14.79/14.65 | V_x = V_y ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Ole__neq__trans,axiom, % 14.79/14.65 ! [V_b,V_a] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 14.79/14.65 => ( V_a != V_b % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 14.79/14.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Oord__eq__le__trans,axiom, % 14.79/14.65 ! [V_c,V_b,V_a] : % 14.79/14.65 ( V_a = V_b % 14.79/14.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 14.79/14.65 % 14.79/14.65 fof(fact_dvd_Oord__le__eq__trans,axiom, % 14.79/14.65 ! [V_c,V_b,V_a] : % 14.79/14.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 14.79/14.65 => ( V_b = V_c % 14.79/14.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 14.79/14.65 % 14.79/14.65 %----Arity declarations (238) % 14.79/14.65 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 14.79/14.65 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Lattices_Obounded__lattice(T_1) % 14.79/14.65 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 14.79/14.65 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Lattices_Obounded__lattice(T_1) % 14.79/14.65 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Lattices_Obounded__lattice(T_1) % 14.79/14.65 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Lattices_Olattice(T_1) % 14.79/14.65 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Lattices_Olattice(T_1) % 14.79/14.65 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Lattices_Odistrib__lattice(T_1) % 14.79/14.65 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Lattices_Oboolean__algebra(T_1) % 14.79/14.65 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Orderings_Opreorder,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Orderings_Opreorder(T_1) % 14.79/14.65 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Finite__Set_Ofinite,axiom, % 14.79/14.65 ! [T_1,T_2] : % 14.79/14.65 ( ( class_Finite__Set_Ofinite(T_2) % 14.79/14.65 & class_Finite__Set_Ofinite(T_1) ) % 14.79/14.65 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Lattices_Olattice,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Lattices_Olattice(T_1) % 14.79/14.65 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Orderings_Oorder,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Orderings_Oorder(T_1) % 14.79/14.65 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Orderings_Otop,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Orderings_Otop(T_1) % 14.79/14.65 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Orderings_Oord,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Orderings_Oord(T_1) % 14.79/14.65 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Orderings_Obot,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Orderings_Obot(T_1) % 14.79/14.65 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Groups_Ouminus,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Groups_Ouminus(T_1) % 14.79/14.65 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Groups_Ominus,axiom, % 14.79/14.65 ! [T_2,T_1] : % 14.79/14.65 ( class_Groups_Ominus(T_1) % 14.79/14.65 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__HOL_Oequal,axiom, % 14.79/14.65 ! [T_1,T_2] : % 14.79/14.65 ( ( class_Enum_Oenum(T_2) % 14.79/14.65 & class_HOL_Oequal(T_1) ) % 14.79/14.65 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_fun__Enum_Oenum,axiom, % 14.79/14.65 ! [T_1,T_2] : % 14.79/14.65 ( ( class_Enum_Oenum(T_2) % 14.79/14.65 & class_Enum_Oenum(T_1) ) % 14.79/14.65 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 14.79/14.65 class_HOL_Oequal(tc_Com_Ocom) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Com__Ocom__Nat_Osize,axiom, % 14.79/14.65 class_Nat_Osize(tc_Com_Ocom) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 14.79/14.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 14.79/14.65 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 14.79/14.65 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 14.79/14.65 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 14.79/14.65 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 14.79/14.65 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 14.79/14.65 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 14.79/14.65 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 14.79/14.65 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 14.79/14.65 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 14.79/14.65 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 14.79/14.65 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 14.79/14.65 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 14.79/14.65 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 14.79/14.65 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 14.79/14.65 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 14.79/14.65 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 14.79/14.65 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 14.79/14.65 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 14.79/14.65 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 14.79/14.65 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 14.79/14.65 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 14.79/14.65 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 14.79/14.65 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 14.79/14.65 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 14.79/14.65 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 14.79/14.65 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 14.79/14.65 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 14.79/14.65 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 14.79/14.65 class_Divides_Osemiring__div(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 14.79/14.65 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 14.79/14.65 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 14.79/14.65 class_Groups_Oab__group__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 14.79/14.65 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 14.79/14.65 class_Rings_Oordered__ring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 14.79/14.65 class_Orderings_Opreorder(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 14.79/14.65 class_Orderings_Olinorder(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 14.79/14.65 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 14.79/14.65 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 14.79/14.65 class_Groups_Omonoid__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 14.79/14.65 class_Rings_Osemiring__1(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 14.79/14.65 class_Rings_Osemiring__0(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 14.79/14.65 class_Lattices_Olattice(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 14.79/14.65 class_Groups_Ogroup__add(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 14.79/14.65 class_Divides_Oring__div(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 14.79/14.65 class_Rings_Omult__zero(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom, % 14.79/14.65 class_Rings_Ocomm__ring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 14.79/14.65 class_Orderings_Oorder(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 14.79/14.65 class_Int_Oring__char__0(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 14.79/14.65 class_Int_Onumber__ring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 14.79/14.65 class_Rings_Osemiring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Orderings_Oord,axiom, % 14.79/14.65 class_Orderings_Oord(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 14.79/14.65 class_Groups_Ouminus(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 14.79/14.65 class_Groups_Osgn__if(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 14.79/14.65 class_Groups_Oabs__if(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 14.79/14.65 class_Rings_Oring__1(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Ominus,axiom, % 14.79/14.65 class_Groups_Ominus(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Power_Opower,axiom, % 14.79/14.65 class_Power_Opower(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Ozero,axiom, % 14.79/14.65 class_Groups_Ozero(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oring,axiom, % 14.79/14.65 class_Rings_Oring(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Oidom,axiom, % 14.79/14.65 class_Rings_Oidom(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Int_Onumber,axiom, % 14.79/14.65 class_Int_Onumber(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Groups_Oone,axiom, % 14.79/14.65 class_Groups_Oone(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__Rings_Odvd,axiom, % 14.79/14.65 class_Rings_Odvd(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Int__Oint__HOL_Oequal,axiom, % 14.79/14.65 class_HOL_Oequal(tc_Int_Oint) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 14.79/14.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 14.79/14.65 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 14.79/14.65 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 14.79/14.65 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 14.79/14.65 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 14.79/14.65 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 14.79/14.65 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 14.79/14.65 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 14.79/14.65 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 14.79/14.65 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 14.79/14.65 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 14.79/14.65 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 14.79/14.65 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 14.79/14.65 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 14.79/14.65 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 14.79/14.65 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 14.79/14.65 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 14.79/14.65 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 14.79/14.65 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 14.79/14.65 class_Orderings_Owellorder(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 14.79/14.65 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 14.79/14.65 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 14.79/14.65 class_Orderings_Opreorder(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 14.79/14.65 class_Orderings_Olinorder(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 14.79/14.65 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 14.79/14.65 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 14.79/14.65 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 14.79/14.65 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 14.79/14.65 class_Lattices_Olattice(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 14.79/14.65 class_Rings_Omult__zero(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 14.79/14.65 class_Orderings_Oorder(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 14.79/14.65 class_Rings_Osemiring(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 14.79/14.65 class_Orderings_Oord(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 14.79/14.65 class_Orderings_Obot(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 14.79/14.65 class_Groups_Ominus(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Power_Opower,axiom, % 14.79/14.65 class_Power_Opower(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 14.79/14.65 class_Groups_Ozero(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Int_Onumber,axiom, % 14.79/14.65 class_Int_Onumber(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Groups_Oone,axiom, % 14.79/14.65 class_Groups_Oone(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Rings_Odvd,axiom, % 14.79/14.65 class_Rings_Odvd(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 14.79/14.65 class_HOL_Oequal(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nat__Onat__Nat_Osize,axiom, % 14.79/14.65 class_Nat_Osize(tc_Nat_Onat) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 14.79/14.65 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 14.79/14.65 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 14.79/14.65 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 14.79/14.65 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 14.79/14.65 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 14.79/14.65 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 14.79/14.65 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 14.79/14.65 class_Orderings_Opreorder(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 14.79/14.65 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 14.79/14.65 class_Lattices_Olattice(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 14.79/14.65 class_Orderings_Oorder(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 14.79/14.65 class_Orderings_Otop(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 14.79/14.65 class_Orderings_Oord(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 14.79/14.65 class_Orderings_Obot(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 14.79/14.65 class_Groups_Ouminus(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 14.79/14.65 class_Groups_Ominus(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 14.79/14.65 class_HOL_Oequal(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 14.79/14.65 class_Enum_Oenum(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_HOL__Obool__Nat_Osize,axiom, % 14.79/14.65 class_Nat_Osize(tc_HOL_Obool) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 14.79/14.65 class_HOL_Oequal(tc_Com_Ostate) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Com__Ostate__Nat_Osize,axiom, % 14.79/14.65 class_Nat_Osize(tc_Com_Ostate) ). % 14.79/14.65 % 14.79/14.65 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 14.79/14.65 ! [T_1] : % 14.79/14.65 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 14.79/14.65 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_List__Olist__HOL_Oequal,axiom, % 14.79/14.65 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_List__Olist__Nat_Osize,axiom, % 14.79/14.65 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_sum__Finite__Set_Ofinite,axiom, % 14.79/14.65 ! [T_1,T_2] : % 14.79/14.65 ( ( class_Finite__Set_Ofinite(T_2) % 14.79/14.65 & class_Finite__Set_Ofinite(T_1) ) % 14.79/14.65 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_sum__HOL_Oequal,axiom, % 14.79/14.65 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_sum__Enum_Oenum,axiom, % 14.79/14.65 ! [T_1,T_2] : % 14.79/14.65 ( ( class_Enum_Oenum(T_2) % 14.79/14.65 & class_Enum_Oenum(T_1) ) % 14.79/14.65 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_sum__Nat_Osize,axiom, % 14.79/14.65 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 14.79/14.65 ! [T_1] : % 14.79/14.65 ( class_Finite__Set_Ofinite(T_1) % 14.79/14.65 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 14.79/14.65 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 14.79/14.65 ! [T_1] : % 14.79/14.65 ( class_Enum_Oenum(T_1) % 14.79/14.65 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Option__Ooption__Nat_Osize,axiom, % 14.79/14.65 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom, % 14.79/14.65 ! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom, % 14.79/14.65 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 14.79/14.65 ! [T_1,T_2] : % 14.79/14.65 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 14.79/14.65 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 14.79/14.65 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_prod__Finite__Set_Ofinite,axiom, % 14.79/14.65 ! [T_1,T_2] : % 14.79/14.65 ( ( class_Finite__Set_Ofinite(T_2) % 14.79/14.65 & class_Finite__Set_Ofinite(T_1) ) % 14.79/14.65 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_prod__HOL_Oequal,axiom, % 14.79/14.65 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_prod__Enum_Oenum,axiom, % 14.79/14.65 ! [T_1,T_2] : % 14.79/14.65 ( ( class_Enum_Oenum(T_2) % 14.79/14.65 & class_Enum_Oenum(T_1) ) % 14.79/14.65 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 14.79/14.65 % 14.79/14.65 fof(arity_prod__Nat_Osize,axiom, % 14.79/14.65 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 14.79/14.65 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 14.79/14.65 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 14.79/14.65 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 14.79/14.65 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 14.79/14.65 class_Nat_Osize(tc_Product__Type_Ounit) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 14.79/14.65 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 14.79/14.65 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 14.79/14.65 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 14.79/14.65 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 14.79/14.65 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 14.79/14.65 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 14.79/14.65 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 14.79/14.65 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 14.79/14.65 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 14.79/14.65 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 14.79/14.65 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 14.79/14.65 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 14.79/14.65 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 14.79/14.65 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 14.79/14.65 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 14.79/14.65 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 14.79/14.65 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 14.79/14.65 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 14.79/14.65 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 14.79/14.65 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 14.79/14.65 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 14.79/14.65 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 14.79/14.65 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 14.79/14.65 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 14.79/14.65 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 14.79/14.65 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 14.79/14.65 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 14.79/14.65 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 14.79/14.65 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 14.79/14.65 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 14.79/14.65 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 14.79/14.65 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 14.79/14.65 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 14.79/14.65 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 14.79/14.65 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 14.79/14.65 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 14.79/14.65 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 14.79/14.65 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom, % 14.79/14.65 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 14.79/14.65 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 14.79/14.65 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 14.79/14.65 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 14.79/14.65 % 14.79/14.65 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 14.79/14.65 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 14.79/14.65 % 14.79/14.65 %----Helper facts (20) % 14.79/14.65 fof(help_c__COMBI__1,axiom, % 14.79/14.65 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 14.79/14.65 % 14.79/14.65 fof(help_c__COMBK__1,axiom, % 14.79/14.65 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 14.79/14.65 % 14.79/14.65 fof(help_c__COMBB__1,axiom, % 14.79/14.65 ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__COMBC__1,axiom, % 14.79/14.65 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__COMBS__1,axiom, % 14.79/14.65 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fequal__1,axiom, % 14.79/14.65 ! [V_y_2,V_x_2] : % 14.79/14.65 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 14.79/14.65 | V_x_2 = V_y_2 ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fequal__2,axiom, % 14.79/14.65 ! [V_y_2,V_x_2] : % 14.79/14.65 ( V_x_2 != V_y_2 % 14.79/14.65 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fFalse__1,axiom, % 14.79/14.65 ~ hBOOL(c_fFalse) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fTrue__1,axiom, % 14.79/14.65 hBOOL(c_fTrue) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fNot__1,axiom, % 14.79/14.65 ! [V_Pa_2] : % 14.79/14.65 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 14.79/14.65 | ~ hBOOL(V_Pa_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fNot__2,axiom, % 14.79/14.65 ! [V_Pa_2] : % 14.79/14.65 ( ~ ~ hBOOL(V_Pa_2) % 14.79/14.65 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fconj__1,axiom, % 14.79/14.65 ! [V_Qa_2,V_Pa_2] : % 14.79/14.65 ( ~ hBOOL(V_Pa_2) % 14.79/14.65 | ~ hBOOL(V_Qa_2) % 14.79/14.65 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fconj__2,axiom, % 14.79/14.65 ! [V_Qa_2,V_Pa_2] : % 14.79/14.65 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) % 14.79/14.65 | hBOOL(V_Pa_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fconj__3,axiom, % 14.79/14.65 ! [V_Qa_2,V_Pa_2] : % 14.79/14.65 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) % 14.79/14.65 | hBOOL(V_Qa_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fdisj__1,axiom, % 14.79/14.65 ! [V_Qa_2,V_Pa_2] : % 14.79/14.65 ( ~ hBOOL(V_Pa_2) % 14.79/14.65 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fdisj__2,axiom, % 14.79/14.65 ! [V_Pa_2,V_Qa_2] : % 14.79/14.65 ( ~ hBOOL(V_Qa_2) % 14.79/14.65 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fdisj__3,axiom, % 14.79/14.65 ! [V_Qa_2,V_Pa_2] : % 14.79/14.65 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) % 14.79/14.65 | hBOOL(V_Pa_2) % 14.79/14.65 | hBOOL(V_Qa_2) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fimplies__1,axiom, % 14.79/14.65 ! [V_Qa_2,V_Pa_2] : % 14.79/14.65 ( hBOOL(V_Pa_2) % 14.79/14.65 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fimplies__2,axiom, % 14.79/14.65 ! [V_Pa_2,V_Qa_2] : % 14.79/14.65 ( ~ hBOOL(V_Qa_2) % 14.79/14.65 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ). % 14.79/14.65 % 14.79/14.65 fof(help_c__fimplies__3,axiom, % 14.79/14.65 ! [V_Qa_2,V_Pa_2] : % 14.79/14.65 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) % 14.79/14.65 | ~ hBOOL(V_Pa_2) % 14.79/14.65 | hBOOL(V_Qa_2) ) ). % 14.79/14.65 % 14.79/14.65 %----Conjectures (2) % 14.79/14.65 fof(conj_0,hypothesis, % 14.79/14.65 ! [B_Z,B_s] : % 14.79/14.65 ( v_P(B_Z,B_s) % 14.79/14.65 => v_P_H(B_Z,B_s) ) ). % 14.79/14.65 % 14.79/14.65 fof(conj_1,conjecture, % 14.79/14.65 ! [B_Z,B_s] : % 14.79/14.65 ( v_P(B_Z,B_s) % 14.79/14.65 => ! [B_s_H] : % 14.79/14.65 ( ! [B_Z_H] : % 14.79/14.65 ( v_P_H(B_Z_H,B_s) % 14.79/14.65 => v_Q(B_Z_H,B_s_H) ) % 14.79/14.65 => v_Q(B_Z,B_s_H) ) ) ). % 14.79/14.65 % 14.79/14.65 %------------------------------------------------------------------------------ % 14.79/14.65 %------------------------------------------- % 14.79/14.65 % Proof found % 14.79/14.65 % SZS status Theorem for theBenchmark % 14.79/14.65 % SZS output start Proof % 14.79/14.65 %ClaNum:10481(EqnAxiom:3107) % 14.79/14.65 %VarNum:70903(SingletonVarNum:20453) % 14.79/14.65 %MaxLitNum:8 % 14.79/14.65 %MaxfuncDepth:13 % 14.79/14.65 %SharedTerms:1012 % 14.79/14.65 %goalClause: 3330 4667 4773 % 14.79/14.65 %singleGoalClaCount:2 % 14.79/14.65 [3111]P1(a180) % 14.79/14.65 [3112]P2(a919) % 14.79/14.65 [3113]P2(a920) % 14.79/14.65 [3114]P2(a921) % 14.79/14.65 [3115]P2(a924) % 14.79/14.65 [3116]P2(a927) % 14.79/14.65 [3117]P2(a1) % 14.79/14.65 [3118]P2(a92) % 14.79/14.65 [3119]P2(a315) % 14.79/14.65 [3120]P3(a921) % 14.79/14.65 [3121]P91(a921) % 14.79/14.65 [3122]P91(a924) % 14.79/14.65 [3123]P91(a1) % 14.79/14.65 [3124]P91(a92) % 14.79/14.65 [3125]P111(a921) % 14.79/14.65 [3126]P92(a921) % 14.79/14.65 [3127]P92(a924) % 14.79/14.65 [3128]P108(a921) % 14.79/14.65 [3129]P108(a924) % 14.79/14.65 [3130]P108(a1) % 14.79/14.65 [3131]P108(a92) % 14.79/14.65 [3132]P109(a924) % 14.79/14.65 [3133]P109(a1) % 14.79/14.65 [3134]P109(a92) % 14.79/14.65 [3135]P110(a921) % 14.79/14.65 [3136]P110(a924) % 14.79/14.65 [3137]P110(a1) % 14.79/14.65 [3138]P110(a92) % 14.79/14.65 [3139]P93(a921) % 14.79/14.65 [3140]P93(a924) % 14.79/14.65 [3141]P93(a1) % 14.79/14.65 [3142]P58(a921) % 14.79/14.65 [3143]P58(a924) % 14.79/14.65 [3144]P58(a1) % 14.79/14.65 [3145]P58(a92) % 14.79/14.65 [3146]P94(a921) % 14.79/14.65 [3147]P103(a921) % 14.79/14.65 [3148]P103(a924) % 14.79/14.65 [3149]P103(a1) % 14.79/14.65 [3150]P104(a921) % 14.79/14.65 [3151]P104(a924) % 14.79/14.65 [3152]P104(a1) % 14.79/14.65 [3153]P95(a921) % 14.79/14.65 [3154]P102(a921) % 14.79/14.65 [3155]P102(a924) % 14.79/14.65 [3156]P102(a1) % 14.79/14.65 [3157]P78(a1) % 14.79/14.65 [3158]P59(a1) % 14.79/14.65 [3159]P96(a921) % 14.79/14.65 [3160]P68(a1) % 14.79/14.65 [3161]P82(a921) % 14.79/14.65 [3162]P82(a1) % 14.79/14.65 [3163]P69(a924) % 14.79/14.65 [3164]P69(a1) % 14.79/14.65 [3165]P69(a92) % 14.79/14.65 [3166]P112(a1) % 14.79/14.65 [3167]P125(a1) % 14.79/14.65 [3168]P113(a1) % 14.79/14.65 [3169]P60(a921) % 14.79/14.65 [3170]P60(a927) % 14.79/14.65 [3171]P71(a924) % 14.79/14.65 [3172]P71(a1) % 14.79/14.65 [3173]P71(a92) % 14.79/14.65 [3174]P72(a924) % 14.79/14.65 [3175]P72(a1) % 14.79/14.65 [3176]P72(a92) % 14.79/14.65 [3177]P83(a924) % 14.79/14.65 [3178]P83(a1) % 14.79/14.65 [3179]P83(a92) % 14.79/14.65 [3180]P70(a924) % 14.79/14.65 [3181]P70(a1) % 14.79/14.65 [3182]P70(a92) % 14.79/14.65 [3183]P73(a924) % 14.79/14.65 [3184]P73(a1) % 14.79/14.65 [3185]P73(a92) % 14.79/14.65 [3186]P74(a924) % 14.79/14.65 [3187]P74(a1) % 14.79/14.65 [3188]P74(a92) % 14.79/14.65 [3189]P84(a924) % 14.79/14.65 [3190]P84(a1) % 14.79/14.65 [3191]P84(a92) % 14.79/14.65 [3192]P85(a924) % 14.79/14.65 [3193]P85(a1) % 14.79/14.65 [3194]P85(a92) % 14.79/14.65 [3195]P140(a924) % 14.79/14.65 [3196]P140(a1) % 14.79/14.65 [3197]P140(a92) % 14.79/14.65 [3198]P114(a924) % 14.79/14.65 [3199]P114(a1) % 14.79/14.65 [3200]P114(a92) % 14.79/14.65 [3201]P126(a1) % 14.79/14.65 [3202]P115(a1) % 14.79/14.65 [3203]P119(a924) % 14.79/14.65 [3204]P119(a1) % 14.79/14.65 [3205]P119(a92) % 14.79/14.65 [3206]P144(a924) % 14.79/14.65 [3207]P144(a1) % 14.79/14.65 [3208]P79(a924) % 14.79/14.65 [3209]P79(a1) % 14.79/14.65 [3210]P79(a92) % 14.79/14.65 [3211]P80(a924) % 14.79/14.65 [3212]P80(a1) % 14.79/14.65 [3213]P80(a92) % 14.79/14.65 [3214]P127(a924) % 14.79/14.65 [3215]P127(a1) % 14.79/14.65 [3216]P127(a92) % 14.79/14.65 [3217]P141(a1) % 14.79/14.65 [3218]P130(a1) % 14.79/14.65 [3219]P90(a924) % 14.79/14.65 [3220]P90(a1) % 14.79/14.65 [3221]P90(a92) % 14.79/14.65 [3222]P81(a924) % 14.79/14.65 [3223]P81(a1) % 14.79/14.65 [3224]P81(a92) % 14.79/14.65 [3225]P76(a1) % 14.79/14.65 [3226]P133(a924) % 14.79/14.65 [3227]P133(a1) % 14.79/14.65 [3228]P133(a92) % 14.79/14.65 [3229]P143(a1) % 14.79/14.65 [3230]P134(a924) % 14.79/14.65 [3231]P134(a1) % 14.79/14.65 [3232]P134(a92) % 14.79/14.65 [3233]P145(a924) % 14.79/14.65 [3234]P145(a1) % 14.79/14.65 [3235]P145(a92) % 14.79/14.65 [3236]P87(a924) % 14.79/14.65 [3237]P87(a1) % 14.79/14.65 [3238]P87(a92) % 14.79/14.65 [3239]P136(a924) % 14.79/14.65 [3240]P136(a1) % 14.79/14.65 [3241]P136(a92) % 14.79/14.65 [3242]P138(a924) % 14.79/14.65 [3243]P138(a1) % 14.79/14.65 [3244]P138(a92) % 14.79/14.65 [3245]P137(a924) % 14.79/14.65 [3246]P137(a1) % 14.79/14.65 [3247]P137(a92) % 14.79/14.65 [3248]P128(a1) % 14.79/14.65 [3249]P129(a1) % 14.79/14.65 [3250]P123(a924) % 14.79/14.65 [3251]P123(a1) % 14.79/14.65 [3252]P123(a92) % 14.79/14.65 [3253]P135(a924) % 14.79/14.65 [3254]P135(a1) % 14.79/14.65 [3255]P135(a92) % 14.79/14.65 [3256]P131(a924) % 14.79/14.65 [3257]P131(a1) % 14.79/14.65 [3258]P131(a92) % 14.79/14.65 [3259]P132(a1) % 14.79/14.65 [3260]P142(a1) % 14.79/14.65 [3261]P97(a1) % 14.79/14.65 [3262]P88(a1) % 14.79/14.65 [3263]P98(a1) % 14.79/14.65 [3264]P99(a924) % 14.79/14.65 [3265]P99(a1) % 14.79/14.65 [3266]P99(a92) % 14.79/14.65 [3267]P116(a924) % 14.79/14.65 [3268]P116(a1) % 14.79/14.65 [3269]P116(a92) % 14.79/14.65 [3270]P146(a924) % 14.79/14.65 [3271]P146(a1) % 14.79/14.65 [3272]P146(a92) % 14.79/14.65 [3273]P105(a924) % 14.79/14.65 [3274]P105(a1) % 14.79/14.65 [3275]P105(a92) % 14.79/14.65 [3276]P61(a924) % 14.79/14.65 [3277]P61(a1) % 14.79/14.65 [3278]P61(a92) % 14.79/14.65 [3279]P147(a924) % 14.79/14.65 [3280]P147(a1) % 14.79/14.65 [3281]P147(a92) % 14.79/14.65 [3282]P62(a1) % 14.79/14.65 [3283]P86(a1) % 14.79/14.65 [3284]P139(a1) % 14.79/14.65 [3285]P75(a1) % 14.79/14.65 [3286]P77(a924) % 14.79/14.65 [3287]P77(a1) % 14.79/14.65 [3288]P77(a92) % 14.79/14.65 [3289]P117(a924) % 14.79/14.65 [3290]P89(a924) % 14.79/14.65 [3291]P89(a1) % 14.79/14.65 [3292]P89(a92) % 14.79/14.65 [3293]P63(a921) % 14.79/14.65 [3294]P63(a927) % 14.79/14.65 [3295]P107(a919) % 14.79/14.65 [3296]P107(a920) % 14.79/14.65 [3297]P107(a921) % 14.79/14.65 [3298]P107(a924) % 14.79/14.65 [3299]P107(a927) % 14.79/14.65 [3300]P107(a92) % 14.79/14.65 [3301]P107(a315) % 14.79/14.65 [3302]P106(a927) % 14.79/14.65 [3303]P106(a1) % 14.79/14.65 [3304]P120(a924) % 14.79/14.65 [3305]P120(a1) % 14.79/14.65 [3306]P120(a92) % 14.79/14.65 [3307]P118(a1) % 14.79/14.65 [3308]P101(a921) % 14.79/14.65 [3327]P35(a924,a232) % 14.79/14.65 [3328]P35(a924,a309) % 14.79/14.65 [3329]P36(a924,a232) % 14.79/14.65 [3330]P150(a316,a861) % 14.79/14.65 [4663]~E(a90,a76) % 14.79/14.65 [4664]~P25(a5000) % 14.79/14.65 [4665]~P1(a231) % 14.79/14.65 [4667]~P151(a316,a863) % 14.79/14.65 [3108]E(f2(a1),a76) % 14.79/14.65 [3109]E(f3(a92),a4) % 14.79/14.65 [3110]E(f93(a92),a5) % 14.79/14.65 [3309]E(f181(a924),f2(a924)) % 14.79/14.65 [3310]E(f94(a924),f225(a924)) % 14.79/14.65 [3311]E(f103(a924),f226(a924)) % 14.79/14.65 [3312]E(f95(a1),f25(a1)) % 14.79/14.65 [3313]E(f77(a231),f2(a924)) % 14.79/14.65 [3314]E(f77(a180),f2(a924)) % 14.79/14.65 [3315]P4(f71(a1)) % 14.79/14.65 [3316]P4(f2(a1)) % 14.79/14.65 [3379]P35(f931(a924,a924),a26) % 14.79/14.65 [3725]E(f311(a924,a924,a232,a232),a26) % 14.79/14.65 [4666]~E(f71(a1),f2(a1)) % 14.79/14.65 [3317]E(f6(f2(a92)),f2(a924)) % 14.79/14.65 [3318]E(f104(f2(a924)),f2(a924)) % 14.79/14.65 [3332]E(f862(f72(a1),a76),a76) % 14.79/14.65 [3335]E(f862(a105,f2(a924)),f71(a924)) % 14.79/14.65 [3336]E(f862(a97,f71(a1)),f71(a924)) % 14.79/14.65 [3337]E(f862(a5,f71(a924)),f71(a92)) % 14.79/14.65 [3339]E(f862(a5,f2(a924)),f2(a92)) % 14.79/14.65 [3341]E(f862(f96(a1),a76),f2(a1)) % 14.79/14.65 [3342]E(f862(f96(a92),a76),f2(a92)) % 14.79/14.65 [3343]E(f862(a97,f2(a1)),f2(a924)) % 14.79/14.65 [3344]E(f862(f96(a924),a76),f2(a924)) % 14.79/14.65 [3345]E(f862(f182(a921),a231),f2(a924)) % 14.79/14.65 [3346]E(f862(f182(a921),a180),f2(a924)) % 14.79/14.65 [3352]E(f862(f72(a1),f71(a1)),a90) % 14.79/14.65 [3359]E(f862(f72(a1),f2(a1)),f2(a1)) % 14.79/14.65 [3360]E(f862(f93(a1),f71(a924)),f71(a1)) % 14.79/14.65 [3361]E(f862(f93(a1),f2(a924)),f2(a1)) % 14.79/14.65 [3363]E(f862(f182(a92),f2(a92)),f2(a924)) % 14.79/14.65 [3376]E(f862(a97,f71(a1)),f862(a105,f2(a924))) % 14.79/14.65 [3377]E(f310(f931(a924,a924),a26),a27) % 14.79/14.65 [3378]E(f312(f931(a924,a924),a26),a62) % 14.79/14.65 [3405]E(f862(f274(a924),f2(a924)),f234(f932(a924,a921))) % 14.79/14.65 [3406]E(f862(f292(a924),f2(a924)),f181(f932(a924,a921))) % 14.79/14.65 [3415]P38(f181(f932(a1,a921))) % 14.79/14.65 [3449]E(f862(f862(f3(a92),f2(a92)),f71(a92)),f2(a92)) % 14.79/14.65 [3528]P1(f862(f862(f228(a1),a90),f2(a1))) % 14.79/14.65 [3552]P1(f862(f862(f227(a1),f2(a1)),f71(a1))) % 14.79/14.65 [3554]P1(f862(f862(f228(a1),f2(a1)),f71(a1))) % 14.79/14.65 [3756]E(f862(f862(f280(a924,a924,a924),a309),f299(a924,a309)),a232) % 14.79/14.65 [3793]P39(a1,a924,a97,f862(f227(a1),f2(a1))) % 14.79/14.65 [3797]E(f862(f862(f32(a924,f932(a924,a921)),f234(f932(a924,a921))),f293(a924)),f181(f932(a924,a921))) % 14.79/14.65 [3798]E(f862(f862(f33(a924,f932(a924,a921)),f234(f932(a924,a921))),f294(a924)),f234(f932(a924,a921))) % 14.79/14.65 [3799]E(f862(f862(f33(a924,f932(a924,a921)),f234(f932(a924,a921))),f274(a924)),f234(f932(a924,a921))) % 14.79/14.65 [3800]E(f862(f862(f33(a924,f932(a924,a921)),f234(f932(a924,a921))),f292(a924)),f234(f932(a924,a921))) % 14.79/14.65 [3815]P22(a924,a1,f93(a1),f234(f932(a924,a921))) % 14.79/14.65 [3829]P39(a924,a1,f93(a1),f862(f18(a921,a924),a180)) % 14.79/14.65 [3963]E(f862(f66(a924,a92,a1,a5),a97),f96(a92)) % 14.79/14.65 [4182]P54(a92,a924,a22,a5,f234(f932(a924,a921))) % 14.79/14.65 [4186]P54(a1,f932(f931(a924,a924),a921),a100,a82,a91) % 14.79/14.65 [4441]E(f250(a1,a1,a1,a1,f25(a1),f72(a1)),a44) % 14.79/14.65 [4676]~E(f862(f96(a1),a90),f862(f96(a1),a76)) % 14.79/14.65 [4677]~P1(f862(a186,f71(a1))) % 14.79/14.65 [4678]~P1(f862(a186,f2(a1))) % 14.79/14.65 [4705]~P1(f862(f862(f228(a1),a76),f2(a1))) % 14.79/14.65 [3397]E(f862(f862(f3(a1),a90),a90),a76) % 14.79/14.65 [3413]E(f862(f93(a1),f862(a105,f2(a924))),f71(a1)) % 14.79/14.65 [3479]E(f862(f28(a927),f234(f932(a927,a921))),f71(a924)) % 14.79/14.65 [3499]P1(f862(a186,f862(f96(a1),a90))) % 14.79/14.65 [3503]P1(f862(f862(f227(a1),a90),a76)) % 14.79/14.65 [3505]P1(f862(f862(f228(a1),a90),a76)) % 14.79/14.65 [3562]E(f862(f862(f301(a924),f2(a924)),f181(f932(a924,a921))),f862(f294(a924),f2(a924))) % 14.79/14.65 [3615]P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),a76))) % 14.79/14.65 [3627]E(f862(f302(a924,a924,a105),f234(f932(a924,a921))),f862(f293(a924),f2(a924))) % 14.79/14.65 [3662]P6(f931(a924,a924),f234(f932(f931(a924,a924),a921)),a101) % 14.79/14.65 [3970]E(f862(f66(a924,a1,a92,f93(a1)),a22),a24) % 14.79/14.65 [4029]P35(a924,f862(f254(f931(a924,a924)),f862(f249(a924,a924,a921),f228(a924)))) % 14.79/14.65 [4694]~P1(f862(a186,f862(f96(a1),a76))) % 14.79/14.65 [4695]~P1(f862(f862(f84(a1),a90),a76)) % 14.79/14.65 [4696]~P1(f862(f862(f84(a1),a76),a90)) % 14.79/14.65 [4697]~P1(f862(f862(f227(a1),a76),a90)) % 14.79/14.65 [4698]~P1(f862(f862(f228(a1),a90),a90)) % 14.79/14.65 [4699]~P1(f862(f862(f228(a1),a76),a90)) % 14.79/14.65 [4700]~P1(f862(f862(f228(a1),a76),a76)) % 14.79/14.65 [4709]~P1(f862(f54(a924),f234(f932(a924,a921)))) % 14.79/14.65 [4710]~P1(f862(f54(a1),f234(f932(a1,a921)))) % 14.79/14.65 [4609]E(f862(f249(a1,a1,a921),f862(f862(f10(f932(a1,a921),f932(a1,a921),a1),f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f228(a1),f2(a1))))),f862(f862(f9(a1,a1,f932(a1,a921)),f862(f862(f10(f932(a1,f932(a1,a921)),f932(a1,f932(a1,a921)),a1),f9(a1,a1,a921)),f862(f862(f10(f932(a1,a1),f932(a1,f932(a1,a921)),a1),f862(f10(a1,f932(a1,a921),a1),a317)),a210))),f71(a1)))),a206) % 14.79/14.65 [3699]E(f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90),f862(f72(a1),a90)) % 14.79/14.65 [3738]E(f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90),f862(f862(f3(a1),a76),a90)) % 14.79/14.65 [3897]E(f862(f862(f53(f931(a924,a924)),f234(f932(f931(a924,a924),a921))),a101),a91) % 14.79/14.65 [3926]E(f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(a1)) % 14.79/14.65 [3927]E(f862(f96(a92),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(a92)) % 14.79/14.65 [3928]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(a924)) % 14.79/14.65 [3931]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(a105,f2(a924))) % 14.79/14.65 [4308]E(f862(f862(f103(f932(f931(f931(a924,a924),f931(a924,a924)),a921)),a26),f299(f931(a924,a924),f181(f932(f931(f931(a924,a924),f931(a924,a924)),a921)))),a64) % 14.79/14.65 [4374]E(f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f71(a924)),f2(a924))),f181(f932(f931(a924,a924),a921))))),f71(a1)) % 14.79/14.65 [4375]E(f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f2(a924)),f2(a924))),f181(f932(f931(a924,a924),a921))))),f2(a1)) % 14.79/14.65 [4388]E(f862(f254(f931(a924,a924)),f862(f249(a924,a924,a921),f862(f862(f10(a924,f932(a924,a921),a924),f862(f9(a924,a924,a921),a317)),a105))),a309) % 14.79/14.65 [4360]E(f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),f862(a105,f862(a105,f2(a924)))) % 14.79/14.65 [4363]E(f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),f862(f862(f73(a924),f71(a924)),f71(a924))) % 14.79/14.65 [4364]E(f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),f862(f28(a921),f234(f932(a921,a921)))) % 14.79/14.65 [4427]P4(f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))) % 14.79/14.65 [4497]P24(f932(f931(a924,a924),a921),f862(f862(f244(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921),f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)),a27),a63)) % 14.79/14.65 [4498]P24(f932(f931(a924,a924),a921),f862(f862(f244(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921),f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)),a62),a65)) % 14.79/14.65 [4540]E(f862(f862(f103(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)),f312(f931(a924,a924),a64)),f862(f862(f301(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f181(f932(f931(a924,a924),a921))),f181(f932(f931(a924,a924),a921)))),f181(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)))),a65) % 14.79/14.65 [4541]E(f862(f862(f103(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)),f310(f931(a924,a924),a64)),f862(f862(f301(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f181(f932(f931(a924,a924),a921))),f181(f932(f931(a924,a924),a921)))),f181(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)))),a63) % 14.79/14.65 [4430]E(f862(a97,f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a105,f862(a105,f2(a924)))) % 14.79/14.65 [4475]E(f862(f93(a1),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))) % 14.79/14.65 [4508]P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.79/14.65 [4509]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90)),f862(a105,f862(a105,f862(a105,f2(a924))))) % 14.79/14.65 [4555]P4(f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))) % 14.79/14.65 [4581]E(f862(f93(a1),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))) % 14.79/14.65 [4594]P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90)))) % 14.79/14.65 [3331]P5(x33311,a317) % 14.79/14.65 [3726]P22(a924,a924,a105,x37261) % 14.79/14.65 [3319]P2(f923(x33191)) % 14.79/14.65 [3320]P2(f928(x33201)) % 14.79/14.65 [3321]P2(f925(x33211)) % 14.79/14.65 [3322]P2(f926(x33221)) % 14.79/14.65 [3323]P107(f923(x33231)) % 14.79/14.65 [3324]P107(f928(x33241)) % 14.79/14.65 [3325]P107(f925(x33251)) % 14.79/14.65 [3326]P107(f926(x33261)) % 14.79/14.65 [3347]P35(a1,f98(x33471)) % 14.79/14.65 [3348]P35(a1,f99(x33481)) % 14.79/14.65 [3401]P35(f932(x34011,a921),f306(x34011)) % 14.79/14.65 [3402]P36(f932(x34021,a921),f306(x34021)) % 14.79/14.65 [3427]E(f235(x34271,x34271,a317),a317) % 14.79/14.65 [3442]E(f38(a1,x34421,x34421),f2(a1)) % 14.79/14.65 [3496]P12(x34961,f932(x34961,a921),f301(x34961)) % 14.79/14.65 [4669]~E(f862(a105,x46691),x46691) % 14.79/14.65 [4675]~E(f862(a105,x46751),f2(a924)) % 14.79/14.65 [3333]E(f862(f96(a1),x33331),x33331) % 14.79/14.65 [3334]E(f862(f182(a924),x33341),x33341) % 14.79/14.65 [3349]E(f862(a82,f320(x33491)),x33491) % 14.79/14.65 [3350]E(f862(a5,f587(x33501)),x33501) % 14.79/14.65 [3351]E(f233(x33511,f2(a92)),f2(a92)) % 14.79/14.65 [3364]E(f107(x33641,f106(x33641)),f106(x33641)) % 14.79/14.65 [3365]E(f145(x33651,f106(x33651)),f106(x33651)) % 14.79/14.65 [3373]E(f862(f160(x33731),f106(x33731)),f106(x33731)) % 14.79/14.65 [3374]E(f862(f164(x33741),f106(x33741)),f106(x33741)) % 14.79/14.65 [3375]E(f862(f161(x33751),f106(x33751)),f106(x33751)) % 14.79/14.65 [3380]E(f862(f96(a1),x33801),f862(f95(a1),x33801)) % 14.79/14.65 [3381]E(f862(a82,f862(a100,x33811)),x33811) % 14.79/14.65 [3383]E(f862(a5,f862(a22,x33831)),x33831) % 14.79/14.65 [3384]E(f862(a22,f862(a5,x33841)),x33841) % 14.79/14.65 [3386]P4(f862(f93(a1),x33861)) % 14.79/14.65 [3395]E(f862(f182(f925(x33951)),f106(x33951)),f2(a924)) % 14.79/14.65 [3396]E(f862(f182(f926(x33961)),f112(x33961)),f2(a924)) % 14.79/14.65 [3418]E(f862(f862(f3(a924),x34181),f2(a924)),x34181) % 14.79/14.65 [3419]E(f862(f862(f74(a924),x34191),f71(a924)),x34191) % 14.79/14.65 [3420]E(f862(f862(f74(a1),x34201),f71(a1)),x34201) % 14.79/14.65 [3421]E(f862(f862(f73(a924),x34211),f2(a924)),x34211) % 14.79/14.65 [3422]E(f862(f862(f73(a1),x34221),f2(a1)),x34221) % 14.79/14.65 [3423]E(f862(f862(f226(a924),x34231),f2(a924)),x34231) % 14.79/14.65 [3424]E(f862(f862(f74(a924),x34241),f2(a924)),f2(a924)) % 14.79/14.65 [3425]E(f862(f862(f29(a1),x34251),f2(a1)),f2(a1)) % 14.79/14.65 [3426]E(f862(f862(f225(a924),x34261),f2(a924)),f2(a924)) % 14.79/14.65 [3433]E(f862(f165(x34331),f106(x34331)),f181(f932(x34331,a921))) % 14.79/14.65 [3437]P1(f862(f130(x34371),f106(x34371))) % 14.79/14.65 [3443]E(f862(f147(x34431,x34431),f7(x34431)),f25(f925(x34431))) % 14.79/14.65 [3444]E(f862(f147(x34441,x34441),f25(x34441)),f25(f925(x34441))) % 14.79/14.65 [3445]E(f38(a1,x34451,f2(a1)),x34451) % 14.79/14.65 [3446]E(f862(f227(a924),f862(a105,x34461)),f862(f228(a924),x34461)) % 14.79/14.65 [3447]E(f862(f274(a924),f862(a105,x34471)),f862(f293(a924),x34471)) % 14.79/14.65 [3448]E(f862(f292(a924),f862(a105,x34481)),f862(f294(a924),x34481)) % 14.79/14.65 [3450]E(f38(a1,f2(a1),x34501),f2(a1)) % 14.79/14.65 [3464]E(f862(f862(f73(a924),x34641),f71(a924)),f862(a105,x34641)) % 14.79/14.65 [3473]E(f862(f295(a924,x34731),f2(a924)),f181(f932(a924,a921))) % 14.79/14.65 [3485]E(f296(a924,f2(a924),x34851),f862(f294(a924),x34851)) % 14.79/14.65 [3531]E(f862(f862(f3(a924),f862(a105,x35311)),f71(a924)),x35311) % 14.79/14.65 [3543]E(f40(f2(a1),x35431),f862(f862(f244(a1,a1),f2(a1)),f2(a1))) % 14.79/14.65 [3590]P1(f862(f862(f228(a924),x35901),f862(a105,x35901))) % 14.79/14.65 [3602]P1(f862(f862(f228(a924),f2(a924)),f862(a105,x36021))) % 14.79/14.65 [3828]E(f86(x38281,x38281,f234(f932(x38281,a921)),f25(x38281)),f25(x38281)) % 14.79/14.65 [3884]E(f862(f862(f3(a92),f862(a5,f862(a105,f862(a22,x38841)))),f71(a92)),x38841) % 14.79/14.65 [3954]P1(f862(f862(f227(a1),f862(f72(a1),f862(f93(a1),x39541))),f2(a1))) % 14.79/14.65 [4097]P1(f862(f862(f228(a1),f862(f72(a1),f862(f93(a1),f862(a105,x40971)))),f2(a1))) % 14.79/14.65 [4683]~E(f234(f932(x46831,a921)),f181(f932(x46831,a921))) % 14.79/14.65 [4708]~P1(f862(f862(f228(a924),x47081),f2(a924))) % 14.79/14.65 [4719]~P1(f862(f862(f228(a1),f862(f93(a1),x47191)),f2(a1))) % 14.79/14.65 [3385]E(f113(x33851,f112(f926(x33851))),f112(x33851)) % 14.79/14.65 [3400]E(f172(x34001,f106(f925(x34001))),f106(f925(x34001))) % 14.79/14.65 [3403]E(f862(f862(f74(a1),a76),x34031),a76) % 14.79/14.65 [3404]E(f862(f862(f73(a1),a76),x34041),x34041) % 14.79/14.65 [3407]E(f862(a97,f862(f93(a1),x34071)),x34071) % 14.79/14.65 [3408]E(f862(f862(f3(a1),x34081),a76),x34081) % 14.79/14.65 [3409]E(f862(f862(f73(a1),x34091),a76),x34091) % 14.79/14.65 [3412]E(f862(f862(f3(a924),x34121),x34121),f2(a924)) % 14.79/14.65 [3416]E(f862(f72(a1),f862(f72(a1),x34161)),x34161) % 14.79/14.65 [3417]E(f862(f28(a924),f862(f292(a924),x34171)),x34171) % 14.79/14.65 [3428]E(f862(f862(f74(a924),f71(a924)),x34281),x34281) % 14.79/14.65 [3429]E(f862(f862(f74(a1),f71(a1)),x34291),x34291) % 14.79/14.65 [3430]E(f862(f862(f73(a924),f2(a924)),x34301),x34301) % 14.79/14.65 [3431]E(f862(f862(f73(a1),f2(a1)),x34311),x34311) % 14.79/14.65 [3432]E(f862(f862(f226(a924),f2(a924)),x34321),x34321) % 14.79/14.65 [3438]E(f862(f862(f3(a924),f2(a924)),x34381),f2(a924)) % 14.79/14.65 [3439]E(f862(f862(f74(a924),f2(a924)),x34391),f2(a924)) % 14.79/14.65 [3440]E(f862(f862(f29(a1),f2(a1)),x34401),f2(a1)) % 14.79/14.65 [3441]E(f862(f862(f225(a924),f2(a924)),x34411),f2(a924)) % 14.79/14.65 [3451]E(f121(x34511,f862(f72(a1),x34511)),f125(a1,x34511)) % 14.79/14.65 [3457]E(f862(f295(a924,f2(a924)),x34571),f862(f292(a924),x34571)) % 14.79/14.65 [3458]E(f862(f862(f74(a1),a90),x34581),f862(f72(a1),x34581)) % 14.79/14.65 [3466]E(f862(a97,f862(f96(a1),x34661)),f862(f96(a924),x34661)) % 14.79/14.65 [3467]E(f862(a22,f862(f96(a92),x34671)),f862(f96(a924),x34671)) % 14.79/14.65 [3468]E(f862(f28(a924),f862(f294(a924),x34681)),f862(a105,x34681)) % 14.79/14.65 [3477]E(f862(f862(f73(a924),f71(a924)),x34771),f862(a105,x34771)) % 14.79/14.65 [3481]E(f862(f95(a1),f862(f93(a1),x34811)),f862(f93(a1),x34811)) % 14.79/14.65 [3482]E(f862(f69(a1),f862(f93(a1),x34821)),f862(f93(a1),x34821)) % 14.79/14.65 [3486]E(f862(f28(x34861),f181(f932(x34861,a921))),f2(a924)) % 14.79/14.65 [3488]E(f862(f862(f29(a924),x34881),f862(a105,f2(a924))),x34881) % 14.79/14.65 [3497]E(f38(a924,x34971,f862(a105,f2(a924))),f2(a924)) % 14.79/14.65 [3498]E(f38(a1,x34981,f862(f96(a1),a90)),f2(a1)) % 14.79/14.65 [3514]E(f862(f862(f29(a1),x35141),f862(f96(a1),a90)),f862(f72(a1),x35141)) % 14.79/14.65 [3518]E(f132(a924,f862(f295(a924,x35181),f2(a924))),f106(a924)) % 14.79/14.65 [3519]E(f862(f862(f73(a1),x35191),f71(a1)),f862(f862(f3(a1),x35191),a90)) % 14.79/14.65 [3520]E(f862(f862(f3(a1),x35201),f71(a1)),f862(f862(f73(a1),x35201),a90)) % 14.79/14.65 [3524]P1(f862(f862(f84(a1),x35241),x35241)) % 14.79/14.65 [3525]P1(f862(f862(f227(a924),x35251),x35251)) % 14.79/14.65 [3526]P1(f862(f862(f227(a1),x35261),x35261)) % 14.79/14.65 [3527]P1(f862(f862(f278(a924),x35271),x35271)) % 14.79/14.65 [3532]E(f862(f72(a1),f862(f96(a1),x35321)),f862(f96(a1),f862(f72(a1),x35321))) % 14.79/14.65 [3533]P1(f862(f54(a924),f862(f294(a924),x35331))) % 14.79/14.65 [3534]P1(f862(f54(a924),f862(f292(a924),x35341))) % 14.79/14.65 [3541]E(f154(x35411,f234(f932(x35411,a921))),f234(f932(f925(x35411),a921))) % 14.79/14.65 [3546]P1(f862(f862(f227(a924),f2(a924)),x35461)) % 14.79/14.65 [3556]E(f862(f862(f73(a924),f104(x35561)),f862(a105,f2(a924))),f104(f862(a105,x35561))) % 14.79/14.65 [3557]E(f862(f254(x35571),f862(f18(a921,x35571),a231)),f181(f932(x35571,a921))) % 14.79/14.65 [3558]E(f862(f254(x35581),f862(f18(a921,x35581),a180)),f234(f932(x35581,a921))) % 14.79/14.65 [3561]E(f862(f862(f301(a924),x35611),f862(f292(a924),x35611)),f862(f292(a924),f862(a105,x35611))) % 14.79/14.65 [3573]E(f862(f862(f73(a1),f71(a1)),f862(f93(a1),x35731)),f862(f93(a1),f862(a105,x35731))) % 14.79/14.65 [3575]E(f862(f862(f144(f925(x35751)),f106(x35751)),f106(f925(x35751))),f47(x35751,f106(x35751))) % 14.79/14.65 [3593]E(f181(f932(f931(x35931,x35931),a921)),f255(x35931,f181(f932(x35931,a921)))) % 14.79/14.65 [3594]E(f862(f300(x35941),f234(f932(x35941,a921))),f234(f932(f932(x35941,a921),a921))) % 14.79/14.65 [3595]E(f862(f72(f932(x35951,a921)),f181(f932(x35951,a921))),f234(f932(x35951,a921))) % 14.79/14.65 [3596]E(f862(f72(f932(x35961,a921)),f234(f932(x35961,a921))),f181(f932(x35961,a921))) % 14.79/14.65 [3598]P1(f862(f54(x35981),f181(f932(x35981,a921)))) % 14.79/14.65 [3600]E(f862(f295(a924,x36001),f862(a105,x36001)),f862(f862(f301(a924),x36001),f181(f932(a924,a921)))) % 14.79/14.65 [3601]E(f78(f931(a924,a924),f41(x36011,f2(a924))),f862(f862(f244(a924,a924),f2(a924)),x36011)) % 14.79/14.66 [3614]E(f862(f862(f301(a924),f862(a105,x36141)),f862(f294(a924),x36141)),f862(f294(a924),f862(a105,x36141))) % 14.79/14.66 [3618]P35(x36181,f181(f932(f931(x36181,x36181),a921))) % 14.79/14.66 [3619]P37(x36191,f181(f932(f931(x36191,x36191),a921))) % 14.79/14.66 [3622]P1(f862(f862(f227(a1),f2(a1)),f862(f93(a1),x36221))) % 14.79/14.66 [3629]E(f862(f862(f73(a924),f862(f182(a924),x36291)),f862(a105,f2(a924))),f862(f182(a924),f862(a105,x36291))) % 14.79/14.66 [3733]P38(f862(f302(a924,a1,f93(a1)),x37331)) % 14.79/14.66 [3771]P50(x37711,f181(f932(x37711,a921)),f181(f932(f931(x37711,x37711),a921))) % 14.79/14.66 [3789]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f3(a1),x37891),f71(a1))),f43(f862(f96(a1),a90),x37891)) % 14.79/14.66 [3841]P57(x38411,f862(f18(f932(x38411,a921),x38411),f862(f18(a921,x38411),a231))) % 14.79/14.66 [4041]P1(f862(f862(f321(f932(f931(a924,a924),a921)),f320(x40411)),a91)) % 14.79/14.66 [4066]P1(f862(f862(f321(f932(f931(a924,a924),a921)),f862(a100,x40661)),a91)) % 14.79/14.66 [4195]P22(x41951,f932(x41951,a921),f862(f862(f9(x41951,f932(x41951,a921),f932(x41951,a921)),f301(x41951)),f181(f932(x41951,a921))),f234(f932(x41951,a921))) % 14.79/14.66 [4429]P54(f923(x44291),f932(f922(f930(a919,f932(x44291,f932(a920,a921))),f930(a920,x44291)),a921),f87(x44291),f85(x44291),f862(f254(f932(f922(f930(a919,f932(x44291,f932(a920,a921))),f930(a920,x44291)),a921)),f88(x44291))) % 14.79/14.66 [4680]~E(f862(f862(f73(a1),x46801),x46801),a90) % 14.79/14.66 [4693]~E(f862(a5,f862(a105,f862(a22,x46931))),f2(a92)) % 14.79/14.66 [4701]~P1(f862(a186,f862(f93(a1),x47011))) % 14.79/14.66 [4704]~P1(f862(f862(f228(a924),x47041),x47041)) % 14.79/14.66 [4712]~P1(f862(f862(f227(a924),f862(a105,x47121)),x47121)) % 14.79/14.66 [3548]E(f862(a97,f862(f72(a1),f862(f93(a1),x35481))),f2(a924)) % 14.79/14.66 [3551]E(f862(f862(f73(a1),f862(f72(a1),x35511)),x35511),f2(a1)) % 14.79/14.66 [3555]E(f862(f28(a1),f862(f295(a1,f2(a1)),x35551)),f862(a97,x35551)) % 14.79/14.66 [3566]E(f862(f862(f236(a924),f862(a105,f2(a924))),x35661),f862(a105,f2(a924))) % 14.79/14.66 [3659]E(f862(f273(x36591),f181(f932(f931(x36591,x36591),a921))),f181(f932(x36591,a921))) % 14.79/14.66 [3667]E(f31(f932(x36671,a921),f181(f932(f932(x36671,a921),a921))),f234(f932(x36671,a921))) % 14.79/14.66 [3668]E(f31(f932(x36681,a921),f234(f932(f932(x36681,a921),a921))),f181(f932(x36681,a921))) % 14.79/14.66 [3669]E(f30(f932(x36691,a921),f181(f932(f932(x36691,a921),a921))),f181(f932(x36691,a921))) % 14.79/14.66 [3670]E(f30(f932(x36701,a921),f234(f932(f932(x36701,a921),a921))),f234(f932(x36701,a921))) % 14.79/14.66 [3674]P1(f862(f862(f278(a924),f862(a105,f2(a924))),x36741)) % 14.79/14.66 [3715]E(f862(f862(f301(f925(x37151)),f106(x37151)),f181(f932(f925(x37151),a921))),f154(x37151,f181(f932(x37151,a921)))) % 14.79/14.66 [3716]E(f862(f862(f301(f925(x37161)),f106(x37161)),f181(f932(f925(x37161),a921))),f155(x37161,f106(f932(x37161,a921)))) % 14.79/14.66 [3755]E(f862(f862(f73(a924),f6(x37551)),f862(a105,f2(a924))),f6(f862(a5,f862(a105,f862(a22,x37551))))) % 14.79/14.66 [3780]E(f862(f28(a1),f862(f302(a924,a1,f93(a1)),x37801)),f862(f28(a924),x37801)) % 14.79/14.66 [3781]P1(f862(f862(f227(a924),x37811),f862(f862(f74(a924),x37811),x37811))) % 14.79/14.66 [3819]E(f862(f302(a1,a924,a97),f296(a1,f2(a1),f862(f93(a1),x38191))),f862(f294(a924),x38191)) % 14.79/14.66 [3836]E(f862(f862(f29(a924),f862(a105,f2(a924))),f862(f96(a924),x38361)),f862(a97,f862(f862(f29(a1),f71(a1)),f862(f96(a1),x38361)))) % 14.79/14.66 [3838]E(f862(f165(a924),f132(a924,f862(f295(a924,f2(a924)),f862(a105,x38381)))),f862(f294(a924),x38381)) % 14.79/14.66 [3839]E(f862(f862(f73(a924),f862(f182(a92),x38391)),f862(a105,f2(a924))),f862(f182(a92),f862(a5,f862(a105,f862(a22,x38391))))) % 14.79/14.66 [3858]P37(x38581,f299(x38581,f181(f932(f931(x38581,x38581),a921)))) % 14.79/14.66 [3859]P49(x38591,f299(x38591,f181(f932(f931(x38591,x38591),a921)))) % 14.79/14.66 [3860]E(f862(f302(a1,a924,a97),f862(f302(a924,a1,f93(a1)),x38601)),x38601) % 14.79/14.66 [3890]E(f862(f862(f301(a924),f2(a924)),f862(f302(a924,a924,a105),f862(f292(a924),x38901))),f862(f292(a924),f862(a105,x38901))) % 14.79/14.66 [3896]P52(x38961,x38961,f299(x38961,f181(f932(f931(x38961,x38961),a921)))) % 14.79/14.66 [3902]P1(f862(a186,f862(f72(a1),f862(f93(a1),f862(a105,x39021))))) % 14.79/14.66 [3912]E(f862(f862(f3(f932(a924,a921)),f862(f274(a924),x39121)),f862(f862(f301(a924),x39121),f181(f932(a924,a921)))),f862(f274(a924),f862(a105,x39121))) % 14.79/14.66 [3929]E(f862(f862(f73(a1),f862(f862(f3(a1),a76),x39291)),f862(f862(f3(a1),a76),x39291)),f862(f862(f3(a1),a76),f862(f862(f73(a1),x39291),x39291))) % 14.79/14.66 [3943]E(f862(f862(f301(f932(x39431,a921)),f181(f932(x39431,a921))),f181(f932(f932(x39431,a921),a921))),f862(f300(x39431),f181(f932(x39431,a921)))) % 14.79/14.66 [3971]E(f862(f862(f3(f932(a924,a921)),f862(f293(a924),x39711)),f862(f862(f301(a924),f862(a105,x39711)),f181(f932(a924,a921)))),f862(f293(a924),f862(a105,x39711))) % 14.79/14.66 [4078]E(f862(f96(a924),f862(f862(f73(a1),x40781),x40781)),f862(f862(f79(a924,a924),f862(f96(a924),x40781)),f862(f862(f20(a924,a924,a924),f73(a924)),f7(a924)))) % 14.79/14.66 [4450]P12(x44501,f932(x44501,a921),f862(f862(f10(f932(x44501,a921),f932(f932(x44501,a921),f932(x44501,a921)),x44501),f862(f9(f932(x44501,a921),f932(x44501,a921),f932(x44501,a921)),f3(f932(x44501,a921)))),f862(f862(f9(x44501,f932(x44501,a921),f932(x44501,a921)),f301(x44501)),f181(f932(x44501,a921))))) % 14.79/14.66 [4539]E(f862(f254(f931(a1,a1)),f862(f249(a1,a1,a921),f862(f862(f10(f932(a1,a921),f932(a1,a921),a1),f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),x45391)))),f228(a1)))),f98(x45391)) % 14.79/14.66 [4572]E(f862(f254(f931(a1,a1)),f862(f249(a1,a1,a921),f862(f862(f20(a1,f932(a1,a921),f932(a1,a921)),f862(f862(f10(f932(a921,a921),f932(f932(a1,a921),f932(a1,a921)),a1),f10(a921,a921,a1)),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),x45721)))),f228(a1)))),f99(x45721)) % 14.79/14.66 [4625]E(f862(f254(f931(f932(x46251,a921),f932(x46251,a921))),f862(f249(f932(x46251,a921),f932(x46251,a921),a921),f862(f862(f9(f932(x46251,a921),f932(f932(x46251,a921),a921),f932(f932(x46251,a921),a921)),f862(f862(f10(f932(f932(x46251,a921),f932(a921,a921)),f932(f932(f932(x46251,a921),a921),f932(f932(x46251,a921),a921)),f932(x46251,a921)),f20(f932(x46251,a921),a921,a921)),f862(f862(f10(f932(f932(x46251,a921),a921),f932(f932(x46251,a921),f932(a921,a921)),f932(x46251,a921)),f862(f10(a921,f932(a921,a921),f932(x46251,a921)),a318)),f228(f932(x46251,a921))))),f54(x46251)))),f306(x46251)) % 14.79/14.66 [4716]~P1(f862(f54(f925(x47161)),f234(f932(f925(x47161),a921)))) % 14.79/14.66 [4721]~P1(f862(f862(f84(a1),a90),f862(f862(f73(a1),x47211),x47211))) % 14.79/14.66 [4730]~P1(f862(f862(f227(a1),f2(a1)),f862(f72(a1),f862(f93(a1),f862(a105,x47301))))) % 14.79/14.66 [3694]E(f862(f862(f3(a1),f862(f862(f73(a1),x36941),a90)),a90),x36941) % 14.79/14.66 [3708]E(f862(f165(a924),f132(a924,f862(f295(a924,f2(a924)),x37081))),f862(f292(a924),x37081)) % 14.79/14.66 [3950]E(f862(f862(f73(a1),f862(f862(f73(a1),f71(a1)),x39501)),x39501),f862(f862(f3(a1),f862(f862(f73(a1),x39501),x39501)),a90)) % 14.79/14.66 [3998]E(f862(f277(x39981,x39981),f299(x39981,f181(f932(f931(x39981,x39981),a921)))),f299(x39981,f181(f932(f931(x39981,x39981),a921)))) % 14.79/14.66 [4044]P1(f862(f862(f227(a924),x40441),f862(f862(f74(a924),x40441),f862(f862(f74(a924),x40441),x40441)))) % 14.79/14.66 [4312]P1(f862(f54(a924),f862(f254(a924),f862(f862(f9(a924,a924,a921),f227(a924)),x43121)))) % 14.79/14.66 [4313]P1(f862(f54(a924),f862(f254(a924),f862(f862(f9(a924,a924,a921),f228(a924)),x43131)))) % 14.79/14.66 [4588]E(f862(f254(f931(x45881,x45881)),f862(f862(f10(f932(x45881,a921),a921,f931(x45881,x45881)),f80(x45881)),f862(f862(f9(f931(x45881,x45881),f932(x45881,f931(x45881,x45881)),f932(x45881,a921)),f862(f862(f10(f932(f931(x45881,x45881),a921),f932(f932(x45881,f931(x45881,x45881)),f932(x45881,a921)),f931(x45881,x45881)),f10(f931(x45881,x45881),a921,x45881)),a317)),f862(f862(f20(x45881,x45881,f931(x45881,x45881)),f244(x45881,x45881)),f7(x45881))))),f299(x45881,f181(f932(f931(x45881,x45881),a921)))) % 14.79/14.66 [4718]~E(f862(f862(f3(a1),f862(f862(f73(a1),x47181),x47181)),a90),a76) % 14.79/14.66 [4720]~E(f862(f862(f73(a1),f862(f862(f73(a1),f71(a1)),x47201)),x47201),f2(a1)) % 14.79/14.66 [4727]~P1(f862(f862(f84(a1),f862(f862(f73(a1),x47271),x47271)),a90)) % 14.79/14.66 [4088]E(f862(f862(f73(a1),f862(f862(f3(a1),a90),x40881)),f862(f862(f3(a1),a90),x40881)),f862(f862(f3(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x40881),x40881)),a90))) % 14.79/14.66 [4203]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),a90),x42031)),f862(f862(f3(a1),a90),x42031))),a90),f862(f862(f3(a1),a90),f862(f862(f73(a1),x42031),x42031))) % 14.79/14.66 [4235]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f73(a1),x42351),a90)),f862(f862(f73(a1),x42351),a90))),a90),f862(f862(f73(a1),f862(f862(f73(a1),x42351),x42351)),a90)) % 14.79/14.66 [4273]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),a90),x42731)),f862(f862(f3(a1),a90),x42731))),a90),f862(f862(f3(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x42731),x42731)),a90))) % 14.79/14.66 [4370]E(f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x43701),f2(a924))),f181(f932(f931(a924,a924),a921))))),f862(f93(a1),x43701)) % 14.79/14.66 [4380]E(f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f324(x43801)),f522(x43801))),f181(f932(f931(a924,a924),a921))))),x43801) % 14.79/14.66 [4413]E(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x44131)),f862(f302(a924,a1,f93(a1)),f862(f254(a924),f862(f862(f10(a1,a921,a924),x44131),f93(a1))))) % 14.79/14.66 [4458]P38(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x44581))) % 14.79/14.66 [4478]P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x44781),f181(f932(f931(a924,a924),a921)))),a65)) % 14.79/14.66 [4483]E(f862(f302(a1,a924,a97),f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),f862(f862(f10(a924,a921,a1),x44831),a97)))),f862(f254(a924),x44831)) % 14.79/14.66 [4640]E(f304(a924,f862(f862(f33(f931(a924,a924),f932(a924,a921)),f862(a100,x46401)),f862(f249(a924,a924,f932(a924,a921)),f862(f862(f9(a924,f932(a924,a921),f932(a924,f932(a924,a921))),f862(f862(f10(f932(a924,f932(f932(a924,a921),f932(a924,a921))),f932(f932(a924,a921),f932(a924,f932(a924,a921))),a924),f9(a924,f932(a924,a921),f932(a924,a921))),f862(f862(f10(f932(a924,a924),f932(a924,f932(f932(a924,a921),f932(a924,a921))),a924),f862(f10(a924,f932(f932(a924,a921),f932(a924,a921)),a924),f301(a924))),f3(a924)))),f181(f932(a924,a921)))))),f862(a97,x46401)) % 14.79/14.66 [4732]~P1(f862(f862(f84(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x47321),x47321)),a90))) % 14.79/14.66 [4133]E(f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),x41331),x41331)),a90)),a90),f862(f862(f73(a1),x41331),x41331)) % 14.79/14.66 [4183]E(f862(f862(f3(a1),f862(f862(f3(a1),f862(f862(f73(a1),x41831),x41831)),a90)),a90),f862(f862(f73(a1),f862(f862(f3(a1),x41831),a90)),f862(f862(f3(a1),x41831),a90))) % 14.79/14.66 [4386]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f73(a1),f862(f72(a1),x43861)),a90)),f862(f862(f73(a1),f862(f72(a1),x43861)),a90))),a90),f862(f72(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43861),x43861)),a90))) % 14.79/14.66 [4740]~P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x47401),x47401)),a90)),a76)) % 14.79/14.66 [4431]E(f862(f862(f73(a924),x44311),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a105,f862(a105,x44311))) % 14.79/14.66 [4432]E(f862(f862(f74(a924),x44321),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f73(a924),x44321),x44321)) % 14.79/14.66 [4433]E(f862(f862(f29(a924),f862(f862(f73(a924),x44331),x44331)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x44331) % 14.79/14.66 [4511]E(f38(a924,f862(a105,f862(a105,x45111)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a924,x45111,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.79/14.66 [4654]E(f862(a82,f862(f862(f33(f931(a924,a924),f932(f931(a924,a924),a921)),f862(a100,x46541)),f862(f249(a924,a924,f932(f931(a924,a924),a921)),f862(f862(f10(f932(a924,f932(f931(a924,a924),a921)),f932(a924,f932(f931(a924,a924),a921)),a924),f862(f10(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921),a924),f276(f931(a924,a924),f931(a924,a924),a101))),f862(f862(f9(a924,f932(f931(a924,a924),a921),f932(a924,f932(f931(a924,a924),a921))),f862(f862(f10(f932(a924,f932(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f932(f932(f931(a924,a924),a921),f932(a924,f932(f931(a924,a924),a921))),a924),f9(a924,f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f10(f932(a924,f931(a924,a924)),f932(a924,f932(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),a924),f862(f10(f931(a924,a924),f932(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a924),f301(f931(a924,a924)))),f862(f9(a924,a924,f931(a924,a924)),f244(a924,a924))))),f181(f932(f931(a924,a924),a921))))))),f862(f72(a1),x46541)) % 14.79/14.66 [4506]E(f862(f862(f73(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x45061),f862(a105,f862(a105,x45061))) % 14.79/14.66 [4507]E(f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x45071),f862(f862(f73(a924),x45071),x45071)) % 14.79/14.66 [4545]E(f862(f862(f29(a924),f862(a105,f862(a105,x45451))),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a105,f862(f862(f29(a924),x45451),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.79/14.66 [4595]E(f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x45951),f862(a105,f862(a105,f862(a105,x45951)))) % 14.79/14.66 [4661]E(f862(f249(a1,a1,f931(a1,a1)),f862(f862(f20(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f20(a1,f931(a1,a1),f931(a1,a1))),f862(f862(f10(f932(a1,f931(a1,a1)),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f862(f20(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f862(f862(f10(a921,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f89(f931(a1,a1))),f862(f862(f10(a1,a921,a1),f862(f227(a1),f2(a1))),f862(f862(f9(a1,a1,a1),f3(a1)),x46611))))),f862(f862(f9(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f10(a1,f931(a1,a1),a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f862(f9(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f73(a1)),f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f71(a1))))),f862(f862(f9(a1,a1,a1),f3(a1)),x46611))))),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))),f36(x46611)) % 14.79/14.66 [3367]P2(f930(x33671,x33672)) % 14.79/14.66 [3368]P2(f931(x33681,x33682)) % 14.79/14.66 [3369]P2(f929(x33691,x33692)) % 14.79/14.66 [3370]P107(f930(x33701,x33702)) % 14.79/14.66 [3371]P107(f931(x33711,x33712)) % 14.79/14.66 [3372]P107(f929(x33721,x33722)) % 14.79/14.66 [3389]P11(a1,f171(x33891,x33892)) % 14.79/14.66 [3390]P35(x33901,f146(x33901,x33902)) % 14.79/14.66 [3391]P36(x33911,f255(x33911,x33912)) % 14.79/14.66 [3392]P36(x33921,f299(x33921,x33922)) % 14.79/14.66 [3393]P37(x33931,f255(x33931,x33932)) % 14.79/14.66 [3394]P49(x33941,f255(x33941,x33942)) % 14.79/14.66 [3459]P29(x34591,x34592,f106(x34591)) % 14.79/14.66 [3492]P50(x34921,x34922,f255(x34921,x34922)) % 14.79/14.66 [3493]P52(x34931,x34931,f255(x34931,x34932)) % 14.79/14.66 [3758]P22(x37581,x37581,f7(x37581),x37582) % 14.79/14.66 [3759]P22(x37591,x37591,f25(x37591),x37592) % 14.79/14.66 [3767]P30(x37671,x37672,f106(x37671),f106(x37671)) % 14.79/14.66 [3774]P22(f925(x37741),f925(x37741),f161(x37741),x37742) % 14.79/14.66 [4173]P23(x41731,x41731,f25(x41731),x41732,x41732) % 14.79/14.66 [4688]~P31(x46881,x46882,f106(x46881)) % 14.79/14.66 [4689]~P33(x46891,x46892,f106(x46891)) % 14.79/14.66 [3353]E(f862(f254(x33531),x33532),x33532) % 14.79/14.66 [3354]E(f862(f7(x33541),x33542),x33542) % 14.79/14.66 [3356]E(f862(f25(x33561),x33562),x33562) % 14.79/14.66 [3366]E(f862(f184(x33661),x33662),f108(x33661)) % 14.79/14.66 [3387]E(f78(x33871,f862(a317,x33872)),x33872) % 14.79/14.66 [3388]E(f83(x33881,f862(a317,x33882)),x33882) % 14.79/14.66 [3410]E(f862(f85(x34101),f588(x34101,x34102)),x34102) % 14.79/14.66 [3411]E(f862(f118(x34111,x34112),f112(x34111)),f2(a924)) % 14.79/14.66 [3414]E(f862(f129(x34141,x34142),f106(x34141)),f106(x34141)) % 14.79/14.66 [3434]E(f299(x34341,f299(x34341,x34342)),f299(x34341,x34342)) % 14.79/14.66 [3435]E(f145(x34351,f145(x34351,x34352)),f145(x34351,x34352)) % 14.79/14.66 [3454]E(f862(f862(f127(x34541),x34542),f106(x34541)),x34542) % 14.79/14.66 [3460]E(f166(x34601,x34602,f106(x34601)),x34602) % 14.79/14.66 [3461]E(f166(x34611,f106(x34611),x34612),x34612) % 14.79/14.66 [3462]E(f109(x34621,f112(x34621),x34622),x34622) % 14.79/14.66 [3463]E(f162(x34631,f2(a924),x34632),f106(x34631)) % 14.79/14.66 [3469]E(f862(f862(f168(x34691),x34692),f106(x34691)),f106(x34691)) % 14.79/14.66 [3470]E(f862(f862(f131(x34701),x34702),f106(x34701)),f106(x34701)) % 14.79/14.66 [3472]E(f148(x34721,x34722,f106(x34721)),f2(a924)) % 14.79/14.66 [3474]E(f163(x34741,x34742,f106(x34741)),f106(x34741)) % 14.79/14.66 [3475]E(f170(x34751,x34752,f106(x34751)),f106(x34751)) % 14.79/14.66 [3476]E(f169(x34761,f106(x34761),x34762),f106(x34761)) % 14.79/14.66 [3480]E(f862(f165(x34801),f145(x34801,x34802)),f862(f165(x34801),x34802)) % 14.79/14.66 [3483]E(f862(f275(x34831,x34831),f255(x34831,x34832)),x34832) % 14.79/14.66 [3484]E(f862(f256(x34841,x34841),f255(x34841,x34842)),x34842) % 14.79/14.66 [3491]E(f862(f277(x34911,x34911),f255(x34911,x34912)),f255(x34911,x34912)) % 14.79/14.66 [3506]E(f299(f925(x35061),f150(x35061,x35062)),f151(x35061,f299(x35061,x35062))) % 14.79/14.66 [3508]P1(f862(f130(a1),f171(x35081,x35082))) % 14.79/14.66 [3516]E(f862(f275(x35161,x35161),f299(x35161,x35162)),f234(f932(x35161,a921))) % 14.79/14.66 [3517]E(f862(f256(x35171,x35171),f299(x35171,x35172)),f234(f932(x35171,a921))) % 14.79/14.66 [3521]P1(f862(f130(x35211),f145(x35211,x35212))) % 14.79/14.66 [3523]P1(f862(f153(x35231,x35232),f106(x35231))) % 14.79/14.66 [3530]E(f862(f165(a1),f171(x35301,x35302)),f296(a1,x35301,x35302)) % 14.79/14.66 [3544]P53(x35441,f181(f932(x35441,a921)),x35442) % 14.79/14.66 [3549]E(f862(f248(a1,a1),f39(x35491,x35492)),f38(a1,x35491,x35492)) % 14.79/14.66 [3550]E(f862(f295(a924,x35501),f862(a105,x35502)),f296(a924,x35501,x35502)) % 14.79/14.66 [3565]E(f862(f862(f144(x35651),x35652),f106(x35651)),f133(x35651,x35652,f106(x35651))) % 14.79/14.66 [3577]E(f296(a924,f862(a105,x35771),x35772),f297(a924,x35771,x35772)) % 14.79/14.66 [3578]P50(x35781,f234(f932(x35781,a921)),f299(x35781,x35782)) % 14.79/14.66 [3640]E(f862(f862(f3(a924),x36401),f862(a105,x36402)),f862(f28(a924),f298(a924,x36402,x36401))) % 14.79/14.66 [3695]E(f159(x36951,x36952,f106(x36951)),f862(f862(f244(f925(x36951),f925(x36951)),f106(x36951)),f106(x36951))) % 14.79/14.66 [3713]E(f862(f249(x37131,x37132,f931(x37131,x37132)),f244(x37131,x37132)),f25(f931(x37131,x37132))) % 14.79/14.66 [3717]P1(f862(f862(f321(f925(x37171)),f106(x37171)),f154(x37171,x37172))) % 14.79/14.66 [3718]E(f862(f182(f925(x37181)),f107(x37181,x37182)),f862(f862(f3(a924),f862(f182(f925(x37181)),x37182)),f71(a924))) % 14.79/14.66 [3727]P1(f862(f54(a924),f298(a924,x37271,x37272))) % 14.79/14.66 [3728]P1(f862(f54(a924),f297(a924,x37281,x37282))) % 14.79/14.66 [3729]P1(f862(f54(a924),f296(a924,x37291,x37292))) % 14.79/14.66 [3730]P1(f862(f54(a1),f298(a1,x37301,x37302))) % 14.79/14.66 [3731]P1(f862(f54(a1),f297(a1,x37311,x37312))) % 14.79/14.66 [3732]P1(f862(f54(a1),f296(a1,x37321,x37322))) % 14.79/14.66 [3835]E(f862(f302(a924,a924,a105),f296(a924,x38351,x38352)),f296(a924,f862(a105,x38351),f862(a105,x38352))) % 14.79/14.66 [3854]E(f862(f862(f280(x38541,x38541,x38541),f299(x38541,x38542)),f299(x38541,x38542)),f299(x38541,x38542)) % 14.79/14.66 [3888]E(f862(f862(f244(a92,a92),f862(f862(f29(a92),x38881),x38882)),f38(a92,x38881,x38882)),f23(x38881,x38882)) % 14.79/14.66 [3889]E(f862(f862(f244(a1,a1),f862(f862(f29(a1),x38891),x38892)),f38(a1,x38891,x38892)),f39(x38891,x38892)) % 14.79/14.66 [3916]E(f862(f862(f244(a924,a924),f862(f862(f29(a924),x39161),x39162)),f38(a924,x39161,x39162)),f78(f931(a924,a924),f41(x39161,x39162))) % 14.79/14.66 [3967]P1(f862(f862(f228(a924),f862(f862(f3(a924),x39671),x39672)),f862(a105,x39671))) % 14.79/14.66 [4015]P36(x40151,f862(f862(f280(x40151,x40151,x40151),x40152),f299(x40151,x40152))) % 14.79/14.66 [4065]E(f862(f862(f73(a1),f862(f862(f74(a1),x40651),f862(f862(f29(a1),x40652),x40651))),f38(a1,x40652,x40651)),x40652) % 14.79/14.66 [4069]E(f862(f862(f33(a924,f932(f931(f925(x40691),f925(x40691)),a921)),f234(f932(a924,a921))),f136(x40691,x40692)),f138(x40691,x40692)) % 14.79/14.66 [4289]P1(f862(f862(f321(f931(f925(x42891),f925(x42891))),f862(f862(f244(f925(x42891),f925(x42891)),f106(x42891)),f106(x42891))),f151(x42891,x42892))) % 14.79/14.66 [4398]E(f245(x43981,x43981,x43981,a317,f245(x43981,x43981,x43981,x43982,a317)),x43982) % 14.79/14.66 [4443]E(f250(x44431,x44431,x44432,x44432,f7(x44431),f7(x44432)),f25(f931(x44431,x44432))) % 14.79/14.66 [4445]E(f250(x44451,x44451,x44452,x44452,f25(x44451),f25(x44452)),f25(f931(x44451,x44452))) % 14.79/14.66 [3452]E(f862(f85(x34521),f862(f87(x34521),x34522)),x34522) % 14.79/14.66 [3453]E(f862(f161(x34531),f862(f161(x34531),x34532)),x34532) % 14.79/14.66 [3455]E(f862(f862(f131(x34551),f2(a924)),x34552),x34552) % 14.79/14.66 [3471]E(f862(f862(f168(x34711),f2(a924)),x34712),f106(x34711)) % 14.79/14.66 [3478]E(f862(f862(f127(x34781),f106(x34781)),x34782),x34782) % 14.79/14.66 [3487]E(f30(f932(x34871,a921),f862(f300(x34871),x34872)),x34872) % 14.79/14.66 [3489]E(f862(f165(x34891),f862(f160(x34891),x34892)),f862(f165(x34891),x34892)) % 14.79/14.66 [3490]E(f862(f165(x34901),f862(f161(x34901),x34902)),f862(f165(x34901),x34902)) % 14.79/14.66 [3495]E(f862(f862(f3(a92),x34951),x34952),f862(f862(a4,x34951),x34952)) % 14.79/14.66 [3510]E(f862(f862(f74(a924),x35101),x35102),f862(f862(f74(a924),x35102),x35101)) % 14.79/14.66 [3511]E(f862(f862(f74(a1),x35111),x35112),f862(f862(f74(a1),x35112),x35111)) % 14.79/14.66 [3512]E(f862(f862(f73(a924),x35121),x35122),f862(f862(f73(a924),x35122),x35121)) % 14.79/14.66 [3513]E(f862(f862(f73(a1),x35131),x35132),f862(f862(f73(a1),x35132),x35131)) % 14.79/14.66 [3536]E(f862(f862(f176(x35361,x35361),f2(a924)),x35362),f25(x35361)) % 14.79/14.66 [3537]E(f862(f182(f925(x35371)),f862(f160(x35371),x35372)),f862(f182(f925(x35371)),x35372)) % 14.79/14.66 [3538]E(f862(f182(f925(x35381)),f862(f161(x35381),x35382)),f862(f182(f925(x35381)),x35382)) % 14.79/14.66 [3539]E(f169(x35391,x35392,f181(f932(a924,a921))),f106(x35391)) % 14.79/14.66 [3540]E(f862(f862(f147(x35401,x35401),f7(x35401)),x35402),x35402) % 14.79/14.66 [3542]E(f862(f243(a1,a1),f39(x35421,x35422)),f862(f862(f29(a1),x35421),x35422)) % 14.79/14.66 [3559]E(f862(f182(f925(x35591)),f145(x35591,x35592)),f862(f28(x35591),f862(f165(x35591),x35592))) % 14.79/14.66 [3560]E(f862(f273(x35601),f862(f277(x35601,x35601),x35602)),f862(f273(x35601),x35602)) % 14.79/14.66 [3564]P1(f862(f54(x35641),f862(f165(x35641),x35642))) % 14.79/14.66 [3572]E(f862(f862(f73(a1),x35721),f862(f72(a1),x35722)),f862(f862(f3(a1),x35721),x35722)) % 14.79/14.66 [3579]E(f862(f302(x35791,x35791,f7(x35791)),x35792),x35792) % 14.79/14.66 [3580]E(f862(f302(x35801,x35801,f25(x35801)),x35802),x35802) % 14.79/14.66 [3581]E(f862(f303(x35811,x35811,f7(x35811)),x35812),x35812) % 14.79/14.66 [3582]E(f862(f303(x35821,x35821,f25(x35821)),x35822),x35822) % 14.79/14.66 [3583]P1(f862(f234(f932(x35831,a921)),x35832)) % 14.79/14.66 [3585]E(f862(f28(a924),f862(f295(a924,x35851),x35852)),f862(f862(f3(a924),x35852),x35851)) % 14.79/14.66 [3586]E(f862(f295(a924,f862(a105,x35861)),x35862),f298(a924,x35861,x35862)) % 14.79/14.66 [3599]E(f862(f862(f301(x35991),x35992),f181(f932(x35991,a921))),f862(f254(x35991),f862(a317,x35992))) % 14.79/14.66 [3604]E(f299(x36041,f862(f277(x36041,x36041),x36042)),f862(f277(x36041,x36041),f299(x36041,x36042))) % 14.79/14.66 [3609]E(f862(f862(f73(a924),f862(a105,x36091)),x36092),f862(f862(f73(a924),x36091),f862(a105,x36092))) % 14.79/14.66 [3610]E(f862(f862(f3(a924),f862(a105,x36101)),f862(a105,x36102)),f862(f862(f3(a924),x36101),x36102)) % 14.79/14.66 [3616]E(f48(x36161,f2(a924),x36162),f862(f862(f144(f925(x36161)),f106(x36161)),f106(f925(x36161)))) % 14.79/14.66 [3617]E(f862(f28(a924),f297(a924,x36171,x36172)),f862(f862(f3(a924),x36172),x36171)) % 14.79/14.66 [3626]P35(x36261,f862(f862(f279(a924,x36261),a232),x36262)) % 14.79/14.66 [3628]P11(a924,f132(a924,f862(f295(a924,x36281),x36282))) % 14.79/14.66 [3630]P1(f862(f54(a924),f862(f295(a924,x36301),x36302))) % 14.79/14.66 [3631]P1(f862(f54(a1),f862(f295(a1,x36311),x36312))) % 14.79/14.66 [3634]E(f862(f277(f925(x36341),f925(x36341)),f150(x36341,x36342)),f150(x36341,f862(f277(x36341,x36341),x36342))) % 14.79/14.66 [3636]E(f862(f295(a1,x36361),f862(f862(f73(a1),x36362),f71(a1))),f296(a1,x36361,x36362)) % 14.79/14.66 [3639]E(f862(f862(f29(a1),f862(f72(a1),x36391)),f862(f72(a1),x36392)),f862(f862(f29(a1),x36391),x36392)) % 14.79/14.66 [3647]E(f862(f862(f176(f931(x36471,x36471),a921),f71(a924)),x36472),x36472) % 14.79/14.66 [3649]E(f862(f862(f103(f932(x36491,a921)),x36492),f181(f932(x36491,a921))),x36492) % 14.79/14.66 [3650]E(f862(f862(f94(f932(x36501,a921)),x36502),f234(f932(x36501,a921))),x36502) % 14.79/14.66 [3651]E(f862(f862(f3(f932(x36511,a921)),x36512),f181(f932(x36511,a921))),x36512) % 14.79/14.66 [3652]E(f862(f243(a924,a924),f78(f931(a924,a924),f41(x36521,x36522))),f862(f862(f29(a924),x36521),x36522)) % 14.79/14.66 [3658]E(f296(a1,f862(f862(f73(a1),x36581),f71(a1)),x36582),f297(a1,x36581,x36582)) % 14.79/14.66 [3663]E(f862(f248(a924,a924),f78(f931(a924,a924),f41(x36631,x36632))),f38(a924,x36631,x36632)) % 14.79/14.66 [3673]P1(f862(f862(f321(x36731),x36732),f234(f932(x36731,a921)))) % 14.79/14.66 [3678]E(f862(f862(f3(a924),f862(a105,x36781)),x36782),f862(f28(a924),f296(a924,x36782,x36781))) % 14.79/14.66 [3704]E(f862(f862(f103(f932(x37041,a921)),x37042),f234(f932(x37041,a921))),f234(f932(x37041,a921))) % 14.79/14.66 [3705]E(f862(f862(f94(f932(x37051,a921)),x37052),f181(f932(x37051,a921))),f181(f932(x37051,a921))) % 14.79/14.66 [3706]E(f862(f862(f3(f932(x37061,a921)),x37062),f234(f932(x37061,a921))),f181(f932(x37061,a921))) % 14.79/14.66 [3722]E(f38(a1,f862(f72(a1),x37221),f862(f72(a1),x37222)),f862(f72(a1),f38(a1,x37221,x37222))) % 14.79/14.66 [3723]E(f38(a1,f862(f93(a1),x37231),f862(f93(a1),x37232)),f862(f93(a1),f38(a924,x37231,x37232))) % 14.79/14.66 [3734]E(f862(f182(f925(x37341)),f862(f164(x37341),x37342)),f862(f862(f3(a924),f862(f182(f925(x37341)),x37342)),f71(a924))) % 14.79/14.66 [3760]E(f862(f862(f29(a1),f38(a1,x37601,x37602)),x37602),f2(a1)) % 14.79/14.66 [3769]E(f862(a5,f38(a924,f862(a22,x37691),f862(a22,x37692))),f38(a92,x37691,x37692)) % 14.79/14.66 [3802]E(f862(a5,f862(f862(f3(a924),f862(a22,x38021)),f862(a22,x38022))),f862(f862(f3(a92),x38021),x38022)) % 14.79/14.66 [3803]E(f862(a5,f862(f862(f74(a924),f862(a22,x38031)),f862(a22,x38032))),f862(f862(f74(a92),x38031),x38032)) % 14.79/14.66 [3804]E(f862(a5,f862(f862(f73(a924),f862(a22,x38041)),f862(a22,x38042))),f862(f862(f73(a92),x38041),x38042)) % 14.79/14.66 [3805]E(f862(a5,f862(f862(f29(a924),f862(a22,x38051)),f862(a22,x38052))),f862(f862(f29(a92),x38051),x38052)) % 14.79/14.66 [3813]E(f862(f302(a924,a924,a105),f862(f295(a924,x38131),x38132)),f862(f295(a924,f862(a105,x38131)),f862(a105,x38132))) % 14.79/14.66 [3840]P1(f862(f41(x38401,x38402),f78(f931(a924,a924),f41(x38401,x38402)))) % 14.79/14.66 [3863]E(f38(a924,f862(a105,f38(a924,x38631,x38632)),x38632),f38(a924,f862(a105,x38631),x38632)) % 14.79/14.66 [3875]E(f862(f862(f32(f932(x38751,a921),f932(x38751,a921)),x38752),f7(f932(x38751,a921))),f31(f932(x38751,a921),x38752)) % 14.79/14.66 [3876]E(f862(f862(f33(f932(x38761,a921),f932(x38761,a921)),x38762),f7(f932(x38761,a921))),f30(f932(x38761,a921),x38762)) % 14.79/14.66 [3877]E(f862(f302(f925(x38771),f932(x38771,a921),f165(x38771)),f862(f165(f925(x38771)),f47(x38771,x38772))),f862(f300(x38771),f862(f165(x38771),x38772))) % 14.79/14.66 [3881]P1(f862(f862(f321(f932(x38811,a921)),x38812),f862(f300(x38811),x38812))) % 14.79/14.66 [3887]E(f38(a1,f862(f72(a1),f38(a1,x38871,x38872)),x38872),f38(a1,f862(f72(a1),x38871),x38872)) % 14.79/14.66 [3898]P1(f862(f862(f227(f932(x38981,a921)),x38982),f234(f932(x38981,a921)))) % 14.79/14.66 [3900]E(f862(f862(f280(x39001,x39001,x39001),f299(x39001,x39002)),f299(x39001,f299(x39001,x39002))),f299(x39001,x39002)) % 14.79/14.66 [3901]E(f862(f862(f103(f932(x39011,a921)),f862(f256(x39011,x39011),x39012)),f862(f275(x39011,x39011),x39012)),f862(f273(x39011),x39012)) % 14.79/14.66 [3922]E(f305(x39221,x39222,f234(f932(x39221,a921)),f234(f932(x39222,a921))),f234(f932(f930(x39221,x39222),a921))) % 14.79/14.66 [3972]P1(f862(f862(f227(a924),f38(a924,x39721,x39722)),x39721)) % 14.79/14.66 [3996]P1(f862(f862(f227(a1),f862(f72(a1),f862(f93(a1),x39961))),f862(f93(a1),x39962))) % 14.79/14.66 [4020]P1(f862(f862(f321(f932(x40201,a921)),f181(f932(x40201,a921))),f862(f300(x40201),x40202))) % 14.79/14.66 [4025]E(f299(x40251,f862(f862(f280(x40251,x40251,x40251),x40252),f299(x40251,x40252))),f299(x40251,x40252)) % 14.79/14.66 [4028]E(f862(f862(f280(x40281,x40281,x40281),f299(x40281,x40282)),x40282),f862(f862(f280(x40281,x40281,x40281),x40282),f299(x40281,x40282))) % 14.79/14.66 [4030]E(f862(a97,f862(f862(f73(a1),f862(f862(f3(a1),x40301),x40302)),f71(a1))),f862(f28(a1),f296(a1,x40302,x40301))) % 14.79/14.66 [4045]E(f862(f275(x40451,x40451),f862(f862(f280(x40451,x40451,x40451),x40452),f299(x40451,x40452))),f862(f275(x40451,x40451),x40452)) % 14.79/14.66 [4046]E(f862(f256(x40461,x40461),f862(f862(f280(x40461,x40461,x40461),x40462),f299(x40461,x40462))),f862(f256(x40461,x40461),x40462)) % 14.79/14.66 [4064]E(f862(f135(f925(x40641),f925(x40641),f127(x40641),f106(x40641)),f162(f925(x40641),x40642,f106(x40641))),f106(x40641)) % 14.79/14.66 [4073]P22(a924,a924,f862(f862(f9(a924,a924,a924),f73(a924)),x40731),x40732) % 14.79/14.66 [4075]P11(a924,f862(f161(a924),f862(f862(f147(f925(x40751),a924),f182(f925(x40751))),f172(x40751,x40752)))) % 14.79/14.66 [4105]P49(x41051,f862(f862(f103(f932(f931(x41051,x41051),a921)),x41052),f862(f277(x41051,x41051),x41052))) % 14.79/14.66 [4106]P49(x41061,f862(f862(f94(f932(f931(x41061,x41061),a921)),x41062),f862(f277(x41061,x41061),x41062))) % 14.79/14.66 [4117]P1(f862(f862(f228(a1),f862(f72(a1),f862(f93(a1),f862(a105,x41171)))),f862(f93(a1),x41172))) % 14.79/14.66 [4162]E(f862(f135(f925(x41621),x41621,f862(f9(x41621,f925(x41621),f925(x41621)),f144(x41621)),f106(x41621)),x41622),f862(f161(x41621),x41622)) % 14.79/14.66 [4210]P1(f862(f862(f227(f932(f931(f925(x42101),f925(x42101)),a921)),f151(x42101,x42102)),f299(f925(x42101),f150(x42101,x42102)))) % 14.79/14.66 [4239]P1(f862(f41(x42391,x42392),f862(f862(f244(a924,a924),f862(f862(f29(a924),x42391),x42392)),f38(a924,x42391,x42392)))) % 14.79/14.66 [4251]P1(f862(f862(f227(f932(f931(f925(x42511),f925(x42511)),a921)),f150(x42511,f299(x42511,x42512))),f299(f925(x42511),f150(x42511,x42512)))) % 14.79/14.66 [4468]E(f862(f862(f251(f931(a92,a92),a92,f931(a92,a92),f931(x44681,f931(a92,a92))),f259(f862(f158(a92),f862(f862(f147(f931(a92,x44681),a92),f243(a92,x44681)),x44682)))),f862(f862(f10(x44681,f932(f931(a92,a92),f931(x44681,f931(a92,a92))),a92),f244(x44681,f931(a92,a92))),f260(x44681,x44682))),f258(x44681,x44682)) % 14.79/14.66 [4524]P1(f862(f862(f321(f932(f922(f930(a919,f932(x45241,f932(a920,a921))),f930(a920,x45241)),a921)),f588(x45241,x45242)),f862(f254(f932(f922(f930(a919,f932(x45241,f932(a920,a921))),f930(a920,x45241)),a921)),f88(x45241)))) % 14.79/14.66 [4525]P1(f862(f862(f321(f932(f922(f930(a919,f932(x45251,f932(a920,a921))),f930(a920,x45251)),a921)),f862(f87(x45251),x45252)),f862(f254(f932(f922(f930(a919,f932(x45251,f932(a920,a921))),f930(a920,x45251)),a921)),f88(x45251)))) % 14.79/14.66 [4547]E(f216(a924,f931(x45471,f926(x45471)),f2(a924),f862(f249(x45471,f926(x45471),a924),f862(f18(f932(f926(x45471),a924),x45471),f862(f862(f9(f926(x45471),a924,a924),f862(f862(f10(a924,f932(a924,a924),f926(x45471)),f73(a924)),f182(f926(x45471)))),f71(a924)))),f862(f128(x45471),x45472)),f862(f182(f926(x45471)),x45472)) % 14.79/14.66 [4653]E(f862(f249(f932(f931(x46531,x46531),a921),f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f862(f862(f9(f932(f931(x46531,x46531),a921),f932(f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921))),f932(f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921))))),f862(f862(f10(f932(f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921)),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f932(f932(f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921))),f932(f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921))))),f932(f931(x46531,x46531),a921)),f10(f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921)),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921))),f932(f931(x46531,x46531),a921))),f862(f862(f10(f932(f932(x46532,x46531),f932(f932(f931(x46532,x46532),a921),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f932(f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921)),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f932(f931(x46531,x46531),a921)),f20(f932(x46532,x46531),f932(f931(x46532,x46532),a921),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f862(f862(f10(f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921)),f932(f932(x46532,x46531),f932(f932(f931(x46532,x46532),a921),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f932(f931(x46531,x46531),a921)),f862(f10(f932(f931(x46532,x46532),a921),f932(f932(f931(x46532,x46532),a921),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921))),f932(x46532,x46531)),f244(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f279(x46531,x46532))))),f279(x46531,x46532))),f67(x46531,x46532)) % 14.79/14.66 [4702]~E(f862(f300(x47021),x47022),f181(f932(f932(x47021,a921),a921))) % 14.79/14.66 [4711]~P1(f862(f862(f165(x47111),f106(x47111)),x47112)) % 14.79/14.66 [4715]~P1(f862(f862(f321(x47151),x47152),f181(f932(x47151,a921)))) % 14.79/14.66 [4724]~P1(f862(f862(f228(f932(x47241,a921)),x47242),f181(f932(x47241,a921)))) % 14.79/14.66 [3588]E(f862(f862(f3(a924),x35881),f862(f862(f73(a924),x35881),x35882)),f2(a924)) % 14.79/14.66 [3591]E(f862(f862(f103(f932(x35911,a921)),x35912),x35912),x35912) % 14.79/14.66 [3592]E(f862(f862(f94(f932(x35921,a921)),x35922),x35922),x35922) % 14.79/14.66 [3620]E(f862(f862(f3(f932(x36201,a921)),x36202),x36202),f181(f932(x36201,a921))) % 14.79/14.66 [3623]E(f862(f136(x36231,x36232),f2(a924)),f181(f932(f931(f925(x36231),f925(x36231)),a921))) % 14.79/14.66 [3624]E(f862(f862(f73(a924),x36241),f862(a105,x36242)),f862(a105,f862(f862(f73(a924),x36241),x36242))) % 14.79/14.66 [3635]E(f187(f862(f93(a1),x36351),f862(f93(a1),x36352)),f862(f93(a1),f862(f862(f3(a924),x36351),x36352))) % 14.79/14.66 [3638]E(f862(f862(f29(a1),f862(f72(a1),x36381)),x36382),f862(f862(f29(a1),x36381),f862(f72(a1),x36382))) % 14.79/14.66 [3642]E(f862(f28(a1),f862(f295(a1,x36421),x36422)),f862(a97,f862(f862(f3(a1),x36422),x36421))) % 14.79/14.66 [3645]E(f862(f862(f73(a924),f862(a105,x36451)),x36452),f862(a105,f862(f862(f73(a924),x36451),x36452))) % 14.79/14.66 [3648]E(f862(f72(f932(x36481,a921)),f862(f72(f932(x36481,a921)),x36482)),x36482) % 14.79/14.66 [3660]E(f172(x36601,f862(f862(f144(f925(x36601)),f106(x36601)),x36602)),f172(x36601,x36602)) % 14.79/14.66 [3664]E(f862(f862(f73(a924),x36641),f862(f862(f74(a924),x36641),x36642)),f862(f862(f74(a924),x36641),f862(a105,x36642))) % 14.79/14.66 [3671]E(f862(f862(a4,f862(a5,x36711)),f862(a5,x36712)),f862(a5,f862(f862(f3(a924),x36711),x36712))) % 14.79/14.66 [3686]E(f862(f862(f74(a1),f862(f72(a1),x36861)),x36862),f862(f72(a1),f862(f862(f74(a1),x36861),x36862))) % 14.79/14.66 [3688]E(f862(f862(f236(a1),f862(f93(a1),x36881)),x36882),f862(f93(a1),f862(f862(f236(a924),x36881),x36882))) % 14.79/14.66 [3689]E(f862(f862(f74(a92),f862(a5,x36891)),f862(a5,x36892)),f862(a5,f862(f862(f74(a924),x36891),x36892))) % 14.79/14.66 [3690]E(f862(f862(f73(a92),f862(a5,x36901)),f862(a5,x36902)),f862(a5,f862(f862(f73(a924),x36901),x36902))) % 14.79/14.66 [3691]E(f862(f862(f225(a924),f862(a105,x36911)),f862(a105,x36912)),f862(a105,f862(f862(f225(a924),x36911),x36912))) % 14.79/14.66 [3692]E(f862(f862(f226(a924),f862(a105,x36921)),f862(a105,x36922)),f862(a105,f862(f862(f226(a924),x36921),x36922))) % 14.79/14.66 [3697]E(f862(f165(a924),f132(a924,f862(f295(a924,x36971),x36972))),f862(f295(a924,x36971),x36972)) % 14.79/14.66 [3698]E(f304(x36981,f862(f862(f301(x36981),x36982),f181(f932(x36981,a921)))),x36982) % 14.79/14.66 [3702]E(f862(f275(x37021,x37022),f181(f932(f931(x37021,x37022),a921))),f181(f932(x37022,a921))) % 14.79/14.66 [3703]E(f862(f256(x37031,x37032),f181(f932(f931(x37031,x37032),a921))),f181(f932(x37031,a921))) % 14.79/14.66 [3707]E(f862(a97,f862(f862(f3(a1),x37071),x37072)),f862(f28(a1),f297(a1,x37072,x37071))) % 14.79/14.66 [3712]E(f862(f862(f73(a924),x37121),f862(f862(f74(a924),x37122),x37121)),f862(f862(f74(a924),f862(a105,x37122)),x37121)) % 14.79/14.66 [3714]E(f862(f862(f53(x37141),f181(f932(x37141,a921))),x37142),f181(f932(f932(x37141,a921),a921))) % 14.79/14.66 [3724]E(f862(f182(f925(a924)),f132(a924,f862(f295(a924,x37241),x37242))),f862(f862(f3(a924),x37242),x37241)) % 14.79/14.66 [3739]E(f862(f862(f103(f932(x37391,a921)),f181(f932(x37391,a921))),x37392),x37392) % 14.79/14.66 [3740]E(f862(f862(f94(f932(x37401,a921)),f234(f932(x37401,a921))),x37402),x37402) % 14.79/14.66 [3741]E(f862(f862(f73(a1),f862(f72(a1),x37411)),f862(f72(a1),x37412)),f862(f72(a1),f862(f862(f73(a1),x37411),x37412))) % 14.79/14.66 [3745]E(f862(f862(f74(a1),f862(f96(a1),x37451)),f862(f96(a1),x37452)),f862(f96(a1),f862(f862(f74(a1),x37451),x37452))) % 14.79/14.66 [3747]E(f862(f862(f74(a1),f862(f93(a1),x37471)),f862(f93(a1),x37472)),f862(f93(a1),f862(f862(f74(a924),x37471),x37472))) % 14.79/14.66 [3748]E(f862(f862(f73(a1),f862(f96(a1),x37481)),f862(f96(a1),x37482)),f862(f96(a1),f862(f862(f73(a1),x37481),x37482))) % 14.79/14.66 [3750]E(f862(f862(f73(a1),f862(f93(a1),x37501)),f862(f93(a1),x37502)),f862(f93(a1),f862(f862(f73(a924),x37501),x37502))) % 14.79/14.66 [3751]E(f862(f862(f29(a1),f862(f93(a1),x37511)),f862(f93(a1),x37512)),f862(f93(a1),f862(f862(f29(a924),x37511),x37512))) % 14.79/14.66 [3770]E(f862(f862(f8(x37701,a924),f862(f18(a924,x37701),f71(a924))),x37702),f862(f28(x37701),x37702)) % 14.79/14.66 [3775]E(f862(f72(a1),f38(a1,f862(f72(a1),x37751),x37752)),f38(a1,x37751,f862(f72(a1),x37752))) % 14.79/14.66 [3777]E(f862(f165(a1),f171(x37771,f862(f862(f3(a1),x37772),f71(a1)))),f862(f295(a1,x37771),x37772)) % 14.79/14.66 [3782]P1(f862(f862(f227(a924),x37821),f862(f862(f73(a924),x37822),x37821))) % 14.79/14.66 [3783]P1(f862(f862(f227(a924),x37831),f862(f862(f73(a924),x37831),x37832))) % 14.79/14.66 [3785]E(f862(f862(f103(f932(x37851,a921)),f234(f932(x37851,a921))),x37852),f234(f932(x37851,a921))) % 14.79/14.66 [3786]E(f862(f862(f94(f932(x37861,a921)),f181(f932(x37861,a921))),x37862),f181(f932(x37861,a921))) % 14.79/14.66 [3787]E(f862(f862(f3(f932(x37871,a921)),f181(f932(x37871,a921))),x37872),f181(f932(x37871,a921))) % 14.79/14.66 [3794]E(f862(f862(f244(a1,a1),x37941),f862(f72(a1),x37942)),f862(a44,f862(f862(f244(a1,a1),x37941),x37942))) % 14.79/14.66 [3795]E(f862(f295(a1,f862(f862(f73(a1),x37951),f71(a1))),x37952),f298(a1,x37951,x37952)) % 14.79/14.66 [3806]E(f862(f862(f74(a924),x38061),f862(f862(f29(a924),x38062),x38061)),f862(f862(f3(a924),x38062),f38(a924,x38062,x38061))) % 14.79/14.66 [3807]E(f862(f862(f74(a1),x38071),f862(f862(f29(a1),x38072),x38071)),f862(f862(f3(a1),x38072),f38(a1,x38072,x38071))) % 14.79/14.66 [3810]E(f862(f165(a1),f171(f862(f862(f73(a1),x38101),f71(a1)),x38102)),f297(a1,x38101,x38102)) % 14.79/14.66 [3814]P1(f862(f862(f227(f932(x38141,a921)),x38142),x38142)) % 14.79/14.66 [3817]E(f862(f862(f103(f932(x38171,a921)),x38172),f862(f72(f932(x38171,a921)),x38172)),f234(f932(x38171,a921))) % 14.79/14.66 [3818]E(f862(f862(f94(f932(x38181,a921)),x38182),f862(f72(f932(x38181,a921)),x38182)),f181(f932(x38181,a921))) % 14.79/14.66 [3826]E(f862(f862(f3(a924),f862(f862(f3(a924),x38261),f71(a924))),x38262),f862(f862(f3(a924),x38261),f862(a105,x38262))) % 14.79/14.66 [3832]E(f862(f862(f3(f932(x38321,a921)),f234(f932(x38321,a921))),x38322),f862(f72(f932(x38321,a921)),x38322)) % 14.79/14.66 [3833]E(f862(f862(f3(a1),f862(f96(a1),x38331)),f862(f96(a1),x38332)),f862(f96(a1),f862(f862(f73(a1),x38331),f862(f72(a1),x38332)))) % 14.79/14.66 [3846]E(f862(f165(a924),f132(a924,f862(f295(a924,x38461),f862(a105,x38462)))),f296(a924,x38461,x38462)) % 14.79/14.66 [3861]E(f862(f182(f925(f925(x38611))),f47(x38611,x38612)),f862(f862(f236(a924),f862(a105,f862(a105,f2(a924)))),f862(f182(f925(x38611)),x38612))) % 14.79/14.66 [3879]E(f862(f862(f176(f931(x38791,x38791),a921),f2(a924)),x38792),f299(x38791,f181(f932(f931(x38791,x38791),a921)))) % 14.79/14.66 [3883]P1(f862(f130(a924),f132(a924,f862(f295(a924,x38831),x38832)))) % 14.79/14.66 [3899]E(f862(f302(a1,a924,a97),f296(a1,f862(f93(a1),x38991),f862(f93(a1),x38992))),f296(a924,x38991,x38992)) % 14.79/14.66 [3908]E(f178(a924,f2(a924),f7(a924),f862(f862(f3(a924),x39081),x39082)),f862(f862(f3(a924),x39081),f862(a105,x39082))) % 14.79/14.66 [3909]E(f862(a97,f862(f862(f3(a1),x39091),f862(f862(f73(a1),x39092),f71(a1)))),f862(f28(a1),f298(a1,x39092,x39091))) % 14.79/14.66 [3944]E(f862(f862(f147(a924,a924),a105),f132(a924,f862(f295(a924,x39441),x39442))),f132(a924,f862(f295(a924,f862(a105,x39441)),f862(a105,x39442)))) % 14.79/14.66 [3952]E(f862(f165(a1),f171(f862(f862(f73(a1),x39521),f71(a1)),f862(f862(f3(a1),x39522),f71(a1)))),f298(a1,x39521,x39522)) % 14.79/14.66 [3964]P1(f862(f862(f227(f932(x39641,a921)),f181(f932(x39641,a921))),x39642)) % 14.79/14.66 [3968]E(f78(x39681,f862(f862(f9(x39681,x39681,a921),a317),x39682)),x39682) % 14.79/14.66 [3969]E(f83(x39691,f862(f862(f9(x39691,x39691,a921),a317),x39692)),x39692) % 14.79/14.66 [3973]E(f862(f165(a924),f132(a924,f862(f295(a924,f862(a105,x39731)),f862(a105,x39732)))),f297(a924,x39731,x39732)) % 14.79/14.66 [3999]E(f862(f862(f246(x39991,x39992),f234(f932(x39991,a921))),f862(f18(f932(x39992,a921),x39991),f234(f932(x39992,a921)))),f234(f932(f931(x39991,x39992),a921))) % 14.79/14.66 [4032]E(f862(f254(x40321),f862(f862(f10(a921,a921,x40321),a314),x40322)),f862(f72(f932(x40321,a921)),f862(f254(x40321),x40322))) % 14.79/14.66 [4035]E(f862(f254(x40351),f862(f862(f9(x40351,x40351,a921),a317),x40352)),f862(f862(f301(x40351),x40352),f181(f932(x40351,a921)))) % 14.79/14.66 [4042]E(f862(f862(f73(a1),f862(f862(f3(a1),x40421),x40422)),f862(f862(f3(a1),x40421),x40422)),f862(f862(f3(a1),f862(f862(f73(a1),x40421),x40421)),f862(f862(f73(a1),x40422),x40422))) % 14.79/14.66 [4043]E(f862(f862(f73(a1),f862(f862(f73(a1),x40431),x40431)),f862(f862(f73(a1),x40432),x40432)),f862(f862(f73(a1),f862(f862(f73(a1),x40431),x40432)),f862(f862(f73(a1),x40431),x40432))) % 14.79/14.66 [4059]P1(f862(f862(f227(a924),f862(f28(x40591),f862(f165(x40591),x40592))),f862(f182(f925(x40591)),x40592))) % 14.79/14.66 [4060]P1(f862(f862(f227(a924),f862(f182(f925(x40601)),f145(x40601,x40602))),f862(f182(f925(x40601)),x40602))) % 14.79/14.66 [4070]E(f862(f254(x40701),f862(f862(f9(x40701,f932(x40701,a921),a921),f321(x40701)),x40702)),x40702) % 14.79/14.66 [4084]E(f862(f862(f168(x40841),f862(f862(f3(a924),f862(f182(f925(x40841)),x40842)),f71(a924))),x40842),f107(x40841,x40842)) % 14.79/14.66 [4104]E(f178(a924,f2(a924),f862(f862(f10(a924,a924,a924),a105),f862(f225(a924),x41041)),x41042),f862(f862(f225(a924),f862(a105,x41041)),x41042)) % 14.79/14.66 [4109]E(f30(f932(x41091,a921),f862(f302(f932(f931(x41091,x41091),a921),f932(x41091,a921),f273(x41091)),x41092)),f862(f273(x41091),f30(f932(f931(x41091,x41091),a921),x41092))) % 14.79/14.66 [4110]E(f178(a924,f862(a105,x41101),f862(f862(f10(a924,a924,a924),a105),f862(f226(a924),x41101)),x41102),f862(f862(f226(a924),f862(a105,x41101)),x41102)) % 14.79/14.66 [4112]E(f862(f862(f244(a1,a1),f862(f862(f29(a1),f862(f69(a1),x41121)),f862(f69(a1),x41122))),f38(a1,f862(f69(a1),x41121),f862(f69(a1),x41122))),f46(x41121,x41122)) % 14.79/14.66 [4135]P1(f862(f862(f227(f932(f932(x41351,a921),a921)),x41352),f862(f300(x41351),f30(f932(x41351,a921),x41352)))) % 14.79/14.66 [4167]E(f862(f862(f33(x41671,f932(x41671,a921)),x41672),f862(f862(f9(x41671,f932(x41671,a921),f932(x41671,a921)),f301(x41671)),f181(f932(x41671,a921)))),x41672) % 14.79/14.66 [4168]E(f862(f862(f280(x41681,x41681,x41681),f862(f277(x41681,x41681),x41682)),f299(x41681,f862(f277(x41681,x41681),x41682))),f862(f277(x41681,x41681),f862(f862(f280(x41681,x41681,x41681),x41682),f299(x41681,x41682)))) % 14.79/14.66 [4231]E(f862(f165(x42311),f862(f135(f925(x42311),f925(x42311),f127(x42311),f106(x42311)),x42312)),f862(f862(f33(f925(x42311),f932(x42311,a921)),f862(f165(f925(x42311)),x42312)),f165(x42311))) % 14.79/14.66 [4262]E(f862(f862(f103(f932(f931(x42621,x42621),a921)),f299(x42621,f181(f932(f931(x42621,x42621),a921)))),f862(f862(f280(x42621,x42621,x42621),f299(x42621,x42622)),x42622)),f299(x42621,x42622)) % 14.79/14.66 [4298]E(f862(f862(f174(x42981,x42981),x42982),x42982),f862(f862(f147(x42981,f931(x42981,x42981)),f862(f862(f20(x42981,x42981,f931(x42981,x42981)),f244(x42981,x42981)),f7(x42981))),x42982)) % 14.79/14.66 [4409]E(f862(f135(a924,f925(x44091),f862(f9(f925(x44091),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x44091)),f226(a924)),f182(f925(x44091)))),f2(a924)),f862(f161(f925(x44091)),x44092)),f862(f182(f925(f925(x44091))),f172(x44091,x44092))) % 14.79/14.66 [4482]E(f862(f862(f279(f931(a924,f925(x44821)),f925(x44821)),f311(a924,f925(x44821),a232,f138(x44821,x44822))),f862(f862(f20(f925(x44821),f925(x44821),f931(a924,f925(x44821))),f862(f862(f10(a924,f932(f925(x44821),f931(a924,f925(x44821))),f925(x44821)),f244(a924,f925(x44821))),f182(f925(x44821)))),f7(f925(x44821)))),f139(x44821,x44822)) % 14.79/14.66 [4611]E(f862(f254(x46111),f862(f862(f10(f932(f932(x46111,a921),a921),a921,x46111),f81(f932(x46111,a921))),f862(f862(f10(f932(f932(x46111,a921),a921),f932(f932(x46111,a921),a921),x46111),f862(f20(f932(x46111,a921),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x46111,a921)),a322),f862(f862(f9(f932(x46111,a921),f932(f932(x46111,a921),a921),a921),f321(f932(x46111,a921))),x46112)))),f321(x46111)))),f31(f932(x46111,a921),x46112)) % 14.79/14.66 [4612]E(f862(f254(x46121),f862(f862(f10(f932(f932(x46121,a921),a921),a921,x46121),f80(f932(x46121,a921))),f862(f862(f10(f932(f932(x46121,a921),a921),f932(f932(x46121,a921),a921),x46121),f862(f20(f932(x46121,a921),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x46121,a921)),a318),f862(f862(f9(f932(x46121,a921),f932(f932(x46121,a921),a921),a921),f321(f932(x46121,a921))),x46122)))),f321(x46121)))),f30(f932(x46121,a921),x46122)) % 14.79/14.66 [4725]~P1(f862(f862(f228(a1),f862(f93(a1),x47251)),f862(f72(a1),f862(f93(a1),x47252)))) % 14.79/14.66 [4741]~P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x47411),x47411)),a90)),f862(f862(f73(a1),x47412),x47412))) % 14.79/14.66 [3710]E(f862(f862(f3(a924),f862(f862(f73(a924),x37101),x37102)),x37102),x37101) % 14.79/14.66 [3711]E(f862(f862(f3(a924),f862(f862(f73(a924),x37111),x37112)),x37111),x37112) % 14.79/14.66 [3776]E(f862(f862(f73(a924),f862(f862(f3(a924),x37761),x37762)),x37762),f862(f862(f226(a924),x37761),x37762)) % 14.79/14.66 [3886]E(f862(f862(f74(a924),f862(f862(f29(a924),x38861),x38862)),x38862),f862(f862(f3(a924),x38861),f38(a924,x38861,x38862))) % 14.79/14.66 [3913]E(f862(f165(a924),f132(a924,f862(f295(a924,f862(a105,x39131)),x39132))),f298(a924,x39131,x39132)) % 14.79/14.66 [3921]E(f862(f93(a1),f209(f862(a97,f862(f69(a1),x39211)),f862(a97,f862(f69(a1),x39212)))),f862(f862(a210,x39211),x39212)) % 14.79/14.66 [3923]E(f862(f862(f103(f932(x39231,a921)),f862(f72(f932(x39231,a921)),x39232)),x39232),f234(f932(x39231,a921))) % 14.79/14.66 [3924]E(f862(f862(f94(f932(x39241,a921)),f862(f72(f932(x39241,a921)),x39242)),x39242),f181(f932(x39241,a921))) % 14.79/14.66 [3940]P1(f862(f862(f227(a924),f862(f862(f3(a924),x39401),x39402)),x39401)) % 14.79/14.66 [3941]P1(f862(f862(f227(a924),f862(f862(f29(a924),x39411),x39412)),x39411)) % 14.79/14.66 [3965]P1(f862(f862(f228(a924),x39651),f862(a105,f862(f862(f73(a924),x39652),x39651)))) % 14.79/14.66 [3966]P1(f862(f862(f228(a924),x39661),f862(a105,f862(f862(f73(a924),x39661),x39662)))) % 14.79/14.66 [3983]E(f862(f862(f74(a924),f862(a97,f862(f69(a1),x39831))),f862(a97,f862(f69(a1),x39832))),f862(a97,f862(f69(a1),f862(f862(f74(a1),x39831),x39832)))) % 14.79/14.66 [3995]P1(f862(f862(f227(a1),f2(a1)),f862(f862(f236(a1),f862(f69(a1),x39951)),x39952))) % 14.79/14.66 [4063]E(f862(f276(f925(x40631),f925(x40631),f151(x40631,x40632)),f862(f862(f301(f925(x40631)),f106(x40631)),f181(f932(f925(x40631),a921)))),f862(f862(f301(f925(x40631)),f106(x40631)),f181(f932(f925(x40631),a921)))) % 14.79/14.66 [4082]E(f862(f862(f103(f932(f931(x40821,x40821),a921)),f299(x40821,x40822)),f299(x40821,f181(f932(f931(x40821,x40821),a921)))),f299(x40821,x40822)) % 14.79/14.66 [4094]E(f862(f862(f29(a1),f862(f96(a1),f862(f862(f73(a1),x40941),x40941))),f862(f96(a1),f862(f862(f73(a1),x40942),x40942))),f862(f862(f29(a1),f862(f96(a1),x40941)),f862(f96(a1),x40942))) % 14.79/14.66 [4157]E(f862(f862(f236(a1),x41571),f862(f96(a924),f862(f862(f73(a1),x41572),x41572))),f862(f862(f79(a1,a1),f862(f862(f236(a1),x41571),f862(f96(a924),x41572))),f862(f862(f20(a1,a1,a1),f74(a1)),f7(a1)))) % 14.79/14.66 [4163]E(f862(f254(f932(x41631,a921)),f862(f862(f9(f932(x41631,a921),f932(x41631,a921),a921),f227(f932(x41631,a921))),x41632)),f862(f300(x41631),x41632)) % 14.79/14.66 [4179]E(f862(f862(f147(a1,a924),a97),f862(f862(f127(a1),f862(f862(f147(a924,a1),f93(a1)),x41791)),f862(f862(f147(a924,a1),f93(a1)),x41792))),f862(f862(f127(a924),x41791),x41792)) % 14.79/14.66 [4209]E(f862(f302(a1,a1,f862(f862(f9(a1,a1,a1),f73(a1)),x42091)),f862(f295(a1,f2(a1)),f862(f862(f3(a1),x42092),x42091))),f862(f295(a1,x42091),x42092)) % 14.79/14.66 [4211]P51(x42111,f862(f862(f3(f932(f931(x42111,x42111),a921)),x42112),f299(x42111,f181(f932(f931(x42111,x42111),a921))))) % 14.79/14.66 [4229]E(f862(f182(f925(x42291)),f862(f135(f925(x42291),f925(x42291),f127(x42291),f106(x42291)),x42292)),f862(f158(a924),f862(f862(f147(f925(x42291),a924),f182(f925(x42291))),x42292))) % 14.79/14.66 [4233]P50(x42331,f234(f932(x42331,a921)),f862(f862(f103(f932(f931(x42331,x42331),a921)),x42332),f299(x42331,f181(f932(f931(x42331,x42331),a921))))) % 14.79/14.66 [4278]E(f178(a924,f2(a924),f862(f862(f10(a924,a924,a924),a105),f862(f862(f9(a924,a924,a924),f225(a924)),x42781)),x42782),f862(f862(f225(a924),x42782),f862(a105,x42781))) % 14.79/14.66 [4281]E(f178(a924,f862(a105,x42811),f862(f862(f10(a924,a924,a924),a105),f862(f862(f9(a924,a924,a924),f226(a924)),x42811)),x42812),f862(f862(f226(a924),x42812),f862(a105,x42811))) % 14.79/14.66 [4284]E(f862(f302(x42841,f925(x42841),f862(f862(f9(x42841,f925(x42841),f925(x42841)),f144(x42841)),f106(x42841))),x42842),f167(x42841,x42842,f862(f862(f301(f925(x42841)),f106(x42841)),f181(f932(f925(x42841),a921))))) % 14.79/14.66 [4286]E(f862(f862(f103(f932(f931(x42861,x42861),a921)),f862(f862(f280(x42861,x42861,x42861),x42862),f299(x42861,x42862))),f299(x42861,f181(f932(f931(x42861,x42861),a921)))),f299(x42861,x42862)) % 14.79/14.66 [4293]P1(f862(f862(f227(f932(f931(x42931,x42931),a921)),f255(x42931,x42932)),f862(f862(f246(x42931,x42931),x42932),f862(f18(f932(x42931,a921),x42931),x42932)))) % 14.79/14.66 [4296]E(f862(f302(a1,a924,a97),f862(f862(f103(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x42961)),f862(f302(a924,a1,f93(a1)),x42962))),f862(f862(f103(f932(a924,a921)),x42961),x42962)) % 14.79/14.66 [4297]E(f862(f302(a1,a924,a97),f862(f862(f94(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x42971)),f862(f302(a924,a1,f93(a1)),x42972))),f862(f862(f94(f932(a924,a921)),x42971),x42972)) % 14.79/14.66 [4300]E(f862(f254(x43001),f862(f862(f10(a921,a921,x43001),a314),f862(f862(f9(x43001,f932(x43001,a921),a921),f321(x43001)),x43002))),f862(f72(f932(x43001,a921)),x43002)) % 14.79/14.66 [4327]E(f862(f135(f925(x43271),f925(x43271),f127(x43271),f106(x43271)),f862(f862(f147(f925(x43271),f925(x43271)),f161(x43271)),f862(f161(f925(x43271)),x43272))),f862(f161(x43271),f862(f135(f925(x43271),f925(x43271),f127(x43271),f106(x43271)),x43272))) % 14.79/14.66 [4353]E(f862(f862(f33(a924,f932(f931(x43531,x43531),a921)),f234(f932(a924,a921))),f862(f862(f9(a924,f932(f931(x43531,x43531),a921),f932(f931(x43531,x43531),a921)),f176(f931(x43531,x43531),a921)),x43532)),f299(x43531,x43532)) % 14.79/14.66 [4371]E(f78(x43711,f862(f862(f10(f932(x43711,a921),a921,x43711),f862(a317,x43712)),f862(f862(f9(x43711,f932(x43711,a921),f932(x43711,a921)),f301(x43711)),f181(f932(x43711,a921))))),f304(x43711,x43712)) % 14.79/14.66 [4379]E(f862(f182(f925(x43791)),f145(x43791,f862(f135(f925(x43791),f925(x43791),f127(x43791),f106(x43791)),x43792))),f862(f28(x43791),f862(f862(f33(f925(x43791),f932(x43791,a921)),f862(f165(f925(x43791)),x43792)),f165(x43791)))) % 14.79/14.66 [4393]E(f862(f862(f103(f932(f931(x43931,x43931),a921)),x43932),f862(f862(f280(x43931,x43931,x43931),f862(f862(f280(x43931,x43931,x43931),x43932),f299(x43931,x43932))),x43932)),f862(f862(f280(x43931,x43931,x43931),x43932),f299(x43931,x43932))) % 14.79/14.66 [4417]P1(f862(f862(f227(f932(f931(x44171,x44171),a921)),f862(f862(f280(x44171,x44171,x44171),x44172),f299(x44171,x44172))),f862(f862(f246(x44171,x44171),f862(f273(x44171),x44172)),f862(f18(f932(x44171,a921),x44171),f862(f273(x44171),x44172))))) % 14.79/14.66 [4459]E(f862(f254(f925(x44591)),f862(f862(f9(f925(x44591),f932(x44591,a921),a921),f862(f862(f10(f932(x44591,a921),f932(f932(x44591,a921),a921),f925(x44591)),f227(f932(x44591,a921))),f165(x44591))),x44592)),f154(x44591,x44592)) % 14.79/14.66 [4470]E(f862(f149(f925(x44701),x44701,f106(x44701),f862(f862(f10(f925(x44701),f932(f925(x44701),f925(x44701)),x44701),f862(f9(f925(x44701),f925(x44701),f925(x44701)),f127(x44701))),f862(f862(f9(x44701,f925(x44701),f925(x44701)),f144(x44701)),f106(x44701)))),x44702),f862(f160(x44701),x44702)) % 14.79/14.66 [4510]P22(f932(x45101,x45102),f932(f931(x45101,x45102),a921),f862(f862(f10(f932(f931(x45101,x45102),a921),f932(f931(x45101,x45102),a921),f932(x45101,x45102)),f254(f931(x45101,x45102))),f862(f862(f10(f932(x45101,f932(x45102,a921)),f932(f931(x45101,x45102),a921),f932(x45101,x45102)),f249(x45101,x45102,a921)),f862(f10(x45102,f932(x45102,a921),x45101),f862(f9(x45102,x45102,a921),a317)))),f234(f932(f932(x45101,x45102),a921))) % 14.79/14.66 [4515]E(f38(a1,f862(f96(a1),f862(f862(f73(a1),x45151),x45151)),f862(f96(a1),f862(f862(f73(a1),x45152),x45152))),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,f862(f96(a1),x45151),f862(f96(a1),x45152)))) % 14.79/14.66 [4561]E(f862(f862(f33(x45611,f932(f931(x45611,x45611),a921)),x45612),f862(f862(f9(x45611,f932(f931(x45611,x45611),a921),f932(f931(x45611,x45611),a921)),f862(f862(f10(f931(x45611,x45611),f932(f932(f931(x45611,x45611),a921),f932(f931(x45611,x45611),a921)),x45611),f301(f931(x45611,x45611))),f862(f862(f20(x45611,x45611,f931(x45611,x45611)),f244(x45611,x45611)),f7(x45611)))),f181(f932(f931(x45611,x45611),a921)))),f255(x45611,x45612)) % 14.79/14.66 [4569]E(f195(x45691,f862(f862(f244(a1,a1),f862(f72(a1),f862(f862(f66(f931(a1,a1),a1,x45691,f243(a1,a1)),f205(x45691)),x45692))),f862(f862(f66(f931(a1,a1),a1,x45691,f248(a1,a1)),f205(x45691)),x45692))),f220(x45691,x45692)) % 14.79/14.66 [4650]E(f862(f254(f932(x46501,a921)),f862(f862(f10(f932(f932(x46501,a921),a921),a921,f932(x46501,a921)),f80(f932(x46501,a921))),f862(f862(f9(f932(x46501,a921),f932(f932(x46501,a921),a921),f932(f932(x46501,a921),a921)),f862(f862(f10(f932(f932(x46501,a921),f932(a921,a921)),f932(f932(f932(x46501,a921),a921),f932(f932(x46501,a921),a921)),f932(x46501,a921)),f20(f932(x46501,a921),a921,a921)),f862(f862(f10(f932(f932(x46501,a921),a921),f932(f932(x46501,a921),f932(a921,a921)),f932(x46501,a921)),f862(f10(a921,f932(a921,a921),f932(x46501,a921)),a318)),f862(f862(f9(f932(x46501,a921),f932(f932(x46501,a921),f932(x46501,a921)),f932(f932(x46501,a921),a921)),f862(f862(f10(f932(f932(x46501,a921),a921),f932(f932(f932(x46501,a921),f932(x46501,a921)),f932(f932(x46501,a921),a921)),f932(x46501,a921)),f10(f932(x46501,a921),a921,f932(x46501,a921))),a317)),f72(f932(x46501,a921)))))),f862(f862(f10(f932(f932(x46501,a921),a921),a921,f932(x46501,a921)),f862(f321(f932(x46501,a921)),x46502)),f300(x46501))))),f862(f300(x46501),f862(f72(f932(x46501,a921)),x46502))) % 14.79/14.66 [4723]~E(f862(f862(f73(a1),x47231),x47231),f862(f862(f3(a1),f862(f862(f73(a1),x47232),x47232)),a90)) % 14.79/14.66 [4728]~P1(f862(f862(f228(a924),f862(f862(f73(a924),x47281),x47282)),x47282)) % 14.79/14.66 [4729]~P1(f862(f862(f228(a924),f862(f862(f73(a924),x47291),x47292)),x47291)) % 14.79/14.66 [4000]E(f862(f862(f3(a924),x40001),f862(f862(f74(a924),f862(f862(f29(a924),x40001),x40002)),x40002)),f38(a924,x40001,x40002)) % 14.79/14.66 [4001]E(f862(f862(f3(a1),x40011),f862(f862(f74(a1),f862(f862(f29(a1),x40011),x40012)),x40012)),f38(a1,x40011,x40012)) % 14.79/14.66 [4033]E(f862(f862(f147(a924,x40331),f862(f157(x40331),x40332)),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(x40331)),x40332)))),x40332) % 14.79/14.66 [4090]E(f862(f276(x40901,x40901,f299(x40901,f181(f932(f931(x40901,x40901),a921)))),x40902),x40902) % 14.79/14.66 [4214]E(f299(x42141,f862(f862(f103(f932(f931(x42141,x42141),a921)),x42142),f299(x42141,f181(f932(f931(x42141,x42141),a921))))),f299(x42141,x42142)) % 14.79/14.66 [4215]E(f299(x42151,f862(f862(f3(f932(f931(x42151,x42151),a921)),x42152),f299(x42151,f181(f932(f931(x42151,x42151),a921))))),f299(x42151,x42152)) % 14.79/14.66 [4265]E(f862(f862(f3(a1),f862(f862(f3(a1),f862(f862(f73(a1),x42651),x42651)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x42652),x42652)),a90)),f862(f862(f73(a1),f862(f862(f3(a1),x42651),x42652)),f862(f862(f3(a1),x42651),x42652))) % 14.79/14.66 [4305]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f73(a1),x43051),x43052)),f862(f862(f73(a1),x43051),x43052))),a90),f862(f862(f73(a1),f862(f862(f73(a1),x43051),x43051)),f862(f862(f3(a1),f862(f862(f73(a1),x43052),x43052)),a90))) % 14.79/14.66 [4330]E(f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43301),x43301)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x43302),x43302)),a90)),f862(f862(f73(a1),f862(f862(f73(a1),x43301),f862(f862(f3(a1),x43302),a90))),f862(f862(f73(a1),x43301),f862(f862(f3(a1),x43302),a90)))) % 14.79/14.66 [4341]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),x43411),x43412)),f862(f862(f3(a1),x43411),x43412))),a90),f862(f862(f3(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43411),x43411)),a90)),f862(f862(f73(a1),x43412),x43412))) % 14.79/14.66 [4342]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f73(a1),x43421),x43422)),f862(f862(f73(a1),x43421),x43422))),a90),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43421),x43421)),a90)),f862(f862(f73(a1),x43422),x43422))) % 14.79/14.66 [4390]E(f862(f93(a1),f862(f862(f29(a924),f862(f862(f74(a924),f862(a97,f862(f69(a1),x43901))),f862(a97,f862(f69(a1),x43902)))),f209(f862(a97,f862(f69(a1),x43901)),f862(a97,f862(f69(a1),x43902))))),f211(x43901,x43902)) % 14.79/14.66 [4436]E(f862(f862(f251(f931(a92,a92),a92,f931(a92,a92),f931(x44361,f931(a92,a92))),f259(f862(a5,f862(f182(f925(x44361)),x44362)))),f862(f862(f10(x44361,f932(f931(a92,a92),f931(x44361,f931(a92,a92))),a92),f244(x44361,f931(a92,a92))),f862(f862(f10(a924,x44361,a92),f862(f157(x44361),x44362)),a22))),f267(x44361,x44362)) % 14.79/14.66 [4516]E(f862(f135(a924,f925(x45161),f862(f9(f925(x45161),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x45161)),f226(a924)),f182(f925(x45161)))),f2(a924)),f862(f161(f925(x45161)),f172(x45161,x45162))),f862(f182(f925(f925(x45161))),f862(f129(f925(x45161),f862(f862(f10(a921,a921,f925(x45161)),a314),f862(f862(f9(f925(x45161),f925(x45161),a921),a317),f106(x45161)))),x45162))) % 14.79/14.66 [4522]E(f862(f862(f33(a924,f932(x45221,a921)),f234(f932(a924,a921))),f862(f862(f9(a924,f932(a924,f932(x45221,a921)),f932(x45221,a921)),f862(f862(f10(f932(a924,a921),f932(f932(a924,f932(x45221,a921)),f932(x45221,a921)),a924),f33(a924,f932(x45221,a921))),f295(a924,f2(a924)))),x45222)),f862(f862(f33(a924,f932(x45221,a921)),f234(f932(a924,a921))),x45222)) % 14.79/14.66 [4546]P1(f862(f54(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),x45461)),f862(f862(f9(a924,a924,a921),f228(a924)),x45462))))) % 14.79/14.66 [4658]E(f862(f254(f931(f925(x46581),f925(x46581))),f862(f249(f925(x46581),f925(x46581),a921),f862(f862(f20(f925(x46581),f932(f925(x46581),a921),f932(f925(x46581),a921)),f862(f862(f10(f932(f925(x46581),f932(a921,a921)),f932(f932(f925(x46581),a921),f932(f925(x46581),a921)),f925(x46581)),f20(f925(x46581),a921,a921)),f862(f862(f10(f932(f925(x46581),a921),f932(f925(x46581),f932(a921,a921)),f925(x46581)),f862(f10(a921,f932(a921,a921),f925(x46581)),a319)),f862(f862(f9(f925(x46581),f932(f925(x46581),a924),f932(f925(x46581),a921)),f862(f862(f10(f932(a924,a921),f932(f932(f925(x46581),a924),f932(f925(x46581),a921)),f925(x46581)),f10(a924,a921,f925(x46581))),f862(f862(f10(a924,f932(a924,a921),f925(x46581)),f228(a924)),f182(f925(x46581))))),f182(f925(x46581)))))),f862(f862(f20(f925(x46581),f932(f925(x46581),a921),f932(f925(x46581),a921)),f862(f862(f10(f932(f925(x46581),f932(a921,a921)),f932(f932(f925(x46581),a921),f932(f925(x46581),a921)),f925(x46581)),f20(f925(x46581),a921,a921)),f862(f862(f10(f932(f925(x46581),a921),f932(f925(x46581),f932(a921,a921)),f925(x46581)),f862(f10(a921,f932(a921,a921),f925(x46581)),a318)),f862(f862(f9(f925(x46581),f932(f925(x46581),a924),f932(f925(x46581),a921)),f862(f862(f10(f932(a924,a921),f932(f932(f925(x46581),a924),f932(f925(x46581),a921)),f925(x46581)),f10(a924,a921,f925(x46581))),f862(f862(f10(a924,f932(a924,a921),f925(x46581)),a317),f182(f925(x46581))))),f182(f925(x46581)))))),f862(f862(f9(f925(x46581),f932(f931(f925(x46581),f925(x46581)),a921),f932(f925(x46581),a921)),f862(f862(f10(f932(f925(x46581),f932(f932(f931(f925(x46581),f925(x46581)),a921),a921)),f932(f932(f931(f925(x46581),f925(x46581)),a921),f932(f925(x46581),a921)),f925(x46581)),f9(f925(x46581),f932(f931(f925(x46581),f925(x46581)),a921),a921)),f862(f862(f10(f932(f925(x46581),f931(f925(x46581),f925(x46581))),f932(f925(x46581),f932(f932(f931(f925(x46581),f925(x46581)),a921),a921)),f925(x46581)),f862(f10(f931(f925(x46581),f925(x46581)),f932(f932(f931(f925(x46581),f925(x46581)),a921),a921),f925(x46581)),f321(f931(f925(x46581),f925(x46581))))),f244(f925(x46581),f925(x46581))))),f138(x46581,x46582)))))),f139(x46581,x46582)) % 14.79/14.66 [4734]~P1(f862(f862(f84(a1),f862(f862(f73(a1),x47341),x47341)),f862(f862(f3(a1),f862(f862(f73(a1),x47342),x47342)),a90))) % 14.79/14.66 [4333]E(f862(f862(f73(a1),f862(f862(f73(a1),f862(f862(f74(a1),x43331),x43332)),f862(f862(f74(a1),x43331),x43332))),x43332),f862(f862(f74(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43331),x43331)),a90)),x43332)) % 14.79/14.66 [4435]E(f862(a97,f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x44351),x44352)),f181(f932(f931(a924,a924),a921)))))),f862(f862(f3(a924),x44351),x44352)) % 14.79/14.66 [4439]E(f862(f862(f280(x44391,x44391,x44391),f862(f862(f103(f932(f931(x44391,x44391),a921)),x44392),f299(x44391,f181(f932(f931(x44391,x44391),a921))))),f299(x44391,f862(f862(f103(f932(f931(x44391,x44391),a921)),x44392),f299(x44391,f181(f932(f931(x44391,x44391),a921)))))),f299(x44391,x44392)) % 14.79/14.66 [4476]E(f260(x44761,f862(f129(f931(a92,x44761),f862(f249(a92,x44761,a921),f862(f862(f10(a921,f932(x44761,a921),a92),f18(a921,x44761)),f862(f228(a92),f2(a92))))),x44762)),f260(x44761,x44762)) % 14.79/14.66 [4477]E(f258(x44771,f862(f129(f931(a92,x44771),f862(f249(a92,x44771,a921),f862(f862(f10(a921,f932(x44771,a921),a92),f18(a921,x44771)),f862(f228(a92),f2(a92))))),x44772)),f258(x44771,x44772)) % 14.79/14.66 [4479]E(f862(f72(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x44791),x44792)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x44792),x44791)),f181(f932(f931(a924,a924),a921)))))) % 14.79/14.66 [4537]E(f862(f862(f279(f925(a924),x45371),f138(a924,a232)),f862(f862(f9(x45371,f925(f932(x45371,a924)),f925(a924)),f862(f862(f10(f932(f932(x45371,a924),a924),f932(f925(f932(x45371,a924)),f925(a924)),x45371),f147(f932(x45371,a924),a924)),f862(f9(f932(x45371,a924),x45371,a924),f7(f932(x45371,a924))))),x45372)),f146(x45371,x45372)) % 14.79/14.66 [4558]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x45581),a90))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f2(a924))),f862(f862(f10(a924,a924,a1),a105),f862(f862(f10(a924,a924,a1),f862(f225(a924),x45582)),a97)))),f862(f862(f225(a924),f862(a105,x45582)),f862(f96(a924),x45581))) % 14.79/14.66 [4559]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x45591),a90))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f862(a105,x45592))),f862(f862(f10(a924,a924,a1),a105),f862(f862(f10(a924,a924,a1),f862(f226(a924),x45592)),a97)))),f862(f862(f226(a924),f862(a105,x45592)),f862(f96(a924),x45591))) % 14.79/14.66 [4579]E(f862(f135(f925(x45791),f925(x45791),f127(x45791),f106(x45791)),f862(f862(f147(f925(x45791),f925(x45791)),f149(f925(x45791),x45791,f106(x45791),f862(f862(f10(f925(x45791),f932(f925(x45791),f925(x45791)),x45791),f18(f925(x45791),f925(x45791))),f862(f862(f9(x45791,f925(x45791),f925(x45791)),f144(x45791)),f106(x45791))))),x45792)),f862(f862(f147(f925(x45791),x45791),f134(x45791)),f862(f129(f925(x45791),f862(f862(f10(a921,a921,f925(x45791)),a314),f862(f862(f9(f925(x45791),f925(x45791),a921),a317),f106(x45791)))),x45792))) % 14.79/14.66 [4641]E(f862(f249(a1,a1,a921),f862(f862(f9(a1,f932(a1,a921),f932(a1,a921)),f862(f862(f10(f932(a1,f932(a921,a921)),f932(f932(a1,a921),f932(a1,a921)),a1),f20(a1,a921,a921)),f862(f862(f10(f932(a1,a921),f932(a1,f932(a921,a921)),a1),f862(f10(a921,f932(a921,a921),a1),a318)),f862(f862(f10(f932(a1,a1),f932(a1,a921),a1),f862(f10(a1,a921,a1),f862(a317,x46411))),f862(f862(f10(a1,f932(a1,a1),a1),f73(a1)),f862(f74(a1),x46412)))))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),f862(a322,f862(f862(f228(a1),f2(a1)),x46412))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),f862(f862(f9(a1,a1,a921),f228(a1)),x46412))))),f862(f862(f10(a921,a921,a1),f862(a322,f862(a314,f862(f862(f228(a1),f2(a1)),x46412)))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f228(a1),x46412))),f862(f862(f9(a1,a1,a921),f227(a1)),f2(a1))))))),f42(x46411,x46412)) % 14.79/14.66 [4644]E(f862(f254(x46441),f862(f862(f10(f932(a924,a921),a921,x46441),f80(a924)),f862(f862(f9(x46441,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),x46441),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),x46441),f862(f10(a921,f932(a921,a921),a924),a318)),f862(f862(f9(x46441,f932(a924,x46441),f932(a924,a921)),f862(f862(f10(f932(x46441,a921),f932(f932(a924,x46441),f932(a924,a921)),x46441),f10(x46441,a921,a924)),a317)),f862(f157(x46441),x46442))))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f182(f925(x46441)),x46442))))),f862(f165(x46441),x46442)) % 14.79/14.66 [4449]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),x44491),a90)),x44492)),f862(f862(f3(a1),f862(f862(f73(a1),x44491),a90)),x44492))),a90),f862(f862(f3(a1),f862(f862(f73(a1),x44491),x44491)),f862(f862(f3(a1),f862(f862(f73(a1),x44492),x44492)),a90))) % 14.79/14.66 [4574]E(f862(f135(f925(f925(x45741)),f925(f925(x45741)),f127(f925(x45741)),f106(f925(x45741))),f862(f862(f147(f925(x45741),f925(f925(x45741))),f149(f925(f925(x45741)),x45741,f106(f925(x45741)),f862(f18(f932(f925(x45741),f925(f925(x45741))),x45741),f862(f862(f9(f925(x45741),f925(f925(x45741)),f925(f925(x45741))),f144(f925(x45741))),f106(f925(x45741)))))),x45742)),f862(f862(f147(f925(x45741),f925(x45741)),f164(x45741)),f862(f129(f925(x45741),f862(f862(f10(a921,a921,f925(x45741)),a314),f862(f862(f9(f925(x45741),f925(x45741),a921),a317),f106(x45741)))),x45742))) % 14.79/14.66 [4584]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x45841),a90))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f2(a924))),f862(f862(f10(a924,a924,a1),a105),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f225(a924)),a97)),x45842)))),f862(f862(f225(a924),f862(f96(a924),x45841)),f862(a105,x45842))) % 14.79/14.66 [4585]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x45851),a90))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f862(a105,x45852))),f862(f862(f10(a924,a924,a1),a105),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f226(a924)),a97)),x45852)))),f862(f862(f226(a924),f862(f96(a924),x45851)),f862(a105,x45852))) % 14.79/14.66 [4573]E(f862(f249(x45731,x45731,a921),f862(f862(f20(x45731,a921,f932(x45731,a921)),f862(f862(f10(f932(x45731,f932(a921,a921)),f932(a921,f932(x45731,a921)),x45731),f9(x45731,a921,a921)),f862(f862(f10(f932(x45731,a921),f932(x45731,f932(a921,a921)),x45731),f862(f10(a921,f932(a921,a921),x45731),a318)),a317))),x45732)),f255(x45731,x45732)) % 14.79/14.66 [4618]E(f862(f862(f29(a924),x46181),f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46182)),f862(f862(f29(a924),x46181),f862(a105,f862(a105,f862(a105,x46182))))) % 14.79/14.66 [4619]E(f38(a924,x46191,f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46192)),f38(a924,x46191,f862(a105,f862(a105,f862(a105,x46192))))) % 14.79/14.66 [4620]E(f38(a924,f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46201),x46202),f38(a924,f862(a105,f862(a105,f862(a105,x46201))),x46202)) % 14.79/14.66 [4632]E(f116(f862(x46321,f862(f862(f74(a92),f862(f96(a92),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46322))),f862(f193(x46321),x46322)) % 14.79/14.66 [4633]E(f862(f862(f29(a924),f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46331)),x46332),f862(f862(f29(a924),f862(a105,f862(a105,f862(a105,x46331)))),x46332)) % 14.79/14.66 [4687]~E(f119(x46871,x46872,x46873),f112(x46871)) % 14.79/14.66 [3436]E(f862(f185(x34361,x34362),x34363),f114(x34361,x34362)) % 14.79/14.66 [3456]E(f862(f192(x34561,x34562),x34563),f862(f122(x34561),x34562)) % 14.79/14.66 [3535]E(f862(f862(f147(x35351,x35352),x35353),f106(x35351)),f106(x35352)) % 14.79/14.66 [3574]E(f862(f177(x35741,x35742,x35743),f2(a924)),x35742) % 14.79/14.66 [3576]E(f862(f862(f174(x35761,x35762),x35763),f106(x35762)),f106(f931(x35761,x35762))) % 14.79/14.66 [3589]E(f862(f182(f925(x35891)),f162(x35891,x35892,x35893)),x35892) % 14.79/14.66 [3608]E(f78(x36081,f55(x36081,x36082,x36083)),f862(f56(x36081,x36082),x36083)) % 14.79/14.66 [3612]E(f235(x36121,x36122,f235(x36122,x36121,x36123)),x36123) % 14.79/14.66 [3632]E(f862(f161(x36321),f162(x36321,x36322,x36323)),f162(x36321,x36322,x36323)) % 14.79/14.66 [3657]E(f133(x36571,x36572,f145(x36571,x36573)),f145(x36571,f133(x36571,x36572,x36573))) % 14.79/14.66 [3676]E(f862(f243(f925(x36761),f925(x36761)),f159(x36761,x36762,x36763)),f862(f129(x36761,x36762),x36763)) % 14.79/14.66 [3720]E(f862(f862(f144(x37201),x37202),f162(x37201,x37203,x37202)),f162(x37201,f862(a105,x37203),x37202)) % 14.79/14.66 [3752]E(f19(x37521,x37522,x37523,f2(a92)),x37522) % 14.79/14.66 [3753]E(f178(x37531,x37532,x37533,f2(a924)),x37532) % 14.79/14.66 [3754]E(f21(x37541,x37542,x37543,f2(a92)),x37542) % 14.79/14.66 [3761]E(f156(x37611,x37612,x37613,f106(x37611)),f106(x37612)) % 14.79/14.66 [3762]E(f123(x37621,x37622,x37623,f112(x37621)),f112(x37622)) % 14.79/14.66 [3768]E(f862(f862(f157(x37681),f862(f862(f144(x37681),x37682),x37683)),f2(a924)),x37682) % 14.79/14.66 [3796]E(f52(x37961,x37962,f106(x37961),x37963),f106(f931(x37961,x37962))) % 14.79/14.66 [3816]P22(x38161,x38162,x38163,f181(f932(x38161,a921))) % 14.79/14.66 [3917]E(f257(x39171,x39172,x39173),f862(f244(f932(a92,f932(a921,f928(f926(x39171)))),f931(a92,a92)),f34(x39171))) % 14.79/14.66 [3974]E(f862(f66(x39741,x39742,x39741,x39743),f25(x39741)),x39743) % 14.79/14.66 [4149]P1(f862(f862(f321(f931(x41491,x41491)),f862(f862(f244(x41491,x41491),x41492),x41492)),f299(x41491,x41493))) % 14.79/14.66 [4735]~P1(f862(f862(f321(f931(f925(x47351),f925(x47351))),f862(f862(f244(f925(x47351),f925(x47351)),x47352),f106(x47351))),f138(x47351,x47353))) % 14.79/14.66 [4736]~P1(f862(f862(f321(f931(f925(x47361),f925(x47361))),f862(f862(f244(f925(x47361),f925(x47361)),x47362),f106(x47361))),f140(x47361,x47363))) % 14.79/14.66 [4737]~P1(f862(f862(f321(f931(f925(x47371),f925(x47371))),f862(f862(f244(f925(x47371),f925(x47371)),x47372),f106(x47371))),f150(x47371,x47373))) % 14.79/14.66 [4738]~P1(f862(f862(f321(f931(f925(x47381),f925(x47381))),f862(f862(f244(f925(x47381),f925(x47381)),f106(x47381)),x47382)),f138(x47381,x47383))) % 14.79/14.66 [4739]~P1(f862(f862(f321(f931(f925(x47391),f925(x47391))),f862(f862(f244(f925(x47391),f925(x47391)),f106(x47391)),x47392)),f150(x47391,x47393))) % 14.79/14.66 [3509]E(f862(f862(f194(x35091),x35092),x35093),f195(x35091,f208(x35092,x35093))) % 14.79/14.66 [3563]E(f862(f277(x35631,x35632),f862(f277(x35632,x35631),x35633)),x35633) % 14.79/14.66 [3584]E(f862(f862(f174(x35841,x35842),f106(x35841)),x35843),f106(f931(x35841,x35842))) % 14.79/14.66 [3587]E(f169(x35871,x35872,f862(f292(a924),x35873)),f862(f862(f168(x35871),x35873),x35872)) % 14.79/14.66 [3605]E(f145(x36051,f862(f129(x36051,x36052),x36053)),f862(f129(x36051,x36052),f145(x36051,x36053))) % 14.79/14.66 [3606]E(f862(f275(x36061,x36062),f862(f277(x36062,x36061),x36063)),f862(f256(x36062,x36061),x36063)) % 14.79/14.66 [3607]E(f862(f256(x36071,x36072),f862(f277(x36072,x36071),x36073)),f862(f275(x36072,x36071),x36073)) % 14.79/14.66 [3625]E(f862(f129(x36251,x36252),f862(f161(x36251),x36253)),f862(f161(x36251),f862(f129(x36251,x36252),x36253))) % 14.79/14.66 [3637]E(f862(f862(f131(x36371),x36372),f862(f164(x36371),x36373)),f862(f862(f131(x36371),f862(a105,x36372)),x36373)) % 14.79/14.66 [3653]E(f862(f302(x36531,x36532,x36533),f181(f932(x36531,a921))),f181(f932(x36532,a921))) % 14.79/14.66 [3654]E(f862(f276(x36541,x36542,x36543),f181(f932(x36541,a921))),f181(f932(x36542,a921))) % 14.79/14.66 [3655]E(f862(f303(x36551,x36552,x36553),f181(f932(x36552,a921))),f181(f932(x36551,a921))) % 14.79/14.66 [3656]E(f862(f303(x36561,x36562,x36563),f234(f932(x36562,a921))),f234(f932(x36561,a921))) % 14.79/14.66 [3682]E(f113(x36821,f119(f926(x36821),x36822,x36823)),f109(x36821,x36822,f113(x36821,x36823))) % 14.79/14.66 [3684]E(f862(f862(f301(x36841),x36842),f862(f165(x36841),x36843)),f862(f165(x36841),f133(x36841,x36842,x36843))) % 14.79/14.66 [3772]E(f862(f302(f931(x37721,x37722),x37722,f248(x37721,x37722)),x37723),f862(f275(x37721,x37722),x37723)) % 14.79/14.66 [3773]E(f862(f302(f931(x37731,x37732),x37731,f243(x37731,x37732)),x37733),f862(f256(x37731,x37732),x37733)) % 14.79/14.66 [3788]E(f862(f165(x37881),f162(x37881,f862(a105,x37882),x37883)),f862(f862(f301(x37881),x37883),f181(f932(x37881,a921)))) % 14.79/14.66 [3845]E(f862(f862(f244(x38451,x38452),f862(f243(x38451,x38452),x38453)),f862(f248(x38451,x38452),x38453)),x38453) % 14.79/14.66 [3852]E(f862(f182(f926(x38521)),f119(x38521,x38522,x38523)),f862(f862(f73(a924),f862(f182(f926(x38521)),x38523)),f862(a105,f2(a924)))) % 14.79/14.66 [3853]E(f862(f862(f249(x38531,x38532,x38531),f18(x38531,x38532)),x38533),f862(f243(x38531,x38532),x38533)) % 14.79/14.66 [3979]E(f862(f66(x39791,x39791,x39792,f25(x39791)),x39793),x39793) % 14.79/14.66 [3986]E(f862(f862(f127(x39861),f162(x39861,x39862,x39863)),f862(f862(f144(x39861),x39863),f106(x39861))),f862(f862(f144(x39861),x39863),f162(x39861,x39862,x39863))) % 14.79/14.66 [4158]P1(f862(f862(f227(f932(x41581,a921)),f862(f165(x41581),f862(f129(x41581,x41582),x41583))),f862(f165(x41581),x41583))) % 14.79/14.66 [4200]P1(f862(f862(f227(f932(x42001,a921)),f862(f165(x42001),f862(f862(f168(x42001),x42002),x42003))),f862(f165(x42001),x42003))) % 14.79/14.66 [4201]P1(f862(f862(f227(f932(x42011,a921)),f862(f165(x42011),f862(f862(f131(x42011),x42012),x42013))),f862(f165(x42011),x42013))) % 14.79/14.66 [4205]P1(f862(f862(f227(f932(x42051,a921)),f862(f165(x42051),f169(x42051,x42052,x42053))),f862(f165(x42051),x42052))) % 14.79/14.66 [4206]P1(f862(f862(f227(f932(x42061,a921)),f862(f165(x42061),f163(x42061,x42062,x42063))),f862(f165(x42061),x42063))) % 14.79/14.66 [4227]P22(f931(x42271,x42272),f931(x42272,x42271),f862(f249(x42271,x42272,f931(x42272,x42271)),f862(f9(x42272,x42271,f931(x42272,x42271)),f244(x42272,x42271))),x42273) % 14.79/14.66 [4238]E(f862(f862(f862(f176(f925(x42381),f925(x42381)),f38(a924,x42382,f862(f182(f925(x42381)),x42383))),f160(x42381)),x42383),f862(f862(f862(f176(f925(x42381),f925(x42381)),x42382),f160(x42381)),x42383)) % 14.79/14.66 [4282]P1(f862(f862(f321(f931(f925(x42821),f925(x42821))),f862(f862(f244(f925(x42821),f925(x42821)),x42822),x42822)),f151(x42821,f299(x42821,x42823)))) % 14.79/14.66 [4421]E(f78(f931(x44211,x44212),f862(f862(f20(f931(x44211,x44212),x44212,a921),f862(f862(f10(x44211,f932(x44212,a921),f931(x44211,x44212)),x44213),f243(x44211,x44212))),f248(x44211,x44212))),f78(f931(x44211,x44212),f862(f249(x44211,x44212,a921),x44213))) % 14.79/14.66 [4422]E(f83(f931(x44221,x44222),f862(f862(f20(f931(x44221,x44222),x44222,a921),f862(f862(f10(x44221,f932(x44222,a921),f931(x44221,x44222)),x44223),f243(x44221,x44222))),f248(x44221,x44222))),f83(f931(x44221,x44222),f862(f249(x44221,x44222,a921),x44223))) % 14.79/14.66 [4456]E(f862(f862(f279(f931(a924,x44561),x44561),f311(a924,x44561,a232,x44562)),f862(f862(f20(x44561,x44561,f931(a924,x44561)),f862(f862(f10(a924,f932(x44561,f931(a924,x44561)),x44561),f244(a924,x44561)),x44563)),f7(x44561))),f313(x44561,x44563,x44562)) % 14.79/14.66 [4518]E(f862(f250(x45181,x45181,x45182,x45182,f7(x45181),f7(x45182)),x45183),x45183) % 14.79/14.66 [4593]E(f862(f135(f925(f925(x45931)),f925(f925(x45931)),f127(f925(x45931)),f106(f925(x45931))),f862(f862(f147(f925(x45931),f925(f925(x45931))),f862(f862(f9(f925(x45931),f925(x45931),f925(f925(x45931))),f862(f862(f10(f932(x45931,f925(x45931)),f932(f925(x45931),f925(f925(x45931))),f925(x45931)),f147(x45931,f925(x45931))),f862(f9(x45931,f925(x45931),f925(x45931)),f144(x45931)))),x45932)),f48(x45931,x45933,x45932))),f48(x45931,f862(a105,x45933),x45932)) % 14.79/14.66 [4649]E(f216(a924,f931(x46491,f926(x46491)),f2(a924),f862(f249(x46491,f926(x46491),a924),f862(f862(f9(x46491,a924,f932(f926(x46491),a924)),f862(f862(f10(f932(f926(x46491),f932(a924,a924)),f932(a924,f932(f926(x46491),a924)),x46491),f9(f926(x46491),a924,a924)),f862(f862(f10(f932(f926(x46491),a924),f932(f926(x46491),f932(a924,a924)),x46491),f862(f10(a924,f932(a924,a924),f926(x46491)),f73(a924))),f862(f862(f9(x46491,f932(f926(x46491),a924),f932(f926(x46491),a924)),f862(f862(f10(f932(a924,a924),f932(f932(f926(x46491),a924),f932(f926(x46491),a924)),x46491),f10(a924,a924,f926(x46491))),f862(f862(f10(a924,f932(a924,a924),x46491),f73(a924)),x46492))),f118(x46491,x46492))))),f71(a924))),f862(f128(x46491),x46493)),f862(f118(x46491,x46492),x46493)) % 14.79/14.66 [4657]E(f862(f862(f79(a1,x46571),f211(f862(f862(f66(f931(a1,a1),a1,x46571,f248(a1,a1)),f205(x46571)),x46572),f862(f862(f66(f931(a1,a1),a1,x46571,f248(a1,a1)),f205(x46571)),x46573))),f862(f862(f20(a1,a1,x46571),f862(f862(f10(a1,f932(a1,x46571),a1),f194(x46571)),f862(f862(f20(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f73(a1)),f862(f862(f10(a1,a1,a1),f862(f74(a1),f862(f862(f66(f931(a1,a1),a1,x46571,f243(a1,a1)),f205(x46571)),x46572))),f862(f862(f9(a1,a1,a1),f29(a1)),f862(f862(f66(f931(a1,a1),a1,x46571,f248(a1,a1)),f205(x46571)),x46572))))),f862(f862(f10(a1,a1,a1),f862(f74(a1),f862(f862(f66(f931(a1,a1),a1,x46571,f243(a1,a1)),f205(x46571)),x46573))),f862(f862(f9(a1,a1,a1),f29(a1)),f862(f862(f66(f931(a1,a1),a1,x46571,f248(a1,a1)),f205(x46571)),x46573)))))),f7(a1))),f223(x46571,x46572,x46573)) % 14.79/14.66 [4682]~E(f862(f862(f144(x46821),x46822),x46823),x46823) % 14.79/14.66 [4685]~E(f862(f862(f144(x46851),x46852),x46853),f106(x46851)) % 14.79/14.66 [4691]~E(f862(f862(f301(x46911),x46912),x46913),f181(f932(x46911,a921))) % 14.79/14.66 [4713]~E(f862(f302(x47131,f932(x47131,a921),x47132),x47133),f862(f300(x47131),x47133)) % 14.79/14.66 [3568]E(f862(f862(f152(x35681,f106(x35681)),x35682),x35683),f106(x35681)) % 14.79/14.66 [3569]E(f862(f134(x35691),f862(f862(f144(x35691),x35692),x35693)),x35692) % 14.79/14.66 [3570]E(f862(f164(x35701),f862(f862(f144(x35701),x35702),x35703)),x35703) % 14.79/14.66 [3611]E(f862(f862(f131(x36111),f71(a924)),f862(f862(f144(x36111),x36112),x36113)),x36113) % 14.79/14.66 [3644]E(f107(x36441,f862(f862(f131(x36441),x36442),x36443)),f862(f862(f131(x36441),x36442),f107(x36441,x36443))) % 14.79/14.66 [3646]E(f862(f862(f152(x36461,x36462),x36463),f862(f862(f157(x36461),x36462),x36463)),x36462) % 14.79/14.66 [3666]E(f862(f862(f301(x36661),x36662),f862(f862(f301(x36661),x36662),x36663)),f862(f862(f301(x36661),x36662),x36663)) % 14.79/14.66 [3679]E(f862(f862(f301(x36791),x36792),f862(f165(x36791),x36793)),f862(f165(x36791),f862(f862(f144(x36791),x36792),x36793))) % 14.79/14.66 [3681]E(f862(f862(f131(x36811),x36812),f862(f164(x36811),x36813)),f862(f164(x36811),f862(f862(f131(x36811),x36812),x36813))) % 14.79/14.66 [3693]E(f862(f862(f168(x36931),f71(a924)),f862(f862(f144(x36931),x36932),x36933)),f862(f862(f144(x36931),x36932),f106(x36931))) % 14.79/14.66 [3737]E(f862(f56(x37371,x37372),f862(f862(f301(x37371),x37373),f181(f932(x37371,a921)))),x37373) % 14.79/14.66 [3778]E(f862(f862(f73(a924),x37781),f862(f862(f73(a924),x37782),x37783)),f862(f862(f73(a924),x37782),f862(f862(f73(a924),x37781),x37783))) % 14.79/14.66 [3779]E(f862(f862(f73(a1),x37791),f862(f862(f73(a1),x37792),x37793)),f862(f862(f73(a1),x37792),f862(f862(f73(a1),x37791),x37793))) % 14.79/14.66 [3784]E(f862(f862(f246(x37841,x37842),f181(f932(x37841,a921))),x37843),f181(f932(f931(x37841,x37842),a921))) % 14.79/14.66 [3808]E(f862(f862(f103(f932(x38081,a921)),x38082),x38083),f862(f862(f103(f932(x38081,a921)),x38083),x38082)) % 14.79/14.66 [3809]E(f862(f862(f94(f932(x38091,a921)),x38092),x38093),f862(f862(f94(f932(x38091,a921)),x38093),x38092)) % 14.79/14.66 [3811]E(f862(f862(f127(x38111),x38112),f862(f862(f144(x38111),x38113),f106(x38111))),f862(f160(x38111),f862(f862(f144(x38111),x38113),x38112))) % 14.79/14.66 [3812]E(f862(f862(f127(x38121),f862(f161(x38121),x38122)),f862(f161(x38121),x38123)),f862(f161(x38121),f862(f862(f127(x38121),x38123),x38122))) % 14.79/14.66 [3822]E(f862(f164(x38221),f862(f862(f168(x38221),f862(a105,x38222)),x38223)),f862(f862(f168(x38221),x38222),f862(f164(x38221),x38223))) % 14.79/14.66 [3830]P1(f862(f862(f321(x38301),x38302),f862(f862(f301(x38301),x38302),x38303))) % 14.79/14.66 [3834]E(f862(f862(f32(x38341,f932(x38342,a921)),f181(f932(x38341,a921))),x38343),f234(f932(x38342,a921))) % 14.79/14.66 [3837]E(f862(f276(x38371,x38371,f255(x38371,x38372)),x38373),f862(f862(f94(f932(x38371,a921)),x38372),x38373)) % 14.79/14.66 [3851]E(f862(f182(f925(x38511)),f862(f862(f144(x38511),x38512),x38513)),f862(f862(f73(a924),f862(f182(f925(x38511)),x38513)),f862(a105,f2(a924)))) % 14.79/14.66 [3855]E(f107(x38551,f862(f862(f127(x38551),x38552),f862(f862(f144(x38551),x38553),f106(x38551)))),x38552) % 14.79/14.66 [3856]E(f137(x38561,f862(f862(f127(x38561),x38562),f862(f862(f144(x38561),x38563),f106(x38561)))),x38563) % 14.79/14.66 [3864]E(f862(f862(f127(x38641),f862(f862(f168(x38641),x38642),x38643)),f862(f862(f131(x38641),x38642),x38643)),x38643) % 14.79/14.66 [3873]E(f862(f862(f3(a924),f862(f862(f73(a924),x38731),x38732)),f862(f862(f73(a924),x38733),x38732)),f862(f862(f3(a924),x38731),x38733)) % 14.79/14.66 [3874]E(f862(f862(f3(a924),f862(f862(f73(a924),x38741),x38742)),f862(f862(f73(a924),x38741),x38743)),f862(f862(f3(a924),x38742),x38743)) % 14.79/14.66 [3880]E(f862(f862(f127(x38801),f862(f161(x38801),x38802)),f862(f862(f144(x38801),x38803),f106(x38801))),f862(f161(x38801),f862(f862(f144(x38801),x38803),x38802))) % 14.79/14.66 [3882]E(f862(f862(f73(a924),f862(f182(f925(x38821)),x38822)),f862(f182(f925(x38821)),x38823)),f862(f182(f925(x38821)),f862(f862(f127(x38821),x38822),x38823))) % 14.79/14.66 [3885]E(f862(f862(f73(a924),f862(f182(f925(x38851)),x38852)),f862(f182(f925(x38851)),x38853)),f862(f182(f925(x38851)),f166(x38851,x38852,x38853))) % 14.79/14.66 [3892]E(f862(f862(f103(f932(x38921,a921)),f862(f165(x38921),x38922)),f862(f165(x38921),x38923)),f862(f165(x38921),f862(f862(f127(x38921),x38922),x38923))) % 14.79/14.66 [3893]E(f38(a924,f862(f862(f74(a924),x38931),x38932),f862(f862(f74(a924),x38931),x38933)),f862(f862(f74(a924),x38931),f38(a924,x38932,x38933))) % 14.79/14.66 [3905]E(f862(f862(f168(x39051),f862(f862(f3(a924),x39052),f71(a924))),f862(f164(x39051),x39053)),f862(f164(x39051),f862(f862(f168(x39051),x39052),x39053))) % 14.79/14.66 [3910]E(f862(f862(f94(f932(x39101,a921)),x39102),f862(f72(f932(x39101,a921)),x39103)),f862(f862(f3(f932(x39101,a921)),x39102),x39103)) % 14.79/14.66 [3911]E(f862(f862(f3(f932(x39111,a921)),x39112),f862(f72(f932(x39111,a921)),x39113)),f862(f862(f94(f932(x39111,a921)),x39112),x39113)) % 14.79/14.66 [3933]E(f862(f862(f246(x39331,x39332),x39333),f862(f18(f932(x39332,a921),x39331),f181(f932(x39332,a921)))),f181(f932(f931(x39331,x39332),a921))) % 14.79/14.66 [3935]E(f862(f862(f3(a924),f862(f862(f74(a924),x39351),x39352)),f862(f862(f74(a924),x39351),x39353)),f862(f862(f74(a924),x39351),f862(f862(f3(a924),x39352),x39353))) % 14.79/14.66 [3936]E(f862(f862(f73(a924),f862(f862(f74(a924),x39361),x39362)),f862(f862(f74(a924),x39361),x39363)),f862(f862(f74(a924),x39361),f862(f862(f73(a924),x39362),x39363))) % 14.79/14.66 [3937]E(f862(f862(f3(a1),f862(f862(f74(a1),x39371),x39372)),f862(f862(f74(a1),x39371),x39373)),f862(f862(f74(a1),x39371),f862(f862(f3(a1),x39372),x39373))) % 14.79/14.66 [3938]E(f862(f862(f73(a1),f862(f862(f74(a1),x39381),x39382)),f862(f862(f74(a1),x39381),x39383)),f862(f862(f74(a1),x39381),f862(f862(f73(a1),x39382),x39383))) % 14.79/14.66 [3939]E(f862(f862(f74(a1),f862(f862(f236(a1),x39391),x39392)),f862(f862(f236(a1),x39391),x39393)),f862(f862(f236(a1),x39391),f862(f862(f73(a924),x39392),x39393))) % 14.79/14.66 [3953]E(f862(f862(f33(x39531,f932(x39532,a921)),x39533),f862(f18(f932(x39532,a921),x39531),f181(f932(x39532,a921)))),f181(f932(x39532,a921))) % 14.79/14.66 [3955]E(f38(a924,f862(f862(f74(a924),x39551),x39552),f862(f862(f74(a924),x39553),x39552)),f862(f862(f74(a924),f38(a924,x39551,x39553)),x39552)) % 14.79/14.66 [3960]E(f38(a1,f862(f862(f3(a1),x39601),f38(a1,x39602,x39603)),x39603),f38(a1,f862(f862(f3(a1),x39601),x39602),x39603)) % 14.79/14.66 [3961]E(f38(a1,f862(f862(f74(a1),x39611),f38(a1,x39612,x39613)),x39613),f38(a1,f862(f862(f74(a1),x39611),x39612),x39613)) % 14.79/14.66 [3962]P1(f862(f862(f227(f932(x39621,a921)),x39622),f862(f862(f301(x39621),x39623),x39622))) % 14.79/14.66 [4037]E(f862(f862(f32(f932(x40371,a921),f932(x40371,a921)),x40372),f862(f103(f932(x40371,a921)),x40373)),f862(f862(f103(f932(x40371,a921)),x40373),f31(f932(x40371,a921),x40372))) % 14.79/14.66 [4038]E(f862(f862(f33(f932(x40381,a921),f932(x40381,a921)),x40382),f862(f94(f932(x40381,a921)),x40383)),f862(f862(f94(f932(x40381,a921)),x40383),f30(f932(x40381,a921),x40382))) % 14.79/14.66 [4050]E(f862(f165(x40501),f862(f862(f862(f176(f925(x40501),f925(x40501)),x40502),f160(x40501)),x40503)),f862(f165(x40501),x40503)) % 14.79/14.66 [4054]E(f862(f862(f168(x40541),f862(f182(f925(x40541)),f170(x40541,x40542,x40543))),x40543),f170(x40541,x40542,x40543)) % 14.79/14.66 [4058]E(f862(f182(f925(x40581)),f862(f862(f862(f176(f925(x40581),f925(x40581)),x40582),f160(x40581)),x40583)),f862(f182(f925(x40581)),x40583)) % 14.79/14.66 [4061]E(f862(f862(f249(x40611,x40612,x40612),f862(f18(f932(x40612,x40612),x40611),f7(x40612))),x40613),f862(f248(x40611,x40612),x40613)) % 14.79/14.66 [4067]E(f38(a1,f862(f862(f3(a1),f38(a1,x40671,x40672)),x40673),x40672),f38(a1,f862(f862(f3(a1),x40671),x40673),x40672)) % 14.79/14.66 [4068]E(f38(a1,f862(f862(f236(a1),f38(a1,x40681,x40682)),x40683),x40682),f38(a1,f862(f862(f236(a1),x40681),x40683),x40682)) % 14.79/14.66 [4071]E(f862(f862(f33(f932(f931(x40711,x40712),a921),f932(x40712,a921)),x40713),f275(x40711,x40712)),f862(f275(x40711,x40712),f30(f932(f931(x40711,x40712),a921),x40713))) % 14.79/14.66 [4072]E(f862(f862(f33(f932(f931(x40721,x40722),a921),f932(x40721,a921)),x40723),f256(x40721,x40722)),f862(f256(x40721,x40722),f30(f932(f931(x40721,x40722),a921),x40723))) % 14.79/14.66 [4095]E(f862(f66(x40951,x40951,x40951,x40952),f862(f862(f176(x40951,x40951),x40953),x40952)),f862(f862(f176(x40951,x40951),f862(a105,x40953)),x40952)) % 14.79/14.66 [4113]E(f862(f862(f131(x41131),f862(f862(f3(a924),f862(f182(f925(x41131)),x41132)),x41133)),f862(f161(x41131),x41132)),f862(f161(x41131),f862(f862(f168(x41131),x41133),x41132))) % 14.79/14.66 [4114]E(f862(f862(f168(x41141),f862(f862(f3(a924),f862(f182(f925(x41141)),x41142)),x41143)),f862(f161(x41141),x41142)),f862(f161(x41141),f862(f862(f131(x41141),x41143),x41142))) % 14.79/14.66 [4116]E(f862(f862(f73(a924),f862(f158(a924),f862(f862(f147(x41161,a924),x41162),x41163))),f862(f182(f925(x41161)),x41163)),f148(x41161,x41162,x41163)) % 14.79/14.66 [4136]E(f862(f160(x41361),f862(f862(f862(f176(f925(x41361),f925(x41361)),x41362),f160(x41361)),x41363)),f862(f862(f862(f176(f925(x41361),f925(x41361)),f862(a105,x41362)),f160(x41361)),x41363)) % 14.79/14.66 [4150]P1(f862(f862(f227(a924),f862(f182(f925(x41501)),f862(f129(x41501,x41502),x41503))),f862(f182(f925(x41501)),x41503))) % 14.79/14.66 [4166]E(f862(f862(f103(f932(f932(x41661,a921),a921)),f862(f300(x41661),x41662)),f862(f302(f932(x41661,a921),f932(x41661,a921),f862(f301(x41661),x41663)),f862(f300(x41661),x41662))),f862(f300(x41661),f862(f862(f301(x41661),x41663),x41662))) % 14.79/14.66 [4197]P1(f862(f862(f227(a924),f862(f182(f925(x41971)),f170(x41971,x41972,x41973))),f862(f182(f925(x41971)),x41973))) % 14.79/14.66 [4204]E(f862(f256(x42041,x42042),f862(f254(f931(x42041,x42042)),f862(f249(x42041,x42042,a921),x42043))),f862(f254(x42041),f862(f862(f10(f932(x42042,a921),a921,x42041),f80(x42042)),x42043))) % 14.79/14.66 [4216]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f73(a924)),x42161)),f296(a924,x42162,x42163)),f296(a924,f862(f862(f73(a924),x42162),x42161),f862(f862(f73(a924),x42163),x42161))) % 14.79/14.66 [4230]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f73(a924)),x42301)),f862(f295(a924,x42302),x42303)),f862(f295(a924,f862(f862(f73(a924),x42302),x42301)),f862(f862(f73(a924),x42303),x42301))) % 14.79/14.66 [4248]E(f862(f862(f174(x42481,x42482),f862(f862(f147(f931(x42481,x42482),x42481),f243(x42481,x42482)),x42483)),f862(f862(f147(f931(x42481,x42482),x42482),f248(x42481,x42482)),x42483)),x42483) % 14.79/14.66 [4253]E(f862(f862(f73(a924),f862(f862(f74(a924),x42531),f38(a924,f862(f862(f29(a924),x42532),x42531),x42533))),f38(a924,x42532,x42531)),f38(a924,x42532,f862(f862(f74(a924),x42531),x42533))) % 14.79/14.66 [4266]E(f862(f862(f127(x42661),x42662),f862(f135(f925(x42661),f925(x42661),f127(x42661),f106(x42661)),x42663)),f862(f135(f925(x42661),f925(x42661),f127(x42661),x42662),x42663)) % 14.79/14.66 [4287]P1(f862(f862(f321(f931(x42871,x42871)),f862(f862(f244(x42871,x42871),x42872),x42872)),f862(f862(f176(f931(x42871,x42871),a921),f2(a924)),x42873))) % 14.79/14.66 [4292]E(f862(f254(x42921),f862(f862(f10(f932(x42922,a921),a921,x42921),f80(x42922)),f862(f9(x42922,x42921,a921),x42923))),f862(f275(x42922,x42921),f862(f254(f931(x42922,x42921)),f862(f249(x42922,x42921,a921),x42923)))) % 14.79/14.66 [4309]E(f862(f862(f103(f932(x43091,a921)),f862(f862(f33(a924,f932(x43091,a921)),f296(a924,f71(a924),x43092)),x43093)),f862(x43093,f2(a924))),f862(f862(f33(a924,f932(x43091,a921)),f862(f294(a924),x43092)),x43093)) % 14.79/14.66 [4324]E(f862(f135(f925(x43241),f925(x43241),f127(x43241),f106(x43241)),f862(f862(f147(f925(x43241),f925(x43241)),f129(x43241,x43242)),x43243)),f862(f129(x43241,x43242),f862(f135(f925(x43241),f925(x43241),f127(x43241),f106(x43241)),x43243))) % 14.79/14.66 [4328]E(f862(f248(f925(x43281),f925(x43281)),f159(x43281,x43282,x43283)),f862(f129(x43281,f862(f66(a921,a921,x43281,a314),x43282)),x43283)) % 14.79/14.66 [4373]E(f862(f862(f73(a1),f862(f862(f73(a1),f862(f862(f74(a1),x43731),f862(f862(f29(a1),x43732),x43731))),f38(a1,x43732,x43731))),x43733),f862(f862(f73(a1),x43732),x43733)) % 14.79/14.66 [4410]E(f862(f862(f73(a1),f862(f862(f73(a1),f862(f862(f74(a1),f862(f862(f29(a1),x44101),x44102)),x44102)),f38(a1,x44101,x44102))),x44103),f862(f862(f73(a1),x44101),x44103)) % 14.79/14.66 [4437]E(f78(f931(x44371,x44372),f862(f249(x44371,x44372,a921),f862(f862(f10(f932(x44372,f931(x44371,x44372)),f932(x44372,a921),x44371),f862(f10(f931(x44371,x44372),a921,x44372),x44373)),f244(x44371,x44372)))),f78(f931(x44371,x44372),x44373)) % 14.79/14.66 [4438]E(f83(f931(x44381,x44382),f862(f249(x44381,x44382,a921),f862(f862(f10(f932(x44382,f931(x44381,x44382)),f932(x44382,a921),x44381),f862(f10(f931(x44381,x44382),a921,x44382),x44383)),f244(x44381,x44382)))),f83(f931(x44381,x44382),x44383)) % 14.79/14.66 [4465]P1(f862(f862(f227(f932(x44651,a921)),f30(f932(x44651,a921),f862(f862(f94(f932(f932(x44651,a921),a921)),x44652),x44653))),f862(f862(f94(f932(x44651,a921)),f30(f932(x44651,a921),x44652)),f30(f932(x44651,a921),x44653)))) % 14.79/14.66 [4466]E(f862(f161(x44661),f862(f862(f862(f176(f925(x44661),f925(x44661)),f862(f862(f3(a924),f862(f182(f925(x44661)),x44662)),f38(a924,x44663,f862(f182(f925(x44661)),x44662)))),f160(x44661)),x44662)),f862(f862(f862(f176(f925(x44661),f925(x44661)),x44663),f160(x44661)),f862(f161(x44661),x44662))) % 14.79/14.66 [4503]P1(f862(f862(f227(a924),f862(f182(f925(x45031)),f862(f862(f131(x45031),f862(f182(f925(x45031)),f170(x45031,x45032,x45033))),x45033))),f862(f182(f925(x45031)),x45033))) % 14.79/14.66 [4726]~P1(f862(f55(x47261,x47262,f181(f932(x47261,a921))),x47263)) % 14.79/14.66 [4733]~P1(f862(f862(f321(f931(x47331,x47331)),f862(f862(f244(x47331,x47331),x47332),x47333)),f146(x47331,f106(f932(x47331,a924))))) % 14.79/14.66 [3823]E(f862(f182(f925(x38231)),f862(f862(f168(x38231),x38232),x38233)),f862(f862(f225(a924),f862(f182(f925(x38231)),x38233)),x38232)) % 14.79/14.66 [3824]E(f862(f182(f925(x38241)),f862(f862(f131(x38241),x38242),x38243)),f862(f862(f3(a924),f862(f182(f925(x38241)),x38243)),x38242)) % 14.79/14.66 [3850]E(f862(f182(f925(f925(x38501))),f48(x38501,x38502,x38503)),f862(f862(f236(a924),f862(f182(f925(x38501)),x38503)),x38502)) % 14.79/14.66 [3866]E(f862(f862(f29(a924),f862(f862(f29(a924),x38661),x38662)),x38663),f862(f862(f29(a924),x38661),f862(f862(f74(a924),x38662),x38663))) % 14.79/14.66 [3867]E(f862(f862(f3(a924),f862(f862(f3(a924),x38671),x38672)),x38673),f862(f862(f3(a924),x38671),f862(f862(f73(a924),x38672),x38673))) % 14.79/14.66 [3868]E(f862(f862(f74(a924),f862(f862(f74(a924),x38681),x38682)),x38683),f862(f862(f74(a924),x38681),f862(f862(f74(a924),x38682),x38683))) % 14.79/14.66 [3869]E(f862(f862(f74(a1),f862(f862(f74(a1),x38691),x38692)),x38693),f862(f862(f74(a1),x38691),f862(f862(f74(a1),x38692),x38693))) % 14.79/14.66 [3870]E(f862(f862(f73(a924),f862(f862(f73(a924),x38701),x38702)),x38703),f862(f862(f73(a924),x38701),f862(f862(f73(a924),x38702),x38703))) % 14.79/14.66 [3871]E(f862(f862(f73(a1),f862(f862(f73(a1),x38711),x38712)),x38713),f862(f862(f73(a1),x38711),f862(f862(f73(a1),x38712),x38713))) % 14.79/14.66 [3872]E(f862(f862(f236(a1),f862(f862(f236(a1),x38721),x38722)),x38723),f862(f862(f236(a1),x38721),f862(f862(f74(a924),x38722),x38723))) % 14.79/14.66 [3891]E(f155(x38911,f862(f862(f144(f932(x38911,a921)),x38912),x38913)),f167(x38911,x38912,f155(x38911,x38913))) % 14.79/14.66 [3934]E(f862(f862(f3(a924),f862(f862(f3(a924),x39341),x39342)),x39343),f862(f862(f3(a924),f862(f862(f3(a924),x39341),x39343)),x39342)) % 14.79/14.66 [3942]E(f862(f862(f94(f932(x39421,a921)),x39422),f862(f862(f3(f932(x39421,a921)),x39423),x39422)),f181(f932(x39421,a921))) % 14.79/14.66 [3946]E(f862(f862(f147(a924,x39461),f862(f18(x39461,a924),x39462)),f132(a924,f862(f295(a924,f2(a924)),x39463))),f162(x39461,x39463,x39462)) % 14.79/14.66 [3984]E(f31(f932(x39841,a921),f862(f862(f301(f932(x39841,a921)),x39842),x39843)),f862(f862(f94(f932(x39841,a921)),x39842),f31(f932(x39841,a921),x39843))) % 14.79/14.66 [3985]E(f30(f932(x39851,a921),f862(f862(f301(f932(x39851,a921)),x39852),x39853)),f862(f862(f103(f932(x39851,a921)),x39852),f30(f932(x39851,a921),x39853))) % 14.79/14.66 [3987]E(f162(x39871,f862(f182(f925(x39871)),f862(f129(x39871,f862(a317,x39872)),x39873)),x39872),f862(f129(x39871,f862(a317,x39872)),x39873)) % 14.79/14.66 [3989]E(f862(f862(f3(a924),f862(f862(f74(a924),x39891),x39892)),f862(f862(f74(a924),x39893),x39892)),f862(f862(f74(a924),f862(f862(f3(a924),x39891),x39893)),x39892)) % 14.79/14.66 [3990]E(f862(f862(f73(a924),f862(f862(f74(a924),x39901),x39902)),f862(f862(f74(a924),x39903),x39902)),f862(f862(f74(a924),f862(f862(f73(a924),x39901),x39903)),x39902)) % 14.79/14.66 [3991]E(f862(f862(f3(a1),f862(f862(f74(a1),x39911),x39912)),f862(f862(f74(a1),x39913),x39912)),f862(f862(f74(a1),f862(f862(f3(a1),x39911),x39913)),x39912)) % 14.79/14.66 [3992]E(f862(f862(f73(a1),f862(f862(f74(a1),x39921),x39922)),f862(f862(f74(a1),x39923),x39922)),f862(f862(f74(a1),f862(f862(f73(a1),x39921),x39923)),x39922)) % 14.79/14.66 [3994]E(f862(f862(f225(a924),f862(f862(f3(a924),x39941),x39942)),f862(f862(f3(a924),x39943),x39942)),f862(f862(f3(a924),f862(f862(f225(a924),x39941),x39943)),x39942)) % 14.79/14.66 [4014]E(f862(f862(f94(f932(f925(x40141),a921)),f153(x40141,x40142)),f153(x40141,x40143)),f153(x40141,f862(f862(f94(f932(x40141,a921)),x40142),x40143))) % 14.79/14.66 [4017]E(f862(f862(f103(f932(x40171,a921)),x40172),f862(f862(f103(f932(x40171,a921)),x40172),x40173)),f862(f862(f103(f932(x40171,a921)),x40172),x40173)) % 14.79/14.66 [4018]E(f862(f862(f103(f932(x40181,a921)),x40182),f862(f862(f3(f932(x40181,a921)),x40183),x40182)),f862(f862(f103(f932(x40181,a921)),x40182),x40183)) % 14.79/14.66 [4019]E(f862(f862(f94(f932(x40191,a921)),x40192),f862(f862(f94(f932(x40191,a921)),x40192),x40193)),f862(f862(f94(f932(x40191,a921)),x40192),x40193)) % 14.79/14.66 [4031]E(f862(f862(f280(x40311,x40312,x40312),x40313),f299(x40312,f181(f932(f931(x40312,x40312),a921)))),x40313) % 14.79/14.66 [4034]E(f862(f862(f103(f932(x40341,a921)),f862(f862(f301(x40341),x40342),f181(f932(x40341,a921)))),x40343),f862(f862(f301(x40341),x40342),x40343)) % 14.79/14.66 [4053]E(f862(f862(f3(a924),f862(f862(f3(a924),f862(a105,x40531)),x40532)),f862(a105,x40533)),f862(f862(f3(a924),f862(f862(f3(a924),x40531),x40532)),x40533)) % 14.79/14.66 [4080]E(f862(f862(f94(f932(f932(x40801,a921),a921)),f862(f300(x40801),x40802)),f862(f300(x40801),x40803)),f862(f300(x40801),f862(f862(f94(f932(x40801,a921)),x40802),x40803))) % 14.79/14.66 [4083]E(f862(f862(f103(f932(x40831,a921)),f862(f72(f932(x40831,a921)),x40832)),x40833),f862(f72(f932(x40831,a921)),f862(f862(f3(f932(x40831,a921)),x40832),x40833))) % 14.79/14.66 [4092]E(f862(f862(f301(x40921),x40922),f862(f862(f3(f932(x40921,a921)),x40923),f862(f862(f301(x40921),x40922),f181(f932(x40921,a921))))),f862(f862(f301(x40921),x40922),x40923)) % 14.79/14.66 [4102]P1(f862(f862(f227(f932(x41021,a921)),x41022),f862(f862(f103(f932(x41021,a921)),x41023),x41022))) % 14.79/14.66 [4103]P1(f862(f862(f227(f932(x41031,a921)),x41032),f862(f862(f103(f932(x41031,a921)),x41032),x41033))) % 14.79/14.66 [4107]E(f862(f862(f94(f932(x41071,a921)),f862(f72(f932(x41071,a921)),x41072)),f862(f72(f932(x41071,a921)),x41073)),f862(f72(f932(x41071,a921)),f862(f862(f103(f932(x41071,a921)),x41072),x41073))) % 14.79/14.66 [4108]E(f862(f862(f103(f932(x41081,a921)),f862(f72(f932(x41081,a921)),x41082)),f862(f72(f932(x41081,a921)),x41083)),f862(f72(f932(x41081,a921)),f862(f862(f94(f932(x41081,a921)),x41082),x41083))) % 14.79/14.66 [4122]P1(f862(f862(f227(f932(x41221,a921)),f862(f165(x41221),x41222)),f862(f165(x41221),f862(f862(f144(x41221),x41223),x41222)))) % 14.79/14.66 [4134]E(f862(f862(f103(f932(x41341,a921)),f862(f862(f3(f932(x41341,a921)),x41342),x41343)),f862(f862(f94(f932(x41341,a921)),x41342),x41343)),x41342) % 14.79/14.66 [4184]E(f862(f862(f8(x41841,a1),f862(f862(f10(a924,a1,x41841),f93(a1)),x41842)),x41843),f862(f93(a1),f862(f862(f8(x41841,a924),x41842),x41843))) % 14.79/14.66 [4185]E(f862(f862(f11(x41851,a1),f862(f862(f10(a924,a1,x41851),f93(a1)),x41852)),x41853),f862(f93(a1),f862(f862(f11(x41851,a924),x41852),x41853))) % 14.79/14.66 [4232]E(f862(f862(f127(x42321),f170(x42321,x42322,x42323)),f862(f862(f131(x42321),f862(f182(f925(x42321)),f170(x42321,x42322,x42323))),x42323)),x42323) % 14.79/14.66 [4236]E(f862(f72(f932(f931(x42361,x42362),a921)),f862(f862(f246(x42361,x42362),x42363),f862(f18(f932(x42362,a921),x42361),f234(f932(x42362,a921))))),f862(f862(f246(x42361,x42362),f862(f72(f932(x42361,a921)),x42363)),f862(f18(f932(x42362,a921),x42361),f234(f932(x42362,a921))))) % 14.79/14.66 [4237]E(f862(f72(f932(f931(x42371,x42372),a921)),f862(f862(f246(x42371,x42372),f234(f932(x42371,a921))),f862(f18(f932(x42372,a921),x42371),x42373))),f862(f862(f246(x42371,x42372),f234(f932(x42371,a921))),f862(f18(f932(x42372,a921),x42371),f862(f72(f932(x42372,a921)),x42373)))) % 14.79/14.66 [4288]E(f862(f862(f33(f932(x42881,a921),f932(x42881,a921)),x42882),f862(f862(f9(f932(x42881,a921),f932(x42881,a921),f932(x42881,a921)),f94(f932(x42881,a921))),x42883)),f862(f862(f94(f932(x42881,a921)),f30(f932(x42881,a921),x42882)),x42883)) % 14.79/14.66 [4294]E(f862(f135(f925(x42941),f925(x42941),f127(x42941),f106(x42941)),f862(f862(f144(f925(x42941)),x42942),x42943)),f862(f862(f127(x42941),x42942),f862(f135(f925(x42941),f925(x42941),f127(x42941),f106(x42941)),x42943))) % 14.79/14.66 [4315]E(f862(f862(f301(f932(x43151,a921)),f862(f276(x43151,x43151,x43152),f862(f862(f301(x43151),x43153),f181(f932(x43151,a921))))),f181(f932(f932(x43151,a921),a921))),f862(f862(f53(x43151),f862(f862(f301(x43151),x43153),f181(f932(x43151,a921)))),x43152)) % 14.79/14.66 [4325]E(f862(f862(f73(a924),f862(f862(f74(a924),x43251),f862(f862(f29(a924),x43252),x43253))),f862(f862(f29(a924),f862(f862(f74(a924),x43251),f38(a924,x43252,x43253))),x43253)),f862(f862(f29(a924),f862(f862(f74(a924),x43251),x43252)),x43253)) % 14.79/14.66 [4326]E(f862(f862(f73(a1),f862(f862(f74(a1),x43261),f862(f862(f29(a1),x43262),x43263))),f862(f862(f29(a1),f862(f862(f74(a1),x43261),f38(a1,x43262,x43263))),x43263)),f862(f862(f29(a1),f862(f862(f74(a1),x43261),x43262)),x43263)) % 14.79/14.66 [4358]E(f862(f862(f3(f932(x43581,a921)),f862(f165(x43581),x43582)),f862(f862(f301(x43581),x43583),f181(f932(x43581,a921)))),f862(f165(x43581),f862(f129(x43581,f862(f862(f10(a921,a921,x43581),a314),f862(a317,x43583))),x43582))) % 14.79/14.66 [4408]E(f862(f862(f127(x44081),f862(f135(f925(x44081),f925(x44081),f127(x44081),f106(x44081)),x44082)),f862(f135(f925(x44081),f925(x44081),f127(x44081),f106(x44081)),x44083)),f862(f135(f925(x44081),f925(x44081),f127(x44081),f106(x44081)),f862(f862(f127(f925(x44081)),x44082),x44083))) % 14.79/14.66 [4411]E(f862(f862(f244(f925(x44111),f925(x44111)),f862(f129(x44111,x44112),x44113)),f862(f129(x44111,f862(f66(a921,a921,x44111,a314),x44112)),x44113)),f159(x44111,x44112,x44113)) % 14.79/14.66 [4414]E(f862(f862(f73(a924),f862(f862(f73(a924),f862(f862(f29(a924),x44141),x44142)),f862(f862(f29(a924),x44143),x44142))),f862(f862(f29(a924),f862(f862(f73(a924),f38(a924,x44141,x44142)),f38(a924,x44143,x44142))),x44142)),f862(f862(f29(a924),f862(f862(f73(a924),x44141),x44143)),x44142)) % 14.79/14.66 [4415]E(f862(f862(f73(a1),f862(f862(f73(a1),f862(f862(f29(a1),x44151),x44152)),f862(f862(f29(a1),x44153),x44152))),f862(f862(f29(a1),f862(f862(f73(a1),f38(a1,x44151,x44152)),f38(a1,x44153,x44152))),x44152)),f862(f862(f29(a1),f862(f862(f73(a1),x44151),x44153)),x44152)) % 14.79/14.66 [4469]E(f862(f862(f94(f932(f925(x44691),a921)),f862(f862(f9(f925(x44691),f932(f925(x44691),a921),a921),f321(f925(x44691))),f154(x44691,x44692))),f862(f862(f9(f925(x44691),f932(f925(x44691),a921),a921),f321(f925(x44691))),f154(x44691,x44693))),f153(x44691,f862(f862(f94(f932(x44691,a921)),f862(f862(f9(x44691,f932(x44691,a921),a921),f321(x44691)),x44692)),f862(f862(f9(x44691,f932(x44691,a921),a921),f321(x44691)),x44693)))) % 14.79/14.66 [4481]E(f862(f254(x44811),f862(f862(f20(x44811,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44811),a319),f862(f862(f9(x44811,x44811,a921),a317),x44812))),f862(f862(f9(x44811,f932(x44811,a921),a921),f321(x44811)),x44813))),f862(f862(f301(x44811),x44812),x44813)) % 14.79/14.66 [4501]E(f862(f862(f79(f925(f925(x45011)),f925(f925(x45011))),f47(x45011,x45012)),f862(f862(f20(f925(f925(x45011)),f925(f925(x45011)),f925(f925(x45011))),f862(f862(f10(f925(f925(x45011)),f932(f925(f925(x45011)),f925(f925(x45011))),f925(f925(x45011))),f127(f925(x45011))),f862(f147(f925(x45011),f925(x45011)),f862(f144(x45011),x45013)))),f7(f925(f925(x45011))))),f47(x45011,f862(f862(f144(x45011),x45013),x45012))) % 14.79/14.66 [4504]E(f862(f254(x45041),f862(f862(f20(x45041,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45041),a319),f862(f862(f9(x45041,f932(x45041,a921),a921),f321(x45041)),x45042))),f862(f862(f9(x45041,f932(x45041,a921),a921),f321(x45041)),x45043))),f862(f862(f103(f932(x45041,a921)),x45042),x45043)) % 14.79/14.66 [4505]E(f862(f254(x45051),f862(f862(f20(x45051,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45051),a318),f862(f862(f9(x45051,f932(x45051,a921),a921),f321(x45051)),x45052))),f862(f862(f9(x45051,f932(x45051,a921),a921),f321(x45051)),x45053))),f862(f862(f94(f932(x45051,a921)),x45052),x45053)) % 14.79/14.66 [4596]E(f862(f862(f33(x45961,f932(f932(x45961,a921),a921)),x45962),f862(f862(f9(x45961,f932(f932(x45961,a921),a921),f932(f932(x45961,a921),a921)),f862(f862(f10(f932(x45961,a921),f932(f932(f932(x45961,a921),a921),f932(f932(x45961,a921),a921)),x45961),f301(f932(x45961,a921))),f862(f862(f10(f932(x45961,a921),f932(x45961,a921),x45961),f276(x45961,x45961,x45963)),f862(f862(f9(x45961,f932(x45961,a921),f932(x45961,a921)),f301(x45961)),f181(f932(x45961,a921)))))),f181(f932(f932(x45961,a921),a921)))),f862(f862(f53(x45961),x45962),x45963)) % 14.79/14.66 [4598]E(f862(f862(f194(x45981),f862(f862(f74(a1),f862(f862(f66(f931(a1,a1),a1,x45981,f243(a1,a1)),f205(x45981)),x45982)),f862(f862(f66(f931(a1,a1),a1,x45981,f243(a1,a1)),f205(x45981)),x45983))),f862(f862(f74(a1),f862(f862(f66(f931(a1,a1),a1,x45981,f248(a1,a1)),f205(x45981)),x45982)),f862(f862(f66(f931(a1,a1),a1,x45981,f248(a1,a1)),f205(x45981)),x45983))),f221(x45981,x45982,x45983)) % 14.79/14.66 [4601]E(f862(f254(f925(x46011)),f862(f862(f20(f925(x46011),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x46011)),a318),f862(f862(f9(f925(x46011),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x46011)),a317),f182(f925(x46011)))),x46012))),f862(f862(f9(f925(x46011),f932(x46011,a921),a921),f862(f862(f10(f932(x46011,a921),f932(f932(x46011,a921),a921),f925(x46011)),f227(f932(x46011,a921))),f165(x46011))),f862(f165(x46011),x46013)))),f862(f165(f925(x46011)),f48(x46011,x46012,x46013))) % 14.79/14.66 [4007]E(f38(a924,f862(f862(f73(a924),f862(f862(f74(a924),x40071),x40072)),x40073),x40072),f38(a924,x40073,x40072)) % 14.79/14.66 [4052]E(f132(a924,f862(f295(a924,f862(f862(f73(a924),x40521),x40522)),x40523)),f862(f862(f131(a924),x40522),f132(a924,f862(f295(a924,x40521),x40523)))) % 14.79/14.66 [4091]E(f862(f862(f73(a1),f862(f93(a1),x40911)),f862(f862(f73(a1),f862(f93(a1),x40912)),x40913)),f862(f862(f73(a1),f862(f93(a1),f862(f862(f73(a924),x40911),x40912))),x40913)) % 14.79/14.66 [4098]E(f862(f862(f103(f932(x40981,a921)),f862(f862(f3(f932(x40981,a921)),x40982),x40983)),x40983),f862(f862(f103(f932(x40981,a921)),x40982),x40983)) % 14.79/14.66 [4099]E(f862(f862(f3(f932(x40991,a921)),f862(f862(f3(f932(x40991,a921)),x40992),x40993)),x40993),f862(f862(f3(f932(x40991,a921)),x40992),x40993)) % 14.79/14.66 [4123]E(f862(f862(f280(x41231,x41231,x41232),f299(x41231,f181(f932(f931(x41231,x41231),a921)))),x41233),x41233) % 14.79/14.66 [4131]E(f862(f862(f103(f932(x41311,a921)),f862(f273(x41311),x41312)),f862(f273(x41311),x41313)),f862(f273(x41311),f862(f862(f103(f932(f931(x41311,x41311),a921)),x41312),x41313))) % 14.79/14.66 [4141]E(f258(x41411,f862(f862(f144(f931(a92,x41411)),f862(f862(f244(a92,x41411),f2(a92)),x41412)),x41413)),f258(x41411,x41413)) % 14.79/14.66 [4143]E(f862(f862(f94(f932(x41431,a921)),f31(f932(x41431,a921),x41432)),f31(f932(x41431,a921),x41433)),f31(f932(x41431,a921),f862(f862(f103(f932(f932(x41431,a921),a921)),x41432),x41433))) % 14.79/14.66 [4144]E(f862(f862(f103(f932(x41441,a921)),f30(f932(x41441,a921),x41442)),f30(f932(x41441,a921),x41443)),f30(f932(x41441,a921),f862(f862(f103(f932(f932(x41441,a921),a921)),x41442),x41443))) % 14.79/14.66 [4181]E(f862(f862(f280(x41811,x41811,x41811),f862(f862(f176(f931(x41811,x41811),a921),x41812),x41813)),x41813),f862(f862(f176(f931(x41811,x41811),a921),f862(a105,x41812)),x41813)) % 14.79/14.66 [4224]P1(f862(f862(f227(f932(x42241,a921)),f862(f862(f94(f932(x42241,a921)),x42242),x42243)),x42243)) % 14.79/14.66 [4225]P1(f862(f862(f227(f932(x42251,a921)),f862(f862(f94(f932(x42251,a921)),x42252),x42253)),x42252)) % 14.79/14.66 [4226]P1(f862(f862(f227(f932(x42261,a921)),f862(f862(f3(f932(x42261,a921)),x42262),x42263)),x42262)) % 14.79/14.66 [4250]E(f299(x42501,f862(f862(f103(f932(f931(x42501,x42501),a921)),f299(x42501,x42502)),f299(x42501,x42503))),f299(x42501,f862(f862(f103(f932(f931(x42501,x42501),a921)),x42502),x42503))) % 14.79/14.66 [4254]E(f30(f932(x42541,a921),f862(f862(f301(f932(x42541,a921)),x42542),f862(f862(f301(f932(x42541,a921)),x42543),f181(f932(f932(x42541,a921),a921))))),f862(f862(f103(f932(x42541,a921)),x42542),x42543)) % 14.79/14.66 [4255]E(f31(f932(x42551,a921),f862(f862(f301(f932(x42551,a921)),x42552),f862(f862(f301(f932(x42551,a921)),x42553),f181(f932(f932(x42551,a921),a921))))),f862(f862(f94(f932(x42551,a921)),x42552),x42553)) % 14.79/14.66 [4260]E(f862(f862(f280(x42601,x42601,x42601),f862(f862(f176(f931(x42601,x42601),a921),x42602),x42603)),x42603),f862(f862(f280(x42601,x42601,x42601),x42603),f862(f862(f176(f931(x42601,x42601),a921),x42602),x42603))) % 14.79/14.66 [4329]E(f862(f862(f103(f932(x43291,a921)),f862(f254(x43291),f862(f862(f9(x43291,x43291,a921),a317),x43292))),x43293),f862(f862(f301(x43291),x43292),x43293)) % 14.79/14.66 [4331]E(f862(a97,f862(f862(f8(x43311,a1),f862(f862(f10(a924,a1,x43311),f93(a1)),x43312)),x43313)),f862(f862(f8(x43311,a924),x43312),x43313)) % 14.79/14.66 [4332]E(f862(a97,f862(f862(f11(x43321,a1),f862(f862(f10(a924,a1,x43321),f93(a1)),x43322)),x43323)),f862(f862(f11(x43321,a924),x43322),x43323)) % 14.79/14.66 [4405]E(f862(f149(f925(x44051),x44051,f862(f164(x44051),x44052),f862(f18(f932(f925(x44051),f925(x44051)),x44051),f862(f862(f9(f925(x44051),f925(x44051),f925(x44051)),f127(x44051)),x44052))),x44053),f862(f164(x44051),f862(f862(f127(x44051),x44053),x44052))) % 14.79/14.66 [4434]P1(f862(f862(f227(f932(f932(x44341,a921),a921)),f862(f862(f103(f932(f932(x44341,a921),a921)),f862(f300(x44341),x44342)),f862(f300(x44341),x44343))),f862(f300(x44341),f862(f862(f103(f932(x44341,a921)),x44342),x44343)))) % 14.79/14.66 [4523]E(f862(f254(x45231),f862(f862(f20(x45231,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45231),a318),f862(f862(f9(x45231,f932(x45231,a921),a921),f321(x45231)),x45232))),f862(f862(f10(a921,a921,x45231),a314),f862(f862(f9(x45231,f932(x45231,a921),a921),f321(x45231)),x45233)))),f862(f862(f3(f932(x45231,a921)),x45232),x45233)) % 14.79/14.66 [4549]E(f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f182(f925(x45491)),x45492)))),f862(f862(f10(x45491,a921,a924),x45493),f862(f157(x45491),x45492))))),f862(f182(f925(x45491)),f862(f129(x45491,x45493),x45492))) % 14.79/14.66 [4551]E(f862(f182(f925(x45511)),f169(x45511,x45512,x45513)),f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f182(f925(x45511)),x45512)))),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x45513))))) % 14.79/14.66 [4647]E(f862(f862(f94(f932(f931(f925(x46471),f925(x46471)),a921)),f862(f302(f931(f931(x46471,f925(x46471)),f931(x46471,f925(x46471))),f931(f925(x46471),f925(x46471)),f250(f931(x46471,f925(x46471)),f925(x46471),f931(x46471,f925(x46471)),f925(x46471),f862(f249(x46471,f925(x46471),f925(x46471)),f144(x46471)),f862(f249(x46471,f925(x46471),f925(x46471)),f144(x46471)))),f311(x46471,f925(x46471),x46472,f862(f136(x46471,x46472),x46473)))),f862(f254(f931(f925(x46471),f925(x46471))),f862(f249(f925(x46471),f925(x46471),a921),f862(f862(f9(f925(x46471),f932(f925(x46471),a921),f932(f925(x46471),a921)),f862(f862(f10(f932(a921,a921),f932(f932(f925(x46471),a921),f932(f925(x46471),a921)),f925(x46471)),f10(a921,a921,f925(x46471))),f862(f862(f10(a921,f932(a921,a921),f925(x46471)),a318),f862(f862(f9(f925(x46471),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x46471)),a317),f182(f925(x46471)))),f862(a105,x46473))))),f862(f862(f9(f925(x46471),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x46471)),a317),f182(f925(x46471)))),f862(a105,x46473)))))),f862(f136(x46471,x46472),f862(a105,x46473))) % 14.79/14.66 [4145]E(f38(a924,f862(a105,f862(f862(f73(a924),f862(f862(f74(a924),x41451),x41452)),x41453)),x41452),f38(a924,f862(a105,x41453),x41452)) % 14.79/14.66 [4391]E(f862(f254(x43911),f862(f862(f20(x43911,a921,a921),f862(f862(f10(a921,f932(a921,a921),x43911),a318),x43912)),x43913)),f862(f862(f94(f932(x43911,a921)),f862(f254(x43911),x43912)),f862(f254(x43911),x43913))) % 14.79/14.66 [4392]E(f862(f254(x43921),f862(f862(f20(x43921,a921,a921),f862(f862(f10(a921,f932(a921,a921),x43921),a319),x43922)),x43923)),f862(f862(f103(f932(x43921,a921)),f862(f254(x43921),x43922)),f862(f254(x43921),x43923))) % 14.79/14.66 [4394]E(f862(f862(f127(x43941),f862(f862(f131(x43941),f38(a924,x43942,f862(f182(f925(x43941)),x43943))),x43943)),f862(f862(f168(x43941),f38(a924,x43942,f862(f182(f925(x43941)),x43943))),x43943)),f862(f862(f862(f176(f925(x43941),f925(x43941)),x43942),f160(x43941)),x43943)) % 14.79/14.66 [4400]E(f862(f254(x44001),f862(f862(f20(x44001,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44001),a322),x44002)),x44003)),f862(f862(f103(f932(x44001,a921)),f862(f72(f932(x44001,a921)),f862(f254(x44001),x44002))),f862(f254(x44001),x44003))) % 14.79/14.66 [4416]E(f862(f862(f73(a924),f862(f182(f925(x44161)),f862(f129(x44161,x44162),x44163))),f862(f182(f925(x44161)),f862(f129(x44161,f862(f862(f10(a921,a921,x44161),a314),x44162)),x44163))),f862(f182(f925(x44161)),x44163)) % 14.79/14.66 [4440]P1(f862(f862(f227(f932(x44401,a921)),f862(f862(f103(f932(x44401,a921)),f31(f932(x44401,a921),x44402)),f31(f932(x44401,a921),x44403))),f31(f932(x44401,a921),f862(f862(f94(f932(f932(x44401,a921),a921)),x44402),x44403)))) % 14.79/14.66 [4454]E(f862(f165(x44541),f862(f129(x44541,f862(f862(f10(a921,a921,x44541),a314),f862(f862(f9(x44541,x44541,a921),a317),x44542))),x44543)),f862(f862(f3(f932(x44541,a921)),f862(f165(x44541),x44543)),f862(f862(f301(x44541),x44542),f181(f932(x44541,a921))))) % 14.79/14.66 [4463]P1(f862(f862(f227(f932(f931(x44631,x44631),a921)),f862(f862(f103(f932(f931(x44631,x44631),a921)),f299(x44631,x44632)),f299(x44631,x44633))),f299(x44631,f862(f862(f103(f932(f931(x44631,x44631),a921)),x44632),x44633)))) % 14.79/14.66 [4486]E(f862(f862(f74(a924),f862(a105,f862(a105,f2(a924)))),f862(f862(f8(a924,a924),f862(f862(f10(a924,a924,a924),f862(f73(a924),x44861)),f862(f862(f9(a924,a924,a924),f74(a924)),x44862))),f862(f292(a924),x44863))),f862(f862(f74(a924),x44863),f862(f862(f73(a924),x44861),f862(f862(f73(a924),x44861),f862(f862(f74(a924),f862(f862(f3(a924),x44863),f71(a924))),x44862))))) % 14.79/14.66 [4496]E(f862(f254(x44961),f862(f862(f20(x44961,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44961),a318),f862(f862(f9(x44961,f932(x44961,a921),a921),f321(x44961)),f862(f165(x44961),x44962)))),x44963)),f862(f165(x44961),f862(f129(x44961,x44963),x44962))) % 14.79/14.66 [4646]E(f862(f254(x46461),f862(f862(f10(f932(a924,a921),a921,x46461),f80(a924)),f862(f862(f9(x46461,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),x46461),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),x46461),f862(f10(a921,f932(a921,a921),a924),a318)),f862(f862(f9(x46461,f932(a924,x46461),f932(a924,a921)),f862(f862(f10(f932(x46461,a921),f932(f932(a924,x46461),f932(a924,a921)),x46461),f10(x46461,a921,a924)),a317)),f862(f157(x46461),x46462))))),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f182(f925(x46461)),x46462)))),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x46463))))),f862(f165(x46461),f169(x46461,x46462,x46463))) % 14.79/14.66 [4538]E(f862(f254(x45381),f862(f862(f20(x45381,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45381),a322),f862(f862(f10(a921,a921,x45381),a314),f862(f862(f9(x45381,x45381,a921),a317),x45382)))),x45383)),f862(f862(f301(x45381),x45382),f862(f254(x45381),x45383))) % 14.79/14.66 [4570]E(f862(f862(f147(f931(x45701,a924),x45701),f243(x45701,a924)),f862(f129(f931(x45701,a924),f862(f862(f9(f931(x45701,a924),f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),f931(x45701,a924)),f321(a924)),f248(x45701,a924))),x45702)),f862(f862(f174(x45701,a924),x45703),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(x45701)),x45703)))))),f169(x45701,x45703,x45702)) % 14.79/14.66 [4597]E(f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f8(a924,a1),f862(f862(f10(a1,a1,a924),f862(f73(a1),x45971)),f862(f862(f9(a924,a1,a1),f862(f862(f10(a1,f932(a1,a1),a924),f74(a1)),f93(a1))),x45972))),f862(f292(a924),x45973))),f862(f862(f74(a1),f862(f93(a1),x45973)),f862(f862(f73(a1),x45971),f862(f862(f73(a1),x45971),f862(f862(f74(a1),f862(f93(a1),f862(f862(f3(a924),x45973),f71(a924)))),x45972))))) % 14.79/14.66 [4639]E(f862(f254(f931(x46391,x46392)),f862(f249(x46391,x46392,a921),f862(f862(f9(x46391,f932(f931(x46392,x46391),a921),f932(x46392,a921)),f862(f862(f10(f932(x46392,f932(f932(f931(x46392,x46391),a921),a921)),f932(f932(f931(x46392,x46391),a921),f932(x46392,a921)),x46391),f9(x46392,f932(f931(x46392,x46391),a921),a921)),f862(f862(f10(f932(x46392,f931(x46392,x46391)),f932(x46392,f932(f932(f931(x46392,x46391),a921),a921)),x46391),f862(f10(f931(x46392,x46391),f932(f932(f931(x46392,x46391),a921),a921),x46392),f321(f931(x46392,x46391)))),f862(f9(x46392,x46391,f931(x46392,x46391)),f244(x46392,x46391))))),x46393))),f862(f277(x46392,x46391),x46393)) % 14.79/14.66 [4659]E(f862(f254(f925(x46591)),f862(f862(f10(f932(x46591,a921),a921,f925(x46591)),f80(x46591)),f862(f862(f10(f932(x46591,f932(f925(x46591),a921)),f932(x46591,a921),f925(x46591)),f862(f10(f932(f925(x46591),a921),a921,x46591),f80(f925(x46591)))),f862(f862(f9(f925(x46591),f932(x46591,f932(f925(x46591),a921)),f932(x46591,f932(f925(x46591),a921))),f862(f862(f10(f932(x46591,f932(f932(f925(x46591),a921),f932(f925(x46591),a921))),f932(f932(x46591,f932(f925(x46591),a921)),f932(x46591,f932(f925(x46591),a921))),f925(x46591)),f20(x46591,f932(f925(x46591),a921),f932(f925(x46591),a921))),f862(f862(f10(f932(x46591,f932(f925(x46591),f932(a921,a921))),f932(x46591,f932(f932(f925(x46591),a921),f932(f925(x46591),a921))),f925(x46591)),f862(f10(f932(f925(x46591),f932(a921,a921)),f932(f932(f925(x46591),a921),f932(f925(x46591),a921)),x46591),f20(f925(x46591),a921,a921))),f862(f862(f10(f932(x46591,f932(f925(x46591),a921)),f932(x46591,f932(f925(x46591),f932(a921,a921))),f925(x46591)),f862(f10(f932(f925(x46591),a921),f932(f925(x46591),f932(a921,a921)),x46591),f862(f10(a921,f932(a921,a921),f925(x46591)),a318))),f862(f862(f9(f925(x46591),f932(x46591,f932(f925(x46591),f925(x46591))),f932(x46591,f932(f925(x46591),a921))),f862(f862(f10(f932(f932(f925(x46591),f925(x46591)),f932(f925(x46591),a921)),f932(f932(x46591,f932(f925(x46591),f925(x46591))),f932(x46591,f932(f925(x46591),a921))),f925(x46591)),f10(f932(f925(x46591),f925(x46591)),f932(f925(x46591),a921),x46591)),f862(f862(f10(f932(f925(x46591),a921),f932(f932(f925(x46591),f925(x46591)),f932(f925(x46591),a921)),f925(x46591)),f10(f925(x46591),a921,f925(x46591))),a317))),f144(x46591)))))),f862(f862(f9(x46591,f932(f925(x46591),a921),f932(f925(x46591),a921)),f862(f862(f10(f932(a921,a921),f932(f932(f925(x46591),a921),f932(f925(x46591),a921)),x46591),f10(a921,a921,f925(x46591))),f862(f862(f10(a921,f932(a921,a921),x46591),a318),f862(f862(f9(x46591,f932(x46591,a921),a921),f321(x46591)),x46592)))),f862(f862(f9(f925(x46591),f932(f925(x46591),a921),a921),f321(f925(x46591))),x46593)))))),f167(x46591,x46592,x46593)) % 14.79/14.66 [4656]E(f862(f862(f79(a1,f931(a1,a1)),f862(f862(f3(a1),x46561),x46562)),f862(f862(f9(a1,f931(a1,a1),f931(a1,a1)),f862(f862(f20(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f862(f862(f10(a921,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f89(f931(a1,a1))),f862(f227(a1),f2(a1)))),f862(f244(a1,a1),f862(f862(f73(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x46563)),f71(a1))))),f862(f862(f244(a1,a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x46563)),x46561))),f862(f36(x46562),f862(f862(f244(a1,a1),x46563),x46561))) % 14.79/14.66 [3709]E(f109(x37091,f862(x37092,x37093),f862(x37094,x37093)),f862(f196(x37091,x37092,x37094),x37093)) % 14.79/14.66 [3763]E(f862(f862(f237(x37631,x37632,x37633),x37634),f2(a924)),x37632) % 14.79/14.66 [3801]E(f178(x38011,x38012,x38013,f862(a105,x38014)),f862(x38013,x38014)) % 14.79/14.66 [3842]E(f163(x38421,x38422,f163(x38421,x38423,x38424)),f163(x38421,x38423,f163(x38421,x38422,x38424))) % 14.79/14.66 [3843]E(f119(x38431,x38432,f109(x38431,x38433,x38434)),f109(x38431,f119(x38431,x38432,x38433),x38434)) % 14.79/14.66 [3975]E(f862(f149(x39751,x39752,x39753,x39754),f106(x39752)),x39753) % 14.79/14.66 [3976]E(f862(f135(x39761,x39762,x39763,x39764),f106(x39762)),x39764) % 14.79/14.66 [4013]E(f862(f182(f929(x40131,x40132)),f213(x40131,x40132,x40133,x40134)),f2(a924)) % 14.79/14.66 [4036]E(f862(f249(x40361,x40362,x40363),f247(x40361,x40362,x40363,x40364)),x40364) % 14.79/14.66 [4079]E(f862(f862(f127(x40791),f162(x40791,x40792,x40793)),f162(x40791,x40794,x40793)),f862(f862(f127(x40791),f162(x40791,x40794,x40793)),f162(x40791,x40792,x40793))) % 14.79/14.66 [4164]E(f862(f862(f251(x41641,x41642,x41643,f931(x41642,x41643)),x41644),f244(x41642,x41643)),x41644) % 14.79/14.66 [4174]E(f120(x41741,x41742,x41743,x41744,f112(x41742)),x41743) % 14.79/14.66 [4180]E(f68(x41801,x41802,x41803,x41804,f862(x41803,x41804)),x41803) % 14.79/14.66 [4447]P40(x44471,x44472,x44473,x44474,f181(f932(x44471,a921)),x44474) % 14.79/14.66 [3515]E(f862(f862(f18(x35151,x35152),x35153),x35154),x35153) % 14.79/14.66 [3791]E(f163(x37911,x37912,f862(f129(x37911,x37913),x37914)),f862(f129(x37911,x37913),f163(x37911,x37912,x37914))) % 14.79/14.66 [3825]E(f862(f862(f57(x38251,x38252,x38253),x38254),f181(f932(x38251,a921))),x38254) % 14.79/14.66 [3849]E(f862(f862(f157(x38491),f862(f862(f144(x38491),x38492),x38493)),f862(a105,x38494)),f862(f862(f157(x38491),x38493),x38494)) % 14.79/14.66 [3915]E(f862(f862(x39151,x39152),f862(f177(x39153,x39154,x39151),x39152)),f862(f177(x39153,x39154,x39151),f862(a105,x39152))) % 14.79/14.66 [3956]E(f247(x39561,x39562,x39563,f862(f249(x39561,x39562,x39563),x39564)),x39564) % 14.79/14.66 [4011]E(f862(f862(f152(x40111,f862(f862(f144(x40111),x40112),x40113)),f2(a924)),x40114),f862(f862(f144(x40111),x40114),x40113)) % 14.79/14.66 [4021]E(f862(f862(f33(f932(x40211,a921),f932(x40212,a921)),x40213),f302(x40211,x40212,x40214)),f862(f302(x40211,x40212,x40214),f30(f932(x40211,a921),x40213))) % 14.79/14.66 [4022]E(f862(f862(f33(f932(x40221,a921),f932(x40222,a921)),x40223),f303(x40222,x40221,x40224)),f862(f303(x40222,x40221,x40224),f30(f932(x40221,a921),x40223))) % 14.79/14.66 [4047]E(f113(x40471,f123(x40472,f926(x40471),x40473,x40474)),f862(f111(x40472,x40471,x40474),x40473)) % 14.79/14.66 [4119]E(f862(f118(x41191,x41192),f119(x41191,x41193,x41194)),f862(f862(f73(a924),f862(f862(f73(a924),f862(x41192,x41193)),f862(f118(x41191,x41192),x41194))),f862(a105,f2(a924)))) % 14.79/14.66 [4140]E(f862(f135(x41401,x41402,f862(f9(x41402,x41401,x41401),x41403),x41404),f862(f161(x41402),f106(x41402))),x41404) % 14.79/14.66 [4244]E(f216(x42441,f931(x42442,f926(x42442)),x42443,f862(f249(x42442,f926(x42442),x42441),x42444),f862(f128(x42442),f112(x42442))),x42443) % 14.79/14.66 [4376]E(f862(f249(x43761,x43762,x43763),f862(f862(f10(f932(x43762,f931(x43761,x43762)),f932(x43762,x43763),x43761),f862(f10(f931(x43761,x43762),x43763,x43762),x43764)),f244(x43761,x43762))),x43764) % 14.79/14.66 [3700]E(f862(f248(x37001,x37002),f862(f862(f244(x37001,x37002),x37003),x37004)),x37004) % 14.79/14.66 [3701]E(f862(f243(x37011,x37012),f862(f862(f244(x37011,x37012),x37013),x37014)),x37013) % 14.79/14.66 [3735]E(f862(f182(f925(x37351)),f862(f862(f152(x37351,x37352),x37353),x37354)),f862(f182(f925(x37351)),x37352)) % 14.79/14.66 [3736]E(f862(f182(f925(x37361)),f862(f862(f147(x37362,x37361),x37363),x37364)),f862(f182(f925(x37362)),x37364)) % 14.79/14.66 [3757]E(f862(f862(f131(x37571),f862(a105,x37572)),f862(f862(f144(x37571),x37573),x37574)),f862(f862(f131(x37571),x37572),x37574)) % 14.79/14.66 [3820]E(f862(f862(f168(x38201),x38202),f162(x38201,x38203,x38204)),f162(x38201,f862(f862(f225(a924),x38202),x38203),x38204)) % 14.79/14.66 [3821]E(f862(f862(f131(x38211),x38212),f162(x38211,x38213,x38214)),f162(x38211,f862(f862(f3(a924),x38213),x38212),x38214)) % 14.79/14.66 [3827]E(f862(f862(f301(x38271),x38272),f862(f862(f301(x38271),x38273),x38274)),f862(f862(f301(x38271),x38273),f862(f862(f301(x38271),x38272),x38274))) % 14.79/14.66 [3831]E(f862(f862(f147(x38311,x38312),x38313),f107(x38311,x38314)),f107(x38312,f862(f862(f147(x38311,x38312),x38313),x38314))) % 14.79/14.66 [3847]E(f862(f161(x38471),f862(f862(f147(x38472,x38471),x38473),x38474)),f862(f862(f147(x38472,x38471),x38473),f862(f161(x38472),x38474))) % 14.79/14.66 [3848]E(f862(f862(f147(x38481,x38482),x38483),f862(f164(x38481),x38484)),f862(f164(x38482),f862(f862(f147(x38481,x38482),x38483),x38484))) % 14.79/14.66 [3862]E(f862(f862(f168(x38621),f862(a105,x38622)),f862(f862(f144(x38621),x38623),x38624)),f862(f862(f144(x38621),x38623),f862(f862(f168(x38621),x38622),x38624))) % 14.79/14.66 [3865]E(f862(f165(x38651),f862(f862(f147(x38652,x38651),x38653),x38654)),f862(f302(x38652,x38651,x38653),f862(f165(x38652),x38654))) % 14.79/14.66 [3878]E(f862(f862(f147(x38781,x38782),f862(f18(x38782,x38781),x38783)),x38784),f162(x38782,f862(f182(f925(x38781)),x38784),x38783)) % 14.79/14.66 [3914]E(f19(x39141,x39142,x39143,f862(a5,f862(a105,f862(a22,x39144)))),f862(x39143,x39144)) % 14.79/14.66 [3918]E(f862(f862(f127(x39181),f862(f129(x39181,x39182),x39183)),f862(f129(x39181,x39182),x39184)),f862(f129(x39181,x39182),f862(f862(f127(x39181),x39183),x39184))) % 14.79/14.66 [3930]E(f145(x39301,f862(f862(f147(x39302,x39301),x39303),f145(x39302,x39304))),f145(x39301,f862(f862(f147(x39302,x39301),x39303),x39304))) % 14.79/14.66 [3945]E(f862(f277(x39451,x39451),f862(f862(f279(x39452,x39451),x39453),x39454)),f862(f862(f279(x39452,x39451),f862(f277(x39452,x39452),x39453)),x39454)) % 14.79/14.66 [3957]E(f862(f862(f280(x39571,x39572,x39573),x39574),f181(f932(f931(x39572,x39573),a921))),f181(f932(f931(x39571,x39573),a921))) % 14.79/14.66 [3958]E(f862(f862(f168(x39581),f862(f862(f3(a924),x39582),x39583)),f862(f862(f131(x39581),x39583),x39584)),f862(f862(f131(x39581),x39583),f862(f862(f168(x39581),x39582),x39584))) % 14.79/14.66 [3977]E(f862(f862(f127(x39771),f162(x39771,x39772,x39773)),f162(x39771,x39774,x39773)),f162(x39771,f862(f862(f73(a924),x39772),x39774),x39773)) % 14.79/14.66 [3978]E(f862(f862(f862(f270(x39781),x39782),x39783),x39784),f862(f244(f932(a92,f932(a921,f928(f926(x39781)))),f931(a92,a92)),f862(f35(x39781),x39782))) % 14.79/14.66 [4004]E(f31(f932(x40041,a921),f862(f302(x40042,f932(x40041,a921),x40043),x40044)),f862(f862(f32(x40042,f932(x40041,a921)),x40044),x40043)) % 14.79/14.66 [4005]E(f30(f932(x40051,a921),f862(f302(x40052,f932(x40051,a921),x40053),x40054)),f862(f862(f33(x40052,f932(x40051,a921)),x40054),x40053)) % 14.79/14.66 [4006]E(f862(f182(f925(f931(x40061,x40062))),f862(f862(f174(x40061,x40062),x40063),x40064)),f862(f862(f225(a924),f862(f182(f925(x40061)),x40063)),f862(f182(f925(x40062)),x40064))) % 14.79/14.66 [4008]E(f862(f303(x40081,x40082,x40083),f862(f72(f932(x40082,a921)),x40084)),f862(f72(f932(x40081,a921)),f862(f303(x40081,x40082,x40083),x40084))) % 14.79/14.66 [4057]E(f862(f303(x40571,x40572,x40573),f862(f254(x40572),x40574)),f862(f254(x40571),f862(f862(f10(x40572,a921,x40571),x40574),x40573))) % 14.79/14.66 [4074]E(f862(f862(f157(x40741),f862(f862(f127(x40741),x40742),f862(f862(f144(x40741),x40743),x40744))),f862(f182(f925(x40741)),x40742)),x40743) % 14.79/14.66 [4096]E(f862(f302(x40961,x40962,x40963),f862(f303(x40961,x40962,x40963),x40964)),f862(f862(f94(f932(x40962,a921)),x40964),f862(f302(x40961,x40962,x40963),f234(f932(x40961,a921))))) % 14.79/14.66 [4115]P1(f862(f862(f321(x41151),f862(x41152,x41153)),f862(f302(x41154,x41151,x41152),f234(f932(x41154,a921))))) % 14.79/14.66 [4124]E(f21(x41241,x41242,x41243,f862(a5,f862(a105,f862(a22,x41244)))),f862(f862(x41243,x41244),f21(x41241,x41242,x41243,x41244))) % 14.79/14.66 [4128]E(f862(f862(f127(x41281),f162(x41281,x41282,x41283)),f862(f862(f144(x41281),x41283),x41284)),f862(f862(f144(x41281),x41283),f862(f862(f127(x41281),f162(x41281,x41282,x41283)),x41284))) % 14.79/14.66 [4130]E(f862(f862(f246(x41301,x41302),f862(f165(x41301),x41303)),f862(f18(f932(x41302,a921),x41301),f862(f165(x41302),x41304))),f862(f165(f931(x41301,x41302)),f52(x41301,x41302,x41303,x41304))) % 14.79/14.66 [4142]E(f148(x41421,x41422,f862(f862(f144(x41421),x41423),x41424)),f862(f862(f73(a924),f862(f862(f73(a924),f862(x41422,x41423)),f148(x41421,x41422,x41424))),f862(a105,f2(a924)))) % 14.79/14.66 [4155]E(f178(f925(x41551),f862(f862(f144(x41551),x41552),x41553),f862(f862(f9(a924,f925(x41551),f925(x41551)),f131(x41551)),x41553),x41554),f862(f862(f131(x41551),x41554),f862(f862(f144(x41551),x41552),x41553))) % 14.79/14.66 [4156]P22(x41561,f931(x41562,x41561),f556(x41563,x41564,x41562,x41561),f862(f862(f33(x41562,f932(x41561,a921)),x41564),x41563)) % 14.79/14.66 [4165]E(f862(f862(f3(f932(x41651,a921)),f862(f862(f3(f932(x41651,a921)),x41652),x41653)),f862(f862(f301(x41651),x41654),f181(f932(x41651,a921)))),f862(f862(f3(f932(x41651,a921)),x41652),f862(f862(f301(x41651),x41654),x41653))) % 14.79/14.66 [4178]E(f862(f862(f176(f932(x41781,x41782),f932(x41781,x41782)),x41783),f66(x41782,x41782,x41781,x41784)),f66(x41782,x41782,x41781,f862(f862(f176(x41782,x41782),x41783),x41784))) % 14.79/14.66 [4249]E(f862(f862(f862(f176(f925(x42491),f925(x42491)),x42492),f160(x42491)),f862(f862(f862(f176(f925(x42491),f925(x42491)),x42493),f160(x42491)),x42494)),f862(f862(f862(f176(f925(x42491),f925(x42491)),f862(f862(f73(a924),x42492),x42493)),f160(x42491)),x42494)) % 14.79/14.66 [4334]P1(f862(f862(f227(f932(x43341,a921)),f862(f165(x43341),f862(f862(f152(x43341,x43342),x43343),x43344))),f862(f862(f301(x43341),x43344),f862(f165(x43341),x43342)))) % 14.79/14.66 [4366]E(f862(f862(f33(f932(x43661,a921),f932(f931(x43661,x43662),a921)),x43663),f862(f862(f9(f932(x43661,a921),f932(x43661,f932(x43662,a921)),f932(f931(x43661,x43662),a921)),f246(x43661,x43662)),x43664)),f862(f862(f246(x43661,x43662),f30(f932(x43661,a921),x43663)),x43664)) % 14.79/14.66 [4404]E(f202(x44041,x44042,x44043,f862(f66(x44042,f932(a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(x44042))))),x44041,f201(x44042)),x44044)),f203(x44041,x44042,x44044,x44043)) % 14.79/14.66 [4419]E(f198(x44191,x44192,x44193,f862(f66(x44192,f932(a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(f928(x44192)))))),x44191,f197(x44192)),x44194)),f199(x44191,x44192,x44194,x44193)) % 14.79/14.66 [4424]P1(f862(f59(x44241,x44242,x44243,x44244,f181(f932(x44241,a921))),x44244)) % 14.79/14.66 [4464]E(f862(f862(f33(x44641,f932(x44642,a921)),x44643),f862(f862(f9(x44641,f932(x44642,a921),f932(x44642,a921)),f862(f862(f10(x44642,f932(f932(x44642,a921),f932(x44642,a921)),x44641),f301(x44642)),x44644)),f181(f932(x44642,a921)))),f862(f302(x44641,x44642,x44644),x44643)) % 14.79/14.66 [4471]P1(f862(f862(f227(f932(x44711,a921)),f862(f275(x44712,x44711),f862(f862(f94(f932(f931(x44712,x44711),a921)),x44713),x44714))),f862(f862(f94(f932(x44711,a921)),f862(f275(x44712,x44711),x44713)),f862(f275(x44712,x44711),x44714)))) % 14.79/14.66 [4472]P1(f862(f862(f227(f932(x44721,a921)),f862(f256(x44721,x44722),f862(f862(f94(f932(f931(x44721,x44722),a921)),x44723),x44724))),f862(f862(f94(f932(x44721,a921)),f862(f256(x44721,x44722),x44723)),f862(f256(x44721,x44722),x44724)))) % 14.79/14.66 [4534]P1(f862(f862(f227(f932(f931(x45341,x45342),a921)),f862(f302(x45342,f931(x45341,x45342),f556(x45343,x45344,x45341,x45342)),f862(f862(f33(x45341,f932(x45342,a921)),x45344),x45343))),f862(f862(f246(x45341,x45342),x45344),x45343))) % 14.79/14.66 [4535]E(f862(f111(x45351,f931(x45351,x45352),x45353),f862(f862(f10(f932(x45352,f926(f931(x45351,x45352))),f926(f931(x45351,x45352)),x45351),f111(x45352,f931(x45351,x45352),x45354)),f862(f862(f10(f932(x45352,f931(x45351,x45352)),f932(x45352,f926(f931(x45351,x45352))),x45351),f862(f10(f931(x45351,x45352),f926(f931(x45351,x45352)),x45352),f122(f931(x45351,x45352)))),f244(x45351,x45352)))),f124(x45351,x45352,x45353,x45354)) % 14.79/14.66 [4536]E(f268(x45361,x45362,x45363,f862(f66(x45362,f932(a92,f932(a92,f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x45362)))),f931(a92,a92))))),x45361,f270(x45362)),x45364)),f271(x45361,x45362,x45364,x45363)) % 14.79/14.66 [4576]E(f78(f931(x45761,x45762),f862(f249(x45761,x45762,a921),f862(f862(f9(x45761,f932(x45762,a921),f932(x45762,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x45762,a921),f932(x45762,a921)),x45761),f10(a921,a921,x45762)),f862(f862(f10(a921,f932(a921,a921),x45761),a318),f862(a317,x45763)))),f862(a317,x45764)))),f862(f862(f244(x45761,x45762),x45763),x45764)) % 14.79/14.66 [4577]E(f83(f931(x45771,x45772),f862(f249(x45771,x45772,a921),f862(f862(f9(x45771,f932(x45772,a921),f932(x45772,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x45772,a921),f932(x45772,a921)),x45771),f10(a921,a921,x45772)),f862(f862(f10(a921,f932(a921,a921),x45771),a318),f862(a317,x45773)))),f862(a317,x45774)))),f862(f862(f244(x45771,x45772),x45773),x45774)) % 14.79/14.66 [4648]E(f862(f862(f249(f925(x46481),f925(x46481),f931(f925(x46481),f925(x46481))),f862(f862(f20(f925(x46481),f932(f925(x46481),f931(f925(x46481),f925(x46481))),f932(f925(x46481),f931(f925(x46481),f925(x46481)))),f862(f862(f10(f932(f925(x46481),f932(f931(f925(x46481),f925(x46481)),f931(f925(x46481),f925(x46481)))),f932(f932(f925(x46481),f931(f925(x46481),f925(x46481))),f932(f925(x46481),f931(f925(x46481),f925(x46481)))),f925(x46481)),f20(f925(x46481),f931(f925(x46481),f925(x46481)),f931(f925(x46481),f925(x46481)))),f862(f862(f10(f932(f925(x46481),f931(f925(x46481),f925(x46481))),f932(f925(x46481),f932(f931(f925(x46481),f925(x46481)),f931(f925(x46481),f925(x46481)))),f925(x46481)),f862(f10(f931(f925(x46481),f925(x46481)),f932(f931(f925(x46481),f925(x46481)),f931(f925(x46481),f925(x46481))),f925(x46481)),f862(f89(f931(f925(x46481),f925(x46481))),f862(x46482,x46483)))),f862(f862(f10(f925(x46481),f932(f925(x46481),f931(f925(x46481),f925(x46481))),f925(x46481)),f244(f925(x46481),f925(x46481))),f862(f144(x46481),x46483))))),f862(f862(f9(f925(x46481),f932(f925(x46481),f925(x46481)),f932(f925(x46481),f931(f925(x46481),f925(x46481)))),f862(f862(f10(f932(f925(x46481),f931(f925(x46481),f925(x46481))),f932(f932(f925(x46481),f925(x46481)),f932(f925(x46481),f931(f925(x46481),f925(x46481)))),f925(x46481)),f10(f925(x46481),f931(f925(x46481),f925(x46481)),f925(x46481))),f244(f925(x46481),f925(x46481)))),f862(f144(x46481),x46483)))),f159(x46481,x46482,x46484)),f159(x46481,x46482,f862(f862(f144(x46481),x46483),x46484))) % 14.79/14.66 [3894]E(f862(f862(f168(x38941),x38942),f862(f862(f168(x38941),x38943),x38944)),f862(f862(f168(x38941),f862(f862(f225(a924),x38942),x38943)),x38944)) % 14.79/14.66 [3895]E(f862(f862(f131(x38951),x38952),f862(f862(f131(x38951),x38953),x38954)),f862(f862(f131(x38951),f862(f862(f73(a924),x38952),x38953)),x38954)) % 14.79/14.66 [3906]E(f862(f862(f127(x39061),f862(f862(f144(x39061),x39062),x39063)),x39064),f862(f862(f144(x39061),x39062),f862(f862(f127(x39061),x39063),x39064))) % 14.79/14.66 [3907]E(f862(f862(f127(x39071),f862(f862(f127(x39071),x39072),x39073)),x39074),f862(f862(f127(x39071),x39072),f862(f862(f127(x39071),x39073),x39074))) % 14.79/14.66 [3988]E(f862(f862(f157(x39881),f862(f862(f144(x39881),x39882),x39883)),x39884),f178(x39881,x39882,f862(f157(x39881),x39883),x39884)) % 14.79/14.66 [3997]E(f862(f862(f176(x39971,x39971),x39972),f862(f862(f176(x39971,x39971),x39973),x39974)),f862(f862(f176(x39971,x39971),f862(f862(f74(a924),x39973),x39972)),x39974)) % 14.79/14.66 [4024]E(f862(f862(f103(f932(x40241,a921)),x40242),f862(f862(f301(x40241),x40243),x40244)),f862(f862(f301(x40241),x40243),f862(f862(f103(f932(x40241,a921)),x40242),x40244))) % 14.79/14.66 [4039]E(f862(f862(f862(f176(x40391,x40391),x40392),x40393),f862(x40393,x40394)),f862(x40393,f862(f862(f862(f176(x40391,x40391),x40392),x40393),x40394))) % 14.79/14.66 [4048]E(f862(f862(f280(x40481,x40482,x40483),f181(f932(f931(x40481,x40482),a921))),x40484),f181(f932(f931(x40481,x40483),a921))) % 14.79/14.66 [4062]E(f862(f862(f103(f932(x40621,a921)),f862(f862(f301(x40621),x40622),x40623)),x40624),f862(f862(f301(x40621),x40622),f862(f862(f103(f932(x40621,a921)),x40623),x40624))) % 14.79/14.66 [4081]E(f862(f28(f931(x40811,x40812)),f862(f862(f246(x40811,x40812),x40813),f862(f18(f932(x40812,a921),x40811),x40814))),f862(f862(f74(a924),f862(f28(x40811),x40813)),f862(f28(x40812),x40814))) % 14.79/14.66 [4087]E(f862(f862(f94(f932(x40871,a921)),f862(f862(f301(x40871),x40872),x40873)),f862(f862(f301(x40871),x40872),x40874)),f862(f862(f301(x40871),x40872),f862(f862(f94(f932(x40871,a921)),x40873),x40874))) % 14.79/14.66 [4100]E(f862(f862(f103(f932(x41001,a921)),x41002),f862(f862(f103(f932(x41001,a921)),x41003),x41004)),f862(f862(f103(f932(x41001,a921)),x41003),f862(f862(f103(f932(x41001,a921)),x41002),x41004))) % 14.79/14.66 [4101]E(f862(f862(f94(f932(x41011,a921)),x41012),f862(f862(f94(f932(x41011,a921)),x41013),x41014)),f862(f862(f94(f932(x41011,a921)),x41013),f862(f862(f94(f932(x41011,a921)),x41012),x41014))) % 14.79/14.66 [4111]E(f57(x41111,x41112,f862(f862(f10(x41112,f932(x41112,x41112),x41111),x41113),x41114)),f862(f58(x41112,x41111,x41113),x41114)) % 14.79/14.66 [4120]E(f172(x41201,f862(f862(f147(f925(x41202),f925(x41201)),f862(f147(x41202,x41201),x41203)),x41204)),f862(f862(f147(f925(x41202),f925(x41201)),f862(f147(x41202,x41201),x41203)),f172(x41202,x41204))) % 14.79/14.66 [4139]E(f862(f135(f925(x41391),f925(x41391),f127(x41391),f106(x41391)),f862(f862(f147(x41392,f925(x41391)),x41393),x41394)),f156(x41392,x41391,x41393,x41394)) % 14.79/14.66 [4196]E(f862(f66(x41961,x41961,x41961,f862(f862(f176(x41961,x41961),x41962),x41963)),f862(f862(f176(x41961,x41961),x41964),x41963)),f862(f862(f176(x41961,x41961),f862(f862(f73(a924),x41962),x41964)),x41963)) % 14.79/14.66 [4219]E(f862(f862(f94(f932(x42191,a921)),f862(f862(f103(f932(x42191,a921)),x42192),x42193)),f862(f862(f103(f932(x42191,a921)),x42192),x42194)),f862(f862(f103(f932(x42191,a921)),x42192),f862(f862(f94(f932(x42191,a921)),x42193),x42194))) % 14.79/14.66 [4220]E(f862(f862(f103(f932(x42201,a921)),f862(f862(f94(f932(x42201,a921)),x42202),x42203)),f862(f862(f94(f932(x42201,a921)),x42202),x42204)),f862(f862(f94(f932(x42201,a921)),x42202),f862(f862(f103(f932(x42201,a921)),x42203),x42204))) % 14.79/14.66 [4221]E(f862(f862(f3(f932(x42211,a921)),f862(f862(f94(f932(x42211,a921)),x42212),x42213)),f862(f862(f94(f932(x42211,a921)),x42212),x42214)),f862(f862(f94(f932(x42211,a921)),x42212),f862(f862(f3(f932(x42211,a921)),x42213),x42214))) % 14.79/14.66 [4222]E(f862(f862(f94(f932(x42221,a921)),f862(f862(f3(f932(x42221,a921)),x42222),x42223)),f862(f862(f3(f932(x42221,a921)),x42222),x42224)),f862(f862(f3(f932(x42221,a921)),x42222),f862(f862(f103(f932(x42221,a921)),x42223),x42224))) % 14.79/14.66 [4223]E(f862(f862(f103(f932(x42231,a921)),f862(f862(f3(f932(x42231,a921)),x42232),x42233)),f862(f862(f3(f932(x42231,a921)),x42232),x42234)),f862(f862(f3(f932(x42231,a921)),x42232),f862(f862(f94(f932(x42231,a921)),x42233),x42234))) % 14.79/14.66 [4228]E(f862(f28(f931(x42281,x42282)),f862(f862(f246(x42281,x42282),f862(f862(f301(x42281),x42283),f181(f932(x42281,a921)))),f862(f18(f932(x42282,a921),x42281),x42284))),f862(f28(x42282),x42284)) % 14.79/14.66 [4263]E(f862(f862(f33(x42631,f932(x42632,a921)),x42633),f862(f862(f10(f932(x42632,a921),f932(x42632,a921),x42631),f72(f932(x42632,a921))),x42634)),f862(f72(f932(x42632,a921)),f862(f862(f32(x42631,f932(x42632,a921)),x42633),x42634))) % 14.79/14.66 [4264]E(f862(f862(f32(x42641,f932(x42642,a921)),x42643),f862(f862(f10(f932(x42642,a921),f932(x42642,a921),x42641),f72(f932(x42642,a921))),x42644)),f862(f72(f932(x42642,a921)),f862(f862(f33(x42641,f932(x42642,a921)),x42643),x42644))) % 14.79/14.66 [4280]E(f862(f862(f280(x42801,x42801,x42801),f862(f862(f176(f931(x42801,x42801),a921),x42802),x42803)),f862(f862(f176(f931(x42801,x42801),a921),x42804),x42803)),f862(f862(f176(f931(x42801,x42801),a921),f862(f862(f73(a924),x42802),x42804)),x42803)) % 14.79/14.66 [4310]E(f862(f862(f32(x43101,f932(f932(x43102,a921),a921)),x43103),f862(f862(f10(f932(x43102,a921),f932(f932(x43102,a921),a921),x43101),f300(x43102)),x43104)),f862(f300(x43102),f862(f862(f32(x43101,f932(x43102,a921)),x43103),x43104))) % 14.79/14.66 [4339]E(f862(f862(f32(f932(x43391,a921),f932(x43392,a921)),x43393),f862(f862(f9(f932(x43391,a921),f932(x43391,f932(x43392,a921)),f932(x43392,a921)),f32(x43391,f932(x43392,a921))),x43394)),f862(f862(f32(x43391,f932(x43392,a921)),f30(f932(x43391,a921),x43393)),x43394)) % 14.79/14.66 [4340]E(f862(f862(f33(f932(x43401,a921),f932(x43402,a921)),x43403),f862(f862(f9(f932(x43401,a921),f932(x43401,f932(x43402,a921)),f932(x43402,a921)),f33(x43401,f932(x43402,a921))),x43404)),f862(f862(f33(x43401,f932(x43402,a921)),f30(f932(x43401,a921),x43403)),x43404)) % 14.79/14.66 [4345]E(f862(f862(f147(x43451,x43452),x43453),f862(f135(f925(x43451),f925(x43451),f127(x43451),f106(x43451)),x43454)),f862(f135(f925(x43452),f925(x43452),f127(x43452),f106(x43452)),f862(f862(f147(f925(x43451),f925(x43452)),f862(f147(x43451,x43452),x43453)),x43454))) % 14.79/14.66 [4347]E(f178(f925(x43471),f106(x43471),f862(f862(f10(f925(x43471),f925(x43471),a924),f862(f144(x43471),x43472)),f862(f862(f9(a924,f925(x43471),f925(x43471)),f168(x43471)),x43473)),x43474),f862(f862(f168(x43471),x43474),f862(f862(f144(x43471),x43472),x43473))) % 14.79/14.66 [4385]P1(f862(f862(f227(f932(x43851,a921)),f862(f302(x43852,x43851,x43853),f862(f303(x43852,x43851,x43853),x43854))),x43854)) % 14.79/14.66 [4387]E(f862(f302(f931(x43871,x43872),f931(x43872,x43871),f862(f249(x43871,x43872,f931(x43872,x43871)),f862(f9(x43872,x43871,f931(x43872,x43871)),f244(x43872,x43871)))),f862(f862(f246(x43871,x43872),x43873),f862(f18(f932(x43872,a921),x43871),x43874))),f862(f862(f246(x43872,x43871),x43874),f862(f18(f932(x43871,a921),x43872),x43873))) % 14.79/14.66 [4396]E(f862(f862(f33(x43961,f932(x43962,a921)),x43963),f862(f862(f10(f932(x43961,a921),f932(x43962,a921),x43961),f276(x43961,x43962,x43964)),f862(f862(f9(x43961,f932(x43961,a921),f932(x43961,a921)),f301(x43961)),f181(f932(x43961,a921))))),f862(f276(x43961,x43962,x43964),x43963)) % 14.79/14.66 [4397]E(f862(f862(f33(x43971,f932(x43972,a921)),x43973),f862(f862(f10(f932(x43971,a921),f932(x43972,a921),x43971),f303(x43972,x43971,x43974)),f862(f862(f9(x43971,f932(x43971,a921),f932(x43971,a921)),f301(x43971)),f181(f932(x43971,a921))))),f862(f303(x43972,x43971,x43974),x43973)) % 14.79/14.66 [4485]E(f862(f862(f103(f932(x44851,a921)),f862(f862(f103(f932(x44851,a921)),f862(f862(f94(f932(x44851,a921)),x44852),x44853)),f862(f862(f94(f932(x44851,a921)),x44853),x44854))),f862(f862(f94(f932(x44851,a921)),x44854),x44852)),f862(f862(f94(f932(x44851,a921)),f862(f862(f94(f932(x44851,a921)),f862(f862(f103(f932(x44851,a921)),x44852),x44853)),f862(f862(f103(f932(x44851,a921)),x44853),x44854))),f862(f862(f103(f932(x44851,a921)),x44854),x44852))) % 14.79/14.66 [4550]E(f862(f135(f925(x45501),f925(x45501),f127(x45501),f106(x45501)),f862(f862(f147(x45502,f925(x45501)),f862(f862(f9(x45502,f925(x45501),f925(x45501)),f862(f862(f10(x45501,f932(f925(x45501),f925(x45501)),x45502),f144(x45501)),x45503)),f106(x45501))),x45504)),f862(f862(f147(x45502,x45501),x45503),x45504)) % 14.79/14.66 [4560]E(f862(f862(f79(a1,x45601),f862(f96(a1),f862(f862(f73(a1),x45602),a90))),f862(f862(f20(a1,x45601,x45601),f862(f862(f9(a1,x45601,f932(x45601,x45601)),f862(f862(f10(a921,f932(x45601,f932(x45601,x45601)),a1),f89(x45601)),a186)),x45603)),f862(f862(f10(a924,x45601,a1),x45604),a97))),f178(x45601,x45603,x45604,f862(f96(a924),x45602))) % 14.79/14.66 [4591]E(f862(f254(x45911),f862(f862(f10(f932(x45912,a921),a921,x45911),f80(x45912)),f862(f862(f10(f932(x45912,a921),f932(x45912,a921),x45911),f862(f20(x45912,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45912),a318),f862(f862(f9(x45912,f932(x45912,a921),a921),f321(x45912)),x45913)))),f862(f9(x45912,x45911,a921),x45914)))),f862(f276(x45912,x45911,f862(f254(f931(x45912,x45911)),f862(f249(x45912,x45911,a921),x45914))),x45913)) % 14.79/14.66 [4731]~P1(f862(f862(f181(f932(x47311,f932(x47312,a921))),x47313),x47314)) % 14.79/14.66 [4051]E(f862(f862(f157(x40511),f862(f862(f127(x40511),x40512),x40513)),f862(f862(f73(a924),f862(f182(f925(x40511)),x40512)),x40514)),f862(f862(f157(x40511),x40513),x40514)) % 14.79/14.66 [4056]E(f862(f862(f131(x40561),x40562),f862(f862(f168(x40561),f862(f862(f73(a924),x40563),x40562)),x40564)),f862(f862(f168(x40561),x40563),f862(f862(f131(x40561),x40562),x40564))) % 14.79/14.66 [4153]E(f862(f862(f103(f932(x41531,a921)),f862(f275(x41532,x41531),x41533)),f862(f275(x41532,x41531),x41534)),f862(f275(x41532,x41531),f862(f862(f103(f932(f931(x41532,x41531),a921)),x41533),x41534))) % 14.79/14.66 [4154]E(f862(f862(f103(f932(x41541,a921)),f862(f256(x41541,x41542),x41543)),f862(f256(x41541,x41542),x41544)),f862(f256(x41541,x41542),f862(f862(f103(f932(f931(x41541,x41542),a921)),x41543),x41544))) % 14.79/14.66 [4159]E(f862(f862(f103(f932(x41591,a921)),f862(f862(f103(f932(x41591,a921)),x41592),x41593)),x41594),f862(f862(f103(f932(x41591,a921)),x41592),f862(f862(f103(f932(x41591,a921)),x41593),x41594))) % 14.79/14.66 [4160]E(f862(f862(f94(f932(x41601,a921)),f862(f862(f94(f932(x41601,a921)),x41602),x41603)),x41604),f862(f862(f94(f932(x41601,a921)),x41602),f862(f862(f94(f932(x41601,a921)),x41603),x41604))) % 14.79/14.66 [4161]E(f862(f862(f3(f932(x41611,a921)),f862(f862(f94(f932(x41611,a921)),x41612),x41613)),x41614),f862(f862(f94(f932(x41611,a921)),x41612),f862(f862(f3(f932(x41611,a921)),x41613),x41614))) % 14.79/14.66 [4198]E(f862(f862(f103(f932(f931(x41981,x41982),a921)),f862(f277(x41982,x41981),x41983)),f862(f277(x41982,x41981),x41984)),f862(f277(x41982,x41981),f862(f862(f103(f932(f931(x41982,x41981),a921)),x41983),x41984))) % 14.79/14.66 [4199]E(f862(f862(f94(f932(f931(x41991,x41992),a921)),f862(f277(x41992,x41991),x41993)),f862(f277(x41992,x41991),x41994)),f862(f277(x41992,x41991),f862(f862(f94(f932(f931(x41992,x41991),a921)),x41993),x41994))) % 14.79/14.66 [4212]E(f862(f862(f103(f932(x42121,f932(x42122,a921))),f235(x42122,x42121,x42123)),f235(x42122,x42121,x42124)),f235(x42122,x42121,f862(f862(f103(f932(x42122,f932(x42121,a921))),x42123),x42124))) % 14.79/14.66 [4213]E(f862(f862(f94(f932(x42131,f932(x42132,a921))),f235(x42132,x42131,x42133)),f235(x42132,x42131,x42134)),f235(x42132,x42131,f862(f862(f94(f932(x42132,f932(x42131,a921))),x42133),x42134))) % 14.79/14.66 [4267]E(f862(f862(f94(f932(x42671,a921)),f862(f862(f103(f932(x42671,a921)),x42672),x42673)),f862(f862(f103(f932(x42671,a921)),x42674),x42673)),f862(f862(f103(f932(x42671,a921)),f862(f862(f94(f932(x42671,a921)),x42672),x42674)),x42673)) % 14.79/14.66 [4268]E(f862(f862(f103(f932(x42681,a921)),f862(f862(f94(f932(x42681,a921)),x42682),x42683)),f862(f862(f94(f932(x42681,a921)),x42684),x42683)),f862(f862(f94(f932(x42681,a921)),f862(f862(f103(f932(x42681,a921)),x42682),x42684)),x42683)) % 14.79/14.66 [4269]E(f862(f862(f3(f932(x42691,a921)),f862(f862(f94(f932(x42691,a921)),x42692),x42693)),f862(f862(f94(f932(x42691,a921)),x42694),x42693)),f862(f862(f94(f932(x42691,a921)),f862(f862(f3(f932(x42691,a921)),x42692),x42694)),x42693)) % 14.79/14.66 [4270]E(f862(f862(f103(f932(x42701,a921)),f862(f862(f3(f932(x42701,a921)),x42702),x42703)),f862(f862(f3(f932(x42701,a921)),x42704),x42703)),f862(f862(f3(f932(x42701,a921)),f862(f862(f103(f932(x42701,a921)),x42702),x42704)),x42703)) % 14.79/14.66 [4271]E(f862(f862(f3(f932(x42711,a921)),f862(f862(f94(f932(x42711,a921)),x42712),x42713)),f862(f862(f94(f932(x42711,a921)),x42714),x42713)),f862(f862(f3(f932(x42711,a921)),f862(f862(f94(f932(x42711,a921)),x42712),x42713)),x42714)) % 14.79/14.66 [4283]E(f862(f862(f3(f932(x42831,a921)),f862(f862(f3(f932(x42831,a921)),x42832),f862(f862(f301(x42831),x42833),f181(f932(x42831,a921))))),x42834),f862(f862(f3(f932(x42831,a921)),x42832),f862(f862(f301(x42831),x42833),x42834))) % 14.79/14.66 [4336]E(f862(f862(f103(f932(x43361,a921)),f862(f862(f301(x43361),x43362),f862(f862(f301(x43361),x43363),f181(f932(x43361,a921))))),f862(f273(x43361),x43364)),f862(f273(x43361),f862(f862(f301(f931(x43361,x43361)),f862(f862(f244(x43361,x43361),x43362),x43363)),x43364))) % 14.79/14.66 [4361]E(f862(f862(f33(a924,f932(x43611,a921)),f862(f294(a924),x43612)),f862(f862(f10(a924,f932(x43611,a921),a924),x43613),f862(f862(f9(a924,a924,a924),f73(a924)),x43614))),f862(f862(f33(a924,f932(x43611,a921)),f296(a924,x43614,f862(f862(f73(a924),x43612),x43614))),x43613)) % 14.79/14.66 [4362]E(f167(x43621,f862(f276(x43621,x43621,x43622),f862(f862(f301(x43621),x43623),f181(f932(x43621,a921)))),f862(f276(f925(x43621),f925(x43621),f151(x43621,x43622)),f862(f862(f301(f925(x43621)),x43624),f181(f932(f925(x43621),a921))))),f862(f276(f925(x43621),f925(x43621),f151(x43621,x43622)),f862(f862(f301(f925(x43621)),f862(f862(f144(x43621),x43623),x43624)),f181(f932(f925(x43621),a921))))) % 14.79/14.66 [4426]E(f862(f254(x44261),f862(f862(f9(x44261,f932(x44262,a921),a921),f862(f862(f10(x44262,f932(f932(x44262,a921),a921),x44261),f321(x44262)),x44263)),x44264)),f862(f303(x44261,x44262,x44263),x44264)) % 14.79/14.66 [4517]E(f862(f254(x45171),f862(f862(f9(x45171,f932(f931(x45172,x45171),a921),a921),f862(f862(f10(f931(x45172,x45171),f932(f932(f931(x45172,x45171),a921),a921),x45171),f321(f931(x45172,x45171))),f862(f244(x45172,x45171),x45173))),x45174)),f862(f276(x45172,x45171,x45174),f862(f862(f301(x45172),x45173),f181(f932(x45172,a921))))) % 14.79/14.66 [4533]E(f862(f862(f147(f931(x45331,a924),x45331),f243(x45331,a924)),f862(f129(f931(x45331,a924),f862(f862(f10(a924,a921,f931(x45331,a924)),x45332),f862(f862(f10(a924,a924,f931(x45331,a924)),a105),f248(x45331,a924)))),f862(f862(f174(x45331,a924),x45333),x45334))),f862(f862(f147(f931(x45331,a924),x45331),f243(x45331,a924)),f862(f129(f931(x45331,a924),f862(f862(f10(a924,a921,f931(x45331,a924)),x45332),f248(x45331,a924))),f862(f862(f174(x45331,a924),x45333),f862(f862(f147(a924,a924),a105),x45334))))) % 14.79/14.66 [4542]P1(f862(f862(f227(f932(f932(x45421,a921),a921)),f862(f862(f33(x45422,f932(f932(x45421,a921),a921)),x45423),f862(f862(f10(f932(x45421,a921),f932(f932(x45421,a921),a921),x45422),f300(x45421)),x45424))),f862(f300(x45421),f862(f862(f33(x45422,f932(x45421,a921)),x45423),x45424)))) % 14.79/14.66 [4583]E(f862(f862(f79(a1,x45831),f862(f96(a1),f862(f862(f73(a1),x45832),a90))),f862(f862(f20(a1,x45831,x45831),f862(f862(f9(a1,x45831,f932(x45831,x45831)),f862(f862(f10(a921,f932(x45831,f932(x45831,x45831)),a1),f89(x45831)),a186)),x45833)),f862(f862(f20(a1,x45831,x45831),f862(f862(f10(a924,f932(x45831,x45831),a1),x45834),a97)),f862(f862(f10(a924,x45831,a1),f177(x45831,x45833,x45834)),a97)))),f862(f177(x45831,x45833,x45834),f862(f96(a924),x45832))) % 14.79/14.66 [4607]E(f862(f254(f931(x46071,x46072)),f862(f249(x46071,x46072,a921),f862(f862(f9(x46071,f932(x46072,a921),f932(x46072,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x46072,a921),f932(x46072,a921)),x46071),f10(a921,a921,x46072)),f862(f862(f10(a921,f932(a921,a921),x46071),a318),f862(f862(f9(x46071,f932(x46071,a921),a921),f321(x46071)),x46073)))),f862(f862(f9(x46072,f932(x46072,a921),a921),f321(x46072)),x46074)))),f222(x46071,x46072,x46073,x46074)) % 14.79/14.66 [4643]E(f862(f862(f33(x46431,f932(f931(x46431,x46432),a921)),x46433),f862(f862(f20(x46431,f932(x46432,f932(f931(x46431,x46432),a921)),f932(f931(x46431,x46432),a921)),f862(f862(f10(f932(x46432,a921),f932(f932(x46432,f932(f931(x46431,x46432),a921)),f932(f931(x46431,x46432),a921)),x46431),f33(x46432,f932(f931(x46431,x46432),a921))),x46434)),f862(f862(f9(x46431,f932(f931(x46431,x46432),a921),f932(x46432,f932(f931(x46431,x46432),a921))),f862(f862(f10(f932(x46432,f932(f932(f931(x46431,x46432),a921),f932(f931(x46431,x46432),a921))),f932(f932(f931(x46431,x46432),a921),f932(x46432,f932(f931(x46431,x46432),a921))),x46431),f9(x46432,f932(f931(x46431,x46432),a921),f932(f931(x46431,x46432),a921))),f862(f862(f10(f932(x46432,f931(x46431,x46432)),f932(x46432,f932(f932(f931(x46431,x46432),a921),f932(f931(x46431,x46432),a921))),x46431),f862(f10(f931(x46431,x46432),f932(f932(f931(x46431,x46432),a921),f932(f931(x46431,x46432),a921)),x46432),f301(f931(x46431,x46432)))),f244(x46431,x46432)))),f181(f932(f931(x46431,x46432),a921))))),f862(f862(f246(x46431,x46432),x46433),x46434)) % 14.79/14.66 [4207]E(f862(f862(f127(x42071),f862(f862(f168(x42071),x42072),x42073)),f862(f862(f168(x42071),f862(f862(f3(a924),x42072),f862(f182(f925(x42071)),x42073))),x42074)),f862(f862(f168(x42071),x42072),f862(f862(f127(x42071),x42073),x42074))) % 14.79/14.66 [4208]E(f862(f862(f127(x42081),f862(f862(f131(x42081),x42082),x42083)),f862(f862(f131(x42081),f862(f862(f3(a924),x42082),f862(f182(f925(x42081)),x42083))),x42084)),f862(f862(f131(x42081),x42082),f862(f862(f127(x42081),x42083),x42084))) % 14.79/14.66 [4257]E(f862(f862(f73(a924),f862(f862(f74(a924),x42571),x42572)),f862(f862(f73(a924),f862(f862(f74(a924),x42573),x42572)),x42574)),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f73(a924),x42571),x42573)),x42572)),x42574)) % 14.79/14.66 [4402]E(f83(x44021,f862(f862(f9(x44021,x44022,a921),f862(f862(f10(x44022,f932(x44022,a921),x44021),a317),x44023)),x44024)),f862(f86(x44021,x44022,f234(f932(x44021,a921)),x44023),x44024)) % 14.79/14.66 [4451]P1(f862(f862(f227(f932(x44511,a921)),f862(f862(f3(f932(x44511,a921)),f862(f275(x44512,x44511),x44513)),f862(f275(x44512,x44511),x44514))),f862(f275(x44512,x44511),f862(f862(f3(f932(f931(x44512,x44511),a921)),x44513),x44514)))) % 14.79/14.66 [4452]P1(f862(f862(f227(f932(x44521,a921)),f862(f862(f3(f932(x44521,a921)),f862(f256(x44521,x44522),x44523)),f862(f256(x44521,x44522),x44524))),f862(f256(x44521,x44522),f862(f862(f3(f932(f931(x44521,x44522),a921)),x44523),x44524)))) % 14.79/14.66 [4562]E(f862(f862(f73(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x45621),x45622)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x45623),x45624)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f862(f862(f73(a924),x45621),x45623)),f862(f862(f73(a924),x45622),x45624))),f181(f932(f931(a924,a924),a921)))))) % 14.79/14.66 [4602]E(f862(f862(f74(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x46021),x46022)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x46023),x46024)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f862(f862(f73(a924),f862(f862(f74(a924),x46021),x46023)),f862(f862(f74(a924),x46022),x46024))),f862(f862(f73(a924),f862(f862(f74(a924),x46021),x46024)),f862(f862(f74(a924),x46022),x46023)))),f181(f932(f931(a924,a924),a921)))))) % 14.79/14.66 [4623]E(f862(f254(x46231),f862(f862(f10(f932(x46232,a921),a921,x46231),f81(x46232)),f862(f862(f10(f932(x46232,a921),f932(x46232,a921),x46231),f862(f20(x46232,a921,a921),f862(f862(f10(a921,f932(a921,a921),x46232),a322),f862(f862(f9(x46232,f932(x46232,a921),a921),f321(x46232)),x46233)))),f862(f862(f9(x46231,f932(x46232,f932(x46231,a921)),f932(x46232,a921)),f862(f862(f10(f932(f932(x46231,a921),a921),f932(f932(x46232,f932(x46231,a921)),f932(x46232,a921)),x46231),f10(f932(x46231,a921),a921,x46232)),f321(x46231))),x46234)))),f862(f862(f32(x46232,f932(x46231,a921)),x46233),x46234)) % 14.79/14.66 [4655]E(f862(f862(f280(x46551,x46551,x46551),f862(f862(f301(f931(x46551,x46551)),f862(f862(f244(x46551,x46551),x46552),x46553)),x46554)),f299(x46551,f862(f862(f301(f931(x46551,x46551)),f862(f862(f244(x46551,x46551),x46552),x46553)),x46554))),f862(f862(f103(f932(f931(x46551,x46551),a921)),f862(f862(f280(x46551,x46551,x46551),x46554),f299(x46551,x46554))),f862(f254(f931(x46551,x46551)),f862(f249(x46551,x46551,a921),f862(f862(f9(x46551,f932(x46551,a921),f932(x46551,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x46551,a921),f932(x46551,a921)),x46551),f10(a921,a921,x46551)),f862(f862(f10(a921,f932(a921,a921),x46551),a318),f862(f862(f9(x46551,f932(f931(x46551,x46551),a921),a921),f862(f862(f10(f931(x46551,x46551),f932(f932(f931(x46551,x46551),a921),a921),x46551),f321(f931(x46551,x46551))),f862(f862(f9(x46551,x46551,f931(x46551,x46551)),f244(x46551,x46551)),x46552))),f299(x46551,x46554))))),f862(f862(f9(x46551,f932(f931(x46551,x46551),a921),a921),f862(f862(f10(f931(x46551,x46551),f932(f932(f931(x46551,x46551),a921),a921),x46551),f321(f931(x46551,x46551))),f862(f244(x46551,x46551),x46553))),f299(x46551,x46554))))))) % 14.79/14.66 [4453]E(f862(f129(x44531,f862(f862(f20(x44531,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44531),a318),x44532)),x44533)),x44534),f862(f129(x44531,x44533),f862(f129(x44531,x44532),x44534))) % 14.79/14.66 [4556]E(f862(f862(f127(x45561),f862(f862(f862(f89(f925(x45561)),f862(f862(f321(a924),f2(a924)),x45562)),f862(f862(f144(x45561),x45563),f106(x45561))),f106(x45561))),f169(x45561,x45564,f862(f254(a924),f862(f862(f9(a924,f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),a924),f321(a924)),a105)),x45562)))),f169(x45561,f862(f862(f144(x45561),x45563),x45564),x45562)) % 14.79/14.66 [4651]E(f862(f254(f931(x46511,x46512)),f862(f862(f10(f932(a924,a921),a921,f931(x46511,x46512)),f80(a924)),f862(f862(f9(f931(x46511,x46512),f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),f931(x46511,x46512)),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),f931(x46511,x46512)),f862(f10(a921,f932(a921,a921),a924),a318)),f862(f862(f9(f931(x46511,x46512),f932(a924,f931(x46511,x46512)),f932(a924,a921)),f862(f862(f10(f932(f931(x46511,x46512),a921),f932(f932(a924,f931(x46511,x46512)),f932(a924,a921)),f931(x46511,x46512)),f10(f931(x46511,x46512),a921,a924)),a317)),f862(f862(f20(a924,x46512,f931(x46511,x46512)),f862(f862(f10(x46511,f932(x46512,f931(x46511,x46512)),a924),f244(x46511,x46512)),f862(f157(x46511),x46513))),f862(f157(x46512),x46514)))))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f862(f225(a924),f862(f182(f925(x46511)),x46513)),f862(f182(f925(x46512)),x46514)))))),f862(f165(f931(x46511,x46512)),f862(f862(f174(x46511,x46512),x46513),x46514))) % 14.79/14.66 [4575]E(f862(f254(f931(x45751,x45752)),f862(f249(x45751,x45752,a921),f862(f862(f9(x45751,f932(x45752,a921),f932(x45752,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x45752,a921),f932(x45752,a921)),x45751),f10(a921,a921,x45752)),f862(f862(f10(a921,f932(a921,a921),x45751),a318),x45753))),x45754))),f862(f862(f246(x45751,x45752),f862(f254(x45751),x45753)),f862(f18(f932(x45752,a921),x45751),f862(f254(x45752),x45754)))) % 14.79/14.66 [4578]E(f862(f254(f931(x45781,x45782)),f862(f249(x45781,x45782,a921),f862(f862(f20(x45781,f932(x45782,a921),f932(x45782,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x45782,a921),f932(x45782,a921)),x45781),f10(a921,a921,x45782)),f862(f862(f10(a921,f932(a921,a921),x45781),a318),x45783))),x45784))),f862(f862(f246(x45781,x45782),f862(f254(x45781),x45783)),f862(f862(f10(f932(x45782,a921),f932(x45782,a921),x45781),f254(x45782)),x45784))) % 14.79/14.66 [4590]E(f862(f254(x45901),f862(f862(f10(f932(x45902,a921),a921,x45901),f81(x45902)),f862(f862(f10(f932(x45902,a921),f932(x45902,a921),x45901),f862(f20(x45902,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45902),a322),f862(f862(f9(x45902,f932(x45902,a921),a921),f321(x45902)),x45903)))),x45904))),f862(f862(f32(x45902,f932(x45901,a921)),x45903),f862(f862(f10(f932(x45901,a921),f932(x45901,a921),x45902),f254(x45901)),f862(f9(x45901,x45902,a921),x45904)))) % 14.79/14.66 [4635]E(f862(f862(f147(f931(x46351,a924),x46351),f243(x46351,a924)),f862(f129(f931(x46351,a924),f862(f862(f9(f931(x46351,a924),f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),f931(x46351,a924)),f321(a924)),f248(x46351,a924))),x46352)),f862(f862(f174(x46351,a924),x46353),f132(a924,f862(f295(a924,x46354),f862(f862(f73(a924),x46354),f862(f182(f925(x46351)),x46353))))))),f862(f862(f147(f931(x46351,a924),x46351),f243(x46351,a924)),f862(f129(f931(x46351,a924),f862(f862(f9(f931(x46351,a924),f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),f931(x46351,a924)),f321(a924)),f862(f862(f9(f931(x46351,a924),a924,a924),f862(f862(f10(a924,f932(a924,a924),f931(x46351,a924)),f73(a924)),f248(x46351,a924))),x46354))),x46352)),f862(f862(f174(x46351,a924),x46353),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(x46351)),x46353))))))) % 14.79/14.66 [4636]E(f862(a105,f862(f862(f226(a924),f862(f182(f925(x46361)),x46362)),f862(f135(a924,f925(x46363),f862(f9(f925(x46363),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x46363)),f226(a924)),f862(f862(f9(f925(x46363),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x46363)),f3(a924)),f182(f925(x46363)))),f862(a105,f2(a924))))),f2(a924)),f862(f161(f925(x46363)),f862(f129(f925(x46363),f862(f862(f10(a921,a921,f925(x46363)),a314),f862(f862(f9(f925(x46363),f925(x46363),a921),a317),f106(x46363)))),x46364))))),f862(f862(f226(a924),f862(a105,f862(f182(f925(x46361)),x46362))),f862(f135(a924,f925(x46363),f862(f9(f925(x46363),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x46363)),f226(a924)),f182(f925(x46363)))),f2(a924)),f862(f161(f925(x46363)),x46364)))) % 14.79/14.66 [4589]E(f862(f862(f127(x45891),f169(x45891,x45892,x45893)),f169(x45891,x45894,f862(f254(a924),f862(f862(f9(a924,f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),a924),f321(a924)),f862(f862(f9(a924,a924,a924),f73(a924)),f862(f182(f925(x45891)),x45892)))),x45893)))),f169(x45891,f862(f862(f127(x45891),x45892),x45894),x45893)) % 14.79/14.66 [4637]E(f31(f932(x46371,a921),f862(f254(f932(x46371,a921)),f862(f862(f10(f932(x46372,a921),a921,f932(x46371,a921)),f80(x46372)),f862(f862(f10(f932(x46372,a921),f932(x46372,a921),f932(x46371,a921)),f862(f20(x46372,a921,a921),f862(f862(f10(a921,f932(a921,a921),x46372),a318),f862(f862(f9(x46372,f932(x46372,a921),a921),f321(x46372)),x46373)))),f862(f862(f9(f932(x46371,a921),f932(x46372,f932(x46371,a921)),f932(x46372,a921)),f862(f862(f10(f932(f932(x46371,a921),a921),f932(f932(x46372,f932(x46371,a921)),f932(x46372,a921)),f932(x46371,a921)),f10(f932(x46371,a921),a921,x46372)),a317)),x46374))))),f862(f862(f32(x46372,f932(x46371,a921)),x46373),x46374)) % 14.79/14.66 [4638]E(f30(f932(x46381,a921),f862(f254(f932(x46381,a921)),f862(f862(f10(f932(x46382,a921),a921,f932(x46381,a921)),f80(x46382)),f862(f862(f10(f932(x46382,a921),f932(x46382,a921),f932(x46381,a921)),f862(f20(x46382,a921,a921),f862(f862(f10(a921,f932(a921,a921),x46382),a318),f862(f862(f9(x46382,f932(x46382,a921),a921),f321(x46382)),x46383)))),f862(f862(f9(f932(x46381,a921),f932(x46382,f932(x46381,a921)),f932(x46382,a921)),f862(f862(f10(f932(f932(x46381,a921),a921),f932(f932(x46382,f932(x46381,a921)),f932(x46382,a921)),f932(x46381,a921)),f10(f932(x46381,a921),a921,x46382)),a317)),x46384))))),f862(f862(f33(x46382,f932(x46381,a921)),x46383),x46384)) % 14.79/14.66 [4645]E(f862(f862(f144(f925(x46451)),f862(f862(f144(x46451),x46452),f862(f135(f925(x46451),f925(x46451),f127(x46451),f106(x46451)),f862(f862(f147(f925(x46451),f925(x46451)),f149(f925(x46451),x46451,f106(x46451),f862(f862(f10(f925(x46451),f932(f925(x46451),f925(x46451)),x46451),f18(f925(x46451),f925(x46451))),f862(f862(f9(x46451,f925(x46451),f925(x46451)),f144(x46451)),f106(x46451))))),x46453)))),f172(x46451,f862(f862(f144(f925(x46451)),x46454),f862(f135(f925(f925(x46451)),f925(f925(x46451)),f127(f925(x46451)),f106(f925(x46451))),f862(f862(f147(f925(x46451),f925(f925(x46451))),f149(f925(f925(x46451)),x46451,f106(f925(x46451)),f862(f18(f932(f925(x46451),f925(f925(x46451))),x46451),f862(f862(f9(f925(x46451),f925(f925(x46451)),f925(f925(x46451))),f144(f925(x46451))),f106(f925(x46451)))))),x46453))))),f172(x46451,f862(f862(f144(f925(x46451)),f862(f862(f144(x46451),x46452),x46454)),x46453))) % 14.79/14.66 [4652]E(f862(f254(f931(x46521,x46521)),f862(f249(x46521,x46521,a921),f862(f862(f9(x46521,f932(f931(x46522,x46522),a921),f932(x46521,a921)),f862(f862(f10(f932(x46521,f932(f932(f931(x46522,x46522),a921),a921)),f932(f932(f931(x46522,x46522),a921),f932(x46521,a921)),x46521),f9(x46521,f932(f931(x46522,x46522),a921),a921)),f862(f862(f10(f932(x46521,f931(x46522,x46522)),f932(x46521,f932(f932(f931(x46522,x46522),a921),a921)),x46521),f862(f10(f931(x46522,x46522),f932(f932(f931(x46522,x46522),a921),a921),x46521),f321(f931(x46522,x46522)))),f862(f862(f9(x46521,f932(x46521,x46522),f932(x46521,f931(x46522,x46522))),f862(f862(f10(f932(x46522,f931(x46522,x46522)),f932(f932(x46521,x46522),f932(x46521,f931(x46522,x46522))),x46521),f10(x46522,f931(x46522,x46522),x46521)),f862(f862(f10(x46522,f932(x46522,f931(x46522,x46522)),x46521),f244(x46522,x46522)),x46523))),x46523)))),x46524))),f862(f862(f279(x46522,x46521),x46524),x46523)) % 14.79/14.66 [3792]E(f862(f862(f147(x37921,x37922),x37923),f162(x37921,x37924,x37925)),f162(x37922,x37924,f862(x37923,x37925))) % 14.79/14.66 [4121]E(f123(x41211,x41212,x41213,f119(x41211,x41214,x41215)),f119(x41212,f862(x41213,x41214),f123(x41211,x41212,x41213,x41215))) % 14.79/14.66 [4351]E(f862(f68(x43511,x43512,x43513,x43514,x43515),x43514),x43515) % 14.79/14.66 [4403]E(f245(x44031,x44032,x44033,f235(x44032,x44031,x44034),f235(x44033,x44032,x44035)),f235(x44033,x44031,f245(x44033,x44032,x44031,x44035,x44034))) % 14.79/14.66 [3982]E(f862(f862(f249(x39821,x39822,x39823),x39824),x39825),f862(f862(x39824,f862(f243(x39821,x39822),x39825)),f862(f248(x39821,x39822),x39825))) % 14.79/14.66 [4016]E(f862(f862(f862(f58(x40161,x40162,x40163),x40164),x40165),f181(f932(x40162,a921))),x40165) % 14.79/14.66 [4291]E(f862(f66(f925(x42911),f925(x42912),f925(x42913),f862(f147(x42911,x42912),x42914)),f862(f147(x42913,x42911),x42915)),f862(f147(x42913,x42912),f862(f66(x42911,x42912,x42913,x42914),x42915))) % 14.79/14.66 [4365]E(f78(x43651,f59(x43652,x43651,x43653,x43654,x43655)),f862(f862(f57(x43652,x43651,x43653),x43654),x43655)) % 14.79/14.66 [4399]E(f862(f862(f73(a924),f862(f862(f73(a924),f862(x43991,f862(f243(x43992,x43993),x43994))),f862(x43995,f862(f248(x43992,x43993),x43994)))),f862(a105,f2(a924))),f253(x43992,x43993,x43991,x43995,x43994)) % 14.79/14.66 [3919]E(f862(f862(f168(x39191),x39192),f862(f862(f147(x39193,x39191),x39194),x39195)),f862(f862(f147(x39193,x39191),x39194),f862(f862(f168(x39193),x39192),x39195))) % 14.79/14.66 [3920]E(f862(f862(f131(x39201),x39202),f862(f862(f147(x39203,x39201),x39204),x39205)),f862(f862(f147(x39203,x39201),x39204),f862(f862(f131(x39203),x39202),x39205))) % 14.79/14.66 [3951]E(f862(f862(f147(x39511,x39512),x39513),f862(f862(f144(x39511),x39514),x39515)),f862(f862(f144(x39512),f862(x39513,x39514)),f862(f862(f147(x39511,x39512),x39513),x39515))) % 14.79/14.66 [4012]E(f862(f302(x40121,x40122,x40123),f862(f862(f301(x40121),x40124),x40125)),f862(f862(f301(x40122),f862(x40123,x40124)),f862(f302(x40121,x40122,x40123),x40125))) % 14.79/14.66 [4040]E(f166(x40401,f862(f862(f144(x40401),x40402),x40403),f862(f862(f144(x40401),x40404),x40405)),f862(f862(f144(x40401),x40402),f862(f862(f144(x40401),x40404),f166(x40401,x40403,x40405)))) % 14.79/14.66 [4076]E(f862(f862(f174(x40761,x40762),f862(f862(f168(x40761),x40763),x40764)),f862(f862(f168(x40762),x40763),x40765)),f862(f862(f168(f931(x40761,x40762)),x40763),f862(f862(f174(x40761,x40762),x40764),x40765))) % 14.79/14.66 [4077]E(f862(f862(f174(x40771,x40772),f862(f862(f131(x40771),x40773),x40774)),f862(f862(f131(x40772),x40773),x40775)),f862(f862(f131(f931(x40771,x40772)),x40773),f862(f862(f174(x40771,x40772),x40774),x40775))) % 14.79/14.66 [4086]E(f862(f862(f152(x40861,f862(f862(f144(x40861),x40862),x40863)),f862(a105,x40864)),x40865),f862(f862(f144(x40861),x40862),f862(f862(f152(x40861,x40863),x40864),x40865))) % 14.79/14.66 [4089]E(f862(f862(f127(x40891),f862(f862(f147(x40892,x40891),x40893),x40894)),f862(f862(f147(x40892,x40891),x40893),x40895)),f862(f862(f147(x40892,x40891),x40893),f862(f862(f127(x40892),x40894),x40895))) % 14.79/14.66 [4093]E(f862(f862(x40931,x40932),f862(f862(f237(x40933,x40934,x40931),x40932),x40935)),f862(f862(f237(x40933,x40934,x40931),x40932),f862(a105,x40935))) % 14.79/14.66 [4125]E(f156(x41251,x41252,x41253,f862(f862(f144(x41251),x41254),x41255)),f862(f862(f127(x41252),f862(x41253,x41254)),f156(x41251,x41252,x41253,x41255))) % 14.79/14.66 [4137]E(f862(f862(f280(x41371,x41372,x41373),f862(f277(x41372,x41371),x41374)),f862(f277(x41373,x41372),x41375)),f862(f277(x41373,x41371),f862(f862(f280(x41373,x41372,x41371),x41375),x41374))) % 14.79/14.66 [4169]E(f862(f862(f862(f176(f925(x41691),f925(x41691)),x41692),f160(x41691)),f862(f862(f147(x41693,x41691),x41694),x41695)),f862(f862(f147(x41693,x41691),x41694),f862(f862(f862(f176(f925(x41693),f925(x41693)),x41692),f160(x41693)),x41695))) % 14.79/14.66 [4170]E(f862(f862(f251(x41701,x41702,x41701,x41703),f862(f244(x41702,x41701),x41704)),x41705),f862(x41705,x41704)) % 14.79/14.66 [4193]E(f148(x41931,x41932,f862(f862(f147(x41933,x41931),x41934),x41935)),f148(x41933,f862(f66(x41931,a924,x41933,x41932),x41934),x41935)) % 14.79/14.66 [4256]E(f170(f931(x42561,x42562),f862(f66(x42562,a921,f931(x42561,x42562),x42563),f248(x42561,x42562)),f862(f862(f174(x42561,x42562),x42564),x42565)),f862(f862(f174(x42561,x42562),x42564),f170(x42562,x42563,x42565))) % 14.79/14.66 [4261]E(f862(f302(x42611,x42612,f862(f862(f10(x42613,x42612,x42611),x42614),x42615)),f234(f932(x42611,a921))),f862(f302(x42613,x42612,x42614),f862(f302(x42611,x42613,x42615),f234(f932(x42611,a921))))) % 14.79/14.66 [4274]E(f170(f931(x42741,x42742),f862(f66(x42741,a921,f931(x42741,x42742),x42743),f243(x42741,x42742)),f862(f862(f174(x42741,x42742),x42744),x42745)),f862(f862(f174(x42741,x42742),f170(x42741,x42743,x42744)),x42745)) % 14.79/14.66 [4295]E(f862(f862(f103(f932(x42951,a921)),f862(f303(x42951,x42952,x42953),f862(f862(f301(x42952),x42954),f181(f932(x42952,a921))))),f862(f303(x42951,x42952,x42953),x42955)),f862(f303(x42951,x42952,x42953),f862(f862(f301(x42952),x42954),x42955))) % 14.79/14.66 [4350]E(f862(f862(f127(f931(x43501,x43502)),f862(f862(f147(x43502,f931(x43501,x43502)),f862(f244(x43501,x43502),x43503)),x43504)),f52(x43501,x43502,x43505,x43504)),f52(x43501,x43502,f862(f862(f144(x43501),x43503),x43505),x43504)) % 14.79/14.66 [4352]E(f862(f862(f147(x43521,x43522),x43523),f170(x43521,f862(f66(x43522,a921,x43521,x43524),x43523),x43525)),f170(x43522,x43524,f862(f862(f147(x43521,x43522),x43523),x43525))) % 14.79/14.66 [4357]E(f862(f135(x43571,x43572,f862(f9(x43572,x43571,x43571),f862(f9(x43571,x43572,x43571),x43573)),x43574),f862(f161(x43572),f862(f161(x43572),x43575))),f862(f135(x43571,x43572,x43573,x43574),x43575)) % 14.79/14.66 [4461]P1(f862(f862(f227(f932(x44611,a921)),f862(f302(x44612,x44611,x44613),f862(f862(f94(f932(x44612,a921)),x44614),x44615))),f862(f862(f94(f932(x44611,a921)),f862(f302(x44612,x44611,x44613),x44614)),f862(f302(x44612,x44611,x44613),x44615)))) % 14.79/14.66 [4462]P1(f862(f862(f227(f932(x44621,a921)),f862(f276(x44622,x44621,x44623),f862(f862(f94(f932(x44622,a921)),x44624),x44625))),f862(f862(f94(f932(x44621,a921)),f862(f276(x44622,x44621,x44623),x44624)),f862(f276(x44622,x44621,x44623),x44625)))) % 14.79/14.66 [4563]E(f862(f248(x45631,x45632),f862(f250(x45633,x45631,x45632,x45632,x45634,f25(x45632)),x45635)),f862(f248(x45633,x45632),x45635)) % 14.79/14.66 [4564]E(f862(f243(x45641,x45642),f862(f250(x45641,x45641,x45643,x45642,f25(x45641),x45644),x45645)),f862(f243(x45641,x45643),x45645)) % 14.79/14.66 [3764]E(f862(f862(f862(f862(f197(x37641),x37642),x37643),x37644),x37645),f185(x37641,x37642)) % 14.79/14.66 [3765]E(f862(f862(f862(f862(f201(x37651),x37652),x37653),x37654),x37655),f192(x37651,x37652)) % 14.79/14.66 [4126]E(f862(f862(f32(x41261,f932(x41262,a921)),f862(f862(f301(x41261),x41263),x41264)),x41265),f862(f862(f94(f932(x41262,a921)),f862(x41265,x41263)),f862(f862(f32(x41261,f932(x41262,a921)),x41264),x41265))) % 14.79/14.66 [4127]E(f862(f862(f33(x41271,f932(x41272,a921)),f862(f862(f301(x41271),x41273),x41274)),x41275),f862(f862(f103(f932(x41272,a921)),f862(x41275,x41273)),f862(f862(f33(x41271,f932(x41272,a921)),x41274),x41275))) % 14.79/14.66 [4177]E(f862(f111(x41771,x41772,f862(x41773,x41774)),f862(f862(f9(x41771,a92,f926(x41772)),x41775),x41774)),f862(f190(x41771,x41772,x41773,x41775),x41774)) % 14.79/14.66 [4187]E(f862(f862(f103(f932(x41871,a921)),f862(f302(x41872,x41871,x41873),x41874)),f862(f302(x41872,x41871,x41873),x41875)),f862(f302(x41872,x41871,x41873),f862(f862(f103(f932(x41872,a921)),x41874),x41875))) % 14.79/14.66 [4188]E(f862(f862(f103(f932(x41881,a921)),f862(f276(x41882,x41881,x41883),x41884)),f862(f276(x41882,x41881,x41883),x41885)),f862(f276(x41882,x41881,x41883),f862(f862(f103(f932(x41882,a921)),x41884),x41885))) % 14.79/14.66 [4189]E(f862(f862(f103(f932(x41891,a921)),f862(f303(x41891,x41892,x41893),x41894)),f862(f303(x41891,x41892,x41893),x41895)),f862(f303(x41891,x41892,x41893),f862(f862(f103(f932(x41892,a921)),x41894),x41895))) % 14.79/14.66 [4190]E(f862(f862(f94(f932(x41901,a921)),f862(f303(x41901,x41902,x41903),x41904)),f862(f303(x41901,x41902,x41903),x41905)),f862(f303(x41901,x41902,x41903),f862(f862(f94(f932(x41902,a921)),x41904),x41905))) % 14.79/14.66 [4191]E(f862(f862(f3(f932(x41911,a921)),f862(f303(x41911,x41912,x41913),x41914)),f862(f303(x41911,x41912,x41913),x41915)),f862(f303(x41911,x41912,x41913),f862(f862(f3(f932(x41912,a921)),x41914),x41915))) % 14.79/14.66 [4252]E(f862(f862(f152(x42521,f862(f862(f127(x42521),x42522),f862(f862(f144(x42521),x42523),x42524))),f862(f182(f925(x42521)),x42522)),x42525),f862(f862(f127(x42521),x42522),f862(f862(f144(x42521),x42525),x42524))) % 14.79/14.66 [4259]E(f862(f862(f32(x42591,f932(x42592,a921)),x42593),f862(f862(f10(f932(x42592,a921),f932(x42592,a921),x42591),f862(f301(x42592),x42594)),x42595)),f862(f862(f301(x42592),x42594),f862(f862(f32(x42591,f932(x42592,a921)),x42593),x42595))) % 14.79/14.66 [4412]E(f862(f862(f147(x44121,x44122),x44123),f862(f129(x44121,f862(f66(x44122,a921,x44121,x44124),x44123)),x44125)),f862(f129(x44122,x44124),f862(f862(f147(x44121,x44122),x44123),x44125))) % 14.79/14.66 [4418]E(f862(f182(f925(x44181)),f862(f129(x44181,x44182),f862(f862(f147(x44183,x44181),x44184),x44185))),f862(f182(f925(x44183)),f862(f129(x44183,f862(f66(x44181,a921,x44183,x44182),x44184)),x44185))) % 14.79/14.66 [4628]E(f862(f149(f925(f931(x46281,x46282)),x46282,f106(f931(x46281,x46282)),f862(f862(f9(x46282,f932(f925(x46282),f925(f931(x46281,x46282))),f932(f925(x46282),f925(f931(x46281,x46282)))),f862(f862(f10(f932(f925(f931(x46281,x46282)),f925(f931(x46281,x46282))),f932(f932(f925(x46282),f925(f931(x46281,x46282))),f932(f925(x46282),f925(f931(x46281,x46282)))),x46282),f10(f925(f931(x46281,x46282)),f925(f931(x46281,x46282)),f925(x46282))),f862(f862(f10(f931(x46281,x46282),f932(f925(f931(x46281,x46282)),f925(f931(x46281,x46282))),x46282),f144(f931(x46281,x46282))),f862(f244(x46281,x46282),x46283)))),f862(f174(x46281,x46282),x46284))),x46285),f862(f862(f174(x46281,x46282),f862(f862(f144(x46281),x46283),x46284)),x46285)) % 14.79/14.66 [4118]E(f862(f862(f152(x41181,f862(f862(f152(x41181,x41182),x41183),x41184)),x41183),x41185),f862(f862(f152(x41181,x41182),x41183),x41185)) % 14.79/14.66 [4171]E(f862(f275(x41711,x41712),f862(f862(f301(f931(x41711,x41712)),f862(f862(f244(x41711,x41712),x41713),x41714)),x41715)),f862(f862(f301(x41712),x41714),f862(f275(x41711,x41712),x41715))) % 14.79/14.66 [4172]E(f862(f256(x41721,x41722),f862(f862(f301(f931(x41721,x41722)),f862(f862(f244(x41721,x41722),x41723),x41724)),x41725)),f862(f862(f301(x41721),x41723),f862(f256(x41721,x41722),x41725))) % 14.79/14.66 [4217]E(f115(x42171,x42172,f862(x42173,x42174),f862(f862(f9(x42171,a92,f926(f928(x42172))),x42175),x42174)),f862(f188(x42171,x42172,x42173,x42175),x42174)) % 14.79/14.66 [4245]E(f862(f862(f103(f932(f931(x42451,x42452),a921)),f862(f862(f246(x42451,x42452),x42453),x42454)),f862(f862(f246(x42451,x42452),x42455),x42454)),f862(f862(f246(x42451,x42452),f862(f862(f103(f932(x42451,a921)),x42453),x42455)),x42454)) % 14.79/14.66 [4246]E(f862(f862(f94(f932(f931(x42461,x42462),a921)),f862(f862(f246(x42461,x42462),x42463),x42464)),f862(f862(f246(x42461,x42462),x42465),x42464)),f862(f862(f246(x42461,x42462),f862(f862(f94(f932(x42461,a921)),x42463),x42465)),x42464)) % 14.79/14.66 [4247]E(f862(f862(f3(f932(f931(x42471,x42472),a921)),f862(f862(f246(x42471,x42472),x42473),x42474)),f862(f862(f246(x42471,x42472),x42475),x42474)),f862(f862(f246(x42471,x42472),f862(f862(f3(f932(x42471,a921)),x42473),x42475)),x42474)) % 14.79/14.66 [4306]E(f862(f862(f94(f932(x43061,a921)),f862(f862(f32(x43062,f932(x43061,a921)),x43063),x43064)),f862(f862(f32(x43062,f932(x43061,a921)),x43065),x43064)),f862(f862(f32(x43062,f932(x43061,a921)),f862(f862(f103(f932(x43062,a921)),x43063),x43065)),x43064)) % 14.79/14.66 [4307]E(f862(f862(f103(f932(x43071,a921)),f862(f862(f33(x43072,f932(x43071,a921)),x43073),x43074)),f862(f862(f33(x43072,f932(x43071,a921)),x43075),x43074)),f862(f862(f33(x43072,f932(x43071,a921)),f862(f862(f103(f932(x43072,a921)),x43073),x43075)),x43074)) % 14.79/14.66 [4321]E(f862(f862(f32(x43211,f932(x43212,a921)),x43213),f862(f862(f10(f932(x43212,a921),f932(x43212,a921),x43211),f862(f103(f932(x43212,a921)),x43214)),x43215)),f862(f862(f103(f932(x43212,a921)),x43214),f862(f862(f32(x43211,f932(x43212,a921)),x43213),x43215))) % 14.79/14.66 [4322]E(f862(f862(f33(x43221,f932(x43222,a921)),x43223),f862(f862(f10(f932(x43222,a921),f932(x43222,a921),x43221),f862(f94(f932(x43222,a921)),x43224)),x43225)),f862(f862(f94(f932(x43222,a921)),x43224),f862(f862(f33(x43221,f932(x43222,a921)),x43223),x43225))) % 14.98/14.66 [4323]E(f862(f862(f33(x43231,f932(x43232,a921)),x43233),f862(f862(f10(f932(x43232,a921),f932(x43232,a921),x43231),f862(f3(f932(x43232,a921)),x43234)),x43235)),f862(f862(f3(f932(x43232,a921)),x43234),f862(f862(f32(x43231,f932(x43232,a921)),x43233),x43235))) % 14.98/14.66 [4377]E(f178(f925(x43771),f862(f862(f144(x43771),x43772),x43773),f862(f862(f10(f925(x43771),f925(x43771),a924),f862(f144(x43771),x43774)),f862(f862(f9(a924,x43771,f925(x43771)),f152(x43771,x43773)),x43772)),x43775),f862(f862(f152(x43771,f862(f862(f144(x43771),x43774),x43773)),x43775),x43772)) % 14.98/14.66 [4381]E(f862(f862(f32(x43811,f932(f931(x43812,x43813),a921)),x43814),f862(f862(f10(f932(f931(x43813,x43812),a921),f932(f931(x43812,x43813),a921),x43811),f277(x43813,x43812)),x43815)),f862(f277(x43813,x43812),f862(f862(f32(x43811,f932(f931(x43813,x43812),a921)),x43814),x43815))) % 14.98/14.66 [4382]E(f862(f862(f33(x43821,f932(f931(x43822,x43823),a921)),x43824),f862(f862(f10(f932(f931(x43823,x43822),a921),f932(f931(x43822,x43823),a921),x43821),f277(x43823,x43822)),x43825)),f862(f277(x43823,x43822),f862(f862(f33(x43821,f932(f931(x43823,x43822),a921)),x43824),x43825))) % 14.98/14.66 [4484]P1(f862(f862(f227(f932(x44841,a921)),f862(f862(f3(f932(x44841,a921)),f862(f302(x44842,x44841,x44843),x44844)),f862(f302(x44842,x44841,x44843),x44845))),f862(f302(x44842,x44841,x44843),f862(f862(f3(f932(x44842,a921)),x44844),x44845)))) % 14.98/14.66 [4631]E(f862(f149(f925(f931(x46311,x46312)),x46311,f106(f931(x46311,x46312)),f862(f862(f9(x46311,f932(f925(x46311),f925(f931(x46311,x46312))),f932(f925(x46311),f925(f931(x46311,x46312)))),f862(f862(f10(f932(f925(f931(x46311,x46312)),f925(f931(x46311,x46312))),f932(f932(f925(x46311),f925(f931(x46311,x46312))),f932(f925(x46311),f925(f931(x46311,x46312)))),x46311),f10(f925(f931(x46311,x46312)),f925(f931(x46311,x46312)),f925(x46311))),f862(f862(f10(f931(x46311,x46312),f932(f925(f931(x46311,x46312)),f925(f931(x46311,x46312))),x46311),f144(f931(x46311,x46312))),f862(f862(f9(x46311,x46312,f931(x46311,x46312)),f244(x46311,x46312)),x46313)))),f862(f862(f9(f925(x46311),f925(x46312),f925(f931(x46311,x46312))),f174(x46311,x46312)),x46314))),x46315),f862(f862(f174(x46311,x46312),x46315),f862(f862(f144(x46312),x46313),x46314))) % 14.98/14.66 [4346]E(f862(f862(f103(f932(x43461,a921)),f862(f276(x43462,x43461,x43463),x43464)),f862(f276(x43462,x43461,x43465),x43464)),f862(f276(x43462,x43461,f862(f862(f103(f932(f931(x43462,x43461),a921)),x43463),x43465)),x43464)) % 14.98/14.66 [4383]E(f862(f862(f127(f931(x43831,x43832)),f862(f862(f174(x43831,x43832),x43833),f862(f862(f168(x43832),f862(f182(f925(x43831)),x43833)),x43834))),f862(f862(f174(x43831,x43832),x43835),f862(f862(f131(x43832),f862(f182(f925(x43831)),x43833)),x43834))),f862(f862(f174(x43831,x43832),f862(f862(f127(x43831),x43833),x43835)),x43834)) % 14.98/14.66 [4487]E(f862(f862(f246(x44871,x44872),x44873),f862(f862(f20(x44871,f932(x44872,a921),f932(x44872,a921)),f862(f862(f10(f932(x44872,a921),f932(f932(x44872,a921),f932(x44872,a921)),x44871),f103(f932(x44872,a921))),x44874)),x44875)),f862(f862(f103(f932(f931(x44871,x44872),a921)),f862(f862(f246(x44871,x44872),x44873),x44874)),f862(f862(f246(x44871,x44872),x44873),x44875))) % 14.98/14.66 [4488]E(f862(f862(f246(x44881,x44882),x44883),f862(f862(f20(x44881,f932(x44882,a921),f932(x44882,a921)),f862(f862(f10(f932(x44882,a921),f932(f932(x44882,a921),f932(x44882,a921)),x44881),f94(f932(x44882,a921))),x44884)),x44885)),f862(f862(f94(f932(f931(x44881,x44882),a921)),f862(f862(f246(x44881,x44882),x44883),x44884)),f862(f862(f246(x44881,x44882),x44883),x44885))) % 14.98/14.66 [4489]E(f862(f862(f246(x44891,x44892),x44893),f862(f862(f20(x44891,f932(x44892,a921),f932(x44892,a921)),f862(f862(f10(f932(x44892,a921),f932(f932(x44892,a921),f932(x44892,a921)),x44891),f3(f932(x44892,a921))),x44894)),x44895)),f862(f862(f3(f932(f931(x44891,x44892),a921)),f862(f862(f246(x44891,x44892),x44893),x44894)),f862(f862(f246(x44891,x44892),x44893),x44895))) % 14.98/14.66 [4493]E(f862(f862(f32(x44931,f932(x44932,a921)),x44933),f862(f862(f9(x44931,f932(x44932,a921),f932(x44932,a921)),f862(f862(f10(f932(x44932,a921),f932(f932(x44932,a921),f932(x44932,a921)),x44931),f103(f932(x44932,a921))),x44934)),x44935)),f862(f862(f103(f932(x44932,a921)),f862(f862(f32(x44931,f932(x44932,a921)),x44933),x44934)),x44935)) % 14.98/14.66 [4494]E(f862(f862(f33(x44941,f932(x44942,a921)),x44943),f862(f862(f9(x44941,f932(x44942,a921),f932(x44942,a921)),f862(f862(f10(f932(x44942,a921),f932(f932(x44942,a921),f932(x44942,a921)),x44941),f94(f932(x44942,a921))),x44944)),x44945)),f862(f862(f94(f932(x44942,a921)),f862(f862(f33(x44941,f932(x44942,a921)),x44943),x44944)),x44945)) % 14.98/14.66 [4495]E(f862(f862(f33(x44951,f932(x44952,a921)),x44953),f862(f862(f9(x44951,f932(x44952,a921),f932(x44952,a921)),f862(f862(f10(f932(x44952,a921),f932(f932(x44952,a921),f932(x44952,a921)),x44951),f3(f932(x44952,a921))),x44954)),x44955)),f862(f862(f3(f932(x44952,a921)),f862(f862(f33(x44951,f932(x44952,a921)),x44953),x44954)),x44955)) % 14.98/14.66 [4499]E(f862(f862(f32(x44991,f932(x44992,a921)),x44993),f862(f862(f20(x44991,f932(x44992,a921),f932(x44992,a921)),f862(f862(f10(f932(x44992,a921),f932(f932(x44992,a921),f932(x44992,a921)),x44991),f94(f932(x44992,a921))),x44994)),x44995)),f862(f862(f94(f932(x44992,a921)),f862(f862(f32(x44991,f932(x44992,a921)),x44993),x44994)),f862(f862(f32(x44991,f932(x44992,a921)),x44993),x44995))) % 14.98/14.66 [4500]E(f862(f862(f33(x45001,f932(x45002,a921)),x45003),f862(f862(f20(x45001,f932(x45002,a921),f932(x45002,a921)),f862(f862(f10(f932(x45002,a921),f932(f932(x45002,a921),f932(x45002,a921)),x45001),f103(f932(x45002,a921))),x45004)),x45005)),f862(f862(f103(f932(x45002,a921)),f862(f862(f33(x45001,f932(x45002,a921)),x45003),x45004)),f862(f862(f33(x45001,f932(x45002,a921)),x45003),x45005))) % 14.98/14.66 [4513]E(f862(f862(f32(x45131,f932(x45132,a921)),x45133),f862(f862(f20(x45131,f932(x45132,a921),f932(x45132,a921)),f862(f862(f10(f932(x45132,a921),f932(f932(x45132,a921),f932(x45132,a921)),x45131),f94(f932(x45132,a921))),x45134)),x45135)),f862(f862(f94(f932(x45132,a921)),f31(f932(x45132,a921),f862(f302(x45131,f932(x45132,a921),x45134),x45133))),f31(f932(x45132,a921),f862(f302(x45131,f932(x45132,a921),x45135),x45133)))) % 14.98/14.66 [4514]E(f862(f862(f33(x45141,f932(x45142,a921)),x45143),f862(f862(f20(x45141,f932(x45142,a921),f932(x45142,a921)),f862(f862(f10(f932(x45142,a921),f932(f932(x45142,a921),f932(x45142,a921)),x45141),f103(f932(x45142,a921))),x45144)),x45145)),f862(f862(f103(f932(x45142,a921)),f30(f932(x45142,a921),f862(f302(x45141,f932(x45142,a921),x45144),x45143))),f30(f932(x45142,a921),f862(f302(x45141,f932(x45142,a921),x45145),x45143)))) % 14.98/14.66 [4552]E(f862(f862(f131(x45521),f862(f182(f925(x45521)),f170(x45521,x45522,f862(f862(f147(x45523,x45521),x45524),x45525)))),f862(f862(f147(x45523,x45521),x45524),x45525)),f862(f862(f147(x45523,x45521),x45524),f862(f862(f131(x45523),f862(f182(f925(x45523)),f170(x45523,f862(f66(x45521,a921,x45523,x45522),x45524),x45525))),x45525))) % 14.98/14.66 [4425]E(f862(f862(f127(f931(x44251,x44252)),f862(f862(f174(x44251,x44252),f862(f862(f168(x44251),f862(f182(f925(x44252)),x44253)),x44254)),x44253)),f862(f862(f174(x44251,x44252),f862(f862(f131(x44251),f862(f182(f925(x44252)),x44253)),x44254)),x44255)),f862(f862(f174(x44251,x44252),x44254),f862(f862(f127(x44252),x44253),x44255))) % 14.98/14.66 [4543]E(f78(x45431,f862(f862(f20(x45431,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45431),a318),f862(f862(f9(x45431,f932(x45431,a921),a921),f321(x45431)),x45432))),f862(f862(f9(x45431,x45433,a921),f862(f862(f10(x45433,f932(x45433,a921),x45431),a317),x45434)),x45435))),f862(f70(x45431,x45433,x45432,x45434),x45435)) % 14.98/14.66 [4544]E(f83(x45441,f862(f862(f20(x45441,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45441),a318),f862(f862(f9(x45441,f932(x45441,a921),a921),f321(x45441)),x45442))),f862(f862(f9(x45441,x45443,a921),f862(f862(f10(x45443,f932(x45443,a921),x45441),a317),x45444)),x45445))),f862(f86(x45441,x45443,x45442,x45444),x45445)) % 14.98/14.66 [4592]E(f862(f862(f79(a1,x45921),f862(f96(a1),f862(f862(f73(a1),x45922),a90))),f862(f862(f20(a1,x45921,x45921),f862(f862(f9(a1,x45921,f932(x45921,x45921)),f862(f862(f10(a921,f932(x45921,f932(x45921,x45921)),a1),f89(x45921)),a186)),f178(x45921,x45923,x45924,x45925))),f862(f862(f10(a924,x45921,a1),x45924),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f73(a924)),a97)),x45925)))),f178(x45921,x45923,x45924,f862(f862(f73(a924),f862(f96(a924),x45922)),x45925))) % 14.98/14.66 [4627]E(f862(f862(f79(a1,x46271),f862(f96(a1),f862(f862(f73(a1),x46272),a90))),f862(f862(f20(a1,x46271,x46271),f862(f862(f9(a1,x46271,f932(x46271,x46271)),f862(f862(f10(a921,f932(x46271,f932(x46271,x46271)),a1),f89(x46271)),a186)),f862(f177(x46271,x46273,x46274),x46275))),f862(f862(f20(a1,x46271,x46271),f862(f862(f10(a924,f932(x46271,x46271),a1),x46274),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f73(a924)),a97)),x46275))),f862(f862(f10(a924,x46271,a1),f177(x46271,x46273,x46274)),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f73(a924)),a97)),x46275))))),f862(f177(x46271,x46273,x46274),f862(f862(f73(a924),f862(f96(a924),x46272)),x46275))) % 14.98/14.66 [4660]E(f862(f254(f931(x46601,x46602)),f862(f249(x46601,x46602,a921),f862(f862(f10(f932(x46602,f932(x46603,a921)),f932(x46602,a921),x46601),f862(f10(f932(x46603,a921),a921,x46602),f80(x46603))),f862(f862(f9(x46601,f932(x46602,f932(x46603,a921)),f932(x46602,f932(x46603,a921))),f862(f862(f10(f932(f932(x46603,a921),f932(x46603,a921)),f932(f932(x46602,f932(x46603,a921)),f932(x46602,f932(x46603,a921))),x46601),f10(f932(x46603,a921),f932(x46603,a921),x46602)),f862(f862(f10(f932(x46603,f932(a921,a921)),f932(f932(x46603,a921),f932(x46603,a921)),x46601),f20(x46603,a921,a921)),f862(f862(f10(f932(x46603,a921),f932(x46603,f932(a921,a921)),x46601),f862(f10(a921,f932(a921,a921),x46603),a318)),f862(f862(f9(x46601,f932(f931(x46601,x46603),a921),f932(x46603,a921)),f862(f862(f10(f932(x46603,f932(f932(f931(x46601,x46603),a921),a921)),f932(f932(f931(x46601,x46603),a921),f932(x46603,a921)),x46601),f9(x46603,f932(f931(x46601,x46603),a921),a921)),f862(f862(f10(f932(x46603,f931(x46601,x46603)),f932(x46603,f932(f932(f931(x46601,x46603),a921),a921)),x46601),f862(f10(f931(x46601,x46603),f932(f932(f931(x46601,x46603),a921),a921),x46603),f321(f931(x46601,x46603)))),f244(x46601,x46603)))),x46604))))),f862(f862(f9(x46602,f932(f931(x46603,x46602),a921),f932(x46603,a921)),f862(f862(f10(f932(x46603,f932(f932(f931(x46603,x46602),a921),a921)),f932(f932(f931(x46603,x46602),a921),f932(x46603,a921)),x46602),f9(x46603,f932(f931(x46603,x46602),a921),a921)),f862(f862(f10(f932(x46603,f931(x46603,x46602)),f932(x46603,f932(f932(f931(x46603,x46602),a921),a921)),x46602),f862(f10(f931(x46603,x46602),f932(f932(f931(x46603,x46602),a921),a921),x46603),f321(f931(x46603,x46602)))),f862(f9(x46603,x46602,f931(x46603,x46602)),f244(x46603,x46602))))),x46605))))),f862(f862(f280(x46601,x46603,x46602),x46604),x46605)) % 14.98/14.66 [4275]E(f217(x42751,x42752,x42753,x42754,f213(x42751,x42752,x42755,x42756)),f862(f862(x42754,x42755),x42756)) % 14.98/14.66 [4276]E(f218(x42761,x42762,x42763,x42764,f213(x42761,x42762,x42765,x42766)),f862(f862(x42764,x42765),x42766)) % 14.98/14.66 [4401]E(f120(x44011,x44012,x44013,x44014,f119(x44012,x44015,x44016)),f862(f862(f862(x44014,x44015),x44016),f120(x44011,x44012,x44013,x44014,x44016))) % 14.98/14.66 [4420]E(f68(x44201,x44202,f68(x44201,x44202,x44203,x44204,x44205),x44204,x44206),f68(x44201,x44202,x44203,x44204,x44206)) % 14.98/14.66 [4531]E(f862(f66(f931(x45311,x45312),x45312,f931(x45313,x45314),f248(x45311,x45312)),f250(x45313,x45311,x45314,x45312,x45315,x45316)),f862(f66(x45314,x45312,f931(x45313,x45314),x45316),f248(x45313,x45314))) % 14.98/14.66 [4532]E(f862(f66(f931(x45321,x45322),x45321,f931(x45323,x45324),f243(x45321,x45322)),f250(x45323,x45321,x45324,x45322,x45325,x45326)),f862(f66(x45323,x45321,f931(x45323,x45324),x45325),f243(x45323,x45324))) % 14.98/14.66 [4147]E(f862(f862(f66(x41471,x41472,x41473,x41474),x41475),x41476),f862(x41474,f862(x41475,x41476))) % 14.98/14.66 [4285]E(f216(x42851,f931(x42852,f926(x42852)),x42853,f862(f249(x42852,f926(x42852),x42851),x42854),f862(f128(x42852),f119(x42852,x42855,x42856))),f862(f862(x42854,x42855),x42856)) % 14.98/14.66 [4335]E(f219(x43351,x43352,x43353,x43354,f213(x43351,x43352,x43355,x43356)),f862(f862(f73(a924),f862(f862(f73(a924),f862(x43353,x43355)),f862(x43354,x43356))),f862(a105,f2(a924)))) % 14.98/14.66 [3949]E(f862(f862(f249(x39491,x39492,x39493),x39494),f862(f862(f244(x39491,x39492),x39495),x39496)),f862(f862(x39494,x39495),x39496)) % 14.98/14.66 [4009]E(f862(f862(f862(f10(x40091,x40092,x40093),x40094),x40095),x40096),f862(x40094,f862(x40095,x40096))) % 14.98/14.66 [4010]E(f862(f862(f862(f9(x40101,x40102,x40103),x40104),x40105),x40106),f862(f862(x40104,x40106),x40105)) % 14.98/14.66 [4026]E(f862(f862(f862(f20(x40261,x40262,x40263),x40264),x40265),x40266),f862(f862(x40264,x40266),f862(x40265,x40266))) % 14.98/14.66 [4049]E(f862(f149(x40491,x40492,x40493,x40494),f862(f862(f144(x40492),x40495),x40496)),f862(f862(x40494,x40495),x40496)) % 14.98/14.66 [4085]E(f162(f931(x40851,x40852),f862(f862(f225(a924),x40853),x40854),f862(f862(f244(x40851,x40852),x40855),x40856)),f862(f862(f174(x40851,x40852),f162(x40851,x40853,x40855)),f162(x40852,x40854,x40856))) % 14.98/14.66 [4151]E(f862(f862(f144(f931(x41511,x41512)),f862(f862(f244(x41511,x41512),x41513),x41514)),f862(f862(f174(x41511,x41512),x41515),x41516)),f862(f862(f174(x41511,x41512),f862(f862(f144(x41511),x41513),x41515)),f862(f862(f144(x41512),x41514),x41516))) % 14.98/14.66 [4152]E(f862(f862(f147(x41521,x41522),x41523),f862(f862(f152(x41521,x41524),x41525),x41526)),f862(f862(f152(x41522,f862(f862(f147(x41521,x41522),x41523),x41524)),x41525),f862(x41523,x41526))) % 14.98/14.66 [4176]E(f862(f862(f247(x41761,x41762,x41763,x41764),x41765),x41766),f862(x41764,f862(f862(f244(x41761,x41762),x41765),x41766))) % 14.98/14.66 [4192]E(f862(f135(x41921,x41922,x41923,x41924),f862(f862(f144(x41922),x41925),x41926)),f862(f135(x41921,x41922,x41923,f862(f862(x41923,x41924),x41925)),x41926)) % 14.98/14.66 [4218]E(f252(x42181,x42182,x42183,x42184,f862(f862(f244(x42181,x42182),x42185),x42186)),f862(f862(x42184,x42185),x42186)) % 14.98/14.66 [4299]E(f862(f862(f33(x42991,f932(x42992,a921)),x42993),f862(f66(x42994,f932(x42992,a921),x42991,x42995),x42996)),f862(f862(f33(x42994,f932(x42992,a921)),f862(f302(x42991,x42994,x42996),x42993)),x42995)) % 14.98/14.66 [4349]E(f862(f862(f147(x43491,x43492),x43493),f862(f862(f147(x43494,x43491),x43495),x43496)),f862(f862(f147(x43494,x43492),f862(f66(x43491,x43492,x43494,x43493),x43495)),x43496)) % 14.98/14.66 [4355]E(f862(f302(x43551,x43552,f862(f66(x43553,x43552,x43551,x43554),x43555)),x43556),f862(f302(x43553,x43552,x43554),f862(f302(x43551,x43553,x43555),x43556))) % 14.98/14.66 [4356]E(f862(f303(x43561,x43562,f862(f66(x43563,x43562,x43561,x43564),x43565)),x43566),f862(f303(x43561,x43563,x43565),f862(f303(x43563,x43562,x43564),x43566))) % 14.98/14.66 [4384]E(f862(f135(x43841,x43842,x43843,f862(f135(x43841,x43842,x43843,x43844),x43845)),x43846),f862(f135(x43841,x43842,x43843,x43844),f862(f862(f127(x43842),x43845),x43846))) % 14.98/14.66 [4519]E(f862(f250(x45191,x45191,x45192,x45193,f25(x45191),x45194),f862(f862(f244(x45191,x45192),x45195),x45196)),f862(f862(f244(x45191,x45193),x45195),f862(x45194,x45196))) % 14.98/14.66 [4520]E(f862(f250(x45201,x45202,x45203,x45203,x45204,f25(x45203)),f862(f862(f244(x45201,x45203),x45205),x45206)),f862(f862(f244(x45202,x45203),f862(x45204,x45205)),x45206)) % 14.98/14.66 [4610]E(f862(f862(f147(f931(x46101,x46102),f931(x46101,x46103)),f862(f249(x46101,x46102,f931(x46101,x46103)),f862(f862(f9(x46101,f932(x46102,x46103),f932(x46102,f931(x46101,x46103))),f862(f862(f10(f932(x46103,f931(x46101,x46103)),f932(f932(x46102,x46103),f932(x46102,f931(x46101,x46103))),x46101),f10(x46103,f931(x46101,x46103),x46102)),f244(x46101,x46103))),x46104))),f862(f862(f174(x46101,x46102),x46105),x46106)),f862(f862(f174(x46101,x46103),x46105),f862(f862(f147(x46102,x46103),x46104),x46106))) % 14.98/14.66 [4202]E(f862(f862(f66(x42021,x42022,x42023,f862(f18(x42022,x42021),x42024)),x42025),x42026),x42024) % 14.98/14.66 [4234]E(f862(f302(x42341,x42342,x42343),f862(f302(x42344,x42341,x42345),x42346)),f862(f302(x42344,x42342,f862(f862(f10(x42341,x42342,x42344),x42343),x42345)),x42346)) % 14.98/14.66 [4240]E(f862(f862(f32(x42401,f932(x42402,a921)),f862(f302(x42403,x42401,x42404),x42405)),x42406),f862(f862(f32(x42403,f932(x42402,a921)),x42405),f862(f862(f10(x42401,f932(x42402,a921),x42403),x42406),x42404))) % 14.98/14.66 [4241]E(f862(f862(f33(x42411,f932(x42412,a921)),f862(f302(x42413,x42411,x42414),x42415)),x42416),f862(f862(f33(x42413,f932(x42412,a921)),x42415),f862(f862(f10(x42411,f932(x42412,a921),x42413),x42416),x42414))) % 14.98/14.66 [4242]E(f862(f862(f32(x42421,f932(x42422,a921)),x42423),f862(f862(f10(x42424,f932(x42422,a921),x42421),x42425),x42426)),f862(f862(f32(x42424,f932(x42422,a921)),f862(f302(x42421,x42424,x42426),x42423)),x42425)) % 14.98/14.66 [4243]E(f862(f862(f33(x42431,f932(x42432,a921)),x42433),f862(f862(f10(x42434,f932(x42432,a921),x42431),x42435),x42436)),f862(f862(f33(x42434,f932(x42432,a921)),f862(f302(x42431,x42434,x42436),x42433)),x42435)) % 14.98/14.66 [4301]E(f862(f862(f33(x43011,f932(x43012,a921)),x43013),f862(f862(f10(f932(x43014,a921),f932(x43012,a921),x43011),f302(x43014,x43012,x43015)),x43016)),f862(f302(x43014,x43012,x43015),f862(f862(f33(x43011,f932(x43014,a921)),x43013),x43016))) % 14.98/14.66 [4302]E(f862(f862(f33(x43021,f932(x43022,a921)),x43023),f862(f862(f10(f932(x43024,a921),f932(x43022,a921),x43021),f276(x43024,x43022,x43025)),x43026)),f862(f276(x43024,x43022,x43025),f862(f862(f33(x43021,f932(x43024,a921)),x43023),x43026))) % 14.98/14.66 [4303]E(f862(f862(f32(x43031,f932(x43032,a921)),x43033),f862(f862(f10(f932(x43034,a921),f932(x43032,a921),x43031),f303(x43032,x43034,x43035)),x43036)),f862(f303(x43032,x43034,x43035),f862(f862(f32(x43031,f932(x43034,a921)),x43033),x43036))) % 14.98/14.66 [4304]E(f862(f862(f33(x43041,f932(x43042,a921)),x43043),f862(f862(f10(f932(x43044,a921),f932(x43042,a921),x43041),f303(x43042,x43044,x43045)),x43046)),f862(f303(x43042,x43044,x43045),f862(f862(f33(x43041,f932(x43044,a921)),x43043),x43046))) % 14.98/14.66 [4389]E(f862(f135(x43891,x43892,f862(f9(x43892,x43891,x43891),x43893),x43894),f862(f161(x43892),f862(f862(f144(x43892),x43895),x43896))),f862(f862(x43893,x43895),f862(f135(x43891,x43892,f862(f9(x43892,x43891,x43891),x43893),x43894),f862(f161(x43892),x43896)))) % 14.98/14.66 [4448]E(f862(f862(f20(f931(x44481,x44482),x44482,x44483),f862(f862(f10(x44484,f932(x44482,x44483),f931(x44481,x44482)),x44485),f862(f862(f10(x44481,x44484,f931(x44481,x44482)),x44486),f243(x44481,x44482)))),f248(x44481,x44482)),f862(f249(x44481,x44482,x44483),f862(f862(f10(x44484,f932(x44482,x44483),x44481),x44485),x44486))) % 14.98/14.66 [4455]E(f862(f135(x44551,x44552,f862(f9(x44552,x44551,x44551),x44553),f862(f135(x44551,x44552,f862(f9(x44552,x44551,x44551),x44553),x44554),f862(f161(x44552),x44555))),f862(f161(x44552),x44556)),f862(f135(x44551,x44552,f862(f9(x44552,x44551,x44551),x44553),x44554),f862(f161(x44552),f862(f862(f127(x44552),x44556),x44555)))) % 14.98/14.66 [4457]E(f862(f862(f147(f931(x44571,x44572),f931(x44573,x44572)),f862(f249(x44571,x44572,f931(x44573,x44572)),f862(f862(f10(x44573,f932(x44572,f931(x44573,x44572)),x44571),f244(x44573,x44572)),x44574))),f862(f862(f174(x44571,x44572),x44575),x44576)),f862(f862(f174(x44573,x44572),f862(f862(f147(x44571,x44573),x44574),x44575)),x44576)) % 14.98/14.66 [4502]P1(f862(f862(f227(f932(x45021,a921)),f862(f276(x45022,x45021,x45023),f862(f862(f32(x45024,f932(x45022,a921)),x45025),x45026))),f862(f862(f32(x45024,f932(x45021,a921)),x45025),f862(f862(f10(f932(x45022,a921),f932(x45021,a921),x45024),f276(x45022,x45021,x45023)),x45026)))) % 14.98/14.66 [4314]E(f862(f862(f174(x43141,x43142),f862(f862(f152(x43141,x43143),x43144),f862(f243(x43141,x43142),x43145))),f862(f862(f152(x43142,x43146),x43144),f862(f248(x43141,x43142),x43145))),f862(f862(f152(f931(x43141,x43142),f862(f862(f174(x43141,x43142),x43143),x43146)),x43144),x43145)) % 14.98/14.66 [4372]E(f862(f862(f103(f932(f931(x43721,x43722),a921)),f862(f862(f280(x43721,x43723,x43722),x43724),x43725)),f862(f862(f280(x43721,x43723,x43722),x43724),x43726)),f862(f862(f280(x43721,x43723,x43722),x43724),f862(f862(f103(f932(f931(x43723,x43722),a921)),x43725),x43726))) % 14.98/14.66 [4467]E(f862(f862(f301(f931(x44671,x44672)),f862(f862(f244(x44671,x44672),x44673),x44674)),f862(f862(f103(f932(f931(x44671,x44672),a921)),f862(f862(f246(x44671,x44672),x44675),f862(f18(f932(x44672,a921),x44671),f862(f862(f301(x44672),x44674),x44676)))),f862(f862(f246(x44671,x44672),f862(f862(f301(x44671),x44673),x44675)),f862(f18(f932(x44672,a921),x44671),x44676)))),f862(f862(f246(x44671,x44672),f862(f862(f301(x44671),x44673),x44675)),f862(f18(f932(x44672,a921),x44671),f862(f862(f301(x44672),x44674),x44676)))) % 14.98/14.66 [4548]E(f862(f862(f94(f932(x45481,a921)),f862(f303(x45481,x45482,f862(f66(f931(x45482,x45483),x45482,x45481,f243(x45482,x45483)),x45484)),x45485)),f862(f303(x45481,x45483,f862(f66(f931(x45482,x45483),x45483,x45481,f248(x45482,x45483)),x45484)),x45486)),f862(f303(x45481,f931(x45482,x45483),x45484),f862(f862(f246(x45482,x45483),x45485),f862(f18(f932(x45483,a921),x45482),x45486)))) % 14.98/14.66 [4395]E(f862(f862(f103(f932(f931(x43951,x43952),a921)),f862(f862(f280(x43951,x43953,x43952),x43954),x43955)),f862(f862(f280(x43951,x43953,x43952),x43956),x43955)),f862(f862(f280(x43951,x43953,x43952),f862(f862(f103(f932(f931(x43951,x43953),a921)),x43954),x43956)),x43955)) % 14.98/14.66 [4529]E(f862(f862(f32(x45291,f932(x45292,a921)),x45293),f862(f862(f9(x45291,f932(x45294,f932(x45292,a921)),f932(x45292,a921)),f862(f862(f10(f932(x45294,a921),f932(f932(x45294,f932(x45292,a921)),f932(x45292,a921)),x45291),f32(x45294,f932(x45292,a921))),x45295)),x45296)),f862(f862(f32(x45294,f932(x45292,a921)),f862(f862(f33(x45291,f932(x45294,a921)),x45293),x45295)),x45296)) % 14.98/14.66 [4530]E(f862(f862(f33(x45301,f932(x45302,a921)),x45303),f862(f862(f9(x45301,f932(x45304,f932(x45302,a921)),f932(x45302,a921)),f862(f862(f10(f932(x45304,a921),f932(f932(x45304,f932(x45302,a921)),f932(x45302,a921)),x45301),f33(x45304,f932(x45302,a921))),x45305)),x45306)),f862(f862(f33(x45304,f932(x45302,a921)),f862(f862(f33(x45301,f932(x45304,a921)),x45303),x45305)),x45306)) % 14.98/14.66 [4582]E(f862(f249(x45821,x45822,f931(x45823,x45824)),f862(f862(f9(x45821,f932(x45822,x45824),f932(x45822,f931(x45823,x45824))),f862(f862(f10(f932(x45824,f931(x45823,x45824)),f932(f932(x45822,x45824),f932(x45822,f931(x45823,x45824))),x45821),f10(x45824,f931(x45823,x45824),x45822)),f862(f862(f10(x45823,f932(x45824,f931(x45823,x45824)),x45821),f244(x45823,x45824)),x45825))),x45826)),f250(x45821,x45823,x45822,x45824,x45825,x45826)) % 14.98/14.66 [4605]E(f862(f302(x46051,x46052,f862(f862(f20(x46051,x46052,x46052),f862(f862(f20(x46051,x46052,f932(x46052,x46052)),f862(f862(f10(a921,f932(x46052,f932(x46052,x46052)),x46051),f89(x46052)),x46053)),x46054)),x46055)),x46056),f862(f862(f103(f932(x46052,a921)),f862(f302(x46051,x46052,x46054),f862(f862(f94(f932(x46051,a921)),x46056),f862(f254(x46051),x46053)))),f862(f302(x46051,x46052,x46055),f862(f862(f94(f932(x46051,a921)),x46056),f862(f254(x46051),f862(f862(f10(a921,a921,x46051),a314),x46053)))))) % 14.98/14.66 [4617]E(f862(f302(x46171,f931(x46172,x46173),f862(f862(f20(x46171,x46173,f931(x46172,x46173)),f862(f862(f10(x46172,f932(x46173,f931(x46172,x46173)),x46171),f244(x46172,x46173)),x46174)),x46175)),x46176),f862(f862(f246(x46172,x46173),f862(f302(x46171,x46172,x46174),x46176)),f862(f862(f10(f932(x46171,a921),f932(x46173,a921),x46172),f302(x46171,x46173,x46175)),f862(f862(f9(x46172,f932(x46171,a921),f932(x46171,a921)),f862(f862(f10(f932(x46171,a921),f932(f932(x46171,a921),f932(x46171,a921)),x46172),f94(f932(x46171,a921))),f862(f862(f10(f932(x46172,a921),f932(x46171,a921),x46172),f303(x46171,x46172,x46174)),f862(f862(f9(x46172,f932(x46172,a921),f932(x46172,a921)),f301(x46172)),f181(f932(x46172,a921)))))),x46176)))) % 14.98/14.66 [4642]E(f238(x46421,x46422,x46423,x46424,x46425,x46426),f862(x46424,f862(f254(x46421),f862(f862(f10(f932(f932(x46423,x46421),a921),a921,x46421),f80(f932(x46423,x46421))),f862(f862(f10(f932(f932(x46423,x46421),a921),f932(f932(x46423,x46421),a921),x46421),f862(f20(f932(x46423,x46421),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x46423,x46421)),a318),f862(f862(f9(f932(x46423,x46421),f932(f932(x46423,x46421),a921),a921),f321(f932(x46423,x46421))),x46425)))),f862(f862(f9(x46421,f932(f932(x46423,x46421),x46421),f932(f932(x46423,x46421),a921)),f862(f862(f10(f932(x46421,a921),f932(f932(f932(x46423,x46421),x46421),f932(f932(x46423,x46421),a921)),x46421),f10(x46421,a921,f932(x46423,x46421))),a317)),f862(f862(f9(f932(x46423,x46421),x46423,x46421),f7(f932(x46423,x46421))),x46426))))))) % 14.98/14.66 [4428]E(f862(f66(x44281,x44282,x44283,x44284),f68(x44283,x44281,x44285,x44286,x44287)),f68(x44283,x44282,f862(f66(x44281,x44282,x44283,x44284),x44285),x44286,f862(x44284,x44287))) % 14.98/14.66 [4565]E(f862(f248(x45651,x45652),f862(f250(x45653,x45651,x45654,x45652,x45655,x45656),x45657)),f862(x45656,f862(f248(x45653,x45654),x45657))) % 14.98/14.66 [4566]E(f862(f243(x45661,x45662),f862(f250(x45663,x45661,x45664,x45662,x45665,x45666),x45667)),f862(x45665,f862(f243(x45663,x45664),x45667))) % 14.98/14.66 [4277]E(f862(f862(f174(x42771,x42772),f862(f862(f152(x42771,x42773),x42774),x42775)),f862(f862(f152(x42772,x42776),x42774),x42777)),f862(f862(f152(f931(x42771,x42772),f862(f862(f174(x42771,x42772),x42773),x42776)),x42774),f862(f862(f244(x42771,x42772),x42775),x42777))) % 14.98/14.66 [4344]E(f862(f862(f862(f251(x43441,x43442,x43443,x43444),x43445),x43446),x43447),f862(f862(f249(x43442,x43443,x43444),x43446),f862(x43445,x43447))) % 14.98/14.66 [4354]E(f862(f862(f862(f251(x43541,x43542,x43543,x43544),x43545),x43546),x43547),f862(f862(x43546,f862(f243(x43542,x43543),f862(x43545,x43547))),f862(f248(x43542,x43543),f862(x43545,x43547)))) % 14.98/14.66 [4406]E(f862(f66(x44061,x44062,x44063,x44064),f862(f66(x44065,x44061,x44063,x44066),x44067)),f862(f66(x44065,x44062,x44063,f862(f66(x44061,x44062,x44065,x44064),x44066)),x44067)) % 14.98/14.66 [4586]E(f862(f250(x45861,x45862,x45863,x45863,x45864,f25(x45863)),f862(f250(x45861,x45861,x45865,x45863,f25(x45861),x45866),x45867)),f862(f862(f244(x45862,x45863),f862(x45864,f862(f243(x45861,x45865),x45867))),f862(x45866,f862(f248(x45861,x45865),x45867)))) % 14.98/14.66 [4587]E(f862(f250(x45871,x45871,x45872,x45873,f25(x45871),x45874),f862(f250(x45875,x45871,x45872,x45872,x45876,f25(x45872)),x45877)),f862(f862(f244(x45871,x45873),f862(x45876,f862(f243(x45875,x45872),x45877))),f862(x45874,f862(f248(x45875,x45872),x45877)))) % 14.98/14.66 [4603]E(f862(f250(x46031,x46032,x46033,x46033,x46034,f25(x46033)),f862(f250(x46035,x46031,x46033,x46033,x46036,f25(x46033)),x46037)),f862(f250(x46035,x46032,x46033,x46033,f862(f66(x46031,x46032,x46035,x46034),x46036),f25(x46033)),x46037)) % 14.98/14.66 [4604]E(f862(f250(x46041,x46041,x46042,x46043,f25(x46041),x46044),f862(f250(x46041,x46041,x46045,x46042,f25(x46041),x46046),x46047)),f862(f250(x46041,x46041,x46045,x46043,f25(x46041),f862(f66(x46042,x46043,x46045,x46044),x46046)),x46047)) % 14.98/14.66 [4614]E(f862(f250(x46141,x46142,x46143,x46143,x46144,f25(x46143)),f862(f250(x46141,x46141,x46145,x46143,f25(x46141),x46146),x46147)),f862(f250(x46142,x46142,x46145,x46143,f25(x46142),x46146),f862(f250(x46141,x46142,x46145,x46145,x46144,f25(x46145)),x46147))) % 14.98/14.66 [4311]E(f862(f862(f280(x43111,x43112,x43113),f862(f862(f280(x43111,x43114,x43112),x43115),x43116)),x43117),f862(f862(f280(x43111,x43114,x43113),x43115),f862(f862(f280(x43114,x43112,x43113),x43116),x43117))) % 14.98/14.66 [4378]E(f862(f862(f249(x43781,x43782,x43783),f862(f66(x43784,f932(x43782,x43783),x43781,x43785),x43786)),x43787),f862(f862(x43785,f862(x43786,f862(f243(x43781,x43782),x43787))),f862(f248(x43781,x43782),x43787))) % 14.98/14.66 [4460]E(f862(f135(x44601,x44602,f862(f9(x44602,x44601,x44601),x44603),x44604),f862(f161(x44602),f862(f862(f147(x44605,x44602),x44606),x44607))),f862(f135(x44601,x44605,f862(f9(x44605,x44601,x44601),f862(f66(x44602,f932(x44601,x44601),x44605,x44603),x44606)),x44604),f862(f161(x44605),x44607))) % 14.98/14.66 [4407]E(f862(f862(f33(x44071,f932(f931(x44072,x44073),a921)),x44074),f862(f862(f10(f932(f931(x44075,x44073),a921),f932(f931(x44072,x44073),a921),x44071),f862(f280(x44072,x44075,x44073),x44076)),x44077)),f862(f862(f280(x44072,x44075,x44073),x44076),f862(f862(f33(x44071,f932(f931(x44075,x44073),a921)),x44074),x44077))) % 14.98/14.66 [4553]E(f862(f862(f33(x45531,f932(f931(x45532,x45533),a921)),x45534),f862(f862(f9(x45531,f932(f931(x45535,x45533),a921),f932(f931(x45532,x45533),a921)),f862(f862(f10(f932(f931(x45532,x45535),a921),f932(f932(f931(x45535,x45533),a921),f932(f931(x45532,x45533),a921)),x45531),f280(x45532,x45535,x45533)),x45536)),x45537)),f862(f862(f280(x45532,x45535,x45533),f862(f862(f33(x45531,f932(f931(x45532,x45535),a921)),x45534),x45536)),x45537)) % 14.98/14.66 [4554]E(f862(f135(x45541,x45542,f862(f862(f9(x45541,f932(x45542,x45543),f932(x45542,x45541)),f862(f862(f10(f932(x45543,x45541),f932(f932(x45542,x45543),f932(x45542,x45541)),x45541),f10(x45543,x45541,x45542)),x45544)),x45545),x45546),x45547),f862(f135(x45541,x45543,x45544,x45546),f862(f862(f147(x45542,x45543),x45545),x45547))) % 14.98/14.66 [4615]E(f862(f862(f32(x46151,f932(x46152,a921)),x46153),f862(f862(f10(f932(x46154,f932(x46152,a921)),f932(x46152,a921),x46151),f862(f32(x46154,f932(x46152,a921)),x46155)),f862(f862(f9(x46151,f932(x46154,f932(x46152,a921)),f932(x46154,f932(x46152,a921))),f862(f862(f10(f932(f932(x46152,a921),f932(x46152,a921)),f932(f932(x46154,f932(x46152,a921)),f932(x46154,f932(x46152,a921))),x46151),f10(f932(x46152,a921),f932(x46152,a921),x46154)),f862(f862(f10(f932(x46152,a921),f932(f932(x46152,a921),f932(x46152,a921)),x46151),f103(f932(x46152,a921))),x46156))),x46157))),f862(f862(f103(f932(x46152,a921)),f862(f862(f32(x46151,f932(x46152,a921)),x46153),x46156)),f862(f862(f32(x46154,f932(x46152,a921)),x46155),x46157))) % 14.98/14.66 [4616]E(f862(f862(f33(x46161,f932(x46162,a921)),x46163),f862(f862(f10(f932(x46164,f932(x46162,a921)),f932(x46162,a921),x46161),f862(f33(x46164,f932(x46162,a921)),x46165)),f862(f862(f9(x46161,f932(x46164,f932(x46162,a921)),f932(x46164,f932(x46162,a921))),f862(f862(f10(f932(f932(x46162,a921),f932(x46162,a921)),f932(f932(x46164,f932(x46162,a921)),f932(x46164,f932(x46162,a921))),x46161),f10(f932(x46162,a921),f932(x46162,a921),x46164)),f862(f862(f10(f932(x46162,a921),f932(f932(x46162,a921),f932(x46162,a921)),x46161),f94(f932(x46162,a921))),x46166))),x46167))),f862(f862(f94(f932(x46162,a921)),f862(f862(f33(x46161,f932(x46162,a921)),x46163),x46166)),f862(f862(f33(x46164,f932(x46162,a921)),x46165),x46167))) % 14.98/14.66 [4608]E(f190(x46081,x46082,f862(f862(f862(x46083,x46084),x46085),x46086),f862(f862(f9(x46081,f931(a92,a92),f932(a92,f926(x46082))),f862(f862(f9(x46081,a92,f932(f931(a92,a92),f932(a92,f926(x46082)))),f862(f862(f9(x46081,a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(x46082))))),x46087),x46084)),x46085)),x46086)),f862(f862(f862(f202(x46081,x46082,x46083,x46087),x46084),x46085),x46086)) % 14.98/14.66 [4622]E(f191(x46221,x46222,f862(f862(f862(x46223,x46224),x46225),x46226),f862(f862(f9(x46221,f931(a92,a92),f932(a92,f926(x46222))),f862(f862(f9(x46221,a92,f932(f931(a92,a92),f932(a92,f926(x46222)))),f862(f862(f9(x46221,a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(x46222))))),x46227),x46224)),x46225)),x46226)),f204(x46221,x46222,x46223,x46227,x46224,x46225,x46226)) % 14.98/14.66 [4613]E(f188(x46131,x46132,f862(f862(f862(x46133,x46134),x46135),x46136),f862(f862(f9(x46131,f931(a92,a92),f932(a92,f926(f928(x46132)))),f862(f862(f9(x46131,a92,f932(f931(a92,a92),f932(a92,f926(f928(x46132))))),f862(f862(f9(x46131,a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(f928(x46132)))))),x46137),x46134)),x46135)),x46136)),f862(f862(f862(f198(x46131,x46132,x46133,x46137),x46134),x46135),x46136)) % 14.98/14.66 [4624]E(f189(x46241,x46242,f862(f862(f862(x46243,x46244),x46245),x46246),f862(f862(f9(x46241,f931(a92,a92),f932(a92,f926(f928(x46242)))),f862(f862(f9(x46241,a92,f932(f931(a92,a92),f932(a92,f926(f928(x46242))))),f862(f862(f9(x46241,a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(f928(x46242)))))),x46247),x46244)),x46245)),x46246)),f200(x46241,x46242,x46243,x46247,x46244,x46245,x46246)) % 14.98/14.66 [4521]E(f862(f250(x45211,x45212,x45213,x45214,x45215,x45216),f862(f862(f244(x45211,x45213),x45217),x45218)),f862(f862(f244(x45212,x45214),f862(x45215,x45217)),f862(x45216,x45218))) % 14.98/14.66 [4626]E(f862(f862(f147(f931(x46261,x46262),f931(x46263,x46264)),f862(f249(x46261,x46262,f931(x46263,x46264)),f862(f862(f9(x46261,f932(x46262,x46264),f932(x46262,f931(x46263,x46264))),f862(f862(f10(f932(x46264,f931(x46263,x46264)),f932(f932(x46262,x46264),f932(x46262,f931(x46263,x46264))),x46261),f10(x46264,f931(x46263,x46264),x46262)),f862(f862(f10(x46263,f932(x46264,f931(x46263,x46264)),x46261),f244(x46263,x46264)),x46265))),x46266))),f862(f862(f174(x46261,x46262),x46267),x46268)),f862(f862(f174(x46263,x46264),f862(f862(f147(x46261,x46263),x46265),x46267)),f862(f862(f147(x46262,x46264),x46266),x46268))) % 14.98/14.66 [4629]E(f862(f862(f147(f931(x46291,x46292),x46293),f862(f249(x46291,x46292,x46293),f862(f862(f10(f932(x46292,f931(x46291,x46294)),f932(x46292,x46293),x46291),f862(f10(f931(x46291,x46294),x46293,x46292),x46295)),f862(f862(f9(x46291,f932(x46292,x46294),f932(x46292,f931(x46291,x46294))),f862(f862(f10(f932(x46294,f931(x46291,x46294)),f932(f932(x46292,x46294),f932(x46292,f931(x46291,x46294))),x46291),f10(x46294,f931(x46291,x46294),x46292)),f244(x46291,x46294))),x46296)))),f862(f862(f174(x46291,x46292),x46297),x46298)),f862(f862(f147(f931(x46291,x46294),x46293),x46295),f862(f862(f174(x46291,x46294),x46297),f862(f862(f147(x46292,x46294),x46296),x46298)))) % 14.98/14.66 [4557]E(f862(f862(f147(f931(x45571,x45572),x45573),f862(f249(x45571,x45572,x45573),f862(f862(f10(f932(x45572,f931(x45574,x45572)),f932(x45572,x45573),x45571),f862(f10(f931(x45574,x45572),x45573,x45572),x45575)),f862(f862(f10(x45574,f932(x45572,f931(x45574,x45572)),x45571),f244(x45574,x45572)),x45576)))),f862(f862(f174(x45571,x45572),x45577),x45578)),f862(f862(f147(f931(x45574,x45572),x45573),x45575),f862(f862(f174(x45574,x45572),f862(f862(f147(x45571,x45574),x45576),x45577)),x45578))) % 14.98/14.66 [4512]E(f862(f862(f249(x45121,x45122,x45123),f862(f862(f10(f932(x45122,f931(x45124,x45125)),f932(x45122,x45123),x45121),f862(f10(f931(x45124,x45125),x45123,x45122),f862(f249(x45124,x45125,x45123),x45126))),x45127)),x45128),f862(f862(f249(x45124,x45125,x45123),x45126),f862(f862(f249(x45121,x45122,f931(x45124,x45125)),x45127),x45128))) % 14.98/14.66 [4630]E(f862(f862(f33(f931(x46301,x46302),f932(f931(x46303,x46304),a921)),f862(f862(f246(x46301,x46302),x46305),f862(f18(f932(x46302,a921),x46301),x46306))),f862(f249(x46301,x46302,f932(f931(x46303,x46304),a921)),f862(f862(f9(x46301,f932(x46302,f932(x46303,f932(x46304,a921))),f932(x46302,f932(f931(x46303,x46304),a921))),f862(f862(f10(f932(f932(x46303,f932(x46304,a921)),f932(f931(x46303,x46304),a921)),f932(f932(x46302,f932(x46303,f932(x46304,a921))),f932(x46302,f932(f931(x46303,x46304),a921))),x46301),f10(f932(x46303,f932(x46304,a921)),f932(f931(x46303,x46304),a921),x46302)),f862(f862(f10(f932(x46303,a921),f932(f932(x46303,f932(x46304,a921)),f932(f931(x46303,x46304),a921)),x46301),f246(x46303,x46304)),x46307))),f862(f862(f10(f932(x46304,a921),f932(x46303,f932(x46304,a921)),x46302),f18(f932(x46304,a921),x46303)),x46308)))),f862(f862(f246(x46303,x46304),f862(f862(f33(x46301,f932(x46303,a921)),x46305),x46307)),f862(f18(f932(x46304,a921),x46303),f862(f862(f33(x46302,f932(x46304,a921)),x46306),x46308)))) % 14.98/14.66 [4571]E(f862(f862(f251(x45711,x45712,x45713,x45714),f862(f862(f251(x45711,x45715,x45716,f931(x45712,x45713)),x45717),x45718)),x45719),f862(f862(f251(x45711,x45715,x45716,x45714),x45717),f862(f862(f9(x45715,f932(x45712,f932(x45713,x45714)),f932(x45716,x45714)),f862(f862(f10(f932(x45716,f931(x45712,x45713)),f932(f932(x45712,f932(x45713,x45714)),f932(x45716,x45714)),x45715),f251(x45716,x45712,x45713,x45714)),x45718)),x45719))) % 14.98/14.66 [4600]E(f862(f66(f931(x46001,x46002),f931(x46003,x46004),f931(x46005,x46006),f250(x46001,x46003,x46002,x46004,x46007,x46008)),f250(x46005,x46001,x46006,x46002,x46009,x460010)),f250(x46005,x46003,x46006,x46004,f862(f66(x46001,x46003,x46005,x46007),x46009),f862(f66(x46002,x46004,x46006,x46008),x460010))) % 14.98/14.66 [4606]E(f862(f250(x46061,x46062,x46063,x46064,x46065,x46066),f862(f250(x46067,x46061,x46068,x46063,x46069,x460610),x460611)),f862(f250(x46067,x46062,x46068,x46064,f862(f66(x46061,x46062,x46067,x46065),x46069),f862(f66(x46063,x46064,x46068,x46066),x460610)),x460611)) % 14.98/14.66 [4773]~P152(x47731,a861)+P151(x47731,a863) % 14.98/14.66 [4743]~P2(x47431)+E(f84(x47431),a317) % 14.98/14.66 [4744]~P60(x47441)+P60(f928(x47441)) % 14.98/14.66 [4745]~P63(x47451)+P63(f928(x47451)) % 14.98/14.66 [4746]~P106(x47461)+P106(f925(x47461)) % 14.98/14.66 [4749]~P145(x47491)+~E(f71(x47491),f2(x47491)) % 14.98/14.66 [4751]~E(x47511,f2(a92))+E(f862(a24,x47511),f2(a1)) % 14.98/14.66 [4752]~E(x47521,f2(a1))+E(f75(a1,x47521),f2(a1)) % 14.98/14.66 [4758]~P147(x47581)+P26(x47581,f2(x47581)) % 14.98/14.66 [4760]~P109(x47601)+P11(x47601,f106(x47601)) % 14.98/14.66 [4769]P1(x47691)+P1(f862(a314,x47691)) % 14.98/14.66 [4825]~P147(x48251)+~P26(x48251,f71(x48251)) % 14.98/14.66 [4863]~P1(x48631)+~P1(f862(a314,x48631)) % 14.98/14.66 [4884]E(f862(a97,x48841),f2(a924))+~P1(f862(a186,x48841)) % 14.98/14.66 [4951]~P69(x49511)+P14(x49511,x49511,f74(x49511)) % 14.98/14.66 [4952]~P103(x49521)+P12(x49521,x49521,f103(x49521)) % 14.98/14.66 [4953]~P104(x49531)+P12(x49531,x49531,f94(x49531)) % 14.98/14.66 [4954]~P100(x49541)+P12(x49541,x49541,f74(x49541)) % 14.98/14.66 [4955]~P109(x49551)+P12(x49551,x49551,f225(x49551)) % 14.98/14.66 [4956]~P109(x49561)+P12(x49561,x49561,f226(x49561)) % 14.98/14.66 [4755]~E(x47551,f2(a924))+E(f862(f93(a1),x47551),f2(a1)) % 14.98/14.66 [4762]~P98(x47621)+E(f862(f96(x47621),a76),f2(x47621)) % 14.98/14.66 [4765]~E(f656(x47651),f2(a924))+E(f862(f158(a924),x47651),f2(a924)) % 14.98/14.66 [4766]~P108(x47661)+E(f229(x47661,f227(x47661)),f225(x47661)) % 14.98/14.66 [4767]~P108(x47671)+E(f230(x47671,f227(x47671)),f226(x47671)) % 14.98/14.66 [4768]~P88(x47681)+E(f75(x47681,f2(x47681)),f2(x47681)) % 14.98/14.66 [4778]~P147(x47781)+E(f862(f93(x47781),f71(a924)),f71(x47781)) % 14.98/14.66 [4779]~P147(x47791)+E(f862(f93(x47791),f2(a924)),f2(x47791)) % 14.98/14.66 [4780]~P142(x47801)+E(f862(f95(x47801),f71(a1)),f71(x47801)) % 14.98/14.66 [4781]~P142(x47811)+E(f862(f95(x47811),f2(a1)),f2(x47811)) % 14.98/14.66 [4782]E(x47821,f2(a924))+~E(f862(f93(a1),x47821),f2(a1)) % 14.98/14.66 [4819]~P96(x48191)+E(f862(f72(x48191),f181(x48191)),f234(x48191)) % 14.98/14.66 [4820]~P96(x48201)+E(f862(f72(x48201),f234(x48201)),f181(x48201)) % 14.98/14.66 [4821]~P68(x48211)+E(f862(f72(x48211),f2(x48211)),f2(x48211)) % 14.98/14.66 [4822]~P112(x48221)+E(f862(f69(x48221),f71(x48221)),f71(x48221)) % 14.98/14.66 [4823]~P86(x48231)+E(f862(f69(x48231),f2(x48231)),f2(x48231)) % 14.98/14.66 [4824]~P81(x48241)+E(f862(f158(x48241),f106(x48241)),f2(x48241)) % 14.98/14.66 [4842]~P34(x48421)+P38(f862(f165(a1),x48421)) % 14.98/14.66 [4868]~P98(x48681)+E(f862(f72(x48681),f71(x48681)),f862(f96(x48681),a90)) % 14.98/14.66 [4883]~P98(x48831)+P26(x48831,f862(f96(x48831),a76)) % 14.98/14.66 [4909]P34(x49091)+~P38(f862(f165(a1),x49091)) % 14.98/14.66 [4957]E(f862(f93(a1),f862(a97,x49571)),x49571)+P1(f862(a186,x49571)) % 14.98/14.66 [5027]~P116(x50271)+E(f237(x50271,f71(x50271),f74(x50271)),f236(x50271)) % 14.98/14.66 [5060]~P98(x50601)+~P26(x50601,f862(f96(x50601),a90)) % 14.98/14.66 [5215]E(f862(f69(a1),x52151),x52151)+P1(f862(f862(f228(a1),x52151),f2(a1))) % 14.98/14.66 [5233]~E(f862(a97,x52331),f2(a924))+P1(f862(f862(f227(a1),x52331),f2(a1))) % 14.98/14.66 [5299]~P1(f862(a186,x52991))+P1(f862(f862(f228(a1),x52991),f2(a1))) % 14.98/14.66 [5339]~P142(x53391)+P1(f862(f862(f321(x53391),f71(x53391)),f102(x53391))) % 14.98/14.66 [5340]~P147(x53401)+P1(f862(f862(f321(x53401),f71(x53401)),f179(x53401))) % 14.98/14.66 [5341]~P142(x53411)+P1(f862(f862(f321(x53411),f2(x53411)),f102(x53411))) % 14.98/14.66 [5342]~P147(x53421)+P1(f862(f862(f321(x53421),f2(x53421)),f179(x53421))) % 14.98/14.66 [5343]~P127(x53431)+P1(f862(f862(f227(x53431),f2(x53431)),f71(x53431))) % 14.98/14.66 [5344]~P127(x53441)+P1(f862(f862(f228(x53441),f2(x53441)),f71(x53441))) % 14.98/14.66 [5398]E(x53981,f71(a924))+~P1(f862(f862(f278(a924),x53981),f71(a924))) % 14.98/14.66 [5399]E(x53991,f2(a924))+~P1(f862(f862(f227(a924),x53991),f2(a924))) % 14.98/14.66 [5442]E(f862(a97,x54421),f2(a924))+~P1(f862(f862(f227(a1),x54421),f2(a1))) % 14.98/14.66 [5499]P1(f862(a186,x54991))+~P1(f862(f862(f228(a1),x54991),f2(a1))) % 14.98/14.66 [5506]~P109(x55061)+P14(x55061,f925(x55061),f141(x55061,x55061,f7(x55061))) % 14.98/14.66 [5524]P38(x55241)+~P1(f862(f862(f227(a1),f2(a1)),f424(x55241))) % 14.98/14.66 [5529]E(f862(f69(a1),x55291),f862(f72(a1),x55291))+~P1(f862(f862(f228(a1),x55291),f2(a1))) % 14.98/14.66 [5702]~P127(x57021)+~P1(f862(f862(f227(x57021),f71(x57021)),f2(x57021))) % 14.98/14.66 [5703]~P127(x57031)+~P1(f862(f862(f228(x57031),f71(x57031)),f2(x57031))) % 14.98/14.66 [5719]~E(x57191,f2(a924))+P1(f862(f862(f227(a1),f862(f93(a1),x57191)),f2(a1))) % 14.98/14.66 [5720]~E(x57201,f2(a1))+P1(f862(f862(f228(a1),f862(f69(a1),x57201)),f71(a1))) % 14.98/14.66 [5845]~P81(x58451)+E(f135(x58451,x58451,f73(x58451),f2(x58451)),f158(x58451)) % 14.98/14.66 [6026]~P105(x60261)+P22(a924,x60261,f93(x60261),f234(f932(a924,a921))) % 14.98/14.66 [6229]E(x62291,f2(a924))+~P1(f862(f862(f227(a1),f862(f93(a1),x62291)),f2(a1))) % 14.98/14.66 [6230]E(x62301,f2(a1))+~P1(f862(f862(f228(a1),f862(f69(a1),x62301)),f71(a1))) % 14.98/14.66 [7031]~P1(f862(f862(f228(a1),x70311),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x70311),x70311)),f2(a1))) % 14.98/14.66 [7594]P1(f862(f862(f228(a1),x75941),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x75941),x75941)),f2(a1))) % 14.98/14.66 [8145]E(x81451,f862(a5,f2(a924)))+P1(f862(f862(f228(a924),f862(f862(f3(a924),f862(a22,x81451)),f862(a105,f2(a924)))),f862(a22,x81451))) % 14.98/14.66 [8921]~P1(f862(f862(f228(a1),x89211),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x89211),x89211)),a90)),f2(a1))) % 14.98/14.66 [9018]~P1(f862(f862(f228(a1),x90181),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f73(a1),f71(a1)),x90181)),x90181)),f2(a1))) % 14.98/14.66 [9340]P1(f862(f862(f228(a1),x93401),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93401),x93401)),a90)),f2(a1))) % 14.98/14.66 [9402]P1(f862(f862(f228(a1),x94021),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f73(a1),f71(a1)),x94021)),x94021)),f2(a1))) % 14.98/14.66 [4857]~E(a76,x48571)+E(f862(f862(f73(a1),x48571),x48571),a76) % 14.98/14.66 [4858]~E(x48581,a76)+E(f862(f862(f73(a1),x48581),x48581),a76) % 14.98/14.66 [4869]E(x48691,f2(a1))+E(f862(f862(f29(a1),x48691),x48691),f71(a1)) % 14.98/14.66 [5004]E(x50041,a76)+~E(f862(f862(f73(a1),x50041),x50041),a76) % 14.98/14.66 [5005]E(a76,x50051)+~E(f862(f862(f73(a1),x50051),x50051),a76) % 14.98/14.66 [5017]~P3(x50171)+E(f31(x50171,f181(f932(x50171,a921))),f234(x50171)) % 14.98/14.66 [5018]~P3(x50181)+E(f31(x50181,f234(f932(x50181,a921))),f181(x50181)) % 14.98/14.66 [5019]~P3(x50191)+E(f30(x50191,f181(f932(x50191,a921))),f181(x50191)) % 14.98/14.66 [5020]~P3(x50201)+E(f30(x50201,f234(f932(x50201,a921))),f234(x50201)) % 14.98/14.66 [5021]~P109(x50211)+E(f132(x50211,f181(f932(x50211,a921))),f106(x50211)) % 14.98/14.66 [5168]E(x51681,f2(a924))+P1(f862(f862(f228(a924),f2(a924)),x51681)) % 14.98/14.66 [5189]~P4(x51891)+P1(f862(f862(f227(a1),f2(a1)),x51891)) % 14.98/14.66 [5224]~E(f862(f96(a924),x52241),f2(a924))+P1(f862(f862(f227(a1),x52241),a76)) % 14.98/14.66 [5229]P38(x52291)+P1(f862(f862(f321(a1),f424(x52291)),x52291)) % 14.98/14.66 [5230]E(x52301,f862(a5,f2(a924)))+P1(f862(f862(f227(a92),f71(a92)),x52301)) % 14.98/14.66 [5271]P1(f862(a186,x52711))+P1(f862(f862(f227(a1),f2(a1)),x52711)) % 14.98/14.66 [5321]E(f862(f93(a1),f862(a97,x53211)),f2(a1))+P1(f862(f862(f227(a1),f2(a1)),x53211)) % 14.98/14.66 [5378]E(f862(f93(a1),f862(f96(a924),x53781)),f862(f96(a1),x53781))+P1(f862(a186,f862(f96(a1),x53781))) % 14.98/14.66 [5405]E(f862(f96(a924),x54051),f2(a924))+~P1(f862(a186,f862(f96(a1),x54051))) % 14.98/14.66 [5406]E(f862(f96(a924),x54061),f2(a924))+~P1(f862(f862(f227(a1),x54061),a76)) % 14.98/14.66 [5439]P4(x54391)+~P1(f862(f862(f227(a1),f2(a1)),x54391)) % 14.98/14.66 [5509]E(f862(a105,f328(x55091)),x55091)+~P1(f862(f862(f228(a924),f2(a924)),x55091)) % 14.98/14.66 [5518]E(f862(a105,f862(f96(a924),x55181)),f71(a924))+~P1(f862(a186,f862(f96(a1),x55181))) % 14.98/14.66 [5525]E(f862(f93(a1),f432(x55251)),x55251)+~P1(f862(f862(f228(a1),f2(a1)),x55251)) % 14.98/14.66 [5532]~E(x55321,f862(a5,f2(a924)))+~P1(f862(f862(f227(a92),f71(a92)),x55321)) % 14.98/14.66 [5539]E(f862(f93(a1),f862(f96(a924),x55391)),f2(a1))+~P1(f862(a186,f862(f96(a1),x55391))) % 14.98/14.66 [5566]E(f862(f158(a924),x55661),f2(a924))+P1(f862(f862(f321(a924),f656(x55661)),f862(f165(a924),x55661))) % 14.98/14.66 [5587]E(f862(f93(a1),f862(a97,x55871)),x55871)+~P1(f862(f862(f227(a1),f2(a1)),x55871)) % 14.98/14.66 [5595]~P1(f862(a186,x55951))+~P1(f862(f862(f227(a1),f2(a1)),x55951)) % 14.98/14.66 [5695]E(f862(f862(f73(a924),f71(a924)),f862(f96(a924),x56951)),f71(a924))+~P1(f862(f862(f228(a1),x56951),a76)) % 14.98/14.66 [5763]E(x57631,f2(a924))+~P1(f862(f862(f228(a924),x57631),f862(a105,f2(a924)))) % 14.98/14.66 [5786]E(x57861,f862(a105,f2(a924)))+~P1(f862(f862(f278(a924),x57861),f862(a105,f2(a924)))) % 14.98/14.66 [5804]E(f862(f862(f3(a924),f862(f96(a924),x58041)),f71(a924)),f2(a924))+~P1(f862(f862(f227(a1),x58041),a76)) % 14.98/14.66 [5805]E(f862(f862(f73(a924),f862(f96(a924),x58051)),f71(a924)),f71(a924))+~P1(f862(f862(f228(a1),x58051),a76)) % 14.98/14.66 [5817]~P38(x58171)+E(f862(f28(a924),f862(f302(a1,a924,a97),x58171)),f862(f28(a1),x58171)) % 14.98/14.66 [5846]~P109(x58461)+E(f229(x58461,f862(f9(x58461,x58461,a921),f227(x58461))),f226(x58461)) % 14.98/14.66 [5847]~P109(x58471)+E(f230(x58471,f862(f9(x58471,x58471,a921),f227(x58471))),f225(x58471)) % 14.98/14.66 [5857]E(f38(a924,f862(a105,f2(a924)),f862(f96(a924),x58571)),f862(a105,f2(a924)))+~P1(f862(a186,f862(f96(a1),x58571))) % 14.98/14.66 [5866]~P1(f862(f862(f228(a1),f2(a1)),x58661))+P1(f862(f862(f227(a1),f71(a1)),x58661)) % 14.98/14.66 [5867]P1(f862(f862(f228(a1),f2(a1)),x58671))+~P1(f862(f862(f227(a1),f71(a1)),x58671)) % 14.98/14.66 [5878]E(f862(a105,f862(f862(f3(a924),x58781),f71(a924))),x58781)+~P1(f862(f862(f228(a924),f2(a924)),x58781)) % 14.98/14.66 [5934]P1(f862(f862(f228(a924),f2(a924)),f432(x59341)))+~P1(f862(f862(f228(a1),f2(a1)),x59341)) % 14.98/14.66 [5995]E(f38(a1,f862(f96(a1),a90),x59951),f862(f862(f3(a1),x59951),f71(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x59951)) % 14.98/14.66 [6039]~P1(f862(f862(f228(a1),a76),x60391))+P1(f862(f862(f228(a924),f2(a924)),f862(f96(a924),x60391))) % 14.98/14.66 [6044]E(f862(a22,f814(x60441)),x60441)+~P1(f862(f862(f321(a924),x60441),f234(f932(a924,a921)))) % 14.98/14.66 [6097]P1(f862(f862(f228(a924),f2(a924)),f862(a97,x60971)))+~P1(f862(f862(f228(a1),f2(a1)),x60971)) % 14.98/14.66 [6147]~P1(f862(f862(f228(a924),f2(a924)),x61471))+P1(f862(f862(f228(a1),f2(a1)),f862(f93(a1),x61471))) % 14.98/14.66 [6182]~P1(f862(f862(f228(a924),f2(a924)),f862(a97,x61821)))+P1(f862(f862(f228(a1),f2(a1)),x61821)) % 14.98/14.66 [6196]~P38(x61961)+E(f862(f302(a924,a1,f93(a1)),f862(f302(a1,a924,a97),x61961)),x61961) % 14.98/14.66 [6209]P1(f862(f862(f228(a1),a76),x62091))+~P1(f862(f862(f228(a924),f2(a924)),f862(f96(a924),x62091))) % 14.98/14.66 [6265]P1(f862(f862(f228(a924),f2(a924)),x62651))+~P1(f862(f862(f228(a1),f2(a1)),f862(f93(a1),x62651))) % 14.98/14.66 [6380]E(f862(f302(a924,a1,f93(a1)),f862(f292(a924),f862(a97,x63801))),f862(f295(a1,f2(a1)),x63801))+~P1(f862(f862(f227(a1),f2(a1)),x63801)) % 14.98/14.66 [6397]~P127(x63971)+P1(f862(f862(f228(x63971),f2(x63971)),f862(f862(f73(x63971),f71(x63971)),f71(x63971)))) % 14.98/14.66 [6446]P1(f862(f862(f228(a924),f862(a105,f2(a924))),f862(a97,x64461)))+~P1(f862(f862(f228(a1),f71(a1)),x64461)) % 14.98/14.66 [6546]E(x65461,f2(a1))+P1(f862(f42(f2(a1),x65461),f862(f862(f244(a1,a1),f2(a1)),f2(a1)))) % 14.98/14.66 [6718]~P1(f862(f862(f228(a924),f862(a105,f2(a924))),f862(a97,x67181)))+P1(f862(f862(f228(a1),f71(a1)),x67181)) % 14.98/14.66 [7143]~P117(x71431)+P35(x71431,f862(f254(f931(x71431,x71431)),f862(f249(x71431,x71431,a921),f228(x71431)))) % 14.98/14.66 [5750]E(f862(f96(a924),f862(f862(f3(a1),x57501),a90)),f862(a105,f862(f96(a924),x57501)))+P1(f862(a186,f862(f96(a1),x57501))) % 14.98/14.66 [5766]~P34(x57661)+E(f862(f862(f147(a924,a1),f93(a1)),f862(f862(f147(a1,a924),a97),x57661)),x57661) % 14.98/14.66 [5884]E(f862(f72(a1),f862(f93(a1),f862(a105,f419(x58841)))),x58841)+~P1(f862(f862(f228(a1),x58841),f2(a1))) % 14.98/14.66 [5894]E(f862(f862(f73(a924),f71(a924)),f862(f96(a924),x58941)),f862(f96(a924),f862(f862(f3(a1),x58941),a90)))+P1(f862(f862(f228(a1),x58941),a76)) % 14.98/14.66 [5936]E(f862(f862(f29(a1),f862(f96(a1),a90)),x59361),f862(f96(a1),a90))+~P1(f862(f862(f228(a1),f2(a1)),x59361)) % 14.98/14.66 [6035]E(f862(f862(f3(a924),f862(f96(a924),x60351)),f71(a924)),f862(f96(a924),f862(f862(f73(a1),x60351),a90)))+P1(f862(f862(f227(a1),x60351),a76)) % 14.98/14.66 [6036]E(f862(f862(f73(a924),f862(f96(a924),x60361)),f71(a924)),f862(f96(a924),f862(f862(f3(a1),x60361),a90)))+P1(f862(f862(f228(a1),x60361),a76)) % 14.98/14.66 [6082]E(f862(a97,f862(f862(f73(a1),f71(a1)),x60821)),f862(a105,f862(a97,x60821)))+~P1(f862(f862(f227(a1),f2(a1)),x60821)) % 14.98/14.66 [6118]E(f862(a105,f862(f862(f3(a924),x61181),f862(a105,f2(a924)))),x61181)+~P1(f862(f862(f228(a924),f2(a924)),x61181)) % 14.98/14.66 [6330]E(f38(a924,f862(a105,f2(a924)),f862(f96(a924),x63301)),f862(a97,f38(a1,f71(a1),f862(f96(a1),x63301))))+P1(f862(a186,f862(f96(a1),x63301))) % 14.98/14.66 [6372]~P1(f862(f862(f84(a1),a76),x63721))+P1(f862(f862(f84(a1),a76),f862(f862(f73(a1),x63721),x63721))) % 14.98/14.66 [6373]~P1(f862(f862(f228(a1),a90),x63731))+P1(f862(f862(f227(a1),a90),f862(f862(f73(a1),x63731),x63731))) % 14.98/14.66 [6374]~P1(f862(f862(f227(a1),a76),x63741))+P1(f862(f862(f227(a1),a76),f862(f862(f73(a1),x63741),x63741))) % 14.98/14.66 [6375]~P1(f862(f862(f228(a1),a90),x63751))+P1(f862(f862(f228(a1),a90),f862(f862(f73(a1),x63751),x63751))) % 14.98/14.66 [6376]~P1(f862(f862(f228(a1),a76),x63761))+P1(f862(f862(f228(a1),a76),f862(f862(f73(a1),x63761),x63761))) % 14.98/14.66 [6560]~P1(f862(f54(x65601),f234(f932(x65601,a921))))+P1(f862(f54(f928(x65601)),f234(f932(f928(x65601),a921)))) % 14.98/14.66 [6648]~P1(f862(f862(f227(a1),f2(a1)),x66481))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f73(a1),f71(a1)),x66481))) % 14.98/14.66 [6655]E(f862(f243(a1,a1),f40(f71(a1),f862(f96(a1),x66551))),f862(f862(f29(a1),f71(a1)),f862(f96(a1),x66551)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x66551))) % 14.98/14.66 [6677]E(f862(f248(a1,a1),f40(f71(a1),f862(f96(a1),x66771))),f38(a1,f71(a1),f862(f96(a1),x66771)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x66771))) % 14.98/14.66 [6689]P1(f862(f54(x66891),f234(f932(x66891,a921))))+~P1(f862(f54(f928(x66891)),f234(f932(f928(x66891),a921)))) % 14.98/14.66 [6719]P1(f862(f862(f84(a1),a76),x67191))+~P1(f862(f862(f84(a1),a76),f862(f862(f73(a1),x67191),x67191))) % 14.98/14.66 [6720]P1(f862(f862(f227(a1),a76),x67201))+~P1(f862(f862(f227(a1),a76),f862(f862(f73(a1),x67201),x67201))) % 14.98/14.66 [6721]P1(f862(f862(f228(a1),a90),x67211))+~P1(f862(f862(f227(a1),a90),f862(f862(f73(a1),x67211),x67211))) % 14.98/14.66 [6722]P1(f862(f862(f228(a1),a90),x67221))+~P1(f862(f862(f228(a1),a90),f862(f862(f73(a1),x67221),x67221))) % 14.98/14.66 [6723]P1(f862(f862(f228(a1),a76),x67231))+~P1(f862(f862(f228(a1),a76),f862(f862(f73(a1),x67231),x67231))) % 14.98/14.66 [7035]~P1(f862(f54(x70351),f234(f932(x70351,a921))))+P1(f862(f862(f228(a924),f2(a924)),f862(f28(x70351),f234(f932(x70351,a921))))) % 14.98/14.66 [7632]P1(f862(f54(a924),x76321))+~P1(f862(f54(a1),f862(f302(a924,a1,f93(a1)),x76321))) % 14.98/14.66 [5671]~E(a90,x56711)+E(f862(f862(f3(a1),f862(f862(f73(a1),x56711),x56711)),a90),a90) % 14.98/14.66 [5672]~E(x56721,a90)+E(f862(f862(f3(a1),f862(f862(f73(a1),x56721),x56721)),a90),a90) % 14.98/14.66 [6204]E(x62041,a90)+~E(f862(f862(f3(a1),f862(f862(f73(a1),x62041),x62041)),a90),a90) % 14.98/14.66 [6205]E(a90,x62051)+~E(f862(f862(f3(a1),f862(f862(f73(a1),x62051),x62051)),a90),a90) % 14.98/14.66 [6617]~E(f862(f96(a924),x66171),f2(a924))+P1(f862(a186,f862(f96(a1),f862(f862(f73(a1),x66171),a90)))) % 14.98/14.66 [6964]~P1(f862(a186,f862(f96(a1),x69641)))+P1(f862(a186,f862(f96(a1),f862(f862(f73(a1),x69641),x69641)))) % 14.98/14.66 [6965]~P1(f862(f862(f84(a1),x69651),a76))+P1(f862(f862(f84(a1),f862(f862(f73(a1),x69651),x69651)),a76)) % 14.98/14.66 [6966]~P1(f862(f862(f227(a1),x69661),a90))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x69661),x69661)),a90)) % 14.98/14.66 [6967]~P1(f862(f862(f227(a1),x69671),a76))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x69671),x69671)),a76)) % 14.98/14.66 [6968]~P1(f862(f862(f227(a1),x69681),a90))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x69681),x69681)),a90)) % 14.98/14.66 [6969]~P1(f862(f862(f228(a1),x69691),a76))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x69691),x69691)),a76)) % 14.98/14.66 [7290]E(f862(f96(a924),x72901),f2(a924))+~P1(f862(a186,f862(f96(a1),f862(f862(f73(a1),x72901),a90)))) % 14.98/14.66 [7546]~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x75461)))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),f862(f862(f73(a1),x75461),x75461)))) % 14.98/14.66 [7547]P1(f862(a186,f862(f96(a1),x75471)))+~P1(f862(a186,f862(f96(a1),f862(f862(f73(a1),x75471),x75471)))) % 14.98/14.66 [7548]P1(f862(f862(f84(a1),x75481),a76))+~P1(f862(f862(f84(a1),f862(f862(f73(a1),x75481),x75481)),a76)) % 14.98/14.66 [7549]P1(f862(f862(f227(a1),x75491),a90))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x75491),x75491)),a90)) % 14.98/14.66 [7550]P1(f862(f862(f227(a1),x75501),a90))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x75501),x75501)),a90)) % 14.98/14.66 [7551]P1(f862(f862(f227(a1),x75511),a76))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x75511),x75511)),a76)) % 14.98/14.66 [7552]P1(f862(f862(f228(a1),x75521),a76))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x75521),x75521)),a76)) % 14.98/14.66 [7913]E(f862(a100,f567(x79131)),x79131)+~P1(f862(f862(f321(f932(f931(a924,a924),a921)),x79131),a91)) % 14.98/14.66 [6533]~P98(x65331)+E(f862(f96(x65331),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(x65331)) % 14.98/14.66 [7015]~P1(f862(a186,f862(f96(a1),x70151)))+E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x70151),x70151)),a90)),f2(a924)) % 14.98/14.66 [8089]~P1(f862(f862(f228(a1),f862(f96(a1),x80891)),f2(a1)))+E(f862(f243(a1,a1),f862(a44,f43(f862(f72(a1),f71(a1)),f862(f72(a1),f862(f96(a1),x80891))))),f862(f862(f29(a1),f71(a1)),f862(f96(a1),x80891))) % 14.98/14.66 [8103]~P1(f862(f862(f228(a1),f862(f96(a1),x81031)),f2(a1)))+E(f862(f248(a1,a1),f862(a44,f43(f862(f72(a1),f71(a1)),f862(f72(a1),f862(f96(a1),x81031))))),f38(a1,f71(a1),f862(f96(a1),x81031))) % 14.98/14.66 [8152]~P1(f862(f862(f84(a1),a90),x81521))+P1(f862(f862(f84(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x81521),x81521)),a90))) % 14.98/14.66 [8153]~P1(f862(f862(f227(a1),a90),x81531))+P1(f862(f862(f227(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x81531),x81531)),a90))) % 14.98/14.66 [8154]~P1(f862(f862(f227(a1),a76),x81541))+P1(f862(f862(f227(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x81541),x81541)),a90))) % 14.98/14.66 [8155]~P1(f862(f862(f228(a1),a90),x81551))+P1(f862(f862(f228(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x81551),x81551)),a90))) % 14.98/14.66 [8156]~P1(f862(f862(f227(a1),a76),x81561))+P1(f862(f862(f228(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x81561),x81561)),a90))) % 14.98/14.66 [8458]~P98(x84581)+~P26(x84581,f862(f96(x84581),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))) % 14.98/14.66 [8642]P1(f862(f862(f84(a1),a90),x86421))+~P1(f862(f862(f84(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x86421),x86421)),a90))) % 14.98/14.66 [8643]P1(f862(f862(f227(a1),a90),x86431))+~P1(f862(f862(f227(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x86431),x86431)),a90))) % 14.98/14.66 [8644]P1(f862(f862(f227(a1),a76),x86441))+~P1(f862(f862(f227(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x86441),x86441)),a90))) % 14.98/14.66 [8645]P1(f862(f862(f227(a1),a76),x86451))+~P1(f862(f862(f228(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x86451),x86451)),a90))) % 14.98/14.66 [8646]P1(f862(f862(f228(a1),a90),x86461))+~P1(f862(f862(f228(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x86461),x86461)),a90))) % 14.98/14.66 [8968]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x89681),x89681)),a90)),f862(f862(f79(a924,a924),f862(f96(a924),x89681)),f862(f862(f10(a924,a924,a924),a105),f862(f862(f20(a924,a924,a924),f73(a924)),f7(a924)))))+P1(f862(a186,f862(f96(a1),x89681))) % 14.98/14.66 [9831]E(x98311,f181(f932(f931(a924,a924),a921)))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x98311),f181(f932(f931(a924,a924),a921)))),a62)) % 14.98/14.66 [8894]~P1(f862(a186,f862(f96(a1),x88941)))+P1(f862(a186,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88941),x88941)),a90)))) % 14.98/14.66 [8895]~P1(f862(f862(f84(a1),x88951),a90))+P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88951),x88951)),a90)),a90)) % 14.98/14.66 [8896]~P1(f862(f862(f227(a1),x88961),a90))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88961),x88961)),a90)),a90)) % 14.98/14.66 [8897]~P1(f862(f862(f228(a1),x88971),a76))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88971),x88971)),a90)),a76)) % 14.98/14.66 [8898]~P1(f862(f862(f228(a1),x88981),a90))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88981),x88981)),a90)),a90)) % 14.98/14.66 [8899]~P1(f862(f862(f228(a1),x88991),a76))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88991),x88991)),a90)),a76)) % 14.98/14.66 [9009]~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x90091)))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x90091),x90091)),a90)))) % 14.98/14.66 [9169]~P98(x91691)+E(f862(f862(f73(x91691),f71(x91691)),f71(x91691)),f862(f96(x91691),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))) % 14.98/14.66 [9323]P1(f862(a186,f862(f96(a1),x93231)))+~P1(f862(a186,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93231),x93231)),a90)))) % 14.98/14.66 [9324]P1(f862(f862(f84(a1),x93241),a90))+~P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93241),x93241)),a90)),a90)) % 14.98/14.66 [9325]P1(f862(f862(f227(a1),x93251),a90))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93251),x93251)),a90)),a90)) % 14.98/14.66 [9326]P1(f862(f862(f228(a1),x93261),a90))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93261),x93261)),a90)),a90)) % 14.98/14.66 [9327]P1(f862(f862(f228(a1),x93271),a76))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93271),x93271)),a90)),a76)) % 14.98/14.66 [9328]P1(f862(f862(f228(a1),x93281),a76))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93281),x93281)),a90)),a76)) % 14.98/14.66 [9876]~P1(f862(f54(f931(a924,a924)),x98761))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f181(f932(f931(a924,a924),a921))),x98761)),a63)) % 14.98/14.66 [9659]~P147(x96591)+E(f862(f862(f236(x96591),f71(x96591)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(x96591)) % 14.98/14.66 [9660]~P147(x96601)+E(f862(f862(f236(x96601),f2(x96601)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(x96601)) % 14.98/14.66 [10105]~P1(f862(f862(f228(a924),f71(a924)),x101051))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f29(a924),x101051),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.66 [10111]~P1(f862(f862(f228(a924),f2(a924)),x101111))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f29(a924),f862(f862(f73(a924),x101111),f71(a924))),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.66 [10149]~E(f38(a924,x101491,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(a924))+P1(f862(f862(f228(a924),f2(a924)),f38(a924,x101491,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.66 [10168]E(f38(a924,x101681,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(a924))+~P1(f862(f862(f228(a924),f2(a924)),f38(a924,x101681,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.66 [4786]~P35(x47861,x47862)+P55(x47861,x47862) % 14.98/14.66 [4787]~P41(x47871,x47872)+P55(x47871,x47872) % 14.98/14.66 [4789]~P5(x47891,x47892)+P46(x47891,x47892) % 14.98/14.66 [4791]~P5(x47911,x47912)+P47(x47911,x47912) % 14.98/14.66 [4793]~P13(x47931,x47932)+P47(x47931,x47932) % 14.98/14.66 [4795]~P5(x47951,x47952)+P48(x47951,x47952) % 14.98/14.66 [4797]~P13(x47971,x47972)+P48(x47971,x47972) % 14.98/14.66 [4798]~P5(x47981,x47982)+P13(x47981,x47982) % 14.98/14.66 [4799]~P150(x47991,x47992)+P152(x47991,x47992) % 14.98/14.66 [4747]~E(x47471,x47472)+E(f261(x47471,x47472),f71(a92)) % 14.98/14.66 [4750]E(f209(x47501,x47502),x47501)+~E(x47502,f2(a924)) % 14.98/14.66 [4757]~E(x47572,f106(x47571))+E(f145(x47571,x47572),f106(x47571)) % 14.98/14.66 [4777]~E(f145(x47772,x47771),f106(x47772))+E(x47771,f106(x47772)) % 14.98/14.66 [4803]~P3(x48032)+P3(f932(x48031,x48032)) % 14.98/14.66 [4804]~P91(x48042)+P91(f932(x48041,x48042)) % 14.98/14.66 [4805]~P111(x48052)+P111(f932(x48051,x48052)) % 14.98/14.66 [4806]~P92(x48062)+P92(f932(x48061,x48062)) % 14.98/14.66 [4807]~P108(x48072)+P108(f932(x48071,x48072)) % 14.98/14.66 [4808]~P110(x48082)+P110(f932(x48081,x48082)) % 14.98/14.66 [4809]~P93(x48092)+P93(f932(x48091,x48092)) % 14.98/14.66 [4810]~P58(x48102)+P58(f932(x48101,x48102)) % 14.98/14.66 [4811]~P101(x48112)+P94(f932(x48111,x48112)) % 14.98/14.66 [4812]~P93(x48122)+P103(f932(x48121,x48122)) % 14.98/14.66 [4813]~P93(x48132)+P104(f932(x48131,x48132)) % 14.98/14.66 [4814]~P101(x48142)+P95(f932(x48141,x48142)) % 14.98/14.66 [4815]~P102(x48152)+P102(f932(x48151,x48152)) % 14.98/14.66 [4816]~P96(x48162)+P96(f932(x48161,x48162)) % 14.98/14.66 [4817]~P82(x48172)+P82(f932(x48171,x48172)) % 14.98/14.66 [4818]~P101(x48182)+P101(f932(x48181,x48182)) % 14.98/14.66 [4831]E(x48311,x48312)+~E(f862(a105,x48311),f862(a105,x48312)) % 14.98/14.66 [4832]E(x48321,x48322)+~E(f862(a100,x48321),f862(a100,x48322)) % 14.98/14.66 [4833]E(x48331,x48332)+~E(f862(a5,x48331),f862(a5,x48332)) % 14.98/14.66 [4835]E(x48351,x48352)+~E(f862(a22,x48351),f862(a22,x48352)) % 14.98/14.66 [4885]P37(x48851,x48852)+~E(f712(x48852,x48851),f713(x48852,x48851)) % 14.98/14.66 [4915]~P55(x49151,x49152)+P37(x49151,f299(x49151,x49152)) % 14.98/14.66 [4916]~P49(x49161,x49162)+P49(x49161,f299(x49161,x49162)) % 14.98/14.66 [4930]~P61(x49301)+E(f38(x49301,x49302,x49302),f2(x49301)) % 14.98/14.66 [4964]~P35(x49641,x49642)+P35(f925(x49641),f139(x49641,x49642)) % 14.98/14.66 [4965]~P35(x49651,x49652)+P35(f925(x49651),f138(x49651,x49652)) % 14.98/14.66 [4966]~P36(x49661,x49662)+P36(f925(x49661),f140(x49661,x49662)) % 14.98/14.66 [4967]~P36(x49671,x49672)+P36(f925(x49671),f151(x49671,x49672)) % 14.98/14.66 [4968]~P49(x49681,x49682)+P49(f925(x49681),f151(x49681,x49682)) % 14.98/14.66 [5065]~P35(x50651,x50652)+P35(f932(x50651,a921),f310(x50651,x50652)) % 14.98/14.66 [5066]~P35(x50661,x50662)+P35(f932(x50661,a921),f312(x50661,x50662)) % 14.98/14.66 [5198]~P4(x51981)+P38(f296(a1,x51981,x51982)) % 14.98/14.66 [5302]~P35(x53021,x53022)+P57(x53021,f60(x53021,x53021,x53022)) % 14.98/14.66 [5811]~P78(x58111)+P22(x58111,x58111,f72(x58111),x58112) % 14.98/14.66 [4771]~E(x47712,f106(x47711))+E(f862(f160(x47711),x47712),f106(x47711)) % 14.98/14.66 [4772]~E(x47722,f106(x47721))+E(f862(f161(x47721),x47722),f106(x47721)) % 14.98/14.66 [4837]E(x48371,f862(a97,x48372))+~E(f862(f93(a1),x48371),x48372) % 14.98/14.66 [4840]E(x48401,f106(x48402))+~E(f862(f160(x48402),x48401),f106(x48402)) % 14.98/14.66 [4841]E(x48411,f106(x48412))+~E(f862(f161(x48412),x48411),f106(x48412)) % 14.98/14.66 [4854]~P98(x48541)+E(f862(f96(x48541),x48542),f862(f95(x48541),x48542)) % 14.98/14.66 [4862]~P60(x48621)+P1(f862(f54(x48621),x48622)) % 14.98/14.66 [4870]~E(f672(x48702,x48701),f106(x48701))+E(f172(x48701,x48702),f106(f925(x48701))) % 14.98/14.66 [4879]~E(x48792,f106(x48791))+E(f862(f165(x48791),x48792),f181(f932(x48791,a921))) % 14.98/14.66 [4880]~E(x48802,f106(x48801))+E(f181(f932(x48801,a921)),f862(f165(x48801),x48802)) % 14.98/14.66 [4882]E(x48821,x48822)+~E(f862(f93(a1),x48821),f862(f93(a1),x48822)) % 14.98/14.66 [4886]E(f207(x48861,x48862),f2(a924))+P1(f862(f54(x48861),x48862)) % 14.98/14.66 [4904]~P112(x49041)+E(f75(x49041,f75(x49041,x49042)),f75(x49041,x49042)) % 14.98/14.66 [4918]~P119(x49181)+E(f862(f862(f236(x49181),x49182),f71(a924)),x49182) % 14.98/14.66 [4919]~P80(x49191)+E(f862(f862(f236(x49191),x49192),f71(a924)),x49192) % 14.98/14.66 [4920]~P49(x49201,x49202)+E(f862(f277(x49201,x49201),x49202),x49202) % 14.98/14.66 [4924]E(x49241,x49242)+E(f261(x49241,x49242),f862(f862(f73(a92),x49242),f71(a92))) % 14.98/14.66 [4927]E(f862(f28(x49271),x49272),f2(a924))+P1(f862(f54(x49271),x49272)) % 14.98/14.66 [4931]~E(f145(x49311,x49312),x49312)+P1(f862(f130(x49311),x49312)) % 14.98/14.66 [4934]~P95(x49341)+E(f862(f862(f103(x49341),x49342),f181(x49341)),x49342) % 14.98/14.66 [4935]~P94(x49351)+E(f862(f862(f94(x49351),x49352),f234(x49351)),x49352) % 14.98/14.66 [4936]~P68(x49361)+E(f862(f862(f3(x49361),x49362),f2(x49361)),x49362) % 14.98/14.66 [4937]~P71(x49371)+E(f862(f862(f74(x49371),x49372),f71(x49371)),x49372) % 14.98/14.66 [4938]~P119(x49381)+E(f862(f862(f74(x49381),x49382),f71(x49381)),x49382) % 14.98/14.66 [4939]~P80(x49391)+E(f862(f862(f74(x49391),x49392),f71(x49391)),x49392) % 14.98/14.66 [4940]~P72(x49401)+E(f862(f862(f73(x49401),x49402),f2(x49401)),x49402) % 14.98/14.66 [4941]~P119(x49411)+E(f862(f862(f73(x49411),x49412),f2(x49411)),x49412) % 14.98/14.66 [4942]~P81(x49421)+E(f862(f862(f73(x49421),x49422),f2(x49421)),x49422) % 14.98/14.66 [4943]~P121(x49431)+E(f862(f862(f281(x49431),x49432),f71(x49431)),x49432) % 14.98/14.66 [4944]~P61(x49441)+E(f862(f862(f29(x49441),x49442),f71(x49441)),x49442) % 14.98/14.66 [4945]~P119(x49451)+E(f862(f862(f236(x49451),x49452),f2(a924)),f71(x49451)) % 14.98/14.66 [4946]~P116(x49461)+E(f862(f862(f236(x49461),x49462),f2(a924)),f71(x49461)) % 14.98/14.66 [4947]~E(x49472,f181(f932(x49471,a921)))+E(f862(f28(x49471),x49472),f2(a924)) % 14.98/14.66 [4958]~P61(x49581)+E(f38(x49581,x49582,f2(x49581)),x49582) % 14.98/14.66 [4969]~P94(x49691)+E(f862(f862(f103(x49691),x49692),f234(x49691)),f234(x49691)) % 14.98/14.66 [4970]~P95(x49701)+E(f862(f862(f94(x49701),x49702),f181(x49701)),f181(x49701)) % 14.98/14.66 [4971]~P119(x49711)+E(f862(f862(f74(x49711),x49712),f2(x49711)),f2(x49711)) % 14.98/14.66 [4972]~P134(x49721)+E(f862(f862(f74(x49721),x49722),f2(x49721)),f2(x49721)) % 14.98/14.66 [4973]~P122(x49731)+E(f862(f862(f281(x49731),x49732),f2(x49731)),f2(x49731)) % 14.98/14.66 [4974]~P61(x49741)+E(f862(f862(f29(x49741),x49742),f2(x49741)),f2(x49741)) % 14.98/14.66 [4976]~P61(x49761)+E(f38(x49761,x49762,f71(x49761)),f2(x49761)) % 14.98/14.66 [4977]~P61(x49771)+E(f38(x49771,f2(x49771),x49772),f2(x49771)) % 14.98/14.66 [5006]E(x50061,f2(a924))+E(f48(x50062,x50061,f106(x50062)),f106(f925(x50062))) % 14.98/14.66 [5029]P49(x50291,x50292)+~E(f862(f277(x50291,x50291),x50292),x50292) % 14.98/14.66 [5030]P35(x50301,x50302)+~E(f589(x50302,x50301),f181(f932(x50301,a921))) % 14.98/14.66 [5031]E(x50311,f106(x50312))+~E(f862(f165(x50312),x50311),f181(f932(x50312,a921))) % 14.98/14.66 [5032]E(x50321,f106(x50322))+~E(f181(f932(x50322,a921)),f862(f165(x50322),x50321)) % 14.98/14.66 [5035]~E(x50351,x50352)+P1(f862(f862(a317,x50351),x50352)) % 14.98/14.66 [5045]P1(x50451)+P1(f862(f862(a322,x50451),x50452)) % 14.98/14.66 [5046]E(x50461,f106(x50462))+E(f862(f862(f157(x50462),x50461),f2(a924)),f862(f134(x50462),x50461)) % 14.98/14.66 [5049]E(f145(x50491,x50492),x50492)+~P1(f862(f130(x50491),x50492)) % 14.98/14.66 [5056]~P1(x50562)+P1(f862(f862(a322,x50561),x50562)) % 14.98/14.66 [5057]~P1(x50572)+P1(f862(f862(a319,x50571),x50572)) % 14.98/14.66 [5058]~P1(x50581)+P1(f862(f862(a319,x50581),x50582)) % 14.98/14.66 [5068]~E(f673(x50682,x50681),f677(x50682,x50681))+P1(f862(f130(x50681),x50682)) % 14.98/14.66 [5075]E(f862(f254(x50751),x50752),f181(f932(x50751,a921)))+P1(f862(x50752,f325(x50752))) % 14.98/14.66 [5076]E(f181(f932(x50761,a921)),f862(f254(x50761),x50762))+P1(f862(x50762,f326(x50762))) % 14.98/14.66 [5149]~P112(x51491)+E(f862(f862(f74(x51491),x51492),f75(x51491,x51492)),f862(f69(x51491),x51492)) % 14.98/14.66 [5161]~E(x51611,f2(a1))+E(f39(x51611,x51612),f862(f862(f244(a1,a1),f2(a1)),f2(a1))) % 14.98/14.66 [5194]~P55(x51941,x51942)+P55(x51941,f862(f277(x51941,x51941),x51942)) % 14.98/14.66 [5195]~P36(x51951,x51952)+P36(x51951,f862(f277(x51951,x51951),x51952)) % 14.98/14.66 [5196]~P37(x51961,x51962)+P37(x51961,f862(f277(x51961,x51961),x51962)) % 14.98/14.66 [5197]~P49(x51971,x51972)+P49(x51971,f862(f277(x51971,x51971),x51972)) % 14.98/14.66 [5220]E(x52201,x52202)+~P1(f862(f862(a317,x52201),x52202)) % 14.98/14.66 [5231]P1(x52311)+~P1(f862(f862(a318,x52312),x52311)) % 14.98/14.66 [5232]P1(x52321)+~P1(f862(f862(a318,x52321),x52322)) % 14.98/14.66 [5237]~P111(x52371)+P1(f862(f862(f227(x52371),x52372),f234(x52371))) % 14.98/14.66 [5238]~P119(x52381)+P1(f862(f862(f278(x52381),x52382),f2(x52381))) % 14.98/14.66 [5242]E(x52421,x52422)+~E(f862(x52421,f431(x52422,x52421)),f862(x52422,f431(x52422,x52421))) % 14.98/14.66 [5273]E(x52731,f2(a924))+E(f209(x52731,f38(a924,x52732,x52731)),f209(x52732,x52731)) % 14.98/14.66 [5278]~P109(x52781)+P11(x52781,f862(f862(f144(x52781),x52782),f106(x52781))) % 14.98/14.66 [5280]E(x52801,f2(a1))+P1(f862(f42(x52802,x52801),f39(x52802,x52801))) % 14.98/14.66 [5297]~P13(x52972,x52971)+P1(f862(f862(x52971,f806(x52971)),f806(x52971))) % 14.98/14.66 [5300]~E(x53001,x53002)+P1(f862(f862(f228(a924),x53001),f862(a105,x53002))) % 14.98/14.66 [5310]~E(x53101,f2(a924))+P1(f862(f862(f228(a924),x53101),f862(a105,x53102))) % 14.98/14.66 [5320]P1(f862(x53201,x53202))+P1(f862(f862(f227(a1),f2(a1)),f425(x53201))) % 14.98/14.66 [5384]E(f862(f862(f301(x53842),f745(x53842,x53841)),f788(x53842,x53841)),x53841)+E(x53841,f181(f932(x53842,a921))) % 14.98/14.66 [5385]P55(x53851,x53852)+~P55(x53851,f862(f277(x53851,x53851),x53852)) % 14.98/14.66 [5386]P36(x53861,x53862)+~P36(x53861,f862(f277(x53861,x53861),x53862)) % 14.98/14.66 [5387]P37(x53871,x53872)+~P37(x53871,f862(f277(x53871,x53871),x53872)) % 14.98/14.66 [5388]P49(x53881,x53882)+~P49(x53881,f862(f277(x53881,x53881),x53882)) % 14.98/14.66 [5391]~E(f38(a924,x53912,x53911),f2(a924))+E(f862(f862(f74(a924),x53911),f427(x53911,x53912)),x53912) % 14.98/14.66 [5392]~E(f38(a1,x53922,x53921),f2(a1))+E(f862(f862(f74(a1),x53921),f415(x53921,x53922)),x53922) % 14.98/14.66 [5419]~P1(f862(x54191,x54192))+P1(f862(f862(f227(a1),f2(a1)),f414(x54191))) % 14.98/14.66 [5430]E(f862(f862(f3(a924),f862(a97,x54301)),f862(a97,x54302)),f862(a97,x54301))+~P1(f862(a186,x54302)) % 14.98/14.66 [5454]E(f264(x54541,x54542),f71(a92))+~P1(f862(f862(f227(a92),x54541),f71(a92))) % 14.98/14.66 [5552]E(f862(f862(f157(x55521),x55522),f673(x55522,x55521)),f862(f862(f157(x55521),x55522),f677(x55522,x55521)))+P1(f862(f130(x55521),x55522)) % 14.98/14.66 [5596]~P1(f862(x55961,f83(x55962,x55961)))+P1(f862(x55961,f606(x55962,x55961))) % 14.98/14.66 [5661]P57(x56611,x56612)+~P1(f862(f307(x56611,x56612),f557(x56612,x56611))) % 14.98/14.66 [5808]~P13(x58082,x58081)+P1(f862(f862(x58081,f807(x58081,x58082)),f807(x58081,x58082))) % 14.98/14.66 [5809]~P13(x58092,x58091)+P1(f862(f862(x58091,f810(x58091,x58092)),f810(x58091,x58092))) % 14.98/14.66 [5818]~E(f862(a105,f38(a924,x58181,x58182)),x58182)+E(f38(a924,f862(a105,x58181),x58182),f2(a924)) % 14.98/14.66 [5873]P35(x58731,x58732)+P1(f862(f862(f321(x58731),f609(x58732,x58731)),f610(x58732,x58731))) % 14.98/14.66 [5880]~P98(x58801)+P1(f862(f862(f321(x58801),f862(f96(x58801),x58802)),f102(x58801))) % 14.98/14.66 [5881]~P142(x58811)+P1(f862(f862(f321(x58811),f862(f93(x58811),x58812)),f102(x58811))) % 14.98/14.66 [5882]~P147(x58821)+P1(f862(f862(f321(x58821),f862(f93(x58821),x58822)),f179(x58821))) % 14.98/14.66 [5883]~P142(x58831)+P1(f862(f862(f321(x58831),f862(f95(x58831),x58832)),f102(x58831))) % 14.98/14.66 [6024]~P36(x60241,x60242)+E(f862(f862(f280(x60241,x60241,x60241),x60242),f299(x60241,x60242)),x60242) % 14.98/14.66 [6038]E(f862(a105,f38(a924,x60381,x60382)),x60382)+E(f38(a924,f862(a105,x60381),x60382),f862(a105,f38(a924,x60381,x60382))) % 14.98/14.66 [6458]P35(x64581,x64582)+~P1(f862(f862(f321(x64581),f545(x64582,x64581)),f308(x64581,x64582))) % 14.98/14.66 [6496]~P127(x64961)+~P1(f862(f862(f228(x64961),f862(f93(x64961),x64962)),f2(x64961))) % 14.98/14.66 [6497]~P86(x64971)+~P1(f862(f862(f228(x64971),f862(f69(x64971),x64972)),f2(x64971))) % 14.98/14.66 [6529]E(x65291,f181(f932(x65292,a921)))+~P1(f862(f862(f321(x65292),f745(x65292,x65291)),f788(x65292,x65291))) % 14.98/14.66 [6588]P1(f862(f862(f228(a1),x65881),f38(a1,x65882,x65881)))+~P1(f862(f862(f228(a1),x65881),f2(a1))) % 14.98/14.66 [6691]E(f862(f862(f301(a924),f862(a105,x66911)),f296(a924,x66912,x66911)),f296(a924,x66912,f862(a105,x66911)))+~P1(f862(f862(f227(a924),x66912),f862(a105,x66911))) % 14.98/14.66 [6780]~P109(x67801)+P11(x67801,f143(x67801,x67801,f7(x67801),x67802)) % 14.98/14.66 [6907]E(f862(f160(x69071),x69072),x69072)+~P1(f862(f862(f227(a924),f862(f182(f925(x69071)),x69072)),f71(a924))) % 14.98/14.66 [6926]~P86(x69261)+P1(f862(f862(f227(x69261),f862(f72(x69261),f862(f69(x69261),x69262))),f2(x69261))) % 14.98/14.66 [6960]~P35(x69601,x69602)+P35(x69601,f862(f862(f280(x69601,x69601,x69601),x69602),f299(x69601,x69602))) % 14.98/14.66 [6961]~P49(x69611,x69612)+P49(x69611,f862(f862(f280(x69611,x69611,x69611),x69612),f299(x69611,x69612))) % 14.98/14.66 [7184]~P1(f862(f862(f228(a1),x71842),f2(a1)))+P1(f862(f862(f227(a1),f38(a1,x71841,x71842)),f2(a1))) % 14.98/14.66 [7588]~P147(x75881)+E(f183(x75881,f862(f862(f9(x75881,x75881,x75881),f73(x75881)),f71(x75881)),x75882,f2(x75881)),f862(f93(x75881),x75882)) % 14.98/14.66 [7618]~P129(x76181)+~P1(f862(f862(f228(x76181),f862(f862(f74(x76181),x76182),x76182)),f2(x76181))) % 14.98/14.66 [10257]~P112(x102571)+~P1(f862(f862(f228(x102571),f862(f862(f236(x102571),x102572),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f2(x102571))) % 14.98/14.66 [4838]~E(x48382,f106(x48381))+E(f862(f182(f925(x48381)),x48382),f2(a924)) % 14.98/14.66 [4871]~E(x48711,f2(a924))+E(f862(f862(f73(a924),x48711),x48712),x48712) % 14.98/14.66 [4872]~E(x48722,f2(a924))+E(f862(f862(f74(a924),x48721),x48722),f2(a924)) % 14.98/14.66 [4874]~E(x48741,f2(a924))+E(f862(f862(f74(a924),x48741),x48742),f2(a924)) % 14.98/14.66 [4875]~E(x48752,f2(a924))+E(f862(f862(f236(a924),x48751),x48752),f71(a924)) % 14.98/14.66 [4876]~E(x48762,f2(a1))+E(f862(f862(f29(a1),x48761),x48762),f2(a1)) % 14.98/14.66 [4887]E(x48871,f106(x48872))+~E(f862(f182(f925(x48872)),x48871),f2(a924)) % 14.98/14.66 [4888]~P93(x48881)+E(f862(f862(f103(x48881),x48882),x48882),x48882) % 14.98/14.66 [4890]~P103(x48901)+E(f862(f862(f103(x48901),x48902),x48902),x48902) % 14.98/14.66 [4891]~P93(x48911)+E(f862(f862(f94(x48911),x48912),x48912),x48912) % 14.98/14.66 [4893]~P104(x48931)+E(f862(f862(f94(x48931),x48932),x48932),x48932) % 14.98/14.66 [4895]~P100(x48951)+E(f862(f862(f74(x48951),x48952),x48952),x48952) % 14.98/14.66 [4897]~P109(x48971)+E(f862(f862(f225(x48971),x48972),x48972),x48972) % 14.98/14.66 [4899]~P109(x48991)+E(f862(f862(f226(x48991),x48992),x48992),x48992) % 14.98/14.66 [4917]~P68(x49171)+E(f862(f862(f3(x49171),x49172),x49172),f2(x49171)) % 14.98/14.66 [4932]~P96(x49321)+E(f862(f72(x49321),f862(f72(x49321),x49322)),x49322) % 14.98/14.66 [4933]~P68(x49331)+E(f862(f72(x49331),f862(f72(x49331),x49332)),x49332) % 14.98/14.66 [4950]~E(x49502,f2(a924))+E(f862(f862(f236(a924),x49501),x49502),f862(a105,f2(a924))) % 14.98/14.66 [4985]~P95(x49851)+E(f862(f862(f103(x49851),f181(x49851)),x49852),x49852) % 14.98/14.66 [4986]~P94(x49861)+E(f862(f862(f94(x49861),f234(x49861)),x49862),x49862) % 14.98/14.66 [4987]~P71(x49871)+E(f862(f862(f74(x49871),f71(x49871)),x49872),x49872) % 14.98/14.66 [4988]~P119(x49881)+E(f862(f862(f74(x49881),f71(x49881)),x49882),x49882) % 14.98/14.66 [4989]~P80(x49891)+E(f862(f862(f74(x49891),f71(x49891)),x49892),x49892) % 14.98/14.66 [4990]~P72(x49901)+E(f862(f862(f73(x49901),f2(x49901)),x49902),x49902) % 14.98/14.66 [4991]~P119(x49911)+E(f862(f862(f73(x49911),f2(x49911)),x49912),x49912) % 14.98/14.66 [4992]~P81(x49921)+E(f862(f862(f73(x49921),f2(x49921)),x49922),x49922) % 14.98/14.66 [5010]~P94(x50101)+E(f862(f862(f103(x50101),f234(x50101)),x50102),f234(x50101)) % 14.98/14.66 [5011]~P95(x50111)+E(f862(f862(f94(x50111),f181(x50111)),x50112),f181(x50111)) % 14.98/14.66 [5012]~P119(x50121)+E(f862(f862(f74(x50121),f2(x50121)),x50122),f2(x50121)) % 14.98/14.66 [5013]~P134(x50131)+E(f862(f862(f74(x50131),f2(x50131)),x50132),f2(x50131)) % 14.98/14.66 [5014]~P121(x50141)+E(f862(f862(f281(x50141),f2(x50141)),x50142),f2(x50141)) % 14.98/14.66 [5015]~P80(x50151)+E(f862(f862(f236(x50151),f71(x50151)),x50152),f71(x50151)) % 14.98/14.66 [5016]~P61(x50161)+E(f862(f862(f29(x50161),f2(x50161)),x50162),f2(x50161)) % 14.98/14.66 [5024]E(x50241,f106(x50242))+E(f137(x50242,f862(f161(x50242),x50241)),f862(f134(x50242),x50241)) % 14.98/14.66 [5025]E(x50251,f106(x50252))+E(f862(f134(x50252),f862(f161(x50252),x50251)),f137(x50252,x50251)) % 14.98/14.66 [5026]E(x50261,f2(a924))+~E(f862(f862(f73(a924),x50262),x50261),x50262) % 14.98/14.66 [5033]~P98(x50331)+E(f862(f95(x50331),f862(f96(a1),x50332)),f862(f96(x50331),x50332)) % 14.98/14.66 [5034]~P142(x50341)+E(f862(f95(x50341),f862(f93(a1),x50342)),f862(f93(x50341),x50342)) % 14.98/14.66 [5041]E(x50411,f71(a924))+~E(f862(f862(f74(a924),x50412),x50411),f71(a924)) % 14.98/14.66 [5042]E(x50421,f71(a924))+~E(f862(f862(f74(a924),x50421),x50422),f71(a924)) % 14.98/14.66 [5043]E(x50431,f2(a924))+~E(f862(f862(f73(a924),x50432),x50431),f2(a924)) % 14.98/14.66 [5044]E(x50441,f2(a924))+~E(f862(f862(f73(a924),x50441),x50442),f2(a924)) % 14.98/14.66 [5061]~P86(x50611)+E(f862(f69(x50611),f862(f72(x50611),x50612)),f862(f69(x50611),x50612)) % 14.98/14.66 [5062]~P112(x50621)+E(f862(f69(x50621),f862(f93(x50621),x50622)),f862(f93(x50621),x50622)) % 14.98/14.66 [5063]~P86(x50631)+E(f862(f69(x50631),f862(f69(x50631),x50632)),f862(f69(x50631),x50632)) % 14.98/14.66 [5064]~P72(x50641)+E(f862(f158(x50641),f862(f161(x50641),x50642)),f862(f158(x50641),x50642)) % 14.98/14.66 [5069]~E(x50691,f862(a105,f2(a924)))+E(f862(f862(f236(a924),x50691),x50692),f862(a105,f2(a924))) % 14.98/14.66 [5078]~P68(x50781)+E(f862(f862(f3(x50781),f2(x50781)),x50782),f862(f72(x50781),x50782)) % 14.98/14.66 [5079]~E(x50792,f2(a924))+E(f132(a924,f862(f295(a924,x50791),x50792)),f106(a924)) % 14.98/14.66 [5088]~P98(x50881)+E(f862(f862(f73(x50881),x50882),f862(f96(x50881),a76)),x50882) % 14.98/14.66 [5089]E(x50891,f2(a1))+E(f40(f862(f69(a1),x50892),f862(f69(a1),x50891)),f46(x50892,x50891)) % 14.98/14.66 [5105]~E(x51051,x51052)+P1(f862(f862(f227(a924),x51051),x51052)) % 14.98/14.66 [5109]~E(x51091,x51092)+P1(f862(f862(f278(a924),x51091),x51092)) % 14.98/14.66 [5116]~E(x51161,f2(a92))+E(f862(f862(f73(a924),f862(a22,x51161)),x51162),x51162) % 14.98/14.66 [5130]~P4(x51301)+P4(f862(f862(f236(a1),x51301),x51302)) % 14.98/14.66 [5131]~P96(x51311)+E(f862(f862(f103(x51311),x51312),f862(f72(x51311),x51312)),f234(x51311)) % 14.98/14.66 [5132]~P96(x51321)+E(f862(f862(f94(x51321),x51322),f862(f72(x51321),x51322)),f181(x51321)) % 14.98/14.66 [5133]~P68(x51331)+E(f862(f862(f73(x51331),x51332),f862(f72(x51331),x51332)),f2(x51331)) % 14.98/14.66 [5158]E(x51581,f2(a924))+~E(f862(f72(a1),f862(f93(a1),x51582)),f862(f93(a1),x51581)) % 14.98/14.66 [5159]E(x51591,f2(a924))+~E(f862(f72(a1),f862(f93(a1),x51591)),f862(f93(a1),x51592)) % 14.98/14.66 [5169]E(f187(x51691,x51692),f2(a1))+P1(f862(f862(f227(a1),x51692),x51691)) % 14.98/14.66 [5170]E(f171(x51701,x51702),f106(a1))+P1(f862(f862(f227(a1),x51701),x51702)) % 14.98/14.66 [5171]E(f233(x51711,x51712),f2(a92))+P1(f862(f862(f228(a92),x51711),x51712)) % 14.98/14.66 [5184]E(x51841,f862(a105,f2(a924)))+~E(f862(f862(f74(a924),x51842),x51841),f862(a105,f2(a924))) % 14.98/14.66 [5185]E(x51851,f862(a105,f2(a924)))+~E(f862(f862(f74(a924),x51851),x51852),f862(a105,f2(a924))) % 14.98/14.66 [5186]~P2(x51861)+P1(f862(f862(f84(x51861),x51862),x51862)) % 14.98/14.66 [5187]~P91(x51871)+P1(f862(f862(f227(x51871),x51872),x51872)) % 14.98/14.66 [5188]~P119(x51881)+P1(f862(f862(f278(x51881),x51882),x51882)) % 14.98/14.66 [5191]~P98(x51911)+E(f862(f862(f74(x51911),x51912),f862(f96(x51911),a90)),f862(f72(x51911),x51912)) % 14.98/14.66 [5212]~P98(x52121)+E(f862(f72(x52121),f862(f96(x52121),x52122)),f862(f96(x52121),f862(f72(a1),x52122))) % 14.98/14.66 [5213]~P142(x52131)+E(f862(f72(x52131),f862(f95(x52131),x52132)),f862(f95(x52131),f862(f72(a1),x52132))) % 14.98/14.66 [5243]~E(x52431,f862(a105,x52432))+P1(f862(f862(f228(a924),f2(a924)),x52431)) % 14.98/14.66 [5261]~P109(x52611)+E(f862(f72(f932(x52611,a921)),f862(f293(x52611),x52612)),f862(f294(x52611),x52612)) % 14.98/14.66 [5262]~P109(x52621)+E(f862(f72(f932(x52621,a921)),f862(f294(x52621),x52622)),f862(f293(x52621),x52622)) % 14.98/14.66 [5263]~P109(x52631)+E(f862(f72(f932(x52631,a921)),f862(f274(x52631),x52632)),f862(f292(x52631),x52632)) % 14.98/14.66 [5264]~P109(x52641)+E(f862(f72(f932(x52641,a921)),f862(f292(x52641),x52642)),f862(f274(x52641),x52642)) % 14.98/14.66 [5272]~E(f862(f93(a1),x52722),x52721)+P1(f862(f862(f227(a1),f2(a1)),x52721)) % 14.98/14.66 [5279]~E(x52792,f2(a1))+E(f46(x52791,x52792),f862(f862(f244(a1,a1),f2(a1)),f862(f69(a1),x52791))) % 14.98/14.66 [5281]~P92(x52811)+P1(f862(f862(f227(x52811),f181(x52811)),x52812)) % 14.98/14.66 [5282]~P119(x52821)+P1(f862(f862(f278(x52821),f71(x52821)),x52822)) % 14.98/14.66 [5315]E(x53151,x53152)+~E(f862(f862(f73(a1),x53151),x53151),f862(f862(f73(a1),x53152),x53152)) % 14.98/14.66 [5319]~P1(f862(x53191,x53192))+P1(f862(x53191,f862(a97,f414(x53191)))) % 14.98/14.66 [5345]~P112(x53451)+E(f862(f862(f74(x53451),f75(x53451,x53452)),f862(f69(x53451),x53452)),x53452) % 14.98/14.66 [5352]~E(x53522,f2(a924))+E(f78(f931(a924,a924),f41(x53521,x53522)),f862(f862(f244(a924,a924),f2(a924)),x53521)) % 14.98/14.66 [5357]~E(x53571,x53572)+~P1(f862(f862(f228(a924),x53571),x53572)) % 14.98/14.66 [5358]~E(x53581,x53582)+~P1(f862(f862(f228(a1),x53581),x53582)) % 14.98/14.66 [5361]~P147(x53611)+E(f862(f862(f73(x53611),f71(x53611)),f862(f93(x53611),x53612)),f862(f93(x53611),f862(a105,x53612))) % 14.98/14.66 [5365]~E(x53651,f2(a924))+~P1(f862(f862(f228(a924),x53652),x53651)) % 14.98/14.66 [5379]E(f145(x53791,x53792),x53792)+~E(f862(f182(f925(x53791)),f145(x53791,x53792)),f862(f182(f925(x53791)),x53792)) % 14.98/14.66 [5380]E(f862(f28(x53801),f862(f165(x53801),x53802)),f862(f182(f925(x53801)),x53802))+~P1(f862(f130(x53801),x53802)) % 14.98/14.66 [5396]~P1(f862(x53961,f357(x53961)))+P1(f862(x53961,f862(f93(a1),x53962))) % 14.98/14.66 [5407]E(f233(x54071,x54072),x54072)+~P1(f862(f862(f228(a92),x54071),x54072)) % 14.98/14.66 [5409]E(f264(x54091,x54092),f71(a92))+~P1(f862(f862(f228(a92),x54092),x54091)) % 14.98/14.66 [5410]E(f171(x54101,x54102),f106(a1))+~P1(f862(f862(f228(a1),x54102),x54101)) % 14.98/14.66 [5411]E(f121(x54111,x54112),f108(a1))+~P1(f862(f862(f228(a1),x54111),x54112)) % 14.98/14.66 [5413]~P110(x54131)+E(f296(x54131,x54132,x54132),f862(f862(f301(x54131),x54132),f181(f932(x54131,a921)))) % 14.98/14.66 [5433]~E(f862(f862(f3(a1),x54331),x54332),f2(a1))+P1(f862(f862(f84(a1),x54331),x54332)) % 14.98/14.66 [5434]~E(f862(f862(f3(a924),x54341),x54342),f2(a924))+P1(f862(f862(f227(a924),x54341),x54342)) % 14.98/14.66 [5451]~E(x54512,f2(a924))+E(f48(x54511,x54512,f106(x54511)),f862(f862(f144(f925(x54511)),f106(x54511)),f106(f925(x54511)))) % 14.98/14.66 [5455]~P91(x54551)+~P1(f862(f862(f228(x54551),x54552),x54552)) % 14.98/14.66 [5457]~E(f38(a1,x54571,x54572),f2(a1))+E(f38(a1,x54571,f862(f72(a1),x54572)),f2(a1)) % 14.98/14.66 [5459]~E(f38(a1,x54591,x54592),f2(a1))+E(f38(a1,f862(f72(a1),x54591),x54592),f2(a1)) % 14.98/14.66 [5467]E(f862(f295(a924,x54671),f862(a105,x54672)),f181(f932(a924,a921)))+P1(f862(f862(f227(a924),x54671),x54672)) % 14.98/14.66 [5491]E(f132(a924,f862(f295(a924,x54911),x54912)),f106(a924))+P1(f862(f862(f228(a924),x54911),x54912)) % 14.98/14.66 [5496]~E(f862(f28(x54961),f862(f165(x54961),x54962)),f862(f182(f925(x54961)),x54962))+P1(f862(f130(x54961),x54962)) % 14.98/14.66 [5500]~P1(f862(f130(x55001),x55002))+P1(f862(f130(x55001),f862(f160(x55001),x55002))) % 14.98/14.66 [5501]~P1(f862(f130(x55011),x55012))+P1(f862(f130(x55011),f862(f164(x55011),x55012))) % 14.98/14.66 [5502]~P1(f862(f130(x55021),x55022))+P1(f862(f130(x55021),f862(f161(x55021),x55022))) % 14.98/14.66 [5510]P1(f862(x55101,x55102))+~P1(f862(x55101,f862(a97,f425(x55101)))) % 14.98/14.66 [5511]P1(f862(f862(f227(a924),x55112),x55111))+P1(f862(f862(f227(a924),x55111),x55112)) % 14.98/14.66 [5512]P1(f862(f862(f227(a1),x55122),x55121))+P1(f862(f862(f227(a1),x55121),x55122)) % 14.98/14.66 [5516]~P86(x55161)+P1(f862(f862(f227(x55161),x55162),f862(f69(x55161),x55162))) % 14.98/14.66 [5519]P1(f862(x55191,f358(x55191)))+~P1(f862(x55191,f862(f93(a1),x55192))) % 14.98/14.66 [5543]E(f862(f862(f3(a924),x55431),x55432),f2(a924))+~P1(f862(f862(f227(a924),x55431),x55432)) % 14.98/14.66 [5544]E(f862(f862(f3(a1),x55441),x55442),f2(a1))+~P1(f862(f862(f84(a1),x55441),x55442)) % 14.98/14.66 [5545]E(f862(f862(f29(a924),x55451),x55452),f2(a924))+~P1(f862(f862(f228(a924),x55451),x55452)) % 14.98/14.66 [5564]E(f38(a924,x55641,x55642),x55641)+~P1(f862(f862(f228(a924),x55641),x55642)) % 14.98/14.66 [5572]E(f38(a1,x55721,f862(f72(a1),x55722)),f282(x55721,x55722))+P1(f862(f862(f227(a1),f2(a1)),x55722)) % 14.98/14.66 [5585]E(f862(f862(f3(a1),x55851),x55852),f187(x55851,x55852))+~P1(f862(f862(f227(a1),x55852),x55851)) % 14.98/14.66 [5605]P1(f862(f862(f227(a1),f2(a1)),f357(x56051)))+P1(f862(x56051,f862(f93(a1),x56052))) % 14.98/14.66 [5618]~P127(x56181)+P1(f862(f862(f227(x56181),f2(x56181)),f862(f93(x56181),x56182))) % 14.98/14.66 [5619]~P86(x56191)+P1(f862(f862(f227(x56191),f2(x56191)),f862(f69(x56191),x56192))) % 14.98/14.66 [5647]E(f862(f862(f73(a924),x56471),f864(x56472,x56471)),x56472)+~P1(f862(f862(f227(a924),x56471),x56472)) % 14.98/14.66 [5662]E(f296(a1,x56621,x56622),f181(f932(a1,a921)))+~P1(f862(f862(f228(a1),x56622),x56621)) % 14.98/14.66 [5665]~P112(x56651)+E(f862(f862(f74(x56651),f862(f69(x56651),x56652)),f862(f69(x56651),x56652)),f862(f862(f74(x56651),x56652),x56652)) % 14.98/14.66 [5670]E(f132(a924,f862(f295(a924,x56701),f862(a105,x56702))),f106(a924))+P1(f862(f862(f227(a924),x56701),x56702)) % 14.98/14.66 [5673]E(f862(f862(f29(a1),x56731),x56732),f283(x56731,x56732))+~P1(f862(f862(f227(a1),f2(a1)),x56732)) % 14.98/14.66 [5693]P1(f862(f130(x56931),x56932))+~P1(f862(f130(x56931),f862(f160(x56931),x56932))) % 14.98/14.66 [5694]P1(f862(f130(x56941),x56942))+~P1(f862(f130(x56941),f862(f161(x56941),x56942))) % 14.98/14.66 [5721]P1(f862(f54(a924),x57211))+P1(f862(f862(f321(a924),f865(x57211,x57212)),x57211)) % 14.98/14.66 [5722]P1(f862(f54(a924),x57221))+P1(f862(f862(f321(a924),f912(x57221,x57222)),x57221)) % 14.98/14.66 [5725]P1(f862(f862(f228(a924),x57252),f862(a105,x57251)))+P1(f862(f862(f228(a924),x57251),x57252)) % 14.98/14.66 [5726]E(f38(a1,x57261,x57262),f282(x57261,x57262))+~P1(f862(f862(f227(a1),f2(a1)),x57262)) % 14.98/14.66 [5730]E(f132(a924,f862(f295(a924,x57301),x57302)),f106(a924))+~P1(f862(f862(f227(a924),x57302),x57301)) % 14.98/14.66 [5731]~P78(x57311)+E(f862(f302(x57311,x57311,f72(x57311)),f862(f293(x57311),x57312)),f862(f292(x57311),f862(f72(x57311),x57312))) % 14.98/14.66 [5732]~P78(x57321)+E(f862(f302(x57321,x57321,f72(x57321)),f862(f294(x57321),x57322)),f862(f274(x57321),f862(f72(x57321),x57322))) % 14.98/14.66 [5733]~P78(x57331)+E(f862(f302(x57331,x57331,f72(x57331)),f862(f274(x57331),x57332)),f862(f294(x57331),f862(f72(x57331),x57332))) % 14.98/14.66 [5734]~P78(x57341)+E(f862(f302(x57341,x57341,f72(x57341)),f862(f292(x57341),x57342)),f862(f293(x57341),f862(f72(x57341),x57342))) % 14.98/14.66 [5745]E(x57451,f181(f932(x57452,a921)))+P1(f862(f862(f321(x57452),f359(x57451,x57452)),x57451)) % 14.98/14.66 [5746]E(x57461,f181(f932(x57462,a921)))+P1(f862(f862(f321(x57462),f570(x57461,x57462)),x57461)) % 14.98/14.66 [5747]E(x57471,f181(f932(x57472,a921)))+P1(f862(f862(f321(x57472),f395(x57471,x57472)),x57471)) % 14.98/14.66 [5758]~P1(f862(f862(f228(a924),x57581),x57582))+P1(f862(f862(f227(a924),x57581),x57582)) % 14.98/14.66 [5759]~P1(f862(f862(f228(a1),x57591),x57592))+P1(f862(f862(f227(a1),x57591),x57592)) % 14.98/14.66 [5776]E(f40(x57761,x57762),f862(f862(f244(a1,a1),f2(a1)),x57761))+~P1(f862(f862(f228(a1),x57761),x57762)) % 14.98/14.66 [5778]E(f208(f862(f72(a1),x57781),f862(f72(a1),x57782)),f208(x57781,x57782))+~P1(f862(f862(f228(a1),x57782),f2(a1))) % 14.98/14.66 [5790]E(x57901,x57902)+~E(f862(a5,f862(a105,f862(a22,x57901))),f862(a5,f862(a105,f862(a22,x57902)))) % 14.98/14.66 [5795]E(f40(x57951,x57952),f862(f862(f244(a1,a1),f2(a1)),x57951))+~P1(f862(f862(f227(a1),x57952),f2(a1))) % 14.98/14.66 [5824]E(f38(a924,f862(f96(a924),x58241),f862(f96(a924),x58242)),f2(a924))+~P1(f862(a186,f862(f96(a1),x58241))) % 14.98/14.66 [5838]P1(f862(f862(f227(a1),f2(a1)),f358(x58381)))+~P1(f862(x58381,f862(f93(a1),x58382))) % 14.98/14.66 [5871]P38(f296(a1,x58711,x58712))+~P1(f862(f862(f227(a1),f2(a1)),x58711)) % 14.98/14.66 [5876]~P1(f862(f54(x58761),x58762))+P1(f862(f54(f932(x58761,a921)),f862(f300(x58761),x58762))) % 14.98/14.66 [5889]E(f862(f862(f73(a1),x58891),f862(f93(a1),f409(x58892,x58891))),x58892)+~P1(f862(f862(f227(a1),x58891),x58892)) % 14.98/14.66 [5897]P1(f862(f862(f227(a924),x58971),x58972))+P1(f862(f862(f227(a924),f862(a105,x58972)),x58971)) % 14.98/14.66 [5941]E(f862(f862(f29(a924),f862(f96(a924),x59411)),f862(f96(a924),x59412)),f2(a924))+~P1(f862(a186,f862(f96(a1),x59411))) % 14.98/14.66 [5942]E(f862(f862(f74(a924),f862(f96(a924),x59421)),f862(f96(a924),x59422)),f2(a924))+~P1(f862(f862(f228(a1),x59421),a76)) % 14.98/14.66 [5944]P1(f862(f862(f227(a924),x59441),f862(a105,x59442)))+~P1(f862(f862(f227(a924),x59441),x59442)) % 14.98/14.66 [5946]P1(f862(f862(f228(a924),x59461),f862(a105,x59462)))+~P1(f862(f862(f227(a924),x59461),x59462)) % 14.98/14.66 [5948]P1(f862(f862(f228(a924),x59481),f862(a105,x59482)))+~P1(f862(f862(f228(a924),x59481),x59482)) % 14.98/14.66 [5951]~E(x59511,x59512)+P1(f862(f862(f228(a1),x59511),f862(f862(f73(a1),x59512),f71(a1)))) % 14.98/14.66 [5954]E(f38(a1,x59541,x59542),f2(a1))+E(f862(f862(f3(a1),x59542),f38(a1,x59541,x59542)),f38(a1,f862(f72(a1),x59541),x59542)) % 14.98/14.66 [5963]E(x59631,f106(x59632))+P1(f862(f862(f321(x59632),f137(x59632,x59631)),f862(f165(x59632),x59631))) % 14.98/14.66 [5975]E(f78(f931(a924,a924),f41(x59751,x59752)),f862(f862(f244(a924,a924),f2(a924)),x59751))+~P1(f862(f862(f228(a924),x59751),x59752)) % 14.98/14.66 [6017]E(f862(f862(f3(a924),f862(f96(a924),x60171)),f862(f96(a924),x60172)),f862(f96(a924),x60171))+~P1(f862(f862(f228(a1),x60172),a76)) % 14.98/14.66 [6018]E(f862(f862(f73(a924),f862(f96(a924),x60181)),f862(f96(a924),x60182)),f862(f96(a924),x60182))+~P1(f862(f862(f228(a1),x60181),a76)) % 14.98/14.66 [6025]E(f862(a105,f862(f862(f73(a924),x60251),f332(x60252,x60251))),x60252)+~P1(f862(f862(f228(a924),x60251),x60252)) % 14.98/14.66 [6049]P1(f862(x60491,x60492))+~P1(f862(x60491,f862(a82,f578(x60492,x60491)))) % 14.98/14.66 [6050]P1(f862(x60501,x60502))+~P1(f862(x60501,f862(a5,f823(x60502,x60501)))) % 14.98/14.66 [6059]~P1(f862(f862(f228(a924),x60591),f862(a105,x60592)))+P1(f862(f862(f227(a924),x60591),x60592)) % 14.98/14.66 [6109]E(f862(f862(f301(a924),x61091),f862(f295(a924,x61092),x61091)),f862(f295(a924,x61092),f862(a105,x61091)))+~P1(f862(f862(f227(a924),x61092),x61091)) % 14.98/14.66 [6111]E(x61111,f106(x61112))+E(f862(f862(f127(x61112),f107(x61112,x61111)),f862(f862(f144(x61112),f137(x61112,x61111)),f106(x61112))),x61111) % 14.98/14.66 [6128]P1(f862(f54(x61281),x61282))+~P1(f862(f862(f228(a924),f2(a924)),f862(f28(x61281),x61282))) % 14.98/14.66 [6132]~E(x61321,f181(f932(x61322,a921)))+~P1(f862(f862(f228(a924),f2(a924)),f862(f28(x61322),x61321))) % 14.98/14.66 [6144]~P1(f862(f862(f228(a924),x61441),x61442))+P1(f862(f862(f227(a924),f862(a105,x61441)),x61442)) % 14.98/14.66 [6148]~P109(x61481)+E(f143(x61481,x61481,f7(x61481),f145(x61481,x61482)),f132(x61481,f862(f165(x61481),x61482))) % 14.98/14.66 [6151]E(x61511,f106(x61512))+P1(f862(f862(f321(x61512),f862(f134(x61512),x61511)),f862(f165(x61512),x61511))) % 14.98/14.66 [6157]~P127(x61571)+P1(f862(f862(f228(x61571),x61572),f862(f862(f73(x61571),x61572),f71(x61571)))) % 14.98/14.66 [6159]~P86(x61591)+P1(f862(f862(f227(x61591),f862(f72(x61591),x61592)),f862(f69(x61591),x61592))) % 14.98/14.66 [6189]P1(f862(f54(a924),x61891))+~P1(f862(f862(f227(a924),f865(x61891,x61892)),x61892)) % 14.98/14.66 [6190]P1(f862(f54(a924),x61901))+~P1(f862(f862(f228(a924),f912(x61901,x61902)),x61902)) % 14.98/14.66 [6193]~P1(f862(f54(f931(x61931,x61931)),x61932))+P1(f862(f54(x61931),f862(f273(x61931),x61932))) % 14.98/14.66 [6215]E(f234(f932(x62151,a921)),x62152)+~P1(f862(f862(f321(x62151),f528(x62152,x62151)),x62152)) % 14.98/14.66 [6249]~P1(f862(f862(f228(a924),x62492),f862(a105,x62491)))+~P1(f862(f862(f228(a924),x62491),x62492)) % 14.98/14.66 [6250]~P110(x62501)+E(f862(f862(f94(f932(x62501,a921)),f862(f294(x62501),x62502)),f862(f274(x62501),x62502)),f862(f862(f301(x62501),x62502),f181(f932(x62501,a921)))) % 14.98/14.66 [6262]P1(f862(f54(x62621),x62622))+~P1(f862(f54(f932(x62621,a921)),f862(f300(x62621),x62622))) % 14.98/14.66 [6284]P1(f862(f862(f227(a924),f862(a105,x62841)),f862(a105,x62842)))+~P1(f862(f862(f227(a924),x62841),x62842)) % 14.98/14.66 [6285]P1(f862(f862(f227(a924),f862(a22,x62851)),f862(a22,x62852)))+~P1(f862(f862(f227(a92),x62851),x62852)) % 14.98/14.66 [6286]P1(f862(f862(f227(a92),f862(a5,x62861)),f862(a5,x62862)))+~P1(f862(f862(f227(a924),x62861),x62862)) % 14.98/14.66 [6288]P1(f862(f862(f228(a924),f862(a105,x62881)),f862(a105,x62882)))+~P1(f862(f862(f228(a924),x62881),x62882)) % 14.98/14.66 [6289]P1(f862(f862(f228(a924),f862(a22,x62891)),f862(a22,x62892)))+~P1(f862(f862(f228(a92),x62891),x62892)) % 14.98/14.66 [6290]P1(f862(f862(f228(a92),f862(a5,x62901)),f862(a5,x62902)))+~P1(f862(f862(f228(a924),x62901),x62902)) % 14.98/14.66 [6295]E(x62951,x62952)+~E(f862(f302(a924,a1,f93(a1)),x62951),f862(f302(a924,a1,f93(a1)),x62952)) % 14.98/14.66 [6311]P1(f862(f862(f227(a924),x63111),x63112))+~P1(f862(f862(f227(a924),f862(a105,x63111)),x63112)) % 14.98/14.66 [6314]P1(f862(f862(f228(a924),x63141),x63142))+~P1(f862(f862(f227(a924),f862(a105,x63141)),x63142)) % 14.98/14.66 [6315]P1(f862(f862(f228(a924),x63151),x63152))+~P1(f862(f862(f228(a924),f862(a105,x63151)),x63152)) % 14.98/14.66 [6333]E(f38(a1,x63331,x63332),f2(a1))+E(f862(f862(f3(a1),f38(a1,x63331,x63332)),x63332),f38(a1,x63331,f862(f72(a1),x63332))) % 14.98/14.66 [6400]E(f862(f28(f932(x64001,a921)),f862(f300(x64001),x64002)),f862(f862(f236(a924),f862(a105,f862(a105,f2(a924)))),f862(f28(x64001),x64002)))+~P1(f862(f54(x64001),x64002)) % 14.98/14.66 [6403]E(x64031,f106(x64032))+E(f862(f862(f157(x64032),x64031),f862(f862(f3(a924),f862(f182(f925(x64032)),x64031)),f71(a924))),f137(x64032,x64031)) % 14.98/14.66 [6425]E(x64251,f106(x64252))+E(f862(f862(f127(x64252),f862(f164(x64252),x64251)),f862(f862(f144(x64252),f862(f134(x64252),x64251)),f106(x64252))),f862(f160(x64252),x64251)) % 14.98/14.66 [6455]~P1(f862(f54(x64551),f30(f932(x64551,a921),x64552)))+P1(f862(f54(f932(x64551,a921)),x64552)) % 14.98/14.66 [6477]P1(f862(f862(f227(a924),f862(f96(a924),x64771)),f862(f96(a924),x64772)))+~P1(f862(f862(f227(a1),x64771),a76)) % 14.98/14.66 [6498]~P1(f862(f862(f228(a1),x64981),x64982))+P1(f862(f862(f227(a1),x64981),f862(f862(f3(a1),x64982),f71(a1)))) % 14.98/14.66 [6499]~P1(f862(f862(f227(a1),x64991),x64992))+P1(f862(f862(f228(a1),x64991),f862(f862(f73(a1),x64992),f71(a1)))) % 14.98/14.66 [6500]~P1(f862(f862(f228(a1),x65001),x65002))+P1(f862(f862(f228(a1),x65001),f862(f862(f73(a1),x65002),f71(a1)))) % 14.98/14.66 [6502]~P1(f862(f862(f84(a1),x65021),x65022))+P1(f862(f862(f84(a1),f862(f96(a1),x65021)),f862(f96(a1),x65022))) % 14.98/14.66 [6503]~P1(f862(f862(f227(a1),x65031),x65032))+P1(f862(f862(f227(a924),f862(f96(a924),x65031)),f862(f96(a924),x65032))) % 14.98/14.66 [6504]~P1(f862(f862(f227(a1),x65041),x65042))+P1(f862(f862(f227(a1),f862(f96(a1),x65041)),f862(f96(a1),x65042))) % 14.98/14.66 [6506]~P1(f862(f862(f227(a924),x65061),x65062))+P1(f862(f862(f227(a1),f862(f93(a1),x65061)),f862(f93(a1),x65062))) % 14.98/14.66 [6507]~P1(f862(f862(f228(a1),x65071),x65072))+P1(f862(f862(f228(a1),f862(f96(a1),x65071)),f862(f96(a1),x65072))) % 14.98/14.66 [6509]~P1(f862(f862(f228(a924),x65091),x65092))+P1(f862(f862(f228(a1),f862(f93(a1),x65091)),f862(f93(a1),x65092))) % 14.98/14.66 [6530]~P1(f862(f862(f227(a924),x65301),x65302))+~P1(f862(f862(f227(a924),f862(a105,x65302)),x65301)) % 14.98/14.66 [6573]~P1(f862(f862(f227(a924),f862(a105,x65731)),f862(a105,x65732)))+P1(f862(f862(f227(a924),x65731),x65732)) % 14.98/14.66 [6574]~P1(f862(f862(f227(a92),f862(a5,x65741)),f862(a5,x65742)))+P1(f862(f862(f227(a924),x65741),x65742)) % 14.98/14.66 [6575]~P1(f862(f862(f227(a924),f862(a22,x65751)),f862(a22,x65752)))+P1(f862(f862(f227(a92),x65751),x65752)) % 14.98/14.66 [6577]~P1(f862(f862(f228(a924),f862(a105,x65771)),f862(a105,x65772)))+P1(f862(f862(f228(a924),x65771),x65772)) % 14.98/14.66 [6578]~P1(f862(f862(f228(a92),f862(a5,x65781)),f862(a5,x65782)))+P1(f862(f862(f228(a924),x65781),x65782)) % 14.98/14.66 [6579]~P1(f862(f862(f228(a924),f862(a97,x65791)),f862(a97,x65792)))+P1(f862(f862(f228(a1),x65791),x65792)) % 14.98/14.66 [6580]~P1(f862(f862(f228(a924),f862(a22,x65801)),f862(a22,x65802)))+P1(f862(f862(f228(a92),x65801),x65802)) % 14.98/14.66 [6623]~P1(f862(f862(f228(a924),f862(a97,x66232)),f862(a97,x66231)))+P1(f862(f862(f228(a1),f2(a1)),x66231)) % 14.98/14.66 [6654]P1(f862(f862(f227(a1),f2(a1)),f38(a1,x66541,x66542)))+~P1(f862(f862(f228(a1),f2(a1)),x66542)) % 14.98/14.66 [6814]P35(x68141,x68142)+~E(f862(f862(f280(x68141,x68141,x68141),x68142),x68142),f181(f932(f931(x68141,x68141),a921))) % 14.98/14.66 [6826]~P35(x68261,x68262)+P35(x68261,f862(f862(f280(x68261,x68261,x68261),x68262),x68262)) % 14.98/14.66 [6837]P1(f862(f862(f227(a1),x68371),x68372))+~P1(f862(f862(f228(a1),x68371),f862(f862(f73(a1),x68372),f71(a1)))) % 14.98/14.66 [6838]P1(f862(f862(f228(a1),x68381),x68382))+~P1(f862(f862(f227(a1),x68381),f862(f862(f3(a1),x68382),f71(a1)))) % 14.98/14.66 [6840]P1(f862(f862(f84(a1),x68401),x68402))+~P1(f862(f862(f84(a1),f862(f96(a1),x68401)),f862(f96(a1),x68402))) % 14.98/14.66 [6842]P1(f862(f862(f227(a924),x68421),x68422))+~P1(f862(f862(f227(a1),f862(f93(a1),x68421)),f862(f93(a1),x68422))) % 14.98/14.66 [6843]P1(f862(f862(f227(a1),x68431),x68432))+~P1(f862(f862(f227(a1),f862(f96(a1),x68431)),f862(f96(a1),x68432))) % 14.98/14.66 [6845]P1(f862(f862(f228(a924),x68451),x68452))+~P1(f862(f862(f228(a1),f862(f93(a1),x68451)),f862(f93(a1),x68452))) % 14.98/14.66 [6846]P1(f862(f862(f228(a1),x68461),x68462))+~P1(f862(f862(f228(a924),f862(f96(a924),x68461)),f862(f96(a924),x68462))) % 14.98/14.66 [6847]P1(f862(f862(f228(a1),x68471),x68472))+~P1(f862(f862(f228(a1),f862(f96(a1),x68471)),f862(f96(a1),x68472))) % 14.98/14.66 [6942]~E(f702(x69422,x69421),f106(x69421))+E(f862(f135(f925(x69421),f925(x69421),f127(x69421),f106(x69421)),x69422),f106(x69421)) % 14.98/14.66 [6943]~E(f708(x69432,x69431),f106(x69431))+E(f862(f135(f925(x69431),f925(x69431),f127(x69431),f106(x69431)),x69432),f106(x69431)) % 14.98/14.66 [6947]~P3(x69471)+E(f862(f135(x69471,x69471,f94(x69471),f234(x69471)),x69472),f31(x69471,f862(f165(x69471),x69472))) % 14.98/14.66 [6948]~P3(x69481)+E(f862(f135(x69481,x69481,f103(x69481),f181(x69481)),x69482),f30(x69481,f862(f165(x69481),x69482))) % 14.98/14.66 [6962]E(x69621,f2(a92))+E(f862(f862(f73(a924),f862(a22,f862(f862(f3(a92),x69621),f71(a92)))),f862(a105,x69622)),f862(f862(f73(a924),f862(a22,x69621)),x69622)) % 14.98/14.66 [7012]P1(f862(f862(f228(a1),f862(f862(f3(a1),x70121),x70122)),f2(a1)))+~P1(f862(f862(f228(a1),x70121),x70122)) % 14.98/14.66 [7037]~P109(x70371)+E(f862(f862(f103(f932(x70371,a921)),f862(f862(f301(x70371),x70372),f181(f932(x70371,a921)))),f862(f293(x70371),x70372)),f862(f274(x70371),x70372)) % 14.98/14.66 [7113]~P57(x71131,x71132)+P35(x71131,f862(f254(f931(x71131,x71131)),f862(f249(x71131,x71131,a921),x71132))) % 14.98/14.66 [7114]~P57(x71141,x71142)+P55(x71141,f862(f254(f931(x71141,x71141)),f862(f249(x71141,x71141,a921),x71142))) % 14.98/14.66 [7115]~P47(x71151,x71152)+P36(x71151,f862(f254(f931(x71151,x71151)),f862(f249(x71151,x71151,a921),x71152))) % 14.98/14.66 [7116]~P48(x71161,x71162)+P49(x71161,f862(f254(f931(x71161,x71161)),f862(f249(x71161,x71161,a921),x71162))) % 14.98/14.66 [7117]E(x71171,f181(f932(x71172,a921)))+~P1(f862(f862(f227(f932(x71172,a921)),x71171),f181(f932(x71172,a921)))) % 14.98/14.66 [7199]~P1(f862(f862(f228(a924),f2(a924)),x71992))+P1(f862(f862(f227(a924),f38(a924,x71991,x71992)),x71992)) % 14.98/14.66 [7200]~P1(f862(f862(f227(a1),f2(a1)),x72001))+P1(f862(f862(f227(a1),f38(a1,x72001,x72002)),x72001)) % 14.98/14.66 [7201]~P1(f862(f862(f228(a924),f2(a924)),x72012))+P1(f862(f862(f228(a924),f38(a924,x72011,x72012)),x72012)) % 14.98/14.66 [7203]~P1(f862(f862(f228(a1),f2(a1)),x72032))+P1(f862(f862(f228(a1),f38(a1,x72031,x72032)),x72032)) % 14.98/14.66 [7280]~P110(x72801)+E(f862(f862(f3(f932(x72801,a921)),f862(f862(f301(x72801),x72802),f181(f932(x72801,a921)))),f862(f292(x72801),x72802)),f862(f862(f301(x72801),x72802),f181(f932(x72801,a921)))) % 14.98/14.66 [7355]~P46(x73551,x73552)+P50(x73551,f234(f932(x73551,a921)),f862(f254(f931(x73551,x73551)),f862(f249(x73551,x73551,a921),x73552))) % 14.98/14.66 [7356]P1(f862(x73561,x73562))+P1(f862(f862(f321(f932(f931(a924,a924),a921)),f578(x73562,x73561)),a91)) % 14.98/14.66 [7401]E(f862(f862(f127(a924),f132(a924,f862(f295(a924,x74011),x74012))),f862(f862(f144(a924),x74012),f106(a924))),f132(a924,f862(f295(a924,x74011),f862(a105,x74012))))+~P1(f862(f862(f227(a924),x74011),x74012)) % 14.98/14.66 [7556]E(x75561,f2(a924))+~E(f862(f135(a924,a924,f73(a924),x75561),x75562),f2(a924)) % 14.98/14.66 [7580]~P1(f862(f862(f228(a1),f862(f862(f3(a1),x75801),x75802)),f2(a1)))+P1(f862(f862(f228(a1),x75801),x75802)) % 14.98/14.66 [7610]P35(x76101,x76102)+~P35(x76101,f862(f862(f280(x76101,x76101,x76101),x76102),x76102)) % 14.98/14.66 [7635]~P1(f862(f862(f227(a924),f862(a105,x76351)),x76352))+P1(f178(a921,a231,f862(f227(a924),x76351),x76352)) % 14.98/14.66 [7790]P22(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x77901),x77902)+P1(f862(f862(f321(a924),f592(x77901,x77902)),x77902)) % 14.98/14.66 [7848]E(f862(f862(f862(f58(a924,x78481,f73(a924)),f862(f18(a924,x78481),f71(a924))),f2(a924)),x78482),f862(f28(x78481),x78482))+~P1(f862(f54(x78481),x78482)) % 14.98/14.66 [7890]P22(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x78901),x78902)+~P1(f862(f862(f227(a924),x78901),f592(x78901,x78902))) % 14.98/14.66 [7945]P35(x79451,x79452)+P1(f862(f862(f227(f932(x79451,a921)),f589(x79452,x79451)),f862(f276(x79451,x79451,x79452),f589(x79452,x79451)))) % 14.98/14.66 [7950]P57(x79501,x79502)+~P35(x79501,f862(f254(f931(x79501,x79501)),f862(f249(x79501,x79501,a921),x79502))) % 14.98/14.66 [7951]P47(x79511,x79512)+~P36(x79511,f862(f254(f931(x79511,x79511)),f862(f249(x79511,x79511,a921),x79512))) % 14.98/14.66 [7952]P48(x79521,x79522)+~P49(x79521,f862(f254(f931(x79521,x79521)),f862(f249(x79521,x79521,a921),x79522))) % 14.98/14.66 [8020]P1(f862(f862(f227(a924),f862(a105,x80201)),x80202))+~P1(f178(a921,a231,f862(f227(a924),x80201),x80202)) % 14.98/14.66 [8077]P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x80771),x80772)),f299(a924,a309)))+~P1(f862(f862(f227(a924),x80771),x80772)) % 14.98/14.66 [8176]P46(x81761,x81762)+~P50(x81761,f234(f932(x81761,a921)),f862(f254(f931(x81761,x81761)),f862(f249(x81761,x81761,a921),x81762))) % 14.98/14.66 [8232]~P1(f862(f130(x82321),x82322))+P1(f862(f130(f932(x82321,a921)),f862(f862(f147(f925(x82321),f932(x82321,a921)),f165(x82321)),f47(x82321,x82322)))) % 14.98/14.66 [8436]~P35(x84361,f862(f277(x84361,x84361),x84362))+P35(x84361,f862(f277(x84361,x84361),f862(f862(f280(x84361,x84361,x84361),x84362),f299(x84361,x84362)))) % 14.98/14.66 [8534]P23(x85341,a924,f826(x85342,x85341),x85342,f862(f295(a924,f2(a924)),f862(f28(x85341),x85342)))+~P1(f862(f54(x85341),x85342)) % 14.98/14.66 [8535]P23(a924,x85351,f827(x85352,x85351),f862(f295(a924,f2(a924)),f862(f28(x85351),x85352)),x85352)+~P1(f862(f54(x85351),x85352)) % 14.98/14.66 [8552]P23(a924,x85521,f828(x85522,x85521),f296(a924,f71(a924),f862(f28(x85521),x85522)),x85522)+~P1(f862(f54(x85521),x85522)) % 14.98/14.66 [8562]P1(f862(f54(f931(x85621,x85621)),f862(f862(f280(x85621,x85621,x85621),x85622),f299(x85621,x85622))))+~P1(f862(f54(f931(x85621,x85621)),x85622)) % 14.98/14.66 [8589]E(x85891,f2(a1))+P1(f862(f42(x85892,x85891),f862(f862(f244(a1,a1),f862(f862(f29(a1),x85892),x85891)),f38(a1,x85892,x85891)))) % 14.98/14.66 [8603]~P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x86031),x86032)),f299(a924,a309)))+P1(f862(f862(f227(a924),x86031),x86032)) % 14.98/14.66 [8620]~P81(x86201)+E(f862(f135(x86201,x86201,f862(f9(x86201,x86201,x86201),f73(x86201)),f2(x86201)),f862(f161(x86201),x86202)),f862(f135(x86201,x86201,f73(x86201),f2(x86201)),x86202)) % 14.98/14.66 [8794]~P109(x87941)+E(f862(f135(f925(x87941),x87941,f862(f9(x87941,f925(x87941),f925(x87941)),f141(x87941,x87941,f7(x87941))),f106(x87941)),x87942),f143(x87941,x87941,f7(x87941),x87942)) % 14.98/14.66 [8906]~P55(x89061,f862(f254(f931(x89061,x89061)),f862(f249(x89061,x89061,a921),x89062)))+P55(x89061,f862(f254(f931(x89061,x89061)),f862(f249(x89061,x89061,a921),f235(x89061,x89061,x89062)))) % 14.98/14.66 [8920]P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x89201),x89202)),f862(f862(f280(a924,a924,a924),a309),f299(a924,a309))))+~P1(f862(f862(f228(a924),x89201),x89202)) % 14.98/14.66 [8966]~P1(f862(f54(f931(x89661,x89661)),f862(f862(f280(x89661,x89661,x89661),x89662),f299(x89661,x89662))))+P1(f862(f54(f931(x89661,x89661)),x89662)) % 14.98/14.66 [9024]~P55(x90241,f862(f254(f931(x90241,x90241)),f862(f249(x90241,x90241,a921),f235(x90241,x90241,x90242))))+P55(x90241,f862(f254(f931(x90241,x90241)),f862(f249(x90241,x90241,a921),x90242))) % 14.98/14.66 [9223]P55(x92231,x92232)+P1(f862(f862(f321(f931(x92231,x92231)),f862(f862(f244(x92231,x92231),f621(x92232,x92231)),f621(x92232,x92231))),f862(f862(f280(x92231,x92231,x92231),x92232),f299(x92231,x92232)))) % 14.98/14.66 [9224]P55(x92241,x92242)+P1(f862(f862(f321(f931(x92241,x92241)),f862(f862(f244(x92241,x92241),f630(x92242,x92241)),f630(x92242,x92241))),f862(f862(f280(x92241,x92241,x92241),x92242),f299(x92241,x92242)))) % 14.98/14.66 [9343]~P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x93431),x93432)),f862(f862(f280(a924,a924,a924),a309),f299(a924,a309))))+P1(f862(f862(f228(a924),x93431),x93432)) % 14.98/14.66 [10092]E(f862(f87(x100921),f879(x100922,x100921)),x100922)+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x100921,f932(a920,a921))),f930(a920,x100921)),a921)),x100922),f862(f254(f932(f922(f930(a919,f932(x100921,f932(a920,a921))),f930(a920,x100921)),a921)),f88(x100921)))) % 14.98/14.66 [10093]E(f862(f87(x100931),f862(f85(x100931),x100932)),x100932)+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x100931,f932(a920,a921))),f930(a920,x100931)),a921)),x100932),f862(f254(f932(f922(f930(a919,f932(x100931,f932(a920,a921))),f930(a920,x100931)),a921)),f88(x100931)))) % 14.98/14.66 [5257]~P98(x52571)+E(f862(f862(f73(x52571),f862(f96(x52571),a76)),x52572),x52572) % 14.98/14.66 [5287]~P96(x52871)+E(f862(f862(f103(x52871),f862(f72(x52871),x52872)),x52872),f234(x52871)) % 14.98/14.66 [5288]~P96(x52881)+E(f862(f862(f94(x52881),f862(f72(x52881),x52882)),x52882),f181(x52881)) % 14.98/14.66 [5289]~P59(x52891)+E(f862(f862(f73(x52891),f862(f72(x52891),x52892)),x52892),f2(x52891)) % 14.98/14.66 [5290]~P68(x52901)+E(f862(f862(f73(x52901),f862(f72(x52901),x52902)),x52902),f2(x52901)) % 14.98/14.66 [5323]~P98(x53231)+E(f862(f862(f74(x53231),f862(f96(x53231),a90)),x53232),f862(f72(x53231),x53232)) % 14.98/14.66 [5483]~P115(x54831)+E(f862(f862(f74(x54831),f862(f72(x54831),f71(x54831))),x54832),f862(f72(x54831),x54832)) % 14.98/14.66 [5528]E(f862(f69(a1),x55281),f71(a1))+~E(f862(f69(a1),f862(f862(f74(a1),x55281),x55282)),f71(a1)) % 14.98/14.66 [5621]~P98(x56211)+E(f862(f862(f73(x56211),f71(x56211)),f862(f96(x56211),x56212)),f862(f96(x56211),f862(f862(f3(a1),x56212),a90))) % 14.98/14.66 [5674]~P3(x56741)+E(f31(x56741,f862(f862(f301(x56741),x56742),f181(f932(x56741,a921)))),x56742) % 14.98/14.66 [5675]~P3(x56751)+E(f30(x56751,f862(f862(f301(x56751),x56752),f181(f932(x56751,a921)))),x56752) % 14.98/14.66 [5676]~P93(x56761)+E(f12(x56761,f862(f862(f301(x56761),x56762),f181(f932(x56761,a921)))),x56762) % 14.98/14.66 [5677]~P93(x56771)+E(f15(x56771,f862(f862(f301(x56771),x56772),f181(f932(x56771,a921)))),x56772) % 14.98/14.66 [5678]~P109(x56781)+E(f16(x56781,f862(f862(f301(x56781),x56782),f181(f932(x56781,a921)))),x56782) % 14.98/14.66 [5679]~P109(x56791)+E(f17(x56791,f862(f862(f301(x56791),x56792),f181(f932(x56791,a921)))),x56792) % 14.98/14.66 [5701]E(f862(f862(f73(a924),x57011),f862(f862(f3(a924),x57012),x57011)),x57012)+P1(f862(f862(f228(a924),x57012),x57011)) % 14.98/14.66 [5740]E(x57401,f106(x57402))+P1(f862(f862(f228(a924),f2(a924)),f862(f182(f925(x57402)),x57401))) % 14.98/14.66 [5868]~P109(x58681)+E(f13(x58681,f225(x58681),f862(f862(f301(x58681),x58682),f181(f932(x58681,a921)))),x58682) % 14.98/14.66 [5869]~P109(x58691)+E(f14(x58691,f226(x58691),f862(f862(f301(x58691),x58692),f181(f932(x58691,a921)))),x58692) % 14.98/14.66 [5930]E(f862(f862(f3(a924),x59301),f862(f862(f3(a924),x59301),x59302)),x59302)+~P1(f862(f862(f227(a924),x59302),x59301)) % 14.98/14.66 [5931]E(f862(f862(f73(a924),x59311),f862(f862(f3(a924),x59312),x59311)),x59312)+~P1(f862(f862(f227(a924),x59311),x59312)) % 14.98/14.66 [5953]E(f38(a924,f862(f862(f3(a924),x59531),x59532),x59532),f38(a924,x59531,x59532))+P1(f862(f862(f228(a924),x59531),x59532)) % 14.98/14.66 [5964]E(f862(f72(a1),f862(f862(f29(a1),x59641),f862(f72(a1),x59642))),f283(x59641,x59642))+P1(f862(f862(f227(a1),f2(a1)),x59642)) % 14.98/14.66 [5966]~E(x59662,f2(a924))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f236(a924),x59661),x59662))) % 14.98/14.66 [6027]~P98(x60271)+E(f862(f862(f73(x60271),f862(f72(x60271),f71(x60271))),f862(f96(x60271),x60272)),f862(f96(x60271),f862(f862(f73(a1),x60272),a90))) % 14.98/14.66 [6029]E(f862(f862(f236(a924),f862(f96(a924),x60291)),x60292),f862(f862(f236(a924),f2(a924)),x60292))+~P1(f862(a186,f862(f96(a1),x60291))) % 14.98/14.66 [6136]E(f862(f134(a924),f132(a924,f862(f295(a924,x61361),x61362))),x61361)+~P1(f862(f862(f228(a924),x61361),x61362)) % 14.98/14.66 [6152]E(f862(f862(f74(a924),f862(f96(a924),x61521)),f862(f96(a924),x61522)),f862(f96(a924),f862(f862(f74(a1),x61521),x61522)))+P1(f862(f862(f228(a1),x61521),a76)) % 14.98/14.66 [6158]~P129(x61581)+P1(f862(f862(f227(x61581),f2(x61581)),f862(f862(f74(x61581),x61582),x61582))) % 14.98/14.66 [6170]E(f862(f862(f3(a924),f862(a105,x61701)),x61702),f862(a105,f862(f862(f3(a924),x61701),x61702)))+~P1(f862(f862(f227(a924),x61702),x61701)) % 14.98/14.66 [6173]E(f38(a924,f862(f862(f3(a924),x61731),x61732),x61732),f38(a924,x61731,x61732))+~P1(f862(f862(f227(a924),x61732),x61731)) % 14.98/14.66 [6225]E(f862(f862(f236(a924),f862(a97,x62251)),x62252),f862(a97,f862(f862(f236(a1),x62251),x62252)))+~P1(f862(f862(f227(a1),f2(a1)),x62251)) % 14.98/14.66 [6243]P1(f862(f130(x62431),x62432))+P1(f862(f862(f228(a924),f673(x62432,x62431)),f862(f182(f925(x62431)),x62432))) % 14.98/14.66 [6244]P1(f862(f130(x62441),x62442))+P1(f862(f862(f228(a924),f677(x62442,x62441)),f862(f182(f925(x62441)),x62442))) % 14.98/14.66 [6256]~E(x62561,f106(x62562))+~P1(f862(f862(f228(a924),f2(a924)),f862(f182(f925(x62562)),x62561))) % 14.98/14.66 [6267]E(f137(a924,f132(a924,f862(f295(a924,x62671),x62672))),f862(f862(f3(a924),x62672),f71(a924)))+~P1(f862(f862(f228(a924),x62671),x62672)) % 14.98/14.66 [6270]E(f862(f862(f73(a1),x62701),f862(f93(a1),f862(a105,f411(x62702,x62701)))),x62702)+~P1(f862(f862(f228(a1),x62701),x62702)) % 14.98/14.66 [6277]E(x62771,f2(a924))+E(f862(f862(f74(a924),x62772),f862(f862(f236(a924),x62772),f862(f862(f3(a924),x62771),f71(a924)))),f862(f862(f236(a924),x62772),x62771)) % 14.98/14.66 [6305]E(f862(f862(f74(a924),f862(a97,x63051)),f862(a97,x63052)),f862(a97,f862(f862(f74(a1),x63051),x63052)))+~P1(f862(f862(f227(a1),f2(a1)),x63051)) % 14.98/14.66 [6306]E(f862(f862(f29(a924),f862(a97,x63061)),f862(a97,x63062)),f862(a97,f862(f862(f29(a1),x63061),x63062)))+~P1(f862(f862(f227(a1),f2(a1)),x63061)) % 14.98/14.66 [6320]~P119(x63201)+E(f862(f862(f73(x63201),x63202),x63202),f862(f862(f74(x63201),f862(f862(f73(x63201),f71(x63201)),f71(x63201))),x63202)) % 14.98/14.66 [6342]E(f862(f862(f3(a1),f862(f93(a1),x63421)),f862(f93(a1),x63422)),f862(f93(a1),f862(f862(f3(a924),x63421),x63422)))+~P1(f862(f862(f227(a924),x63422),x63421)) % 14.98/14.66 [6344]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),x63441),x63442)),f43(x63441,x63442))+~P1(f862(f862(f227(a1),x63442),f2(a1))) % 14.98/14.66 [6377]E(f172(x63771,x63772),f106(f925(x63771)))+P1(f862(f862(f321(f925(x63771)),f672(x63772,x63771)),f862(f165(f925(x63771)),x63772))) % 14.98/14.66 [6387]E(f109(a1,f862(f122(a1),x63871),f121(x63872,f862(f862(f73(a1),x63871),f71(a1)))),f121(x63872,x63871))+P1(f862(f862(f228(a1),x63872),x63871)) % 14.98/14.66 [6461]E(f862(f862(f144(a1),x64611),f171(f862(f862(f73(a1),x64611),f71(a1)),x64612)),f171(x64611,x64612))+~P1(f862(f862(f227(a1),x64611),x64612)) % 14.98/14.66 [6501]~P1(f862(f862(f228(a924),x65012),x65011))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f3(a924),x65011),x65012))) % 14.98/14.66 [6535]~P1(f862(f862(f228(a924),x65351),f862(a97,x65352)))+P1(f862(f862(f228(a1),f862(f93(a1),x65351)),x65352)) % 14.98/14.66 [6564]~P109(x65641)+E(f862(f862(f103(f932(x65641,a921)),f862(f292(x65641),x65642)),f862(f862(f301(x65641),x65642),f181(f932(x65641,a921)))),f862(f294(x65641),x65642)) % 14.98/14.66 [6565]~P1(f862(f862(f227(a1),f2(a1)),x65651))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f236(a1),x65651),x65652))) % 14.98/14.66 [6568]~P1(f862(f862(f228(a924),f2(a924)),x65681))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f236(a924),x65681),x65682))) % 14.98/14.66 [6596]~E(f862(x65961,f2(a924)),f2(a924))+E(f862(f862(f8(a924,a924),x65961),f296(a924,f862(a105,f2(a924)),x65962)),f862(f862(f8(a924,a924),x65961),f296(a924,f2(a924),x65962))) % 14.98/14.66 [6662]~P98(x66621)+E(f862(f862(f74(x66621),f862(f862(f73(x66621),f71(x66621)),f71(x66621))),f862(f96(x66621),x66622)),f862(f96(x66621),f862(f862(f73(a1),x66622),x66622))) % 14.98/14.66 [6679]E(f862(f862(f301(a1),x66791),f296(a1,f862(f862(f73(a1),x66791),f71(a1)),x66792)),f296(a1,x66791,x66792))+P1(f862(f862(f228(a1),x66792),x66791)) % 14.98/14.66 [6680]P1(f862(f862(f228(a924),x66801),f862(a97,x66802)))+~P1(f862(f862(f228(a1),f862(f93(a1),x66801)),x66802)) % 14.98/14.66 [6783]E(f862(a97,f862(f862(f29(a1),f862(f96(a1),x67831)),f862(f96(a1),x67832))),f862(f862(f29(a924),f862(f96(a924),x67831)),f862(f96(a924),x67832)))+P1(f862(a186,f862(f96(a1),x67831))) % 14.98/14.66 [6839]P1(f862(f862(f228(a924),x68391),x68392))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f3(a924),x68392),x68391))) % 14.98/14.66 [6883]P1(f862(f862(f228(a924),f2(a924)),x68831))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f74(a924),x68832),x68831))) % 14.98/14.66 [6884]P1(f862(f862(f228(a924),f2(a924)),x68841))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f74(a924),x68841),x68842))) % 14.98/14.66 [6902]~P1(f862(f862(f227(a1),x69021),f2(a1)))+E(f862(f862(f74(a924),f862(a97,f862(f72(a1),x69021))),f862(a97,f862(f72(a1),x69022))),f862(a97,f862(f862(f74(a1),x69021),x69022))) % 14.98/14.66 [6959]~E(x69592,f181(f932(x69591,a921)))+P1(f862(f862(f227(f932(x69591,a921)),x69592),f862(f72(f932(x69591,a921)),x69592))) % 14.98/14.66 [7022]~P98(x70221)+E(f862(f862(f73(x70221),f862(f862(f73(x70221),f2(x70221)),f862(f96(x70221),x70222))),f862(f96(x70221),x70222)),f862(f96(x70221),f862(f862(f73(a1),x70222),x70222))) % 14.98/14.66 [7078]~P1(f862(f862(f228(a1),x70781),x70782))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x70781),f71(a1))),x70782)) % 14.98/14.66 [7144]E(x71441,f2(a924))+~P1(f862(f862(f227(a1),f862(f93(a1),x71442)),f862(f72(a1),f862(f93(a1),x71441)))) % 14.98/14.66 [7145]E(x71451,f2(a924))+~P1(f862(f862(f227(a1),f862(f93(a1),x71451)),f862(f72(a1),f862(f93(a1),x71452)))) % 14.98/14.66 [7247]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),x72471),x72472)),f43(x72471,x72472))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x72471),x72472))) % 14.98/14.66 [7292]~P24(x72921,x72922)+P35(x72921,f862(f243(f932(f931(x72921,x72921),a921),f932(f931(x72921,x72921),a921)),x72922)) % 14.98/14.66 [7311]~P1(f862(f862(f227(a924),f862(a105,f2(a924))),x73111))+P1(f862(f862(f227(a924),f862(a105,f2(a924))),f862(f862(f236(a924),x73111),x73112))) % 14.98/14.66 [7481]~P1(f862(f862(f84(a1),x74811),x74812))+P1(f862(f862(f84(a1),f862(f862(f73(a1),x74811),x74811)),f862(f862(f73(a1),x74812),x74812))) % 14.98/14.66 [7493]~P1(f862(f862(f227(a1),x74931),x74932))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x74931),x74931)),f862(f862(f73(a1),x74932),x74932))) % 14.98/14.66 [7498]~P1(f862(f862(f228(a1),x74981),x74982))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x74981),x74981)),f862(f862(f73(a1),x74982),x74982))) % 14.98/14.66 [7557]~P1(f862(f862(f228(a924),f2(a924)),x75571))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x75571),f862(a105,x75572))),x75571)) % 14.98/14.66 [7592]P1(f862(f862(f227(a924),f862(a105,f2(a924))),x75921))+~P1(f862(f862(f227(a924),f862(a105,f2(a924))),f862(f862(f74(a924),x75922),x75921))) % 14.98/14.66 [7593]P1(f862(f862(f227(a924),f862(a105,f2(a924))),x75931))+~P1(f862(f862(f227(a924),f862(a105,f2(a924))),f862(f862(f74(a924),x75931),x75932))) % 14.98/14.66 [7597]P1(f862(f862(f227(a924),f862(f862(f157(a924),x75971),x75972)),f862(f158(a924),x75971)))+~P1(f862(f862(f228(a924),x75972),f862(f182(f925(a924)),x75971))) % 14.98/14.66 [7634]P1(f862(f862(f228(a1),x76341),x76342))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x76341),f71(a1))),x76342)) % 14.98/14.66 [7675]P1(f862(f54(x76751),f234(f932(x76751,a921))))+~P1(f862(f54(f932(x76752,x76751)),f234(f932(f932(x76752,x76751),a921)))) % 14.98/14.66 [7676]P1(f862(f54(x76761),f234(f932(x76761,a921))))+~P1(f862(f54(f930(x76762,x76761)),f234(f932(f930(x76762,x76761),a921)))) % 14.98/14.66 [7677]P1(f862(f54(x76771),f234(f932(x76771,a921))))+~P1(f862(f54(f930(x76771,x76772)),f234(f932(f930(x76771,x76772),a921)))) % 14.98/14.66 [7716]E(x77161,f181(f932(x77162,a921)))+~P1(f862(f862(f227(f932(x77162,a921)),x77161),f862(f72(f932(x77162,a921)),x77161))) % 14.98/14.66 [7858]E(f862(f135(f925(x78581),f925(x78581),f127(x78581),f106(x78581)),x78582),f106(x78581))+P1(f862(f862(f321(f925(x78581)),f702(x78582,x78581)),f862(f165(f925(x78581)),x78582))) % 14.98/14.66 [7859]E(f862(f135(f925(x78591),f925(x78591),f127(x78591),f106(x78591)),x78592),f106(x78591))+P1(f862(f862(f321(f925(x78591)),f708(x78592,x78591)),f862(f165(f925(x78591)),x78592))) % 14.98/14.66 [8093]P1(f862(f862(f84(a1),x80931),x80932))+~P1(f862(f862(f84(a1),f862(f862(f73(a1),x80931),x80931)),f862(f862(f73(a1),x80932),x80932))) % 14.98/14.66 [8096]P1(f862(f862(f227(a1),x80961),x80962))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x80961),x80961)),f862(f862(f73(a1),x80962),x80962))) % 14.98/14.66 [8101]P1(f862(f862(f228(a1),x81011),x81012))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x81011),x81011)),f862(f862(f73(a1),x81012),x81012))) % 14.98/14.66 [8196]~P119(x81961)+E(f862(f862(f74(x81961),f862(f862(f73(x81961),f71(x81961)),f71(x81961))),f862(f862(f8(a924,x81961),f93(x81961)),f296(a924,f71(a924),x81962))),f862(f862(f74(x81961),f862(f93(x81961),x81962)),f862(f862(f73(x81961),f862(f93(x81961),x81962)),f71(x81961)))) % 14.98/14.66 [8246]P1(f862(f862(f321(a924),x82461),x82462))+~P1(f862(f862(f321(a1),f862(f93(a1),x82461)),f862(f302(a924,a1,f93(a1)),x82462))) % 14.98/14.66 [8408]~P1(f862(f54(x84081),x84082))+E(f862(f302(a924,x84081,f548(x84082,x84081)),f862(f254(a924),f862(f862(f9(a924,a924,a921),f228(a924)),f542(x84082,x84081)))),x84082) % 14.98/14.66 [8689]P51(x86891,x86892)+P1(f862(f862(f321(f931(x86891,x86891)),f862(f862(f244(x86891,x86891),f513(x86892,x86891)),f513(x86892,x86891))),x86892)) % 14.98/14.66 [8690]P36(x86901,x86902)+P1(f862(f862(f321(f931(x86901,x86901)),f862(f862(f244(x86901,x86901),f794(x86902,x86901)),f797(x86902,x86901))),x86902)) % 14.98/14.66 [8691]P36(x86911,x86912)+P1(f862(f862(f321(f931(x86911,x86911)),f862(f862(f244(x86911,x86911),f797(x86912,x86911)),f798(x86912,x86911))),x86912)) % 14.98/14.66 [8692]P37(x86921,x86922)+P1(f862(f862(f321(f931(x86921,x86921)),f862(f862(f244(x86921,x86921),f713(x86922,x86921)),f712(x86922,x86921))),x86922)) % 14.98/14.66 [8693]P37(x86931,x86932)+P1(f862(f862(f321(f931(x86931,x86931)),f862(f862(f244(x86931,x86931),f712(x86932,x86931)),f713(x86932,x86931))),x86932)) % 14.98/14.66 [8694]P49(x86941,x86942)+P1(f862(f862(f321(f931(x86941,x86941)),f862(f862(f244(x86941,x86941),f808(x86942,x86941)),f809(x86942,x86941))),x86942)) % 14.98/14.66 [8837]~P98(x88371)+E(f862(f862(f3(x88371),f71(x88371)),f862(f96(x88371),x88372)),f862(f96(x88371),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f72(a1),x88372)))) % 14.98/14.66 [8963]~P1(f862(f862(f228(f932(a924,a921)),x89631),x89632))+P1(f862(f862(f228(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x89631)),f862(f302(a924,a1,f93(a1)),x89632))) % 14.98/14.66 [8997]~P1(f862(f862(f228(a1),x89971),x89972))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x89971),x89971)),a90)),f862(f862(f73(a1),x89972),x89972))) % 14.98/14.66 [8999]~P1(f862(f862(f228(a1),x89991),x89992))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x89991),x89991)),a90)),f862(f862(f73(a1),x89992),x89992))) % 14.98/14.66 [9074]~P1(f862(f862(f321(a924),x90741),f862(f165(a924),x90742)))+P1(f862(f862(f227(a924),x90741),f862(f135(a924,a924,f73(a924),f2(a924)),x90742))) % 14.98/14.66 [9163]P43(x91631,x91632)+~P1(f862(f862(f321(f931(x91631,x91631)),f862(f862(f244(x91631,x91631),f493(x91632,x91631)),f493(x91632,x91631))),x91632)) % 14.98/14.66 [9164]P36(x91641,x91642)+~P1(f862(f862(f321(f931(x91641,x91641)),f862(f862(f244(x91641,x91641),f794(x91642,x91641)),f798(x91642,x91641))),x91642)) % 14.98/14.66 [9165]P49(x91651,x91652)+~P1(f862(f862(f321(f931(x91651,x91651)),f862(f862(f244(x91651,x91651),f809(x91652,x91651)),f808(x91652,x91651))),x91652)) % 14.98/14.66 [9305]~P1(f862(f862(f227(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x93051)),f862(f302(a924,a1,f93(a1)),x93052)))+P1(f862(f862(f227(f932(a924,a921)),x93051),x93052)) % 14.98/14.66 [9306]~P1(f862(f862(f228(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x93061)),f862(f302(a924,a1,f93(a1)),x93062)))+P1(f862(f862(f228(f932(a924,a921)),x93061),x93062)) % 14.98/14.66 [9392]P1(f862(f862(f228(a1),x93921),x93922))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93921),x93921)),a90)),f862(f862(f73(a1),x93922),x93922))) % 14.98/14.66 [9394]P1(f862(f862(f228(a1),x93941),x93942))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93941),x93941)),a90)),f862(f862(f73(a1),x93942),x93942))) % 14.98/14.66 [10277]~P106(x102771)+E(f109(f925(x102771),f862(f122(f925(x102771)),f106(x102771)),f862(f862(f862(f89(f926(f925(x102771))),f862(f862(f228(a1),f2(a1)),x102772)),f862(f111(f931(x102771,f925(x102771)),f925(x102771),f124(x102771,f925(x102771),f125(x102771,f862(f862(f3(a1),x102772),f71(a1))),f125(f925(x102771),f862(f862(f3(a1),x102772),f71(a1))))),f862(f249(x102771,f925(x102771),f926(f925(x102771))),f862(f862(f10(f932(f925(x102771),f925(x102771)),f932(f925(x102771),f926(f925(x102771))),x102771),f862(f10(f925(x102771),f926(f925(x102771)),f925(x102771)),f122(f925(x102771)))),f144(x102771))))),f108(f925(x102771)))),f125(f925(x102771),x102772)) % 14.98/14.66 [10299]~P1(f862(f54(x102991),x102992))+E(f862(f182(f925(x102991)),f83(f925(x102991),f862(f862(f20(f925(x102991),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x102991)),a318),f862(f862(f9(f925(x102991),f932(x102991,a921),a921),f862(f862(f10(f932(x102991,a921),f932(f932(x102991,a921),a921),f925(x102991)),a317),f165(x102991))),x102992))),f130(x102991)))),f207(x102991,x102992)) % 14.98/14.66 [6266]E(f862(f862(f73(a924),f862(f862(f3(a924),x62661),x62662)),x62662),x62661)+~P1(f862(f862(f227(a924),x62662),x62661)) % 14.98/14.66 [6338]E(f862(f862(f29(a924),f862(f862(f74(a924),x63381),x63382)),x63382),x63381)+~P1(f862(f862(f228(a924),f2(a924)),x63382)) % 14.98/14.66 [6339]E(f862(f862(f29(a924),f862(f862(f74(a924),x63391),x63392)),x63391),x63392)+~P1(f862(f862(f228(a924),f2(a924)),x63391)) % 14.98/14.66 [6343]~P72(x63431)+E(f862(f862(f8(a924,x63431),f862(f157(x63431),x63432)),f862(f295(a924,f2(a924)),f862(f182(f925(x63431)),x63432))),f862(f158(x63431),x63432)) % 14.98/14.66 [6453]E(f38(a924,f862(a105,f862(f862(f74(a924),x64531),x64532)),x64531),f71(a924))+~P1(f862(f862(f228(a924),f71(a924)),x64531)) % 14.98/14.66 [6459]E(f862(a105,f862(f862(f73(a924),f862(f96(a924),x64591)),x64592)),f862(f862(f73(a924),f71(a924)),x64592))+~P1(f862(a186,f862(f96(a1),x64591))) % 14.98/14.66 [6488]E(f862(a97,f862(f862(f236(a1),f862(f96(a1),x64881)),x64882)),f862(f862(f236(a924),f862(f96(a924),x64881)),x64882))+P1(f862(a186,f862(f96(a1),x64881))) % 14.98/14.66 [6735]E(f862(f862(f3(a924),x67351),f862(f96(a924),f862(f862(f73(a1),x67352),a90))),f862(f862(f3(a924),f862(a105,x67351)),f862(f96(a924),x67352)))+~P1(f862(f862(f228(a1),a76),x67352)) % 14.98/14.66 [6813]E(x68131,f2(a924))+E(f862(a105,f862(f862(f73(a924),f862(f862(f3(a924),x68131),f71(a924))),x68132)),f862(f862(f73(a924),x68131),x68132)) % 14.98/14.66 [6853]E(x68531,f2(a1))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f236(a1),f862(f69(a1),x68531)),x68532))) % 14.98/14.66 [6868]~E(x68682,f2(a924))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f236(a1),f862(f69(a1),x68681)),x68682))) % 14.98/14.66 [6905]E(x69051,f2(a924))+E(f862(f862(f73(a924),x69052),f862(f862(f74(a924),f862(f862(f3(a924),x69051),f71(a924))),x69052)),f862(f862(f74(a924),x69051),x69052)) % 14.98/14.66 [6952]~P1(f862(f862(f227(a1),x69521),x69522))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x69521),a90)),x69522)) % 14.98/14.66 [7082]E(f862(f862(f144(a924),x70821),f132(a924,f862(f295(a924,f862(a105,x70821)),x70822))),f132(a924,f862(f295(a924,x70821),x70822)))+~P1(f862(f862(f228(a924),x70821),x70822)) % 14.98/14.66 [7283]E(x72831,x72832)+~E(f862(f862(f3(a1),f862(f862(f73(a1),x72831),x72831)),a90),f862(f862(f3(a1),f862(f862(f73(a1),x72832),x72832)),a90)) % 14.98/14.66 [7286]E(x72861,f106(x72862))+E(f258(x72862,f862(f862(f147(x72862,f931(a92,x72862)),f862(f244(a92,x72862),f71(a92))),x72861)),f267(x72862,x72861)) % 14.98/14.66 [7526]P1(f862(f862(f227(a1),x75261),x75262))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x75261),a90)),x75262)) % 14.98/14.66 [7998]~P1(f862(f862(f228(a924),x79981),x79982))+P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x79981),x79982)),a232)) % 14.98/14.66 [8223]~P1(f862(f862(f228(a92),f2(a92)),x82231))+P1(f862(f862(f228(a92),f862(f243(a92,f931(a92,a92)),f862(f259(x82231),x82232))),x82231)) % 14.98/14.66 [8489]~P36(x84891,x84892)+P36(x84891,f862(f862(f103(f932(f931(x84891,x84891),a921)),x84892),f299(x84891,f181(f932(f931(x84891,x84891),a921))))) % 14.98/14.66 [8490]~P37(x84901,x84902)+P37(x84901,f862(f862(f103(f932(f931(x84901,x84901),a921)),x84902),f299(x84901,f181(f932(f931(x84901,x84901),a921))))) % 14.98/14.66 [8538]~P86(x85381)+P1(f862(f862(f227(x85381),f862(f69(x85381),f862(f158(x85381),x85382))),f862(f158(x85381),f862(f862(f147(x85381,x85381),f69(x85381)),x85382)))) % 14.98/14.66 [8564]P1(f862(f862(f228(a924),x85641),x85642))+~P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x85641),x85642)),a232)) % 14.98/14.66 [8714]E(f862(f862(f244(x87141,x87141),f646(x87142,x87141)),f646(x87142,x87141)),x87142)+~P1(f862(f862(f321(f931(x87141,x87141)),x87142),f299(x87141,f181(f932(f931(x87141,x87141),a921))))) % 14.98/14.66 [8759]E(f862(f295(a924,x87591),f862(f862(f73(a924),x87591),f862(f28(a924),x87592))),x87592)+~P1(f862(f862(f227(f932(a924,a921)),x87592),f862(f295(a924,x87591),f862(f862(f73(a924),x87591),f862(f28(a924),x87592))))) % 14.98/14.66 [8990]P37(x89901,x89902)+~P37(x89901,f862(f862(f103(f932(f931(x89901,x89901),a921)),x89902),f299(x89901,f181(f932(f931(x89901,x89901),a921))))) % 14.98/14.66 [9118]E(f862(f862(f29(a1),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x91181),x91181)),a90))),f862(f96(a1),f862(f862(f73(a1),x91182),x91182))),f862(f862(f29(a1),f862(f96(a1),x91181)),f862(f96(a1),x91182)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x91182))) % 14.98/14.66 [9208]~P36(x92081,x92082)+P1(f862(f862(f227(f932(f931(x92081,x92081),a921)),f862(f862(f280(x92081,x92081,x92081),x92082),x92082)),x92082)) % 14.98/14.66 [9234]E(f170(f925(x92341),f862(f862(f10(a921,a921,f925(x92341)),a314),f862(f862(f9(f925(x92341),f925(x92341),a921),a317),f106(x92341))),x92342),f172(x92341,f172(x92341,x92342)))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x92341),a924),f182(f925(x92341))),x92342))) % 14.98/14.66 [9237]E(f862(f862(f29(a1),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92371),x92371)),a90))),f862(f96(a1),f862(f862(f73(a1),x92372),x92372))),f862(f862(f29(a1),f862(f862(f73(a1),f862(f96(a1),x92371)),f71(a1))),f862(f96(a1),x92372)))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x92372))) % 14.98/14.66 [10083]P1(f862(a186,x100832))+E(f862(f862(f79(a1,a924),f862(f862(f3(a1),x100831),x100832)),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f2(a924))),a97)),f862(f862(f3(a924),f862(a97,x100831)),f862(a97,x100832))) % 14.98/14.66 [10091]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x100911),f862(f72(a1),x100912)))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f2(a924))),a97)),f862(f862(f3(a924),f862(f96(a924),x100911)),f862(f96(a924),x100912)))+P1(f862(f862(f228(a1),x100912),a76)) % 14.98/14.66 [10094]~P24(x100941,x100942)+P1(f862(f862(f227(f932(f931(x100941,x100941),a921)),f862(f862(f280(x100941,x100941,x100941),f862(f243(f932(f931(x100941,x100941),a921),f932(f931(x100941,x100941),a921)),x100942)),f862(f248(f932(f931(x100941,x100941),a921),f932(f931(x100941,x100941),a921)),x100942))),f862(f243(f932(f931(x100941,x100941),a921),f932(f931(x100941,x100941),a921)),x100942))) % 14.98/14.66 [10150]~E(f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x101501))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(a105,x101502))))),f2(a924))+~P1(f862(f862(f321(a924),f2(a924)),x101501)) % 14.98/14.66 [10206]E(f38(a1,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x102061),x102061)),a90)),f862(f96(a1),f862(f862(f73(a1),x102062),x102062))),f862(f862(f73(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,f862(f96(a1),x102061),f862(f96(a1),x102062)))),f71(a1)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x102062))) % 14.98/14.66 [10215]E(f38(a1,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x102151),x102151)),a90)),f862(f96(a1),f862(f862(f73(a1),x102152),x102152))),f862(f862(f3(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,f862(f862(f73(a1),f862(f96(a1),x102151)),f71(a1)),f862(f96(a1),x102152)))),f71(a1)))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x102152))) % 14.98/14.66 [10266]~P3(x102661)+E(f30(x102661,f862(f254(x102661),f862(f862(f10(f932(x102661,a921),a921,x102661),f81(x102661)),f862(f862(f10(f932(x102661,a921),f932(x102661,a921),x102661),f862(f20(x102661,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102661),a322),f862(f862(f9(x102661,f932(x102661,a921),a921),f321(x102661)),x102662)))),f227(x102661))))),f31(x102661,x102662)) % 14.98/14.66 [10292]~P35(x102921,x102922)+P57(x102921,f862(f862(f9(x102921,f932(f931(x102921,x102921),a921),f932(x102921,a921)),f862(f862(f10(f932(x102921,f932(f932(f931(x102921,x102921),a921),a921)),f932(f932(f931(x102921,x102921),a921),f932(x102921,a921)),x102921),f9(x102921,f932(f931(x102921,x102921),a921),a921)),f862(f862(f10(f932(x102921,f931(x102921,x102921)),f932(x102921,f932(f932(f931(x102921,x102921),a921),a921)),x102921),f862(f10(f931(x102921,x102921),f932(f932(f931(x102921,x102921),a921),a921),x102921),f321(f931(x102921,x102921)))),f244(x102921,x102921)))),x102922)) % 14.98/14.66 [10293]~P6(x102931,f234(f932(x102931,a921)),x102932)+P5(x102931,f862(f862(f9(x102931,f932(f931(x102931,x102931),a921),f932(x102931,a921)),f862(f862(f10(f932(x102931,f932(f932(f931(x102931,x102931),a921),a921)),f932(f932(f931(x102931,x102931),a921),f932(x102931,a921)),x102931),f9(x102931,f932(f931(x102931,x102931),a921),a921)),f862(f862(f10(f932(x102931,f931(x102931,x102931)),f932(x102931,f932(f932(f931(x102931,x102931),a921),a921)),x102931),f862(f10(f931(x102931,x102931),f932(f932(f931(x102931,x102931),a921),a921),x102931),f321(f931(x102931,x102931)))),f244(x102931,x102931)))),x102932)) % 14.98/14.66 [10336]P35(x103361,x103362)+~P57(x103361,f862(f862(f9(x103361,f932(f931(x103361,x103361),a921),f932(x103361,a921)),f862(f862(f10(f932(x103361,f932(f932(f931(x103361,x103361),a921),a921)),f932(f932(f931(x103361,x103361),a921),f932(x103361,a921)),x103361),f9(x103361,f932(f931(x103361,x103361),a921),a921)),f862(f862(f10(f932(x103361,f931(x103361,x103361)),f932(x103361,f932(f932(f931(x103361,x103361),a921),a921)),x103361),f862(f10(f931(x103361,x103361),f932(f932(f931(x103361,x103361),a921),a921),x103361),f321(f931(x103361,x103361)))),f244(x103361,x103361)))),x103362)) % 14.98/14.66 [10337]P6(x103371,f234(f932(x103371,a921)),x103372)+~P5(x103371,f862(f862(f9(x103371,f932(f931(x103371,x103371),a921),f932(x103371,a921)),f862(f862(f10(f932(x103371,f932(f932(f931(x103371,x103371),a921),a921)),f932(f932(f931(x103371,x103371),a921),f932(x103371,a921)),x103371),f9(x103371,f932(f931(x103371,x103371),a921),a921)),f862(f862(f10(f932(x103371,f931(x103371,x103371)),f932(x103371,f932(f932(f931(x103371,x103371),a921),a921)),x103371),f862(f10(f931(x103371,x103371),f932(f932(f931(x103371,x103371),a921),a921),x103371),f321(f931(x103371,x103371)))),f244(x103371,x103371)))),x103372)) % 14.98/14.66 [7472]E(f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),x74721),a90))),x74722),f862(a105,f862(f862(f73(a924),f862(f96(a924),x74721)),x74722)))+P1(f862(a186,f862(f96(a1),x74721))) % 14.98/14.66 [7916]~P98(x79161)+E(f862(f862(f73(x79161),f862(f862(f73(x79161),f71(x79161)),f862(f96(x79161),x79162))),f862(f96(x79161),x79162)),f862(f96(x79161),f862(f862(f3(a1),f862(f862(f73(a1),x79162),x79162)),a90))) % 14.98/14.66 [8566]~P1(f862(f862(f227(a1),x85661),x85662))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x85661),x85661)),f862(f862(f3(a1),f862(f862(f73(a1),x85662),x85662)),a90))) % 14.98/14.66 [8568]~P1(f862(f862(f227(a1),x85681),x85682))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x85681),x85681)),f862(f862(f3(a1),f862(f862(f73(a1),x85682),x85682)),a90))) % 14.98/14.66 [9001]P1(f862(f862(f227(a1),x90011),x90012))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x90011),x90011)),f862(f862(f3(a1),f862(f862(f73(a1),x90012),x90012)),a90))) % 14.98/14.66 [9003]P1(f862(f862(f227(a1),x90031),x90032))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x90031),x90031)),f862(f862(f3(a1),f862(f862(f73(a1),x90032),x90032)),a90))) % 14.98/14.66 [9292]~P1(f862(f862(f84(a1),x92921),x92922))+P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92921),x92921)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x92922),x92922)),a90))) % 14.98/14.66 [9294]~P1(f862(f862(f227(a1),x92941),x92942))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92941),x92941)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x92942),x92942)),a90))) % 14.98/14.66 [9296]~P1(f862(f862(f228(a1),x92961),x92962))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92961),x92961)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x92962),x92962)),a90))) % 14.98/14.66 [9565]P1(f862(f862(f84(a1),x95651),x95652))+~P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x95651),x95651)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x95652),x95652)),a90))) % 14.98/14.66 [9567]P1(f862(f862(f227(a1),x95671),x95672))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x95671),x95671)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x95672),x95672)),a90))) % 14.98/14.66 [9569]P1(f862(f862(f228(a1),x95691),x95692))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x95691),x95691)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x95692),x95692)),a90))) % 14.98/14.66 [9603]~P1(f862(f54(x96031),x96032))+P1(f862(f54(f932(x96031,a921)),f862(f254(f932(x96031,a921)),f862(f862(f9(f932(x96031,a921),f932(x96031,a921),a921),f227(f932(x96031,a921))),x96032)))) % 14.98/14.66 [9654]~E(f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),x96541),f181(f932(f931(a924,a924),a921)))),f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),x96542),f181(f932(f931(a924,a924),a921)))))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x96541),x96542)),a101)) % 14.98/14.66 [9742]E(f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),x97421),f181(f932(f931(a924,a924),a921)))),f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),x97422),f181(f932(f931(a924,a924),a921)))))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x97421),x97422)),a101)) % 14.98/14.66 [9778]P1(f862(f862(f227(a1),f2(a1)),f649(x97781,x97782)))+E(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97781)),f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97782))) % 14.98/14.66 [10274]~P3(x102741)+E(f31(x102741,f862(f254(x102741),f862(f862(f10(f932(x102741,a921),a921,x102741),f81(x102741)),f862(f862(f10(f932(x102741,a921),f932(x102741,a921),x102741),f862(f20(x102741,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102741),a322),f862(f862(f9(x102741,f932(x102741,a921),a921),f321(x102741)),x102742)))),f862(f9(x102741,x102741,a921),f227(x102741)))))),f30(x102741,x102742)) % 14.98/14.66 [10298]P1(f862(f862(f321(a924),f2(a924)),x102981))+E(f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),a924),f321(a924)),a105)),x102981))),f862(f862(f9(a924,a924,a921),f228(a924)),x102982)))),f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x102981))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(a105,x102982)))))) % 14.98/14.66 [10356]P1(f862(f862(f278(a924),x103561),x103562))+~P1(f862(f862(f321(a924),x103562),f285(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103561))) % 14.98/14.66 [10357]P1(f862(f862(f278(a924),x103571),x103572))+~P1(f862(f862(f321(a924),x103571),f289(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103572))) % 14.98/14.66 [10358]~P1(f862(f862(f278(a924),x103581),x103582))+~P1(f862(f862(f321(a924),x103582),f289(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103581))) % 14.98/14.66 [10359]~P1(f862(f862(f278(a924),x103591),x103592))+~P1(f862(f862(f321(a924),x103591),f285(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103592))) % 14.98/14.66 [7784]~P98(x77841)+E(f862(f862(f74(x77841),x77842),f862(f96(x77841),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),x77842) % 14.98/14.66 [8047]~P98(x80471)+E(f862(f862(f73(x80471),f862(f96(x80471),x80472)),f71(x80471)),f862(f96(x80471),f862(f862(f73(a1),x80472),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))) % 14.98/14.66 [8194]P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x81942)))+E(f862(f862(f236(a1),x81941),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x81942),x81942)),a90))),f71(a1)) % 14.98/14.66 [9630]~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x96302)))+E(f862(f862(f236(a1),x96301),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x96302),x96302)),a90))),f862(f862(f79(a1,a1),f862(f862(f236(a1),x96301),f862(f96(a924),x96302))),f862(f862(f20(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f74(a1)),f862(f74(a1),x96301))),f7(a1)))) % 14.98/14.66 [10001]~P1(f862(f862(f227(a924),f651(x100012,x100011)),f862(x100011,f651(x100012,x100011))))+P1(f862(f54(a924),f862(f254(a924),f862(f862(f9(a924,a924,a921),f862(f862(f10(a924,f932(a924,a921),a924),f227(a924)),x100011)),x100012)))) % 14.98/14.66 [10140]~P1(f862(f862(f227(a924),f862(f96(a924),x101401)),f862(a105,x101402)))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x101401),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),f227(a924)),a97)),x101402)))) % 14.98/14.66 [10141]~P1(f862(f862(f228(a924),f862(f96(a924),x101411)),f862(a105,x101412)))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x101411),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),f228(a924)),a97)),x101412)))) % 14.98/14.66 [10190]P1(f862(f862(f227(a924),f862(f96(a924),x101901)),f862(a105,x101902)))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x101901),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),f227(a924)),a97)),x101902)))) % 14.98/14.66 [10191]P1(f862(f862(f228(a924),f862(f96(a924),x101911)),f862(a105,x101912)))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x101911),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),f228(a924)),a97)),x101912)))) % 14.98/14.66 [10221]~P1(f862(f862(f227(a924),f862(a105,x102212)),f862(f96(a924),x102211)))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102211),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f10(a924,a921,a1),f862(f227(a924),x102212)),a97))))) % 14.98/14.66 [10222]~P1(f862(f862(f228(a924),f862(a105,x102222)),f862(f96(a924),x102221)))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102221),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f10(a924,a921,a1),f862(f228(a924),x102222)),a97))))) % 14.98/14.66 [10264]P1(f862(f862(f227(a924),f862(a105,x102641)),f862(f96(a924),x102642)))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102642),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f10(a924,a921,a1),f862(f227(a924),x102641)),a97))))) % 14.98/14.66 [10265]P1(f862(f862(f228(a924),f862(a105,x102651)),f862(f96(a924),x102652)))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102652),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f10(a924,a921,a1),f862(f228(a924),x102651)),a97))))) % 14.98/14.66 [10346]~P1(f862(f862(f321(a924),f2(a924)),x103461))+E(f862(a105,f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),a924),f321(a924)),a105)),x103461))),f862(f862(f9(a924,a924,a921),f228(a924)),x103462))))),f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x103461))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(a105,x103462)))))) % 14.98/14.66 [8741]~P98(x87411)+E(f862(f862(f74(x87411),f862(f96(x87411),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),x87412),x87412) % 14.98/14.66 [8803]~P98(x88031)+E(f862(f862(f73(x88031),f71(x88031)),f862(f96(x88031),x88032)),f862(f96(x88031),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x88032))) % 14.98/14.66 [8865]~P98(x88651)+E(f862(f862(f3(x88651),f862(f96(x88651),x88652)),f71(x88651)),f862(f96(x88651),f862(f862(f73(a1),x88652),f862(f72(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.66 [9020]~P1(f862(f862(f228(a924),f862(f96(a924),a76)),x90202))+E(f862(f862(f3(a924),x90201),f862(f862(f3(a924),x90202),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f3(a924),f862(a105,x90201)),x90202)) % 14.98/14.66 [9672]~P119(x96721)+E(f862(f862(f74(x96721),x96722),x96722),f862(f862(f236(x96721),x96722),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.66 [9673]~P80(x96731)+E(f862(f862(f236(x96731),x96732),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f74(x96731),x96732),x96732)) % 14.98/14.66 [9675]~P98(x96751)+E(f862(f862(f74(x96751),x96752),f862(f96(x96751),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f73(x96751),x96752),x96752)) % 14.98/14.66 [9918]~P142(x99181)+E(f862(f862(f236(x99181),f862(f72(x99181),x99182)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f236(x99181),x99182),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.66 [9919]~P112(x99191)+E(f862(f862(f236(x99191),f862(f69(x99191),x99192)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f236(x99191),x99192),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.66 [9915]~P98(x99151)+E(f862(f862(f74(x99151),f862(f96(x99151),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x99152),f862(f862(f73(x99151),x99152),x99152)) % 14.98/14.66 [10035]~P112(x100351)+E(f862(f69(x100351),f862(f862(f236(x100351),x100352),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x100351),x100352),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.66 [10102]~P112(x101021)+P1(f862(f862(f227(x101021),f2(x101021)),f862(f862(f236(x101021),x101022),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.66 [10255]~E(f862(a105,x102552),f862(f96(a924),x102551))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102551),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),a317),a97)),x102552))))) % 14.98/14.66 [10256]~E(f862(f96(a924),x102561),f862(a105,x102562))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102561),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),a317),a97)),x102562))))) % 14.98/14.66 [10301]E(f862(a105,x103011),f862(f96(a924),x103012))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x103012),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),a317),a97)),x103011))))) % 14.98/14.66 [10302]E(f862(f96(a924),x103021),f862(a105,x103022))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x103021),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),a317),a97)),x103022))))) % 14.98/14.66 [10347]~P13(x103471,x103472)+P1(f862(f862(f321(f932(x103471,a921)),f817(x103472,x103471)),f862(f862(f10(f932(x103471,a921),a921,f932(x103471,a921)),f80(x103471)),f862(f862(f10(f932(x103471,a921),f932(x103471,a921),f932(x103471,a921)),f862(f20(x103471,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103471),a318),f862(f862(f20(x103471,x103471,a921),x103472),f7(x103471))))),f862(f862(f9(f932(x103471,a921),f932(x103471,f932(x103471,a921)),f932(x103471,a921)),f862(f862(f10(f932(f932(x103471,a921),a921),f932(f932(x103471,f932(x103471,a921)),f932(x103471,a921)),f932(x103471,a921)),f10(f932(x103471,a921),a921,x103471)),a317)),x103472))))) % 14.98/14.66 [10099]~P98(x100991)+E(f862(f862(f236(x100991),f862(f96(x100991),a90)),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x100992)),f71(x100991)) % 14.98/14.66 [10100]~P142(x101001)+E(f862(f862(f236(x101001),f862(f72(x101001),f71(x101001))),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101002)),f71(x101001)) % 14.98/14.66 [10104]~P80(x101041)+E(f862(f862(f236(x101041),x101042),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),f862(f862(f74(x101041),f862(f862(f74(x101041),x101042),x101042)),x101042)) % 14.98/14.66 [10281]~P1(f862(f862(f227(a1),f2(a1)),x102812))+E(f38(a1,f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x102811)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x102812)),f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,x102811,x102812)))) % 14.98/14.66 [10304]~P1(f862(f862(f227(a1),f2(a1)),x103042))+E(f862(f862(f29(a1),f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103041))),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103042)),f862(f862(f29(a1),x103041),x103042)) % 14.98/14.66 [10306]~P1(f862(f862(f227(a1),x103062),f2(a1)))+E(f862(f862(f29(a1),f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103061))),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103062)),f862(f862(f29(a1),f862(f862(f73(a1),x103061),f71(a1))),x103062)) % 14.98/14.66 [10307]~P1(f862(f862(f227(a1),x103072),f2(a1)))+E(f38(a1,f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103071)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103072)),f862(f862(f3(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,f862(f862(f73(a1),x103071),f71(a1)),x103072))),f71(a1))) % 14.98/14.66 [10181]~P98(x101811)+E(f862(f862(f236(x101811),f862(f96(x101811),a90)),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101812))),f862(f96(x101811),a90)) % 14.98/14.66 [10183]~P142(x101831)+E(f862(f862(f236(x101831),f862(f72(x101831),f71(x101831))),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101832))),f862(f72(x101831),f71(x101831))) % 14.98/14.66 [5119]P36(x51191,x51192)+~P6(x51191,x51193,x51192) % 14.98/14.66 [5121]P49(x51211,x51212)+~P6(x51211,x51213,x51212) % 14.98/14.66 [5296]~P6(x52961,x52962,x52963)+P50(x52961,x52962,x52963) % 14.98/14.66 [8261]~E(x82612,x82613)+P32(x82611,x82611,a317,x82612,x82613) % 14.98/14.66 [8816]E(x88161,x88162)+~P32(x88163,x88163,a317,x88161,x88162) % 14.98/14.66 [4922]E(f162(x49221,x49222,x49223),f106(x49221))+~E(x49222,f2(a924)) % 14.98/14.66 [5091]~E(f162(x50912,x50911,x50913),f106(x50912))+E(x50911,f2(a924)) % 14.98/14.66 [5301]~P35(x53011,x53013)+P35(x53011,f313(x53011,x53012,x53013)) % 14.98/14.66 [5412]~P27(x54121,x54122,x54123)+P29(a1,x54121,f171(x54122,x54123)) % 14.98/14.66 [5481]P27(x54811,x54812,x54813)+~P29(a1,x54811,f171(x54812,x54813)) % 14.98/14.66 [5553]~P6(x55531,x55532,x55533)+P6(f925(x55531),f154(x55531,x55532),f151(x55531,x55533)) % 14.98/14.66 [5554]~P50(x55541,x55542,x55543)+P50(f925(x55541),f154(x55541,x55542),f151(x55541,x55543)) % 14.98/14.66 [5667]P52(x56671,x56672,x56673)+~E(f607(x56673,x56672,x56671),f608(x56673,x56672,x56671)) % 14.98/14.66 [5668]P53(x56681,x56682,x56683)+~E(f625(x56683,x56682,x56681),f626(x56683,x56682,x56681)) % 14.98/14.66 [8267]~E(x82672,x82673)+P23(x82671,x82671,f25(x82671),x82672,x82673) % 14.98/14.66 [8824]E(x88241,x88242)+~P23(x88243,x88243,f25(x88243),x88241,x88242) % 14.98/14.66 [4877]~E(f862(f161(x48772),x48771),x48773)+E(x48771,f862(f161(x48772),x48773)) % 14.98/14.66 [4878]~E(x48782,f862(f161(x48781),x48783))+E(f862(f161(x48781),x48782),x48783) % 14.98/14.66 [4928]E(x49281,x49282)+~E(f862(f87(x49283),x49281),f862(f87(x49283),x49282)) % 14.98/14.66 [4929]E(x49291,x49292)+~E(f862(f161(x49293),x49291),f862(f161(x49293),x49292)) % 14.98/14.66 [5145]~P5(x51453,x51451)+P1(f862(f862(x51451,x51452),x51452)) % 14.98/14.66 [5146]~P46(x51463,x51461)+P1(f862(f862(x51461,x51462),x51462)) % 14.98/14.66 [5148]~P57(x51481,x51482)+P1(f862(f307(x51481,x51482),x51483)) % 14.98/14.66 [5216]~P35(x52161,x52162)+P35(f925(x52161),f862(f136(x52161,x52162),x52163)) % 14.98/14.66 [5221]~P1(f862(x52212,x52213))+~E(f862(f254(x52211),x52212),f181(f932(x52211,a921))) % 14.98/14.66 [5222]~P1(f862(x52222,x52223))+~E(f181(f932(x52221,a921)),f862(f254(x52221),x52222)) % 14.98/14.66 [5234]E(x52341,f2(a924))+E(f137(x52342,f162(x52342,x52341,x52343)),x52343) % 14.98/14.66 [5253]~P1(f862(x52531,x52533))+P1(f862(x52531,f83(x52532,x52531))) % 14.98/14.66 [5254]~P1(f862(x52541,x52543))+P1(f862(x52541,f743(x52541,x52542))) % 14.98/14.66 [5266]E(x52661,f2(a924))+E(f862(f134(x52662),f162(x52662,x52661,x52663)),x52663) % 14.98/14.66 [5372]~E(x53722,x53723)+P1(f862(f862(f321(x53721),x53722),f862(a317,x53723))) % 14.98/14.66 [5389]~E(x53892,f2(a924))+E(f862(f165(x53891),f162(x53891,x53892,x53893)),f181(f932(x53891,a921))) % 14.98/14.66 [5435]E(f862(f161(x54351),x54352),f862(f862(f144(x54351),x54353),f106(x54351)))+~E(x54352,f862(f862(f144(x54351),x54353),f106(x54351))) % 14.98/14.66 [5436]~E(x54363,f862(f862(f144(x54361),x54362),f106(x54361)))+E(f862(f862(f144(x54361),x54362),f106(x54361)),f862(f161(x54361),x54363)) % 14.98/14.66 [5477]~P31(x54771,x54772,x54773)+P31(x54771,x54772,f862(f161(x54771),x54773)) % 14.98/14.66 [5478]~P29(x54781,x54782,x54783)+P29(x54781,x54782,f862(f161(x54781),x54783)) % 14.98/14.66 [5482]E(f862(f28(x54821),f327(x54822,x54823,x54821)),x54822)+~E(f862(f28(x54821),x54823),f862(a105,x54822)) % 14.98/14.66 [5489]~P35(x54891,x54893)+P1(f862(f862(f321(x54891),x54892),f308(x54891,x54893))) % 14.98/14.66 [5493]~E(f862(f161(x54932),x54931),f862(f862(f144(x54932),x54933),f106(x54932)))+E(x54931,f862(f862(f144(x54932),x54933),f106(x54932))) % 14.98/14.66 [5494]~E(f862(f862(f144(x54942),x54943),f106(x54942)),f862(f161(x54942),x54941))+E(x54941,f862(f862(f144(x54942),x54943),f106(x54942))) % 14.98/14.66 [5517]E(f78(f931(a924,a924),f41(x55171,x55172)),x55173)+~P1(f862(f41(x55171,x55172),x55173)) % 14.98/14.66 [5557]P31(x55571,x55572,x55573)+~P31(x55571,x55572,f862(f161(x55571),x55573)) % 14.98/14.66 [5558]P29(x55581,x55582,x55583)+~P29(x55581,x55582,f862(f161(x55581),x55583)) % 14.98/14.66 [5597]P1(f862(f862(x55971,x55972),x55972))+~P1(f862(f262(x55973,x55971),x55972)) % 14.98/14.66 [5598]~P1(f862(f862(x55982,x55983),x55983))+P1(f862(f262(x55981,x55982),x55983)) % 14.98/14.66 [5620]~E(x56202,f106(x56201))+P1(f862(f862(f321(f925(x56201)),x56202),f154(x56201,x56203))) % 14.98/14.66 [5630]~P50(x56301,x56302,x56303)+P50(x56301,x56302,f862(f277(x56301,x56301),x56303)) % 14.98/14.66 [5631]~P53(x56311,x56312,x56313)+P53(x56311,x56312,f862(f277(x56311,x56311),x56313)) % 14.98/14.66 [5648]~P61(x56481)+E(f38(x56481,f38(x56481,x56482,x56483),x56483),f38(x56481,x56482,x56483)) % 14.98/14.66 [5752]E(x57521,x57522)+~P1(f862(f862(f321(x57523),x57521),f862(a317,x57522))) % 14.98/14.66 [5800]~P147(x58001)+E(f183(x58001,x58002,f2(a924),x58003),x58003) % 14.98/14.66 [5822]P50(x58221,x58222,x58223)+~P50(x58221,x58222,f862(f277(x58221,x58221),x58223)) % 14.98/14.66 [5823]P53(x58231,x58232,x58233)+~P53(x58231,x58232,f862(f277(x58231,x58231),x58233)) % 14.98/14.66 [5827]~P109(x58272)+E(f143(x58271,x58272,x58273,f106(x58271)),f106(x58271)) % 14.98/14.66 [5839]E(f163(x58391,x58392,f145(x58391,x58393)),f145(x58391,f163(x58391,x58392,x58393)))+~P1(f862(f130(x58391),x58393)) % 14.98/14.66 [5938]~P1(f862(f862(x59383,x59382),x59382))+P1(f862(f862(f321(x59381),x59382),f262(x59381,x59383))) % 14.98/14.66 [5940]E(f862(f129(x59401,x59402),x59403),f106(x59401))+P1(f862(x59402,f678(x59403,x59402,x59401))) % 14.98/14.66 [6006]E(f61(x60061,x60062,x60063),x60062)+P1(f862(x60063,f744(x60062,x60061,x60063))) % 14.98/14.66 [6102]~P1(f862(f130(x61021),x61022))+P1(f862(f130(x61021),f169(x61021,x61022,x61023))) % 14.98/14.66 [6103]~P1(f862(f130(x61031),x61033))+P1(f862(f130(x61031),f163(x61031,x61032,x61033))) % 14.98/14.66 [6104]~P1(f862(f130(x61041),x61043))+P1(f862(f130(x61041),f170(x61041,x61042,x61043))) % 14.98/14.66 [6105]~P1(f862(f130(x61051),x61053))+P1(f862(f130(x61051),f133(x61051,x61052,x61053))) % 14.98/14.66 [6106]~P148(x61061,x61063,x61062)+P1(f862(x61061,f38(a1,x61062,x61063))) % 14.98/14.66 [6122]~P31(x61223,x61221,x61222)+P1(f862(x61221,f757(x61222,x61221,x61223))) % 14.98/14.66 [6123]~P33(x61233,x61231,x61232)+P1(f862(x61231,f764(x61232,x61231,x61233))) % 14.98/14.66 [6124]~P33(x61243,x61241,x61242)+P1(f862(x61241,f775(x61242,x61241,x61243))) % 14.98/14.66 [6125]~P31(x61253,x61251,x61252)+P1(f862(x61251,f799(x61252,x61251,x61253))) % 14.98/14.66 [6126]~P31(x61263,x61261,x61262)+P1(f862(x61261,f801(x61261,x61262,x61263))) % 14.98/14.66 [6131]P1(f862(f862(x61311,x61312),x61312))+~P1(f862(f862(f321(x61313),x61312),f262(x61313,x61311))) % 14.98/14.66 [6146]E(f862(f129(x61461,x61462),x61463),f170(x61461,x61462,x61463))+P1(f862(x61462,f728(x61463,x61462,x61461))) % 14.98/14.66 [6185]~P1(f862(f130(x61851),x61853))+P1(f862(f130(f925(x61851)),f48(x61851,x61852,x61853))) % 14.98/14.66 [6219]~P110(x62191)+E(f862(f862(f94(f932(x62191,a921)),f862(f294(x62191),x62192)),f298(x62191,x62192,x62193)),f181(f932(x62191,a921))) % 14.98/14.66 [6220]~P110(x62201)+E(f862(f862(f94(f932(x62201,a921)),f862(f294(x62201),x62202)),f297(x62201,x62202,x62203)),f181(f932(x62201,a921))) % 14.98/14.66 [6221]~P110(x62211)+E(f862(f862(f94(f932(x62211,a921)),f862(f292(x62211),x62212)),f296(x62211,x62212,x62213)),f181(f932(x62211,a921))) % 14.98/14.66 [6449]E(f862(f129(x64491,x64492),x64493),x64493)+~P1(f862(x64492,f679(x64493,x64492,x64491))) % 14.98/14.66 [6451]E(f862(f862(f301(x64511),f351(x64512,x64513,x64511)),f327(x64512,x64513,x64511)),x64513)+~E(f862(f28(x64511),x64513),f862(a105,x64512)) % 14.98/14.66 [6466]P148(x64661,x64662,x64663)+~P1(f862(x64661,f38(a1,x64663,x64662))) % 14.98/14.66 [6517]P29(x65171,x65172,x65173)+~P1(f862(x65172,f765(x65173,x65172,x65171))) % 14.98/14.66 [6518]P29(x65181,x65182,x65183)+~P1(f862(x65182,f771(x65182,x65183,x65181))) % 14.98/14.66 [6519]P29(x65191,x65192,x65193)+~P1(f862(x65192,f774(x65193,x65192,x65191))) % 14.98/14.66 [6520]P27(x65201,x65202,x65203)+~P1(f862(x65201,f793(x65203,x65202,x65201))) % 14.98/14.66 [6521]P28(x65211,x65212,x65213)+~P1(f862(x65211,f833(x65213,x65212,x65211))) % 14.98/14.66 [6523]E(f170(x65231,x65232,x65233),x65233)+~P1(f862(x65232,f723(x65233,x65232,x65231))) % 14.98/14.66 [6606]~P1(f862(x66062,f590(x66063,x66062,x66061)))+P1(f862(f240(x66061,x66062),x66063)) % 14.98/14.66 [6607]~P1(f862(x66072,f680(x66073,x66072,x66071)))+P1(f862(f153(x66071,x66072),x66073)) % 14.98/14.66 [6854]~P1(f862(f307(x68541,x68542),f448(x68543,x68542,x68541)))+P1(f862(f307(x68541,x68542),x68543)) % 14.98/14.66 [6855]~P1(f862(f307(x68551,x68552),f497(x68553,x68552,x68551)))+P1(f862(f307(x68551,x68552),x68553)) % 14.98/14.66 [7473]~P61(x74731)+E(f862(f862(f73(x74731),f862(f862(f74(x74731),x74732),f862(f862(f29(x74731),x74733),x74732))),f38(x74731,x74733,x74732)),x74733) % 14.98/14.66 [7504]P27(x75041,x75042,x75043)+P1(f862(f862(f321(a1),f793(x75043,x75042,x75041)),f296(a1,x75042,x75043))) % 14.98/14.66 [7937]E(f862(f862(f244(x79371,x79371),f536(x79372,x79373,x79371)),f536(x79372,x79373,x79371)),x79373)+~P1(f862(f862(f321(f931(x79371,x79371)),x79373),f255(x79371,x79372))) % 14.98/14.66 [8055]~P1(f862(f862(f321(x80551),f547(x80553,x80552,x80551)),f308(x80551,x80553)))+P1(f862(f862(f321(x80551),x80552),f308(x80551,x80553))) % 14.98/14.66 [8056]~P1(f862(f862(f321(x80561),f612(x80563,x80562,x80561)),f308(x80561,x80563)))+P1(f862(f862(f321(x80561),x80562),f308(x80561,x80563))) % 14.98/14.66 [8057]~P1(f862(f862(f321(x80571),f614(x80573,x80572,x80571)),f308(x80571,x80573)))+P1(f862(f862(f321(x80571),x80572),f308(x80571,x80573))) % 14.98/14.66 [8151]P31(a1,x81511,f171(x81512,x81513))+P27(f862(f66(a921,a921,a1,a314),x81511),x81512,x81513) % 14.98/14.66 [8242]~P61(x82421)+E(f862(f862(f73(x82421),f862(f862(f74(x82421),f862(f862(f29(x82421),x82422),x82423)),x82423)),f38(x82421,x82422,x82423)),x82422) % 14.98/14.66 [8289]~E(f862(f28(x82891),x82892),f862(a105,x82893))+~P1(f862(f862(f321(x82891),f351(x82893,x82892,x82891)),f327(x82893,x82892,x82891))) % 14.98/14.66 [8733]~P31(a1,x87331,f171(x87332,x87333))+~P27(f862(f66(a921,a921,a1,a314),x87331),x87332,x87333) % 14.98/14.66 [8922]P1(f862(f862(f227(f932(f931(x89221,x89221),a921)),f299(x89221,x89222)),f299(x89221,x89223)))+~P1(f862(f862(f227(f932(f931(x89221,x89221),a921)),x89222),f299(x89221,x89223))) % 14.98/14.66 [9204]E(x92041,f106(x92042))+~P1(f862(f862(f321(f931(f925(x92042),f925(x92042))),f862(f862(f244(f925(x92042),f925(x92042)),x92041),f106(x92042))),f151(x92042,x92043))) % 14.98/14.66 [9228]E(x92281,f106(x92282))+~P1(f862(f862(f321(f931(f925(x92282),f925(x92282))),f862(f862(f244(f925(x92282),f925(x92282)),f106(x92282)),x92281)),f151(x92282,x92283))) % 14.98/14.66 [9355]E(f862(f862(f144(x93551),f697(x93552,x93553,x93551)),f698(x93552,x93553,x93551)),x93553)+~P1(f862(f862(f321(f931(f925(x93551),f925(x93551))),f862(f862(f244(f925(x93551),f925(x93551)),f106(x93551)),x93553)),f140(x93551,x93552))) % 14.98/14.66 [9596]~P129(x95961)+~P1(f862(f862(f228(x95961),f862(f862(f73(x95961),f862(f862(f74(x95961),x95962),x95962)),f862(f862(f74(x95961),x95963),x95963))),f2(x95961))) % 14.98/14.66 [9647]P1(f862(f54(x96471),x96472))+~P1(f862(f862(f321(f931(f932(x96471,a921),f932(x96471,a921))),f862(f862(f244(f932(x96471,a921),f932(x96471,a921)),x96473),x96472)),f306(x96471))) % 14.98/14.66 [9944]~P44(x99441,x99442,x99443)+P1(f862(f862(f227(a1),f862(f862(f66(f931(a1,a1),a1,x99441,f243(a1,a1)),f205(x99441)),f223(x99441,x99442,f220(x99441,x99443)))),f2(a1))) % 14.98/14.66 [9945]~P45(x99451,x99452,x99453)+P1(f862(f862(f228(a1),f862(f862(f66(f931(a1,a1),a1,x99451,f243(a1,a1)),f205(x99451)),f223(x99451,x99452,f220(x99451,x99453)))),f2(a1))) % 14.98/14.66 [10065]P45(x100651,x100652,x100653)+~P1(f862(f862(f228(a1),f862(f862(f66(f931(a1,a1),a1,x100651,f243(a1,a1)),f205(x100651)),f223(x100651,x100652,f220(x100651,x100653)))),f2(a1))) % 14.98/14.66 [10066]P44(x100661,x100662,x100663)+~P1(f862(f862(f227(a1),f862(f862(f66(f931(a1,a1),a1,x100661,f243(a1,a1)),f205(x100661)),f223(x100661,x100662,f220(x100661,x100663)))),f2(a1))) % 14.98/14.66 [10409]~P112(x104091)+~P1(f862(f862(f228(x104091),f862(f862(f73(x104091),f862(f862(f236(x104091),x104092),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x104091),x104093),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f2(x104091))) % 14.98/14.66 [4907]~E(x49073,f106(x49071))+E(f862(f862(f127(x49071),x49072),x49073),x49072) % 14.98/14.66 [4908]~E(x49082,f106(x49081))+E(f862(f862(f127(x49081),x49082),x49083),x49083) % 14.98/14.66 [4914]~E(x49142,f2(a924))+E(f862(f862(f168(x49141),x49142),x49143),f106(x49141)) % 14.98/14.66 [4923]~E(x49233,f106(x49231))+E(f862(f862(f168(x49231),x49232),x49233),f106(x49231)) % 14.98/14.66 [4963]~E(x49631,x49633)+E(x49631,f862(f862(f127(x49632),f106(x49632)),x49633)) % 14.98/14.66 [5054]~P92(x50542)+E(f862(f181(f932(x50541,x50542)),x50543),f181(x50542)) % 14.98/14.66 [5055]~P111(x50552)+E(f862(f234(f932(x50551,x50552)),x50553),f234(x50552)) % 14.98/14.66 [5073]E(x50731,f106(x50732))+~E(f862(f862(f127(x50732),x50733),x50731),x50733) % 14.98/14.66 [5074]E(x50741,f106(x50742))+~E(f862(f862(f127(x50742),x50741),x50743),x50743) % 14.98/14.66 [5082]E(x50821,f106(x50822))+~E(f862(f862(f127(x50822),x50823),x50821),f106(x50822)) % 14.98/14.66 [5083]E(x50831,f106(x50832))+~E(f862(f862(f127(x50832),x50831),x50833),f106(x50832)) % 14.98/14.66 [5112]~E(x51122,f2(a924))+E(f862(f862(f74(a924),x51121),x51122),f862(f862(f74(a924),x51123),x51122)) % 14.98/14.66 [5114]~E(x51141,f2(a924))+E(f862(f862(f74(a924),x51141),x51142),f862(f862(f74(a924),x51141),x51143)) % 14.98/14.66 [5172]~P93(x51721)+E(f862(f862(f103(x51721),x51722),x51723),f862(f862(f103(x51721),x51723),x51722)) % 14.98/14.66 [5174]~P103(x51741)+E(f862(f862(f103(x51741),x51742),x51743),f862(f862(f103(x51741),x51743),x51742)) % 14.98/14.66 [5175]~P93(x51751)+E(f862(f862(f94(x51751),x51752),x51753),f862(f862(f94(x51751),x51753),x51752)) % 14.98/14.66 [5177]~P104(x51771)+E(f862(f862(f94(x51771),x51772),x51773),f862(f862(f94(x51771),x51773),x51772)) % 14.98/14.66 [5178]~P119(x51781)+E(f862(f862(f74(x51781),x51782),x51783),f862(f862(f74(x51781),x51783),x51782)) % 14.98/14.66 [5179]~P119(x51791)+E(f862(f862(f73(x51791),x51792),x51793),f862(f862(f73(x51791),x51793),x51792)) % 14.98/14.66 [5181]~P109(x51811)+E(f862(f862(f225(x51811),x51812),x51813),f862(f862(f225(x51811),x51813),x51812)) % 14.98/14.66 [5183]~P109(x51831)+E(f862(f862(f226(x51831),x51832),x51833),f862(f862(f226(x51831),x51833),x51832)) % 14.98/14.66 [5248]E(f38(a924,x52481,x52482),f2(a924))+~E(x52481,f862(f862(f74(a924),x52482),x52483)) % 14.98/14.66 [5249]E(f38(a1,x52491,x52492),f2(a1))+~E(x52491,f862(f862(f74(a1),x52492),x52493)) % 14.98/14.66 [5313]E(x53131,x53132)+~E(f862(f862(f73(a924),x53133),x53131),f862(f862(f73(a924),x53133),x53132)) % 14.98/14.66 [5314]E(x53141,x53142)+~E(f862(f862(f73(a924),x53141),x53143),f862(f862(f73(a924),x53142),x53143)) % 14.98/14.66 [5324]~P96(x53241)+E(f862(f862(f94(x53241),x53242),f862(f72(x53241),x53243)),f862(f862(f3(x53241),x53242),x53243)) % 14.98/14.66 [5325]~P59(x53251)+E(f862(f862(f73(x53251),x53252),f862(f72(x53251),x53253)),f862(f862(f3(x53251),x53252),x53253)) % 14.98/14.66 [5326]~P68(x53261)+E(f862(f862(f73(x53261),x53262),f862(f72(x53261),x53263)),f862(f862(f3(x53261),x53262),x53263)) % 14.98/14.66 [5327]~P115(x53271)+E(f862(f862(f73(x53271),x53272),f862(f72(x53271),x53273)),f862(f862(f3(x53271),x53272),x53273)) % 14.98/14.66 [5328]~P68(x53281)+E(f862(f862(f3(x53281),x53282),f862(f72(x53281),x53283)),f862(f862(f73(x53281),x53282),x53283)) % 14.98/14.66 [5366]~P1(f862(x53663,x53662))+P1(f862(f862(f321(x53661),x53662),x53663)) % 14.98/14.66 [5368]~P72(x53682)+E(f862(f862(f8(x53681,x53682),x53683),f181(f932(x53681,a921))),f2(x53682)) % 14.98/14.66 [5370]~P71(x53702)+E(f862(f862(f11(x53701,x53702),x53703),f181(f932(x53701,a921))),f71(x53702)) % 14.98/14.66 [5424]~E(x54242,f862(f862(f73(a924),x54241),x54243))+P1(f862(f862(f227(a924),x54241),x54242)) % 14.98/14.66 [5427]~E(x54272,f181(f932(x54271,a921)))+E(f862(f862(f53(x54271),x54272),x54273),f181(f932(f932(x54271,a921),a921))) % 14.98/14.66 [5428]~E(x54282,f181(f932(x54281,a921)))+E(f181(f932(f932(x54281,a921),a921)),f862(f862(f53(x54281),x54282),x54283)) % 14.98/14.66 [5497]~E(f862(f275(x54972,x54973),x54971),f181(f932(x54973,a921)))+E(x54971,f181(f932(f931(x54972,x54973),a921))) % 14.98/14.66 [5498]~E(f862(f256(x54982,x54983),x54981),f181(f932(x54982,a921)))+E(x54981,f181(f932(f931(x54982,x54983),a921))) % 14.98/14.66 [5530]E(f862(f275(x55301,x55302),x55303),f181(f932(x55302,a921)))+~E(x55303,f181(f932(f931(x55301,x55302),a921))) % 14.98/14.66 [5531]E(f862(f256(x55311,x55312),x55313),f181(f932(x55311,a921)))+~E(x55313,f181(f932(f931(x55311,x55312),a921))) % 14.98/14.66 [5534]E(f266(x55341,x55342,x55343),f862(f862(f3(a92),x55342),x55343))+P1(f862(f862(f228(a92),x55342),x55343)) % 14.98/14.66 [5551]P1(f862(x55511,x55512))+~P1(f862(f862(f321(x55513),x55512),x55511)) % 14.98/14.66 [5590]E(x55901,x55902)+~E(f862(f72(f932(x55903,a921)),x55901),f862(f72(f932(x55903,a921)),x55902)) % 14.98/14.66 [5601]~E(x56011,f181(f932(x56012,a921)))+~P1(f862(f862(f321(x56012),x56013),x56011)) % 14.98/14.66 [5632]~E(x56322,f862(f862(f73(a1),x56321),f862(f93(a1),x56323)))+P1(f862(f862(f227(a1),x56321),x56322)) % 14.98/14.66 [5646]E(f862(f862(f301(x56461),x56462),x56463),x56463)+~P1(f862(f862(f321(x56461),x56462),x56463)) % 14.98/14.66 [5657]E(x56571,f181(f932(x56572,a921)))+~E(f862(f862(f53(x56572),x56571),x56573),f181(f932(f932(x56572,a921),a921))) % 14.98/14.66 [5658]E(x56581,f181(f932(x56582,a921)))+~E(f181(f932(f932(x56582,a921),a921)),f862(f862(f53(x56582),x56581),x56583)) % 14.98/14.66 [5664]~P125(x56641)+E(f862(f862(f74(x56641),f862(f72(x56641),x56642)),f862(f72(x56641),x56643)),f862(f862(f74(x56641),x56642),x56643)) % 14.98/14.66 [5666]~P64(x56661)+E(f862(f862(f281(x56661),f862(f72(x56661),x56662)),f862(f72(x56661),x56663)),f862(f862(f281(x56661),x56662),x56663)) % 14.98/14.66 [5697]~P1(f862(x56973,x56972))+P1(f862(f862(f321(x56971),x56972),f862(f254(x56971),x56973))) % 14.98/14.66 [5724]E(x57241,f2(a924))+E(f862(f165(x57242),f162(x57242,x57241,x57243)),f862(f862(f301(x57242),x57243),f181(f932(x57242,a921)))) % 14.98/14.66 [5744]E(f163(x57441,x57442,x57443),x57443)+P1(f862(f862(f321(x57441),x57442),f862(f165(x57441),x57443))) % 14.98/14.66 [5831]~P1(f862(f130(x58311),x58313))+P1(f862(f130(x58311),f862(f129(x58311,x58312),x58313))) % 14.98/14.66 [5874]~P61(x58741)+E(f862(f862(f29(x58741),f38(x58741,x58742,x58743)),x58743),f2(x58741)) % 14.98/14.66 [5893]E(f169(x58931,f862(f862(f144(x58931),x58932),f106(x58931)),x58933),f106(x58931))+P1(f862(f862(f321(a924),f2(a924)),x58933)) % 14.98/14.66 [5899]E(x58991,f2(a924))+E(f862(f164(x58992),f162(x58992,x58991,x58993)),f162(x58992,f862(f862(f3(a924),x58991),f71(a924)),x58993)) % 14.98/14.66 [5950]E(f862(f862(f144(x59501),x59502),x59503),f133(x59501,x59502,x59503))+P1(f862(f862(f321(x59501),x59502),f862(f165(x59501),x59503))) % 14.98/14.66 [5959]E(x59591,x59592)+~E(f862(f862(f74(a924),f862(a105,x59593)),x59591),f862(f862(f74(a924),f862(a105,x59593)),x59592)) % 14.98/14.66 [5960]~E(x59602,f862(f862(f73(a1),x59601),f862(f93(a1),f862(a105,x59603))))+P1(f862(f862(f228(a1),x59601),x59602)) % 14.98/14.66 [6028]~P28(x60281,x60282,x60283)+P29(a924,x60281,f132(a924,f862(f295(a924,x60282),x60283))) % 14.98/14.66 [6081]~E(x60813,f106(x60811))+E(f862(f862(f862(f176(f925(x60811),f925(x60811)),x60812),f160(x60811)),x60813),f106(x60811)) % 14.98/14.66 [6085]P1(f862(x60851,x60852))+~P1(f862(f862(f321(x60853),x60852),f862(f254(x60853),x60851))) % 14.98/14.66 [6117]E(x61171,x61172)+~E(f862(f862(f301(x61173),x61171),f181(f932(x61173,a921))),f862(f862(f301(x61173),x61172),f181(f932(x61173,a921)))) % 14.98/14.66 [6133]~P110(x61331)+E(f862(f862(f94(f932(x61331,a921)),f862(f292(x61331),x61332)),f862(f295(x61331,x61332),x61333)),f181(f932(x61331,a921))) % 14.98/14.66 [6172]E(f133(x61721,x61722,x61723),x61723)+~P1(f862(f862(f321(x61721),x61722),f862(f165(x61721),x61723))) % 14.98/14.66 [6192]~P78(x61921)+E(f862(f302(x61921,x61921,f72(x61921)),f862(f295(x61921,x61922),x61923)),f297(x61921,f862(f72(x61921),x61923),f862(f72(x61921),x61922))) % 14.98/14.66 [6203]E(f862(f182(f925(x62031)),f163(x62031,x62032,x62033)),f862(f182(f925(x62031)),x62033))+P1(f862(f862(f321(x62031),x62032),f862(f165(x62031),x62033))) % 14.98/14.66 [6255]~P110(x62551)+E(f862(f862(f94(f932(x62551,a921)),f862(f295(x62551,x62552),x62553)),f862(f274(x62551),x62553)),f181(f932(x62551,a921))) % 14.98/14.66 [6275]~P78(x62751)+E(f862(f302(x62751,x62751,f72(x62751)),f298(x62751,x62752,x62753)),f298(x62751,f862(f72(x62751),x62753),f862(f72(x62751),x62752))) % 14.98/14.66 [6276]~P78(x62761)+E(f862(f302(x62761,x62761,f72(x62761)),f296(x62761,x62762,x62763)),f296(x62761,f862(f72(x62761),x62763),f862(f72(x62761),x62762))) % 14.98/14.66 [6340]E(f169(x63401,f862(f862(f144(x63401),x63402),f106(x63401)),x63403),f862(f862(f144(x63401),x63402),f106(x63401)))+~P1(f862(f862(f321(a924),f2(a924)),x63403)) % 14.98/14.66 [6345]P28(x63451,x63452,x63453)+~P29(a924,x63451,f132(a924,f862(f295(a924,x63452),x63453))) % 14.98/14.66 [6348]~P78(x63481)+E(f862(f302(x63481,x63481,f72(x63481)),f297(x63481,x63482,x63483)),f862(f295(x63481,f862(f72(x63481),x63483)),f862(f72(x63481),x63482))) % 14.98/14.66 [6368]~P62(x63681)+E(f38(x63681,f862(f72(x63681),f38(x63681,x63682,x63683)),x63683),f38(x63681,f862(f72(x63681),x63682),x63683)) % 14.98/14.66 [6464]~P1(f862(f54(f931(x64642,x64641)),x64643))+P1(f862(f54(x64641),f862(f275(x64642,x64641),x64643))) % 14.98/14.66 [6465]~P1(f862(f54(f931(x64651,x64652)),x64653))+P1(f862(f54(x64651),f862(f256(x64651,x64652),x64653))) % 14.98/14.66 [6470]~P110(x64701)+E(f862(f862(f94(f932(x64701,a921)),f298(x64701,x64702,x64703)),f862(f274(x64701),x64703)),f181(f932(x64701,a921))) % 14.98/14.66 [6471]~P110(x64711)+E(f862(f862(f94(f932(x64711,a921)),f297(x64711,x64712,x64713)),f862(f293(x64711),x64713)),f181(f932(x64711,a921))) % 14.98/14.66 [6472]~P110(x64721)+E(f862(f862(f94(f932(x64721,a921)),f296(x64721,x64722,x64723)),f862(f293(x64721),x64723)),f181(f932(x64721,a921))) % 14.98/14.66 [6544]E(f862(f862(f157(x65441),x65442),f668(x65442,x65443,x65441)),x65443)+~P1(f862(f862(f321(x65441),x65443),f862(f165(x65441),x65442))) % 14.98/14.66 [6690]E(x66901,f106(x66902))+~E(f862(f862(f862(f176(f925(x66902),f925(x66902)),x66903),f160(x66902)),x66901),f106(x66902)) % 14.98/14.66 [6793]~P1(f862(f54(f931(x67932,x67931)),x67933))+P1(f862(f54(f931(x67931,x67932)),f862(f277(x67932,x67931),x67933))) % 14.98/14.66 [6944]P53(x69441,x69442,x69443)+P1(f862(f862(f321(x69441),f626(x69443,x69442,x69441)),x69442)) % 14.98/14.66 [6945]P53(x69451,x69452,x69453)+P1(f862(f862(f321(x69451),f625(x69453,x69452,x69451)),x69452)) % 14.98/14.66 [6955]P1(f862(f307(x69551,x69552),x69553))+P1(f862(f862(x69552,f448(x69553,x69552,x69551)),x69553)) % 14.98/14.66 [6956]P1(f862(f307(x69561,x69562),x69563))+P1(f862(f862(x69562,f497(x69563,x69562,x69561)),x69563)) % 14.98/14.66 [6988]E(f862(f182(f925(x69881)),f163(x69881,x69882,x69883)),f862(f862(f3(a924),f862(f182(f925(x69881)),x69883)),f71(a924)))+~P1(f862(f862(f321(x69881),x69882),f862(f165(x69881),x69883))) % 14.98/14.66 [7027]P1(f862(f240(x70271,x70272),x70273))+P1(f862(f862(f321(x70271),f590(x70273,x70272,x70271)),x70273)) % 14.98/14.66 [7036]~P1(f862(f54(f931(x70362,x70361)),f862(f277(x70361,x70362),x70363)))+P1(f862(f54(f931(x70361,x70362)),x70363)) % 14.98/14.66 [7094]~P1(f862(f862(f321(x70941),x70942),f862(f165(x70941),f107(x70941,x70943))))+P1(f862(f862(f321(x70941),x70942),f862(f165(x70941),x70943))) % 14.98/14.66 [7128]E(f862(f129(x71281,x71282),x71283),x71283)+P1(f862(f862(f321(x71281),f679(x71283,x71282,x71281)),f862(f165(x71281),x71283))) % 14.98/14.66 [7142]E(f862(f129(x71421,x71422),x71423),f106(x71421))+P1(f862(f862(f321(x71421),f678(x71423,x71422,x71421)),f862(f165(x71421),x71423))) % 14.98/14.66 [7167]P29(x71671,x71672,x71673)+P1(f862(f862(f321(x71671),f765(x71673,x71672,x71671)),f862(f165(x71671),x71673))) % 14.98/14.66 [7168]P29(x71681,x71682,x71683)+P1(f862(f862(f321(x71681),f774(x71683,x71682,x71681)),f862(f165(x71681),x71683))) % 14.98/14.66 [7169]P29(x71691,x71692,x71693)+P1(f862(f862(f321(x71691),f771(x71692,x71693,x71691)),f862(f165(x71691),x71693))) % 14.98/14.66 [7172]E(f170(x71721,x71722,x71723),x71723)+P1(f862(f862(f321(x71721),f723(x71723,x71722,x71721)),f862(f165(x71721),x71723))) % 14.98/14.66 [7248]P1(f862(f153(x72481,x72482),x72483))+P1(f862(f862(f321(x72481),f680(x72483,x72482,x72481)),f862(f165(x72481),x72483))) % 14.98/14.66 [7257]~P31(x72571,x72573,x72572)+P1(f862(f862(f321(x72571),f757(x72572,x72573,x72571)),f862(f165(x72571),x72572))) % 14.98/14.66 [7258]~P33(x72581,x72583,x72582)+P1(f862(f862(f321(x72581),f764(x72582,x72583,x72581)),f862(f165(x72581),x72582))) % 14.98/14.66 [7259]~P33(x72591,x72593,x72592)+P1(f862(f862(f321(x72591),f775(x72592,x72593,x72591)),f862(f165(x72591),x72592))) % 14.98/14.66 [7260]~P31(x72601,x72603,x72602)+P1(f862(f862(f321(x72601),f799(x72602,x72603,x72601)),f862(f165(x72601),x72602))) % 14.98/14.66 [7261]~P31(x72611,x72612,x72613)+P1(f862(f862(f321(x72611),f801(x72612,x72613,x72611)),f862(f165(x72611),x72613))) % 14.98/14.66 [7296]P1(f862(f862(f321(x72961),x72962),f449(x72963,x72962,x72961)))+~P1(f862(f862(f321(x72961),x72962),f30(f932(x72961,a921),x72963))) % 14.98/14.66 [7297]~P72(x72971)+E(f862(f862(f73(x72971),f862(f862(f8(a924,x72971),x72972),f862(f292(a924),x72973))),f862(x72972,x72973)),f862(f862(f8(a924,x72971),x72972),f862(f292(a924),f862(a105,x72973)))) % 14.98/14.66 [7309]P28(x73091,x73092,x73093)+P1(f862(f862(f321(a924),f833(x73093,x73092,x73091)),f862(f295(a924,x73092),x73093))) % 14.98/14.66 [7389]~P31(x73892,x73891,x73893)+P1(f862(x73891,f862(f862(f157(x73892),x73893),f760(x73893,x73891,x73892)))) % 14.98/14.66 [7402]~P1(f862(f862(f321(x74021),x74022),f447(x74022,x74023,x74021)))+P1(f862(f862(f321(x74021),x74022),f31(f932(x74021,a921),x74023))) % 14.98/14.66 [7435]~P72(x74351)+E(f862(f862(f73(x74351),f862(f862(f8(a924,x74351),x74352),f862(f294(a924),x74353))),f862(x74352,f862(a105,x74353))),f862(f862(f8(a924,x74351),x74352),f862(f294(a924),f862(a105,x74353)))) % 14.98/14.66 [7441]P1(f862(x74411,f529(x74412,x74413,x74411)))+P1(f862(f862(f227(f932(x74412,a921)),f862(f254(x74412),x74411)),f862(f254(x74412),x74413))) % 14.98/14.66 [7578]P1(f862(f862(f321(f925(x75781)),x75782),f154(x75781,x75783)))+P1(f862(f862(f321(x75781),f669(x75783,x75782,x75781)),f862(f165(x75781),x75782))) % 14.98/14.66 [7595]~P1(f862(f862(f321(f925(x75951)),x75952),f154(x75951,f308(x75951,x75953))))+P1(f862(f862(f321(f925(x75951)),x75952),f308(f925(x75951),f150(x75951,x75953)))) % 14.98/14.66 [7619]~P1(f862(f862(f321(f925(x76191)),x76192),f308(f925(x76191),f150(x76191,x76193))))+P1(f862(f862(f321(f925(x76191)),x76192),f154(x76191,f308(x76191,x76193)))) % 14.98/14.66 [7651]E(f862(f862(f862(f176(f925(x76511),f925(x76511)),x76512),f160(x76511)),x76513),x76513)+~P1(f862(f862(f227(a924),f862(f182(f925(x76511)),x76513)),f71(a924))) % 14.98/14.66 [7683]P1(f862(x76831,x76832))+~P1(f862(x76831,f862(f85(x76833),f546(x76832,x76831,x76833)))) % 14.98/14.66 [7685]E(f862(f862(f127(x76851),f762(x76852,x76853,x76851)),f862(f862(f144(x76851),x76853),f763(x76852,x76853,x76851))),x76852)+~P1(f862(f862(f321(x76851),x76853),f862(f165(x76851),x76852))) % 14.98/14.66 [7686]E(f862(f862(f127(x76861),f767(x76862,x76863,x76861)),f862(f862(f144(x76861),x76863),f768(x76862,x76863,x76861))),x76862)+~P1(f862(f862(f321(x76861),x76863),f862(f165(x76861),x76862))) % 14.98/14.66 [7687]E(f862(f862(f127(x76871),f769(x76872,x76873,x76871)),f862(f862(f144(x76871),x76873),f770(x76872,x76873,x76871))),x76872)+~P1(f862(f862(f321(x76871),x76873),f862(f165(x76871),x76872))) % 14.98/14.66 [7708]~P22(x77081,x77082,x77083,f234(f932(x77081,a921)))+P22(f925(x77081),f925(x77082),f862(f147(x77081,x77082),x77083),f234(f932(f925(x77081),a921))) % 14.98/14.66 [7746]~P1(f862(x77463,f529(x77461,x77463,x77462)))+P1(f862(f862(f227(f932(x77461,a921)),f862(f254(x77461),x77462)),f862(f254(x77461),x77463))) % 14.98/14.66 [7860]E(x78601,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x78602)),x78603)),f862(f248(a924,a924),x78602)))+~P1(f862(f41(x78601,x78603),x78602)) % 14.98/14.66 [7868]P22(x78681,x78682,x78683,f234(f932(x78681,a921)))+~P22(f925(x78681),f925(x78682),f862(f147(x78681,x78682),x78683),f234(f932(f925(x78681),a921))) % 14.98/14.66 [7912]P1(f862(f862(f321(f932(x79121,a921)),f447(x79122,x79123,x79121)),x79123))+P1(f862(f862(f321(x79121),x79122),f31(f932(x79121,a921),x79123))) % 14.98/14.66 [8002]P1(f862(f862(f321(f925(x80021)),x80022),f154(x80021,x80023)))+~P1(f862(f862(f321(x80021),f669(x80023,x80022,x80021)),x80023)) % 14.98/14.66 [8105]P29(x81051,x81052,x81053)+~P1(f862(x81052,f862(f862(f157(x81051),x81053),f766(x81053,x81052,x81051)))) % 14.98/14.66 [8130]E(x81301,x81302)+~E(f862(f862(f9(x81303,f932(x81303,a921),a921),f321(x81303)),x81301),f862(f862(f9(x81303,f932(x81303,a921),a921),f321(x81303)),x81302)) % 14.98/14.66 [8138]~P1(f862(f862(f321(f931(x81381,x81381)),x81383),f255(x81381,x81382)))+P1(f862(f862(f321(x81381),f536(x81382,x81383,x81381)),x81382)) % 14.98/14.66 [8140]~P1(f862(f862(f321(x81401),x81403),f30(f932(x81401,a921),x81402)))+P1(f862(f862(f321(f932(x81401,a921)),f449(x81402,x81403,x81401)),x81402)) % 14.98/14.66 [8198]P1(f862(f862(f227(f932(x81981,a921)),x81982),f31(f932(x81981,a921),x81983)))+P1(f862(f862(f321(f932(x81981,a921)),f467(x81982,x81983,x81981)),x81983)) % 14.98/14.66 [8262]P22(x82621,x82622,f86(x82622,x82621,f234(f932(x82622,a921)),x82623),f234(f932(x82621,a921)))+~E(f862(f302(x82622,x82621,x82623),f234(f932(x82622,a921))),f234(f932(x82621,a921))) % 14.98/14.66 [8288]~P1(f862(f862(f227(f932(x82881,a921)),x82882),f467(x82882,x82883,x82881)))+P1(f862(f862(f227(f932(x82881,a921)),x82882),f31(f932(x82881,a921),x82883))) % 14.98/14.66 [8318]~P1(f862(f862(f321(x83181),x83182),f862(f165(x83181),f767(x83183,x83182,x83181))))+~P1(f862(f862(f321(x83181),x83182),f862(f165(x83181),x83183))) % 14.98/14.66 [8319]~P1(f862(f862(f321(x83191),x83192),f862(f165(x83191),f770(x83193,x83192,x83191))))+~P1(f862(f862(f321(x83191),x83192),f862(f165(x83191),x83193))) % 14.98/14.66 [8348]P28(f862(f66(a921,a921,a924,a314),x83481),x83482,x83483)+P31(a924,x83481,f132(a924,f862(f295(a924,x83482),x83483))) % 14.98/14.66 [8509]E(x85091,f106(x85092))+P1(f862(f862(f321(x85092),f862(f243(x85092,f931(a92,a92)),f862(f267(x85092,x85091),x85093))),f862(f165(x85092),x85091))) % 14.98/14.66 [8609]~P70(x86091)+E(f862(f135(x86091,x86091,f862(f9(x86091,x86091,x86091),f73(x86091)),x86092),f862(f161(x86091),x86093)),f862(f135(x86091,x86091,f73(x86091),x86092),x86093)) % 14.98/14.66 [8804]~P22(x88042,x88041,x88043,f234(f932(x88042,a921)))+E(f862(f302(x88041,x88042,f86(x88042,x88041,f234(f932(x88042,a921)),x88043)),f234(f932(x88041,a921))),f234(f932(x88042,a921))) % 14.98/14.66 [8874]~P28(f862(f66(a921,a921,a924,a314),x88741),x88742,x88743)+~P31(a924,x88741,f132(a924,f862(f295(a924,x88742),x88743))) % 14.98/14.66 [9124]~P109(x91241)+E(f862(f165(x91241),f142(x91241,x91241,f7(x91241),x91242,x91243)),f862(f862(f301(x91241),x91242),f862(f165(x91241),x91243))) % 14.98/14.66 [9133]~E(f862(x91333,f862(f86(x91331,x91332,f234(f932(x91331,a921)),x91333),f816(x91333,x91332,x91331))),f816(x91333,x91332,x91331))+E(f862(f302(x91331,x91332,x91333),f234(f932(x91331,a921))),f234(f932(x91332,a921))) % 14.98/14.66 [9135]P1(f862(f862(f228(a924),f2(a924)),f631(x91351,x91352,x91353)))+~P1(f862(f862(f321(f931(x91353,x91353)),x91352),f862(f862(f280(x91353,x91353,x91353),x91351),f299(x91353,x91351)))) % 14.98/14.66 [9413]~P55(x94131,x94132)+~P1(f862(f862(f321(f931(x94131,x94131)),f862(f862(f244(x94131,x94131),x94133),x94133)),f862(f862(f280(x94131,x94131,x94131),x94132),f299(x94131,x94132)))) % 14.98/14.66 [9549]~E(f862(f862(f94(f932(f931(x95491,x95491),a921)),f862(f277(x95491,x95491),x95492)),f299(x95491,x95492)),f181(f932(f931(x95491,x95491),a921)))+~P1(f862(f862(f321(f931(x95491,x95491)),f862(f862(f244(x95491,x95491),x95493),x95493)),f862(f862(f280(x95491,x95491,x95491),x95492),f299(x95491,x95492)))) % 14.98/14.66 [9735]~P1(f862(f54(x97351),x97352))+P1(f862(f862(f227(a924),f862(f28(x97351),f862(f862(f3(f932(x97351,a921)),x97352),f862(f862(f301(x97351),x97353),f181(f932(x97351,a921)))))),f862(f28(x97351),x97352))) % 14.98/14.66 [10004]P1(f862(x100041,x100042))+P1(f862(f862(f321(f932(f922(f930(a919,f932(x100043,f932(a920,a921))),f930(a920,x100043)),a921)),f546(x100042,x100041,x100043)),f862(f254(f932(f922(f930(a919,f932(x100043,f932(a920,a921))),f930(a920,x100043)),a921)),f88(x100043)))) % 14.98/14.66 [5236]~E(x52363,f106(x52361))+E(f137(x52361,f862(f862(f144(x52361),x52362),x52363)),x52362) % 14.98/14.66 [5245]~E(x52453,f106(x52451))+E(f107(x52451,f862(f862(f144(x52451),x52452),x52453)),f106(x52451)) % 14.98/14.66 [5275]E(x52751,f106(x52752))+E(f137(x52752,f862(f862(f144(x52752),x52753),x52751)),f137(x52752,x52751)) % 14.98/14.66 [5277]E(x52771,f106(x52772))+E(f137(x52772,f862(f862(f127(x52772),x52773),x52771)),f137(x52772,x52771)) % 14.98/14.66 [5283]~E(x52833,f106(x52831))+E(f107(x52831,f862(f862(f127(x52831),x52832),x52833)),f107(x52831,x52832)) % 14.98/14.66 [5285]~E(x52853,f106(x52851))+E(f137(x52851,f862(f862(f127(x52851),x52852),x52853)),f137(x52851,x52852)) % 14.98/14.66 [5318]E(x53181,f106(x53182))+E(f862(f134(x53182),f862(f862(f127(x53182),x53181),x53183)),f862(f134(x53182),x53181)) % 14.98/14.66 [5346]~E(x53462,f106(x53461))+E(f862(f134(x53461),f862(f862(f127(x53461),x53462),x53463)),f862(f134(x53461),x53463)) % 14.98/14.66 [5382]~E(x53822,x53823)+P1(f862(f862(f84(f923(x53821)),x53822),x53823)) % 14.98/14.66 [5400]~P93(x54001)+E(f862(f862(f103(x54001),x54002),f862(f862(f94(x54001),x54002),x54003)),x54002) % 14.98/14.66 [5401]~P93(x54011)+E(f862(f862(f94(x54011),x54012),f862(f862(f103(x54011),x54012),x54013)),x54012) % 14.98/14.66 [5402]~P109(x54021)+E(f862(f862(f225(x54021),x54022),f862(f862(f226(x54021),x54022),x54023)),x54022) % 14.98/14.66 [5403]~P109(x54031)+E(f862(f862(f226(x54031),x54032),f862(f862(f225(x54031),x54032),x54033)),x54032) % 14.98/14.66 [5422]~P61(x54221)+E(f38(x54221,f862(f862(f74(x54221),x54222),x54223),x54223),f2(x54221)) % 14.98/14.66 [5423]~P61(x54231)+E(f38(x54231,f862(f862(f74(x54231),x54232),x54233),x54232),f2(x54231)) % 14.98/14.66 [5492]~P59(x54921)+E(f862(f72(x54921),f862(f862(f3(x54921),x54922),x54923)),f862(f862(f3(x54921),x54923),x54922)) % 14.98/14.66 [5555]E(x55551,f106(x55552))+E(f107(x55552,f862(f862(f144(x55552),x55553),x55551)),f862(f862(f144(x55552),x55553),f107(x55552,x55551))) % 14.98/14.66 [5556]E(x55561,f106(x55562))+E(f107(x55562,f862(f862(f127(x55562),x55563),x55561)),f862(f862(f127(x55562),x55563),f107(x55562,x55561))) % 14.98/14.66 [5559]~P3(x55591)+E(f31(x55591,f862(f862(f301(x55591),x55592),x55593)),f862(f862(f94(x55591),x55592),f31(x55591,x55593))) % 14.98/14.66 [5560]~P3(x55601)+E(f30(x55601,f862(f862(f301(x55601),x55602),x55603)),f862(f862(f103(x55601),x55602),f30(x55601,x55603))) % 14.98/14.66 [5606]~P93(x56061)+E(f862(f862(f103(x56061),x56062),f862(f862(f103(x56061),x56062),x56063)),f862(f862(f103(x56061),x56062),x56063)) % 14.98/14.66 [5608]~P103(x56081)+E(f862(f862(f103(x56081),x56082),f862(f862(f103(x56081),x56082),x56083)),f862(f862(f103(x56081),x56082),x56083)) % 14.98/14.66 [5609]~P93(x56091)+E(f862(f862(f94(x56091),x56092),f862(f862(f94(x56091),x56092),x56093)),f862(f862(f94(x56091),x56092),x56093)) % 14.98/14.66 [5611]~P104(x56111)+E(f862(f862(f94(x56111),x56112),f862(f862(f94(x56111),x56112),x56113)),f862(f862(f94(x56111),x56112),x56113)) % 14.98/14.66 [5612]~P100(x56121)+E(f862(f862(f74(x56121),x56122),f862(f862(f74(x56121),x56122),x56123)),f862(f862(f74(x56121),x56122),x56123)) % 14.98/14.66 [5614]~P109(x56141)+E(f862(f862(f225(x56141),x56142),f862(f862(f225(x56141),x56142),x56143)),f862(f862(f225(x56141),x56142),x56143)) % 14.98/14.66 [5616]~P109(x56161)+E(f862(f862(f226(x56161),x56162),f862(f862(f226(x56161),x56162),x56163)),f862(f862(f226(x56161),x56162),x56163)) % 14.98/14.66 [5623]~P61(x56231)+E(f38(x56231,f862(f862(f73(x56231),x56232),x56233),x56233),f38(x56231,x56232,x56233)) % 14.98/14.66 [5624]~P61(x56241)+E(f38(x56241,f862(f862(f73(x56241),x56242),x56243),x56242),f38(x56241,x56243,x56242)) % 14.98/14.66 [5633]~P125(x56331)+E(f862(f862(f74(x56331),x56332),f862(f72(x56331),x56333)),f862(f72(x56331),f862(f862(f74(x56331),x56332),x56333))) % 14.98/14.66 [5634]~P64(x56341)+E(f862(f862(f281(x56341),x56342),f862(f72(x56341),x56343)),f862(f72(x56341),f862(f862(f281(x56341),x56342),x56343))) % 14.98/14.66 [5635]~P81(x56351)+E(f862(f862(f73(x56351),x56352),f862(f158(x56351),x56353)),f862(f158(x56351),f862(f862(f144(x56351),x56352),x56353))) % 14.98/14.66 [5663]~P125(x56631)+E(f862(f862(f74(x56631),f862(f72(x56631),x56632)),x56633),f862(f862(f74(x56631),x56632),f862(f72(x56631),x56633))) % 14.98/14.66 [5669]~P6(x56691,x56692,x56693)+E(f30(f932(x56691,a921),f862(f862(f53(x56691),x56692),x56693)),x56692) % 14.98/14.66 [5736]~P116(x57361)+E(f862(f862(f74(x57361),x57362),f862(f862(f236(x57361),x57362),x57363)),f862(f862(f236(x57361),x57362),f862(a105,x57363))) % 14.98/14.66 [5737]~P119(x57371)+E(f862(f862(f74(x57371),x57372),f862(f862(f236(x57371),x57372),x57373)),f862(f862(f236(x57371),x57372),f862(a105,x57373))) % 14.98/14.66 [5748]~P68(x57481)+E(f862(f862(f73(x57481),f862(f72(x57481),x57482)),f862(f862(f73(x57481),x57482),x57483)),x57483) % 14.98/14.66 [5771]~P147(x57711)+E(f862(f862(f236(x57711),f862(f93(x57711),x57712)),x57713),f862(f93(x57711),f862(f862(f236(a924),x57712),x57713))) % 14.98/14.66 [5772]~P142(x57721)+E(f862(f862(f236(x57721),f862(f95(x57721),x57722)),x57723),f862(f95(x57721),f862(f862(f236(a1),x57722),x57723))) % 14.98/14.66 [5773]E(x57731,x57732)+~P1(f862(f862(f84(f923(x57733)),x57731),x57732)) % 14.98/14.66 [5779]~P86(x57791)+E(f862(f69(x57791),f862(f862(f3(x57791),x57792),x57793)),f862(f69(x57791),f862(f862(f3(x57791),x57793),x57792))) % 14.98/14.66 [5781]~P112(x57811)+E(f862(f862(f74(x57811),f75(x57811,x57812)),f75(x57811,x57813)),f75(x57811,f862(f862(f74(x57811),x57812),x57813))) % 14.98/14.66 [5785]E(x57851,f106(x57852))+E(f862(f862(f127(x57852),f862(f164(x57852),x57851)),x57853),f862(f164(x57852),f862(f862(f127(x57852),x57851),x57853))) % 14.98/14.66 [5791]~E(x57912,f862(a105,f862(f862(f73(a924),x57911),x57913)))+P1(f862(f862(f228(a924),x57911),x57912)) % 14.98/14.66 [5792]~P125(x57921)+E(f862(f862(f74(x57921),f862(f72(x57921),x57922)),x57923),f862(f72(x57921),f862(f862(f74(x57921),x57922),x57923))) % 14.98/14.66 [5793]~P121(x57931)+E(f862(f862(f281(x57931),f862(f72(x57931),x57932)),x57933),f862(f72(x57931),f862(f862(f281(x57931),x57932),x57933))) % 14.98/14.66 [5794]~P112(x57941)+E(f862(f862(f236(x57941),f862(f69(x57941),x57942)),x57943),f862(f69(x57941),f862(f862(f236(x57941),x57942),x57943))) % 14.98/14.66 [5892]E(f627(x58921,x58922,x58923),f657(x58921,x58922,x58923))+E(f862(f862(f94(f932(x58923,a921)),x58922),x58921),f181(f932(x58923,a921))) % 14.98/14.66 [5907]~P72(x59072)+E(f862(f862(f8(x59071,x59072),f862(f18(x59072,x59071),f2(x59072))),x59073),f2(x59072)) % 14.98/14.66 [5908]~P71(x59082)+E(f862(f862(f11(x59081,x59082),f862(f18(x59082,x59081),f71(x59082))),x59083),f71(x59082)) % 14.98/14.66 [5910]~P98(x59101)+E(f862(f862(f3(x59101),f862(f96(x59101),x59102)),f862(f96(x59101),x59103)),f862(f96(x59101),f862(f862(f3(a1),x59102),x59103))) % 14.98/14.66 [5913]~P147(x59131)+E(f862(f862(f74(x59131),f862(f93(x59131),x59132)),f862(f93(x59131),x59133)),f862(f93(x59131),f862(f862(f74(a924),x59132),x59133))) % 14.98/14.66 [5914]~P147(x59141)+E(f862(f862(f73(x59141),f862(f93(x59141),x59142)),f862(f93(x59141),x59143)),f862(f93(x59141),f862(f862(f73(a924),x59142),x59143))) % 14.98/14.66 [5915]~P142(x59151)+E(f862(f862(f3(x59151),f862(f95(x59151),x59152)),f862(f95(x59151),x59153)),f862(f95(x59151),f862(f862(f3(a1),x59152),x59153))) % 14.98/14.66 [5916]~P142(x59161)+E(f862(f862(f74(x59161),f862(f95(x59161),x59162)),f862(f95(x59161),x59163)),f862(f95(x59161),f862(f862(f74(a1),x59162),x59163))) % 14.98/14.66 [5917]~P142(x59171)+E(f862(f862(f73(x59171),f862(f95(x59171),x59172)),f862(f95(x59171),x59173)),f862(f95(x59171),f862(f862(f73(a1),x59172),x59173))) % 14.98/14.66 [5918]~P98(x59181)+E(f862(f862(f74(x59181),f862(f96(x59181),x59182)),f862(f96(x59181),x59183)),f862(f96(x59181),f862(f862(f74(a1),x59182),x59183))) % 14.98/14.66 [5919]~P98(x59191)+E(f862(f862(f73(x59191),f862(f96(x59191),x59192)),f862(f96(x59191),x59193)),f862(f96(x59191),f862(f862(f73(a1),x59192),x59193))) % 14.98/14.66 [5967]~E(x59673,x59672)+P1(f862(f862(f227(f932(x59671,a921)),x59672),x59673)) % 14.98/14.66 [5973]~E(x59732,x59733)+P1(f862(f862(f227(f932(x59731,a921)),x59732),x59733)) % 14.98/14.66 [5978]~P96(x59781)+E(f862(f862(f94(x59781),f862(f72(x59781),x59782)),f862(f72(x59781),x59783)),f862(f72(x59781),f862(f862(f103(x59781),x59782),x59783))) % 14.98/14.66 [5979]~P96(x59791)+E(f862(f862(f103(x59791),f862(f72(x59791),x59792)),f862(f72(x59791),x59793)),f862(f72(x59791),f862(f862(f94(x59791),x59792),x59793))) % 14.98/14.66 [5980]~P68(x59801)+E(f862(f862(f73(x59801),f862(f72(x59801),x59802)),f862(f72(x59801),x59803)),f862(f72(x59801),f862(f862(f73(x59801),x59803),x59802))) % 14.98/14.66 [5981]~P59(x59811)+E(f862(f862(f73(x59811),f862(f72(x59811),x59812)),f862(f72(x59811),x59813)),f862(f72(x59811),f862(f862(f73(x59811),x59812),x59813))) % 14.98/14.66 [5982]~P76(x59821)+E(f862(f862(f226(x59821),f862(f72(x59821),x59822)),f862(f72(x59821),x59823)),f862(f72(x59821),f862(f862(f225(x59821),x59822),x59823))) % 14.98/14.66 [5983]~P76(x59831)+E(f862(f862(f225(x59831),f862(f72(x59831),x59832)),f862(f72(x59831),x59833)),f862(f72(x59831),f862(f862(f226(x59831),x59832),x59833))) % 14.98/14.66 [5984]~P112(x59841)+E(f862(f862(f74(x59841),f862(f69(x59841),x59842)),f862(f69(x59841),x59843)),f862(f69(x59841),f862(f862(f74(x59841),x59842),x59843))) % 14.98/14.66 [5985]~P66(x59851)+E(f862(f862(f281(x59851),f862(f69(x59851),x59852)),f862(f69(x59851),x59853)),f862(f69(x59851),f862(f862(f281(x59851),x59852),x59853))) % 14.98/14.66 [5986]~P81(x59861)+E(f862(f862(f73(x59861),f862(f158(x59861),x59862)),f862(f158(x59861),x59863)),f862(f158(x59861),f862(f862(f127(x59861),x59862),x59863))) % 14.98/14.66 [5987]E(x59871,f181(f932(x59872,a921)))+~E(f862(f862(f103(f932(x59872,a921)),x59873),x59871),f181(f932(x59872,a921))) % 14.98/14.66 [5988]E(x59881,f181(f932(x59882,a921)))+~E(f862(f862(f103(f932(x59882,a921)),x59881),x59883),f181(f932(x59882,a921))) % 14.98/14.66 [5989]~P149(x59891,x59893,x59892)+P1(f862(x59891,f862(f862(f29(a1),x59892),x59893))) % 14.98/14.66 [6052]~P1(f862(f54(x60521),x60523))+P1(f862(f54(x60521),f862(f862(f301(x60521),x60522),x60523))) % 14.98/14.66 [6053]~P1(f862(f130(x60531),x60533))+P1(f862(f130(x60531),f862(f862(f168(x60531),x60532),x60533))) % 14.98/14.66 [6054]~P1(f862(f130(x60541),x60543))+P1(f862(f130(x60541),f862(f862(f131(x60541),x60542),x60543))) % 14.98/14.66 [6086]~P93(x60861)+P1(f862(f862(f227(x60861),x60862),f862(f862(f103(x60861),x60863),x60862))) % 14.98/14.66 [6087]~P103(x60871)+P1(f862(f862(f227(x60871),x60872),f862(f862(f103(x60871),x60873),x60872))) % 14.98/14.66 [6088]~P93(x60881)+P1(f862(f862(f227(x60881),x60882),f862(f862(f103(x60881),x60882),x60883))) % 14.98/14.66 [6089]~P103(x60891)+P1(f862(f862(f227(x60891),x60892),f862(f862(f103(x60891),x60892),x60893))) % 14.98/14.66 [6090]~P109(x60901)+P1(f862(f862(f227(x60901),x60902),f862(f862(f226(x60901),x60903),x60902))) % 14.98/14.66 [6091]~P109(x60911)+P1(f862(f862(f227(x60911),x60912),f862(f862(f226(x60911),x60912),x60913))) % 14.98/14.66 [6092]~P119(x60921)+P1(f862(f862(f278(x60921),x60922),f862(f862(f74(x60921),x60923),x60922))) % 14.98/14.66 [6093]~P119(x60931)+P1(f862(f862(f278(x60931),x60932),f862(f862(f74(x60931),x60932),x60933))) % 14.98/14.66 [6107]~E(x61071,f2(a924))+E(f862(f862(f29(a924),f862(f862(f74(a924),x61071),x61072)),f862(f862(f74(a924),x61071),x61073)),f2(a924)) % 14.98/14.66 [6187]~P98(x61871)+E(f862(f862(f3(x61871),f862(f96(x61871),x61872)),f862(f96(x61871),x61873)),f862(f96(x61871),f862(f862(f73(a1),x61872),f862(f72(a1),x61873)))) % 14.98/14.66 [6245]E(x62451,f2(a924))+E(f862(f862(f29(a924),f862(f862(f74(a924),x62451),x62452)),f862(f862(f74(a924),x62451),x62453)),f862(f862(f29(a924),x62452),x62453)) % 14.98/14.66 [6273]E(f145(x62731,f862(f862(f144(x62731),x62732),x62733)),f862(f862(f144(x62731),x62732),f145(x62731,x62733)))+P1(f862(f862(f321(x62731),x62732),f862(f165(x62731),x62733))) % 14.98/14.66 [6309]P149(x63091,x63092,x63093)+~P1(f862(x63091,f862(f862(f29(a1),x63093),x63092))) % 14.98/14.66 [6382]E(x63821,f106(x63822))+E(f862(f862(f144(x63822),f862(f134(x63822),x63821)),f862(f862(f168(x63822),x63823),f862(f164(x63822),x63821))),f862(f862(f168(x63822),f862(a105,x63823)),x63821)) % 14.98/14.66 [6390]E(f862(f862(f3(f932(x63901,a921)),x63902),x63903),x63902)+~E(f862(f862(f94(f932(x63901,a921)),x63902),x63903),f181(f932(x63901,a921))) % 14.98/14.66 [6404]E(f145(x64041,f862(f862(f144(x64041),x64042),x64043)),f145(x64041,x64043))+~P1(f862(f862(f321(x64041),x64042),f862(f165(x64041),x64043))) % 14.98/14.66 [6434]~P1(f862(f862(f227(a924),x64341),x64343))+P1(f862(f862(f227(a924),x64341),f862(f862(f73(a924),x64342),x64343))) % 14.98/14.66 [6436]~P1(f862(f862(f227(a924),x64361),x64362))+P1(f862(f862(f227(a924),x64361),f862(f862(f73(a924),x64362),x64363))) % 14.98/14.66 [6438]~P1(f862(f862(f228(a924),x64381),x64383))+P1(f862(f862(f228(a924),x64381),f862(f862(f73(a924),x64382),x64383))) % 14.98/14.66 [6440]~P1(f862(f862(f228(a924),x64401),x64402))+P1(f862(f862(f228(a924),x64401),f862(f862(f73(a924),x64402),x64403))) % 14.98/14.66 [6478]P1(f862(f54(x64781),x64782))+~P1(f862(f54(x64781),f862(f862(f301(x64781),x64783),x64782))) % 14.98/14.66 [6479]P1(f862(f130(x64791),x64792))+~P1(f862(f130(x64791),f862(f862(f144(x64791),x64793),x64792))) % 14.98/14.66 [6480]P1(f862(f130(x64801),x64802))+~P1(f862(f130(x64801),f862(f862(f127(x64801),x64803),x64802))) % 14.98/14.66 [6481]P1(f862(f130(x64811),x64812))+~P1(f862(f130(x64811),f862(f862(f127(x64811),x64812),x64813))) % 14.98/14.66 [6534]~P119(x65341)+E(f862(f862(f73(x65341),x65342),f862(f862(f74(x65341),x65343),x65342)),f862(f862(f74(x65341),f862(f862(f73(x65341),x65343),f71(x65341))),x65342)) % 14.98/14.66 [6581]~E(x65811,x65812)+~P1(f862(f862(f228(f932(x65813,a921)),x65811),x65812)) % 14.98/14.66 [6628]P1(f862(f862(f321(x66281),x66282),x66283))+P1(f862(f862(f321(x66281),x66282),f862(f72(f932(x66281,a921)),x66283))) % 14.98/14.66 [6634]E(f137(x66341,f862(f862(f131(x66341),x66342),x66343)),f137(x66341,x66343))+~P1(f862(f862(f228(a924),x66342),f862(f182(f925(x66341)),x66343))) % 14.98/14.66 [6635]E(f862(f862(f168(x66351),x66352),f107(x66351,x66353)),f862(f862(f168(x66351),x66352),x66353))+~P1(f862(f862(f228(a924),x66352),f862(f182(f925(x66351)),x66353))) % 14.98/14.66 [6692]E(f862(f862(f862(f176(f925(x66921),f925(x66921)),x66922),f160(x66921)),x66923),x66923)+~E(f38(a924,x66922,f862(f182(f925(x66921)),x66923)),f2(a924)) % 14.98/14.66 [6699]~P6(x66991,x66993,x66992)+E(f862(f862(f280(x66991,x66991,x66991),f862(f277(x66991,x66991),x66992)),x66992),x66992) % 14.98/14.66 [6742]~E(f862(f862(f103(f932(x67421,a921)),x67422),x67423),x67423)+P1(f862(f862(f227(f932(x67421,a921)),x67422),x67423)) % 14.98/14.66 [6747]~P52(x67471,x67471,x67473)+P52(x67471,x67471,f862(f862(f176(f931(x67471,x67471),a921),x67472),x67473)) % 14.98/14.66 [6750]~P1(f862(f862(f321(x67501),x67503),f862(f165(x67501),x67502)))+P1(f862(f862(f228(a924),f2(a924)),f862(f182(f925(x67501)),x67502))) % 14.98/14.66 [6776]~P86(x67761)+E(f862(f69(x67761),f862(f862(f73(x67761),f862(f69(x67761),x67762)),f862(f69(x67761),x67763))),f862(f862(f73(x67761),f862(f69(x67761),x67762)),f862(f69(x67761),x67763))) % 14.98/14.66 [6786]E(f862(f862(f29(a924),f862(f862(f74(a924),x67861),x67862)),f862(f862(f74(a924),x67861),x67863)),f862(f862(f29(a924),x67862),x67863))+~P1(f862(f862(f228(a924),f2(a924)),x67861)) % 14.98/14.66 [6922]~P1(f862(f54(x69221),x69223))+E(f862(f862(f57(x69221,f932(x69221,a921),f301(x69221)),x69222),x69223),f862(f862(f103(f932(x69221,a921)),x69223),x69222)) % 14.98/14.66 [6981]E(f862(f862(f103(f932(x69811,a921)),x69812),x69813),x69812)+~P1(f862(f862(f227(f932(x69811,a921)),x69813),x69812)) % 14.98/14.66 [6983]E(f862(f862(f103(f932(x69831,a921)),x69832),x69833),x69833)+~P1(f862(f862(f227(f932(x69831,a921)),x69832),x69833)) % 14.98/14.66 [6984]E(f862(f862(f94(f932(x69841,a921)),x69842),x69843),x69843)+~P1(f862(f862(f227(f932(x69841,a921)),x69843),x69842)) % 14.98/14.66 [6985]E(f862(f862(f94(f932(x69851,a921)),x69852),x69853),x69852)+~P1(f862(f862(f227(f932(x69851,a921)),x69852),x69853)) % 14.98/14.66 [7034]~P1(f862(f130(x70341),x70342))+E(f862(f862(f3(f932(x70341,a921)),f862(f165(x70341),x70342)),f862(f862(f301(x70341),x70343),f181(f932(x70341,a921)))),f862(f165(x70341),f163(x70341,x70343,x70342))) % 14.98/14.66 [7089]P35(x70891,x70892)+~P35(x70891,f862(f862(f176(f931(x70891,x70891),a921),x70893),x70892)) % 14.98/14.66 [7105]~E(x71051,f2(a924))+P1(f862(f862(f278(a924),f862(f862(f74(a924),x71051),x71052)),f862(f862(f74(a924),x71051),x71053))) % 14.98/14.66 [7154]P1(f862(f42(x71541,x71542),f862(a44,x71543)))+~P1(f862(f42(f862(f72(a1),x71541),f862(f72(a1),x71542)),x71543)) % 14.98/14.66 [7159]E(f862(f862(f3(f932(x71591,a921)),f862(f862(f301(x71591),x71592),x71593)),f862(f862(f301(x71591),x71592),f181(f932(x71591,a921)))),x71593)+P1(f862(f862(f321(x71591),x71592),x71593)) % 14.98/14.66 [7182]E(f862(f862(f94(f932(x71821,a921)),f862(f165(x71821),x71822)),f862(f165(x71821),x71823)),f181(f932(x71821,a921)))+~P1(f862(f130(x71821),f862(f862(f127(x71821),x71822),x71823))) % 14.98/14.66 [7197]~P1(f862(f862(f321(x71971),x71972),f862(f165(x71971),x71973)))+~P1(f862(f130(x71971),f862(f862(f144(x71971),x71972),x71973))) % 14.98/14.66 [7268]P29(x72681,x72682,x72683)+P1(f862(f862(f228(a924),f766(x72683,x72682,x72681)),f862(f182(f925(x72681)),x72683))) % 14.98/14.66 [7278]E(f862(f862(f94(f932(x72781,a921)),x72782),x72783),f181(f932(x72781,a921)))+P1(f862(f862(f321(x72781),f627(x72783,x72782,x72781)),x72782)) % 14.98/14.66 [7279]E(f862(f862(f94(f932(x72791,a921)),x72792),x72793),f181(f932(x72791,a921)))+P1(f862(f862(f321(x72791),f657(x72793,x72792,x72791)),x72793)) % 14.98/14.66 [7282]E(f107(x72821,f862(f862(f168(x72821),x72822),x72823)),f862(f862(f168(x72821),f862(f862(f3(a924),x72822),f71(a924))),x72823))+~P1(f862(f862(f227(a924),x72822),f862(f182(f925(x72821)),x72823))) % 14.98/14.66 [7342]~P31(x73423,x73422,x73421)+P1(f862(f862(f228(a924),f760(x73421,x73422,x73423)),f862(f182(f925(x73423)),x73421))) % 14.98/14.66 [7362]P1(f862(f862(f228(a924),f2(a924)),x73621))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x73622),x73621)),f862(f862(f74(a924),x73623),x73621))) % 14.98/14.66 [7363]P1(f862(f862(f228(a924),f2(a924)),x73631))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x73631),x73632)),f862(f862(f74(a924),x73631),x73633))) % 14.98/14.66 [7366]~P1(f862(f862(f321(x73661),x73662),x73663))+~P1(f862(f862(f321(x73661),x73662),f862(f72(f932(x73661,a921)),x73663))) % 14.98/14.66 [7372]~P1(f862(f862(f228(f932(x73721,a921)),x73722),x73723))+P1(f862(f862(f227(f932(x73721,a921)),x73722),x73723)) % 14.98/14.66 [7482]~P1(f862(f862(f227(a924),x74823),x74822))+P1(f862(f862(f227(a924),f862(f862(f3(a924),x74821),x74822)),f862(f862(f3(a924),x74821),x74823))) % 14.98/14.66 [7483]~P1(f862(f862(f227(a924),x74831),x74833))+P1(f862(f862(f227(a924),f862(f862(f3(a924),x74831),x74832)),f862(f862(f3(a924),x74833),x74832))) % 14.98/14.66 [7485]~P1(f862(f862(f227(a924),x74852),x74853))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x74851),x74852)),f862(f862(f74(a924),x74851),x74853))) % 14.98/14.66 [7487]~P1(f862(f862(f227(a924),x74871),x74873))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x74871),x74872)),f862(f862(f74(a924),x74873),x74872))) % 14.98/14.66 [7488]~P1(f862(f862(f227(a924),x74882),x74883))+P1(f862(f862(f227(a924),f862(f862(f73(a924),x74881),x74882)),f862(f862(f73(a924),x74881),x74883))) % 14.98/14.66 [7489]~P1(f862(f862(f227(a924),x74891),x74893))+P1(f862(f862(f227(a924),f862(f862(f73(a924),x74891),x74892)),f862(f862(f73(a924),x74893),x74892))) % 14.98/14.66 [7490]~P1(f862(f862(f227(a924),x74901),x74903))+P1(f862(f862(f227(a924),f862(f862(f29(a924),x74901),x74902)),f862(f862(f29(a924),x74903),x74902))) % 14.98/14.66 [7491]~P1(f862(f862(f227(a1),x74912),x74913))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x74911),x74912)),f862(f862(f73(a1),x74911),x74913))) % 14.98/14.66 [7494]~P1(f862(f862(f228(a924),x74942),x74943))+P1(f862(f862(f228(a924),f862(f862(f73(a924),x74941),x74942)),f862(f862(f73(a924),x74941),x74943))) % 14.98/14.66 [7495]~P1(f862(f862(f228(a924),x74951),x74953))+P1(f862(f862(f228(a924),f862(f862(f73(a924),x74951),x74952)),f862(f862(f73(a924),x74953),x74952))) % 14.98/14.66 [7496]~P1(f862(f862(f228(a1),x74961),x74963))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x74961),x74962)),f862(f862(f73(a1),x74963),x74962))) % 14.98/14.66 [7499]~P1(f862(f862(f278(a924),x74992),x74993))+P1(f862(f862(f278(a924),f862(f862(f74(a924),x74991),x74992)),f862(f862(f74(a924),x74991),x74993))) % 14.98/14.66 [7577]E(x75771,x75772)+~P1(f862(f862(f321(x75773),x75771),f862(f862(f301(x75773),x75772),f181(f932(x75773,a921))))) % 14.98/14.66 [7579]~E(f862(f862(f94(f932(x75791,a921)),x75792),x75793),f181(f932(x75791,a921)))+P1(f862(f862(f227(f932(x75791,a921)),x75792),f862(f72(f932(x75791,a921)),x75793))) % 14.98/14.66 [7584]P1(f862(f862(f321(f932(x75841,a921)),x75842),f862(f300(x75841),x75843)))+~P1(f862(f862(f227(f932(x75841,a921)),x75842),x75843)) % 14.98/14.66 [7591]P1(f862(f862(f321(x75911),f523(x75912,x75913,x75911)),x75913))+P1(f862(f862(f227(f932(x75911,a921)),x75913),x75912)) % 14.98/14.66 [7636]E(f862(f862(f144(x76361),f862(f862(f157(x76361),x76362),x76363)),f862(f862(f131(x76361),f862(a105,x76363)),x76362)),f862(f862(f131(x76361),x76363),x76362))+~P1(f862(f862(f228(a924),x76363),f862(f182(f925(x76361)),x76362))) % 14.98/14.66 [7661]P1(f862(f862(f321(f931(x76611,x76611)),x76612),f299(x76611,x76613)))+~P1(f862(f862(f321(f931(x76611,x76611)),x76612),x76613)) % 14.98/14.66 [7670]~P1(f862(f862(f321(f932(x76701,a921)),x76702),f862(f300(x76701),x76703)))+P1(f862(f862(f227(f932(x76701,a921)),x76702),x76703)) % 14.98/14.66 [7714]P1(f862(f862(f227(f932(x77141,a921)),x77142),f30(f932(x77141,a921),x77143)))+~P1(f862(f862(f321(f932(x77141,a921)),x77142),x77143)) % 14.98/14.66 [7739]~P142(x77391)+E(f862(f862(f74(x77391),f862(f862(f236(x77391),f862(f72(x77391),f71(x77391))),x77392)),f862(f862(f236(x77391),x77393),x77392)),f862(f862(f236(x77391),f862(f72(x77391),x77393)),x77392)) % 14.98/14.66 [7762]E(f862(f862(f157(x77621),x77622),f862(f862(f3(a924),f862(f182(f925(x77621)),x77622)),f862(a105,x77623))),f862(f862(f157(x77621),f862(f161(x77621),x77622)),x77623))+~P1(f862(f862(f228(a924),x77623),f862(f182(f925(x77621)),x77622))) % 14.98/14.66 [7779]~E(f862(f862(f94(f932(x77791,a921)),f682(x77793,x77792,x77791)),x77793),f181(f932(x77791,a921)))+E(f862(f862(f94(f932(x77791,a921)),f30(f932(x77791,a921),x77792)),x77793),f181(f932(x77791,a921))) % 14.98/14.66 [7843]~P1(f862(f862(f321(x78433),x78432),f862(f165(x78433),x78431)))+P1(f862(f862(f228(a924),f668(x78431,x78432,x78433)),f862(f182(f925(x78433)),x78431))) % 14.98/14.66 [7851]P1(f862(f862(f321(x78511),f862(f862(f157(x78511),x78512),x78513)),f862(f165(x78511),x78512)))+~P1(f862(f862(f228(a924),x78513),f862(f182(f925(x78511)),x78512))) % 14.98/14.66 [7948]~P1(f862(x79482,f725(x79483,x79482,x79481)))+E(f862(f862(f131(x79481),f862(f182(f925(x79481)),f170(x79481,x79482,x79483))),x79483),f106(x79481)) % 14.98/14.66 [7961]P1(f862(f862(f227(f932(f925(x79611),a921)),f154(x79611,x79612)),f154(x79611,x79613)))+~P1(f862(f862(f227(f932(x79611,a921)),x79612),x79613)) % 14.98/14.66 [7962]P1(f862(f862(f227(f932(f925(x79621),a921)),f153(x79621,x79622)),f153(x79621,x79623)))+~P1(f862(f862(f227(f932(x79621,a921)),x79622),x79623)) % 14.98/14.66 [7988]E(f862(f862(f94(f932(x79881,a921)),f30(f932(x79881,a921),x79882)),x79883),f181(f932(x79881,a921)))+P1(f862(f862(f321(f932(x79881,a921)),f682(x79883,x79882,x79881)),x79882)) % 14.98/14.66 [7990]~P1(f862(f862(f321(f932(x79901,a921)),x79903),x79902))+P1(f862(f862(f227(f932(x79901,a921)),f31(f932(x79901,a921),x79902)),x79903)) % 14.98/14.66 [7992]E(f862(f862(f94(f932(x79921,a921)),x79922),x79923),f181(f932(x79921,a921)))+~P1(f862(f862(f227(f932(x79921,a921)),x79922),f862(f72(f932(x79921,a921)),x79923))) % 14.98/14.66 [8042]E(f862(f862(f3(a924),f862(f862(f73(a924),f862(f158(a924),x80421)),x80422)),f862(f862(f157(a924),x80421),x80423)),f862(f158(a924),f862(f862(f152(a924,x80421),x80423),x80422)))+~P1(f862(f862(f228(a924),x80423),f862(f182(f925(a924)),x80421))) % 14.98/14.66 [8094]P1(f862(f862(f227(a924),x80941),x80942))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x80943),x80941)),f862(f862(f73(a924),x80943),x80942))) % 14.98/14.66 [8097]P1(f862(f862(f228(a924),x80971),x80972))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),x80973),x80971)),f862(f862(f73(a924),x80973),x80972))) % 14.98/14.66 [8098]P1(f862(f862(f228(a924),x80981),x80982))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x80983),x80981)),f862(f862(f74(a924),x80983),x80982))) % 14.98/14.66 [8099]P1(f862(f862(f228(a924),x80991),x80992))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x80991),x80993)),f862(f862(f74(a924),x80992),x80993))) % 14.98/14.66 [8128]P1(f862(f862(f228(a924),f2(a924)),x81281))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x81282),x81281)),f862(f862(f74(a924),x81283),x81281))) % 14.98/14.66 [8129]P1(f862(f862(f228(a924),f2(a924)),x81291))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x81291),x81292)),f862(f862(f74(a924),x81291),x81293))) % 14.98/14.66 [8168]~P1(f862(f862(f321(x81681),f523(x81683,x81682,x81681)),x81683))+P1(f862(f862(f227(f932(x81681,a921)),x81682),x81683)) % 14.98/14.66 [8205]E(f239(x82051,x82052,x82053),x82052)+~P1(f862(f862(f227(f932(x82051,a921)),x82053),f862(f862(f301(x82051),x82052),f181(f932(x82051,a921))))) % 14.98/14.66 [8255]~P1(f862(f130(x82551),x82553))+E(f862(f129(x82551,f862(f862(f10(a921,a921,x82551),a314),f862(a317,x82552))),x82553),f163(x82551,x82552,x82553)) % 14.98/14.66 [8280]E(f862(f862(f131(x82801),f862(f182(f925(x82801)),f170(x82801,x82802,x82803))),x82803),f106(x82801))+P1(f862(f862(f321(x82801),f725(x82803,x82802,x82801)),f862(f165(x82801),x82803))) % 14.98/14.66 [8284]E(f862(f862(f127(x82841),f862(f862(f168(x82841),x82842),x82843)),f862(f862(f144(x82841),f862(f862(f157(x82841),x82843),x82842)),f106(x82841))),f862(f862(f168(x82841),f862(a105,x82842)),x82843))+~P1(f862(f862(f228(a924),x82842),f862(f182(f925(x82841)),x82843))) % 14.98/14.66 [8353]E(f862(f129(x83531,f862(f862(f10(a921,a921,x83531),a314),f862(a317,x83532))),x83533),x83533)+P1(f862(f862(f321(x83531),x83532),f862(f165(x83531),x83533))) % 14.98/14.66 [8359]P1(f862(f862(f227(f932(f932(x83591,a921),a921)),f240(x83591,x83592)),f240(x83591,x83593)))+~P1(f862(f862(f227(f932(x83591,a921)),x83592),x83593)) % 14.98/14.66 [8378]P1(f862(f862(f321(f932(x83781,a921)),f490(x83782,x83783,x83781)),x83783))+P1(f862(f862(f227(f932(x83781,a921)),f30(f932(x83781,a921),x83783)),x83782)) % 14.98/14.66 [8399]~P1(f862(f130(x83991),x83993))+P1(f862(f130(x83991),f862(f862(f862(f176(f925(x83991),f925(x83991)),x83992),f160(x83991)),x83993))) % 14.98/14.66 [8405]~P1(f862(f862(f228(a924),x84052),x84053))+P1(f862(f862(f228(a924),f862(f862(f74(a924),f862(a105,x84051)),x84052)),f862(f862(f74(a924),f862(a105,x84051)),x84053))) % 14.98/14.66 [8425]P1(f862(f862(f227(f932(f932(x84251,a921),a921)),f862(f300(x84251),x84252)),f862(f300(x84251),x84253)))+~P1(f862(f862(f227(f932(x84251,a921)),x84252),x84253)) % 14.98/14.66 [8494]~E(f862(f302(x84941,x84942,x84943),f234(f932(x84941,a921))),f234(f932(x84942,a921)))+E(f862(f66(x84941,x84942,x84942,x84943),f86(x84941,x84942,f234(f932(x84941,a921)),x84943)),f25(x84942)) % 14.98/14.66 [8588]~P1(f862(f862(f227(f932(x85881,a921)),x85883),x85882))+P1(f862(f862(f227(f932(x85881,a921)),f862(f72(f932(x85881,a921)),x85882)),f862(f72(f932(x85881,a921)),x85883))) % 14.98/14.66 [8623]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x86231)),f862(f295(a924,x86232),x86233)),f862(f295(a924,f862(f862(f3(a924),x86232),x86231)),f862(f862(f3(a924),x86233),x86231)))+~P1(f862(f862(f228(a924),x86231),x86233)) % 14.98/14.66 [8650]~P81(x86501)+E(f862(f862(f73(x86501),x86502),f862(f135(x86501,x86501,f73(x86501),f2(x86501)),x86503)),f862(f135(x86501,x86501,f73(x86501),x86502),x86503)) % 14.98/14.66 [8705]~P1(f862(f862(f227(f932(x87051,a921)),f490(x87053,x87052,x87051)),x87053))+P1(f862(f862(f227(f932(x87051,a921)),f30(f932(x87051,a921),x87052)),x87053)) % 14.98/14.66 [8727]~P86(x87271)+P1(f862(f862(f227(x87271),f862(f69(x87271),f862(f862(f3(x87271),x87272),x87273))),f862(f862(f73(x87271),f862(f69(x87271),x87272)),f862(f69(x87271),x87273)))) % 14.98/14.66 [8728]~P86(x87281)+P1(f862(f862(f227(x87281),f862(f69(x87281),f862(f862(f73(x87281),x87282),x87283))),f862(f862(f73(x87281),f862(f69(x87281),x87282)),f862(f69(x87281),x87283)))) % 14.98/14.66 [8739]E(f862(f862(f73(a1),f862(f862(f74(a1),x87391),f38(a1,f862(f862(f29(a1),x87392),x87391),x87393))),f38(a1,x87392,x87391)),f38(a1,x87392,f862(f862(f74(a1),x87391),x87393)))+~P1(f862(f862(f228(a1),f2(a1)),x87393)) % 14.98/14.66 [8745]E(f862(f862(f127(x87451),f862(f862(f168(x87451),x87452),x87453)),f862(f862(f144(x87451),f862(f134(x87451),f862(f862(f131(x87451),x87452),x87453))),f106(x87451))),f862(f862(f168(x87451),f862(a105,x87452)),x87453))+~P1(f862(f862(f228(a924),x87452),f862(f182(f925(x87451)),x87453))) % 14.98/14.66 [8766]E(f862(f260(x87661,f862(f862(f147(x87661,f931(a92,x87661)),f862(f244(a92,x87661),f71(a92))),x87662)),f862(a5,x87663)),f862(f862(f157(x87661),x87662),x87663))+~P1(f862(f862(f228(a924),x87663),f862(f182(f925(x87661)),x87662))) % 14.98/14.66 [8834]P1(f862(f862(f321(f931(x88341,x88341)),x88342),f862(f862(f280(x88341,x88341,x88341),x88343),f299(x88341,x88343))))+~P1(f862(f862(f321(f931(x88341,x88341)),x88342),x88343)) % 14.98/14.66 [8845]E(f862(f302(x88451,x88452,x88453),f234(f932(x88451,a921))),f234(f932(x88452,a921)))+~E(f862(f66(x88451,x88452,x88452,x88453),f86(x88451,x88452,f234(f932(x88451,a921)),x88453)),f25(x88452)) % 14.98/14.66 [8854]P1(f862(f862(f227(a924),x88541),x88542))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),f862(a105,x88543)),x88541)),f862(f862(f74(a924),f862(a105,x88543)),x88542))) % 14.98/14.66 [8870]P1(f862(f862(f227(f932(x88701,a921)),x88702),x88703))+~P1(f862(f862(f227(f932(x88701,a921)),f862(f72(f932(x88701,a921)),x88703)),f862(f72(f932(x88701,a921)),x88702))) % 14.98/14.66 [8893]P1(f862(f130(x88931),x88932))+~P1(f862(f130(x88931),f862(f862(f862(f176(f925(x88931),f925(x88931)),x88933),f160(x88931)),x88932))) % 14.98/14.66 [8967]E(f862(f276(x89671,x89671,f299(x89671,x89672)),x89673),x89673)+~P1(f862(f862(f227(f932(x89671,a921)),f862(f276(x89671,x89671,x89672),x89673)),x89673)) % 14.98/14.66 [9015]~P109(x90151)+P11(x90151,f862(f129(x90151,f862(f862(f9(x90151,x90151,a921),a317),f862(x90152,x90153))),x90153)) % 14.98/14.66 [9022]~P1(f862(f862(f227(a924),x90221),x90222))+P1(f862(f862(f227(a924),x90221),f862(f135(a924,a924,f73(a924),x90222),x90223))) % 14.98/14.66 [9110]~P1(f862(f862(f321(f931(x91101,x91101)),x91102),f299(x91101,x91103)))+P1(f862(f862(f321(f931(x91101,x91101)),x91102),f862(f862(f176(f931(x91101,x91101),a921),f629(x91103,x91102,x91101)),x91103))) % 14.98/14.66 [9191]~P81(x91911)+E(f862(f862(f73(x91911),x91912),f862(f135(x91911,x91911,f862(f9(x91911,x91911,x91911),f73(x91911)),f2(x91911)),f862(f161(x91911),x91913))),f862(f135(x91911,x91911,f73(x91911),x91912),x91913)) % 14.98/14.66 [9309]~P23(x93092,x93091,x93093,f234(f932(x93092,a921)),f234(f932(x93091,a921)))+E(f86(x93091,x93092,f234(f932(x93091,a921)),f86(x93092,x93091,f234(f932(x93092,a921)),x93093)),x93093) % 14.98/14.66 [9464]P52(x94641,x94642,x94643)+P1(f862(f862(f321(f931(x94641,x94642)),f862(f862(f244(x94641,x94642),f623(x94643,x94642,x94641)),f608(x94643,x94642,x94641))),x94643)) % 14.98/14.66 [9465]P52(x94651,x94652,x94653)+P1(f862(f862(f321(f931(x94651,x94652)),f862(f862(f244(x94651,x94652),f623(x94653,x94652,x94651)),f607(x94653,x94652,x94651))),x94653)) % 14.98/14.66 [9533]~P1(f862(f862(f321(f931(x95331,x95331)),x95332),f862(f862(f280(x95331,x95331,x95331),x95333),f299(x95331,x95333))))+P1(f862(f862(f321(f931(x95331,x95331)),x95332),f862(f862(f176(f931(x95331,x95331),a921),f631(x95333,x95332,x95331)),x95333))) % 14.98/14.66 [9534]~P1(f862(x95341,f862(f862(f157(x95342),x95343),f862(f182(f925(x95342)),f170(x95342,x95341,x95343)))))+~P1(f862(f862(f228(a924),f862(f182(f925(x95342)),f170(x95342,x95341,x95343))),f862(f182(f925(x95342)),x95343))) % 14.98/14.66 [9628]~P1(f862(f862(f227(f932(x96281,a921)),x96282),x96283))+P1(f862(f862(f227(f932(x96281,a921)),f862(f862(f9(x96281,f932(x96281,a921),a921),f321(x96281)),x96282)),f862(f862(f9(x96281,f932(x96281,a921),a921),f321(x96281)),x96283))) % 14.98/14.66 [9687]~P1(f862(f862(f321(f931(f932(x96871,a921),f932(x96871,a921))),f862(f862(f244(f932(x96871,a921),f932(x96871,a921)),x96872),x96873)),f306(x96871)))+P1(f862(f862(f228(f932(x96871,a921)),x96872),x96873)) % 14.98/14.66 [9711]P53(x97111,x97112,x97113)+~P1(f862(f862(f321(f931(x97111,x97111)),f862(f862(f244(x97111,x97111),f626(x97113,x97112,x97111)),f625(x97113,x97112,x97111))),x97113)) % 14.98/14.66 [9712]P53(x97121,x97122,x97123)+~P1(f862(f862(f321(f931(x97121,x97121)),f862(f862(f244(x97121,x97121),f625(x97123,x97122,x97121)),f626(x97123,x97122,x97121))),x97123)) % 14.98/14.66 [9749]~P1(f862(f862(f321(f931(f925(x97491),f925(x97491))),f862(f862(f244(f925(x97491),f925(x97491)),x97492),x97492)),f140(x97491,x97493)))+P1(f862(f862(f321(f931(x97491,x97491)),f862(f862(f244(x97491,x97491),f664(x97492,x97493,x97491)),f664(x97492,x97493,x97491))),x97493)) % 14.98/14.66 [9799]P1(f862(f862(f227(f932(x97991,a921)),x97992),x97993))+~P1(f862(f862(f227(f932(x97991,a921)),f862(f862(f9(x97991,f932(x97991,a921),a921),f321(x97991)),x97992)),f862(f862(f9(x97991,f932(x97991,a921),a921),f321(x97991)),x97993))) % 14.98/14.66 [9880]E(f862(f862(f3(a924),f862(f862(f8(a924,a924),x98801),f862(f292(a924),x98802))),f862(f862(f8(a924,a924),x98803),f862(f292(a924),x98802))),f862(f862(f8(a924,a924),f862(f862(f20(a924,a924,a924),f862(f862(f10(a924,f932(a924,a924),a924),f3(a924)),x98801)),x98803)),f862(f292(a924),x98802)))+~P1(f862(f862(f227(a924),f862(x98803,f515(x98802,x98801,x98803))),f862(x98801,f515(x98802,x98801,x98803)))) % 14.98/14.66 [5828]~P68(x58281)+E(f862(f862(f3(x58281),f862(f862(f73(x58281),x58282),x58283)),x58283),x58282) % 14.98/14.66 [5829]~P68(x58291)+E(f862(f862(f73(x58291),f862(f862(f3(x58291),x58292),x58293)),x58293),x58292) % 14.98/14.66 [6061]~P68(x60611)+E(f862(f862(f73(x60611),x60612),f862(f862(f73(x60611),f862(f72(x60611),x60612)),x60613)),x60613) % 14.98/14.66 [6149]~P80(x61491)+E(f862(f862(f74(x61491),f862(f862(f236(x61491),x61492),x61493)),x61492),f862(f862(f236(x61491),x61492),f862(a105,x61493))) % 14.98/14.66 [6150]~P119(x61501)+E(f862(f862(f74(x61501),f862(f862(f236(x61501),x61502),x61503)),x61502),f862(f862(f236(x61501),x61502),f862(a105,x61503))) % 14.98/14.66 [6365]~P112(x63651)+E(f862(f69(x63651),f862(f862(f236(x63651),f862(f72(x63651),x63652)),x63653)),f862(f69(x63651),f862(f862(f236(x63651),x63652),x63653))) % 14.98/14.66 [6416]~P80(x64161)+E(f862(f862(f74(x64161),f862(f862(f236(x64161),x64162),x64163)),x64162),f862(f862(f74(x64161),x64162),f862(f862(f236(x64161),x64162),x64163))) % 14.98/14.66 [6469]E(f862(f862(f3(a92),f862(f862(f73(a92),x64691),x64692)),x64693),f266(x64691,x64692,x64693))+~P1(f862(f862(f228(a92),x64692),x64693)) % 14.98/14.66 [6493]~E(f862(f862(f131(x64931),x64933),x64932),f106(x64931))+P1(f862(f862(f227(a924),f862(f182(f925(x64931)),x64932)),x64933)) % 14.98/14.66 [6633]E(f862(f862(f74(a924),f862(f96(a924),x66331)),f862(f862(f74(a924),f862(f96(a924),x66332)),x66333)),f2(a924))+~P1(f862(f862(f228(a1),x66331),a76)) % 14.98/14.66 [6649]~P64(x66491)+E(f862(f862(f236(x66491),f862(f862(f281(x66491),f71(x66491)),x66492)),x66493),f862(f862(f281(x66491),f71(x66491)),f862(f862(f236(x66491),x66492),x66493))) % 14.98/14.66 [6729]E(f862(f862(f3(a924),f862(f862(f73(a924),x67291),x67292)),x67293),f862(f862(f3(a924),x67291),f862(f862(f3(a924),x67293),x67292)))+~P1(f862(f862(f227(a924),x67292),x67293)) % 14.98/14.66 [6731]E(f862(f862(f3(a924),f862(f862(f73(a924),x67311),x67312)),x67313),f862(f862(f73(a924),x67311),f862(f862(f3(a924),x67312),x67313)))+~P1(f862(f862(f227(a924),x67313),x67312)) % 14.98/14.66 [6767]~P93(x67671)+P1(f862(f862(f227(x67671),f862(f862(f94(x67671),x67672),x67673)),x67673)) % 14.98/14.66 [6768]~P104(x67681)+P1(f862(f862(f227(x67681),f862(f862(f94(x67681),x67682),x67683)),x67683)) % 14.98/14.66 [6769]~P93(x67691)+P1(f862(f862(f227(x67691),f862(f862(f94(x67691),x67692),x67693)),x67692)) % 14.98/14.66 [6770]~P104(x67701)+P1(f862(f862(f227(x67701),f862(f862(f94(x67701),x67702),x67703)),x67702)) % 14.98/14.66 [6771]~P109(x67711)+P1(f862(f862(f227(x67711),f862(f862(f225(x67711),x67712),x67713)),x67713)) % 14.98/14.66 [6772]~P109(x67721)+P1(f862(f862(f227(x67721),f862(f862(f225(x67721),x67722),x67723)),x67722)) % 14.98/14.66 [6785]E(f862(f862(f29(a1),f862(f862(f29(a1),x67851),x67852)),x67853),f862(f862(f29(a1),x67851),f862(f862(f74(a1),x67852),x67853)))+~P1(f862(f862(f228(a1),f2(a1)),x67853)) % 14.98/14.66 [6835]~P119(x68351)+E(f862(f862(f73(x68351),f862(f862(f74(x68351),x68352),x68353)),x68353),f862(f862(f74(x68351),f862(f862(f73(x68351),x68352),f71(x68351))),x68353)) % 14.98/14.66 [6836]~P98(x68361)+E(f862(f862(f74(x68361),f862(f72(x68361),f862(f96(x68361),x68362))),x68363),f862(f862(f74(x68361),f862(f96(x68361),f862(f72(a1),x68362))),x68363)) % 14.98/14.66 [6908]~P81(x69081)+E(f862(f158(x69081),f862(f862(f147(x69082,x69081),f862(f18(x69081,x69082),f2(x69081))),x69083)),f2(x69081)) % 14.98/14.66 [6923]E(f862(f862(f73(a924),f862(f96(a924),x69231)),f862(f862(f73(a924),f862(f96(a924),x69232)),x69233)),f862(f862(f73(a924),f862(f96(a924),x69232)),x69233))+~P1(f862(a186,f862(f96(a1),x69231))) % 14.98/14.66 [6938]~P3(x69381)+E(f31(x69381,f862(f862(f301(x69381),x69382),f862(f862(f301(x69381),x69383),f181(f932(x69381,a921))))),f862(f862(f94(x69381),x69382),x69383)) % 14.98/14.66 [6939]~P3(x69391)+E(f30(x69391,f862(f862(f301(x69391),x69392),f862(f862(f301(x69391),x69393),f181(f932(x69391,a921))))),f862(f862(f103(x69391),x69392),x69393)) % 14.98/14.66 [6963]E(f862(f862(f168(x69631),x69632),x69633),x69633)+~P1(f862(f862(f227(a924),f862(f182(f925(x69631)),x69633)),x69632)) % 14.98/14.66 [6976]E(f862(f862(f131(x69761),x69762),x69763),f106(x69761))+~P1(f862(f862(f227(a924),f862(f182(f925(x69761)),x69763)),x69762)) % 14.98/14.66 [6987]E(f862(f862(f73(a924),f862(f862(f3(a924),x69871),x69872)),x69873),f862(f862(f3(a924),f862(f862(f73(a924),x69871),x69873)),x69872))+~P1(f862(f862(f227(a924),x69872),x69871)) % 14.98/14.66 [7001]~P1(f862(f862(f228(a924),x70011),x70013))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x70011),x70012)),x70013)) % 14.98/14.66 [7028]~P109(x70281)+E(f163(x70281,x70282,f862(f862(f141(x70281,x70281,f7(x70281)),x70282),x70283)),x70283) % 14.98/14.66 [7118]E(f862(f862(f3(a924),f862(f862(f73(a924),x71181),x71182)),f862(a105,x71183)),f862(f862(f3(a924),x71181),f862(a105,f862(f862(f3(a924),x71183),x71182))))+~P1(f862(f862(f227(a924),x71182),x71183)) % 14.98/14.66 [7119]~P112(x71191)+P1(f862(f862(f227(x71191),f2(x71191)),f862(f862(f236(x71191),f862(f69(x71191),x71192)),x71193))) % 14.98/14.66 [7208]~P1(f862(f54(x72081),x72083))+P1(f862(f54(x72081),f862(f862(f94(f932(x72081,a921)),x72082),x72083))) % 14.98/14.66 [7209]~P1(f862(f54(x72091),x72092))+P1(f862(f54(x72091),f862(f862(f94(f932(x72091,a921)),x72092),x72093))) % 14.98/14.66 [7210]~P1(f862(f54(x72101),x72102))+P1(f862(f54(x72101),f862(f862(f3(f932(x72101,a921)),x72102),x72103))) % 14.98/14.66 [7352]~P35(x73521,x73523)+P35(x73521,f862(f862(f94(f932(f931(x73521,x73521),a921)),x73522),x73523)) % 14.98/14.66 [7353]~P35(x73531,x73532)+P35(x73531,f862(f862(f94(f932(f931(x73531,x73531),a921)),x73532),x73533)) % 14.98/14.66 [7477]~P93(x74771)+E(f12(x74771,f862(f165(x74771),f862(f862(f144(x74771),x74772),x74773))),f862(f135(x74771,x74771,f94(x74771),x74772),x74773)) % 14.98/14.66 [7478]~P93(x74781)+E(f15(x74781,f862(f165(x74781),f862(f862(f144(x74781),x74782),x74783))),f862(f135(x74781,x74781,f103(x74781),x74782),x74783)) % 14.98/14.66 [7479]~P109(x74791)+E(f16(x74791,f862(f165(x74791),f862(f862(f144(x74791),x74792),x74793))),f862(f135(x74791,x74791,f225(x74791),x74792),x74793)) % 14.98/14.66 [7480]~P109(x74801)+E(f17(x74801,f862(f165(x74801),f862(f862(f144(x74801),x74802),x74803))),f862(f135(x74801,x74801,f226(x74801),x74802),x74803)) % 14.98/14.66 [7545]~P1(f862(f54(x75451),x75452))+P1(f862(f862(f227(a924),f862(f28(x75451),x75452)),f862(f28(x75451),f862(f862(f301(x75451),x75453),x75452)))) % 14.98/14.66 [7553]E(f862(f862(f103(f932(a924,a921)),f862(f295(a924,x75531),x75532)),f862(f295(a924,x75532),f862(f862(f73(a924),x75532),x75533))),f862(f295(a924,x75531),f862(f862(f73(a924),x75532),x75533)))+~P1(f862(f862(f227(a924),x75531),x75532)) % 14.98/14.66 [7562]P1(f862(f862(f227(a924),x75621),x75622))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x75623),x75621)),x75622)) % 14.98/14.66 [7563]P1(f862(f862(f227(a924),x75631),x75632))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x75631),x75633)),x75632)) % 14.98/14.66 [7564]P1(f862(f862(f228(a924),x75641),x75642))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),x75641),x75643)),x75642)) % 14.98/14.66 [7604]~P109(x76041)+E(f13(x76041,f225(x76041),f862(f165(x76041),f862(f862(f144(x76041),x76042),x76043))),f862(f135(x76041,x76041,f225(x76041),x76042),x76043)) % 14.98/14.66 [7605]~P109(x76051)+E(f14(x76051,f226(x76051),f862(f165(x76051),f862(f862(f144(x76051),x76052),x76053))),f862(f135(x76051,x76051,f226(x76051),x76052),x76053)) % 14.98/14.66 [7609]~E(x76092,f181(f932(f931(x76091,x76091),a921)))+P1(f862(f862(f227(f932(f931(x76091,x76091),a921)),x76092),x76093)) % 14.98/14.66 [7709]E(f862(f862(f103(f932(x77091,a921)),x77092),f862(f862(f3(f932(x77091,a921)),x77093),x77092)),x77093)+~P1(f862(f862(f227(f932(x77091,a921)),x77092),x77093)) % 14.98/14.66 [7710]~P1(f862(f862(f227(a924),x77101),f862(f862(f73(a924),x77103),x77102)))+P1(f862(f862(f227(a924),f862(f862(f3(a924),x77101),x77102)),x77103)) % 14.98/14.66 [7711]~P1(f862(f862(f228(a924),x77111),f862(f862(f3(a924),x77113),x77112)))+P1(f862(f862(f228(a924),f862(f862(f73(a924),x77111),x77112)),x77113)) % 14.98/14.66 [7769]E(x77691,f106(x77692))+E(f862(f134(x77692),f862(f862(f862(f176(f925(x77692),f925(x77692)),x77693),f160(x77692)),x77691)),f862(f862(f157(x77692),x77691),f38(a924,x77693,f862(f182(f925(x77692)),x77691)))) % 14.98/14.66 [7778]E(f862(f862(f301(x77781),x77782),f862(f862(f3(f932(x77781,a921)),x77783),f862(f862(f301(x77781),x77782),f181(f932(x77781,a921))))),x77783)+~P1(f862(f862(f321(x77781),x77782),x77783)) % 14.98/14.66 [7939]P1(f862(f862(f227(a924),x79391),f862(f862(f73(a924),x79392),x79393)))+~P1(f862(f862(f227(a924),f862(f862(f3(a924),x79391),x79393)),x79392)) % 14.98/14.66 [7940]P1(f862(f862(f228(a924),x79401),f862(f862(f3(a924),x79402),x79403)))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),x79401),x79403)),x79402)) % 14.98/14.66 [7965]P1(f862(f54(x79651),x79652))+~P1(f862(f54(x79651),f862(f862(f103(f932(x79651,a921)),x79653),x79652))) % 14.98/14.66 [7966]P1(f862(f54(x79661),x79662))+~P1(f862(f54(x79661),f862(f862(f103(f932(x79661,a921)),x79662),x79663))) % 14.98/14.66 [8041]~P43(x80411,x80413)+P1(f862(f862(f321(f931(x80411,x80411)),f862(f862(f244(x80411,x80411),x80412),x80412)),x80413)) % 14.98/14.66 [8177]E(f862(f862(f157(a924),f132(a924,f862(f295(a924,x81771),x81772))),x81773),f862(f862(f73(a924),x81771),x81773))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),x81771),x81773)),x81772)) % 14.98/14.66 [8244]E(f862(f862(f168(a924),x82441),f132(a924,f862(f295(a924,x82442),x82443))),f132(a924,f862(f295(a924,x82442),f862(f862(f73(a924),x82442),x82441))))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x82442),x82441)),x82443)) % 14.98/14.66 [8303]~P98(x83031)+E(f862(f862(f236(x83031),x83032),f862(f96(a924),f862(f862(f73(a1),x83033),x83033))),f862(f862(f79(x83031,x83031),f862(f862(f236(x83031),x83032),f862(f96(a924),x83033))),f862(f862(f20(x83031,x83031,x83031),f74(x83031)),f7(x83031)))) % 14.98/14.66 [8569]E(f862(f862(f127(x85691),f862(f862(f168(x85691),x85692),x85693)),f862(f862(f144(x85691),f862(f862(f157(x85691),x85693),x85692)),f862(f862(f131(x85691),f862(a105,x85692)),x85693))),x85693)+~P1(f862(f862(f228(a924),x85692),f862(f182(f925(x85691)),x85693))) % 14.98/14.66 [8576]P1(f862(f862(f227(f932(x85761,a921)),f307(x85761,x85762)),f307(x85761,x85763)))+~P1(f862(f862(f227(f932(x85761,f932(x85761,a921))),x85763),x85762)) % 14.98/14.66 [8577]~P53(x85771,x85772,x85773)+P53(x85771,x85772,f862(f862(f3(f932(f931(x85771,x85771),a921)),x85773),f299(x85771,f181(f932(f931(x85771,x85771),a921))))) % 14.98/14.66 [8596]P1(f862(f862(f227(f932(x85961,a921)),f308(x85961,x85962)),f308(x85961,x85963)))+~P1(f862(f862(f227(f932(f931(x85961,x85961),a921)),x85963),x85962)) % 14.98/14.66 [8602]~P1(f862(f862(f228(f932(x86021,a921)),x86023),x86022))+P1(f862(f862(f321(x86021),f772(x86022,x86023,x86021)),f862(f862(f3(f932(x86021,a921)),x86022),x86023))) % 14.98/14.66 [8604]~P129(x86041)+P1(f862(f862(f227(x86041),f2(x86041)),f862(f862(f73(x86041),f862(f862(f74(x86041),x86042),x86042)),f862(f862(f74(x86041),x86043),x86043)))) % 14.98/14.66 [8638]P1(f862(f862(f227(f932(x86381,a921)),f862(f273(x86381),x86382)),f862(f273(x86381),x86383)))+~P1(f862(f862(f227(f932(f931(x86381,x86381),a921)),x86382),x86383)) % 14.98/14.66 [8668]~P51(x86681,x86682)+~P1(f862(f862(f321(f931(x86681,x86681)),f862(f862(f244(x86681,x86681),x86683),x86683)),x86682)) % 14.98/14.66 [8670]~P35(x86701,x86702)+~P1(f862(f862(f321(f931(x86701,x86701)),f862(f862(f244(x86701,x86701),x86703),x86703)),x86702)) % 14.98/14.66 [8729]P1(f862(f862(f227(f932(x87291,a921)),f31(f932(x87291,a921),x87292)),f31(f932(x87291,a921),x87293)))+~P1(f862(f862(f227(f932(f932(x87291,a921),a921)),x87293),x87292)) % 14.98/14.66 [8730]P1(f862(f862(f227(f932(x87301,a921)),f30(f932(x87301,a921),x87302)),f30(f932(x87301,a921),x87303)))+~P1(f862(f862(f227(f932(f932(x87301,a921),a921)),x87302),x87303)) % 14.98/14.66 [8785]~P6(x87851,x87853,x87852)+P1(f862(f862(f227(f932(f931(x87851,x87851),a921)),x87852),f862(f862(f246(x87851,x87851),x87853),f862(f18(f932(x87851,a921),x87851),x87853)))) % 14.98/14.66 [8786]~P50(x87861,x87863,x87862)+P1(f862(f862(f227(f932(f931(x87861,x87861),a921)),x87862),f862(f862(f246(x87861,x87861),x87863),f862(f18(f932(x87861,a921),x87861),x87863)))) % 14.98/14.66 [8835]~P86(x88351)+P1(f862(f862(f227(x88351),f862(f862(f3(x88351),f862(f69(x88351),x88352)),f862(f69(x88351),x88353))),f862(f69(x88351),f862(f862(f3(x88351),x88353),x88352)))) % 14.98/14.66 [8836]~P86(x88361)+P1(f862(f862(f227(x88361),f862(f862(f3(x88361),f862(f69(x88361),x88362)),f862(f69(x88361),x88363))),f862(f69(x88361),f862(f862(f3(x88361),x88362),x88363)))) % 14.98/14.66 [8868]P1(f862(f862(f227(f932(f931(x88681,x88681),a921)),f299(x88681,x88682)),f299(x88681,x88683)))+~P1(f862(f862(f227(f932(f931(x88681,x88681),a921)),x88682),x88683)) % 14.98/14.66 [8980]~P22(x89802,x89801,x89803,f234(f932(x89802,a921)))+E(f862(f66(x89801,x89802,x89802,f86(x89802,x89801,f234(f932(x89802,a921)),x89803)),x89803),f25(x89802)) % 14.98/14.66 [9042]P53(x90421,x90422,x90423)+~P53(x90421,x90422,f862(f862(f3(f932(f931(x90421,x90421),a921)),x90423),f299(x90421,f181(f932(f931(x90421,x90421),a921))))) % 14.98/14.66 [9062]P1(f862(f862(f227(f932(f931(f925(x90621),f925(x90621)),a921)),f150(x90621,x90622)),f150(x90621,x90623)))+~P1(f862(f862(f227(f932(f931(x90621,x90621),a921)),x90622),x90623)) % 14.98/14.66 [9063]P1(f862(f862(f227(f932(f931(f925(x90631),f925(x90631)),a921)),f151(x90631,x90632)),f151(x90631,x90633)))+~P1(f862(f862(f227(f932(f931(x90631,x90631),a921)),x90632),x90633)) % 14.98/14.66 [9084]~P50(x90841,x90843,x90842)+P1(f862(f862(f227(f932(f931(x90841,x90841),a921)),x90842),f862(f862(f280(x90841,x90841,x90841),f862(f277(x90841,x90841),x90842)),x90842))) % 14.98/14.66 [9136]~P1(f862(f130(x91361),x91362))+E(f862(f129(x91361,f862(f862(f9(x91361,f932(x91361,a921),a921),f321(x91361)),f862(f165(x91361),f169(x91361,x91362,x91363)))),x91362),f169(x91361,x91362,x91363)) % 14.98/14.66 [9189]E(x91891,x91892)+~P1(f862(f862(f321(f931(x91893,x91893)),f862(f862(f244(x91893,x91893),x91891),x91892)),f299(x91893,f181(f932(f931(x91893,x91893),a921))))) % 14.98/14.66 [9271]P1(f862(f862(f321(x92711),x92712),f308(x92711,x92713)))+P1(f862(f862(f321(f931(x92711,x92711)),f862(f862(f244(x92711,x92711),f547(x92713,x92712,x92711)),x92712)),x92713)) % 14.98/14.66 [9272]P1(f862(f862(f321(x92721),x92722),f308(x92721,x92723)))+P1(f862(f862(f321(f931(x92721,x92721)),f862(f862(f244(x92721,x92721),f612(x92723,x92722,x92721)),x92722)),x92723)) % 14.98/14.66 [9273]P1(f862(f862(f321(x92731),x92732),f308(x92731,x92733)))+P1(f862(f862(f321(f931(x92731,x92731)),f862(f862(f244(x92731,x92731),f614(x92733,x92732,x92731)),x92732)),x92733)) % 14.98/14.66 [9310]P22(x93101,x93102,x93103,f234(f932(x93101,a921)))+~E(f862(f66(x93102,x93101,x93101,f86(x93101,x93102,f234(f932(x93101,a921)),x93103)),x93103),f25(x93101)) % 14.98/14.66 [9364]~P1(f862(f862(f321(f925(x93641)),x93643),f154(x93641,x93642)))+P1(f862(f153(x93641,f862(f862(f9(x93641,f932(x93641,a921),a921),f321(x93641)),x93642)),x93643)) % 14.98/14.66 [9387]P1(f862(x93873,x93872))+E(f862(f254(x93871),f862(f862(f20(x93871,a921,a921),f862(f862(f10(a921,f932(a921,a921),x93871),a318),f862(a317,x93872))),x93873)),f181(f932(x93871,a921))) % 14.98/14.66 [9404]~P86(x94041)+P1(f862(f862(f227(x94041),f862(f69(x94041),f862(f862(f3(x94041),f862(f69(x94041),x94042)),f862(f69(x94041),x94043)))),f862(f69(x94041),f862(f862(f3(x94041),x94042),x94043)))) % 14.98/14.66 [9418]~P1(f862(x94183,x94182))+E(f862(f254(x94181),f862(f862(f20(x94181,a921,a921),f862(f862(f10(a921,f932(a921,a921),x94181),a318),f862(a317,x94182))),x94183)),f862(f862(f301(x94181),x94182),f181(f932(x94181,a921)))) % 14.98/14.66 [9427]~P1(f862(f862(f321(f932(x94271,a921)),x94273),f862(f300(x94271),x94272)))+P1(f862(f240(x94271,f862(f862(f9(x94271,f932(x94271,a921),a921),f321(x94271)),x94272)),x94273)) % 14.98/14.66 [9463]P35(x94631,x94632)+P1(f862(f862(f321(f931(x94631,x94631)),f862(f862(f244(x94631,x94631),f862(f553(x94632,x94631),f862(a105,x94633))),f862(f553(x94632,x94631),x94633))),x94632)) % 14.98/14.66 [9605]P1(f862(f862(f321(f925(x96051)),x96052),f154(x96051,x96053)))+~P1(f862(f153(x96051,f862(f862(f9(x96051,f932(x96051,a921),a921),f321(x96051)),x96053)),x96052)) % 14.98/14.66 [9620]P1(f862(f862(f321(f932(x96201,a921)),x96202),f862(f300(x96201),x96203)))+~P1(f862(f240(x96201,f862(f862(f9(x96201,f932(x96201,a921),a921),f321(x96201)),x96203)),x96202)) % 14.98/14.66 [9682]P1(f862(f862(f321(x96821),f862(f260(x96821,x96822),x96823)),f862(f165(x96821),f862(f862(f147(f931(a92,x96821),x96821),f248(a92,x96821)),x96822))))+~P1(f862(f862(f228(a92),x96823),f862(f158(a92),f862(f862(f147(f931(a92,x96821),a92),f243(a92,x96821)),x96822)))) % 14.98/14.66 [9728]P1(f862(f862(f227(f932(f931(f925(x97281),f925(x97281)),a921)),f151(x97281,x97282)),f862(f862(f246(f925(x97281),f925(x97281)),f154(x97281,x97283)),f862(f18(f932(f925(x97281),a921),f925(x97281)),f154(x97281,x97283)))))+~P1(f862(f862(f227(f932(f931(x97281,x97281),a921)),x97282),f862(f862(f246(x97281,x97281),x97283),f862(f18(f932(x97281,a921),x97281),x97283)))) % 14.98/14.66 [9752]P1(f862(f862(f321(x97521),f862(f243(x97521,f931(a92,a92)),f862(f258(x97521,x97522),x97523))),f862(f165(x97521),f862(f862(f147(f931(a92,x97521),x97521),f248(a92,x97521)),x97522))))+~P1(f862(f862(f228(a92),f2(a92)),f862(f158(a92),f862(f862(f147(f931(a92,x97521),a92),f243(a92,x97521)),x97522)))) % 14.98/14.66 [9767]~P1(f862(f862(f227(f932(f931(x97671,x97671),a921)),x97672),f862(f862(f246(x97671,x97671),x97673),f862(f18(f932(x97671,a921),x97671),x97673))))+P1(f862(f862(f227(f932(f931(x97671,x97671),a921)),f862(f862(f280(x97671,x97671,x97671),x97672),f299(x97671,x97672))),f862(f862(f246(x97671,x97671),x97673),f862(f18(f932(x97671,a921),x97671),x97673)))) % 14.98/14.66 [10068]~P35(x100681,x100682)+~P1(f862(f862(f321(f931(x100681,x100681)),f862(f862(f244(x100681,x100681),f862(x100683,f862(a105,f554(x100682,x100681,x100683)))),f862(x100683,f554(x100682,x100681,x100683)))),x100682)) % 14.98/14.66 [10069]~P35(x100691,x100692)+~P1(f862(f862(f321(f931(x100691,x100691)),f862(f862(f244(x100691,x100691),f862(x100693,f862(a105,f618(x100693,x100692,x100691)))),f862(x100693,f618(x100693,x100692,x100691)))),x100692)) % 14.98/14.66 [10315]P1(f862(f862(f227(f932(f931(f932(x103151,a921),f932(x103151,a921)),a921)),f862(f862(f280(f932(x103151,a921),f932(x103151,a921),f932(x103151,a921)),f310(x103151,x103152)),f862(f862(f103(f932(f931(f932(x103151,a921),f932(x103151,a921)),a921)),f310(x103151,x103153)),f862(f862(f301(f931(f932(x103151,a921),f932(x103151,a921))),f862(f862(f244(f932(x103151,a921),f932(x103151,a921)),f181(f932(x103151,a921))),f181(f932(x103151,a921)))),f181(f932(f931(f932(x103151,a921),f932(x103151,a921)),a921)))))),f310(x103151,x103152)))+~P1(f862(f862(f227(f932(f931(x103151,x103151),a921)),f862(f862(f280(x103151,x103151,x103151),x103152),x103153)),x103152)) % 14.98/14.66 [10316]P1(f862(f862(f227(f932(f931(f932(x103161,a921),f932(x103161,a921)),a921)),f862(f862(f280(f932(x103161,a921),f932(x103161,a921),f932(x103161,a921)),f312(x103161,x103162)),f862(f862(f103(f932(f931(f932(x103161,a921),f932(x103161,a921)),a921)),f312(x103161,x103163)),f862(f862(f301(f931(f932(x103161,a921),f932(x103161,a921))),f862(f862(f244(f932(x103161,a921),f932(x103161,a921)),f181(f932(x103161,a921))),f181(f932(x103161,a921)))),f181(f932(f931(f932(x103161,a921),f932(x103161,a921)),a921)))))),f312(x103161,x103162)))+~P1(f862(f862(f227(f932(f931(x103161,x103161),a921)),f862(f862(f280(x103161,x103161,x103161),x103162),x103163)),x103162)) % 14.98/14.66 [7476]~P1(f862(f862(f227(a924),x74762),x74761))+E(f862(f862(f3(a924),f862(a105,f862(f862(f3(a924),x74761),x74762))),x74763),f862(f862(f3(a924),f862(a105,x74761)),f862(f862(f73(a924),x74762),x74763))) % 14.98/14.66 [7517]~P61(x75171)+E(f862(f862(f73(x75171),f38(x75171,x75172,x75173)),f862(f862(f74(x75171),f862(f862(f29(x75171),x75172),x75173)),x75173)),x75172) % 14.98/14.66 [7715]E(f862(f862(f74(a924),f862(f96(a924),x77151)),f862(f862(f74(a924),f862(f96(a924),x77152)),x77153)),f862(f862(f74(a924),f862(f96(a924),f862(f862(f74(a1),x77151),x77152))),x77153))+P1(f862(f862(f228(a1),x77151),a76)) % 14.98/14.66 [8186]~P1(f862(f862(f227(a924),x81863),x81862))+P1(f862(f862(f227(a924),x81861),f862(f862(f3(a924),f862(f862(f73(a924),x81862),x81861)),x81863))) % 14.98/14.66 [8390]~P1(f862(f862(f227(a924),x83901),x83902))+E(f862(f862(f127(a924),f132(a924,f862(f295(a924,x83901),x83902))),f132(a924,f862(f295(a924,x83902),f862(f862(f73(a924),x83902),x83903)))),f132(a924,f862(f295(a924,x83901),f862(f862(f73(a924),x83902),x83903)))) % 14.98/14.66 [8647]~P1(f862(f54(x86471),x86472))+E(f862(a105,f862(f28(x86471),f862(f862(f3(f932(x86471,a921)),x86472),f862(f862(f301(x86471),x86473),f181(f932(x86471,a921)))))),f862(f28(x86471),f862(f862(f301(x86471),x86473),x86472))) % 14.98/14.66 [8686]~P1(f862(f54(x86861),x86862))+E(f862(f862(f73(a924),f71(a924)),f862(f28(x86861),f862(f862(f3(f932(x86861,a921)),x86862),f862(f862(f301(x86861),x86863),f181(f932(x86861,a921)))))),f862(f28(x86861),f862(f862(f301(x86861),x86863),x86862))) % 14.98/14.66 [8877]E(f862(f862(f3(a924),f862(f28(x88771),x88772)),f862(f28(x88771),f862(f862(f94(f932(x88771,a921)),x88772),x88773))),f862(f28(x88771),f862(f862(f3(f932(x88771,a921)),x88772),x88773)))+~P1(f862(f54(x88771),f862(f862(f94(f932(x88771,a921)),x88772),x88773))) % 14.98/14.66 [9131]~P4(f862(x91312,f505(x91312,x91313,x91311)))+E(f862(f93(a1),f862(f862(f8(x91311,a924),f862(f862(f10(a1,a924,x91311),a97),x91312)),x91313)),f862(f862(f8(x91311,a1),x91312),x91313)) % 14.98/14.66 [9132]~P4(f862(x91322,f506(x91322,x91323,x91321)))+E(f862(f93(a1),f862(f862(f11(x91321,a924),f862(f862(f10(a1,a924,x91321),a97),x91322)),x91323)),f862(f862(f11(x91321,a1),x91322),x91323)) % 14.98/14.66 [9172]~P1(f862(f54(x91721),x91723))+P1(f862(f862(f227(a924),f862(f862(f3(a924),f862(f28(x91721),x91722)),f862(f28(x91721),x91723))),f862(f28(x91721),f862(f862(f3(f932(x91721,a921)),x91722),x91723)))) % 14.98/14.66 [9199]P1(f862(f862(f321(x91991),f505(x91992,x91993,x91991)),x91993))+E(f862(f93(a1),f862(f862(f8(x91991,a924),f862(f862(f10(a1,a924,x91991),a97),x91992)),x91993)),f862(f862(f8(x91991,a1),x91992),x91993)) % 14.98/14.66 [9200]P1(f862(f862(f321(x92001),f506(x92002,x92003,x92001)),x92003))+E(f862(f93(a1),f862(f862(f11(x92001,a924),f862(f862(f10(a1,a924,x92001),a97),x92002)),x92003)),f862(f862(f11(x92001,a1),x92002),x92003)) % 14.98/14.66 [9263]E(f78(x92631,f862(f862(f9(x92631,f932(x92631,a921),a921),f321(x92631)),f862(f862(f3(f932(x92631,a921)),x92632),f862(f862(f301(x92631),x92633),f181(f932(x92631,a921)))))),f239(x92631,x92633,x92632))+P1(f862(f862(f227(f932(x92631,a921)),x92632),f862(f862(f301(x92631),x92633),f181(f932(x92631,a921))))) % 14.98/14.66 [9621]E(f862(f862(f147(f925(x96211),x96211),f862(f862(f9(f925(x96211),a924,x96211),f157(x96211)),x96212)),f862(f129(f925(x96211),f862(f862(f10(a924,a921,f925(x96211)),f862(f228(a924),x96212)),f182(f925(x96211)))),x96213)),f862(f862(f157(f925(x96211)),f172(x96211,x96213)),x96212))+~P1(f862(f862(f228(a924),x96212),f862(f182(f925(f925(x96211))),f172(x96211,x96213)))) % 14.98/14.66 [9702]E(f862(f129(x97021,x97022),x97023),f170(x97021,x97022,x97023))+P1(f862(f862(f321(x97021),f728(x97023,x97022,x97021)),f862(f165(x97021),f862(f862(f131(x97021),f862(f182(f925(x97021)),f170(x97021,x97022,x97023))),x97023)))) % 14.98/14.66 [9840]E(f862(f862(f131(x98401),f862(f182(f925(x98401)),f170(x98401,x98402,x98403))),x98403),f106(x98401))+~P1(f862(x98402,f862(f134(x98401),f862(f862(f131(x98401),f862(f182(f925(x98401)),f170(x98401,x98402,x98403))),x98403)))) % 14.98/14.66 [9933]~P1(f862(f862(f321(f931(x99331,x99331)),x99332),f299(x99331,x99333)))+P1(f862(f862(f321(f931(x99331,x99331)),x99332),f862(f862(f33(a924,f932(f931(x99331,x99331),a921)),f234(f932(a924,a921))),f862(f862(f9(a924,f932(f931(x99331,x99331),a921),f932(f931(x99331,x99331),a921)),f176(f931(x99331,x99331),a921)),x99333)))) % 14.98/14.66 [9994]~P1(f862(f862(f227(f932(x99941,a921)),f862(f862(f33(a924,f932(x99941,a921)),f862(f295(a924,f2(a924)),f517(x99943,x99942,x99941))),x99942)),x99943))+P1(f862(f862(f227(f932(x99941,a921)),f862(f862(f33(a924,f932(x99941,a921)),f234(f932(a924,a921))),x99942)),x99943)) % 14.98/14.66 [10041]~P1(f862(f862(f228(a1),f2(a1)),x100413))+P1(f862(f862(f228(a1),x100411),f862(f862(f73(a1),x100412),f862(f862(f74(a1),f862(f862(f73(a1),f862(f69(a1),f862(f862(f3(a1),x100412),x100411))),f71(a1))),x100413)))) % 14.98/14.66 [10055]~P35(x100551,f862(f862(f103(f932(f931(x100551,x100551),a921)),x100552),x100553))+P35(x100551,f862(f862(f103(f932(f931(x100551,x100551),a921)),f862(f862(f103(f932(f931(x100551,x100551),a921)),f862(f862(f280(x100551,x100551,x100551),x100552),x100552)),f862(f862(f280(x100551,x100551,x100551),x100553),x100552))),x100553)) % 14.98/14.66 [10133]P35(x101331,f862(f862(f103(f932(f931(x101331,x101331),a921)),x101332),x101333))+~P35(x101331,f862(f862(f103(f932(f931(x101331,x101331),a921)),f862(f862(f103(f932(f931(x101331,x101331),a921)),f862(f862(f280(x101331,x101331,x101331),x101332),x101332)),f862(f862(f280(x101331,x101331,x101331),x101333),x101332))),x101333)) % 14.98/14.66 [9705]~P142(x97051)+E(f862(f95(x97051),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x97052),x97053)),f181(f932(f931(a924,a924),a921)))))),f862(f862(f3(x97051),f862(f93(x97051),x97052)),f862(f93(x97051),x97053))) % 14.98/14.66 [9787]P1(f862(x97873,x97872))+E(f862(f254(x97871),f862(f862(f20(x97871,a921,a921),f862(f862(f10(a921,f932(a921,a921),x97871),a318),f862(f862(f9(x97871,x97871,a921),a317),x97872))),x97873)),f181(f932(x97871,a921))) % 14.98/14.66 [9789]~P1(f862(x97893,x97892))+E(f862(f254(x97891),f862(f862(f20(x97891,a921,a921),f862(f862(f10(a921,f932(a921,a921),x97891),a318),f862(f862(f9(x97891,x97891,a921),a317),x97892))),x97893)),f862(f862(f301(x97891),x97892),f181(f932(x97891,a921)))) % 14.98/14.66 [10021]E(x100211,x100212)+P1(f862(f862(f235(x100213,x100213,f862(f862(f10(f932(x100213,a921),f932(x100213,a921),x100213),f862(f10(a921,a921,x100213),a314)),a317)),x100211),x100212)) % 14.98/14.66 [10113]~E(x101131,x101132)+~P1(f862(f862(f235(x101133,x101133,f862(f862(f10(f932(x101133,a921),f932(x101133,a921),x101133),f862(f10(a921,a921,x101133),a314)),a317)),x101131),x101132)) % 14.98/14.66 [10125]~P1(f862(f54(x101251),x101253))+E(f862(f862(f57(x101251,f932(x101251,a921),f862(f862(f10(f932(x101251,a921),f932(f932(x101251,a921),f932(x101251,a921)),x101251),f862(f9(f932(x101251,a921),f932(x101251,a921),f932(x101251,a921)),f3(f932(x101251,a921)))),f862(f862(f9(x101251,f932(x101251,a921),f932(x101251,a921)),f301(x101251)),f181(f932(x101251,a921))))),x101252),x101253),f862(f862(f3(f932(x101251,a921)),x101252),x101253)) % 14.98/14.66 [10155]~P1(f862(f862(f228(a1),f2(a1)),x101553))+P1(f862(f862(f228(a1),f862(f862(f3(a1),x101551),f862(f862(f74(a1),f862(f862(f73(a1),f862(f69(a1),f862(f862(f3(a1),x101551),x101552))),f71(a1))),x101553))),x101552)) % 14.98/14.66 [10405]~P1(f862(f862(f321(x104051),x104053),f308(x104051,x104052)))+P1(f862(f307(x104051,f862(f862(f9(x104051,f932(f931(x104051,x104051),a921),f932(x104051,a921)),f862(f862(f10(f932(x104051,f932(f932(f931(x104051,x104051),a921),a921)),f932(f932(f931(x104051,x104051),a921),f932(x104051,a921)),x104051),f9(x104051,f932(f931(x104051,x104051),a921),a921)),f862(f862(f10(f932(x104051,f931(x104051,x104051)),f932(x104051,f932(f932(f931(x104051,x104051),a921),a921)),x104051),f862(f10(f931(x104051,x104051),f932(f932(f931(x104051,x104051),a921),a921),x104051),f321(f931(x104051,x104051)))),f244(x104051,x104051)))),x104052)),x104053)) % 14.98/14.66 [10418]P1(f862(f862(f321(x104181),x104182),f308(x104181,x104183)))+~P1(f862(f307(x104181,f862(f862(f9(x104181,f932(f931(x104181,x104181),a921),f932(x104181,a921)),f862(f862(f10(f932(x104181,f932(f932(f931(x104181,x104181),a921),a921)),f932(f932(f931(x104181,x104181),a921),f932(x104181,a921)),x104181),f9(x104181,f932(f931(x104181,x104181),a921),a921)),f862(f862(f10(f932(x104181,f931(x104181,x104181)),f932(x104181,f932(f932(f931(x104181,x104181),a921),a921)),x104181),f862(f10(f931(x104181,x104181),f932(f932(f931(x104181,x104181),a921),a921),x104181),f321(f931(x104181,x104181)))),f244(x104181,x104181)))),x104183)),x104182)) % 14.98/14.66 [9992]~P1(f862(f54(x99921),f862(f254(x99921),x99923)))+P1(f862(f54(x99921),f862(f254(x99921),f862(f862(f20(x99921,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99921),a318),x99922)),x99923)))) % 14.98/14.66 [9993]~P1(f862(f54(x99931),f862(f254(x99931),x99932)))+P1(f862(f54(x99931),f862(f254(x99931),f862(f862(f20(x99931,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99931),a318),x99932)),x99933)))) % 14.98/14.66 [10089]P1(f862(f54(x100891),f862(f254(x100891),x100892)))+~P1(f862(f54(x100891),f862(f254(x100891),f862(f862(f20(x100891,a921,a921),f862(f862(f10(a921,f932(a921,a921),x100891),a319),x100893)),x100892)))) % 14.98/14.66 [10090]P1(f862(f54(x100901),f862(f254(x100901),x100902)))+~P1(f862(f54(x100901),f862(f254(x100901),f862(f862(f20(x100901,a921,a921),f862(f862(f10(a921,f932(a921,a921),x100901),a319),x100902)),x100903)))) % 14.98/14.66 [10384]~P1(f862(f54(x103841),x103842))+P1(f862(f54(f925(x103841)),f862(f254(f925(x103841)),f862(f862(f20(f925(x103841),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x103841)),a318),f862(f862(f9(f925(x103841),f932(x103841,a921),a921),f862(f862(f10(f932(x103841,a921),f932(f932(x103841,a921),a921),f925(x103841)),f227(f932(x103841,a921))),f165(x103841))),x103842))),f862(f862(f9(f925(x103841),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x103841)),a317),f182(f925(x103841)))),x103843))))) % 14.98/14.66 [10385]~P1(f862(f54(x103851),x103852))+P1(f862(f54(f925(x103851)),f862(f254(f925(x103851)),f862(f862(f20(f925(x103851),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x103851)),a318),f862(f862(f9(f925(x103851),f932(x103851,a921),a921),f862(f862(f10(f932(x103851,a921),f932(f932(x103851,a921),a921),f925(x103851)),f227(f932(x103851,a921))),f165(x103851))),x103852))),f862(f862(f9(f925(x103851),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x103851)),f227(a924)),f182(f925(x103851)))),x103853))))) % 14.98/14.66 [10106]~P119(x101061)+E(f862(f862(f236(x101061),x101062),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101063)),f862(f862(f74(x101061),f862(f862(f236(x101061),x101062),x101063)),f862(f862(f236(x101061),x101062),x101063))) % 14.98/14.66 [10136]~P80(x101361)+E(f862(f862(f236(x101361),f862(f862(f236(x101361),x101362),x101363)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f236(x101361),x101362),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101363))) % 14.98/14.66 [10182]~P142(x101821)+E(f862(f862(f236(x101821),f862(f72(x101821),x101822)),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101823)),f862(f862(f236(x101821),x101822),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101823))) % 14.98/14.66 [10323]~P112(x103231)+P1(f862(f862(f227(x103231),f2(x103231)),f862(f862(f73(x103231),f862(f862(f236(x103231),x103232),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103231),x103233),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))) % 14.98/14.66 [10192]~P119(x101921)+E(f862(f862(f236(x101921),x101922),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101923))),f862(f862(f74(x101921),x101922),f862(f862(f74(x101921),f862(f862(f236(x101921),x101922),x101923)),f862(f862(f236(x101921),x101922),x101923)))) % 14.98/14.66 [10243]~P80(x102431)+E(f862(f862(f74(x102431),x102432),f862(f862(f236(x102431),f862(f862(f236(x102431),x102432),x102433)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102431),x102432),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x102433)))) % 14.98/14.66 [10280]~P112(x102801)+P1(f862(f862(f227(x102801),f2(x102801)),f862(f862(f236(x102801),x102802),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x102803)))) % 14.98/14.66 [10360]~P98(x103601)+E(f862(f862(f3(x103601),f862(f862(f73(x103601),f862(f862(f236(x103601),x103602),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103601),x103603),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f862(f862(f74(x103601),f862(f862(f74(x103601),f862(f96(x103601),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103602)),x103603)),f862(f862(f236(x103601),f862(f862(f3(x103601),x103602),x103603)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.66 [10361]~P98(x103611)+E(f862(f862(f73(x103611),f862(f862(f73(x103611),f862(f862(f236(x103611),x103612),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103611),x103613),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f862(f862(f74(x103611),f862(f862(f74(x103611),f862(f96(x103611),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103612)),x103613)),f862(f862(f236(x103611),f862(f862(f73(x103611),x103612),x103613)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.66 [7982]P22(x79821,x79822,x79823,x79824)+~E(f537(x79824,x79823,x79822,x79821),f538(x79824,x79823,x79822,x79821)) % 14.98/14.66 [8278]P32(x82781,x82782,x82783,x82784,f106(x82782))+~E(x82784,f106(x82781)) % 14.98/14.66 [8279]P32(x82791,x82792,x82793,f106(x82791),x82794)+~E(x82794,f106(x82792)) % 14.98/14.66 [8825]~P32(x88252,x88253,x88254,x88251,f106(x88253))+E(x88251,f106(x88252)) % 14.98/14.66 [8826]~P32(x88263,x88262,x88264,f106(x88263),x88261)+E(x88261,f106(x88262)) % 14.98/14.66 [5241]~P15(x52413,x52411,x52414)+E(f862(f862(x52411,x52412),x52412),x52412) % 14.98/14.66 [5490]P1(f862(x54902,x54904))+E(f862(f129(x54901,x54902),f162(x54901,x54903,x54904)),f106(x54901)) % 14.98/14.66 [5527]~E(x55274,f181(f932(x55271,a921)))+E(f862(f302(x55271,x55272,x55273),x55274),f181(f932(x55272,a921))) % 14.98/14.66 [5777]~P1(f862(x57772,x57774))+E(f862(f129(x57771,x57772),f162(x57771,x57773,x57774)),f162(x57771,x57773,x57774)) % 14.98/14.66 [5807]~E(f862(f302(x58072,x58073,x58074),x58071),f181(f932(x58073,a921)))+E(x58071,f181(f932(x58072,a921))) % 14.98/14.66 [5994]~P5(x59941,x59943)+E(f263(x59941,x59942,f262(x59941,x59943),x59944),x59944) % 14.98/14.66 [6108]~P109(x61082)+E(f862(f862(f141(x61081,x61082,x61083),x61084),f106(x61081)),f862(f862(f144(x61081),x61084),f106(x61081))) % 14.98/14.66 [6463]~E(x64631,f181(f932(x64632,a921)))+~P1(f862(f55(x64632,x64633,x64631),x64634)) % 14.98/14.66 [6485]~P56(x64851,x64853,x64854,x64852)+P1(f862(f54(x64851),x64852)) % 14.98/14.66 [6487]~P56(x64871,x64873,x64872,x64874)+P1(f862(f54(x64871),x64872)) % 14.98/14.66 [6495]~P56(x64952,x64953,x64954,x64951)+~E(x64951,f181(f932(x64952,a921))) % 14.98/14.66 [6528]~P110(x65281)+E(f862(f862(f94(f932(x65281,a921)),f862(f295(x65281,x65282),x65283)),f296(x65281,x65283,x65284)),f181(f932(x65281,a921))) % 14.98/14.66 [6556]~P1(f862(f862(x65563,x65564),x65562))+P1(f862(f862(f321(x65561),x65562),f284(x65561,x65563,x65564))) % 14.98/14.66 [6557]~P1(f862(f862(x65573,x65574),x65572))+P1(f862(f862(f321(x65571),x65572),f285(x65571,x65573,x65574))) % 14.98/14.66 [6558]~P1(f862(f862(x65583,x65582),x65584))+P1(f862(f862(f321(x65581),x65582),f286(x65581,x65583,x65584))) % 14.98/14.66 [6559]~P1(f862(f862(x65593,x65592),x65594))+P1(f862(f862(f321(x65591),x65592),f289(x65591,x65593,x65594))) % 14.98/14.66 [6703]~P110(x67031)+E(f862(f862(f94(f932(x67031,a921)),f298(x67031,x67032,x67033)),f296(x67031,x67033,x67034)),f181(f932(x67031,a921))) % 14.98/14.66 [6704]~P110(x67041)+E(f862(f862(f94(f932(x67041,a921)),f297(x67041,x67042,x67043)),f298(x67041,x67043,x67044)),f181(f932(x67041,a921))) % 14.98/14.66 [6705]~P110(x67051)+E(f862(f862(f94(f932(x67051,a921)),f297(x67051,x67052,x67053)),f297(x67051,x67053,x67054)),f181(f932(x67051,a921))) % 14.98/14.66 [6706]~P110(x67061)+E(f862(f862(f94(f932(x67061,a921)),f296(x67061,x67062,x67063)),f298(x67061,x67063,x67064)),f181(f932(x67061,a921))) % 14.98/14.66 [6707]~P110(x67071)+E(f862(f862(f94(f932(x67071,a921)),f296(x67071,x67072,x67073)),f297(x67071,x67073,x67074)),f181(f932(x67071,a921))) % 14.98/14.66 [6745]P1(f862(f862(x67451,x67452),f561(x67452,x67451)))+~P1(f862(f241(x67453,x67454,x67451),x67452)) % 14.98/14.66 [6822]~P109(x68222)+E(f862(f165(x68221),f143(x68221,x68222,x68223,x68224)),f862(f165(x68221),x68224)) % 14.98/14.66 [6873]~P147(x68731)+E(f183(x68731,x68732,f862(a105,x68733),x68734),f183(x68731,x68732,x68733,f862(x68732,x68734))) % 14.98/14.66 [6932]~P1(f862(f862(f321(x69324),x69323),f284(x69324,x69321,x69322)))+P1(f862(f862(x69321,x69322),x69323)) % 14.98/14.66 [6933]~P1(f862(f862(f321(x69334),x69333),f285(x69334,x69331,x69332)))+P1(f862(f862(x69331,x69332),x69333)) % 14.98/14.66 [6934]~P1(f862(f862(f321(x69344),x69342),f286(x69344,x69341,x69343)))+P1(f862(f862(x69341,x69342),x69343)) % 14.98/14.66 [6935]~P1(f862(f862(f321(x69354),x69352),f289(x69354,x69351,x69353)))+P1(f862(f862(x69351,x69352),x69353)) % 14.98/14.66 [7013]E(f862(f28(f930(x70131,x70132)),f305(x70131,x70132,x70133,x70134)),f2(a924))+P1(f862(f54(x70132),x70134)) % 14.98/14.66 [7014]E(f862(f28(f930(x70141,x70142)),f305(x70141,x70142,x70143,x70144)),f2(a924))+P1(f862(f54(x70141),x70143)) % 14.98/14.66 [7216]~P12(x72164,x72161,x72162)+E(f862(f66(x72161,x72161,x72161,f862(x72162,x72163)),f862(x72162,x72163)),f862(x72162,x72163)) % 14.98/14.66 [7461]E(f269(x74611,x74612,x74613,x74614),f862(f244(f932(a92,f932(a921,f928(f926(x74611)))),f931(a92,a92)),f34(x74611)))+~P1(f862(f862(f227(a92),x74613),f2(a92))) % 14.98/14.66 [8107]~E(x81072,x81073)+P1(f862(f862(f321(f931(x81071,x81071)),f862(f862(f244(x81071,x81071),x81072),x81073)),f299(x81071,x81074))) % 14.98/14.66 [8136]~P22(x81361,x81362,x81363,f234(f932(x81361,a921)))+E(f862(f70(x81361,x81362,f234(f932(x81361,a921)),x81363),f862(x81363,x81364)),x81364) % 14.98/14.66 [8137]~P22(x81371,x81372,x81373,f234(f932(x81371,a921)))+E(f862(f86(x81371,x81372,f234(f932(x81371,a921)),x81373),f862(x81373,x81374)),x81374) % 14.98/14.66 [8227]~P1(f862(f862(f321(f925(x82271)),f862(f862(f144(x82271),x82274),x82272)),f154(x82271,x82273)))+P1(f862(f862(f321(f925(x82271)),x82272),f154(x82271,x82273))) % 14.98/14.66 [8228]~P1(f862(f862(f321(f925(x82281)),f862(f862(f127(x82281),x82284),x82282)),f154(x82281,x82283)))+P1(f862(f862(f321(f925(x82281)),x82282),f154(x82281,x82283))) % 14.98/14.66 [8229]~P1(f862(f862(f321(f925(x82291)),f862(f862(f127(x82291),x82292),x82294)),f154(x82291,x82293)))+P1(f862(f862(f321(f925(x82291)),x82292),f154(x82291,x82293))) % 14.98/14.66 [8240]~P109(x82401)+P11(x82401,f862(f862(f147(x82402,x82401),x82403),f143(x82402,x82401,x82403,x82404))) % 14.98/14.66 [8347]P22(x83474,x83473,x83471,x83472)+E(f862(x83471,f537(x83472,x83471,x83473,x83474)),f862(x83471,f538(x83472,x83471,x83473,x83474))) % 14.98/14.66 [8454]~P22(x84542,x84541,x84544,x84543)+P22(x84541,x84542,f70(x84542,x84541,x84543,x84544),f862(f302(x84542,x84541,x84544),x84543)) % 14.98/14.66 [8594]P35(f931(x85942,x85944),f272(x85942,x85944,x85941,x85943))+P1(f862(x85941,f558(x85942,x85943,x85944,x85941))) % 14.98/14.66 [8712]E(x87121,x87122)+~P1(f862(f862(f321(f931(x87123,x87123)),f862(f862(f244(x87123,x87123),x87121),x87122)),f255(x87123,x87124))) % 14.98/14.66 [8777]~P1(f862(f54(f930(x87773,x87771)),f305(x87773,x87771,x87774,x87772)))+P1(f862(f54(x87771),x87772)) % 14.98/14.66 [8778]~P1(f862(f54(f930(x87781,x87783)),f305(x87781,x87783,x87782,x87784)))+P1(f862(f54(x87781),x87782)) % 14.98/14.66 [8787]~P22(x87871,x87872,x87873,x87874)+P23(x87871,x87872,x87873,x87874,f862(f302(x87871,x87872,x87873),x87874)) % 14.98/14.66 [8788]P9(x87881,x87882,x87883,x87884)+~E(f862(x87884,f834(x87882,x87884,x87883,x87881)),f862(x87884,f835(x87882,x87884,x87883,x87881))) % 14.98/14.66 [8878]~P23(x88782,x88783,x88784,x88781,f181(f932(x88783,a921)))+E(x88781,f181(f932(x88782,a921))) % 14.98/14.66 [8879]~P23(x88793,x88792,x88794,f181(f932(x88793,a921)),x88791)+E(x88791,f181(f932(x88792,a921))) % 14.98/14.66 [8972]P35(f931(x89721,x89722),f272(x89721,x89722,x89723,x89724))+~P35(x89722,f862(x89724,f558(x89721,x89724,x89722,x89723))) % 14.98/14.66 [9538]E(f862(f862(f152(x95381,x95382),f675(x95383,x95384,x95382,x95381)),f676(x95383,x95384,x95382,x95381)),x95384)+~P1(f862(f862(f321(f931(f925(x95381),f925(x95381))),f862(f862(f244(f925(x95381),f925(x95381)),x95382),x95384)),f150(x95381,x95383))) % 14.98/14.66 [9544]~P1(f862(f862(f321(f931(f925(x95441),f925(x95441))),f862(f862(f244(f925(x95441),f925(x95441)),x95442),x95443)),f138(x95441,x95444)))+P1(f862(f862(f321(f931(f925(x95441),f925(x95441))),f862(f862(f244(f925(x95441),f925(x95441)),x95442),x95443)),f140(x95441,x95444))) % 14.98/14.66 [9657]P1(f862(f54(x96571),x96572))+~P1(f862(f862(f321(f931(f932(x96571,a921),f932(x96571,a921))),f862(f862(f244(f932(x96571,a921),f932(x96571,a921)),x96573),x96572)),f310(x96571,x96574))) % 14.98/14.66 [9658]P1(f862(f54(x96581),x96582))+~P1(f862(f862(f321(f931(f932(x96581,a921),f932(x96581,a921))),f862(f862(f244(f932(x96581,a921),f932(x96581,a921)),x96582),x96583)),f310(x96581,x96584))) % 14.98/14.66 [9661]~E(x96611,f181(f932(x96612,a921)))+~P1(f862(f862(f321(f931(f932(x96612,a921),f932(x96612,a921))),f862(f862(f244(f932(x96612,a921),f932(x96612,a921)),x96613),x96611)),f310(x96612,x96614))) % 14.98/14.66 [10291]P9(x102911,x102912,x102913,x102914)+~P1(f862(f862(f249(x102911,x102911,a921),f862(f862(f9(x102911,f932(x102911,x102912),f932(x102911,a921)),f862(f862(f10(f932(x102912,a921),f932(f932(x102911,x102912),f932(x102911,a921)),x102911),f10(x102912,a921,x102911)),f862(f862(f10(x102912,f932(x102912,a921),x102911),a317),x102914))),x102914)),f593(x102914,x102913,x102912,x102911))) % 14.98/14.66 [5137]~E(x51372,f106(x51371))+E(f862(f862(f152(x51371,x51372),x51373),x51374),f106(x51371)) % 14.98/14.66 [5138]~E(x51384,f106(x51381))+E(f862(f862(f147(x51381,x51382),x51383),x51384),f106(x51382)) % 14.98/14.66 [5374]E(x53741,f106(x53742))+~E(f862(f862(f147(x53742,x53743),x53744),x53741),f106(x53743)) % 14.98/14.66 [5375]E(x53751,f106(x53752))+~E(f862(f862(f152(x53752,x53751),x53753),x53754),f106(x53752)) % 14.98/14.66 [5414]E(x54141,x54142)+~E(f862(f862(f127(x54143),x54144),x54141),f862(f862(f127(x54143),x54144),x54142)) % 14.98/14.66 [5415]E(x54151,x54152)+~E(f862(f862(f127(x54153),x54151),x54154),f862(f862(f127(x54153),x54152),x54154)) % 14.98/14.66 [5565]P1(f862(x55653,x55652))+E(f163(x55651,x55652,f862(f129(x55651,x55653),x55654)),f862(f129(x55651,x55653),x55654)) % 14.98/14.66 [5567]~P1(f862(x55672,x55673))+P31(x55671,x55672,f862(f862(f144(x55671),x55673),x55674)) % 14.98/14.66 [5577]E(x55771,x55772)+~E(f132(a924,f862(f295(a924,x55771),x55773)),f862(f862(f144(a924),x55772),x55774)) % 14.98/14.66 [5626]~P24(x56262,x56263)+P24(x56261,f862(f862(f67(x56262,x56261),x56263),x56264)) % 14.98/14.66 [5627]~P35(x56272,x56273)+P35(x56271,f862(f862(f279(x56272,x56271),x56273),x56274)) % 14.98/14.66 [5628]~P36(x56282,x56283)+P36(x56281,f862(f862(f279(x56282,x56281),x56283),x56284)) % 14.98/14.66 [5629]~P49(x56292,x56293)+P49(x56291,f862(f862(f279(x56292,x56291),x56293),x56294)) % 14.98/14.66 [5760]~P31(x57601,x57602,x57604)+P31(x57601,x57602,f862(f862(f144(x57601),x57603),x57604)) % 14.98/14.66 [5761]~P31(x57611,x57612,x57614)+P31(x57611,x57612,f862(f862(f127(x57611),x57613),x57614)) % 14.98/14.66 [5762]~P31(x57621,x57622,x57623)+P31(x57621,x57622,f862(f862(f127(x57621),x57623),x57624)) % 14.98/14.66 [5850]~E(x58501,f106(x58502))+~E(f862(f862(f127(x58502),x58503),f862(f862(f144(x58502),x58504),f106(x58502))),x58501) % 14.98/14.66 [5875]~P29(x58753,x58751,f862(f862(f144(x58753),x58752),x58754))+P1(f862(x58751,x58752)) % 14.98/14.66 [5885]E(f107(x58851,x58852),x58853)+~E(f862(f862(f127(x58851),x58853),f862(f862(f144(x58851),x58854),f106(x58851))),x58852) % 14.98/14.66 [5886]E(f137(x58861,x58862),x58863)+~E(f862(f862(f127(x58861),x58864),f862(f862(f144(x58861),x58863),f106(x58861))),x58862) % 14.98/14.66 [5996]~E(f132(a924,f862(f295(a924,x59961),x59962)),f862(f862(f144(a924),x59963),x59964))+P1(f862(f862(f228(a924),x59961),x59962)) % 14.98/14.66 [6012]P29(x60121,x60122,x60123)+~P29(x60121,x60122,f862(f862(f144(x60121),x60124),x60123)) % 14.98/14.66 [6013]P29(x60131,x60132,x60133)+~P29(x60131,x60132,f862(f862(f127(x60131),x60134),x60133)) % 14.98/14.66 [6014]P29(x60141,x60142,x60143)+~P29(x60141,x60142,f862(f862(f127(x60141),x60143),x60144)) % 14.98/14.66 [6210]E(x62101,f862(f862(f127(x62102),f862(f161(x62102),x62103)),f862(f862(f144(x62102),x62104),f106(x62102))))+~E(f862(f161(x62102),x62101),f862(f862(f144(x62102),x62104),x62103)) % 14.98/14.66 [6385]~P110(x63851)+E(f862(f862(f94(f932(x63851,a921)),f862(f295(x63851,x63852),x63853)),f862(f295(x63851,x63853),x63854)),f181(f932(x63851,a921))) % 14.98/14.66 [6396]E(f862(f862(f157(x63961),f162(x63961,x63962,x63963)),x63964),x63963)+~P1(f862(f862(f228(a924),x63964),x63962)) % 14.98/14.66 [6423]~P72(x64231)+E(f862(f158(x64231),f862(f862(f147(a1,x64231),x64232),f171(x64233,x64234))),f862(f862(f8(a1,x64231),x64232),f862(f165(a1),f171(x64233,x64234)))) % 14.98/14.66 [6424]~P72(x64241)+E(f862(f862(f8(a1,x64241),x64242),f862(f165(a1),f171(x64243,x64244))),f862(f158(x64241),f862(f862(f147(a1,x64241),x64242),f171(x64243,x64244)))) % 14.98/14.66 [6569]~E(x65692,f862(f862(f127(x65691),f862(f161(x65691),x65694)),f862(f862(f144(x65691),x65693),f106(x65691))))+E(f862(f161(x65691),x65692),f862(f862(f144(x65691),x65693),x65694)) % 14.98/14.66 [6585]~P17(x65852,x65853,x65854,x65851)+E(f862(x65851,f181(f932(x65852,a921))),f25(x65853)) % 14.98/14.66 [6614]~P110(x66141)+E(f862(f862(f94(f932(x66141,a921)),f298(x66141,x66142,x66143)),f862(f295(x66141,x66143),x66144)),f181(f932(x66141,a921))) % 14.98/14.66 [6823]E(x68231,f181(f932(x68232,a921)))+~E(f305(x68233,x68232,x68234,x68231),f181(f932(f930(x68233,x68232),a921))) % 14.98/14.66 [6824]E(x68241,f181(f932(x68242,a921)))+~E(f305(x68242,x68243,x68241,x68244),f181(f932(f930(x68242,x68243),a921))) % 14.98/14.66 [6893]~P109(x68932)+E(f862(f182(f925(x68931)),f143(x68931,x68932,x68933,x68934)),f862(f182(f925(x68931)),x68934)) % 14.98/14.66 [6904]~P1(f862(f242(x69043,x69044,x69041),x69042))+P1(f862(f862(x69041,f562(x69042,x69041)),x69042)) % 14.98/14.66 [6946]~P1(f862(f54(x69462),x69464))+P1(f862(f54(x69461),f862(f302(x69462,x69461,x69463),x69464))) % 14.98/14.66 [7178]~P22(x71782,x71781,x71783,x71784)+E(f862(f28(x71781),f862(f302(x71782,x71781,x71783),x71784)),f862(f28(x71782),x71784)) % 14.98/14.66 [7196]E(f862(f302(x71961,x71962,x71963),f862(f303(x71961,x71962,x71963),x71964)),x71964)+~E(f862(f302(x71961,x71962,x71963),f234(f932(x71961,a921))),f234(f932(x71962,a921))) % 14.98/14.66 [7617]~P22(x76171,x76172,x76173,f234(f932(x76171,a921)))+E(f862(f303(x76171,x76172,x76173),f862(f302(x76171,x76172,x76173),x76174)),x76174) % 14.98/14.66 [7900]E(x79001,x79002)+~P1(f862(f862(f321(x79003),x79001),f862(f165(x79003),f162(x79003,x79004,x79002)))) % 14.98/14.66 [7909]~E(x79091,f2(a924))+~P1(f862(f862(f321(x79092),x79093),f862(f165(x79092),f162(x79092,x79091,x79094)))) % 14.98/14.66 [7942]P1(f862(x79421,x79422))+~P1(f862(f862(f321(x79423),x79422),f862(f165(x79423),f170(x79423,x79421,x79424)))) % 14.98/14.66 [8052]~P1(f862(f862(f321(f925(x80521)),f862(f862(f144(x80521),x80522),x80524)),f154(x80521,x80523)))+P1(f862(f862(f321(x80521),x80522),x80523)) % 14.98/14.66 [8183]~P1(f862(f862(f321(x81831),x81832),f862(f165(x81831),f169(x81831,x81833,x81834))))+P1(f862(f862(f321(x81831),x81832),f862(f165(x81831),x81833))) % 14.98/14.66 [8184]~P1(f862(f862(f321(x81841),x81842),f862(f165(x81841),f163(x81841,x81844,x81843))))+P1(f862(f862(f321(x81841),x81842),f862(f165(x81841),x81843))) % 14.98/14.66 [8185]~P1(f862(f862(f321(x81851),x81852),f862(f165(x81851),f170(x81851,x81854,x81853))))+P1(f862(f862(f321(x81851),x81852),f862(f165(x81851),x81853))) % 14.98/14.66 [8195]E(f862(f182(f925(x81951)),x81952),x81953)+~P1(f862(f862(f321(f925(x81951)),x81952),f862(f165(f925(x81951)),f48(x81951,x81953,x81954)))) % 14.98/14.66 [8292]P1(f862(x82923,x82922))+E(f862(f129(x82921,f862(f862(f10(a921,a921,x82921),a314),f862(a317,x82922))),f862(f129(x82921,x82923),x82924)),f862(f129(x82921,x82923),x82924)) % 14.98/14.66 [8406]E(f862(f862(f157(x84061),f170(x84061,x84062,x84063)),x84064),f862(f862(f157(x84061),x84063),x84064))+~P1(f862(f862(f228(a924),x84064),f862(f182(f925(x84061)),f170(x84061,x84062,x84063)))) % 14.98/14.66 [8492]~P72(x84921)+E(f862(f862(f8(a924,x84921),f862(f862(f10(a924,x84921,a924),x84922),a105)),f862(f295(a924,x84923),x84924)),f862(f862(f8(a924,x84921),x84922),f862(f295(a924,f862(a105,x84923)),f862(a105,x84924)))) % 14.98/14.66 [8501]~P72(x85011)+E(f862(f862(f8(a924,x85011),f862(f862(f10(a924,x85011,a924),x85012),a105)),f296(a924,x85013,x85014)),f862(f862(f8(a924,x85011),x85012),f296(a924,f862(a105,x85013),f862(a105,x85014)))) % 14.98/14.66 [8631]~P22(x86311,x86313,x86314,f234(f932(x86311,a921)))+P22(x86311,f932(x86312,x86313),f862(f862(f10(x86313,f932(x86312,x86313),x86311),f18(x86313,x86312)),x86314),f234(f932(x86311,a921))) % 14.98/14.66 [8718]~P22(x87182,x87181,x87184,x87183)+E(f862(f302(x87181,x87182,f70(x87182,x87181,x87183,x87184)),f862(f302(x87182,x87181,x87184),x87183)),x87183) % 14.98/14.66 [8779]~P1(f862(f862(f321(f931(x87791,x87791)),f862(f862(f244(x87791,x87791),x87792),x87794)),f255(x87791,x87793)))+P1(f862(f862(f321(x87791),x87792),x87793)) % 14.98/14.66 [8903]~P22(x89032,x89031,x89033,f234(f932(x89032,a921)))+E(f862(f302(x89031,x89032,f86(x89032,x89031,f234(f932(x89032,a921)),x89033)),f862(f302(x89032,x89031,x89033),x89034)),x89034) % 14.98/14.66 [8978]~P23(x89781,x89782,x89783,x89784,f234(f932(x89782,a921)))+E(f862(f302(x89781,x89782,x89783),f234(f932(x89781,a921))),f234(f932(x89782,a921))) % 14.98/14.66 [9011]~E(f862(f862(f8(x90111,a924),x90114),x90113),f862(a105,x90112))+P1(f862(f862(f321(x90111),f373(x90112,x90113,x90114,x90111)),x90113)) % 14.98/14.66 [9033]~E(f862(f862(f8(x90334,a924),x90331),x90333),f862(a105,x90332))+P1(f862(f862(f228(a924),f2(a924)),f862(x90331,f373(x90332,x90333,x90331,x90334)))) % 14.98/14.66 [9045]~P1(f862(f54(x90452),x90454))+P1(f862(f862(f227(a924),f862(f28(x90451),f862(f302(x90452,x90451,x90453),x90454))),f862(f28(x90452),x90454))) % 14.98/14.66 [9046]E(f862(f862(f244(x90461,x90462),f647(x90463,x90464,x90462,x90461)),f648(x90463,x90464,x90462,x90461)),x90464)+~P1(f862(f862(f321(f931(x90461,x90462)),x90464),f862(f277(x90462,x90461),x90463))) % 14.98/14.66 [9054]P22(x90541,x90542,x90543,x90544)+P1(f862(f862(f321(x90541),f537(x90544,x90543,x90542,x90541)),x90544)) % 14.98/14.66 [9055]P22(x90551,x90552,x90553,x90554)+P1(f862(f862(f321(x90551),f538(x90554,x90553,x90552,x90551)),x90554)) % 14.98/14.66 [9123]P9(x91231,x91232,x91233,x91234)+P1(f862(f862(f321(f931(x91231,x91231)),f593(x91234,x91233,x91232,x91231)),x91233)) % 14.98/14.66 [9177]P1(f862(x91771,x91772))+~P1(f862(x91771,f862(f862(f244(x91773,x91774),f495(x91774,x91773,x91771)),f496(x91774,x91773,x91771)))) % 14.98/14.66 [9194]E(f862(f182(f925(x91941)),x91942),f862(f182(f925(x91941)),x91943))+~P1(f862(f862(f321(f931(f925(x91941),f925(x91941))),f862(f862(f244(f925(x91941),f925(x91941)),x91942),x91943)),f138(x91941,x91944))) % 14.98/14.66 [9195]E(f862(f182(f925(x91951)),x91952),f862(f182(f925(x91951)),x91953))+~P1(f862(f862(f321(f931(f925(x91951),f925(x91951))),f862(f862(f244(f925(x91951),f925(x91951)),x91952),x91953)),f150(x91951,x91954))) % 14.98/14.66 [9198]E(f862(f182(f925(x91981)),x91982),f862(f182(f925(x91981)),x91983))+~P1(f862(f862(f321(f931(f925(x91981),f925(x91981))),f862(f862(f244(f925(x91981),f925(x91981)),x91982),x91983)),f151(x91981,x91984))) % 14.98/14.66 [9267]P1(f862(f862(f227(a924),f148(x92671,x92672,x92673)),f148(x92671,x92674,x92673)))+P1(f862(f862(f321(x92671),f674(x92674,x92672,x92673,x92671)),f862(f165(x92671),x92673))) % 14.98/14.66 [9270]E(f862(f182(f925(x92701)),x92702),f862(f182(f925(x92701)),x92703))+~P1(f862(f862(f321(f931(f925(x92701),f925(x92701))),f862(f862(f244(f925(x92701),f925(x92701)),x92702),x92703)),f299(f925(x92701),f150(x92701,x92704)))) % 14.98/14.66 [9390]P1(f862(f862(f278(a924),x93901),x93902))+P1(f862(f862(f227(f932(a924,a921)),f287(a924,f278(a924),x93901,x93902)),f287(a924,f278(a924),x93903,x93904))) % 14.98/14.66 [9509]~P22(x95091,x95092,x95093,x95094)+~P1(f862(f862(f228(a924),f862(f28(x95092),f862(f302(x95091,x95092,x95093),x95094))),f862(f28(x95091),x95094))) % 14.98/14.66 [9557]~P1(f862(f862(f321(f931(f925(x95571),f925(x95571))),f862(f862(f244(f925(x95571),f925(x95571)),x95572),x95573)),f150(x95571,x95574)))+P1(f862(f862(f321(f931(f925(x95571),f925(x95571))),f862(f862(f244(f925(x95571),f925(x95571)),x95572),x95573)),f151(x95571,f299(x95571,x95574)))) % 14.98/14.66 [9561]~P1(f862(f862(f321(f931(f925(x95611),f925(x95611))),f862(f862(f244(f925(x95611),f925(x95611)),x95612),x95613)),f151(x95611,x95614)))+P1(f862(f862(f321(f931(f925(x95611),f925(x95611))),f862(f862(f244(f925(x95611),f925(x95611)),x95612),x95613)),f299(f925(x95611),f150(x95611,x95614)))) % 14.98/14.66 [9578]P1(f862(f862(f321(f931(x95781,x95781)),f862(f862(f244(x95781,x95781),x95782),x95783)),f299(x95781,x95784)))+~P1(f862(f862(f321(f931(x95781,x95781)),f862(f862(f244(x95781,x95781),x95782),x95783)),f862(f862(f280(x95781,x95781,x95781),x95784),f299(x95781,x95784)))) % 14.98/14.66 [9768]E(f862(f862(f127(x97681),f690(x97682,x97683,x97684,x97681)),f862(f862(f144(x97681),f691(x97682,x97683,x97684,x97681)),f693(x97682,x97683,x97684,x97681))),x97684)+~P1(f862(f862(f321(f931(f925(x97681),f925(x97681))),f862(f862(f244(f925(x97681),f925(x97681)),x97684),x97683)),f150(x97681,x97682))) % 14.98/14.66 [9769]E(f862(f862(f127(x97691),f690(x97692,x97693,x97694,x97691)),f862(f862(f144(x97691),f692(x97692,x97693,x97694,x97691)),f693(x97692,x97693,x97694,x97691))),x97693)+~P1(f862(f862(f321(f931(f925(x97691),f925(x97691))),f862(f862(f244(f925(x97691),f925(x97691)),x97694),x97693)),f150(x97691,x97692))) % 14.98/14.66 [9847]P1(f862(f862(f321(f931(x98471,x98471)),f862(f862(f244(x98471,x98471),x98472),f645(x98473,x98474,x98472,x98471))),f299(x98471,x98473)))+~P1(f862(f862(f321(f931(x98471,x98471)),f862(f862(f244(x98471,x98471),x98472),x98474)),f862(f862(f280(x98471,x98471,x98471),x98473),f299(x98471,x98473)))) % 14.98/14.66 [9916]P1(f862(f862(f227(a924),f148(x99161,x99162,x99163)),f148(x99161,x99164,x99163)))+~P1(f862(f862(f228(a924),f862(x99162,f674(x99164,x99162,x99163,x99161))),f862(x99164,f674(x99164,x99162,x99163,x99161)))) % 14.98/14.66 [9988]P1(f862(f862(f321(f931(x99881,x99881)),f862(f862(f244(x99881,x99881),f637(x99882,x99883,x99884,x99881)),x99883)),f299(x99881,x99882)))+~P1(f862(f862(f321(f931(x99881,x99881)),f862(f862(f244(x99881,x99881),x99884),x99883)),f862(f862(f280(x99881,x99881,x99881),x99882),f299(x99881,x99882)))) % 14.98/14.66 [5395]~E(x53952,x53953)+E(f163(x53951,x53952,f862(f862(f144(x53951),x53953),x53954)),x53954) % 14.98/14.66 [5520]P1(f862(x55202,x55203))+E(f170(x55201,x55202,f862(f862(f144(x55201),x55203),x55204)),f106(x55201)) % 14.98/14.66 [5589]~P82(x55892)+E(f862(f862(f72(f932(x55891,x55892)),x55893),x55894),f862(f72(x55892),f862(x55893,x55894))) % 14.98/14.66 [5602]~E(x56022,f2(a924))+E(f862(f862(f131(x56021),x56022),f862(f862(f144(x56021),x56023),x56024)),f862(f862(f144(x56021),x56023),x56024)) % 14.98/14.66 [5603]P1(f862(x56032,x56033))+E(f862(f129(x56031,x56032),f862(f862(f144(x56031),x56033),x56034)),f862(f129(x56031,x56032),x56034)) % 14.98/14.66 [5742]~E(x57422,x57424)+P1(f862(f862(f862(f301(x57421),x57422),x57423),x57424)) % 14.98/14.66 [5751]E(x57511,f106(x57512))+E(f137(x57513,f862(f862(f147(x57512,x57513),x57514),x57511)),f862(x57514,f137(x57512,x57511))) % 14.98/14.66 [5765]~E(x57651,f56(x57652,x57654))+E(f862(x57651,f862(f862(f301(x57652),x57653),f181(f932(x57652,a921)))),x57653) % 14.98/14.66 [5802]E(x58021,f106(x58022))+E(f862(f134(x58023),f862(f862(f147(x58022,x58023),x58024),x58021)),f862(x58024,f862(f134(x58022),x58021))) % 14.98/14.66 [5905]~P1(f862(x59053,x59054))+P1(f862(f862(f862(f301(x59051),x59052),x59053),x59054)) % 14.98/14.66 [6031]~P16(x60312,x60314,x60311)+E(f862(x60311,f862(f862(f301(x60312),x60313),f181(f932(x60312,a921)))),x60313) % 14.98/14.66 [6057]~E(x60572,x60573)+P1(f862(f862(f321(x60571),x60572),f862(f862(f301(x60571),x60573),x60574))) % 14.98/14.66 [6062]~P93(x60621)+E(f862(f862(f103(x60621),x60622),f862(f862(f103(x60621),x60623),x60624)),f862(f862(f103(x60621),x60623),f862(f862(f103(x60621),x60622),x60624))) % 14.98/14.66 [6064]~P103(x60641)+E(f862(f862(f103(x60641),x60642),f862(f862(f103(x60641),x60643),x60644)),f862(f862(f103(x60641),x60643),f862(f862(f103(x60641),x60642),x60644))) % 14.98/14.66 [6065]~P93(x60651)+E(f862(f862(f94(x60651),x60652),f862(f862(f94(x60651),x60653),x60654)),f862(f862(f94(x60651),x60653),f862(f862(f94(x60651),x60652),x60654))) % 14.98/14.66 [6067]~P104(x60671)+E(f862(f862(f94(x60671),x60672),f862(f862(f94(x60671),x60673),x60674)),f862(f862(f94(x60671),x60673),f862(f862(f94(x60671),x60672),x60674))) % 14.98/14.66 [6068]~P119(x60681)+E(f862(f862(f74(x60681),x60682),f862(f862(f74(x60681),x60683),x60684)),f862(f862(f74(x60681),x60683),f862(f862(f74(x60681),x60682),x60684))) % 14.98/14.66 [6069]~P119(x60691)+E(f862(f862(f73(x60691),x60692),f862(f862(f73(x60691),x60693),x60694)),f862(f862(f73(x60691),x60693),f862(f862(f73(x60691),x60692),x60694))) % 14.98/14.66 [6071]~P109(x60711)+E(f862(f862(f225(x60711),x60712),f862(f862(f225(x60711),x60713),x60714)),f862(f862(f225(x60711),x60713),f862(f862(f225(x60711),x60712),x60714))) % 14.98/14.66 [6073]~P109(x60731)+E(f862(f862(f226(x60731),x60732),f862(f862(f226(x60731),x60733),x60734)),f862(f862(f226(x60731),x60733),f862(f862(f226(x60731),x60732),x60734))) % 14.98/14.66 [6080]E(x60801,x60802)+E(f163(x60803,x60801,f862(f862(f144(x60803),x60802),x60804)),f862(f862(f144(x60803),x60802),f163(x60803,x60801,x60804))) % 14.98/14.66 [6095]~P1(f862(x60952,x60953))+E(f862(f129(x60951,x60952),f862(f862(f144(x60951),x60953),x60954)),f862(f862(f144(x60951),x60953),f862(f129(x60951,x60952),x60954))) % 14.98/14.66 [6231]~P1(f862(x62312,x62313))+E(f170(x62311,x62312,f862(f862(f144(x62311),x62313),x62314)),f862(f862(f144(x62311),x62313),f170(x62311,x62312,x62314))) % 14.98/14.66 [6293]E(x62931,f181(f932(x62932,a921)))+E(f862(f862(f32(x62932,f932(x62933,a921)),x62931),f862(f18(f932(x62933,a921),x62932),x62934)),x62934) % 14.98/14.66 [6294]E(x62941,f181(f932(x62942,a921)))+E(f862(f862(f33(x62942,f932(x62943,a921)),x62941),f862(f18(f932(x62943,a921),x62942),x62944)),x62944) % 14.98/14.66 [6303]~E(x63034,f181(f932(x63032,a921)))+E(f862(f862(f246(x63031,x63032),x63033),f862(f18(f932(x63032,a921),x63031),x63034)),f181(f932(f931(x63031,x63032),a921))) % 14.98/14.66 [6304]~E(x63043,f181(f932(x63041,a921)))+E(f862(f862(f246(x63041,x63042),x63043),f862(f18(f932(x63042,a921),x63041),x63044)),f181(f932(f931(x63041,x63042),a921))) % 14.98/14.66 [6356]E(x63561,f2(a924))+E(f862(f862(f131(x63562),x63561),f862(f862(f144(x63562),x63563),x63564)),f862(f862(f131(x63562),f862(f862(f3(a924),x63561),f71(a924))),x63564)) % 14.98/14.66 [6378]E(x63781,f181(f932(x63782,a921)))+E(f862(f302(x63782,x63783,f862(f18(x63783,x63782),x63784)),x63781),f862(f862(f301(x63783),x63784),f181(f932(x63783,a921)))) % 14.98/14.66 [6381]E(f862(f303(x63811,x63812,f862(f18(x63812,x63811),x63813)),x63814),f181(f932(x63811,a921)))+P1(f862(f862(f321(x63812),x63813),x63814)) % 14.98/14.66 [6447]~E(x64473,f181(f932(x64471,a921)))+E(f862(f862(f32(x64471,f932(x64472,a921)),x64473),f862(f18(f932(x64472,a921),x64471),x64474)),f234(f932(x64472,a921))) % 14.98/14.66 [6448]~E(x64483,f181(f932(x64481,a921)))+E(f862(f862(f33(x64481,f932(x64482,a921)),x64483),f862(f18(f932(x64482,a921),x64481),x64484)),f181(f932(x64482,a921))) % 14.98/14.66 [6450]~P61(x64501)+E(f38(x64501,f862(f862(f74(x64501),x64502),x64503),f862(f862(f74(x64501),x64502),x64504)),f862(f862(f74(x64501),x64502),f38(x64501,x64503,x64504))) % 14.98/14.66 [6624]E(f862(f303(x66241,x66242,f862(f18(x66242,x66241),x66243)),x66244),f234(f932(x66241,a921)))+~P1(f862(f862(f321(x66242),x66243),x66244)) % 14.98/14.66 [6647]~P1(f862(f862(f321(x66471),x66472),x66474))+P1(f862(f862(f321(x66471),x66472),f862(f862(f301(x66471),x66473),x66474))) % 14.98/14.66 [6652]P1(f862(x66521,x66522))+~P1(f862(f153(x66523,x66521),f862(f862(f144(x66523),x66522),x66524))) % 14.98/14.66 [6661]~E(x66613,f862(f862(f3(a924),f862(f182(f925(x66611)),x66612)),f71(a924)))+E(f107(x66611,f862(f862(f152(x66611,x66612),x66613),x66614)),f107(x66611,x66612)) % 14.98/14.66 [6681]~P109(x66811)+E(f862(f862(f94(f932(x66811,a921)),f862(f294(x66811),x66812)),f296(x66811,x66813,x66814)),f296(x66811,x66813,f862(f862(f225(x66811),x66812),x66814))) % 14.98/14.66 [6682]~P109(x66821)+E(f862(f862(f94(f932(x66821,a921)),f862(f274(x66821),x66822)),f296(x66821,x66823,x66824)),f296(x66821,f862(f862(f226(x66821),x66822),x66823),x66824)) % 14.98/14.66 [6698]E(f862(f862(f94(f932(x66981,a921)),x66982),f862(f862(f301(x66981),x66983),x66984)),f862(f862(f94(f932(x66981,a921)),x66982),x66984))+P1(f862(f862(f321(x66981),x66983),x66982)) % 14.98/14.66 [6710]E(f163(x67101,x67102,f862(f862(f127(x67101),x67103),x67104)),f862(f862(f127(x67101),x67103),f163(x67101,x67102,x67104)))+P1(f862(f862(f321(x67101),x67102),f862(f165(x67101),x67103))) % 14.98/14.66 [6715]~P80(x67151)+E(f862(f862(f74(x67151),f862(f862(f236(x67151),x67152),x67153)),f862(f862(f236(x67151),x67152),x67154)),f862(f862(f236(x67151),x67152),f862(f862(f73(a924),x67153),x67154))) % 14.98/14.66 [6716]~P119(x67161)+E(f862(f862(f74(x67161),f862(f862(f236(x67161),x67162),x67163)),f862(f862(f236(x67161),x67162),x67164)),f862(f862(f236(x67161),x67162),f862(f862(f73(a924),x67163),x67164))) % 14.98/14.66 [6753]~P102(x67531)+E(f862(f862(f94(x67531),f862(f862(f103(x67531),x67532),x67533)),f862(f862(f103(x67531),x67532),x67534)),f862(f862(f103(x67531),x67532),f862(f862(f94(x67531),x67533),x67534))) % 14.98/14.66 [6754]~P102(x67541)+E(f862(f862(f103(x67541),f862(f862(f94(x67541),x67542),x67543)),f862(f862(f94(x67541),x67542),x67544)),f862(f862(f94(x67541),x67542),f862(f862(f103(x67541),x67543),x67544))) % 14.98/14.66 [6755]~P119(x67551)+E(f862(f862(f73(x67551),f862(f862(f74(x67551),x67552),x67553)),f862(f862(f74(x67551),x67552),x67554)),f862(f862(f74(x67551),x67552),f862(f862(f73(x67551),x67553),x67554))) % 14.98/14.66 [6756]~P109(x67561)+E(f862(f862(f226(x67561),f862(f862(f225(x67561),x67562),x67563)),f862(f862(f225(x67561),x67562),x67564)),f862(f862(f225(x67561),x67562),f862(f862(f226(x67561),x67563),x67564))) % 14.98/14.66 [6757]~P109(x67571)+E(f862(f862(f225(x67571),f862(f862(f226(x67571),x67572),x67573)),f862(f862(f226(x67571),x67572),x67574)),f862(f862(f226(x67571),x67572),f862(f862(f225(x67571),x67573),x67574))) % 14.98/14.66 [6788]~P61(x67881)+E(f38(x67881,f862(f862(f74(x67881),x67882),x67883),f862(f862(f74(x67881),x67884),x67883)),f862(f862(f74(x67881),f38(x67881,x67882,x67884)),x67883)) % 14.98/14.66 [6791]~E(f862(f182(f925(x67911)),x67913),f862(f182(f925(x67912)),x67914))+E(f862(f862(f147(f931(x67911,x67912),x67912),f248(x67911,x67912)),f862(f862(f174(x67911,x67912),x67913),x67914)),x67914) % 14.98/14.66 [6792]~E(f862(f182(f925(x67921)),x67923),f862(f182(f925(x67922)),x67924))+E(f862(f862(f147(f931(x67921,x67922),x67921),f243(x67921,x67922)),f862(f862(f174(x67921,x67922),x67923),x67924)),x67923) % 14.98/14.66 [6797]P1(f862(f153(x67971,x67972),x67973))+~P1(f862(f153(x67971,x67972),f862(f862(f144(x67971),x67974),x67973))) % 14.98/14.66 [6798]P1(f862(f153(x67981,x67982),x67983))+~P1(f862(f153(x67981,x67982),f862(f862(f127(x67981),x67984),x67983))) % 14.98/14.66 [6799]P1(f862(f153(x67991,x67992),x67993))+~P1(f862(f153(x67991,x67992),f862(f862(f127(x67991),x67993),x67994))) % 14.98/14.66 [6804]~P62(x68041)+E(f38(x68041,f862(f862(f3(x68041),x68042),f38(x68041,x68043,x68044)),x68044),f38(x68041,f862(f862(f3(x68041),x68042),x68043),x68044)) % 14.98/14.66 [6805]~P61(x68051)+E(f38(x68051,f862(f862(f74(x68051),x68052),f38(x68051,x68053,x68054)),x68054),f38(x68051,f862(f862(f74(x68051),x68052),x68053),x68054)) % 14.98/14.66 [6807]~P61(x68071)+E(f38(x68071,f862(f862(f73(x68071),x68072),f38(x68071,x68073,x68074)),x68074),f38(x68071,f862(f862(f73(x68071),x68072),x68073),x68074)) % 14.98/14.66 [6886]~P109(x68861)+E(f862(f862(f94(f932(x68861,a921)),f296(x68861,x68862,x68863)),f862(f294(x68861),x68864)),f296(x68861,x68862,f862(f862(f225(x68861),x68863),x68864))) % 14.98/14.66 [6887]~P109(x68871)+E(f862(f862(f94(f932(x68871,a921)),f296(x68871,x68872,x68873)),f862(f274(x68871),x68874)),f296(x68871,f862(f862(f226(x68871),x68872),x68874),x68873)) % 14.98/14.66 [6890]~E(f862(f182(f925(x68901)),x68903),f862(f182(f925(x68902)),x68904))+E(f862(f862(f174(x68901,x68902),f862(f161(x68901),x68903)),f862(f161(x68902),x68904)),f862(f161(f931(x68901,x68902)),f862(f862(f174(x68901,x68902),x68903),x68904))) % 14.98/14.66 [6901]E(x69011,f862(f862(f3(a924),f862(f182(f925(x69012)),x69013)),f71(a924)))+E(f107(x69012,f862(f862(f152(x69012,x69013),x69011),x69014)),f862(f862(f152(x69012,f107(x69012,x69013)),x69011),x69014)) % 14.98/14.66 [6915]~P1(f862(f130(x69152),x69154))+P1(f862(f130(f931(x69151,x69152)),f862(f862(f174(x69151,x69152),x69153),x69154))) % 14.98/14.66 [6916]~P1(f862(f130(x69161),x69163))+P1(f862(f130(f931(x69161,x69162)),f862(f862(f174(x69161,x69162),x69163),x69164))) % 14.98/14.66 [7181]E(f862(f862(f29(a924),x71811),x71812),x71813)+~P1(f862(f41(x71811,x71812),f862(f862(f244(a924,a924),x71813),x71814))) % 14.98/14.66 [7204]E(f38(a924,x72041,x72042),x72043)+~P1(f862(f41(x72041,x72042),f862(f862(f244(a924,a924),x72044),x72043))) % 14.98/14.66 [7207]P1(f862(f130(x72071),x72072))+~P1(f862(f130(x72073),f862(f862(f147(x72071,x72073),x72074),x72072))) % 14.98/14.66 [7291]E(f163(x72911,x72912,f862(f862(f127(x72911),x72913),x72914)),f862(f862(f127(x72911),f163(x72911,x72912,x72913)),x72914))+~P1(f862(f862(f321(x72911),x72912),f862(f165(x72911),x72913))) % 14.98/14.66 [7384]~P62(x73841)+E(f38(x73841,f862(f862(f3(x73841),f38(x73841,x73842,x73843)),x73844),x73843),f38(x73841,f862(f862(f3(x73841),x73842),x73844),x73843)) % 14.98/14.66 [7387]~P61(x73871)+E(f38(x73871,f862(f862(f74(x73871),f38(x73871,x73872,x73873)),x73874),x73873),f38(x73871,f862(f862(f74(x73871),x73872),x73874),x73873)) % 14.98/14.66 [7388]~P61(x73881)+E(f38(x73881,f862(f862(f73(x73881),f38(x73881,x73882,x73883)),x73884),x73883),f38(x73881,f862(f862(f73(x73881),x73882),x73884),x73883)) % 14.98/14.66 [7586]~E(x75861,f862(f862(f144(x75862),x75863),x75864))+~P1(f862(f862(f227(a924),f862(f182(f925(x75862)),x75861)),f862(f182(f925(x75862)),x75864))) % 14.98/14.66 [7791]P22(x77911,x77912,x77913,f862(f165(x77911),x77914))+~P1(f862(f130(x77912),f862(f862(f147(x77911,x77912),x77913),x77914))) % 14.98/14.66 [7866]~P1(f862(f862(f227(f932(x78661,a921)),x78662),x78664))+P1(f862(f862(f227(f932(x78661,a921)),x78662),f862(f862(f301(x78661),x78663),x78664))) % 14.98/14.66 [7901]~P62(x79011)+E(f38(x79011,f862(f862(f3(x79011),f38(x79011,x79012,x79013)),f38(x79011,x79014,x79013)),x79013),f38(x79011,f862(f862(f3(x79011),x79012),x79014),x79013)) % 14.98/14.66 [7902]~P61(x79021)+E(f38(x79021,f862(f862(f74(x79021),f38(x79021,x79022,x79023)),f38(x79021,x79024,x79023)),x79023),f38(x79021,f862(f862(f74(x79021),x79022),x79024),x79023)) % 14.98/14.66 [7903]~P61(x79031)+E(f38(x79031,f862(f862(f73(x79031),f38(x79031,x79032,x79033)),f38(x79031,x79034,x79033)),x79033),f38(x79031,f862(f862(f73(x79031),x79032),x79034),x79033)) % 14.98/14.66 [8006]~E(f862(x80064,f466(x80064,x80063,x80061,x80062)),f181(f932(x80062,a921)))+E(f862(f862(f33(x80061,f932(x80062,a921)),x80063),x80064),f181(f932(x80062,a921))) % 14.98/14.66 [8007]~E(f862(x80074,f486(x80074,x80073,x80071,x80072)),f234(f932(x80072,a921)))+E(f862(f862(f32(x80071,f932(x80072,a921)),x80073),x80074),f234(f932(x80072,a921))) % 14.98/14.66 [8008]~E(f862(x80084,f489(x80084,x80083,x80082,x80081)),f234(f932(x80082,a921)))+E(f862(f862(f32(x80081,f932(x80082,a921)),x80083),x80084),f234(f932(x80082,a921))) % 14.98/14.66 [8009]~E(f862(x80094,f487(x80094,x80093,x80092,x80091)),f181(f932(x80092,a921)))+E(f862(f862(f33(x80091,f932(x80092,a921)),x80093),x80094),f181(f932(x80092,a921))) % 14.98/14.66 [8407]P1(f862(x84071,x84072))+~P1(f862(f862(f321(x84073),x84072),f862(f862(f94(f932(x84073,a921)),x84074),f862(f254(x84073),x84071)))) % 14.98/14.66 [8444]~P1(f862(f862(f227(f932(x84441,a921)),x84443),x84444))+P1(f862(f862(f227(f932(x84441,a921)),f862(f862(f301(x84441),x84442),x84443)),f862(f862(f301(x84441),x84442),x84444))) % 14.98/14.66 [8624]P1(f862(x86242,x86243))+E(f862(f862(f131(x86241),f862(f182(f925(x86241)),f170(x86241,x86242,f862(f862(f144(x86241),x86243),x86244)))),f862(f862(f144(x86241),x86243),x86244)),f862(f862(f144(x86241),x86243),x86244)) % 14.98/14.66 [8732]~P1(f862(f862(f228(a924),f862(x87324,x87322)),f862(x87324,x87323)))+P1(f862(f862(f321(f931(x87321,x87321)),f862(f862(f244(x87321,x87321),x87322),x87323)),f862(f862(f279(a924,x87321),a232),x87324))) % 14.98/14.66 [8829]~P1(f862(x88292,f747(x88294,x88292,x88293,x88291)))+E(f170(x88291,x88292,f862(f862(f127(x88291),x88293),x88294)),f862(f862(f127(x88291),x88293),f170(x88291,x88292,x88294))) % 14.98/14.66 [8907]P22(f925(x89071),f925(x89072),f862(f147(x89071,x89072),x89073),x89074)+~P22(x89071,x89072,x89073,f30(f932(x89071,a921),f862(f302(f925(x89071),f932(x89071,a921),f165(x89071)),x89074))) % 14.98/14.66 [8982]~P1(f862(x89822,x89823))+E(f862(f862(f131(x89821),f862(f182(f925(x89821)),f170(x89821,x89822,f862(f862(f144(x89821),x89823),x89824)))),f862(f862(f144(x89821),x89823),x89824)),f862(f862(f131(x89821),f862(f182(f925(x89821)),f170(x89821,x89822,x89824))),x89824)) % 14.98/14.66 [9023]~E(x90232,x90233)+E(f862(f129(x90231,f862(f862(f10(a921,a921,x90231),a314),f862(a317,x90232))),f862(f862(f144(x90231),x90233),x90234)),f862(f129(x90231,f862(f862(f10(a921,a921,x90231),a314),f862(a317,x90232))),x90234)) % 14.98/14.66 [9034]E(f862(f862(f33(x90341,f932(x90342,a921)),x90343),x90344),f181(f932(x90342,a921)))+P1(f862(f862(f321(x90341),f466(x90344,x90343,x90341,x90342)),x90343)) % 14.98/14.66 [9035]E(f862(f862(f32(x90351,f932(x90352,a921)),x90353),x90354),f234(f932(x90352,a921)))+P1(f862(f862(f321(x90351),f486(x90354,x90353,x90351,x90352)),x90353)) % 14.98/14.66 [9036]E(f862(f862(f32(x90361,f932(x90362,a921)),x90363),x90364),f234(f932(x90362,a921)))+P1(f862(f862(f321(x90361),f489(x90364,x90363,x90362,x90361)),x90363)) % 14.98/14.66 [9037]E(f862(f862(f33(x90371,f932(x90372,a921)),x90373),x90374),f181(f932(x90372,a921)))+P1(f862(f862(f321(x90371),f487(x90374,x90373,x90372,x90371)),x90373)) % 14.98/14.66 [9076]P1(f862(f862(f228(a924),f862(x90761,x90762)),f862(x90761,x90763)))+~P1(f862(f862(f321(f931(x90764,x90764)),f862(f862(f244(x90764,x90764),x90762),x90763)),f862(f862(f279(a924,x90764),a232),x90761))) % 14.98/14.66 [9102]E(f170(x91021,x91022,f862(f862(f127(x91021),x91023),x91024)),f862(f862(f127(x91021),x91023),f170(x91021,x91022,x91024)))+P1(f862(f862(f321(x91021),f747(x91024,x91022,x91023,x91021)),f862(f165(x91021),x91023))) % 14.98/14.66 [9153]~P23(x91531,x91532,x91533,f234(f932(x91531,a921)),f234(f932(x91532,a921)))+E(f862(f302(x91531,x91532,x91533),f862(f72(f932(x91531,a921)),x91534)),f862(f72(f932(x91532,a921)),f862(f302(x91531,x91532,x91533),x91534))) % 14.98/14.66 [9256]P1(f862(f862(f321(x92561),f525(x92562,x92563,x92564,x92561)),x92563))+~P1(f862(f862(f321(f932(x92561,a921)),x92564),f862(f862(f53(x92561),x92563),x92562))) % 14.98/14.66 [9259]E(x92591,x92592)+~P1(f862(f862(f321(f931(x92593,x92593)),f862(f862(f244(x92593,x92593),x92591),x92592)),f862(f862(f176(f931(x92593,x92593),a921),f2(a924)),x92594))) % 14.98/14.66 [9342]E(f862(f276(x93421,x93421,x93422),f862(f862(f301(x93421),f525(x93422,x93423,x93424,x93421)),f181(f932(x93421,a921)))),x93424)+~P1(f862(f862(f321(f932(x93421,a921)),x93424),f862(f862(f53(x93421),x93423),x93422))) % 14.98/14.66 [9347]~P1(f862(f862(f321(f931(x93471,x93471)),f862(f862(f244(x93471,x93471),x93473),x93472)),f299(x93471,x93474)))+P1(f862(f862(f321(f931(x93471,x93471)),f862(f862(f244(x93471,x93471),x93472),x93473)),f299(x93471,f862(f277(x93471,x93471),x93474)))) % 14.98/14.66 [9360]~P61(x93601)+E(f862(f862(f73(x93601),f862(f862(f73(x93601),f862(f862(f74(x93601),x93602),f862(f862(f29(x93601),x93603),x93602))),f38(x93601,x93603,x93602))),x93604),f862(f862(f73(x93601),x93603),x93604)) % 14.98/14.66 [9371]~P1(f862(f862(f321(x93711),x93713),x93714))+P1(f862(f862(f321(f932(x93711,a921)),f862(f276(x93711,x93711,x93712),f862(f862(f301(x93711),x93713),f181(f932(x93711,a921))))),f862(f862(f53(x93711),x93714),x93712))) % 14.98/14.66 [9383]P1(f862(f862(f321(f931(x93831,x93831)),f862(f862(f244(x93831,x93831),x93832),x93833)),f299(x93831,x93834)))+~P1(f862(f862(f321(f931(x93831,x93831)),f862(f862(f244(x93831,x93831),x93833),x93832)),f299(x93831,f862(f277(x93831,x93831),x93834)))) % 14.98/14.66 [9470]E(f862(f862(f152(x94701,f862(f161(x94701),x94702)),f862(f862(f3(a924),f862(f862(f3(a924),f862(f182(f925(x94701)),x94702)),x94703)),f71(a924))),x94704),f862(f161(x94701),f862(f862(f152(x94701,x94702),x94703),x94704)))+~P1(f862(f862(f228(a924),x94703),f862(f182(f925(x94701)),x94702))) % 14.98/14.66 [9473]~P1(f862(x94732,f741(x94734,x94732,x94733,x94731)))+E(f862(f862(f131(x94731),f862(f182(f925(x94731)),f170(x94731,x94732,f862(f862(f127(x94731),x94733),x94734)))),f862(f862(f127(x94731),x94733),x94734)),f862(f862(f131(x94731),f862(f182(f925(x94731)),f170(x94731,x94732,x94734))),x94734)) % 14.98/14.66 [9517]~P22(x95172,x95171,x95173,f234(f932(x95172,a921)))+P1(f862(f862(f227(f932(x95171,a921)),f862(f302(x95172,x95171,x95173),f862(f72(f932(x95172,a921)),x95174))),f862(f72(f932(x95171,a921)),f862(f302(x95172,x95171,x95173),x95174)))) % 14.98/14.66 [9529]~P3(x95291)+E(f862(f135(x95291,x95292,f862(f9(x95292,x95291,x95291),f862(f862(f10(x95291,f932(x95291,x95291),x95292),f94(x95291)),x95293)),f234(x95291)),x95294),f862(f862(f32(x95292,x95291),f862(f165(x95292),x95294)),x95293)) % 14.98/14.66 [9530]~P3(x95301)+E(f862(f135(x95301,x95302,f862(f9(x95302,x95301,x95301),f862(f862(f10(x95301,f932(x95301,x95301),x95302),f103(x95301)),x95303)),f181(x95301)),x95304),f862(f862(f33(x95302,x95301),f862(f165(x95302),x95304)),x95303)) % 14.98/14.66 [9540]E(f862(f862(f131(x95401),f862(f182(f925(x95401)),f170(x95401,x95402,f862(f862(f127(x95401),x95403),x95404)))),f862(f862(f127(x95401),x95403),x95404)),f862(f862(f131(x95401),f862(f182(f925(x95401)),f170(x95401,x95402,x95404))),x95404))+P1(f862(f862(f321(x95401),f741(x95404,x95402,x95403,x95401)),f862(f165(x95401),x95403))) % 14.98/14.66 [9613]~P1(f862(f862(f321(f931(f925(x96134),f925(x96134))),f862(f862(f244(f925(x96134),f925(x96134)),x96133),x96132)),f150(x96134,x96131)))+P1(f862(f862(f228(a924),f675(x96131,x96132,x96133,x96134)),f862(f182(f925(x96134)),x96133))) % 14.98/14.66 [9614]~P61(x96141)+E(f862(f862(f73(x96141),f862(f862(f73(x96141),f862(f862(f74(x96141),f862(f862(f29(x96141),x96142),x96143)),x96143)),f38(x96141,x96142,x96143))),x96144),f862(f862(f73(x96141),x96142),x96144)) % 14.98/14.66 [9643]~P1(f862(f862(f321(f931(f925(x96431),f925(x96431))),f862(f862(f244(f925(x96431),f925(x96431)),x96432),x96433)),f862(f277(f925(x96431),f925(x96431)),f150(x96431,x96434))))+P1(f862(f862(f321(f931(f925(x96431),f925(x96431))),f862(f862(f244(f925(x96431),f925(x96431)),x96432),x96433)),f150(x96431,f862(f277(x96431,x96431),x96434)))) % 14.98/14.66 [9644]P1(f862(f862(f321(f931(f925(x96441),f925(x96441))),f862(f862(f244(f925(x96441),f925(x96441)),x96442),x96443)),f862(f277(f925(x96441),f925(x96441)),f150(x96441,x96444))))+~P1(f862(f862(f321(f931(f925(x96441),f925(x96441))),f862(f862(f244(f925(x96441),f925(x96441)),x96442),x96443)),f150(x96441,f862(f277(x96441,x96441),x96444)))) % 14.98/14.66 [9685]~P1(f862(f862(f321(x96851),x96853),f862(f256(x96851,x96852),x96854)))+P1(f862(f862(f321(f931(x96851,x96852)),f862(f862(f244(x96851,x96852),x96853),f564(x96854,x96852,x96853,x96851))),x96854)) % 14.98/14.66 [9686]~P1(f862(f862(f321(x96861),x96863),f862(f256(x96861,x96862),x96864)))+P1(f862(f862(f321(f931(x96861,x96862)),f862(f862(f244(x96861,x96862),x96863),f566(x96864,x96862,x96863,x96861))),x96864)) % 14.98/14.66 [9842]~P1(f862(f862(f321(f931(x98421,x98421)),f862(f862(f244(x98421,x98421),x98422),x98424)),f862(f862(f280(x98421,x98421,x98421),x98423),f299(x98421,x98423))))+P1(f862(f862(f321(f931(x98421,x98421)),f862(f862(f244(x98421,x98421),x98422),f637(x98423,x98424,x98422,x98421))),x98423)) % 14.98/14.66 [10002]P9(x100021,x100022,x100023,x100024)+P1(f862(f862(f321(f931(x100021,x100021)),f862(f862(f244(x100021,x100021),f835(x100022,x100024,x100023,x100021)),f834(x100022,x100024,x100023,x100021))),x100023)) % 14.98/14.66 [10010]~P1(f862(f862(f321(f931(x100102,x100101)),x100104),f862(f277(x100101,x100102),x100103)))+P1(f862(f862(f321(f931(x100101,x100102)),f862(f862(f244(x100101,x100102),f648(x100103,x100104,x100101,x100102)),f647(x100103,x100104,x100101,x100102))),x100103)) % 14.98/14.66 [10034]~P1(f862(f862(f321(f931(f925(x100341),f925(x100341))),f862(f862(f244(f925(x100341),f925(x100341)),x100344),x100343)),f150(x100341,x100342)))+P1(f862(f862(f321(f931(x100341,x100341)),f862(f862(f244(x100341,x100341),f691(x100342,x100343,x100344,x100341)),f692(x100342,x100343,x100344,x100341))),x100342)) % 14.98/14.66 [10127]~P1(f862(f862(f321(f931(f925(x101271),f925(x101271))),f862(f862(f244(f925(x101271),f925(x101271)),x101272),x101274)),f150(x101271,x101273)))+P1(f862(f862(f321(f931(x101271,x101271)),f862(f862(f244(x101271,x101271),f862(f862(f157(x101271),x101272),f675(x101273,x101274,x101272,x101271))),f676(x101273,x101274,x101272,x101271))),x101273)) % 14.98/14.66 [10147]~P1(f862(f54(x101472),x101474))+E(f862(f862(f862(f58(f932(x101471,a921),x101472,f103(f932(x101471,a921))),f862(f862(f9(x101472,f932(x101471,a921),f932(x101471,a921)),f862(f862(f10(x101471,f932(f932(x101471,a921),f932(x101471,a921)),x101472),f301(x101471)),x101473)),f181(f932(x101471,a921)))),f181(f932(x101471,a921))),x101474),f862(f302(x101472,x101471,x101473),x101474)) % 14.98/14.66 [10244]~P22(x102441,x102442,x102443,f234(f932(x102441,a921)))+P1(f862(f862(f227(f932(x102441,a921)),f862(f303(x102441,x102442,x102443),f862(f862(f301(x102442),x102444),f181(f932(x102442,a921))))),f862(f862(f301(x102441),f78(x102441,f862(f862(f9(x102441,x102442,a921),f862(f862(f10(x102442,f932(x102442,a921),x102441),a317),x102443)),x102444))),f181(f932(x102441,a921))))) % 14.98/14.66 [5813]~E(f862(f862(f127(x58131),x58132),x58134),x58133)+E(f862(f862(f168(x58131),f862(f182(f925(x58131)),x58132)),x58133),x58132) % 14.98/14.66 [5814]~E(f862(f862(f127(x58142),x58143),x58141),x58144)+E(x58141,f862(f862(f131(x58142),f862(f182(f925(x58142)),x58143)),x58144)) % 14.98/14.66 [5825]~E(x58254,f2(a924))+E(f862(f862(f157(x58251),f862(f862(f144(x58251),x58252),x58253)),x58254),x58252) % 14.98/14.66 [6369]~P119(x63691)+E(f862(f862(f236(x63691),f862(f862(f236(x63691),x63692),x63693)),x63694),f862(f862(f236(x63691),x63692),f862(f862(f74(a924),x63693),x63694))) % 14.98/14.66 [6370]~P80(x63701)+E(f862(f862(f236(x63701),f862(f862(f236(x63701),x63702),x63703)),x63704),f862(f862(f236(x63701),x63702),f862(f862(f74(a924),x63703),x63704))) % 14.98/14.66 [6379]E(x63791,f2(a924))+E(f862(f862(f157(x63792),f862(f862(f144(x63792),x63793),x63794)),x63791),f862(f862(f157(x63792),x63794),f862(f862(f3(a924),x63791),f71(a924)))) % 14.98/14.66 [6406]~P121(x64061)+E(f862(f862(f281(x64061),f862(f862(f74(x64061),x64062),x64063)),x64064),f862(f862(f74(x64061),x64062),f862(f862(f281(x64061),x64063),x64064))) % 14.98/14.66 [6408]~P93(x64081)+E(f862(f862(f103(x64081),f862(f862(f103(x64081),x64082),x64083)),x64084),f862(f862(f103(x64081),x64082),f862(f862(f103(x64081),x64083),x64084))) % 14.98/14.66 [6410]~P103(x64101)+E(f862(f862(f103(x64101),f862(f862(f103(x64101),x64102),x64103)),x64104),f862(f862(f103(x64101),x64102),f862(f862(f103(x64101),x64103),x64104))) % 14.98/14.66 [6411]~P93(x64111)+E(f862(f862(f94(x64111),f862(f862(f94(x64111),x64112),x64113)),x64114),f862(f862(f94(x64111),x64112),f862(f862(f94(x64111),x64113),x64114))) % 14.98/14.66 [6413]~P104(x64131)+E(f862(f862(f94(x64131),f862(f862(f94(x64131),x64132),x64133)),x64134),f862(f862(f94(x64131),x64132),f862(f862(f94(x64131),x64133),x64134))) % 14.98/14.66 [6414]~P69(x64141)+E(f862(f862(f74(x64141),f862(f862(f74(x64141),x64142),x64143)),x64144),f862(f862(f74(x64141),x64142),f862(f862(f74(x64141),x64143),x64144))) % 14.98/14.66 [6415]~P119(x64151)+E(f862(f862(f74(x64151),f862(f862(f74(x64151),x64152),x64153)),x64154),f862(f862(f74(x64151),x64152),f862(f862(f74(x64151),x64153),x64154))) % 14.98/14.66 [6417]~P70(x64171)+E(f862(f862(f73(x64171),f862(f862(f73(x64171),x64172),x64173)),x64174),f862(f862(f73(x64171),x64172),f862(f862(f73(x64171),x64173),x64174))) % 14.98/14.66 [6418]~P119(x64181)+E(f862(f862(f73(x64181),f862(f862(f73(x64181),x64182),x64183)),x64184),f862(f862(f73(x64181),x64182),f862(f862(f73(x64181),x64183),x64184))) % 14.98/14.66 [6420]~P109(x64201)+E(f862(f862(f225(x64201),f862(f862(f225(x64201),x64202),x64203)),x64204),f862(f862(f225(x64201),x64202),f862(f862(f225(x64201),x64203),x64204))) % 14.98/14.66 [6422]~P109(x64221)+E(f862(f862(f226(x64221),f862(f862(f226(x64221),x64222),x64223)),x64224),f862(f862(f226(x64221),x64222),f862(f862(f226(x64221),x64223),x64224))) % 14.98/14.66 [6431]~P61(x64311)+E(f38(x64311,f862(f862(f73(x64311),x64312),f862(f862(f74(x64311),x64313),x64314)),x64314),f38(x64311,x64312,x64314)) % 14.98/14.66 [6432]~P61(x64321)+E(f38(x64321,f862(f862(f73(x64321),x64322),f862(f862(f74(x64321),x64323),x64324)),x64323),f38(x64321,x64322,x64323)) % 14.98/14.66 [6570]E(f862(f862(f157(x65701),f862(f862(f168(x65701),x65702),x65703)),x65704),f862(f862(f157(x65701),x65703),x65704))+~P1(f862(f862(f228(a924),x65704),x65702)) % 14.98/14.66 [6749]~E(x67492,x67494)+P1(f862(f862(f165(x67491),f862(f862(f144(x67491),x67492),x67493)),x67494)) % 14.98/14.66 [6751]~P119(x67511)+E(f862(f862(f74(x67511),f862(f862(f74(x67511),x67512),x67513)),x67514),f862(f862(f74(x67511),f862(f862(f74(x67511),x67512),x67514)),x67513)) % 14.98/14.66 [6752]~P119(x67521)+E(f862(f862(f73(x67521),f862(f862(f73(x67521),x67522),x67523)),x67524),f862(f862(f73(x67521),f862(f862(f73(x67521),x67522),x67524)),x67523)) % 14.98/14.66 [6810]~P147(x68102)+E(f862(f862(f8(x68101,x68102),f862(f18(x68102,x68101),x68103)),x68104),f862(f862(f74(x68102),f862(f93(x68102),f862(f28(x68101),x68104))),x68103)) % 14.98/14.66 [6979]E(f862(f862(f94(f932(x69791,a921)),f862(f862(f301(x69791),x69792),x69793)),x69794),f862(f862(f94(f932(x69791,a921)),x69793),x69794))+P1(f862(f862(f321(x69791),x69792),x69794)) % 14.98/14.66 [7048]~P102(x70481)+E(f862(f862(f94(x70481),f862(f862(f103(x70481),x70482),x70483)),f862(f862(f103(x70481),x70484),x70483)),f862(f862(f103(x70481),f862(f862(f94(x70481),x70482),x70484)),x70483)) % 14.98/14.66 [7049]~P102(x70491)+E(f862(f862(f103(x70491),f862(f862(f94(x70491),x70492),x70493)),f862(f862(f94(x70491),x70494),x70493)),f862(f862(f94(x70491),f862(f862(f103(x70491),x70492),x70494)),x70493)) % 14.98/14.66 [7050]~P78(x70501)+E(f862(f862(f225(x70501),f862(f862(f3(x70501),x70502),x70503)),f862(f862(f3(x70501),x70504),x70503)),f862(f862(f3(x70501),f862(f862(f225(x70501),x70502),x70504)),x70503)) % 14.98/14.66 [7051]~P78(x70511)+E(f862(f862(f226(x70511),f862(f862(f3(x70511),x70512),x70513)),f862(f862(f3(x70511),x70514),x70513)),f862(f862(f3(x70511),f862(f862(f226(x70511),x70512),x70514)),x70513)) % 14.98/14.66 [7052]~P114(x70521)+E(f862(f862(f73(x70521),f862(f862(f74(x70521),x70522),x70523)),f862(f862(f74(x70521),x70524),x70523)),f862(f862(f74(x70521),f862(f862(f73(x70521),x70522),x70524)),x70523)) % 14.98/14.66 [7054]~P84(x70541)+E(f862(f862(f225(x70541),f862(f862(f73(x70541),x70542),x70543)),f862(f862(f73(x70541),x70544),x70543)),f862(f862(f73(x70541),f862(f862(f225(x70541),x70542),x70544)),x70543)) % 14.98/14.66 [7055]~P84(x70551)+E(f862(f862(f226(x70551),f862(f862(f73(x70551),x70552),x70553)),f862(f862(f73(x70551),x70554),x70553)),f862(f862(f73(x70551),f862(f862(f226(x70551),x70552),x70554)),x70553)) % 14.98/14.66 [7056]~P121(x70561)+E(f862(f862(f3(x70561),f862(f862(f281(x70561),x70562),x70563)),f862(f862(f281(x70561),x70564),x70563)),f862(f862(f281(x70561),f862(f862(f3(x70561),x70562),x70564)),x70563)) % 14.98/14.66 [7057]~P121(x70571)+E(f862(f862(f73(x70571),f862(f862(f281(x70571),x70572),x70573)),f862(f862(f281(x70571),x70574),x70573)),f862(f862(f281(x70571),f862(f862(f73(x70571),x70572),x70574)),x70573)) % 14.98/14.66 [7058]~P71(x70581)+E(f862(f862(f74(x70581),f862(f862(f236(x70581),x70582),x70583)),f862(f862(f236(x70581),x70584),x70583)),f862(f862(f236(x70581),f862(f862(f74(x70581),x70582),x70584)),x70583)) % 14.98/14.66 [7059]~P119(x70591)+E(f862(f862(f74(x70591),f862(f862(f236(x70591),x70592),x70593)),f862(f862(f236(x70591),x70594),x70593)),f862(f862(f236(x70591),f862(f862(f74(x70591),x70592),x70594)),x70593)) % 14.98/14.66 [7060]~P64(x70601)+E(f862(f862(f281(x70601),f862(f862(f236(x70601),x70602),x70603)),f862(f862(f236(x70601),x70604),x70603)),f862(f862(f236(x70601),f862(f862(f281(x70601),x70602),x70604)),x70603)) % 14.98/14.66 [7061]~P109(x70611)+E(f862(f862(f226(x70611),f862(f862(f225(x70611),x70612),x70613)),f862(f862(f225(x70611),x70614),x70613)),f862(f862(f225(x70611),f862(f862(f226(x70611),x70612),x70614)),x70613)) % 14.98/14.66 [7062]~P109(x70621)+E(f862(f862(f225(x70621),f862(f862(f226(x70621),x70622),x70623)),f862(f862(f226(x70621),x70624),x70623)),f862(f862(f226(x70621),f862(f862(f225(x70621),x70622),x70624)),x70623)) % 14.98/14.66 [7063]~P119(x70631)+E(f862(f862(f73(x70631),f862(f862(f74(x70631),x70632),x70633)),f862(f862(f74(x70631),x70634),x70633)),f862(f862(f74(x70631),f862(f862(f73(x70631),x70632),x70634)),x70633)) % 14.98/14.66 [7095]E(f862(f862(f152(x70951,x70952),x70953),x70954),x70952)+~P1(f862(f862(f227(a924),f862(f182(f925(x70951)),x70952)),x70953)) % 14.98/14.66 [7121]~P1(f862(x71213,x71214))+P1(f862(f862(f862(f103(f932(x71211,a921)),x71212),x71213),x71214)) % 14.98/14.66 [7123]~P1(f862(x71232,x71234))+P1(f862(f862(f862(f103(f932(x71231,a921)),x71232),x71233),x71234)) % 14.98/14.66 [7141]E(f862(f862(f157(x71411),f862(f862(f127(x71411),x71412),x71413)),x71414),f862(f862(f157(x71411),x71412),x71414))+~P1(f862(f862(f228(a924),x71414),f862(f182(f925(x71411)),x71412))) % 14.98/14.66 [7152]E(f862(f862(f3(f932(x71521,a921)),f862(f862(f301(x71521),x71522),x71523)),x71524),f862(f862(f3(f932(x71521,a921)),x71523),x71524))+~P1(f862(f862(f321(x71521),x71522),x71524)) % 14.98/14.66 [7194]~E(f132(a924,f862(f295(a924,x71941),x71942)),f862(f862(f144(a924),x71944),x71943))+E(f132(a924,f862(f295(a924,f862(f862(f73(a924),x71941),f71(a924))),x71942)),x71943) % 14.98/14.66 [7215]~P1(f862(f862(f165(x72151),x72153),x72154))+P1(f862(f862(f165(x72151),f862(f862(f144(x72151),x72152),x72153)),x72154)) % 14.98/14.66 [7265]E(x72651,f2(a924))+E(f862(f862(f144(x72652),x72653),f862(f862(f168(x72652),f862(f862(f3(a924),x72651),f71(a924))),x72654)),f862(f862(f168(x72652),x72651),f862(f862(f144(x72652),x72653),x72654))) % 14.98/14.66 [7368]E(f862(f862(f157(x73681),x73682),f862(f862(f3(a924),x73683),f862(f182(f925(x73681)),x73684))),f862(f862(f157(x73681),f862(f862(f127(x73681),x73684),x73682)),x73683))+P1(f862(f862(f228(a924),x73683),f862(f182(f925(x73681)),x73684))) % 14.98/14.66 [7397]E(f862(f862(f94(f932(x73971,a921)),x73972),f862(f862(f301(x73971),x73973),x73974)),f862(f862(f301(x73971),x73973),f862(f862(f94(f932(x73971,a921)),x73972),x73974)))+~P1(f862(f862(f321(x73971),x73973),x73972)) % 14.98/14.66 [7436]E(f862(f862(f157(x74361),f862(f862(f152(x74361,x74362),x74363),x74364)),x74363),x74364)+~P1(f862(f862(f228(a924),x74363),f862(f182(f925(x74361)),x74362))) % 14.98/14.66 [7459]E(x74591,f181(f932(x74592,a921)))+E(f862(f302(f931(x74593,x74592),x74593,f243(x74593,x74592)),f862(f862(f246(x74593,x74592),x74594),f862(f18(f932(x74592,a921),x74593),x74591))),x74594) % 14.98/14.66 [7460]E(x74601,f181(f932(x74602,a921)))+E(f862(f302(f931(x74602,x74603),x74603,f248(x74602,x74603)),f862(f862(f246(x74602,x74603),x74601),f862(f18(f932(x74603,a921),x74602),x74604))),x74604) % 14.98/14.66 [7536]E(f862(f862(f3(f932(x75361,a921)),f862(f862(f301(x75361),x75362),x75363)),x75364),f862(f862(f301(x75361),x75362),f862(f862(f3(f932(x75361,a921)),x75363),x75364)))+P1(f862(f862(f321(x75361),x75362),x75364)) % 14.98/14.66 [7572]~E(x75724,f181(f932(x75722,a921)))+E(f862(f302(f931(x75721,x75722),x75721,f243(x75721,x75722)),f862(f862(f246(x75721,x75722),x75723),f862(f18(f932(x75722,a921),x75721),x75724))),f181(f932(x75721,a921))) % 14.98/14.66 [7573]~E(x75733,f181(f932(x75731,a921)))+E(f862(f302(f931(x75731,x75732),x75732,f248(x75731,x75732)),f862(f862(f246(x75731,x75732),x75733),f862(f18(f932(x75732,a921),x75731),x75734))),f181(f932(x75732,a921))) % 14.98/14.66 [7626]~P1(f862(f862(f321(x76261),x76262),x76264))+P1(f862(f862(f321(x76261),x76262),f862(f862(f103(f932(x76261,a921)),x76263),x76264))) % 14.98/14.66 [7629]~P1(f862(f862(f321(x76291),x76292),x76293))+P1(f862(f862(f321(x76291),x76292),f862(f862(f103(f932(x76291,a921)),x76293),x76294))) % 14.98/14.66 [7647]E(f862(f862(f94(f932(x76471,a921)),f862(f862(f301(x76471),x76472),x76473)),x76474),f862(f862(f301(x76471),x76472),f862(f862(f94(f932(x76471,a921)),x76473),x76474)))+~P1(f862(f862(f321(x76471),x76472),x76474)) % 14.98/14.66 [7923]P1(f862(x79231,x79232))+~P1(f862(f862(f862(f94(f932(x79233,a921)),x79234),x79231),x79232)) % 14.98/14.66 [7924]P1(f862(x79241,x79242))+~P1(f862(f862(f862(f94(f932(x79243,a921)),x79241),x79244),x79242)) % 14.98/14.66 [7925]E(f862(f862(f8(x79251,a924),x79252),f862(f862(f3(f932(x79251,a921)),x79253),f862(f862(f301(x79251),x79254),f181(f932(x79251,a921))))),f862(f862(f8(x79251,a924),x79252),x79253))+P1(f862(f862(f321(x79251),x79254),x79253)) % 14.98/14.66 [7930]~P72(x79301)+E(f862(f158(x79301),f862(f862(f147(a924,x79301),x79302),f132(a924,f862(f295(a924,x79303),x79304)))),f862(f862(f8(a924,x79301),x79302),f862(f165(a924),f132(a924,f862(f295(a924,x79303),x79304))))) % 14.98/14.66 [7931]~P72(x79311)+E(f862(f862(f8(a924,x79311),x79312),f862(f165(a924),f132(a924,f862(f295(a924,x79313),x79314)))),f862(f158(x79311),f862(f862(f147(a924,x79311),x79312),f132(a924,f862(f295(a924,x79313),x79314))))) % 14.98/14.66 [8045]~E(x80453,x80454)+P1(f862(f55(x80451,x80452,f862(f862(f301(x80451),x80453),f181(f932(x80451,a921)))),x80454)) % 14.98/14.66 [8143]P1(f862(f862(f321(x81431),x81432),f862(f165(x81431),x81433)))+~P1(f862(f862(f321(x81431),x81432),f862(f165(x81431),f862(f862(f168(x81431),x81434),x81433)))) % 14.98/14.66 [8144]P1(f862(f862(f321(x81441),x81442),f862(f165(x81441),x81443)))+~P1(f862(f862(f321(x81441),x81442),f862(f165(x81441),f862(f862(f131(x81441),x81444),x81443)))) % 14.98/14.66 [8216]P1(f862(f862(f321(x82161),x82162),x82163))+~P1(f862(f862(f321(x82161),x82162),f862(f862(f94(f932(x82161,a921)),x82164),x82163))) % 14.98/14.66 [8219]P1(f862(f862(f321(x82191),x82192),x82193))+~P1(f862(f862(f321(x82191),x82192),f862(f862(f94(f932(x82191,a921)),x82193),x82194))) % 14.98/14.66 [8222]P1(f862(f862(f321(x82221),x82222),x82223))+~P1(f862(f862(f321(x82221),x82222),f862(f862(f3(f932(x82221,a921)),x82223),x82224))) % 14.98/14.66 [8237]E(f862(f862(f127(x82371),f862(f862(f168(x82371),x82372),x82373)),f862(f862(f144(x82371),x82374),f862(f862(f131(x82371),f862(a105,x82372)),x82373))),f862(f862(f152(x82371,x82373),x82372),x82374))+~P1(f862(f862(f228(a924),x82372),f862(f182(f925(x82371)),x82373))) % 14.98/14.66 [8260]P1(f862(f862(f321(x82601),x82602),x82603))+~P1(f862(f862(f227(f932(x82601,a921)),f862(f862(f301(x82601),x82602),x82604)),x82603)) % 14.98/14.66 [8299]~P1(f862(f862(f321(x82991),x82992),x82993))+~P1(f862(f862(f321(x82991),x82992),f862(f862(f3(f932(x82991,a921)),x82994),x82993))) % 14.98/14.66 [8332]~P1(f862(f862(f228(a924),x83324),f862(f182(f925(x83321)),x83323)))+P1(f862(f862(f321(x83321),x83322),f862(f165(x83321),f862(f862(f152(x83321,x83323),x83324),x83322)))) % 14.98/14.66 [8386]E(f862(f862(f157(x83861),f862(f862(f131(x83861),x83862),x83863)),x83864),f862(f862(f157(x83861),x83863),f862(f862(f73(a924),x83862),x83864)))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x83862),x83864)),f862(f182(f925(x83861)),x83863))) % 14.98/14.66 [8395]~P147(x83952)+E(f862(f862(f8(x83951,x83952),f862(f862(f10(a924,x83952,x83951),f93(x83952)),x83953)),x83954),f862(f93(x83952),f862(f862(f8(x83951,a924),x83953),x83954))) % 14.98/14.66 [8396]~P142(x83962)+E(f862(f862(f8(x83961,x83962),f862(f862(f10(a1,x83962,x83961),f95(x83962)),x83963)),x83964),f862(f95(x83962),f862(f862(f8(x83961,a1),x83963),x83964))) % 14.98/14.66 [8446]~P67(x84462)+E(f862(f862(f11(x84461,x84462),f862(f862(f10(x84462,x84462,x84461),f69(x84462)),x84463)),x84464),f862(f69(x84462),f862(f862(f11(x84461,x84462),x84463),x84464))) % 14.98/14.66 [8447]~P59(x84472)+E(f862(f862(f8(x84471,x84472),f862(f862(f10(x84472,x84472,x84471),f72(x84472)),x84473)),x84474),f862(f72(x84472),f862(f862(f8(x84471,x84472),x84473),x84474))) % 14.98/14.66 [8449]E(f862(f862(f8(x84491,a924),x84492),f862(f862(f3(f932(x84491,a921)),x84493),f862(f862(f301(x84491),x84494),f181(f932(x84491,a921))))),f862(f862(f3(a924),f862(f862(f8(x84491,a924),x84492),x84493)),f862(x84492,x84494)))+~P1(f862(f862(f321(x84491),x84494),x84493)) % 14.98/14.66 [8468]P1(f862(f862(f227(f932(x84681,a921)),x84682),x84683))+~P1(f862(f862(f227(f932(x84681,a921)),f862(f862(f301(x84681),x84684),x84682)),x84683)) % 14.98/14.66 [8592]~E(f862(f302(x85922,x85923,x85921),f234(f932(x85922,a921))),f234(f932(x85923,a921)))+E(f862(x85921,f862(f86(x85922,x85923,f234(f932(x85922,a921)),x85921),x85924)),x85924) % 14.98/14.66 [8677]P35(x86771,x86772)+~P35(x86771,f862(f862(f301(f931(x86771,x86771)),f862(f862(f244(x86771,x86771),x86773),x86774)),x86772)) % 14.98/14.66 [8678]P55(x86781,x86782)+~P55(x86781,f862(f862(f301(f931(x86781,x86781)),f862(f862(f244(x86781,x86781),x86783),x86784)),x86782)) % 14.98/14.66 [8683]~P109(x86831)+E(f862(f862(f141(x86831,x86831,f7(x86831)),x86832),f862(f862(f141(x86831,x86831,f7(x86831)),x86833),x86834)),f862(f862(f141(x86831,x86831,f7(x86831)),x86833),f862(f862(f141(x86831,x86831,f7(x86831)),x86832),x86834))) % 14.98/14.66 [8698]E(x86981,x86982)+~P1(f862(f55(x86983,x86984,f862(f862(f301(x86983),x86981),f181(f932(x86983,a921)))),x86982)) % 14.98/14.66 [8708]E(f862(f862(f127(x87081),f862(f862(f168(x87081),x87082),x87083)),f862(f862(f168(x87081),x87084),f862(f862(f131(x87081),x87082),x87083))),f862(f862(f168(x87081),f862(f862(f73(a924),x87082),x87084)),x87083))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x87082),x87084)),f862(f182(f925(x87081)),x87083))) % 14.98/14.66 [8748]P1(f862(f54(x87481),x87482))+~E(x87482,f862(f302(a924,x87481,x87483),f862(f254(a924),f862(f862(f9(a924,a924,a921),f228(a924)),x87484)))) % 14.98/14.66 [8769]~P89(x87691)+E(f862(f135(x87691,x87691,f73(x87691),f862(f862(f73(x87691),x87692),x87693)),x87694),f862(f862(f73(x87691),x87692),f862(f135(x87691,x87691,f73(x87691),x87693),x87694))) % 14.98/14.66 [8805]P1(f862(f862(f227(f932(x88051,a921)),f862(f256(x88051,x88052),x88053)),f862(f256(x88051,x88052),x88054)))+~P1(f862(f862(f227(f932(f931(x88051,x88052),a921)),x88053),x88054)) % 14.98/14.66 [8817]~P1(f862(f862(f227(a924),x88172),x88174))+P1(f862(f862(f227(f932(x88171,a921)),f862(f165(x88171),f862(f862(f168(x88171),x88172),x88173))),f862(f165(x88171),f862(f862(f168(x88171),x88174),x88173)))) % 14.98/14.66 [8818]~P1(f862(f862(f227(a924),x88184),x88182))+P1(f862(f862(f227(f932(x88181,a921)),f862(f165(x88181),f862(f862(f131(x88181),x88182),x88183))),f862(f165(x88181),f862(f862(f131(x88181),x88184),x88183)))) % 14.98/14.66 [8875]~P1(f862(f54(x88751),f862(f862(f3(f932(x88751,a921)),x88752),x88754)))+P1(f862(f54(x88751),f862(f862(f3(f932(x88751,a921)),x88752),f862(f862(f301(x88751),x88753),x88754)))) % 14.98/14.66 [8918]P1(f862(f862(f321(f931(x89181,x89181)),x89182),f299(x89181,x89183)))+~P1(f862(f862(f321(f931(x89181,x89181)),x89182),f862(f862(f176(f931(x89181,x89181),a921),x89184),x89183))) % 14.98/14.66 [9004]~P1(f862(f54(x90041),f862(f862(f3(f932(x90041,a921)),x90042),f862(f862(f301(x90041),x90044),x90043))))+P1(f862(f54(x90041),f862(f862(f3(f932(x90041,a921)),x90042),x90043))) % 14.98/14.66 [9217]~P93(x92171)+P1(f862(f862(f227(x92171),f862(f862(f103(x92171),x92172),f862(f862(f94(x92171),x92173),x92174))),f862(f862(f94(x92171),f862(f862(f103(x92171),x92172),x92173)),f862(f862(f103(x92171),x92172),x92174)))) % 14.98/14.66 [9218]~P109(x92181)+P1(f862(f862(f227(x92181),f862(f862(f226(x92181),x92182),f862(f862(f225(x92181),x92183),x92184))),f862(f862(f225(x92181),f862(f862(f226(x92181),x92182),x92183)),f862(f862(f226(x92181),x92182),x92184)))) % 14.98/14.66 [9367]E(x93671,x93672)+~P1(f862(f862(f321(f931(x93673,x93673)),f862(f862(f244(x93673,x93673),x93671),x93672)),f862(f165(f931(x93673,x93673)),f862(f862(f174(x93673,x93673),x93674),x93674)))) % 14.98/14.66 [9398]~P1(f862(f862(f321(f931(x93981,x93981)),f862(f862(f244(x93981,x93981),x93983),x93982)),f299(x93981,x93984)))+~P35(x93981,f862(f862(f301(f931(x93981,x93981)),f862(f862(f244(x93981,x93981),x93982),x93983)),x93984)) % 14.98/14.66 [9399]~P1(f862(f862(f321(f931(x93991,x93991)),f862(f862(f244(x93991,x93991),x93993),x93992)),f299(x93991,x93994)))+~P55(x93991,f862(f862(f301(f931(x93991,x93991)),f862(f862(f244(x93991,x93991),x93992),x93993)),x93994)) % 14.98/14.66 [9403]E(x94031,x94032)+E(f862(f129(x94033,f862(f862(f10(a921,a921,x94033),a314),f862(a317,x94031))),f862(f862(f144(x94033),x94032),x94034)),f862(f862(f144(x94033),x94032),f862(f129(x94033,f862(f862(f10(a921,a921,x94033),a314),f862(a317,x94031))),x94034))) % 14.98/14.66 [9433]~P23(x94332,x94331,x94333,f234(f932(x94332,a921)),f234(f932(x94331,a921)))+E(f862(f302(x94331,x94332,f86(x94332,x94331,f234(f932(x94332,a921)),x94333)),x94334),f862(f303(x94332,x94331,x94333),x94334)) % 14.98/14.66 [9449]~P93(x94491)+P1(f862(f862(f227(x94491),f862(f862(f103(x94491),f862(f862(f94(x94491),x94492),x94493)),f862(f862(f94(x94491),x94492),x94494))),f862(f862(f94(x94491),x94492),f862(f862(f103(x94491),x94493),x94494)))) % 14.98/14.66 [9450]~P109(x94501)+P1(f862(f862(f227(x94501),f862(f862(f226(x94501),f862(f862(f225(x94501),x94502),x94503)),f862(f862(f225(x94501),x94502),x94504))),f862(f862(f225(x94501),x94502),f862(f862(f226(x94501),x94503),x94504)))) % 14.98/14.66 [9511]~P23(x95112,x95111,x95114,f234(f932(x95112,a921)),f234(f932(x95111,a921)))+E(f862(f254(x95111),f862(f862(f10(x95112,a921,x95111),x95113),f86(x95112,x95111,f234(f932(x95112,a921)),x95114))),f862(f302(x95112,x95111,x95114),f862(f254(x95112),x95113))) % 14.98/14.66 [9525]~E(f862(f302(x95252,x95251,x95253),f234(f932(x95252,a921))),f234(f932(x95251,a921)))+P1(f862(f862(f227(f932(x95251,a921)),f862(f72(f932(x95251,a921)),f862(f302(x95252,x95251,x95253),x95254))),f862(f302(x95252,x95251,x95253),f862(f72(f932(x95252,a921)),x95254)))) % 14.98/14.66 [9855]P1(f862(f862(f321(f931(x98551,x98551)),f862(f862(f244(x98551,x98551),x98552),x98553)),f862(f277(x98551,x98551),f862(f862(f280(x98551,x98551,x98551),x98554),f299(x98551,x98554)))))+~P1(f862(f862(f321(f931(x98551,x98551)),f862(f862(f244(x98551,x98551),x98552),x98553)),f862(f862(f280(x98551,x98551,x98551),f862(f277(x98551,x98551),x98554)),f299(x98551,f862(f277(x98551,x98551),x98554))))) % 14.98/14.66 [9856]~P1(f862(f862(f321(f931(x98561,x98561)),f862(f862(f244(x98561,x98561),x98562),x98563)),f862(f277(x98561,x98561),f862(f862(f280(x98561,x98561,x98561),x98564),f299(x98561,x98564)))))+P1(f862(f862(f321(f931(x98561,x98561)),f862(f862(f244(x98561,x98561),x98562),x98563)),f862(f862(f280(x98561,x98561,x98561),f862(f277(x98561,x98561),x98564)),f299(x98561,f862(f277(x98561,x98561),x98564))))) % 14.98/14.66 [9877]~P1(f862(f862(f321(x98772),x98774),f862(f275(x98771,x98772),x98773)))+P1(f862(f862(f321(f931(x98771,x98772)),f862(f862(f244(x98771,x98772),f563(x98773,x98771,x98774,x98772)),x98774)),x98773)) % 14.98/14.66 [9878]~P1(f862(f862(f321(x98782),x98784),f862(f275(x98781,x98782),x98783)))+P1(f862(f862(f321(f931(x98781,x98782)),f862(f862(f244(x98781,x98782),f565(x98783,x98781,x98784,x98782)),x98784)),x98783)) % 14.98/14.66 [9904]~P1(f862(f862(f321(x99041),x99044),f862(f862(f103(f932(x99041,a921)),x99042),x99043)))+P1(f862(f862(f862(f103(f932(x99041,a921)),f862(f862(f9(x99041,f932(x99041,a921),a921),f321(x99041)),x99042)),f862(f862(f9(x99041,f932(x99041,a921),a921),f321(x99041)),x99043)),x99044)) % 14.98/14.66 [9905]~P1(f862(f862(f321(x99051),x99054),f862(f862(f94(f932(x99051,a921)),x99052),x99053)))+P1(f862(f862(f862(f94(f932(x99051,a921)),f862(f862(f9(x99051,f932(x99051,a921),a921),f321(x99051)),x99052)),f862(f862(f9(x99051,f932(x99051,a921),a921),f321(x99051)),x99053)),x99054)) % 14.98/14.66 [9986]~P1(f862(f862(f321(f931(x99861,x99861)),f862(f862(f244(x99861,x99861),x99864),x99863)),f862(f862(f280(x99861,x99861,x99861),x99862),f299(x99861,x99862))))+P1(f862(f862(f321(f931(x99861,x99861)),f862(f862(f244(x99861,x99861),f645(x99862,x99863,x99864,x99861)),x99863)),x99862)) % 14.98/14.66 [10022]P1(f862(f862(f321(x100221),x100222),f862(f862(f103(f932(x100221,a921)),x100223),x100224)))+~P1(f862(f862(f862(f103(f932(x100221,a921)),f862(f862(f9(x100221,f932(x100221,a921),a921),f321(x100221)),x100223)),f862(f862(f9(x100221,f932(x100221,a921),a921),f321(x100221)),x100224)),x100222)) % 14.98/14.66 [10023]P1(f862(f862(f321(x100231),x100232),f862(f862(f94(f932(x100231,a921)),x100233),x100234)))+~P1(f862(f862(f862(f94(f932(x100231,a921)),f862(f862(f9(x100231,f932(x100231,a921),a921),f321(x100231)),x100233)),f862(f862(f9(x100231,f932(x100231,a921),a921),f321(x100231)),x100234)),x100232)) % 14.98/14.66 [10296]P30(x102961,f862(f862(f9(x102961,f932(f931(x102961,x102961),a921),f932(x102961,a921)),f862(f862(f10(f932(x102961,f932(f932(f931(x102961,x102961),a921),a921)),f932(f932(f931(x102961,x102961),a921),f932(x102961,a921)),x102961),f9(x102961,f932(f931(x102961,x102961),a921),a921)),f862(f862(f10(f932(x102961,f931(x102961,x102961)),f932(x102961,f932(f932(f931(x102961,x102961),a921),a921)),x102961),f862(f10(f931(x102961,x102961),f932(f932(f931(x102961,x102961),a921),a921),x102961),f321(f931(x102961,x102961)))),f244(x102961,x102961)))),x102962),x102963,x102964)+~P1(f862(f862(f321(f931(f925(x102961),f925(x102961))),f862(f862(f244(f925(x102961),f925(x102961)),x102963),x102964)),f151(x102961,x102962))) % 14.98/14.66 [10300]P56(x103001,f862(f862(f9(x103001,f932(f931(x103001,x103001),a921),f932(x103001,a921)),f862(f862(f10(f932(x103001,f932(f932(f931(x103001,x103001),a921),a921)),f932(f932(f931(x103001,x103001),a921),f932(x103001,a921)),x103001),f9(x103001,f932(f931(x103001,x103001),a921),a921)),f862(f862(f10(f932(x103001,f931(x103001,x103001)),f932(x103001,f932(f932(f931(x103001,x103001),a921),a921)),x103001),f862(f10(f931(x103001,x103001),f932(f932(f931(x103001,x103001),a921),a921),x103001),f321(f931(x103001,x103001)))),f244(x103001,x103001)))),x103002),x103003,x103004)+~P1(f862(f862(f321(f931(f932(x103001,a921),f932(x103001,a921))),f862(f862(f244(f932(x103001,a921),f932(x103001,a921)),x103003),x103004)),f310(x103001,x103002))) % 14.98/14.66 [10335]E(x103351,x103352)+~E(f862(f862(f9(x103353,f932(f931(x103353,x103354),a921),f932(x103354,a921)),f862(f862(f10(f932(x103354,f932(f932(f931(x103353,x103354),a921),a921)),f932(f932(f931(x103353,x103354),a921),f932(x103354,a921)),x103353),f9(x103354,f932(f931(x103353,x103354),a921),a921)),f862(f862(f10(f932(x103354,f931(x103353,x103354)),f932(x103354,f932(f932(f931(x103353,x103354),a921),a921)),x103353),f862(f10(f931(x103353,x103354),f932(f932(f931(x103353,x103354),a921),a921),x103354),f321(f931(x103353,x103354)))),f244(x103353,x103354)))),x103351),f862(f862(f9(x103353,f932(f931(x103353,x103354),a921),f932(x103354,a921)),f862(f862(f10(f932(x103354,f932(f932(f931(x103353,x103354),a921),a921)),f932(f932(f931(x103353,x103354),a921),f932(x103354,a921)),x103353),f9(x103354,f932(f931(x103353,x103354),a921),a921)),f862(f862(f10(f932(x103354,f931(x103353,x103354)),f932(x103354,f932(f932(f931(x103353,x103354),a921),a921)),x103353),f862(f10(f931(x103353,x103354),f932(f932(f931(x103353,x103354),a921),a921),x103354),f321(f931(x103353,x103354)))),f244(x103353,x103354)))),x103352)) % 14.98/14.66 [10338]~P30(x103381,f862(f862(f9(x103381,f932(f931(x103381,x103381),a921),f932(x103381,a921)),f862(f862(f10(f932(x103381,f932(f932(f931(x103381,x103381),a921),a921)),f932(f932(f931(x103381,x103381),a921),f932(x103381,a921)),x103381),f9(x103381,f932(f931(x103381,x103381),a921),a921)),f862(f862(f10(f932(x103381,f931(x103381,x103381)),f932(x103381,f932(f932(f931(x103381,x103381),a921),a921)),x103381),f862(f10(f931(x103381,x103381),f932(f932(f931(x103381,x103381),a921),a921),x103381),f321(f931(x103381,x103381)))),f244(x103381,x103381)))),x103384),x103382,x103383)+P1(f862(f862(f321(f931(f925(x103381),f925(x103381))),f862(f862(f244(f925(x103381),f925(x103381)),x103382),x103383)),f151(x103381,x103384))) % 14.98/14.66 [10339]~P56(x103391,f862(f862(f9(x103391,f932(f931(x103391,x103391),a921),f932(x103391,a921)),f862(f862(f10(f932(x103391,f932(f932(f931(x103391,x103391),a921),a921)),f932(f932(f931(x103391,x103391),a921),f932(x103391,a921)),x103391),f9(x103391,f932(f931(x103391,x103391),a921),a921)),f862(f862(f10(f932(x103391,f931(x103391,x103391)),f932(x103391,f932(f932(f931(x103391,x103391),a921),a921)),x103391),f862(f10(f931(x103391,x103391),f932(f932(f931(x103391,x103391),a921),a921),x103391),f321(f931(x103391,x103391)))),f244(x103391,x103391)))),x103394),x103392,x103393)+P1(f862(f862(f321(f931(f932(x103391,a921),f932(x103391,a921))),f862(f862(f244(f932(x103391,a921),f932(x103391,a921)),x103392),x103393)),f310(x103391,x103394))) % 14.98/14.66 [7697]~P98(x76971)+E(f862(f862(f74(x76971),f862(f96(x76971),x76972)),f862(f862(f74(x76971),f862(f96(x76971),x76973)),x76974)),f862(f862(f74(x76971),f862(f96(x76971),f862(f862(f74(a1),x76972),x76973))),x76974)) % 14.98/14.66 [7698]~P98(x76981)+E(f862(f862(f73(x76981),f862(f96(x76981),x76982)),f862(f862(f3(x76981),f862(f96(x76981),x76983)),x76984)),f862(f862(f3(x76981),f862(f96(x76981),f862(f862(f73(a1),x76982),x76983))),x76984)) % 14.98/14.66 [7699]~P98(x76991)+E(f862(f862(f73(x76991),f862(f96(x76991),x76992)),f862(f862(f73(x76991),f862(f96(x76991),x76993)),x76994)),f862(f862(f73(x76991),f862(f96(x76991),f862(f862(f73(a1),x76992),x76993))),x76994)) % 14.98/14.66 [7740]~P147(x77401)+E(f862(f158(x77401),f862(f862(f147(x77402,x77401),f862(f18(x77401,x77402),x77403)),x77404)),f862(f862(f74(x77401),f862(f93(x77401),f862(f182(f925(x77402)),x77404))),x77403)) % 14.98/14.66 [7979]E(f862(f260(x79791,f862(f862(f144(f931(a92,x79791)),x79792),x79793)),x79794),f862(f248(a92,x79791),x79792))+~P1(f862(f862(f228(a92),x79794),f862(f243(a92,x79791),x79792))) % 14.98/14.66 [8021]~P98(x80211)+E(f862(f862(f73(x80211),f862(f96(x80211),x80212)),f862(f862(f3(x80211),x80213),f862(f96(x80211),x80214))),f862(f862(f73(x80211),f862(f96(x80211),f862(f862(f73(a1),x80212),f862(f72(a1),x80214)))),x80213)) % 14.98/14.66 [8157]E(f862(f260(x81571,x81572),f862(f862(f3(a92),x81573),f862(f243(a92,x81571),x81574))),f862(f260(x81571,f862(f862(f144(f931(a92,x81571)),x81574),x81572)),x81573))+P1(f862(f862(f228(a92),x81573),f862(f243(a92,x81571),x81574))) % 14.98/14.66 [8598]~P1(f862(f862(f321(x85981),x85982),f862(f165(x85981),f107(x85981,x85984))))+P1(f862(f862(f321(x85981),x85982),f862(f165(x85981),f107(x85981,f862(f862(f127(x85981),x85983),x85984))))) % 14.98/14.66 [8599]~P1(f862(f862(f321(x85991),x85992),f862(f165(x85991),f107(x85991,x85993))))+P1(f862(f862(f321(x85991),x85992),f862(f165(x85991),f107(x85991,f862(f862(f127(x85991),x85993),x85994))))) % 14.98/14.66 [8619]E(f862(f862(f103(f932(x86191,a921)),f862(f862(f94(f932(x86191,a921)),x86192),x86193)),x86194),f862(f862(f94(f932(x86191,a921)),x86192),f862(f862(f103(f932(x86191,a921)),x86193),x86194)))+~P1(f862(f862(f227(f932(x86191,a921)),x86194),x86192)) % 14.98/14.66 [8932]~E(f862(f862(f103(f932(x89321,a921)),f862(f862(f94(f932(x89321,a921)),x89323),x89324)),x89322),f862(f862(f94(f932(x89321,a921)),x89323),f862(f862(f103(f932(x89321,a921)),x89324),x89322)))+P1(f862(f862(f227(f932(x89321,a921)),x89322),x89323)) % 14.98/14.66 [9222]~P1(f862(f862(f227(f932(x92221,a921)),x92222),f862(f862(f103(f932(x92221,a921)),x92223),x92224)))+P1(f862(f862(f227(f932(x92221,a921)),f862(f862(f3(f932(x92221,a921)),x92222),x92223)),x92224)) % 14.98/14.66 [9339]~E(f862(f302(x93391,x93392,x93393),f234(f932(x93391,a921))),f234(f932(x93392,a921)))+E(f862(f302(x93391,x93392,x93393),f862(f302(x93392,x93391,f86(x93391,x93392,f234(f932(x93391,a921)),x93393)),x93394)),x93394) % 14.98/14.66 [9344]P1(f862(f862(f227(f932(x93441,a921)),x93442),f862(f862(f103(f932(x93441,a921)),x93443),x93444)))+~P1(f862(f862(f227(f932(x93441,a921)),f862(f862(f3(f932(x93441,a921)),x93442),x93443)),x93444)) % 14.98/14.66 [9429]~P86(x94291)+E(f862(f69(x94291),f862(f862(f8(x94292,x94291),f862(f862(f10(x94291,x94291,x94292),f69(x94291)),x94293)),x94294)),f862(f862(f8(x94292,x94291),f862(f862(f10(x94291,x94291,x94292),f69(x94291)),x94293)),x94294)) % 14.98/14.66 [9604]~P86(x96041)+P1(f862(f862(f227(x96041),f2(x96041)),f862(f862(f8(x96042,x96041),f862(f862(f10(x96041,x96041,x96042),f69(x96041)),x96043)),x96044))) % 14.98/14.66 [9608]~P59(x96081)+E(f862(f158(x96081),f862(f862(f147(x96082,x96081),f862(f66(x96081,x96081,x96082,f72(x96081)),x96083)),x96084)),f862(f72(x96081),f862(f158(x96081),f862(f862(f147(x96082,x96081),x96083),x96084)))) % 14.98/14.66 [9751]~P86(x97511)+P1(f862(f862(f227(x97511),f862(f69(x97511),f862(f862(f8(x97512,x97511),x97513),x97514))),f862(f862(f8(x97512,x97511),f862(f862(f10(x97511,x97511,x97512),f69(x97511)),x97513)),x97514))) % 14.98/14.66 [9780]~E(f862(f862(f73(a924),x97801),x97804),f862(f862(f73(a924),x97803),x97802))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97801),x97802)),f862(f862(f244(a924,a924),x97803),x97804))),a101)) % 14.98/14.66 [9781]~P1(f862(f862(f228(a924),x97811),x97813))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97811),x97812)),f862(f862(f244(a924,a924),x97813),x97814))),a26)) % 14.98/14.66 [9782]~P1(f862(f862(f228(a924),x97821),x97823))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97821),x97822)),f862(f862(f244(a924,a924),x97823),x97824))),a64)) % 14.98/14.66 [9929]E(f862(f862(f73(a924),x99291),x99292),f862(f862(f73(a924),x99293),x99294))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x99291),x99294)),f862(f862(f244(a924,a924),x99293),x99292))),a101)) % 14.98/14.66 [9960]E(f862(f862(f157(x99601),f862(f862(f131(x99601),f862(f182(f925(x99601)),f170(x99601,x99602,x99603))),x99603)),x99604),f862(f862(f157(x99601),x99603),f862(f862(f73(a924),x99604),f862(f182(f925(x99601)),f170(x99601,x99602,x99603)))))+~P1(f862(f862(f228(a924),x99604),f862(f182(f925(x99601)),f862(f862(f131(x99601),f862(f182(f925(x99601)),f170(x99601,x99602,x99603))),x99603)))) % 14.98/14.66 [9977]~P1(f862(f862(f321(x99772),x99774),f862(f862(f32(x99771,f932(x99772,a921)),f234(f932(x99771,a921))),x99773)))+P1(f862(f862(f862(f32(x99771,f932(x99772,a921)),f234(f932(x99771,a921))),f862(f862(f10(f932(x99772,a921),f932(x99772,a921),x99771),f862(f9(x99772,f932(x99772,a921),a921),f321(x99772))),x99773)),x99774)) % 14.98/14.66 [9978]~P1(f862(f862(f321(x99782),x99784),f862(f862(f33(x99781,f932(x99782,a921)),f234(f932(x99781,a921))),x99783)))+P1(f862(f862(f862(f33(x99781,f932(x99782,a921)),f234(f932(x99781,a921))),f862(f862(f10(f932(x99782,a921),f932(x99782,a921),x99781),f862(f9(x99782,f932(x99782,a921),a921),f321(x99782))),x99783)),x99784)) % 14.98/14.66 [10048]~P1(f862(f42(x100481,x100482),f862(f862(f244(a1,a1),x100484),x100483)))+P1(f862(f42(f862(f72(a1),x100481),x100482),f862(f862(f244(a1,a1),f862(f862(f862(f89(a1),f862(f862(a317,x100483),f2(a1))),f862(f72(a1),x100484)),f862(f862(f3(a1),f862(f72(a1),x100484)),f71(a1)))),f862(f862(f862(f89(a1),f862(f862(a317,x100483),f2(a1))),f2(a1)),f862(f862(f3(a1),x100482),x100483))))) % 14.98/14.66 [10060]P1(f862(f862(f321(x100601),x100602),f862(f862(f32(x100603,f932(x100601,a921)),f234(f932(x100603,a921))),x100604)))+~P1(f862(f862(f862(f32(x100603,f932(x100601,a921)),f234(f932(x100603,a921))),f862(f862(f10(f932(x100601,a921),f932(x100601,a921),x100603),f862(f9(x100601,f932(x100601,a921),a921),f321(x100601))),x100604)),x100602)) % 14.98/14.66 [10061]P1(f862(f862(f321(x100611),x100612),f862(f862(f33(x100613,f932(x100611,a921)),f234(f932(x100613,a921))),x100614)))+~P1(f862(f862(f862(f33(x100613,f932(x100611,a921)),f234(f932(x100613,a921))),f862(f862(f10(f932(x100611,a921),f932(x100611,a921),x100613),f862(f9(x100611,f932(x100611,a921),a921),f321(x100611))),x100614)),x100612)) % 14.98/14.66 [10073]E(f862(f862(f33(a924,f932(x100731,a921)),f234(f932(a924,a921))),x100732),f862(f862(f33(a924,f932(x100731,a921)),f234(f932(a924,a921))),x100733))+~E(f862(f862(f33(a924,f932(x100731,a921)),f862(f295(a924,f2(a924)),f518(x100732,x100734,x100733,x100731))),x100733),f862(f862(f33(a924,f932(x100731,a921)),f862(f295(a924,f2(a924)),f862(f862(f73(a924),f518(x100732,x100734,x100733,x100731)),x100734))),x100732)) % 14.98/14.66 [10416]~P1(f862(f862(f227(f932(f931(x104161,x104162),a921)),x104163),x104164))+P1(f862(f862(f227(f932(x104161,f932(x104162,a921))),f862(f862(f9(x104161,f932(f931(x104161,x104162),a921),f932(x104162,a921)),f862(f862(f10(f932(x104162,f932(f932(f931(x104161,x104162),a921),a921)),f932(f932(f931(x104161,x104162),a921),f932(x104162,a921)),x104161),f9(x104162,f932(f931(x104161,x104162),a921),a921)),f862(f862(f10(f932(x104162,f931(x104161,x104162)),f932(x104162,f932(f932(f931(x104161,x104162),a921),a921)),x104161),f862(f10(f931(x104161,x104162),f932(f932(f931(x104161,x104162),a921),a921),x104162),f321(f931(x104161,x104162)))),f244(x104161,x104162)))),x104163)),f862(f862(f9(x104161,f932(f931(x104161,x104162),a921),f932(x104162,a921)),f862(f862(f10(f932(x104162,f932(f932(f931(x104161,x104162),a921),a921)),f932(f932(f931(x104161,x104162),a921),f932(x104162,a921)),x104161),f9(x104162,f932(f931(x104161,x104162),a921),a921)),f862(f862(f10(f932(x104162,f931(x104161,x104162)),f932(x104162,f932(f932(f931(x104161,x104162),a921),a921)),x104161),f862(f10(f931(x104161,x104162),f932(f932(f931(x104161,x104162),a921),a921),x104162),f321(f931(x104161,x104162)))),f244(x104161,x104162)))),x104164))) % 14.98/14.66 [10432]P1(f862(f862(f227(f932(f931(x104321,x104322),a921)),x104323),x104324))+~P1(f862(f862(f227(f932(x104321,f932(x104322,a921))),f862(f862(f9(x104321,f932(f931(x104321,x104322),a921),f932(x104322,a921)),f862(f862(f10(f932(x104322,f932(f932(f931(x104321,x104322),a921),a921)),f932(f932(f931(x104321,x104322),a921),f932(x104322,a921)),x104321),f9(x104322,f932(f931(x104321,x104322),a921),a921)),f862(f862(f10(f932(x104322,f931(x104321,x104322)),f932(x104322,f932(f932(f931(x104321,x104322),a921),a921)),x104321),f862(f10(f931(x104321,x104322),f932(f932(f931(x104321,x104322),a921),a921),x104322),f321(f931(x104321,x104322)))),f244(x104321,x104322)))),x104323)),f862(f862(f9(x104321,f932(f931(x104321,x104322),a921),f932(x104322,a921)),f862(f862(f10(f932(x104322,f932(f932(f931(x104321,x104322),a921),a921)),f932(f932(f931(x104321,x104322),a921),f932(x104322,a921)),x104321),f9(x104322,f932(f931(x104321,x104322),a921),a921)),f862(f862(f10(f932(x104322,f931(x104321,x104322)),f932(x104322,f932(f932(f931(x104321,x104322),a921),a921)),x104321),f862(f10(f931(x104321,x104322),f932(f932(f931(x104321,x104322),a921),a921),x104322),f321(f931(x104321,x104322)))),f244(x104321,x104322)))),x104324))) % 14.98/14.66 [9476]~P1(f862(f862(f321(f931(x94761,x94761)),x94762),f299(x94761,x94764)))+P1(f862(f862(f321(f931(x94761,x94761)),x94762),f299(x94761,f862(f862(f103(f932(f931(x94761,x94761),a921)),x94763),x94764)))) % 14.98/14.66 [9477]~P1(f862(f862(f321(f931(x94771,x94771)),x94772),f299(x94771,x94773)))+P1(f862(f862(f321(f931(x94771,x94771)),x94772),f299(x94771,f862(f862(f103(f932(f931(x94771,x94771),a921)),x94773),x94774)))) % 14.98/14.66 [10161]~P1(f862(f862(f227(a924),f862(f862(f73(a924),x101611),x101614)),f862(f862(f73(a924),x101613),x101612)))+P1(f862(f862(f227(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x101611),x101612)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x101613),x101614)),f181(f932(f931(a924,a924),a921))))))) % 14.98/14.66 [10162]~P1(f862(f862(f228(a924),f862(f862(f73(a924),x101621),x101624)),f862(f862(f73(a924),x101623),x101622)))+P1(f862(f862(f228(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x101621),x101622)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x101623),x101624)),f181(f932(f931(a924,a924),a921))))))) % 14.98/14.66 [10241]P1(f862(f862(f227(a924),f862(f862(f73(a924),x102411),x102412)),f862(f862(f73(a924),x102413),x102414)))+~P1(f862(f862(f227(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x102411),x102414)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x102413),x102412)),f181(f932(f931(a924,a924),a921))))))) % 14.98/14.66 [10242]P1(f862(f862(f228(a924),f862(f862(f73(a924),x102421),x102422)),f862(f862(f73(a924),x102423),x102424)))+~P1(f862(f862(f228(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x102421),x102424)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x102423),x102422)),f181(f932(f931(a924,a924),a921))))))) % 14.98/14.66 [10282]P1(f862(f862(f227(f932(x102821,a921)),f862(f862(f33(a924,f932(x102821,a921)),f234(f932(a924,a921))),x102822)),f862(f862(f33(a924,f932(x102821,a921)),f234(f932(a924,a921))),x102823)))+~P1(f862(f862(f227(f932(x102821,a921)),f862(f862(f33(a924,f932(x102821,a921)),f862(f295(a924,f2(a924)),f509(x102823,x102824,x102822,x102821))),x102822)),f862(f862(f33(a924,f932(x102821,a921)),f862(f295(a924,f2(a924)),f862(f862(f73(a924),f509(x102823,x102824,x102822,x102821)),x102824))),x102823))) % 14.98/14.66 [10342]P1(f862(f862(f227(a92),x103424),f2(a92)))+E(f862(f862(f251(f931(a92,a92),f931(x103421,f932(a927,a315)),f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103421)))),f931(a92,a92))),f862(x103422,x103423)),f862(f862(f10(f932(f932(a92,f932(a921,f928(f926(x103421)))),f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103421)))),f931(a92,a92)))),f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103421)))),f931(a92,a92))),f931(x103421,f932(a927,a315))),f862(f251(f931(a92,a92),f932(a92,f932(a921,f928(f926(x103421)))),f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103421)))),f931(a92,a92))),f269(x103421,x103422,f862(f862(f3(a92),x103424),f71(a92)),x103423))),f862(f862(f10(f932(f932(a92,f932(a921,f928(f926(x103421)))),f932(a92,f932(a921,f928(f926(x103421))))),f932(f932(a92,f932(a921,f928(f926(x103421)))),f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103421)))),f931(a92,a92)))),f931(x103421,f932(a927,a315))),f862(f10(f932(a92,f932(a921,f928(f926(x103421)))),f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103421)))),f931(a92,a92))),f932(a92,f932(a921,f928(f926(x103421))))),f244(f932(a92,f932(a921,f928(f926(x103421)))),f931(a92,a92)))),f862(f862(f10(f932(a92,f932(a921,f928(f926(x103421)))),f932(f932(a92,f932(a921,f928(f926(x103421)))),f932(a92,f932(a921,f928(f926(x103421))))),f931(x103421,f932(a927,a315))),f37(x103421)),f862(f862(f10(x103421,f932(a92,f932(a921,f928(f926(x103421)))),f931(x103421,f932(a927,a315))),f35(x103421)),f243(x103421,f932(a927,a315))))))),f269(x103421,x103422,x103424,x103423)) % 14.98/14.66 [10406]~P1(f862(f862(f321(x104062),x104064),f862(f275(x104061,x104062),x104063)))+P1(f862(f242(x104061,x104062,f862(f862(f9(x104061,f932(f931(x104061,x104062),a921),f932(x104062,a921)),f862(f862(f10(f932(x104062,f932(f932(f931(x104061,x104062),a921),a921)),f932(f932(f931(x104061,x104062),a921),f932(x104062,a921)),x104061),f9(x104062,f932(f931(x104061,x104062),a921),a921)),f862(f862(f10(f932(x104062,f931(x104061,x104062)),f932(x104062,f932(f932(f931(x104061,x104062),a921),a921)),x104061),f862(f10(f931(x104061,x104062),f932(f932(f931(x104061,x104062),a921),a921),x104062),f321(f931(x104061,x104062)))),f244(x104061,x104062)))),x104063)),x104064)) % 14.98/14.66 [10407]~P1(f862(f862(f321(x104071),x104074),f862(f256(x104071,x104072),x104073)))+P1(f862(f241(x104071,x104072,f862(f862(f9(x104071,f932(f931(x104071,x104072),a921),f932(x104072,a921)),f862(f862(f10(f932(x104072,f932(f932(f931(x104071,x104072),a921),a921)),f932(f932(f931(x104071,x104072),a921),f932(x104072,a921)),x104071),f9(x104072,f932(f931(x104071,x104072),a921),a921)),f862(f862(f10(f932(x104072,f931(x104071,x104072)),f932(x104072,f932(f932(f931(x104071,x104072),a921),a921)),x104071),f862(f10(f931(x104071,x104072),f932(f932(f931(x104071,x104072),a921),a921),x104072),f321(f931(x104071,x104072)))),f244(x104071,x104072)))),x104073)),x104074)) % 14.98/14.66 [10419]P1(f862(f862(f321(x104191),x104192),f862(f275(x104193,x104191),x104194)))+~P1(f862(f242(x104193,x104191,f862(f862(f9(x104193,f932(f931(x104193,x104191),a921),f932(x104191,a921)),f862(f862(f10(f932(x104191,f932(f932(f931(x104193,x104191),a921),a921)),f932(f932(f931(x104193,x104191),a921),f932(x104191,a921)),x104193),f9(x104191,f932(f931(x104193,x104191),a921),a921)),f862(f862(f10(f932(x104191,f931(x104193,x104191)),f932(x104191,f932(f932(f931(x104193,x104191),a921),a921)),x104193),f862(f10(f931(x104193,x104191),f932(f932(f931(x104193,x104191),a921),a921),x104191),f321(f931(x104193,x104191)))),f244(x104193,x104191)))),x104194)),x104192)) % 14.98/14.66 [10420]P1(f862(f862(f321(x104201),x104202),f862(f256(x104201,x104203),x104204)))+~P1(f862(f241(x104201,x104203,f862(f862(f9(x104201,f932(f931(x104201,x104203),a921),f932(x104203,a921)),f862(f862(f10(f932(x104203,f932(f932(f931(x104201,x104203),a921),a921)),f932(f932(f931(x104201,x104203),a921),f932(x104203,a921)),x104201),f9(x104203,f932(f931(x104201,x104203),a921),a921)),f862(f862(f10(f932(x104203,f931(x104201,x104203)),f932(x104203,f932(f932(f931(x104201,x104203),a921),a921)),x104201),f862(f10(f931(x104201,x104203),f932(f932(f931(x104201,x104203),a921),a921),x104203),f321(f931(x104201,x104203)))),f244(x104201,x104203)))),x104204)),x104202)) % 14.98/14.66 [10084]P1(f862(f153(x100841,x100842),x100843))+~P1(f862(f153(x100841,f862(f862(f20(x100841,a921,a921),f862(f862(f10(a921,f932(a921,a921),x100841),a318),x100844)),x100842)),x100843)) % 14.98/14.66 [10085]P1(f862(f153(x100851,x100852),x100853))+~P1(f862(f153(x100851,f862(f862(f20(x100851,a921,a921),f862(f862(f10(a921,f932(a921,a921),x100851),a318),x100852)),x100854)),x100853)) % 14.98/14.66 [10163]~P119(x101631)+E(f862(f862(f74(x101631),f862(f862(f73(x101631),f71(x101631)),f71(x101631))),f862(f862(f8(a924,x101631),f862(f862(f10(x101631,x101631,a924),f862(f73(x101631),x101632)),f862(f862(f9(a924,x101631,x101631),f862(f862(f10(x101631,f932(x101631,x101631),a924),f74(x101631)),f93(x101631))),x101633))),f862(f292(a924),x101634))),f862(f862(f74(x101631),f862(f93(x101631),x101634)),f862(f862(f73(x101631),x101632),f862(f862(f73(x101631),x101632),f862(f862(f74(x101631),f862(f93(x101631),f862(f862(f3(a924),x101634),f71(a924)))),x101633))))) % 14.98/14.66 [10303]P1(f862(x103031,f555(x103032,x103033,x103034,x103031)))+P35(x103032,f862(f254(f931(x103032,x103032)),f862(f249(x103032,x103032,a921),f862(f862(f10(f932(x103032,a921),f932(x103032,a921),x103032),f862(f20(x103032,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103032),a318),x103031))),f862(f862(f9(x103032,f932(x103032,x103032),f932(x103032,a921)),f862(f862(f10(f932(x103032,a921),f932(f932(x103032,x103032),f932(x103032,a921)),x103032),f10(x103032,a921,x103032)),a317)),x103033))))) % 14.98/14.66 [10317]~P1(f862(f862(f228(a924),f862(x103174,f862(x103173,f555(x103171,x103173,x103174,x103172)))),f862(x103174,f555(x103171,x103173,x103174,x103172))))+P35(x103171,f862(f254(f931(x103171,x103171)),f862(f249(x103171,x103171,a921),f862(f862(f10(f932(x103171,a921),f932(x103171,a921),x103171),f862(f20(x103171,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103171),a318),x103172))),f862(f862(f9(x103171,f932(x103171,x103171),f932(x103171,a921)),f862(f862(f10(f932(x103171,a921),f932(f932(x103171,x103171),f932(x103171,a921)),x103171),f10(x103171,a921,x103171)),a317)),x103173))))) % 14.98/14.66 [10393]~P3(x103931)+E(f31(x103931,f862(f254(x103931),f862(f862(f10(f932(f932(x103932,x103931),a921),a921,x103931),f80(f932(x103932,x103931))),f862(f862(f10(f932(f932(x103932,x103931),a921),f932(f932(x103932,x103931),a921),x103931),f862(f20(f932(x103932,x103931),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x103932,x103931)),a318),f862(f862(f9(f932(x103932,x103931),f932(f932(x103932,x103931),a921),a921),f321(f932(x103932,x103931))),x103933)))),f862(f862(f9(x103931,f932(f932(x103932,x103931),x103931),f932(f932(x103932,x103931),a921)),f862(f862(f10(f932(x103931,a921),f932(f932(f932(x103932,x103931),x103931),f932(f932(x103932,x103931),a921)),x103931),f10(x103931,a921,f932(x103932,x103931))),a317)),f862(f862(f9(f932(x103932,x103931),x103932,x103931),f7(f932(x103932,x103931))),x103934)))))),f862(f31(f932(x103932,x103931),x103933),x103934)) % 14.98/14.66 [10394]~P3(x103941)+E(f31(x103941,f862(f254(x103941),f862(f862(f10(f932(f932(x103942,x103941),a921),a921,x103941),f80(f932(x103942,x103941))),f862(f862(f10(f932(f932(x103942,x103941),a921),f932(f932(x103942,x103941),a921),x103941),f862(f20(f932(x103942,x103941),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x103942,x103941)),a318),f862(f862(f9(f932(x103942,x103941),f932(f932(x103942,x103941),a921),a921),f321(f932(x103942,x103941))),x103943)))),f862(f862(f9(x103941,f932(f932(x103942,x103941),x103941),f932(f932(x103942,x103941),a921)),f862(f862(f10(f932(x103941,a921),f932(f932(f932(x103942,x103941),x103941),f932(f932(x103942,x103941),a921)),x103941),f10(x103941,a921,f932(x103942,x103941))),a317)),f862(f862(f9(f932(x103942,x103941),x103942,x103941),f7(f932(x103942,x103941))),x103944)))))),f862(f31(f932(x103942,x103941),x103943),x103944)) % 14.98/14.66 [10395]~P3(x103951)+E(f30(x103951,f862(f254(x103951),f862(f862(f10(f932(f932(x103952,x103951),a921),a921,x103951),f80(f932(x103952,x103951))),f862(f862(f10(f932(f932(x103952,x103951),a921),f932(f932(x103952,x103951),a921),x103951),f862(f20(f932(x103952,x103951),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x103952,x103951)),a318),f862(f862(f9(f932(x103952,x103951),f932(f932(x103952,x103951),a921),a921),f321(f932(x103952,x103951))),x103953)))),f862(f862(f9(x103951,f932(f932(x103952,x103951),x103951),f932(f932(x103952,x103951),a921)),f862(f862(f10(f932(x103951,a921),f932(f932(f932(x103952,x103951),x103951),f932(f932(x103952,x103951),a921)),x103951),f10(x103951,a921,f932(x103952,x103951))),a317)),f862(f862(f9(f932(x103952,x103951),x103952,x103951),f7(f932(x103952,x103951))),x103954)))))),f862(f30(f932(x103952,x103951),x103953),x103954)) % 14.98/14.66 [10396]~P3(x103961)+E(f30(x103961,f862(f254(x103961),f862(f862(f10(f932(f932(x103962,x103961),a921),a921,x103961),f80(f932(x103962,x103961))),f862(f862(f10(f932(f932(x103962,x103961),a921),f932(f932(x103962,x103961),a921),x103961),f862(f20(f932(x103962,x103961),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x103962,x103961)),a318),f862(f862(f9(f932(x103962,x103961),f932(f932(x103962,x103961),a921),a921),f321(f932(x103962,x103961))),x103963)))),f862(f862(f9(x103961,f932(f932(x103962,x103961),x103961),f932(f932(x103962,x103961),a921)),f862(f862(f10(f932(x103961,a921),f932(f932(f932(x103962,x103961),x103961),f932(f932(x103962,x103961),a921)),x103961),f10(x103961,a921,f932(x103962,x103961))),a317)),f862(f862(f9(f932(x103962,x103961),x103962,x103961),f7(f932(x103962,x103961))),x103964)))))),f862(f30(f932(x103962,x103961),x103963),x103964)) % 14.98/14.66 [10445]~P1(f862(f862(f321(f931(x104451,x104451)),f862(f862(f244(x104451,x104451),x104453),x104454)),f862(f862(f103(f932(f931(x104451,x104451),a921)),x104452),f299(x104451,f181(f932(f931(x104451,x104451),a921))))))+P1(f862(f862(f862(f862(f103(f932(x104451,f932(x104451,a921))),f862(f862(f9(x104451,f932(f931(x104451,x104451),a921),f932(x104451,a921)),f862(f862(f10(f932(x104451,f932(f932(f931(x104451,x104451),a921),a921)),f932(f932(f931(x104451,x104451),a921),f932(x104451,a921)),x104451),f9(x104451,f932(f931(x104451,x104451),a921),a921)),f862(f862(f10(f932(x104451,f931(x104451,x104451)),f932(x104451,f932(f932(f931(x104451,x104451),a921),a921)),x104451),f862(f10(f931(x104451,x104451),f932(f932(f931(x104451,x104451),a921),a921),x104451),f321(f931(x104451,x104451)))),f244(x104451,x104451)))),x104452)),a317),x104453),x104454)) % 14.98/14.66 [10455]P1(f862(f862(f321(f931(x104551,x104551)),f862(f862(f244(x104551,x104551),x104552),x104553)),f862(f862(f103(f932(f931(x104551,x104551),a921)),x104554),f299(x104551,f181(f932(f931(x104551,x104551),a921))))))+~P1(f862(f862(f862(f862(f103(f932(x104551,f932(x104551,a921))),f862(f862(f9(x104551,f932(f931(x104551,x104551),a921),f932(x104551,a921)),f862(f862(f10(f932(x104551,f932(f932(f931(x104551,x104551),a921),a921)),f932(f932(f931(x104551,x104551),a921),f932(x104551,a921)),x104551),f9(x104551,f932(f931(x104551,x104551),a921),a921)),f862(f862(f10(f932(x104551,f931(x104551,x104551)),f932(x104551,f932(f932(f931(x104551,x104551),a921),a921)),x104551),f862(f10(f931(x104551,x104551),f932(f932(f931(x104551,x104551),a921),a921),x104551),f321(f931(x104551,x104551)))),f244(x104551,x104551)))),x104554)),a317),x104552),x104553)) % 14.98/14.66 [10403]E(f862(f862(f144(f925(x104031)),f862(f862(f144(x104031),x104032),f862(f135(f925(x104031),f925(x104031),f127(x104031),f106(x104031)),f862(f862(f147(f925(x104031),f925(x104031)),f149(f925(x104031),x104031,f106(x104031),f862(f862(f10(f925(x104031),f932(f925(x104031),f925(x104031)),x104031),f18(f925(x104031),f925(x104031))),f862(f862(f9(x104031,f925(x104031),f925(x104031)),f144(x104031)),f106(x104031))))),x104033)))),f172(x104031,f862(f862(f144(f925(x104031)),x104034),f862(f135(f925(f925(x104031)),f925(f925(x104031)),f127(f925(x104031)),f106(f925(x104031))),f862(f862(f147(f925(x104031),f925(f925(x104031))),f149(f925(f925(x104031)),x104031,f106(f925(x104031)),f862(f18(f932(f925(x104031),f925(f925(x104031))),x104031),f862(f862(f9(f925(x104031),f925(f925(x104031)),f925(f925(x104031))),f144(f925(x104031))),f106(f925(x104031)))))),x104033))))),f172(x104031,f862(f862(f144(f925(x104031)),f862(f862(f144(x104031),x104032),x104034)),x104033)))+~P1(f862(f307(f925(f925(x104031)),f173(x104031)),f862(f862(f144(f925(x104031)),f862(f862(f144(x104031),x104032),x104034)),x104033))) % 14.98/14.66 [10444]~P1(f862(f54(x104442),f862(f254(x104442),x104444)))+P1(f862(f54(x104441),f862(f254(x104441),f862(f862(f10(f932(x104442,a921),a921,x104441),f80(x104442)),f862(f862(f9(x104441,f932(x104442,a921),f932(x104442,a921)),f862(f862(f10(f932(x104442,f932(a921,a921)),f932(f932(x104442,a921),f932(x104442,a921)),x104441),f20(x104442,a921,a921)),f862(f862(f10(f932(x104442,a921),f932(x104442,f932(a921,a921)),x104441),f862(f10(a921,f932(a921,a921),x104442),a318)),f862(f862(f9(x104441,f932(x104442,x104441),f932(x104442,a921)),f862(f862(f10(f932(x104441,a921),f932(f932(x104442,x104441),f932(x104442,a921)),x104441),f10(x104441,a921,x104442)),a317)),x104443)))),x104444))))) % 14.98/14.66 [8970]P22(x89701,x89702,x89703,x89704)+~P23(x89701,x89702,x89703,x89704,x89705) % 14.98/14.66 [5443]E(x54431,x54432)+~E(f162(x54433,x54431,x54434),f162(x54433,x54432,x54435)) % 14.98/14.66 [5444]E(x54441,x54442)+~E(f119(x54443,x54444,x54441),f119(x54443,x54445,x54442)) % 14.98/14.66 [5445]E(x54451,x54452)+~E(f119(x54453,x54451,x54454),f119(x54453,x54452,x54455)) % 14.98/14.66 [8291]~E(f862(x82913,x82914),x82915)+E(f68(x82911,x82912,x82913,x82914,x82915),x82913) % 14.98/14.66 [8827]~E(f68(x88274,x88275,x88271,x88272,x88273),x88271)+E(f862(x88271,x88272),x88273) % 14.98/14.66 [9447]~P23(x94472,x94471,x94474,x94473,x94475)+P23(x94471,x94472,f70(x94472,x94471,x94473,x94474),x94475,x94473) % 14.98/14.66 [9448]~P23(x94482,x94481,x94484,x94483,x94485)+P23(x94481,x94482,f86(x94482,x94481,x94483,x94484),x94485,x94483) % 14.98/14.66 [6259]P1(f862(f242(x62591,x62592,x62593),x62594))+~P1(f862(f862(x62593,x62595),x62594)) % 14.98/14.66 [6261]P1(f862(f241(x62611,x62612,x62613),x62614))+~P1(f862(f862(x62613,x62614),x62615)) % 14.98/14.66 [6740]~E(x67405,f2(a92))+E(f862(f189(x67401,x67402,x67403,x67404),x67405),f117(x67402)) % 14.98/14.66 [6741]~E(x67415,f2(a92))+E(f862(f191(x67411,x67412,x67413,x67414),x67415),f108(x67412)) % 14.98/14.66 [6875]~E(x68753,f2(a92))+E(f862(f265(x68751,x68752,x68753,x68754),x68755),f862(f244(x68751,x68752),x68755)) % 14.98/14.66 [7935]~P18(x79354,x79351,x79352,x79355)+E(f862(f66(x79351,x79351,x79351,f862(x79352,x79353)),f862(x79352,x79353)),f862(x79352,x79353)) % 14.98/14.66 [8333]~P14(x83335,x83331,x83332)+E(f862(f66(x83331,x83331,x83331,f862(x83332,x83333)),f862(x83332,x83334)),f862(f66(x83331,x83331,x83331,f862(x83332,x83334)),f862(x83332,x83333))) % 14.98/14.66 [8660]P1(f862(f862(f321(f931(x86601,x86601)),f862(f862(f244(x86601,x86601),x86602),x86603)),f313(x86601,x86604,x86605)))+~P1(f862(f862(f228(a924),f862(x86604,x86602)),f862(x86604,x86603))) % 14.98/14.66 [8755]~P1(f862(f862(f321(x87554),x87553),f287(x87554,x87551,x87552,x87555)))+P1(f862(f862(x87551,x87552),x87553)) % 14.98/14.66 [8756]~P1(f862(f862(f321(x87564),x87563),f290(x87564,x87561,x87562,x87565)))+P1(f862(f862(x87561,x87562),x87563)) % 14.98/14.66 [8757]~P1(f862(f862(f321(x87574),x87572),f287(x87574,x87571,x87575,x87573)))+P1(f862(f862(x87571,x87572),x87573)) % 14.98/14.66 [8758]~P1(f862(f862(f321(x87584),x87582),f290(x87584,x87581,x87585,x87583)))+P1(f862(f862(x87581,x87582),x87583)) % 14.98/14.66 [8839]~P23(x88391,x88393,x88395,x88392,x88394)+E(f862(f28(x88391),x88392),f862(f28(x88393),x88394)) % 14.98/14.66 [8887]~P23(x88871,x88872,x88873,x88874,x88875)+E(f862(f302(x88871,x88872,x88873),x88874),x88875) % 14.98/14.66 [8908]~P54(x89082,x89081,x89085,x89083,x89084)+E(f862(f302(x89081,x89082,x89083),x89084),f234(f932(x89082,a921))) % 14.98/14.66 [9356]~P32(x93561,x93562,x93563,x93564,x93565)+P32(x93561,x93562,x93563,f862(f161(x93561),x93564),f862(f161(x93562),x93565)) % 14.98/14.66 [9358]~P32(x93581,x93582,x93583,f862(f161(x93581),x93584),x93585)+P32(x93581,x93582,x93583,x93584,f862(f161(x93582),x93585)) % 14.98/14.66 [9359]~P32(x93591,x93592,x93593,x93594,f862(f161(x93592),x93595))+P32(x93591,x93592,x93593,f862(f161(x93591),x93594),x93595) % 14.98/14.66 [9365]P32(x93651,x93652,x93653,x93654,x93655)+~P32(x93651,x93652,x93653,f862(f161(x93651),x93654),f862(f161(x93652),x93655)) % 14.98/14.66 [9770]P1(f862(f862(f321(f931(f925(x97701),f925(x97701))),f862(f862(f244(f925(x97701),f925(x97701)),f862(f862(f144(x97701),x97702),x97703)),f862(f862(f144(x97701),x97702),x97704))),f150(x97701,x97705)))+~P1(f862(f862(f321(f931(f925(x97701),f925(x97701))),f862(f862(f244(f925(x97701),f925(x97701)),x97703),x97704)),f150(x97701,x97705))) % 14.98/14.66 [9771]P1(f862(f862(f321(f931(f925(x97711),f925(x97711))),f862(f862(f244(f925(x97711),f925(x97711)),f862(f862(f127(x97711),x97712),x97713)),f862(f862(f127(x97711),x97712),x97714))),f140(x97711,x97715)))+~P1(f862(f862(f321(f931(f925(x97711),f925(x97711))),f862(f862(f244(f925(x97711),f925(x97711)),x97713),x97714)),f140(x97711,x97715))) % 14.98/14.66 [9967]E(f862(f862(f144(x99671),f660(x99672,x99673,x99674,x99675,x99671)),f663(x99672,x99673,x99674,x99675,x99671)),x99675)+~P1(f862(f862(f321(f931(f925(x99671),f925(x99671))),f862(f862(f244(f925(x99671),f925(x99671)),x99675),f862(f862(f144(x99671),x99674),x99673))),f151(x99671,x99672))) % 14.98/14.66 [9989]E(f862(f862(f144(x99891),f661(x99892,x99893,x99894,x99895,x99891)),f662(x99892,x99893,x99894,x99895,x99891)),x99893)+~P1(f862(f862(f321(f931(f925(x99891),f925(x99891))),f862(f862(f244(f925(x99891),f925(x99891)),f862(f862(f144(x99891),x99895),x99894)),x99893)),f151(x99891,x99892))) % 14.98/14.66 [10137]~P1(f862(f862(f321(f931(f925(x101371),f925(x101371))),f862(f862(f244(f925(x101371),f925(x101371)),f862(f862(f144(x101371),x101375),x101372)),x101374)),f151(x101371,x101373)))+P1(f862(f862(f321(f931(f925(x101371),f925(x101371))),f862(f862(f244(f925(x101371),f925(x101371)),x101372),f662(x101373,x101374,x101372,x101375,x101371))),f151(x101371,x101373))) % 14.98/14.66 [10207]~P1(f862(f862(f321(f931(f925(x102071),f925(x102071))),f862(f862(f244(f925(x102071),f925(x102071)),x102075),f862(f862(f144(x102071),x102074),x102073))),f151(x102071,x102072)))+P1(f862(f862(f321(f931(f925(x102071),f925(x102071))),f862(f862(f244(f925(x102071),f925(x102071)),f663(x102072,x102073,x102074,x102075,x102071)),x102073)),f151(x102071,x102072))) % 14.98/14.66 [10397]P1(f862(f862(f321(f931(x103971,x103971)),f862(f862(f244(x103971,x103971),f862(x103972,f862(f862(f73(a924),x103973),x103974))),f862(x103972,x103973))),f299(x103971,x103975)))+~P1(f862(f862(f321(f931(x103971,x103971)),f862(f862(f244(x103971,x103971),f862(x103972,f862(a105,f624(x103974,x103973,x103975,x103972,x103971)))),f862(x103972,f624(x103974,x103973,x103975,x103972,x103971)))),f299(x103971,x103975))) % 14.98/14.66 [5416]E(x54161,x54162)+~E(f862(f862(f144(x54163),x54164),x54161),f862(f862(f144(x54163),x54165),x54162)) % 14.98/14.66 [5417]E(x54171,x54172)+~E(f862(f862(f144(x54173),x54171),x54174),f862(f862(f144(x54173),x54172),x54175)) % 14.98/14.66 [5460]P1(f862(x54601,x54602))+~E(f862(f129(x54603,x54601),x54604),f862(f862(f144(x54603),x54602),x54605)) % 14.98/14.66 [5461]P1(f862(x54611,x54612))+~E(f862(f862(f144(x54613),x54612),x54614),f862(f129(x54613,x54611),x54615)) % 14.98/14.66 [5622]~E(f862(f862(f131(x56221),x56223),x56222),f862(f862(f144(x56221),x56224),x56225))+E(f862(f862(f157(x56221),x56222),x56223),x56224) % 14.98/14.66 [5764]~P12(x57644,x57645,x57641)+E(f862(f862(x57641,x57642),f862(f862(x57641,x57642),x57643)),f862(f862(x57641,x57642),x57643)) % 14.98/14.66 [6317]~E(x63174,f2(a92))+E(f862(f862(f110(x63171,x63172,x63173),x63174),x63175),f862(f862(f244(f925(x63172),x63171),f106(x63172)),x63175)) % 14.98/14.66 [6389]~P109(x63892)+~E(f862(f862(f141(x63891,x63892,x63893),x63894),x63895),f106(x63891)) % 14.98/14.66 [6778]E(x67781,x67782)+~E(f862(f862(f127(x67783),x67784),f862(f862(f144(x67783),x67781),f106(x67783))),f862(f862(f127(x67783),x67785),f862(f862(f144(x67783),x67782),f106(x67783)))) % 14.98/14.66 [6779]E(x67791,x67792)+~E(f862(f862(f127(x67793),x67791),f862(f862(f144(x67793),x67794),f106(x67793))),f862(f862(f127(x67793),x67792),f862(f862(f144(x67793),x67795),f106(x67793)))) % 14.98/14.66 [7093]E(f862(f862(f301(x70931),f862(x70932,x70933)),f862(f302(x70934,x70931,x70932),x70935)),f862(f302(x70934,x70931,x70932),x70935))+~P1(f862(f862(f321(x70934),x70933),x70935)) % 14.98/14.66 [7099]~P1(f862(x70994,f862(x70993,x70995)))+P1(f862(f862(f303(x70991,x70992,x70993),x70994),x70995)) % 14.98/14.66 [7102]~P1(f862(f862(x71023,x71025),x71024))+P1(f862(f862(f235(x71021,x71022,x71023),x71024),x71025)) % 14.98/14.66 [7198]~E(f862(f302(x71981,x71982,x71983),x71984),x71985)+E(f862(f302(f932(x71981,a921),f932(x71982,a921),f302(x71981,x71982,x71983)),f862(f300(x71981),x71984)),f862(f300(x71982),x71985)) % 14.98/14.66 [7225]E(f862(f263(x72251,x72252,x72253,x72254),x72255),f862(x72254,x72255))+~P1(f862(f862(f321(x72251),x72255),x72253)) % 14.98/14.66 [7544]P22(x75441,x75442,x75443,x75444)+~P22(x75441,x75442,x75443,f862(f862(f301(x75441),x75445),x75444)) % 14.98/14.66 [7650]~P1(f862(f862(f321(x76504),x76503),x76505))+P1(f862(f862(f321(x76501),f862(x76502,x76503)),f862(f302(x76504,x76501,x76502),x76505))) % 14.98/14.66 [7671]~P109(x76712)+E(f143(x76711,x76712,x76713,f862(f129(x76711,x76714),x76715)),f862(f129(x76711,x76714),f143(x76711,x76712,x76713,x76715))) % 14.98/14.66 [7703]P1(f862(x77031,f862(x77032,x77033)))+~P1(f862(f862(f303(x77034,x77035,x77032),x77031),x77033)) % 14.98/14.66 [7706]P1(f862(f862(x77061,x77062),x77063))+~P1(f862(f862(f235(x77064,x77065,x77061),x77063),x77062)) % 14.98/14.66 [7771]~P1(f862(f862(f321(x77713),f862(x77714,x77712)),x77715))+P1(f862(f862(f321(x77711),x77712),f862(f303(x77711,x77713,x77714),x77715))) % 14.98/14.66 [8171]~P1(f862(f862(f321(x81715),x81713),f862(f303(x81715,x81711,x81712),x81714)))+P1(f862(f862(f321(x81711),f862(x81712,x81713)),x81714)) % 14.98/14.66 [8473]~P14(x84732,x84731,x84733)+E(f862(f135(x84731,x84732,f862(f9(x84732,x84731,x84731),x84733),x84734),f145(x84732,x84735)),f862(f862(f57(x84732,x84731,x84733),x84734),f862(f165(x84732),x84735))) % 14.98/14.66 [8495]E(f862(x84951,f812(x84952,x84951,x84953,x84954)),x84954)+~P1(f862(f862(f321(x84955),x84954),f862(f302(x84953,x84955,x84951),x84952))) % 14.98/14.66 [8802]~E(x88022,f862(f862(f144(x88021),x88024),x88025))+P1(f862(f862(f321(f931(f925(x88021),f925(x88021))),f862(f862(f244(f925(x88021),f925(x88021)),f106(x88021)),x88022)),f140(x88021,x88023))) % 14.98/14.66 [8848]E(f862(x88481,f862(f86(x88482,x88483,x88484,x88481),x88485)),x88485)+~P1(f862(f862(f321(x88483),x88485),f862(f302(x88482,x88483,x88481),x88484))) % 14.98/14.66 [8851]P22(x88511,x88512,f86(x88512,x88511,x88513,x88514),x88515)+~P1(f862(f862(f227(f932(x88511,a921)),x88515),f862(f302(x88512,x88511,x88514),x88513))) % 14.98/14.66 [8858]~P32(x88581,x88583,x88585,x88582,x88584)+E(f862(f182(f925(x88581)),x88582),f862(f182(f925(x88583)),x88584)) % 14.98/14.66 [8869]P1(f862(f862(f227(f932(x88691,a921)),f862(f862(f32(x88692,f932(x88691,a921)),x88693),x88694)),f862(x88694,x88695)))+~P1(f862(f862(f321(x88692),x88695),x88693)) % 14.98/14.66 [8924]~P54(x89241,x89242,x89243,x89245,x89244)+E(f862(f302(x89241,x89242,x89243),f234(f932(x89241,a921))),x89244) % 14.98/14.66 [9151]E(f862(f129(x91511,x91512),f748(x91513,x91514,x91515,x91512,x91511)),x91513)+~E(f862(f129(x91511,x91512),x91515),f862(f862(f144(x91511),x91514),x91513)) % 14.98/14.66 [9152]E(f862(f129(x91521,x91522),f752(x91523,x91522,x91524,x91525,x91521)),x91524)+~E(f862(f862(f144(x91521),x91525),x91524),f862(f129(x91521,x91522),x91523)) % 14.98/14.66 [9243]E(f862(f182(f925(x92431)),x92432),x92433)+~P1(f862(f862(f321(f931(f925(x92431),f925(x92431))),f862(f862(f244(f925(x92431),f925(x92431)),x92434),x92432)),f862(f136(x92431,x92435),x92433))) % 14.98/14.66 [9244]E(f862(f182(f925(x92441)),x92442),x92443)+~P1(f862(f862(f321(f931(f925(x92441),f925(x92441))),f862(f862(f244(f925(x92441),f925(x92441)),x92442),x92444)),f862(f136(x92441,x92445),x92443))) % 14.98/14.66 [9314]P1(f862(f862(f321(x93141),f812(x93142,x93143,x93141,x93144)),x93142))+~P1(f862(f862(f321(x93145),x93144),f862(f302(x93141,x93145,x93143),x93142))) % 14.98/14.66 [9474]E(f862(f302(x94741,x94742,x94743),f822(x94744,x94743,x94741,x94745,x94742)),x94745)+~P1(f862(f862(f227(f932(x94742,a921)),x94745),f862(f302(x94741,x94742,x94743),x94744))) % 14.98/14.66 [9788]P1(f862(f862(f321(f931(f925(x97881),f925(x97881))),f862(f862(f244(f925(x97881),f925(x97881)),f862(f862(f144(x97881),x97882),x97883)),f862(f862(f144(x97881),x97882),x97884))),f299(f925(x97881),f150(x97881,x97885))))+~P1(f862(f862(f321(f931(f925(x97881),f925(x97881))),f862(f862(f244(f925(x97881),f925(x97881)),x97883),x97884)),f299(f925(x97881),f150(x97881,x97885)))) % 14.98/14.66 [9819]~E(f862(x98193,f700(x98195,x98194,x98193,x98192,x98191)),f862(x98195,f700(x98195,x98194,x98193,x98192,x98191)))+E(f862(f862(f147(x98191,x98192),x98193),x98194),f862(f862(f147(x98191,x98192),x98195),x98194)) % 14.98/14.66 [9894]~E(f862(f129(x98941,x98945),x98944),f862(f862(f144(x98941),x98943),x98942))+E(f862(f862(f127(x98941),f749(x98942,x98943,x98944,x98945,x98941)),f862(f862(f144(x98941),x98943),f748(x98942,x98943,x98944,x98945,x98941))),x98944) % 14.98/14.66 [9895]~E(f862(f862(f144(x98951),x98955),x98954),f862(f129(x98951,x98953),x98952))+E(f862(f862(f127(x98951),f753(x98952,x98953,x98954,x98955,x98951)),f862(f862(f144(x98951),x98955),f752(x98952,x98953,x98954,x98955,x98951))),x98952) % 14.98/14.66 [9899]E(f862(f862(f147(x98991,x98992),x98993),x98994),f862(f862(f147(x98991,x98992),x98995),x98994))+P1(f862(f862(f321(x98991),f700(x98993,x98994,x98995,x98992,x98991)),f862(f165(x98991),x98994))) % 14.98/14.66 [9930]~P1(f862(f862(f321(x99305),x99304),f862(f276(x99301,x99305,x99303),x99302)))+P1(f862(f862(f321(x99301),f521(x99302,x99303,x99301,x99304,x99305)),x99302)) % 14.98/14.66 [9931]~P1(f862(f862(f321(x99315),x99314),f862(f276(x99311,x99315,x99313),x99312)))+P1(f862(f862(f321(x99311),f526(x99312,x99313,x99311,x99314,x99315)),x99312)) % 14.98/14.66 [9961]~P1(f862(f862(f227(f932(x99615,a921)),x99614),f862(f302(x99611,x99615,x99613),x99612)))+P1(f862(f862(f227(f932(x99611,a921)),f822(x99612,x99613,x99611,x99614,x99615)),x99612)) % 14.98/14.66 [10398]E(x103981,f2(a92))+E(f216(f931(f925(x103982),x103983),f931(x103982,x103983),f862(f862(f244(f925(x103982),x103983),f106(x103982)),x103984),f862(f249(x103982,x103983,f931(f925(x103982),x103983)),f862(f862(f9(x103982,f932(x103983,f931(f925(x103982),x103983)),f932(x103983,f931(f925(x103982),x103983))),f862(f862(f10(f932(f931(f925(x103982),x103983),f931(f925(x103982),x103983)),f932(f932(x103983,f931(f925(x103982),x103983)),f932(x103983,f931(f925(x103982),x103983))),x103982),f10(f931(f925(x103982),x103983),f931(f925(x103982),x103983),x103983)),f862(f862(f10(f932(f925(x103982),f932(x103983,f931(f925(x103982),x103983))),f932(f931(f925(x103982),x103983),f931(f925(x103982),x103983)),x103982),f249(f925(x103982),x103983,f931(f925(x103982),x103983))),f862(f862(f10(f932(f925(x103982),f925(x103982)),f932(f925(x103982),f932(x103983,f931(f925(x103982),x103983))),x103982),f862(f10(f925(x103982),f932(x103983,f931(f925(x103982),x103983)),f925(x103982)),f244(f925(x103982),x103983))),f144(x103982))))),f862(f110(x103983,x103982,x103985),f862(f862(f3(a92),x103981),f71(a92))))),f862(x103985,x103984)),f862(f862(f110(x103983,x103982,x103985),x103981),x103984)) % 14.98/14.66 [6199]E(x61991,x61992)+~E(f862(f248(x61993,x61994),f862(f862(f244(x61993,x61994),x61995),x61991)),x61992) % 14.98/14.66 [6200]E(x62001,x62002)+~E(f862(f243(x62003,x62004),f862(f862(f244(x62003,x62004),x62001),x62005)),x62002) % 14.98/14.66 [6462]~E(x64623,f862(f862(f127(x64621),x64624),f862(f862(f144(x64621),x64622),x64625)))+P1(f862(f862(f321(x64621),x64622),f862(f165(x64621),x64623))) % 14.98/14.66 [6862]E(f862(f302(x68621,x68622,f862(f18(x68622,x68621),x68623)),x68624),f862(f862(f301(x68622),x68623),f181(f932(x68622,a921))))+~P1(f862(f862(f321(x68621),x68625),x68624)) % 14.98/14.66 [6931]E(f862(f862(f103(f932(x69311,a921)),f862(f165(x69311),x69312)),f862(f165(x69311),x69313)),f862(f165(x69311),x69314))+~E(f159(x69311,x69315,x69314),f862(f862(f244(f925(x69311),f925(x69311)),x69312),x69313)) % 14.98/14.66 [7033]~P109(x70332)+E(f862(f182(f925(x70331)),f862(f862(f141(x70331,x70332,x70333),x70334),x70335)),f862(a105,f862(f182(f925(x70331)),x70335))) % 14.98/14.66 [7047]~P109(x70472)+E(f862(f165(x70471),f862(f862(f141(x70471,x70472,x70473),x70474),x70475)),f862(f862(f301(x70471),x70474),f862(f165(x70471),x70475))) % 14.98/14.66 [7320]~P119(x73201)+E(f862(f862(f74(x73201),f862(f862(f74(x73201),x73202),x73203)),f862(f862(f74(x73201),x73204),x73205)),f862(f862(f74(x73201),f862(f862(f74(x73201),x73202),x73204)),f862(f862(f74(x73201),x73203),x73205))) % 14.98/14.66 [7321]~P119(x73211)+E(f862(f862(f73(x73211),f862(f862(f73(x73211),x73212),x73213)),f862(f862(f73(x73211),x73214),x73215)),f862(f862(f73(x73211),f862(f862(f73(x73211),x73212),x73214)),f862(f862(f73(x73211),x73213),x73215))) % 14.98/14.66 [7322]~P64(x73221)+E(f862(f862(f281(x73221),f862(f862(f74(x73221),x73222),x73223)),f862(f862(f74(x73221),x73224),x73225)),f862(f862(f74(x73221),f862(f862(f281(x73221),x73222),x73224)),f862(f862(f281(x73221),x73223),x73225))) % 14.98/14.66 [7336]~P109(x73361)+E(f298(x73361,f862(f862(f226(x73361),x73362),x73363),f862(f862(f225(x73361),x73364),x73365)),f862(f862(f94(f932(x73361,a921)),f298(x73361,x73362,x73364)),f298(x73361,x73363,x73365))) % 14.98/14.66 [7337]~P109(x73371)+E(f297(x73371,f862(f862(f226(x73371),x73372),x73373),f862(f862(f225(x73371),x73374),x73375)),f862(f862(f94(f932(x73371,a921)),f297(x73371,x73372,x73374)),f297(x73371,x73373,x73375))) % 14.98/14.66 [7338]~P109(x73381)+E(f296(x73381,f862(f862(f226(x73381),x73382),x73383),f862(f862(f225(x73381),x73384),x73385)),f862(f862(f94(f932(x73381,a921)),f296(x73381,x73382,x73384)),f296(x73381,x73383,x73385))) % 14.98/14.66 [7339]~P109(x73391)+E(f862(f862(f94(f932(x73391,a921)),f862(f295(x73391,x73392),x73393)),f862(f295(x73391,x73394),x73395)),f862(f295(x73391,f862(f862(f226(x73391),x73392),x73394)),f862(f862(f225(x73391),x73393),x73395))) % 14.98/14.66 [7462]~P1(f862(x74621,f464(x74623,x74622,x74621)))+P1(f862(x74621,f862(f862(f244(x74622,x74623),x74624),x74625))) % 14.98/14.66 [7575]~E(x75752,f862(x75754,x75755))+P1(f862(f862(f321(x75751),x75752),f862(f302(x75753,x75751,x75754),f234(f932(x75753,a921))))) % 14.98/14.66 [7648]~P14(x76483,x76482,x76484)+P14(x76481,x76482,f862(f862(f10(x76483,f932(x76482,x76482),x76481),x76484),x76485)) % 14.98/14.66 [7649]~P12(x76493,x76492,x76494)+P12(x76491,x76492,f862(f862(f10(x76493,f932(x76492,x76492),x76491),x76494),x76495)) % 14.98/14.66 [7788]~P22(x77881,x77882,x77883,x77884)+P22(x77881,x77882,x77883,f862(f862(f3(f932(x77881,a921)),x77884),x77885)) % 14.98/14.66 [7944]~P1(f862(f862(x79443,x79444),x79445))+P1(f862(f862(f249(x79441,x79442,a921),x79443),f862(f862(f244(x79441,x79442),x79444),x79445))) % 14.98/14.66 [8058]~P1(f862(x80582,x80584))+~E(f862(f862(f131(x80581),f862(f182(f925(x80581)),f170(x80581,x80582,x80583))),x80583),f862(f862(f144(x80581),x80584),x80585)) % 14.98/14.66 [8078]P22(x80781,x80782,x80783,x80784)+~P22(x80781,x80782,x80783,f862(f862(f103(f932(x80781,a921)),x80785),x80784)) % 14.98/14.66 [8079]P22(x80791,x80792,x80793,x80794)+~P22(x80791,x80792,x80793,f862(f862(f103(f932(x80791,a921)),x80794),x80795)) % 14.98/14.66 [8127]~P109(x81272)+E(f862(f862(f141(x81271,x81272,x81273),x81274),f143(x81271,x81272,x81273,x81275)),f143(x81271,x81272,x81273,f862(f862(f144(x81271),x81274),x81275))) % 14.98/14.66 [8450]~P12(x84502,x84501,x84503)+E(f862(f135(x84501,x84502,f862(f9(x84502,x84501,x84501),x84503),x84504),x84505),f862(f862(f57(x84502,x84501,x84503),x84504),f862(f165(x84502),x84505))) % 14.98/14.66 [8478]~E(f862(f862(f131(x84781),f862(f182(f925(x84781)),f170(x84781,x84782,x84783))),x84783),f862(f862(f144(x84781),x84784),x84785))+E(f862(f862(f127(x84781),f170(x84781,x84782,x84783)),f862(f862(f144(x84781),x84784),x84785)),x84783) % 14.98/14.66 [8505]P1(f862(f862(x85051,x85052),x85053))+~P1(f862(f862(f249(x85054,x85055,a921),x85051),f862(f862(f244(x85054,x85055),x85052),x85053))) % 14.98/14.66 [8987]P1(f862(f862(f227(f932(x89871,a921)),f862(f302(x89872,x89871,x89873),x89874)),f862(f302(x89872,x89871,x89873),x89875)))+~P1(f862(f862(f227(f932(x89872,a921)),x89874),x89875)) % 14.98/14.66 [8988]P1(f862(f862(f227(f932(x89881,a921)),f862(f303(x89881,x89882,x89883),x89884)),f862(f303(x89881,x89882,x89883),x89885)))+~P1(f862(f862(f227(f932(x89882,a921)),x89884),x89885)) % 14.98/14.66 [9069]E(x90691,f2(a92))+E(f862(f862(f251(x90692,x90693,x90692,f931(x90693,x90692)),f862(x90694,x90695)),f265(x90693,x90692,f862(f862(f3(a92),x90691),f71(a92)),x90694)),f862(f265(x90693,x90692,x90691,x90694),x90695)) % 14.98/14.66 [9176]P1(f862(f862(f247(x91761,x91762,a921,x91763),x91764),x91765))+~P1(f862(x91763,f862(f862(f244(x91761,x91762),x91764),x91765))) % 14.98/14.66 [9453]~P1(f862(f862(f247(x94532,x94533,a921,x94531),x94534),x94535))+P1(f862(x94531,f862(f862(f244(x94532,x94533),x94534),x94535))) % 14.98/14.66 [9638]~P1(f862(f862(f321(x96382),x96385),f862(f302(x96381,x96382,x96384),x96383)))+P1(f862(f862(f321(x96381),f862(f86(x96381,x96382,x96383,x96384),x96385)),x96383)) % 14.98/14.66 [9730]~P1(f862(f54(x97303),f862(f302(x97302,x97303,x97305),f234(f932(x97302,a921)))))+P1(f862(f54(x97301),f862(f302(x97302,x97301,f862(f862(f10(x97303,x97301,x97302),x97304),x97305)),f234(f932(x97302,a921))))) % 14.98/14.66 [9755]P1(f862(f862(f227(f932(f932(x97551,a921),a921)),f862(f302(f932(x97552,a921),f932(x97551,a921),f302(x97552,x97551,x97553)),f862(f300(x97552),x97554))),f862(f300(x97551),x97555)))+~P1(f862(f862(f227(f932(x97551,a921)),f862(f302(x97552,x97551,x97553),x97554)),x97555)) % 14.98/14.66 [9827]E(x98271,x98272)+~P1(f862(f59(x98273,x98274,x98275,x98271,f181(f932(x98273,a921))),x98272)) % 14.98/14.66 [9843]E(f862(f862(f244(x98431,x98432),f576(x98433,x98434,x98435,x98432,x98431)),f577(x98433,x98434,x98435,x98432,x98431)),x98435)+~P1(f862(f862(f321(f931(x98431,x98432)),x98435),f862(f862(f246(x98431,x98432),x98434),x98433))) % 14.98/14.66 [9936]P1(f862(f862(f321(x99361),f576(x99362,x99363,x99364,x99365,x99361)),x99363))+~P1(f862(f862(f321(f931(x99361,x99365)),x99364),f862(f862(f246(x99361,x99365),x99363),x99362))) % 14.98/14.66 [10095]P1(f862(f862(f321(x100951),f577(x100952,x100953,x100954,x100951,x100955)),f862(x100952,f576(x100952,x100953,x100954,x100951,x100955))))+~P1(f862(f862(f321(f931(x100955,x100951)),x100954),f862(f862(f246(x100955,x100951),x100953),x100952))) % 14.98/14.66 [10116]P1(f862(f862(f321(f931(x101161,x101161)),f862(f862(f244(x101161,x101161),x101162),f642(x101163,x101164,x101165,x101162,x101161))),x101163))+~P1(f862(f862(f321(f931(x101161,x101161)),f862(f862(f244(x101161,x101161),x101162),x101165)),f862(f862(f176(f931(x101161,x101161),a921),f862(a105,x101164)),x101163))) % 14.98/14.66 [10117]P1(f862(f862(f321(f931(x101171,x101171)),f862(f862(f244(x101171,x101171),x101172),f643(x101173,x101174,x101175,x101172,x101171))),x101173))+~P1(f862(f862(f321(f931(x101171,x101171)),f862(f862(f244(x101171,x101171),x101172),x101175)),f862(f862(f176(f931(x101171,x101171),a921),f862(a105,x101174)),x101173))) % 14.98/14.66 [10134]~P1(f862(f862(f321(f931(f925(x101341),f925(x101341))),f862(f862(f244(f925(x101341),f925(x101341)),f862(f862(f144(x101341),x101342),x101345)),x101344)),f151(x101341,x101343)))+P1(f862(f862(f321(f931(x101341,x101341)),f862(f862(f244(x101341,x101341),x101342),f661(x101343,x101344,x101345,x101342,x101341))),x101343)) % 14.98/14.66 [6541]P1(f862(x65412,x65414))+E(f170(x65411,x65412,f862(f862(f127(x65411),x65413),f862(f862(f144(x65411),x65414),x65415))),f170(x65411,x65412,x65413)) % 14.98/14.66 [6591]~P93(x65912)+E(f862(f862(f862(f103(f932(x65911,x65912)),x65913),x65914),x65915),f862(f862(f103(x65912),f862(x65913,x65915)),f862(x65914,x65915))) % 14.98/14.66 [6593]~P93(x65932)+E(f862(f862(f862(f94(f932(x65931,x65932)),x65933),x65934),x65935),f862(f862(f94(x65932),f862(x65933,x65935)),f862(x65934,x65935))) % 14.98/14.66 [6595]~P58(x65952)+E(f862(f862(f862(f3(f932(x65951,x65952)),x65953),x65954),x65955),f862(f862(f3(x65952),f862(x65953,x65955)),f862(x65954,x65955))) % 14.98/14.66 [6615]E(x66151,x66152)+E(f862(f862(f157(x66153),f862(f862(f152(x66153,x66154),x66151),x66155)),x66152),f862(f862(f157(x66153),x66154),x66152)) % 14.98/14.66 [6880]~E(x68804,f181(f932(x68803,a921)))+E(f862(f862(f103(f932(x68801,a921)),x68802),f862(f862(f33(x68803,f932(x68801,a921)),x68804),x68805)),x68802) % 14.98/14.66 [6881]~E(x68814,f181(f932(x68813,a921)))+E(f862(f862(f94(f932(x68811,a921)),x68812),f862(f862(f32(x68813,f932(x68811,a921)),x68814),x68815)),x68812) % 14.98/14.66 [6882]~E(x68824,f181(f932(x68823,a921)))+E(f862(f862(f3(f932(x68821,a921)),x68822),f862(f862(f33(x68823,f932(x68821,a921)),x68824),x68825)),x68822) % 14.98/14.66 [6897]~E(x68974,f181(f932(x68973,a921)))+E(f862(f862(f301(x68971),x68972),f862(f862(f33(x68973,f932(x68971,a921)),x68974),x68975)),f862(f862(f301(x68971),x68972),f181(f932(x68971,a921)))) % 14.98/14.66 [7695]E(f862(f862(f157(x76951),f862(f862(f147(x76952,x76951),x76953),x76954)),x76955),f862(x76953,f862(f862(f157(x76952),x76954),x76955)))+~P1(f862(f862(f228(a924),x76955),f862(f182(f925(x76952)),x76954))) % 14.98/14.66 [7759]E(f862(f862(f103(f932(x77591,a921)),f862(x77592,x77593)),f862(f862(f33(x77594,f932(x77591,a921)),x77595),x77592)),f862(f862(f33(x77594,f932(x77591,a921)),x77595),x77592))+~P1(f862(f862(f321(x77594),x77593),x77595)) % 14.98/14.66 [7760]E(f862(f862(f94(f932(x77601,a921)),f862(x77602,x77603)),f862(f862(f32(x77604,f932(x77601,a921)),x77605),x77602)),f862(f862(f32(x77604,f932(x77601,a921)),x77605),x77602))+~P1(f862(f862(f321(x77604),x77603),x77605)) % 14.98/14.66 [8372]~E(x83723,f181(f932(x83721,a921)))+E(f862(f862(f33(x83721,f932(x83722,a921)),x83723),f862(f862(f10(f932(x83722,a921),f932(x83722,a921),x83721),f862(f301(x83722),x83724)),x83725)),f181(f932(x83722,a921))) % 14.98/14.66 [8377]~P1(f862(f862(f321(x83774),x83773),x83775))+P1(f862(f862(f227(f932(x83771,a921)),f862(x83772,x83773)),f862(f862(f33(x83774,f932(x83771,a921)),x83775),x83772))) % 14.98/14.66 [8504]~E(f862(x85044,x85042),x85045)+P1(f862(f862(f321(x85041),x85042),f862(f303(x85041,x85043,x85044),f862(f862(f301(x85043),x85045),f181(f932(x85043,a921)))))) % 14.98/14.66 [8551]~P52(x85511,x85512,f862(f277(x85512,x85511),x85513))+E(f862(f862(f94(f932(x85511,a921)),f862(f276(x85512,x85511,x85513),x85514)),f862(f276(x85512,x85511,x85513),x85515)),f862(f276(x85512,x85511,x85513),f862(f862(f94(f932(x85512,a921)),x85514),x85515))) % 14.98/14.66 [8628]E(x86281,f2(a92))+E(f862(f111(x86282,x86283,f862(x86284,f862(f862(f3(a92),x86281),f71(a92)))),f862(f862(f9(x86282,a92,f926(x86283)),x86285),x86281)),f862(f191(x86282,x86283,x86284,x86285),x86281)) % 14.98/14.66 [8667]E(x86671,f181(f932(x86672,a921)))+E(f862(f862(f33(x86672,f932(x86673,a921)),x86671),f862(f862(f10(f932(x86673,a921),f932(x86673,a921),x86672),f862(f301(x86673),x86674)),x86675)),f862(f862(f301(x86673),x86674),f862(f862(f33(x86672,f932(x86673,a921)),x86671),x86675))) % 14.98/14.66 [8719]~P22(x87192,x87191,x87193,f234(f932(x87192,a921)))+E(f862(f862(f94(f932(x87191,a921)),f862(f302(x87192,x87191,x87193),x87194)),f862(f302(x87192,x87191,x87193),x87195)),f862(f302(x87192,x87191,x87193),f862(f862(f94(f932(x87192,a921)),x87194),x87195))) % 14.98/14.66 [8720]~P22(x87202,x87201,x87203,f234(f932(x87202,a921)))+E(f862(f862(f3(f932(x87201,a921)),f862(f302(x87202,x87201,x87203),x87204)),f862(f302(x87202,x87201,x87203),x87205)),f862(f302(x87202,x87201,x87203),f862(f862(f3(f932(x87202,a921)),x87204),x87205))) % 14.98/14.66 [8789]~P1(f862(f862(f60(x87891,x87892,x87895),x87893),x87894))+P1(f862(f862(f321(f931(x87891,x87892)),f862(f862(f244(x87891,x87892),x87893),x87894)),x87895)) % 14.98/14.66 [8821]P1(f862(f862(f321(x88211),x88212),f862(f275(x88213,x88211),x88214)))+~P1(f862(f862(f321(f931(x88213,x88211)),f862(f862(f244(x88213,x88211),x88215),x88212)),x88214)) % 14.98/14.66 [8823]P1(f862(f862(f321(x88231),x88232),f862(f256(x88231,x88233),x88234)))+~P1(f862(f862(f321(f931(x88231,x88233)),f862(f862(f244(x88231,x88233),x88232),x88235)),x88234)) % 14.98/14.66 [8971]P1(f862(f862(f60(x89711,x89712,x89713),x89714),x89715))+~P1(f862(f862(f321(f931(x89711,x89712)),f862(f862(f244(x89711,x89712),x89714),x89715)),x89713)) % 14.98/14.66 [9010]E(f862(x90101,x90102),x90103)+~P1(f862(f862(f321(x90104),x90102),f862(f303(x90104,x90105,x90101),f862(f862(f301(x90105),x90103),f181(f932(x90105,a921)))))) % 14.98/14.66 [9240]P1(f862(f862(f321(f931(x92401,x92402)),f862(f862(f244(x92401,x92402),x92403),x92404)),f862(f277(x92402,x92401),x92405)))+~P1(f862(f862(f321(f931(x92402,x92401)),f862(f862(f244(x92402,x92401),x92404),x92403)),x92405)) % 14.98/14.66 [9258]~P1(f862(f862(x92581,x92585),x92584))+P1(f862(f862(x92581,f862(f248(x92582,x92583),f862(f862(f244(x92582,x92583),x92584),x92585))),f862(f243(x92582,x92583),f862(f862(f244(x92582,x92583),x92584),x92585)))) % 14.98/14.66 [9288]~P1(f862(f862(f321(f931(x92882,x92881)),f862(f862(f244(x92882,x92881),x92884),x92883)),f862(f277(x92881,x92882),x92885)))+P1(f862(f862(f321(f931(x92881,x92882)),f862(f862(f244(x92881,x92882),x92883),x92884)),x92885)) % 14.98/14.66 [9321]~P1(f862(f862(f321(f931(x93213,x93211)),f862(f862(f244(x93213,x93211),x93215),x93212)),x93214))+P1(f862(f862(f321(x93211),x93212),f862(f276(x93213,x93211,x93214),f862(f862(f301(x93213),x93215),f181(f932(x93213,a921)))))) % 14.98/14.66 [9369]P1(f862(f862(f321(f931(x93691,x93692)),f862(f862(f244(x93691,x93692),x93693),x93694)),x93695))+~P1(f862(f862(f321(x93692),x93694),f862(f276(x93691,x93692,x93695),f862(f862(f301(x93691),x93693),f181(f932(x93691,a921)))))) % 14.98/14.66 [9460]~P72(x94601)+E(f862(f862(f8(a924,x94601),x94602),f296(a924,f862(f862(f73(a924),x94603),x94604),f862(f862(f73(a924),x94605),x94604))),f862(f862(f8(a924,x94601),f862(f862(f10(a924,x94601,a924),x94602),f862(f862(f9(a924,a924,a924),f73(a924)),x94604))),f296(a924,x94603,x94605))) % 14.98/14.66 [9479]~P72(x94791)+E(f862(f862(f8(a924,x94791),x94792),f862(f295(a924,f862(f862(f73(a924),x94793),x94794)),f862(f862(f73(a924),x94795),x94794))),f862(f862(f8(a924,x94791),f862(f862(f10(a924,x94791,a924),x94792),f862(f862(f9(a924,a924,a924),f73(a924)),x94794))),f862(f295(a924,x94793),x94795))) % 14.98/14.66 [9535]~P22(x95351,x95352,x95353,f234(f932(x95351,a921)))+E(f862(f862(f147(x95351,x95352),x95353),f862(f129(x95351,f862(f862(f10(a921,a921,x95351),a314),f862(a317,x95354))),x95355)),f862(f129(x95352,f862(f862(f10(a921,a921,x95352),a314),f862(a317,f862(x95353,x95354)))),f862(f862(f147(x95351,x95352),x95353),x95355))) % 14.98/14.66 [9554]~P22(x95541,x95542,x95543,f862(f862(f301(x95541),x95544),f862(f165(x95541),x95545)))+E(f862(f862(f147(x95541,x95542),x95543),f862(f129(x95541,f862(f862(f10(a921,a921,x95541),a314),f862(a317,x95544))),x95545)),f862(f129(x95542,f862(f862(f10(a921,a921,x95542),a314),f862(a317,f862(x95543,x95544)))),f862(f862(f147(x95541,x95542),x95543),x95545))) % 14.98/14.66 [9718]P1(f862(f862(f321(f931(f925(x97181),f925(x97181))),f862(f862(f244(f925(x97181),f925(x97181)),f862(f862(f144(x97181),x97182),x97183)),f862(f862(f144(x97181),x97184),x97183))),f150(x97181,x97185)))+~P1(f862(f862(f321(f931(x97181,x97181)),f862(f862(f244(x97181,x97181),x97182),x97184)),x97185)) % 14.98/14.66 [9838]E(f862(f862(f301(x98381),f832(x98382,x98383,x98384,x98385,x98381)),f838(x98382,x98383,x98384,x98385,x98381)),f862(f862(f301(x98381),x98384),x98383))+~P1(f862(f55(x98381,x98385,f862(f862(f301(x98381),x98384),x98383)),x98382)) % 14.98/14.66 [9839]E(f862(f862(f301(x98391),f853(x98392,x98393,x98394,x98395,x98391)),f870(x98392,x98393,x98394,x98395,x98391)),f862(f862(f301(x98391),x98394),x98393))+~P1(f862(f55(x98391,x98395,f862(f862(f301(x98391),x98394),x98393)),x98392)) % 14.98/14.66 [9921]P1(f862(f862(f321(x99211),f491(x99212,x99213,x99214,x99215,x99211)),x99214))+P1(f862(f862(f862(f32(x99211,f932(x99215,a921)),x99214),x99213),x99212)) % 14.98/14.66 [9926]P1(f862(f862(f321(x99261),f483(x99262,x99263,x99261,x99264,x99265)),x99263))+P1(f862(f862(f321(x99265),x99264),f862(f862(f32(x99261,f932(x99265,a921)),x99263),x99262))) % 14.98/14.66 [9934]P1(f862(f862(f321(x99341),f482(x99342,x99343,x99341,x99344,x99345)),x99343))+P1(f862(f862(f227(f932(x99345,a921)),x99344),f862(f862(f32(x99341,f932(x99345,a921)),x99343),x99342))) % 14.98/14.66 [9935]P1(f862(f862(f321(x99351),f839(x99352,x99353,x99354,x99355,x99351)),x99355))+P1(f862(f862(f227(f932(x99354,a921)),x99353),f862(f862(f32(x99351,f932(x99354,a921)),x99355),x99352))) % 14.98/14.66 [9937]P1(f862(f862(x99371,f488(x99372,x99371,x99373,x99374,x99375)),x99372))+~P1(f862(f862(f862(f33(x99375,f932(x99374,a921)),x99373),x99371),x99372)) % 14.98/14.66 [9941]P1(f862(f862(f321(x99411),f488(x99412,x99413,x99414,x99415,x99411)),x99414))+~P1(f862(f862(f862(f33(x99411,f932(x99415,a921)),x99414),x99413),x99412)) % 14.98/14.66 [9942]P50(x99424,f862(f862(f32(x99421,f932(x99424,a921)),x99425),x99423),f862(f862(f32(x99421,f932(f931(x99424,x99424),a921)),x99425),x99422))+P1(f862(f862(f321(x99421),f781(x99422,x99423,x99424,x99425,x99421)),x99425)) % 14.98/14.66 [9943]P50(x99434,f862(f862(f33(x99431,f932(x99434,a921)),x99435),x99433),f862(f862(f33(x99431,f932(f931(x99434,x99434),a921)),x99435),x99432))+P1(f862(f862(f321(x99431),f831(x99432,x99433,x99434,x99435,x99431)),x99435)) % 14.98/14.66 [9953]P1(f862(f862(f321(x99531),f484(x99532,x99533,x99531,x99534,x99535)),x99533))+~P1(f862(f862(f321(x99535),x99534),f862(f862(f33(x99531,f932(x99535,a921)),x99533),x99532))) % 14.98/14.66 [9959]P1(f862(f862(f321(x99591),x99592),f862(x99593,f484(x99593,x99594,x99595,x99592,x99591))))+~P1(f862(f862(f321(x99591),x99592),f862(f862(f33(x99595,f932(x99591,a921)),x99594),x99593))) % 14.98/14.66 [10042]~P1(f862(f862(x100424,f491(x100425,x100424,x100423,x100422,x100421)),x100425))+P1(f862(f862(f862(f32(x100421,f932(x100422,a921)),x100423),x100424),x100425)) % 14.98/14.66 [10045]~P1(f862(f862(f321(x100451),x100452),f862(x100455,f483(x100455,x100454,x100453,x100452,x100451))))+P1(f862(f862(f321(x100451),x100452),f862(f862(f32(x100453,f932(x100451,a921)),x100454),x100455))) % 14.98/14.66 [10049]~P50(x100491,f862(x100494,f781(x100495,x100494,x100491,x100493,x100492)),f862(x100495,f781(x100495,x100494,x100491,x100493,x100492)))+P50(x100491,f862(f862(f32(x100492,f932(x100491,a921)),x100493),x100494),f862(f862(f32(x100492,f932(f931(x100491,x100491),a921)),x100493),x100495)) % 14.98/14.66 [10050]~P50(x100501,f862(x100504,f831(x100505,x100504,x100501,x100503,x100502)),f862(x100505,f831(x100505,x100504,x100501,x100503,x100502)))+P50(x100501,f862(f862(f33(x100502,f932(x100501,a921)),x100503),x100504),f862(f862(f33(x100502,f932(f931(x100501,x100501),a921)),x100503),x100505)) % 14.98/14.66 [10051]~P1(f862(f862(f227(f932(x100511,a921)),x100512),f862(x100515,f482(x100515,x100514,x100513,x100512,x100511))))+P1(f862(f862(f227(f932(x100511,a921)),x100512),f862(f862(f32(x100513,f932(x100511,a921)),x100514),x100515))) % 14.98/14.66 [10052]~P1(f862(f862(f227(f932(x100521,a921)),x100522),f862(x100525,f839(x100525,x100522,x100521,x100524,x100523))))+P1(f862(f862(f227(f932(x100521,a921)),x100522),f862(f862(f32(x100523,f932(x100521,a921)),x100524),x100525))) % 14.98/14.66 [10120]~P1(f862(f862(f321(x101201),f832(x101205,x101204,x101203,x101202,x101201)),f838(x101205,x101204,x101203,x101202,x101201)))+~P1(f862(f55(x101201,x101202,f862(f862(f301(x101201),x101203),x101204)),x101205)) % 14.98/14.66 [10121]~P1(f862(f862(f321(x101211),f853(x101215,x101214,x101213,x101212,x101211)),f870(x101215,x101214,x101213,x101212,x101211)))+~P1(f862(f55(x101211,x101212,f862(f862(f301(x101211),x101213),x101214)),x101215)) % 14.98/14.66 [10122]~P1(f862(f862(f321(f931(x101221,x101221)),f862(f862(f244(x101221,x101221),x101222),x101225)),f862(f862(f176(f931(x101221,x101221),a921),f862(a105,x101224)),x101223)))+P1(f862(f862(f321(f931(x101221,x101221)),f862(f862(f244(x101221,x101221),x101222),f644(x101223,x101224,x101225,x101222,x101221))),f862(f862(f176(f931(x101221,x101221),a921),x101224),x101223))) % 14.98/14.66 [10128]P1(f862(f59(x101281,x101281,x101282,f832(x101283,x101284,x101285,x101282,x101281),f838(x101283,x101284,x101285,x101282,x101281)),x101283))+~P1(f862(f55(x101281,x101282,f862(f862(f301(x101281),x101285),x101284)),x101283)) % 14.98/14.66 [10129]P1(f862(f59(x101291,x101291,x101292,f853(x101293,x101294,x101295,x101292,x101291),f870(x101293,x101294,x101295,x101292,x101291)),x101293))+~P1(f862(f55(x101291,x101292,f862(f862(f301(x101291),x101295),x101294)),x101293)) % 14.98/14.66 [10139]~P109(x101391)+P11(x101391,f862(f862(f147(x101392,x101391),x101393),f862(f129(x101392,f862(f862(f9(x101392,x101391,a921),f862(f862(f10(x101391,f932(x101391,a921),x101392),a317),x101393)),f862(x101394,x101395))),x101395))) % 14.98/14.66 [10179]~P1(f862(f862(f321(x101792),x101795),f862(f276(x101791,x101792,x101794),x101793)))+P1(f862(f862(f321(f931(x101791,x101792)),f862(f862(f244(x101791,x101792),f521(x101793,x101794,x101791,x101795,x101792)),x101795)),x101794)) % 14.98/14.66 [10180]~P1(f862(f862(f321(x101802),x101805),f862(f276(x101801,x101802,x101804),x101803)))+P1(f862(f862(f321(f931(x101801,x101802)),f862(f862(f244(x101801,x101802),f526(x101803,x101804,x101801,x101805,x101802)),x101805)),x101804)) % 14.98/14.66 [10200]~P1(f862(f862(f321(f931(x102001,x102001)),f862(f862(f244(x102001,x102001),x102005),x102004)),f862(f862(f176(f931(x102001,x102001),a921),f862(a105,x102003)),x102002)))+P1(f862(f862(f321(f931(x102001,x102001)),f862(f862(f244(x102001,x102001),f644(x102002,x102003,x102004,x102005,x102001)),x102004)),x102002)) % 14.98/14.66 [10203]~P1(f862(f862(f321(f931(x102031,x102031)),f862(f862(f244(x102031,x102031),x102035),x102034)),f862(f862(f176(f931(x102031,x102031),a921),f862(a105,x102033)),x102032)))+P1(f862(f862(f321(f931(x102031,x102031)),f862(f862(f244(x102031,x102031),f642(x102032,x102033,x102034,x102035,x102031)),x102034)),f862(f862(f176(f931(x102031,x102031),a921),x102033),x102032))) % 14.98/14.66 [10204]~P1(f862(f862(f321(f931(x102041,x102041)),f862(f862(f244(x102041,x102041),x102045),x102044)),f862(f862(f176(f931(x102041,x102041),a921),f862(a105,x102043)),x102042)))+P1(f862(f862(f321(f931(x102041,x102041)),f862(f862(f244(x102041,x102041),f643(x102042,x102043,x102044,x102045,x102041)),x102044)),f862(f862(f176(f931(x102041,x102041),a921),x102043),x102042))) % 14.98/14.66 [10205]~P1(f862(f862(f321(f931(f925(x102051),f925(x102051))),f862(f862(f244(f925(x102051),f925(x102051)),x102055),f862(f862(f144(x102051),x102054),x102053))),f151(x102051,x102052)))+P1(f862(f862(f321(f931(x102051,x102051)),f862(f862(f244(x102051,x102051),f660(x102052,x102053,x102054,x102055,x102051)),x102054)),x102052)) % 14.98/14.66 [7780]~E(x77803,f181(f932(x77802,a921)))+E(f862(f862(f103(f932(x77801,a921)),f862(f862(f33(x77802,f932(x77801,a921)),x77803),x77804)),x77805),x77805) % 14.98/14.66 [7781]~E(x77813,f181(f932(x77812,a921)))+E(f862(f862(f94(f932(x77811,a921)),f862(f862(f32(x77812,f932(x77811,a921)),x77813),x77814)),x77815),x77815) % 14.98/14.66 [8211]~E(x82113,f181(f932(x82112,a921)))+E(f862(f862(f3(f932(x82111,a921)),f862(f862(f32(x82112,f932(x82111,a921)),x82113),x82114)),x82115),f862(f862(f3(f932(x82111,a921)),f234(f932(x82111,a921))),x82115)) % 14.98/14.66 [8346]E(f862(f862(f152(x83461,f862(f862(f127(x83461),x83462),x83463)),x83464),x83465),f862(f862(f127(x83461),f862(f862(f152(x83461,x83462),x83464),x83465)),x83463))+~P1(f862(f862(f228(a924),x83464),f862(f182(f925(x83461)),x83462))) % 14.98/14.66 [8618]E(f862(f862(f157(x86181),f862(f862(f147(a924,x86181),x86182),f132(a924,f862(f295(a924,x86183),x86184)))),x86185),f862(x86182,f862(f862(f73(a924),x86183),x86185)))+~P1(f862(f862(f228(a924),x86185),f862(f862(f3(a924),x86184),x86183))) % 14.98/14.66 [8632]E(x86321,f2(a92))+E(f115(x86322,x86323,f862(x86324,f862(f862(f3(a92),x86321),f71(a92))),f862(f862(f9(x86322,a92,f926(f928(x86323))),x86325),x86321)),f862(f189(x86322,x86323,x86324,x86325),x86321)) % 14.98/14.66 [8657]~E(x86573,f181(f932(x86571,a921)))+E(f862(f862(f32(x86571,f932(x86572,a921)),x86573),f862(f862(f10(f932(x86572,a921),f932(x86572,a921),x86571),f862(f94(f932(x86572,a921)),x86574)),x86575)),f234(f932(x86572,a921))) % 14.98/14.66 [8658]~E(x86583,f181(f932(x86581,a921)))+E(f862(f862(f32(x86581,f932(x86582,a921)),x86583),f862(f862(f10(f932(x86582,a921),f932(x86582,a921),x86581),f862(f3(f932(x86582,a921)),x86584)),x86585)),f234(f932(x86582,a921))) % 14.98/14.66 [8659]~E(x86593,f181(f932(x86591,a921)))+E(f862(f862(f33(x86591,f932(x86592,a921)),x86593),f862(f862(f10(f932(x86592,a921),f932(x86592,a921),x86591),f862(f103(f932(x86592,a921)),x86594)),x86595)),f181(f932(x86592,a921))) % 14.98/14.66 [8661]~P146(x86612)+E(f862(f862(f8(x86611,x86612),f862(f862(f10(x86612,x86612,x86611),f862(f74(x86612),x86613)),x86614)),x86615),f862(f862(f74(x86612),x86613),f862(f862(f8(x86611,x86612),x86614),x86615))) % 14.98/14.66 [8955]E(x89551,f181(f932(x89552,a921)))+E(f862(f862(f32(x89552,f932(x89553,a921)),x89551),f862(f862(f10(f932(x89553,a921),f932(x89553,a921),x89552),f862(f94(f932(x89553,a921)),x89554)),x89555)),f862(f862(f94(f932(x89553,a921)),x89554),f862(f862(f32(x89552,f932(x89553,a921)),x89551),x89555))) % 14.98/14.66 [8956]E(x89561,f181(f932(x89562,a921)))+E(f862(f862(f32(x89562,f932(x89563,a921)),x89561),f862(f862(f10(f932(x89563,a921),f932(x89563,a921),x89562),f862(f3(f932(x89563,a921)),x89564)),x89565)),f862(f862(f3(f932(x89563,a921)),x89564),f862(f862(f33(x89562,f932(x89563,a921)),x89561),x89565))) % 14.98/14.66 [8957]E(x89571,f181(f932(x89572,a921)))+E(f862(f862(f33(x89572,f932(x89573,a921)),x89571),f862(f862(f10(f932(x89573,a921),f932(x89573,a921),x89572),f862(f103(f932(x89573,a921)),x89574)),x89575)),f862(f862(f103(f932(x89573,a921)),x89574),f862(f862(f33(x89572,f932(x89573,a921)),x89571),x89575))) % 14.98/14.66 [9158]~P1(f862(f862(f228(a924),f862(x91584,x91582)),f862(x91584,x91583)))+P1(f862(f862(f321(f931(x91581,x91581)),f862(f862(f244(x91581,x91581),x91582),x91583)),f146(x91581,f862(f862(f144(f932(x91581,a924)),x91584),x91585)))) % 14.98/14.66 [9425]~P22(x94252,x94251,x94253,f862(f862(f103(f932(x94252,a921)),x94254),x94255))+E(f862(f862(f94(f932(x94251,a921)),f862(f302(x94252,x94251,x94253),f862(f862(f3(f932(x94252,a921)),x94254),x94255))),f862(f302(x94252,x94251,x94253),f862(f862(f3(f932(x94252,a921)),x94255),x94254))),f181(f932(x94251,a921))) % 14.98/14.66 [9684]~P22(x96843,x96841,x96845,f234(f932(x96843,a921)))+E(f862(f66(x96841,x96842,x96843,f862(f66(x96843,x96842,x96841,x96844),f86(x96843,x96841,f234(f932(x96843,a921)),x96845))),x96845),x96844) % 14.98/14.66 [9714]~P1(f862(f862(f227(f932(x97143,a921)),f862(f276(x97141,x97143,x97144),x97142)),x97145))+P1(f862(f862(f227(f932(x97141,a921)),x97142),f862(f72(f932(x97141,a921)),f862(f276(x97143,x97141,f862(f277(x97141,x97143),x97144)),f862(f72(f932(x97143,a921)),x97145))))) % 14.98/14.66 [9739]~P22(x97391,x97392,x97393,f862(f862(f301(x97391),x97394),x97395))+~P1(f862(f862(f321(x97392),f862(x97393,x97394)),f862(f302(x97391,x97392,x97393),f862(f862(f3(f932(x97391,a921)),x97395),f862(f862(f301(x97391),x97394),f181(f932(x97391,a921))))))) % 14.98/14.66 [9792]P1(f862(f862(f227(f932(x97921,a921)),f862(f276(x97922,x97921,x97923),x97924)),x97925))+~P1(f862(f862(f227(f932(x97922,a921)),x97924),f862(f72(f932(x97922,a921)),f862(f276(x97921,x97922,f862(f277(x97922,x97921),x97923)),f862(f72(f932(x97921,a921)),x97925))))) % 14.98/14.66 [9865]~P86(x98651)+P1(f862(f862(f227(x98651),f862(f69(x98651),f862(f862(f3(x98651),f862(f862(f73(x98651),x98652),x98653)),f862(f862(f73(x98651),x98654),x98655)))),f862(f862(f73(x98651),f862(f69(x98651),f862(f862(f3(x98651),x98652),x98654))),f862(f69(x98651),f862(f862(f3(x98651),x98653),x98655))))) % 14.98/14.66 [9974]P1(f862(f862(f321(x99741),f485(x99742,x99743,x99744,x99741,x99745)),x99744))+P1(f862(f862(f227(f932(x99745,a921)),f862(f862(f33(x99741,f932(x99745,a921)),x99744),x99743)),x99742)) % 14.98/14.66 [10157]~P1(f862(f862(f227(f932(x101571,a921)),f862(x101574,f485(x101575,x101574,x101573,x101572,x101571))),x101575))+P1(f862(f862(f227(f932(x101571,a921)),f862(f862(f33(x101572,f932(x101571,a921)),x101573),x101574)),x101575)) % 14.98/14.66 [8768]E(f862(f862(f127(x87681),x87682),f862(f862(f152(x87681,x87683),f862(f862(f3(a924),x87684),f862(f182(f925(x87681)),x87682))),x87685)),f862(f862(f152(x87681,f862(f862(f127(x87681),x87682),x87683)),x87684),x87685))+P1(f862(f862(f228(a924),x87684),f862(f182(f925(x87681)),x87682))) % 14.98/14.66 [8796]~P140(x87961)+E(f862(f862(f73(x87961),f862(f862(f74(x87961),x87962),x87963)),f862(f862(f73(x87961),f862(f862(f74(x87961),x87964),x87963)),x87965)),f862(f862(f73(x87961),f862(f862(f74(x87961),f862(f862(f73(x87961),x87962),x87964)),x87963)),x87965)) % 14.98/14.66 [9378]~P146(x93781)+E(f862(f158(x93781),f862(f862(f147(x93782,x93781),f862(f862(f10(x93781,x93781,x93782),f862(f74(x93781),x93783)),x93784)),x93785)),f862(f862(f74(x93781),x93783),f862(f158(x93781),f862(f862(f147(x93782,x93781),x93784),x93785)))) % 14.98/14.66 [9553]E(f862(f182(f925(x95531)),f862(f862(f168(x95531),f862(f862(f225(a924),f862(f182(f925(x95531)),x95532)),f862(f182(f925(x95533)),x95534))),x95532)),f862(f182(f925(x95533)),f862(f862(f168(x95533),f862(f862(f225(a924),f862(f182(f925(x95531)),x95532)),f862(f182(f925(x95533)),x95534))),x95534)))+P1(f862(x95535,f862(f862(f174(x95531,x95533),x95532),x95534))) % 14.98/14.66 [9802]~P146(x98022)+E(f862(f862(f8(x98021,x98022),f862(f862(f9(x98021,x98022,x98022),f862(f862(f10(x98022,f932(x98022,x98022),x98021),f74(x98022)),x98023)),x98024)),x98025),f862(f862(f74(x98022),f862(f862(f8(x98021,x98022),x98023),x98025)),x98024)) % 14.98/14.66 [9803]~P65(x98032)+E(f862(f862(f8(x98031,x98032),f862(f862(f9(x98031,x98032,x98032),f862(f862(f10(x98032,f932(x98032,x98032),x98031),f281(x98032)),x98033)),x98034)),x98035),f862(f862(f281(x98032),f862(f862(f8(x98031,x98032),x98033),x98035)),x98034)) % 14.98/14.66 [9810]~P59(x98102)+E(f862(f862(f8(x98101,x98102),f862(f862(f20(x98101,x98102,x98102),f862(f862(f10(x98102,f932(x98102,x98102),x98101),f3(x98102)),x98103)),x98104)),x98105),f862(f862(f3(x98102),f862(f862(f8(x98101,x98102),x98103),x98105)),f862(f862(f8(x98101,x98102),x98104),x98105))) % 14.98/14.66 [9811]~P72(x98112)+E(f862(f862(f8(x98111,x98112),f862(f862(f20(x98111,x98112,x98112),f862(f862(f10(x98112,f932(x98112,x98112),x98111),f73(x98112)),x98113)),x98114)),x98115),f862(f862(f73(x98112),f862(f862(f8(x98111,x98112),x98113),x98115)),f862(f862(f8(x98111,x98112),x98114),x98115))) % 14.98/14.66 [9812]~P71(x98122)+E(f862(f862(f11(x98121,x98122),f862(f862(f20(x98121,x98122,x98122),f862(f862(f10(x98122,f932(x98122,x98122),x98121),f74(x98122)),x98123)),x98124)),x98125),f862(f862(f74(x98122),f862(f862(f11(x98121,x98122),x98123),x98125)),f862(f862(f11(x98121,x98122),x98124),x98125))) % 14.98/14.66 [9850]~E(x98503,f181(f932(x98501,a921)))+E(f862(f862(f32(x98501,f932(x98502,a921)),x98503),f862(f862(f9(x98501,f932(x98502,a921),f932(x98502,a921)),f862(f862(f10(f932(x98502,a921),f932(f932(x98502,a921),f932(x98502,a921)),x98501),f94(f932(x98502,a921))),x98504)),x98505)),f234(f932(x98502,a921))) % 14.98/14.66 [9851]~E(x98513,f181(f932(x98511,a921)))+E(f862(f862(f32(x98511,f932(x98512,a921)),x98513),f862(f862(f9(x98511,f932(x98512,a921),f932(x98512,a921)),f862(f862(f10(f932(x98512,a921),f932(f932(x98512,a921),f932(x98512,a921)),x98511),f3(f932(x98512,a921))),x98514)),x98515)),f234(f932(x98512,a921))) % 14.98/14.66 [9852]~E(x98523,f181(f932(x98521,a921)))+E(f862(f862(f33(x98521,f932(x98522,a921)),x98523),f862(f862(f9(x98521,f932(x98522,a921),f932(x98522,a921)),f862(f862(f10(f932(x98522,a921),f932(f932(x98522,a921),f932(x98522,a921)),x98521),f103(f932(x98522,a921))),x98524)),x98525)),f181(f932(x98522,a921))) % 14.98/14.66 [9873]E(x98731,f181(f932(x98732,a921)))+E(f862(f862(f32(x98732,f932(x98733,a921)),x98731),f862(f862(f9(x98732,f932(x98733,a921),f932(x98733,a921)),f862(f862(f10(f932(x98733,a921),f932(f932(x98733,a921),f932(x98733,a921)),x98732),f94(f932(x98733,a921))),x98734)),x98735)),f862(f862(f94(f932(x98733,a921)),f862(f862(f32(x98732,f932(x98733,a921)),x98731),x98734)),x98735)) % 14.98/14.66 [9874]E(x98741,f181(f932(x98742,a921)))+E(f862(f862(f32(x98742,f932(x98743,a921)),x98741),f862(f862(f9(x98742,f932(x98743,a921),f932(x98743,a921)),f862(f862(f10(f932(x98743,a921),f932(f932(x98743,a921),f932(x98743,a921)),x98742),f3(f932(x98743,a921))),x98744)),x98745)),f862(f862(f3(f932(x98743,a921)),f862(f862(f32(x98742,f932(x98743,a921)),x98741),x98744)),x98745)) % 14.98/14.66 [9875]E(x98751,f181(f932(x98752,a921)))+E(f862(f862(f33(x98752,f932(x98753,a921)),x98751),f862(f862(f9(x98752,f932(x98753,a921),f932(x98753,a921)),f862(f862(f10(f932(x98753,a921),f932(f932(x98753,a921),f932(x98753,a921)),x98752),f103(f932(x98753,a921))),x98754)),x98755)),f862(f862(f103(f932(x98753,a921)),f862(f862(f33(x98752,f932(x98753,a921)),x98751),x98754)),x98755)) % 14.98/14.66 [9430]~P1(f862(f862(f227(a924),x94301),x94304))+E(f862(f862(f3(a924),f862(f862(f73(a924),f862(f862(f74(a924),x94301),x94302)),x94303)),f862(f862(f73(a924),f862(f862(f74(a924),x94304),x94302)),x94305)),f862(f862(f3(a924),x94303),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x94304),x94301)),x94302)),x94305))) % 14.98/14.66 [10025]~P146(x100251)+E(f862(f158(x100251),f862(f862(f147(x100252,x100251),f862(f862(f9(x100252,x100251,x100251),f862(f862(f10(x100251,f932(x100251,x100251),x100252),f74(x100251)),x100253)),x100254)),x100255)),f862(f862(f74(x100251),f862(f158(x100251),f862(f862(f147(x100252,x100251),x100253),x100255))),x100254)) % 14.98/14.66 [10031]~P59(x100311)+E(f862(f158(x100311),f862(f862(f147(x100312,x100311),f862(f862(f20(x100312,x100311,x100311),f862(f862(f10(x100311,f932(x100311,x100311),x100312),f3(x100311)),x100313)),x100314)),x100315)),f862(f862(f3(x100311),f862(f158(x100311),f862(f862(f147(x100312,x100311),x100313),x100315))),f862(f158(x100311),f862(f862(f147(x100312,x100311),x100314),x100315)))) % 14.98/14.66 [10032]~P72(x100321)+E(f862(f158(x100321),f862(f862(f147(x100322,x100321),f862(f862(f20(x100322,x100321,x100321),f862(f862(f10(x100321,f932(x100321,x100321),x100322),f73(x100321)),x100323)),x100324)),x100325)),f862(f862(f73(x100321),f862(f158(x100321),f862(f862(f147(x100322,x100321),x100323),x100325))),f862(f158(x100321),f862(f862(f147(x100322,x100321),x100324),x100325)))) % 14.98/14.66 [10170]P1(f862(x101701,f862(f862(f174(x101702,x101703),x101704),x101705)))+~P1(f862(x101701,f862(f862(f174(x101702,x101703),f862(f862(f168(x101702),f862(f862(f225(a924),f862(f182(f925(x101702)),x101704)),f862(f182(f925(x101703)),x101705))),x101704)),f862(f862(f168(x101703),f862(f862(f225(a924),f862(f182(f925(x101702)),x101704)),f862(f182(f925(x101703)),x101705))),x101705)))) % 14.98/14.66 [10431]~P1(f862(f862(f321(f931(x104312,x104311)),f862(f862(f244(x104312,x104311),x104314),x104315)),f862(f277(x104311,x104312),x104313)))+P1(f862(f862(f235(x104311,x104312,f862(f862(f9(x104311,f932(f931(x104311,x104312),a921),f932(x104312,a921)),f862(f862(f10(f932(x104312,f932(f932(f931(x104311,x104312),a921),a921)),f932(f932(f931(x104311,x104312),a921),f932(x104312,a921)),x104311),f9(x104312,f932(f931(x104311,x104312),a921),a921)),f862(f862(f10(f932(x104312,f931(x104311,x104312)),f932(x104312,f932(f932(f931(x104311,x104312),a921),a921)),x104311),f862(f10(f931(x104311,x104312),f932(f932(f931(x104311,x104312),a921),a921),x104312),f321(f931(x104311,x104312)))),f244(x104311,x104312)))),x104313)),x104314),x104315)) % 14.98/14.66 [10441]P1(f862(f862(f321(f931(x104411,x104412)),f862(f862(f244(x104411,x104412),x104413),x104414)),f862(f277(x104412,x104411),x104415)))+~P1(f862(f862(f235(x104412,x104411,f862(f862(f9(x104412,f932(f931(x104412,x104411),a921),f932(x104411,a921)),f862(f862(f10(f932(x104411,f932(f932(f931(x104412,x104411),a921),a921)),f932(f932(f931(x104412,x104411),a921),f932(x104411,a921)),x104412),f9(x104411,f932(f931(x104412,x104411),a921),a921)),f862(f862(f10(f932(x104411,f931(x104412,x104411)),f932(x104411,f932(f932(f931(x104412,x104411),a921),a921)),x104412),f862(f10(f931(x104412,x104411),f932(f932(f931(x104412,x104411),a921),a921),x104411),f321(f931(x104412,x104411)))),f244(x104412,x104411)))),x104415)),x104413),x104414)) % 14.98/14.66 [9683]~P1(f862(f862(f227(a924),x96834),x96831))+E(f862(f862(f3(a924),f862(f862(f73(a924),f862(f862(f74(a924),x96831),x96832)),x96833)),f862(f862(f73(a924),f862(f862(f74(a924),x96834),x96832)),x96835)),f862(f862(f3(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x96831),x96834)),x96832)),x96833)),x96835)) % 14.98/14.66 [7470]E(x74701,x74702)+~E(f213(x74703,x74704,x74705,x74701),f213(x74703,x74704,x74706,x74702)) % 14.98/14.66 [7471]E(x74711,x74712)+~E(f213(x74713,x74714,x74711,x74715),f213(x74713,x74714,x74712,x74716)) % 14.98/14.66 [8601]~P17(x86015,x86011,x86012,x86016)+E(f862(f66(x86011,x86011,x86011,f862(x86012,x86013)),f862(x86012,x86014)),f862(f66(x86011,x86011,x86011,f862(x86012,x86014)),f862(x86012,x86013))) % 14.98/14.66 [8840]~P54(x88404,x88405,x88402,x88401,x88406)+E(f862(x88401,f862(x88402,x88403)),x88403) % 14.98/14.66 [9008]P22(x90081,x90082,x90083,x90084)+~P22(x90081,x90085,f862(f66(x90082,x90085,x90081,x90086),x90083),x90084) % 14.98/14.66 [9083]~E(x90836,x90834)+E(f862(f68(x90831,x90832,x90833,x90834,x90835),x90836),x90835) % 14.98/14.66 [9089]E(x90891,x90892)+E(f862(f68(x90893,x90894,x90895,x90892,x90896),x90891),f862(x90895,x90891)) % 14.98/14.66 [9101]~P22(x91014,x91012,f862(f66(x91011,x91012,x91014,x91013),x91015),x91016)+P22(x91011,x91012,x91013,f862(f302(x91014,x91011,x91015),x91016)) % 14.98/14.66 [9543]~P54(x95436,x95435,x95434,x95431,x95433)+E(f862(x95431,f884(x95432,x95433,x95431,x95434,x95435)),x95432) % 14.98/14.66 [9813]P1(f862(f54(x98131),x98132))+~P1(f862(f59(x98131,x98133,x98134,x98135,x98132),x98136)) % 14.98/14.66 [9822]~P1(f862(f862(f321(x98224),x98223),f291(x98224,x98225,x98221,x98222,x98226)))+P1(f862(f862(x98221,x98222),x98223)) % 14.98/14.66 [9823]~P1(f862(f862(f321(x98234),x98233),f288(x98234,x98231,x98235,x98232,x98236)))+P1(f862(f862(x98231,x98232),x98233)) % 14.98/14.66 [9824]~P1(f862(f862(f321(x98244),x98242),f291(x98244,x98241,x98245,x98246,x98243)))+P1(f862(f862(x98241,x98242),x98243)) % 14.98/14.66 [9825]~P1(f862(f862(f321(x98254),x98252),f288(x98254,x98255,x98251,x98256,x98253)))+P1(f862(f862(x98251,x98252),x98253)) % 14.98/14.66 [10318]P10(x103181,x103182,x103183,x103184,x103185,x103186)+~E(f862(f862(x103186,f855(x103183,x103186,x103185,x103182,x103184,x103181)),f856(x103183,x103186,x103185,x103182,x103184,x103181)),f862(f862(x103186,f854(x103183,x103186,x103185,x103182,x103184,x103181)),f857(x103183,x103186,x103185,x103182,x103184,x103181))) % 14.98/14.66 [5956]E(x59561,x59562)+~E(f862(f862(f244(x59563,x59564),x59565),x59561),f862(f862(f244(x59563,x59564),x59566),x59562)) % 14.98/14.66 [5958]E(x59581,x59582)+~E(f862(f862(f244(x59583,x59584),x59581),x59585),f862(f862(f244(x59583,x59584),x59582),x59586)) % 14.98/14.66 [6101]~P14(x61015,x61016,x61011)+E(f862(f862(x61011,x61012),f862(f862(x61011,x61013),x61014)),f862(f862(x61011,x61013),f862(f862(x61011,x61012),x61014))) % 14.98/14.66 [7538]~P30(x75384,x75381,f862(f862(f144(x75384),x75382),x75385),f862(f862(f144(x75384),x75383),x75386))+P1(f862(f862(x75381,x75382),x75383)) % 14.98/14.66 [7897]P30(x78971,x78972,x78973,x78974)+~P30(x78971,x78972,f862(f862(f144(x78971),x78975),x78973),f862(f862(f144(x78971),x78976),x78974)) % 14.98/14.66 [8945]~P54(x89455,x89451,x89452,x89456,x89454)+P1(f862(f862(f321(x89451),f862(x89452,x89453)),x89454)) % 14.98/14.66 [9149]~E(x91493,f862(f862(f144(x91491),x91495),x91496))+P1(f862(f862(f321(f931(f925(x91491),f925(x91491))),f862(f862(f244(f925(x91491),f925(x91491)),x91492),f862(f862(f127(x91491),x91492),x91493))),f140(x91491,x91494))) % 14.98/14.66 [9384]~P32(x93841,x93842,x93843,x93845,x93846)+P32(x93841,x93842,x93843,f862(f862(f168(x93841),x93844),x93845),f862(f862(f168(x93842),x93844),x93846)) % 14.98/14.66 [9385]~P32(x93851,x93852,x93853,x93855,x93856)+P32(x93851,x93852,x93853,f862(f862(f131(x93851),x93854),x93855),f862(f862(f131(x93852),x93854),x93856)) % 14.98/14.66 [9648]E(f862(f302(x96481,x96482,f68(x96481,x96482,x96483,x96484,x96485)),x96486),f862(f302(x96481,x96482,x96483),x96486))+P1(f862(f862(f321(x96481),x96484),x96486)) % 14.98/14.66 [9651]E(f862(f862(f147(x96511,x96512),f68(x96511,x96512,x96513,x96514,x96515)),x96516),f862(f862(f147(x96511,x96512),x96513),x96516))+P1(f862(f862(f321(x96511),x96514),f862(f165(x96511),x96516))) % 14.98/14.66 [9885]~P21(x98854,x98852,x98855,x98853,x98856,x98851)+E(f862(x98851,f181(f932(x98852,a921))),x98853) % 14.98/14.66 [9975]~P54(x99756,x99751,x99755,x99754,x99753)+P1(f862(f862(f321(x99751),f884(x99752,x99753,x99754,x99755,x99751)),x99753)) % 14.98/14.66 [10123]~E(f862(x101234,f862(f243(x101231,x101233),x101235)),f862(x101236,f862(f243(x101231,x101233),x101235)))+E(f862(f250(x101231,x101232,x101233,x101233,x101234,f25(x101233)),x101235),f862(f250(x101231,x101232,x101233,x101233,x101236,f25(x101233)),x101235)) % 14.98/14.66 [10124]~E(f862(x101244,f862(f248(x101241,x101242),x101245)),f862(x101246,f862(f248(x101241,x101242),x101245)))+E(f862(f250(x101241,x101241,x101242,x101243,f25(x101241),x101244),x101245),f862(f250(x101241,x101241,x101242,x101243,f25(x101241),x101246),x101245)) % 14.98/14.66 [10166]~E(f862(f250(x101662,x101666,x101663,x101663,x101661,f25(x101663)),x101664),f862(f250(x101662,x101666,x101663,x101663,x101665,f25(x101663)),x101664))+E(f862(x101661,f862(f243(x101662,x101663),x101664)),f862(x101665,f862(f243(x101662,x101663),x101664))) % 14.98/14.66 [10167]~E(f862(f250(x101672,x101672,x101673,x101676,f25(x101672),x101671),x101674),f862(f250(x101672,x101672,x101673,x101676,f25(x101672),x101675),x101674))+E(f862(x101671,f862(f248(x101672,x101673),x101674)),f862(x101675,f862(f248(x101672,x101673),x101674))) % 14.98/14.66 [9050]P1(f862(f862(f321(x90501),x90502),x90503))+~P1(f862(f862(f321(f931(x90501,x90504)),f862(f862(f244(x90501,x90504),x90502),x90505)),f862(f862(f246(x90501,x90504),x90503),x90506))) % 14.98/14.66 [9066]P1(f862(f862(f321(x90661),x90662),f862(x90663,x90664)))+~P1(f862(f862(f321(f931(x90665,x90661)),f862(f862(f244(x90665,x90661),x90664),x90662)),f862(f862(f246(x90665,x90661),x90666),x90663))) % 14.98/14.66 [9502]P1(f862(f862(f321(f931(x95021,x95021)),f862(f862(f244(x95021,x95021),f862(x95022,x95023)),f862(x95022,x95024))),x95025))+~P1(f862(f862(f321(f931(x95026,x95026)),f862(f862(f244(x95026,x95026),x95023),x95024)),f862(f862(f279(x95021,x95026),x95025),x95022))) % 14.98/14.66 [9522]~P1(f862(f862(f321(f931(x95224,x95224)),f862(f862(f244(x95224,x95224),f862(x95226,x95222)),f862(x95226,x95223))),x95225))+P1(f862(f862(f321(f931(x95221,x95221)),f862(f862(f244(x95221,x95221),x95222),x95223)),f862(f862(f279(x95224,x95221),x95225),x95226))) % 14.98/14.66 [10169]E(f862(f862(f244(x101691,x101692),f652(x101693,x101694,x101695,x101696,x101692,x101691)),f653(x101693,x101694,x101695,x101696,x101692,x101691)),x101696)+~P1(f862(f862(f321(f931(x101691,x101692)),x101696),f862(f862(f280(x101691,x101695,x101692),x101694),x101693))) % 14.98/14.66 [10389]~P1(f862(f862(f321(f931(x103891,x103896)),x103895),f862(f862(f280(x103891,x103892,x103896),x103894),x103893)))+P1(f862(f862(f321(f931(x103891,x103892)),f862(f862(f244(x103891,x103892),f652(x103893,x103894,x103892,x103895,x103896,x103891)),f654(x103893,x103894,x103892,x103895,x103896,x103891))),x103894)) % 14.98/14.66 [10390]~P1(f862(f862(f321(f931(x103906,x103902)),x103905),f862(f862(f280(x103906,x103901,x103902),x103904),x103903)))+P1(f862(f862(f321(f931(x103901,x103902)),f862(f862(f244(x103901,x103902),f654(x103903,x103904,x103901,x103905,x103902,x103906)),f653(x103903,x103904,x103901,x103905,x103902,x103906))),x103903)) % 14.98/14.66 [10391]P10(x103911,x103912,x103913,x103914,x103915,x103916)+P1(f862(f862(f321(f931(x103912,x103912)),f862(f862(f244(x103912,x103912),f857(x103913,x103916,x103915,x103912,x103914,x103911)),f856(x103913,x103916,x103915,x103912,x103914,x103911))),x103915)) % 14.98/14.66 [10392]P10(x103921,x103922,x103923,x103924,x103925,x103926)+P1(f862(f862(f321(f931(x103921,x103921)),f862(f862(f244(x103921,x103921),f854(x103923,x103926,x103925,x103922,x103924,x103921)),f855(x103923,x103926,x103925,x103922,x103924,x103921))),x103924)) % 14.98/14.66 [7967]~P3(x79672)+E(f862(f862(f32(x79671,x79672),x79673),f862(f862(f9(x79671,x79674,x79672),x79675),x79676)),f862(f862(f862(f32(x79671,f932(x79674,x79672)),x79673),x79675),x79676)) % 14.98/14.66 [7968]~P3(x79682)+E(f862(f862(f33(x79681,x79682),x79683),f862(f862(f9(x79681,x79684,x79682),x79685),x79686)),f862(f862(f862(f33(x79681,f932(x79684,x79682)),x79683),x79685),x79686)) % 14.98/14.66 [8750]E(f862(f862(f33(x87501,f932(x87502,a921)),x87503),f862(f862(f10(f932(x87502,a921),f932(x87502,a921),x87501),f862(f301(x87502),x87504)),x87505)),f862(f862(f301(x87502),x87504),f862(f862(f33(x87501,f932(x87502,a921)),x87503),x87505)))+~P1(f862(f862(f321(x87501),x87506),x87503)) % 14.98/14.66 [9202]~P3(x92022)+E(f862(f862(f32(x92021,x92022),x92023),f862(f862(f10(f932(x92024,x92022),x92022,x92021),f862(f32(x92024,x92022),x92025)),f862(f9(x92024,x92021,x92022),x92026))),f862(f862(f32(x92024,x92022),x92025),f862(f862(f10(f932(x92021,x92022),x92022,x92024),f862(f32(x92021,x92022),x92023)),x92026))) % 14.98/14.66 [9203]~P3(x92032)+E(f862(f862(f33(x92031,x92032),x92033),f862(f862(f10(f932(x92034,x92032),x92032,x92031),f862(f33(x92034,x92032),x92035)),f862(f9(x92034,x92031,x92032),x92036))),f862(f862(f33(x92034,x92032),x92035),f862(f862(f10(f932(x92031,x92032),x92032,x92034),f862(f33(x92031,x92032),x92033)),x92036))) % 14.98/14.66 [9410]P1(f862(f862(f321(x94101),x94102),f862(f165(x94101),x94103)))+~P1(f862(f862(f321(f931(x94104,x94101)),f862(f862(f244(x94104,x94101),x94105),x94102)),f862(f165(f931(x94104,x94101)),f862(f862(f174(x94104,x94101),x94106),x94103)))) % 14.98/14.66 [9411]P1(f862(f862(f321(x94111),x94112),f862(f165(x94111),x94113)))+~P1(f862(f862(f321(f931(x94111,x94114)),f862(f862(f244(x94111,x94114),x94112),x94115)),f862(f165(f931(x94111,x94114)),f862(f862(f174(x94111,x94114),x94113),x94116)))) % 14.98/14.66 [9518]P1(f862(f862(f227(f932(x95181,a921)),f862(f276(x95182,x95181,x95183),x95184)),x95185))+~P1(f862(f862(f227(f932(f931(x95182,x95181),a921)),x95183),f862(f862(f246(x95182,x95181),x95186),f862(f18(f932(x95181,a921),x95182),x95185)))) % 14.98/14.66 [9523]~P23(x95234,x95232,x95235,f234(f932(x95234,a921)),f234(f932(x95232,a921)))+E(f862(f862(f32(x95231,f932(x95232,a921)),x95233),f862(f862(f10(f932(x95234,a921),f932(x95232,a921),x95231),f302(x95234,x95232,x95235)),x95236)),f862(f302(x95234,x95232,x95235),f862(f862(f32(x95231,f932(x95234,a921)),x95233),x95236))) % 14.98/14.66 [9717]P1(f862(f862(f321(f931(f925(x97171),f925(x97171))),f862(f862(f244(f925(x97171),f925(x97171)),f862(f862(f144(x97171),x97172),x97173)),f862(f862(f144(x97171),x97174),x97175))),f140(x97171,x97176)))+~P1(f862(f862(f321(f931(x97171,x97171)),f862(f862(f244(x97171,x97171),x97172),x97174)),x97176)) % 14.98/14.66 [10165]E(f862(f862(f244(x101651,x101652),f599(x101653,x101654,x101655,x101652,x101651,x101656)),f600(x101653,x101654,x101655,x101652,x101651,x101656)),x101656)+P1(f862(f862(f321(x101655),x101654),f862(f862(f249(x101651,x101652,f932(x101655,a921)),x101653),x101656))) % 14.98/14.66 [10171]E(f862(f862(f244(x101711,x101712),f601(x101713,x101714,x101712,x101711,x101715,x101716)),f604(x101713,x101714,x101712,x101711,x101715,x101716)),x101713)+~P1(f862(f862(f321(x101716),x101715),f862(f862(f249(x101711,x101712,f932(x101716,a921)),x101714),x101713))) % 14.98/14.66 [10333]P1(f862(f862(f321(x103331),x103332),f862(f862(x103333,f601(x103334,x103333,x103335,x103336,x103332,x103331)),f604(x103334,x103333,x103335,x103336,x103332,x103331))))+~P1(f862(f862(f321(x103331),x103332),f862(f862(f249(x103336,x103335,f932(x103331,a921)),x103333),x103334))) % 14.98/14.66 [10362]~P1(f862(f862(f321(x103621),x103622),f862(f862(x103625,f599(x103625,x103622,x103621,x103624,x103623,x103626)),f600(x103625,x103622,x103621,x103624,x103623,x103626))))+P1(f862(f862(f321(x103621),x103622),f862(f862(f249(x103623,x103624,f932(x103621,a921)),x103625),x103626))) % 14.98/14.66 [8649]E(x86491,x86492)+E(f862(f862(f152(x86493,f862(f862(f152(x86493,x86494),x86491),x86495)),x86492),x86496),f862(f862(f152(x86493,f862(f862(f152(x86493,x86494),x86492),x86496)),x86491),x86495)) % 14.98/14.66 [9777]~P1(f862(f862(f321(x97773),x97776),x97775))+E(f862(f862(f301(x97771),x97772),f862(f302(x97773,x97771,x97774),f862(f862(f3(f932(x97773,a921)),x97775),f862(f862(f301(x97773),x97776),f181(f932(x97773,a921)))))),f862(f302(x97773,x97771,f68(x97773,x97771,x97774,x97776,x97772)),x97775)) % 14.98/14.66 [9281]~P1(f862(f862(x92814,x92815),x92816))+P1(f862(f862(f862(f862(f103(f932(x92811,f932(x92812,a921))),x92813),x92814),x92815),x92816)) % 14.98/14.66 [9283]~P1(f862(f862(x92833,x92835),x92836))+P1(f862(f862(f862(f862(f103(f932(x92831,f932(x92832,a921))),x92833),x92834),x92835),x92836)) % 14.98/14.66 [9575]P1(f862(f862(x95751,x95752),x95753))+~P1(f862(f862(f862(f862(f94(f932(x95754,f932(x95755,a921))),x95756),x95751),x95752),x95753)) % 14.98/14.66 [9576]P1(f862(f862(x95761,x95762),x95763))+~P1(f862(f862(f862(f862(f94(f932(x95764,f932(x95765,a921))),x95761),x95766),x95762),x95763)) % 14.98/14.66 [10013]~P72(x100132)+E(f862(f862(f8(x100131,x100132),f862(f862(f9(x100131,f932(x100133,a921),x100132),f862(f862(f10(f932(x100133,x100132),f932(f932(x100133,a921),x100132),x100131),f8(x100133,x100132)),x100134)),x100135)),x100136),f862(f862(f8(f931(x100131,x100133),x100132),f862(f249(x100131,x100133,x100132),x100134)),f862(f862(f246(x100131,x100133),x100136),f862(f18(f932(x100133,a921),x100131),x100135)))) % 14.98/14.66 [10014]~P71(x100142)+E(f862(f862(f11(x100141,x100142),f862(f862(f9(x100141,f932(x100143,a921),x100142),f862(f862(f10(f932(x100143,x100142),f932(f932(x100143,a921),x100142),x100141),f11(x100143,x100142)),x100144)),x100145)),x100146),f862(f862(f11(f931(x100141,x100143),x100142),f862(f249(x100141,x100143,x100142),x100144)),f862(f862(f246(x100141,x100143),x100146),f862(f18(f932(x100143,a921),x100141),x100145)))) % 14.98/14.66 [10148]~P72(x101482)+E(f862(f862(f8(x101481,x101482),f862(f862(f9(x101481,f932(x101483,a921),x101482),f862(f862(f10(f932(x101483,x101482),f932(f932(x101483,a921),x101482),x101481),f8(x101483,x101482)),f862(f9(x101483,x101481,x101482),x101484))),x101485)),x101486),f862(f862(f8(x101483,x101482),f862(f862(f9(x101483,f932(x101481,a921),x101482),f862(f862(f10(f932(x101481,x101482),f932(f932(x101481,a921),x101482),x101483),f8(x101481,x101482)),x101484)),x101486)),x101485)) % 14.98/14.66 [10453]~P1(f862(f862(f321(f931(x104531,x104532)),f862(f862(f244(x104531,x104532),x104535),x104536)),f862(f862(f103(f932(f931(x104531,x104532),a921)),x104533),x104534)))+P1(f862(f862(f862(f862(f103(f932(x104531,f932(x104532,a921))),f862(f862(f9(x104531,f932(f931(x104531,x104532),a921),f932(x104532,a921)),f862(f862(f10(f932(x104532,f932(f932(f931(x104531,x104532),a921),a921)),f932(f932(f931(x104531,x104532),a921),f932(x104532,a921)),x104531),f9(x104532,f932(f931(x104531,x104532),a921),a921)),f862(f862(f10(f932(x104532,f931(x104531,x104532)),f932(x104532,f932(f932(f931(x104531,x104532),a921),a921)),x104531),f862(f10(f931(x104531,x104532),f932(f932(f931(x104531,x104532),a921),a921),x104532),f321(f931(x104531,x104532)))),f244(x104531,x104532)))),x104533)),f862(f862(f9(x104531,f932(f931(x104531,x104532),a921),f932(x104532,a921)),f862(f862(f10(f932(x104532,f932(f932(f931(x104531,x104532),a921),a921)),f932(f932(f931(x104531,x104532),a921),f932(x104532,a921)),x104531),f9(x104532,f932(f931(x104531,x104532),a921),a921)),f862(f862(f10(f932(x104532,f931(x104531,x104532)),f932(x104532,f932(f932(f931(x104531,x104532),a921),a921)),x104531),f862(f10(f931(x104531,x104532),f932(f932(f931(x104531,x104532),a921),a921),x104532),f321(f931(x104531,x104532)))),f244(x104531,x104532)))),x104534)),x104535),x104536)) % 14.98/14.66 [10454]~P1(f862(f862(f321(f931(x104541,x104542)),f862(f862(f244(x104541,x104542),x104545),x104546)),f862(f862(f94(f932(f931(x104541,x104542),a921)),x104543),x104544)))+P1(f862(f862(f862(f862(f94(f932(x104541,f932(x104542,a921))),f862(f862(f9(x104541,f932(f931(x104541,x104542),a921),f932(x104542,a921)),f862(f862(f10(f932(x104542,f932(f932(f931(x104541,x104542),a921),a921)),f932(f932(f931(x104541,x104542),a921),f932(x104542,a921)),x104541),f9(x104542,f932(f931(x104541,x104542),a921),a921)),f862(f862(f10(f932(x104542,f931(x104541,x104542)),f932(x104542,f932(f932(f931(x104541,x104542),a921),a921)),x104541),f862(f10(f931(x104541,x104542),f932(f932(f931(x104541,x104542),a921),a921),x104542),f321(f931(x104541,x104542)))),f244(x104541,x104542)))),x104543)),f862(f862(f9(x104541,f932(f931(x104541,x104542),a921),f932(x104542,a921)),f862(f862(f10(f932(x104542,f932(f932(f931(x104541,x104542),a921),a921)),f932(f932(f931(x104541,x104542),a921),f932(x104542,a921)),x104541),f9(x104542,f932(f931(x104541,x104542),a921),a921)),f862(f862(f10(f932(x104542,f931(x104541,x104542)),f932(x104542,f932(f932(f931(x104541,x104542),a921),a921)),x104541),f862(f10(f931(x104541,x104542),f932(f932(f931(x104541,x104542),a921),a921),x104542),f321(f931(x104541,x104542)))),f244(x104541,x104542)))),x104544)),x104545),x104546)) % 14.98/14.66 [10463]P1(f862(f862(f321(f931(x104631,x104632)),f862(f862(f244(x104631,x104632),x104633),x104634)),f862(f862(f103(f932(f931(x104631,x104632),a921)),x104635),x104636)))+~P1(f862(f862(f862(f862(f103(f932(x104631,f932(x104632,a921))),f862(f862(f9(x104631,f932(f931(x104631,x104632),a921),f932(x104632,a921)),f862(f862(f10(f932(x104632,f932(f932(f931(x104631,x104632),a921),a921)),f932(f932(f931(x104631,x104632),a921),f932(x104632,a921)),x104631),f9(x104632,f932(f931(x104631,x104632),a921),a921)),f862(f862(f10(f932(x104632,f931(x104631,x104632)),f932(x104632,f932(f932(f931(x104631,x104632),a921),a921)),x104631),f862(f10(f931(x104631,x104632),f932(f932(f931(x104631,x104632),a921),a921),x104632),f321(f931(x104631,x104632)))),f244(x104631,x104632)))),x104635)),f862(f862(f9(x104631,f932(f931(x104631,x104632),a921),f932(x104632,a921)),f862(f862(f10(f932(x104632,f932(f932(f931(x104631,x104632),a921),a921)),f932(f932(f931(x104631,x104632),a921),f932(x104632,a921)),x104631),f9(x104632,f932(f931(x104631,x104632),a921),a921)),f862(f862(f10(f932(x104632,f931(x104631,x104632)),f932(x104632,f932(f932(f931(x104631,x104632),a921),a921)),x104631),f862(f10(f931(x104631,x104632),f932(f932(f931(x104631,x104632),a921),a921),x104632),f321(f931(x104631,x104632)))),f244(x104631,x104632)))),x104636)),x104633),x104634)) % 14.98/14.66 [10464]P1(f862(f862(f321(f931(x104641,x104642)),f862(f862(f244(x104641,x104642),x104643),x104644)),f862(f862(f94(f932(f931(x104641,x104642),a921)),x104645),x104646)))+~P1(f862(f862(f862(f862(f94(f932(x104641,f932(x104642,a921))),f862(f862(f9(x104641,f932(f931(x104641,x104642),a921),f932(x104642,a921)),f862(f862(f10(f932(x104642,f932(f932(f931(x104641,x104642),a921),a921)),f932(f932(f931(x104641,x104642),a921),f932(x104642,a921)),x104641),f9(x104642,f932(f931(x104641,x104642),a921),a921)),f862(f862(f10(f932(x104642,f931(x104641,x104642)),f932(x104642,f932(f932(f931(x104641,x104642),a921),a921)),x104641),f862(f10(f931(x104641,x104642),f932(f932(f931(x104641,x104642),a921),a921),x104642),f321(f931(x104641,x104642)))),f244(x104641,x104642)))),x104645)),f862(f862(f9(x104641,f932(f931(x104641,x104642),a921),f932(x104642,a921)),f862(f862(f10(f932(x104642,f932(f932(f931(x104641,x104642),a921),a921)),f932(f932(f931(x104641,x104642),a921),f932(x104642,a921)),x104641),f9(x104642,f932(f931(x104641,x104642),a921),a921)),f862(f862(f10(f932(x104642,f931(x104641,x104642)),f932(x104642,f932(f932(f931(x104641,x104642),a921),a921)),x104641),f862(f10(f931(x104641,x104642),f932(f932(f931(x104641,x104642),a921),a921),x104642),f321(f931(x104641,x104642)))),f244(x104641,x104642)))),x104646)),x104643),x104644)) % 14.98/14.66 [10447]~P1(f862(f862(f321(f931(x104472,x104473)),f862(f862(f244(x104472,x104473),x104475),x104476)),f862(f862(f32(x104471,f932(f931(x104472,x104473),a921)),f234(f932(x104471,a921))),x104474)))+P1(f862(f862(f862(f862(f32(x104471,f932(x104472,f932(x104473,a921))),f234(f932(x104471,a921))),f862(f862(f10(f932(f931(x104472,x104473),a921),f932(x104472,f932(x104473,a921)),x104471),f862(f9(x104472,f932(f931(x104472,x104473),a921),f932(x104473,a921)),f862(f862(f10(f932(x104473,f932(f932(f931(x104472,x104473),a921),a921)),f932(f932(f931(x104472,x104473),a921),f932(x104473,a921)),x104472),f9(x104473,f932(f931(x104472,x104473),a921),a921)),f862(f862(f10(f932(x104473,f931(x104472,x104473)),f932(x104473,f932(f932(f931(x104472,x104473),a921),a921)),x104472),f862(f10(f931(x104472,x104473),f932(f932(f931(x104472,x104473),a921),a921),x104473),f321(f931(x104472,x104473)))),f244(x104472,x104473))))),x104474)),x104475),x104476)) % 14.98/14.66 [10448]~P1(f862(f862(f321(f931(x104482,x104483)),f862(f862(f244(x104482,x104483),x104485),x104486)),f862(f862(f33(x104481,f932(f931(x104482,x104483),a921)),f234(f932(x104481,a921))),x104484)))+P1(f862(f862(f862(f862(f33(x104481,f932(x104482,f932(x104483,a921))),f234(f932(x104481,a921))),f862(f862(f10(f932(f931(x104482,x104483),a921),f932(x104482,f932(x104483,a921)),x104481),f862(f9(x104482,f932(f931(x104482,x104483),a921),f932(x104483,a921)),f862(f862(f10(f932(x104483,f932(f932(f931(x104482,x104483),a921),a921)),f932(f932(f931(x104482,x104483),a921),f932(x104483,a921)),x104482),f9(x104483,f932(f931(x104482,x104483),a921),a921)),f862(f862(f10(f932(x104483,f931(x104482,x104483)),f932(x104483,f932(f932(f931(x104482,x104483),a921),a921)),x104482),f862(f10(f931(x104482,x104483),f932(f932(f931(x104482,x104483),a921),a921),x104483),f321(f931(x104482,x104483)))),f244(x104482,x104483))))),x104484)),x104485),x104486)) % 14.98/14.66 [10457]P1(f862(f862(f321(f931(x104571,x104572)),f862(f862(f244(x104571,x104572),x104573),x104574)),f862(f862(f32(x104575,f932(f931(x104571,x104572),a921)),f234(f932(x104575,a921))),x104576)))+~P1(f862(f862(f862(f862(f32(x104575,f932(x104571,f932(x104572,a921))),f234(f932(x104575,a921))),f862(f862(f10(f932(f931(x104571,x104572),a921),f932(x104571,f932(x104572,a921)),x104575),f862(f9(x104571,f932(f931(x104571,x104572),a921),f932(x104572,a921)),f862(f862(f10(f932(x104572,f932(f932(f931(x104571,x104572),a921),a921)),f932(f932(f931(x104571,x104572),a921),f932(x104572,a921)),x104571),f9(x104572,f932(f931(x104571,x104572),a921),a921)),f862(f862(f10(f932(x104572,f931(x104571,x104572)),f932(x104572,f932(f932(f931(x104571,x104572),a921),a921)),x104571),f862(f10(f931(x104571,x104572),f932(f932(f931(x104571,x104572),a921),a921),x104572),f321(f931(x104571,x104572)))),f244(x104571,x104572))))),x104576)),x104573),x104574)) % 14.98/14.66 [10458]P1(f862(f862(f321(f931(x104581,x104582)),f862(f862(f244(x104581,x104582),x104583),x104584)),f862(f862(f33(x104585,f932(f931(x104581,x104582),a921)),f234(f932(x104585,a921))),x104586)))+~P1(f862(f862(f862(f862(f33(x104585,f932(x104581,f932(x104582,a921))),f234(f932(x104585,a921))),f862(f862(f10(f932(f931(x104581,x104582),a921),f932(x104581,f932(x104582,a921)),x104585),f862(f9(x104581,f932(f931(x104581,x104582),a921),f932(x104582,a921)),f862(f862(f10(f932(x104582,f932(f932(f931(x104581,x104582),a921),a921)),f932(f932(f931(x104581,x104582),a921),f932(x104582,a921)),x104581),f9(x104582,f932(f931(x104581,x104582),a921),a921)),f862(f862(f10(f932(x104582,f931(x104581,x104582)),f932(x104582,f932(f932(f931(x104581,x104582),a921),a921)),x104581),f862(f10(f931(x104581,x104582),f932(f932(f931(x104581,x104582),a921),a921),x104582),f321(f931(x104581,x104582)))),f244(x104581,x104582))))),x104586)),x104583),x104584)) % 14.98/14.66 [7644]E(f862(x76441,f862(x76442,x76443)),f862(x76444,x76443))+~E(f862(f66(x76445,x76446,x76447,x76441),x76442),x76444) % 14.98/14.66 [9793]E(x97931,x97932)+E(f68(x97933,x97934,f68(x97933,x97934,x97935,x97931,x97936),x97932,x97937),f68(x97933,x97934,f68(x97933,x97934,x97935,x97932,x97937),x97931,x97936)) % 14.98/14.66 [9884]~P20(x98843,x98844,x98841,x98845,x98846,x98847)+E(f862(f862(x98841,x98842),x98842),x98842) % 14.98/14.66 [6201]~E(f862(f862(f147(x62011,x62015),x62016),x62012),f862(f862(f147(x62013,x62015),x62017),x62014))+E(f862(f182(f925(x62011)),x62012),f862(f182(f925(x62013)),x62014)) % 14.98/14.66 [8680]E(f862(x86801,f862(x86802,x86803)),f862(x86804,x86803))+~E(f862(f66(x86805,x86806,x86807,x86801),x86802),f862(f66(x86806,x86806,x86807,f25(x86806)),x86804)) % 14.98/14.66 [9039]~P32(x90394,x90395,x90391,f862(f862(f144(x90394),x90392),x90396),f862(f862(f144(x90395),x90393),x90397))+P1(f862(f862(x90391,x90392),x90393)) % 14.98/14.66 [9417]P32(x94171,x94172,x94173,x94174,x94175)+~P32(x94171,x94172,x94173,f862(f862(f144(x94171),x94176),x94174),f862(f862(f144(x94172),x94177),x94175)) % 14.98/14.66 [10046]P1(f862(f862(x100461,x100462),f552(x100463,x100462,x100464,x100461)))+~P1(f862(f862(f245(x100465,x100466,x100467,x100461,x100464),x100462),x100463)) % 14.98/14.66 [10070]P1(f862(f862(x100701,f552(x100702,x100703,x100701,x100704)),x100702))+~P1(f862(f862(f245(x100705,x100706,x100707,x100704,x100701),x100703),x100702)) % 14.98/14.66 [9156]~P18(x91566,x91561,x91563,x91567)+E(f862(f66(x91561,x91561,x91562,f862(x91563,x91564)),f862(f66(x91561,x91561,x91562,f862(x91563,x91564)),x91565)),f862(f66(x91561,x91561,x91562,f862(x91563,x91564)),x91565)) % 14.98/14.66 [9526]~P32(x95263,x95262,x95264,f862(f862(f147(x95261,x95263),x95265),x95266),x95267)+P32(x95261,x95262,f862(f862(f10(x95263,f932(x95262,a921),x95261),x95264),x95265),x95266,x95267) % 14.98/14.66 [9550]P32(x95501,x95502,x95503,f862(f862(f147(x95504,x95501),x95505),x95506),x95507)+~P32(x95504,x95502,f862(f862(f10(x95501,f932(x95502,a921),x95504),x95503),x95505),x95506,x95507) % 14.98/14.66 [9155]~P1(f862(f862(f321(x91551),x91552),f862(f862(x91555,x91556),x91557)))+P1(f862(f862(f321(x91551),x91552),f862(f862(f249(x91553,x91554,f932(x91551,a921)),x91555),f862(f862(f244(x91553,x91554),x91556),x91557)))) % 14.98/14.67 [9442]P1(f862(f862(f862(x94421,x94422),x94423),x94424))+~P1(f862(f862(f862(f249(x94425,x94426,f932(x94427,a921)),x94421),f862(f862(f244(x94425,x94426),x94422),x94423)),x94424)) % 14.98/14.67 [9591]P1(f862(f862(f321(x95911),f862(f862(x95912,x95913),x95914)),f862(f302(f931(x95915,x95916),x95911,f862(f249(x95915,x95916,x95911),x95912)),x95917)))+~P1(f862(f862(f321(f931(x95915,x95916)),f862(f862(f244(x95915,x95916),x95913),x95914)),x95917)) % 14.98/14.67 [9932]P1(f862(f862(f321(f931(f925(x99321),f925(x99321))),f862(f862(f244(f925(x99321),f925(x99321)),f862(f862(f127(x99321),x99322),f862(f862(f144(x99321),x99323),x99324))),f862(f862(f127(x99321),x99322),f862(f862(f144(x99321),x99325),x99326)))),f140(x99321,x99327)))+~P1(f862(f862(f321(f931(x99321,x99321)),f862(f862(f244(x99321,x99321),x99323),x99325)),x99327)) % 14.98/14.67 [9997]~P32(x99971,x99973,x99974,x99976,f862(f862(f147(x99972,x99973),x99975),x99977))+P32(x99971,x99972,f862(f862(f9(x99971,f932(x99972,x99973),f932(x99972,a921)),f862(f862(f10(f932(x99973,a921),f932(f932(x99972,x99973),f932(x99972,a921)),x99971),f10(x99973,a921,x99972)),x99974)),x99975),x99976,x99977) % 14.98/14.67 [10074]P32(x100741,x100742,x100743,x100744,f862(f862(f147(x100745,x100742),x100746),x100747))+~P32(x100741,x100745,f862(f862(f9(x100741,f932(x100745,x100742),f932(x100745,a921)),f862(f862(f10(f932(x100742,a921),f932(f932(x100745,x100742),f932(x100745,a921)),x100741),f10(x100742,a921,x100745)),x100743)),x100746),x100744,x100747) % 14.98/14.67 [10376]P1(f862(f862(f321(x103761),f492(x103762,x103763,x103764,x103765,x103766,x103767,x103761)),x103765))+P1(f862(f862(f862(f862(f32(x103761,f932(x103767,f932(x103766,a921))),x103765),x103764),x103763),x103762)) % 14.98/14.67 [10377]P1(f862(f862(f321(x103771),f790(x103772,x103773,x103774,x103775,x103776,x103777,x103771)),x103777))+P1(f862(f862(f862(f862(f32(x103771,f932(x103773,f932(x103772,a921))),x103777),x103776),x103775),x103774)) % 14.98/14.67 [10378]P1(f862(f862(f321(x103781),f494(x103782,x103783,x103784,x103785,x103786,x103787,x103781)),x103785))+~P1(f862(f862(f862(f862(f33(x103781,f932(x103787,f932(x103786,a921))),x103785),x103784),x103783),x103782)) % 14.98/14.67 [10379]P1(f862(f862(f321(x103791),f791(x103792,x103793,x103794,x103795,x103796,x103797,x103791)),x103795))+~P1(f862(f862(f862(f862(f33(x103791,f932(x103797,f932(x103796,a921))),x103795),x103794),x103793),x103792)) % 14.98/14.67 [10412]P1(f862(f862(f862(x104121,f494(x104122,x104123,x104121,x104124,x104125,x104126,x104127)),x104123),x104122))+~P1(f862(f862(f862(f862(f33(x104127,f932(x104126,f932(x104125,a921))),x104124),x104121),x104123),x104122)) % 14.98/14.67 [10413]P1(f862(f862(f862(x104131,f791(x104132,x104133,x104131,x104134,x104135,x104136,x104137)),x104133),x104132))+~P1(f862(f862(f862(f862(f33(x104137,f932(x104136,f932(x104135,a921))),x104134),x104131),x104133),x104132)) % 14.98/14.67 [10428]~P1(f862(f862(f862(x104285,f492(x104287,x104286,x104285,x104284,x104283,x104282,x104281)),x104286),x104287))+P1(f862(f862(f862(f862(f32(x104281,f932(x104282,f932(x104283,a921))),x104284),x104285),x104286),x104287)) % 14.98/14.67 [10429]~P1(f862(f862(f862(x104295,f790(x104293,x104292,x104297,x104296,x104295,x104294,x104291)),x104296),x104297))+P1(f862(f862(f862(f862(f32(x104291,f932(x104292,f932(x104293,a921))),x104294),x104295),x104296),x104297)) % 14.98/14.67 [10446]~P1(f862(f862(f321(f931(x104461,x104463)),f862(f862(f244(x104461,x104463),x104466),x104467)),f862(f862(f280(x104461,x104462,x104463),x104464),x104465)))+P1(f862(f862(f245(x104461,x104462,x104463,f862(f862(f9(x104461,f932(f931(x104461,x104462),a921),f932(x104462,a921)),f862(f862(f10(f932(x104462,f932(f932(f931(x104461,x104462),a921),a921)),f932(f932(f931(x104461,x104462),a921),f932(x104462,a921)),x104461),f9(x104462,f932(f931(x104461,x104462),a921),a921)),f862(f862(f10(f932(x104462,f931(x104461,x104462)),f932(x104462,f932(f932(f931(x104461,x104462),a921),a921)),x104461),f862(f10(f931(x104461,x104462),f932(f932(f931(x104461,x104462),a921),a921),x104462),f321(f931(x104461,x104462)))),f244(x104461,x104462)))),x104464),f862(f862(f9(x104462,f932(f931(x104462,x104463),a921),f932(x104463,a921)),f862(f862(f10(f932(x104463,f932(f932(f931(x104462,x104463),a921),a921)),f932(f932(f931(x104462,x104463),a921),f932(x104463,a921)),x104462),f9(x104463,f932(f931(x104462,x104463),a921),a921)),f862(f862(f10(f932(x104463,f931(x104462,x104463)),f932(x104463,f932(f932(f931(x104462,x104463),a921),a921)),x104462),f862(f10(f931(x104462,x104463),f932(f932(f931(x104462,x104463),a921),a921),x104463),f321(f931(x104462,x104463)))),f244(x104462,x104463)))),x104465)),x104466),x104467)) % 14.98/14.67 [10456]P1(f862(f862(f321(f931(x104561,x104562)),f862(f862(f244(x104561,x104562),x104563),x104564)),f862(f862(f280(x104561,x104565,x104562),x104566),x104567)))+~P1(f862(f862(f245(x104561,x104565,x104562,f862(f862(f9(x104561,f932(f931(x104561,x104565),a921),f932(x104565,a921)),f862(f862(f10(f932(x104565,f932(f932(f931(x104561,x104565),a921),a921)),f932(f932(f931(x104561,x104565),a921),f932(x104565,a921)),x104561),f9(x104565,f932(f931(x104561,x104565),a921),a921)),f862(f862(f10(f932(x104565,f931(x104561,x104565)),f932(x104565,f932(f932(f931(x104561,x104565),a921),a921)),x104561),f862(f10(f931(x104561,x104565),f932(f932(f931(x104561,x104565),a921),a921),x104565),f321(f931(x104561,x104565)))),f244(x104561,x104565)))),x104566),f862(f862(f9(x104565,f932(f931(x104565,x104562),a921),f932(x104562,a921)),f862(f862(f10(f932(x104562,f932(f932(f931(x104565,x104562),a921),a921)),f932(f932(f931(x104565,x104562),a921),f932(x104562,a921)),x104565),f9(x104562,f932(f931(x104565,x104562),a921),a921)),f862(f862(f10(f932(x104562,f931(x104565,x104562)),f932(x104562,f932(f932(f931(x104565,x104562),a921),a921)),x104565),f862(f10(f931(x104565,x104562),f932(f932(f931(x104565,x104562),a921),a921),x104562),f321(f931(x104565,x104562)))),f244(x104565,x104562)))),x104567)),x104563),x104564)) % 14.98/14.67 [10388]~P146(x103882)+E(f862(f862(f8(x103881,x103882),f862(f862(f9(x103881,f932(x103883,a921),x103882),f862(f862(f10(f932(x103883,x103882),f932(f932(x103883,a921),x103882),x103881),f8(x103883,x103882)),f862(f862(f9(x103881,f932(x103883,x103882),f932(x103883,x103882)),f862(f862(f10(f932(x103882,x103882),f932(f932(x103883,x103882),f932(x103883,x103882)),x103881),f10(x103882,x103882,x103883)),f862(f862(f10(x103882,f932(x103882,x103882),x103881),f74(x103882)),x103884))),x103885))),x103886)),x103887),f862(f862(f74(x103882),f862(f862(f8(x103881,x103882),x103884),x103887)),f862(f862(f8(x103883,x103882),x103885),x103886))) % 14.98/14.67 [9475]~P17(x94757,x94751,x94753,x94758)+E(f862(f66(x94751,x94751,x94752,f862(x94753,x94754)),f862(f66(x94751,x94751,x94752,f862(x94753,x94755)),x94756)),f862(f66(x94751,x94751,x94752,f862(x94753,x94755)),f862(f66(x94751,x94751,x94752,f862(x94753,x94754)),x94756))) % 14.98/14.67 [10451]E(f862(f862(f244(x104511,x104512),f862(x104513,f583(x104514,x104515,x104513,x104516,x104517,x104518,x104512,x104511))),f862(x104515,f584(x104514,x104515,x104513,x104516,x104517,x104518,x104512,x104511))),x104518)+~P1(f862(f862(f321(f931(x104511,x104512)),x104518),f862(f302(f931(x104517,x104516),f931(x104511,x104512),f250(x104517,x104511,x104516,x104512,x104513,x104515)),x104514))) % 14.98/14.67 [10469]~P1(f862(f862(f321(f931(x104698,x104697)),x104696),f862(f302(f931(x104691,x104692),f931(x104698,x104697),f250(x104691,x104698,x104692,x104697,x104695,x104694)),x104693)))+P1(f862(f862(f321(f931(x104691,x104692)),f862(f862(f244(x104691,x104692),f583(x104693,x104694,x104695,x104692,x104691,x104696,x104697,x104698)),f584(x104693,x104694,x104695,x104692,x104691,x104696,x104697,x104698))),x104693)) % 14.98/14.67 [9922]P1(f862(f862(f321(f931(f931(x99221,x99222),f931(x99221,x99222))),f862(f862(f244(f931(x99221,x99222),f931(x99221,x99222)),f862(f862(f244(x99221,x99222),x99223),x99224)),f862(f862(f244(x99221,x99222),x99225),x99226))),f311(x99221,x99222,x99227,x99228)))+~P1(f862(f862(f321(f931(x99221,x99221)),f862(f862(f244(x99221,x99221),x99223),x99225)),x99227)) % 14.98/14.67 [10440]E(f862(f135(x104401,x104402,f862(f9(x104402,x104401,x104401),x104403),f862(x104404,x104405)),x104406),f862(x104404,f862(f135(x104407,x104402,f862(f9(x104402,x104407,x104407),x104408),x104405),x104406)))+P1(f862(f862(f321(x104402),f739(x104405,x104408,x104404,x104403,x104407,x104401,x104406,x104402)),f862(f165(x104402),x104406))) % 14.98/14.67 [10459]~E(f862(f66(x104591,x104591,x104597,f862(x104593,f739(x104595,x104598,x104594,x104593,x104597,x104591,x104596,x104592))),x104594),f862(f66(x104597,x104591,x104597,x104594),f862(x104598,f739(x104595,x104598,x104594,x104593,x104597,x104591,x104596,x104592))))+E(f862(f135(x104591,x104592,f862(f9(x104592,x104591,x104591),x104593),f862(x104594,x104595)),x104596),f862(x104594,f862(f135(x104597,x104592,f862(f9(x104592,x104597,x104597),x104598),x104595),x104596))) % 14.98/14.67 [8685]E(f862(x86851,f862(x86852,x86853)),f862(x86854,f862(x86855,x86853)))+~E(f862(f66(x86856,x86857,x86858,x86851),x86852),f862(f66(x86859,x86857,x86858,x86854),x86855)) % 14.98/14.67 [10297]P1(f862(f862(f321(f931(x102971,x102972)),f862(f862(f244(x102971,x102972),f862(x102973,x102974)),f862(x102975,x102976))),f862(f302(f931(x102977,x102978),f931(x102971,x102972),f250(x102977,x102971,x102978,x102972,x102973,x102975)),x102979)))+~P1(f862(f862(f321(f931(x102977,x102978)),f862(f862(f244(x102977,x102978),x102974),x102976)),x102979)) % 14.98/14.67 [8983]~E(f862(x89834,f862(x89835,x89836)),f862(x89839,f862(x898310,x898311)))+E(f862(f862(f66(x89831,x89832,x89833,x89834),x89835),x89836),f862(f862(f66(x89837,x89832,x89838,x89839),x898310),x898311)) % 14.98/14.67 [4753]~P109(x47531)+~P104(x47531)+E(f94(x47531),f225(x47531)) % 14.98/14.67 [4754]~P109(x47541)+~P103(x47541)+E(f103(x47541),f226(x47541)) % 14.98/14.67 [5003]~P112(x50031)+~P98(x50031)+E(f862(f69(x50031),f862(f96(x50031),a90)),f71(x50031)) % 14.98/14.67 [5298]E(x52981,f2(a1))+E(f75(a1,x52981),f862(f72(a1),f71(a1)))+P1(f862(f862(f228(a1),f2(a1)),x52981)) % 14.98/14.67 [5505]E(x55051,f2(a1))+E(f75(a1,x55051),f71(a1))+~P1(f862(f862(f228(a1),f2(a1)),x55051)) % 14.98/14.67 [7542]~P38(x75421)+P1(f862(f54(a1),x75421))+~P1(f862(f54(a924),f862(f302(a1,a924,a97),x75421))) % 14.98/14.67 [9883]E(x98831,f181(f932(f931(a924,a924),a921)))+~P1(f862(f54(f931(a924,a924)),x98831))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f181(f932(f931(a924,a924),a921))),x98831)),a27)) % 14.98/14.67 [10047]E(x100471,f2(a924))+E(x100471,f862(a105,f2(a924)))+~P1(f862(f862(f228(a924),x100471),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.67 [10326]E(x103261,f2(a92))+E(f862(f862(f73(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a24,f862(f862(f29(a92),x103261),f862(f96(a92),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))),f71(a1)),f862(a24,x103261))+E(f38(a92,x103261,f862(f96(a92),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(a92)) % 14.98/14.67 [10175]E(x101751,f2(a92))+~E(f38(a92,x101751,f862(f96(a92),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(a92))+E(f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a24,f862(f862(f29(a92),x101751),f862(f96(a92),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f862(a24,x101751)) % 14.98/14.67 [4836]~P55(x48361,x48362)+P41(x48361,x48362)+~P42(a921) % 14.98/14.67 [4763]~P147(x47631)+P26(x47631,x47632)+~E(x47632,f2(x47631)) % 14.98/14.67 [4764]~P109(x47641)+P11(x47641,x47642)+~E(x47642,f106(x47641)) % 14.98/14.67 [4774]~P112(x47741)+~E(x47742,f2(x47741))+E(f75(x47741,x47742),f2(x47741)) % 14.98/14.67 [4775]~P88(x47751)+~E(x47752,f2(x47751))+E(f75(x47751,x47752),f2(x47751)) % 14.98/14.67 [4783]~P147(x47832)+~P26(x47832,x47831)+E(x47831,f2(x47832)) % 14.98/14.67 [4829]~P112(x48292)+~E(f75(x48292,x48291),f2(x48292))+E(x48291,f2(x48292)) % 14.98/14.67 [4843]~P2(x48432)+~P63(x48431)+P2(f932(x48431,x48432)) % 14.98/14.67 [4844]~P60(x48442)+~P60(x48441)+P60(f932(x48441,x48442)) % 14.98/14.67 [4845]~P60(x48452)+~P60(x48451)+P60(f930(x48451,x48452)) % 14.98/14.67 [4846]~P60(x48462)+~P60(x48461)+P60(f931(x48461,x48462)) % 14.98/14.67 [4847]~P4(x48472)+~P4(x48471)+P4(f187(x48471,x48472)) % 14.98/14.67 [4848]~P63(x48482)+~P63(x48481)+P63(f932(x48481,x48482)) % 14.98/14.67 [4849]~P63(x48492)+~P63(x48491)+P63(f930(x48491,x48492)) % 14.98/14.67 [4850]~P63(x48502)+~P63(x48501)+P63(f931(x48501,x48502)) % 14.98/14.67 [4851]~P106(x48512)+~P106(x48511)+P106(f931(x48511,x48512)) % 14.98/14.67 [4975]~P109(x49751)+~P11(x49751,x49752)+P11(x49751,f145(x49751,x49752)) % 14.98/14.67 [5225]~P4(x52252)+~P4(x52251)+P4(f38(a1,x52251,x52252)) % 14.98/14.67 [4785]~P76(x47851)+~E(x47852,f2(x47851))+E(f862(f72(x47851),x47852),x47852) % 14.98/14.67 [4801]~P142(x48011)+~E(x48012,f2(a1))+E(f862(f95(x48011),x48012),f2(x48011)) % 14.98/14.67 [4802]~P97(x48021)+~E(x48022,f2(a1))+E(f862(f95(x48021),x48022),f2(x48021)) % 14.98/14.67 [4826]~P68(x48261)+~E(f2(x48261),x48262)+E(f862(f72(x48261),x48262),f2(x48261)) % 14.98/14.67 [4827]~P68(x48271)+~E(x48272,f2(x48271))+E(f862(f72(x48271),x48272),f2(x48271)) % 14.98/14.67 [4828]~P86(x48281)+~E(x48282,f2(x48281))+E(f862(f69(x48281),x48282),f2(x48281)) % 14.98/14.67 [4853]~P76(x48532)+E(x48531,f2(x48532))+~E(f862(f72(x48532),x48531),x48531) % 14.98/14.67 [4855]E(x48551,f862(a97,x48552))+~E(x48551,f2(a924))+~E(x48552,f862(f93(a1),x48551)) % 14.98/14.67 [4856]E(f862(a97,x48561),x48562)+~E(x48562,f2(a924))+~E(x48561,f862(f93(a1),x48562)) % 14.98/14.67 [4860]~P97(x48602)+E(x48601,f2(a1))+~E(f862(f95(x48602),x48601),f2(x48602)) % 14.98/14.67 [4864]~P68(x48642)+E(x48641,f2(x48642))+~E(f862(f72(x48642),x48641),f2(x48642)) % 14.98/14.67 [4865]~P86(x48652)+E(x48651,f2(x48652))+~E(f862(f69(x48652),x48651),f2(x48652)) % 14.98/14.67 [4866]~P68(x48661)+E(f2(x48661),x48662)+~E(f862(f72(x48661),x48662),f2(x48661)) % 14.98/14.67 [5050]~P109(x50501)+~P11(x50501,x50502)+P11(x50501,f862(f164(x50501),x50502)) % 14.98/14.67 [5077]~P1(x50772)+~P1(x50771)+P1(f862(f862(a318,x50771),x50772)) % 14.98/14.67 [5115]~E(f71(a924),f2(a924))+E(f862(f28(x51151),x51152),f2(a924))+~P1(f862(f54(x51151),x51152)) % 14.98/14.67 [5151]~P116(x51511)+~P146(x51511)+E(f862(f862(f236(x51511),f2(x51511)),f862(a105,x51512)),f2(x51511)) % 14.98/14.67 [5192]~P109(x51921)+P11(x51921,f132(x51921,x51922))+~P1(f862(f54(x51921),x51922)) % 14.98/14.67 [5193]~P109(x51931)+P11(x51931,f731(x51932,x51931))+~P1(f862(f54(x51931),x51932)) % 14.98/14.67 [5217]~P109(x52171)+E(f862(f165(x52171),f132(x52171,x52172)),x52172)+~P1(f862(f54(x52171),x52172)) % 14.98/14.67 [5218]~P109(x52181)+E(f862(f165(x52181),f731(x52182,x52181)),x52182)+~P1(f862(f54(x52181),x52182)) % 14.98/14.67 [5247]P1(x52471)+P1(x52472)+~P1(f862(f862(a319,x52472),x52471)) % 14.98/14.67 [5260]E(x52601,f181(f932(x52602,a921)))+~E(f862(f28(x52602),x52601),f2(a924))+~P1(f862(f54(x52602),x52601)) % 14.98/14.67 [5265]P1(x52651)+~P1(x52652)+~P1(f862(f862(a322,x52652),x52651)) % 14.98/14.67 [5316]~P75(x53161)+E(f862(f69(x53161),x53162),x53162)+P1(f862(f862(f228(x53161),x53162),f2(x53161))) % 14.98/14.67 [5376]~P63(x53762)+~P1(f862(f49(x53762),x53761))+P1(f862(x53761,f732(x53761,x53762))) % 14.98/14.67 [5377]~P63(x53772)+~P1(f862(f49(x53772),x53771))+P1(f862(x53771,f740(x53771,x53772))) % 14.98/14.67 [5420]E(x54201,f106(x54202))+P1(f862(f130(x54202),f107(x54202,x54201)))+~P1(f862(f130(x54202),x54201)) % 14.98/14.67 [5425]~P109(x54251)+~P1(f862(f54(x54251),x54252))+P1(f862(f130(x54251),f132(x54251,x54252))) % 14.98/14.67 [5426]~P109(x54261)+~P1(f862(f54(x54261),x54262))+P1(f862(f130(x54261),f731(x54262,x54261))) % 14.98/14.67 [5431]~P142(x54311)+E(f862(f93(x54311),f862(a97,x54312)),f862(f95(x54311),x54312))+P1(f862(f862(f228(a1),x54312),f2(a1))) % 14.98/14.67 [5453]P5(x54532,x54531)+E(f862(x54531,f524(x54531)),f862(x54531,f527(x54531)))+P1(f862(f862(x54531,f524(x54531)),f527(x54531))) % 14.98/14.67 [5466]E(f862(f93(a1),f428(x54661,x54662)),x54661)+P1(f862(x54662,f862(a97,x54661)))+~P1(f862(x54662,f2(a924))) % 14.98/14.67 [5479]~P63(x54791)+~P1(f862(x54792,f746(x54792,x54791)))+P1(f862(f50(x54791),x54792)) % 14.98/14.67 [5480]~P63(x54801)+~P1(f862(x54802,f756(x54802,x54801)))+P1(f862(f50(x54801),x54802)) % 14.98/14.67 [5515]~P112(x55151)+~E(f75(x55151,x55152),f862(f72(x55151),f71(x55151)))+P1(f862(f862(f228(x55151),x55152),f2(x55151))) % 14.98/14.67 [5591]~E(x55912,f2(a1))+E(f208(x55911,x55912),f862(f862(f244(a1,a1),f2(a1)),f71(a1)))+P1(f862(f862(f228(a1),x55912),f2(a1))) % 14.98/14.67 [5592]~E(x55921,f2(a1))+E(f208(x55921,x55922),f862(f862(f244(a1,a1),f2(a1)),f71(a1)))+P1(f862(f862(f228(a1),x55922),f2(a1))) % 14.98/14.67 [5645]E(f862(f93(a1),f428(x56451,x56452)),x56451)+P1(f862(x56452,f862(a97,x56451)))+P1(f862(f862(f228(a1),x56451),f2(a1))) % 14.98/14.67 [5713]~P112(x57131)+E(f75(x57131,x57132),f862(f72(x57131),f71(x57131)))+~P1(f862(f862(f228(x57131),x57132),f2(x57131))) % 14.98/14.67 [5714]~P86(x57141)+E(f862(f69(x57141),x57142),f862(f72(x57141),x57142))+~P1(f862(f862(f227(x57141),x57142),f2(x57141))) % 14.98/14.67 [5715]~P86(x57151)+E(f862(f69(x57151),x57152),f862(f72(x57151),x57152))+~P1(f862(f862(f228(x57151),x57152),f2(x57151))) % 14.98/14.67 [5716]~P75(x57161)+E(f862(f69(x57161),x57162),f862(f72(x57161),x57162))+~P1(f862(f862(f228(x57161),x57162),f2(x57161))) % 14.98/14.67 [5819]~P1(f862(x58191,f428(x58192,x58191)))+P1(f862(x58191,f862(a97,x58192)))+~P1(f862(x58191,f2(a924))) % 14.98/14.67 [5826]E(x58261,f2(a924))+E(f862(a105,f329(x58262,x58261)),x58261)+~P1(f862(f862(f228(a924),x58261),f862(a105,x58262))) % 14.98/14.67 [5830]P5(x58301,x58302)+~E(f862(x58302,f524(x58302)),f862(x58302,f527(x58302)))+~P1(f862(f862(x58302,f524(x58302)),f527(x58302))) % 14.98/14.67 [5848]~P109(x58481)+P11(x58481,x58482)+P1(f862(f862(f227(a924),f715(x58482,x58481)),f716(x58482,x58481))) % 14.98/14.67 [5849]~P109(x58491)+P11(x58491,x58492)+P1(f862(f862(f227(a924),f722(x58492,x58491)),f727(x58492,x58491))) % 14.98/14.67 [5935]~P86(x59351)+~E(x59352,f2(x59351))+P1(f862(f862(f227(x59351),f862(f69(x59351),x59352)),f2(x59351))) % 14.98/14.67 [6030]~P1(f862(x60301,f428(x60302,x60301)))+P1(f862(x60301,f862(a97,x60302)))+P1(f862(f862(f228(a1),x60302),f2(a1))) % 14.98/14.67 [6055]~P1(f862(x60551,f862(a97,x60552)))+P1(f862(x60551,f2(a924)))+~P1(f862(f862(f228(a1),x60552),f2(a1))) % 14.98/14.67 [6399]~P112(x63991)+~P1(f862(f862(f228(x63991),x63992),f2(x63991)))+P1(f862(f862(f228(x63991),f75(x63991,x63992)),f2(x63991))) % 14.98/14.67 [6514]~P112(x65141)+P1(f862(f862(f227(x65141),f862(f95(x65141),x65142)),f2(x65141)))+~P1(f862(f862(f227(a1),x65142),f2(a1))) % 14.98/14.67 [6515]~P112(x65151)+P1(f862(f862(f228(x65151),f862(f95(x65151),x65152)),f2(x65151)))+~P1(f862(f862(f228(a1),x65152),f2(a1))) % 14.98/14.67 [6524]~P86(x65242)+E(x65241,f2(x65242))+~P1(f862(f862(f227(x65242),f862(f69(x65242),x65241)),f2(x65242))) % 14.98/14.67 [6604]~P142(x66041)+~P1(f862(f862(f321(x66041),x66042),f102(x66041)))+P1(f862(f862(f321(x66041),f862(f72(x66041),x66042)),f102(x66041))) % 14.98/14.67 [6636]~P112(x66361)+~P1(f862(f862(f228(x66361),f75(x66361,x66362)),f2(x66361)))+P1(f862(f862(f228(x66361),x66362),f2(x66361))) % 14.98/14.67 [6808]~P112(x68082)+~P1(f862(f862(f227(x68082),f862(f95(x68082),x68081)),f2(x68082)))+P1(f862(f862(f227(a1),x68081),f2(a1))) % 14.98/14.67 [6809]~P112(x68092)+~P1(f862(f862(f228(x68092),f862(f95(x68092),x68091)),f2(x68092)))+P1(f862(f862(f228(a1),x68091),f2(a1))) % 14.98/14.67 [7313]~P76(x73131)+~P1(f862(f862(f227(x73131),x73132),f2(x73131)))+P1(f862(f862(f227(x73131),f862(f862(f73(x73131),x73132),x73132)),f2(x73131))) % 14.98/14.67 [7314]~P112(x73141)+~P1(f862(f862(f228(x73141),x73142),f2(x73141)))+P1(f862(f862(f228(x73141),f862(f862(f73(x73141),x73142),x73142)),f2(x73141))) % 14.98/14.67 [7315]~P76(x73151)+~P1(f862(f862(f228(x73151),x73152),f2(x73151)))+P1(f862(f862(f228(x73151),f862(f862(f73(x73151),x73152),x73152)),f2(x73151))) % 14.98/14.67 [7891]~P76(x78911)+~P1(f862(f862(f227(x78911),f862(f862(f73(x78911),x78912),x78912)),f2(x78911)))+P1(f862(f862(f227(x78911),x78912),f2(x78911))) % 14.98/14.67 [7892]~P112(x78921)+~P1(f862(f862(f228(x78921),f862(f862(f73(x78921),x78922),x78922)),f2(x78921)))+P1(f862(f862(f228(x78921),x78922),f2(x78921))) % 14.98/14.67 [7893]~P76(x78931)+~P1(f862(f862(f228(x78931),f862(f862(f73(x78931),x78932),x78932)),f2(x78931)))+P1(f862(f862(f228(x78931),x78932),f2(x78931))) % 14.98/14.67 [4901]~E(x49012,f71(a924))+~E(x49011,f71(a924))+E(f862(f862(f74(a924),x49011),x49012),f71(a924)) % 14.98/14.67 [4902]~E(x49022,f71(a1))+~E(x49021,f71(a1))+E(f862(f862(f74(a1),x49021),x49022),f71(a1)) % 14.98/14.67 [4903]~E(x49032,f2(a924))+~E(x49031,f2(a924))+E(f862(f862(f73(a924),x49031),x49032),f2(a924)) % 14.98/14.67 [4959]~P121(x49592)+E(x49591,f2(x49592))+E(f862(f862(f281(x49592),x49591),x49591),f71(x49592)) % 14.98/14.67 [4960]~P61(x49602)+E(x49601,f2(x49602))+E(f862(f862(f29(x49602),x49601),x49601),f71(x49602)) % 14.98/14.67 [4961]~P122(x49612)+E(x49611,f2(x49612))+E(f862(f862(f281(x49612),x49611),x49611),f71(x49612)) % 14.98/14.67 [4981]~P141(x49811)+~E(x49812,f71(x49811))+E(f862(f862(f74(x49811),x49812),x49812),f71(x49811)) % 14.98/14.67 [4982]~P76(x49821)+~E(x49822,f2(x49821))+E(f862(f862(f73(x49821),x49822),x49822),f2(x49821)) % 14.98/14.67 [4983]~P122(x49831)+~E(x49832,f2(x49831))+E(f862(f862(f281(x49831),x49832),x49832),f2(x49831)) % 14.98/14.67 [5028]~E(x50282,f2(a924))+~E(x50281,f2(a924))+E(f862(f72(a1),f862(f93(a1),x50281)),f862(f93(a1),x50282)) % 14.98/14.67 [5047]E(x50471,f71(a924))+E(x50472,f2(a924))+~E(f862(f862(f74(a924),x50472),x50471),x50472) % 14.98/14.67 [5059]E(x50591,f2(a924))+E(x50592,f2(a924))+~E(f862(f862(f74(a924),x50592),x50591),f2(a924)) % 14.98/14.67 [5086]~E(x50862,f2(a924))+~E(x50861,f862(a105,f2(a924)))+E(f862(f862(f73(a924),x50861),x50862),f862(a105,f2(a924))) % 14.98/14.67 [5087]~E(x50871,f2(a924))+~E(x50872,f862(a105,f2(a924)))+E(f862(f862(f73(a924),x50871),x50872),f862(a105,f2(a924))) % 14.98/14.67 [5094]E(x50941,f71(a1))+E(x50942,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50941),x50942),f71(a1)) % 14.98/14.67 [5095]E(x50951,f71(a1))+E(x50952,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50952),x50951),f71(a1)) % 14.98/14.67 [5096]E(x50961,f71(a1))+E(x50961,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50962),x50961),f71(a1)) % 14.98/14.67 [5098]E(x50981,f71(a1))+E(x50981,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50981),x50982),f71(a1)) % 14.98/14.67 [5123]~P76(x51232)+E(x51231,f2(x51232))+~E(f862(f862(f73(x51232),x51231),x51231),f2(x51232)) % 14.98/14.67 [5129]~E(x51291,f862(f96(a1),a90))+~E(x51292,f862(f96(a1),a90))+E(f862(f862(f74(a1),x51291),x51292),f71(a1)) % 14.98/14.67 [5140]E(x51401,f2(a924))+E(x51402,f2(a924))+~E(f862(f862(f73(a924),x51402),x51401),f862(a105,f2(a924))) % 14.98/14.67 [5150]~P64(x51501)+~P98(x51501)+E(f862(f862(f281(x51501),x51502),f862(f96(x51501),a76)),f2(x51501)) % 14.98/14.67 [5157]~P141(x51571)+~E(x51572,f862(f72(x51571),f71(x51571)))+E(f862(f862(f74(x51571),x51572),x51572),f71(x51571)) % 14.98/14.67 [5162]~P4(x51622)+~P4(x51621)+P4(f862(f862(f74(a1),x51621),x51622)) % 14.98/14.67 [5163]~P4(x51632)+~P4(x51631)+P4(f862(f862(f73(a1),x51631),x51632)) % 14.98/14.67 [5164]~P4(x51642)+~P4(x51641)+P4(f862(f862(f29(a1),x51641),x51642)) % 14.98/14.67 [5166]~E(x51662,f2(a1))+E(x51661,f2(a1))+E(f39(x51661,x51662),f862(f862(f244(a1,a1),f2(a1)),x51661)) % 14.98/14.67 [5190]~E(x51902,f862(a105,f2(a924)))+~E(x51901,f862(a105,f2(a924)))+E(f862(f862(f74(a924),x51901),x51902),f862(a105,f2(a924))) % 14.98/14.67 [5208]E(x52081,f2(a924))+E(x52082,f862(a105,f2(a924)))+~E(f862(f862(f236(a924),x52082),x52081),f862(a105,f2(a924))) % 14.98/14.67 [5209]E(x52091,f2(a924))+E(x52091,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52092),x52091),f862(a105,f2(a924))) % 14.98/14.67 [5210]E(x52101,f2(a924))+E(x52101,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52101),x52102),f862(a105,f2(a924))) % 14.98/14.67 [5219]~P64(x52191)+~P98(x52191)+E(f862(f862(f281(x52191),x52192),f862(f96(x52191),a90)),f862(f72(x52191),x52192)) % 14.98/14.67 [5239]E(x52391,f862(a97,x52392))+~E(x52391,f2(a924))+P1(f862(f862(f227(a1),f2(a1)),x52392)) % 14.98/14.67 [5240]E(f862(a97,x52401),x52402)+~E(x52402,f2(a924))+P1(f862(f862(f227(a1),f2(a1)),x52401)) % 14.98/14.67 [5256]E(x52561,f862(a105,f2(a924)))+E(x52562,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52561),x52562),f862(a105,f2(a924))) % 14.98/14.67 [5267]~E(x52671,f862(a97,x52672))+E(x52671,f2(a924))+P1(f862(f862(f227(a1),f2(a1)),x52672)) % 14.98/14.67 [5268]~E(f862(a97,x52682),x52681)+E(x52681,f2(a924))+P1(f862(f862(f227(a1),f2(a1)),x52682)) % 14.98/14.67 [5291]~P93(x52911)+E(f862(f56(x52911,f94(x52911)),x52912),f12(x52911,x52912))+~P1(f862(f54(x52911),x52912)) % 14.98/14.67 [5292]~P93(x52921)+E(f862(f56(x52921,f103(x52921)),x52922),f15(x52921,x52922))+~P1(f862(f54(x52921),x52922)) % 14.98/14.67 [5293]~P109(x52931)+E(f862(f56(x52931,f225(x52931)),x52932),f16(x52931,x52932))+~P1(f862(f54(x52931),x52932)) % 14.98/14.67 [5294]~P109(x52941)+E(f862(f56(x52941,f226(x52941)),x52942),f17(x52941,x52942))+~P1(f862(f54(x52941),x52942)) % 14.98/14.67 [5371]E(x53711,x53712)+~E(f862(f862(f3(a924),x53712),x53711),f2(a924))+~E(f862(f862(f3(a924),x53711),x53712),f2(a924)) % 14.98/14.67 [5390]P4(x53901)+~P38(x53902)+~P1(f862(f862(f321(a1),x53901),x53902)) % 14.98/14.67 [5421]~P112(x54211)+~E(f75(x54211,x54212),f71(x54211))+P1(f862(f862(f228(x54211),f2(x54211)),x54212)) % 14.98/14.67 [5432]~P98(x54321)+E(f862(f93(x54321),f862(f96(a924),x54322)),f862(f96(x54321),x54322))+P1(f862(a186,f862(f96(a1),x54322))) % 14.98/14.67 [5438]~P41(x54381,x54382)+P42(a921)+P1(f862(f54(f931(x54381,x54381)),x54382)) % 14.98/14.67 [5507]~P109(x55071)+E(f862(f56(x55071,f225(x55071)),x55072),f13(x55071,f225(x55071),x55072))+~P1(f862(f54(x55071),x55072)) % 14.98/14.67 [5508]~P109(x55081)+E(f862(f56(x55081,f226(x55081)),x55082),f14(x55081,f226(x55081),x55082))+~P1(f862(f54(x55081),x55082)) % 14.98/14.67 [5522]E(x55221,x55222)+P1(f862(f862(f228(a924),x55222),x55221))+P1(f862(f862(f228(a924),x55221),x55222)) % 14.98/14.67 [5523]E(x55231,x55232)+P1(f862(f862(f228(a1),x55232),x55231))+P1(f862(f862(f228(a1),x55231),x55232)) % 14.98/14.67 [5578]~P98(x55781)+E(f862(f93(x55781),f862(f96(a924),x55782)),f2(x55781))+~P1(f862(a186,f862(f96(a1),x55782))) % 14.98/14.67 [5581]~E(x55812,f862(a97,x55811))+E(x55811,f862(f93(a1),x55812))+~P1(f862(f862(f227(a1),f2(a1)),x55811)) % 14.98/14.67 [5582]~E(f862(a97,x55821),x55822)+E(x55821,f862(f93(a1),x55822))+~P1(f862(f862(f227(a1),f2(a1)),x55821)) % 14.98/14.67 [5583]~E(x55831,f862(a97,x55832))+E(f862(f93(a1),x55831),x55832)+~P1(f862(f862(f227(a1),f2(a1)),x55832)) % 14.98/14.67 [5593]E(x55931,f862(a97,x55932))+~E(x55932,f862(f93(a1),x55931))+~P1(f862(f862(f227(a1),f2(a1)),x55932)) % 14.98/14.67 [5594]E(f862(a97,x55941),x55942)+~E(x55941,f862(f93(a1),x55942))+~P1(f862(f862(f227(a1),f2(a1)),x55941)) % 14.98/14.67 [5625]~P119(x56252)+E(x56251,f2(x56252))+~P1(f862(f862(f278(x56252),f2(x56252)),x56251)) % 14.98/14.67 [5636]~P86(x56362)+E(x56361,f2(x56362))+P1(f862(f862(f228(x56362),f2(x56362)),f862(f69(x56362),x56361))) % 14.98/14.67 [5700]~P112(x57001)+E(f75(x57001,x57002),f71(x57001))+~P1(f862(f862(f228(x57001),f2(x57001)),x57002)) % 14.98/14.67 [5706]~P98(x57061)+E(f862(f93(x57061),f862(f96(a924),x57062)),f2(x57061))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x57062))) % 14.98/14.67 [5717]~P86(x57171)+E(f862(f69(x57171),x57172),x57172)+~P1(f862(f862(f227(x57171),f2(x57171)),x57172)) % 14.98/14.67 [5718]~P86(x57181)+E(f862(f69(x57181),x57182),x57182)+~P1(f862(f862(f228(x57181),f2(x57181)),x57182)) % 14.98/14.67 [5727]E(x57271,f2(a924))+~E(f132(a924,f862(f295(a924,x57272),x57271)),f106(a924))+P1(f862(f862(f227(a924),x57271),x57272)) % 14.98/14.67 [5738]~P72(x57381)+E(f862(f862(f8(x57381,x57381),f7(x57381)),f862(f165(x57381),x57382)),f862(f158(x57381),x57382))+~P1(f862(f130(x57381),x57382)) % 14.98/14.67 [5741]~P142(x57411)+E(f862(f93(x57411),f862(a97,x57412)),f862(f95(x57411),x57412))+~P1(f862(f862(f227(a1),f2(a1)),x57412)) % 14.98/14.67 [5769]E(x57691,x57692)+P1(f862(f862(f228(a924),x57691),x57692))+~P1(f862(f862(f227(a924),x57691),x57692)) % 14.98/14.67 [5770]E(x57701,x57702)+P1(f862(f862(f228(a1),x57701),x57702))+~P1(f862(f862(f227(a1),x57701),x57702)) % 14.98/14.67 [5774]E(x57741,f71(a1))+~E(f862(f862(f74(a1),x57742),x57741),f71(a1))+~P1(f862(f862(f228(a1),f2(a1)),x57742)) % 14.98/14.67 [5775]E(x57751,f71(a1))+~E(f862(f862(f74(a1),x57751),x57752),f71(a1))+~P1(f862(f862(f228(a1),f2(a1)),x57751)) % 14.98/14.67 [5816]~P38(x58162)+P1(f862(f862(f227(a1),f2(a1)),x58161))+~P1(f862(f862(f321(a1),x58161),x58162)) % 14.98/14.67 [5835]~P55(x58351,x58352)+P35(x58351,x58352)+~P1(f862(f54(f931(x58351,x58351)),x58352)) % 14.98/14.67 [5837]~P55(x58371,x58372)+P41(x58371,x58372)+~P1(f862(f54(f931(x58371,x58371)),x58372)) % 14.98/14.67 [5879]E(x58791,f181(f932(x58792,a921)))+~P1(f862(f54(x58792),x58791))+P1(f862(f862(f228(a924),f2(a924)),f862(f28(x58792),x58791))) % 14.98/14.67 [5906]~P1(f862(x59061,x59062))+P1(f862(x59061,f2(a924)))+P1(f862(f862(f228(a924),f360(x59062,x59061)),x59062)) % 14.98/14.67 [5929]E(x59291,f2(a924))+~E(f862(f158(a924),x59292),f2(a924))+~P1(f862(f862(f321(a924),x59291),f862(f165(a924),x59292))) % 14.98/14.67 [5997]E(x59971,x59972)+~P1(f862(f862(f227(a924),x59972),x59971))+~P1(f862(f862(f227(a924),x59971),x59972)) % 14.98/14.67 [5998]E(x59981,x59982)+~P1(f862(f862(f227(a1),x59982),x59981))+~P1(f862(f862(f227(a1),x59981),x59982)) % 14.98/14.67 [6005]E(x60051,x60052)+~P1(f862(f862(f278(a924),x60052),x60051))+~P1(f862(f862(f278(a924),x60051),x60052)) % 14.98/14.67 [6007]E(f862(f28(x60071),x60072),f2(a924))+~P1(f862(f54(x60071),x60072))+P1(f862(f862(f321(x60071),f362(x60072,x60071)),x60072)) % 14.98/14.67 [6016]E(f43(x60161,x60162),f39(x60161,x60162))+P1(f862(f862(f227(a1),f2(a1)),x60161))+~P1(f862(f862(f228(a1),f2(a1)),x60162)) % 14.98/14.67 [6042]~P1(f862(x60421,f426(x60421)))+P1(f862(x60421,f862(a97,x60422)))+~P1(f862(f862(f227(a1),f2(a1)),x60422)) % 14.98/14.67 [6045]P1(f862(f862(f227(a924),x60451),f866(x60452)))+~P1(f862(f54(a924),x60452))+~P1(f862(f862(f321(a924),x60451),x60452)) % 14.98/14.67 [6046]P1(f862(f862(f228(a924),x60461),f913(x60462)))+~P1(f862(f54(a924),x60462))+~P1(f862(f862(f321(a924),x60461),x60462)) % 14.98/14.67 [6077]E(x60771,x60772)+~P1(f862(f862(f228(a924),x60771),f862(a105,x60772)))+P1(f862(f862(f228(a924),x60771),x60772)) % 14.98/14.67 [6113]E(x61131,f862(a105,x61132))+~P1(f862(f862(f227(a924),x61131),f862(a105,x61132)))+P1(f862(f862(f227(a924),x61131),x61132)) % 14.98/14.67 [6129]P1(f862(x61291,f423(x61291)))+~P1(f862(x61291,f862(a97,x61292)))+~P1(f862(f862(f227(a1),f2(a1)),x61292)) % 14.98/14.67 [6145]~P1(f862(x61451,x61452))+~P1(f862(f862(f227(a1),f2(a1)),x61452))+P1(f862(x61451,f862(f93(a1),f406(x61451)))) % 14.98/14.67 [6156]~P86(x61562)+~E(x61561,f2(x61562))+~P1(f862(f862(f228(x61562),f2(x61562)),f862(f69(x61562),x61561))) % 14.98/14.67 [6180]~P55(x61801,x61802)+P35(x61801,f862(f277(x61801,x61801),x61802))+~P1(f862(f54(f931(x61801,x61801)),x61802)) % 14.98/14.67 [6188]~P98(x61881)+E(f862(f93(x61881),f862(f96(a924),x61882)),f862(f96(x61881),x61882))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x61882))) % 14.98/14.67 [6191]E(f862(a105,x61911),x61912)+~P1(f862(f862(f228(a924),x61911),x61912))+P1(f862(f862(f228(a924),f862(a105,x61911)),x61912)) % 14.98/14.67 [6207]E(f862(f862(f29(a1),x62071),x62072),f2(a1))+~P1(f862(f862(f227(a1),x62071),f2(a1)))+~P1(f862(f862(f228(a1),x62072),x62071)) % 14.98/14.67 [6218]E(f38(a1,x62181,x62182),x62181)+~P1(f862(f862(f227(a1),x62181),f2(a1)))+~P1(f862(f862(f228(a1),x62182),x62181)) % 14.98/14.67 [6232]E(f40(x62321,x62322),f39(x62321,x62322))+~P1(f862(f862(f227(a1),f2(a1)),x62321))+~P1(f862(f862(f227(a1),f2(a1)),x62322)) % 14.98/14.67 [6242]E(f862(f862(f29(a1),x62421),x62422),f2(a1))+~P1(f862(f862(f227(a1),f2(a1)),x62421))+~P1(f862(f862(f228(a1),x62421),x62422)) % 14.98/14.67 [6251]E(f38(a924,f862(f96(a924),x62511),f862(f96(a924),x62512)),f862(f96(a924),x62511))+P1(f862(a186,f862(f96(a1),x62511)))+~P1(f862(a186,f862(f96(a1),x62512))) % 14.98/14.67 [6253]E(f38(a1,x62531,x62532),x62531)+~P1(f862(f862(f227(a1),f2(a1)),x62531))+~P1(f862(f862(f228(a1),x62531),x62532)) % 14.98/14.67 [6254]E(x62541,x62542)+~P1(f862(f862(f228(a924),x62541),f862(a105,x62542)))+~P1(f862(f862(f227(a924),x62542),x62541)) % 14.98/14.67 [6268]~P76(x62681)+~P1(f862(f862(f227(x62681),x62682),f2(x62681)))+P1(f862(f862(f227(x62681),x62682),f862(f72(x62681),x62682))) % 14.98/14.67 [6269]~P112(x62691)+~P1(f862(f862(f228(x62691),x62692),f2(x62691)))+P1(f862(f862(f228(x62691),x62692),f862(f72(x62691),x62692))) % 14.98/14.67 [6278]~P3(x62781)+E(f862(f862(f57(x62781,x62781,f94(x62781)),f234(x62781)),x62782),f31(x62781,x62782))+~P1(f862(f54(x62781),x62782)) % 14.98/14.67 [6279]~P3(x62791)+E(f862(f862(f57(x62791,x62791,f103(x62791)),f181(x62791)),x62792),f30(x62791,x62792))+~P1(f862(f54(x62791),x62792)) % 14.98/14.67 [6296]~P112(x62961)+~P1(f862(f862(f227(a1),f2(a1)),x62962))+P1(f862(f862(f227(x62961),f2(x62961)),f862(f95(x62961),x62962))) % 14.98/14.67 [6297]~P127(x62971)+~P1(f862(f862(f228(a924),f2(a924)),x62972))+P1(f862(f862(f228(x62971),f2(x62971)),f862(f93(x62971),x62972))) % 14.98/14.67 [6298]~P112(x62981)+~P1(f862(f862(f228(a1),f2(a1)),x62982))+P1(f862(f862(f228(x62981),f2(x62981)),f862(f95(x62981),x62982))) % 14.98/14.67 [6301]~P4(x63012)+~P4(x63011)+E(f862(f302(a924,a1,f93(a1)),f296(a924,f862(a97,x63011),f862(a97,x63012))),f296(a1,x63011,x63012)) % 14.98/14.67 [6307]P1(f862(x63071,x63072))+~P1(f862(f862(f227(a1),f2(a1)),x63072))+~P1(f862(x63071,f862(f93(a1),f410(x63071)))) % 14.98/14.67 [6337]E(f862(f862(f73(a924),f862(f96(a924),x63371)),f862(f96(a924),x63372)),f862(f96(a924),x63371))+P1(f862(f862(f228(a1),x63371),a76))+~P1(f862(f862(f228(a1),x63372),a76)) % 14.98/14.67 [6341]~P112(x63411)+P1(f862(f862(f228(x63411),f2(x63411)),f75(x63411,x63412)))+~P1(f862(f862(f228(x63411),f2(x63411)),x63412)) % 14.98/14.67 [6353]~P78(x63531)+~P1(f862(f862(f227(x63531),x63532),f2(x63531)))+P1(f862(f862(f227(x63531),f2(x63531)),f862(f72(x63531),x63532))) % 14.98/14.67 [6354]~P78(x63541)+~P1(f862(f862(f228(x63541),x63542),f2(x63541)))+P1(f862(f862(f228(x63541),f2(x63541)),f862(f72(x63541),x63542))) % 14.98/14.67 [6357]E(x63571,f234(f932(x63572,a921)))+~E(f862(f28(x63572),x63571),f862(f28(x63572),f234(f932(x63572,a921))))+~P1(f862(f54(x63572),f234(f932(x63572,a921)))) % 14.98/14.67 [6384]~P1(f862(f862(f228(a924),f2(a924)),x63842))+~P1(f862(f862(f278(a924),x63841),x63842))+P1(f862(f862(f227(a924),x63841),x63842)) % 14.98/14.67 [6391]~P76(x63911)+P1(f862(f862(f227(x63911),x63912),f2(x63911)))+~P1(f862(f862(f227(x63911),x63912),f862(f72(x63911),x63912))) % 14.98/14.67 [6392]~P112(x63921)+P1(f862(f862(f228(x63921),x63922),f2(x63921)))+~P1(f862(f862(f228(x63921),x63922),f862(f72(x63921),x63922))) % 14.98/14.67 [6401]~P98(x64011)+P1(f862(f862(f321(x64011),f862(f96(x64011),x64012)),f179(x64011)))+~P1(f862(f862(f227(a1),a76),x64012)) % 14.98/14.67 [6430]E(x64301,f2(a924))+~P1(f862(f862(f228(a924),x64301),f862(a105,x64302)))+P1(f862(f862(f228(a924),f329(x64302,x64301)),x64302)) % 14.98/14.67 [6452]~P112(x64521)+~P1(f862(f862(f228(x64521),f2(x64521)),f75(x64521,x64522)))+P1(f862(f862(f228(x64521),f2(x64521)),x64522)) % 14.98/14.67 [6454]~E(f862(f96(a924),x64542),f862(f96(a924),x64541))+P1(f862(f862(f227(a1),f862(f96(a1),x64541)),f2(a1)))+~P1(f862(a186,f862(f96(a1),x64542))) % 14.98/14.67 [6483]E(f862(f243(a1,a1),f43(x64831,x64832)),f862(f862(f29(a1),x64831),x64832))+~P1(f862(f862(f228(a1),x64831),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x64832)) % 14.98/14.67 [6522]E(f862(f248(a1,a1),f43(x65221,x65222)),f38(a1,x65221,x65222))+~P1(f862(f862(f228(a1),x65221),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x65222)) % 14.98/14.67 [6525]~P112(x65252)+~P1(f862(f862(f227(x65252),f2(x65252)),f862(f95(x65252),x65251)))+P1(f862(f862(f227(a1),f2(a1)),x65251)) % 14.98/14.67 [6526]~P127(x65262)+~P1(f862(f862(f228(x65262),f2(x65262)),f862(f93(x65262),x65261)))+P1(f862(f862(f228(a924),f2(a924)),x65261)) % 14.98/14.67 [6527]~P112(x65272)+~P1(f862(f862(f228(x65272),f2(x65272)),f862(f95(x65272),x65271)))+P1(f862(f862(f228(a1),f2(a1)),x65271)) % 14.98/14.67 [6531]E(f862(f243(a1,a1),f40(x65311,x65312)),f862(f862(f29(a1),x65311),x65312))+~P1(f862(f862(f227(a1),f2(a1)),x65312))+~P1(f862(f862(f228(a1),f2(a1)),x65311)) % 14.98/14.67 [6545]E(f862(f248(a1,a1),f40(x65451,x65452)),f38(a1,x65451,x65452))+~P1(f862(f862(f227(a1),f2(a1)),x65452))+~P1(f862(f862(f228(a1),f2(a1)),x65451)) % 14.98/14.67 [6561]~P78(x65611)+P1(f862(f862(f227(x65611),x65612),f2(x65611)))+~P1(f862(f862(f227(x65611),f2(x65611)),f862(f72(x65611),x65612))) % 14.98/14.67 [6562]~P78(x65621)+P1(f862(f862(f228(x65621),x65622),f2(x65621)))+~P1(f862(f862(f228(x65621),f2(x65621)),f862(f72(x65621),x65622))) % 14.98/14.67 [6589]P1(f862(f42(x65891,x65892),f43(x65891,x65892)))+~P1(f862(f862(f228(a1),x65891),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x65892)) % 14.98/14.67 [6603]~P1(f862(f862(f228(a924),f2(a924)),x66031))+~P1(f862(f862(f278(a924),x66032),x66031))+~P1(f862(f862(f228(a924),x66031),x66032)) % 14.98/14.67 [6616]P1(f862(f42(x66161,x66162),f40(x66161,x66162)))+~P1(f862(f862(f227(a1),f2(a1)),x66161))+~P1(f862(f862(f228(a1),f2(a1)),x66162)) % 14.98/14.67 [6659]~P78(x66591)+P1(f862(f862(f227(x66591),f862(f72(x66591),x66592)),f2(x66591)))+~P1(f862(f862(f227(x66591),f2(x66591)),x66592)) % 14.98/14.67 [6660]~P78(x66601)+P1(f862(f862(f228(x66601),f862(f72(x66601),x66602)),f2(x66601)))+~P1(f862(f862(f228(x66601),f2(x66601)),x66602)) % 14.98/14.67 [6678]E(f862(f862(f3(a924),f862(a97,x66781)),f862(a97,x66782)),f862(a97,f187(x66781,x66782)))+~P1(f862(f862(f227(a1),f2(a1)),x66782))+~P1(f862(f862(f227(a1),f2(a1)),x66781)) % 14.98/14.67 [6696]P1(f862(f862(f227(a1),f2(a1)),f187(x66961,x66962)))+~P1(f862(f862(f227(a1),f2(a1)),x66962))+~P1(f862(f862(f227(a1),f2(a1)),x66961)) % 14.98/14.67 [6734]~P1(f862(x67341,x67342))+P1(f862(x67341,f2(a924)))+P1(f862(x67341,f862(f862(f73(a924),f360(x67342,x67341)),f71(a924)))) % 14.98/14.67 [6815]E(f862(f96(a924),x68151),f862(f96(a924),x68152))+~P1(f862(f862(f227(a1),f862(f96(a1),x68152)),f2(a1)))+~P1(f862(a186,f862(f96(a1),x68151))) % 14.98/14.67 [6825]~E(x68251,f2(a924))+~E(f681(x68252,x68251),f2(a924))+E(f862(f135(a924,a924,f73(a924),x68251),x68252),f2(a924)) % 14.98/14.67 [6850]~P1(f862(f54(x68501),f883(x68502,x68501)))+~P1(f862(f54(f932(x68501,a921)),x68502))+P1(f862(f54(x68501),f30(f932(x68501,a921),x68502))) % 14.98/14.67 [6856]E(x68561,x68562)+P1(f862(f862(f228(a1),x68561),x68562))+~P1(f862(f862(f228(a1),x68561),f862(f862(f73(a1),x68562),f71(a1)))) % 14.98/14.67 [6857]P1(f862(f862(f227(a924),f862(a97,x68571)),f862(a97,x68572)))+~P1(f862(f862(f227(a1),f2(a1)),x68572))+~P1(f862(f862(f227(a1),x68571),x68572)) % 14.98/14.67 [6858]P1(f862(f862(f227(a924),f862(a97,x68581)),f862(a97,x68582)))+~P1(f862(f862(f228(a1),f2(a1)),x68581))+~P1(f862(f862(f227(a1),x68581),x68582)) % 14.98/14.67 [6860]P1(f862(f862(f228(a924),f862(a97,x68601)),f862(a97,x68602)))+~P1(f862(f862(f227(a1),f2(a1)),x68601))+~P1(f862(f862(f228(a1),x68601),x68602)) % 14.98/14.67 [6861]P1(f862(f862(f228(a924),f862(a97,x68611)),f862(a97,x68612)))+~P1(f862(f862(f228(a1),f2(a1)),x68612))+~P1(f862(f862(f228(a1),x68611),x68612)) % 14.98/14.67 [6872]E(f38(a924,f862(a97,x68721),f862(a97,x68722)),f862(a97,f38(a1,x68721,x68722)))+~P1(f862(f862(f227(a1),f2(a1)),x68722))+~P1(f862(f862(f227(a1),f2(a1)),x68721)) % 14.98/14.67 [6895]~P78(x68951)+~P1(f862(f862(f227(x68951),f862(f72(x68951),x68952)),f2(x68951)))+P1(f862(f862(f227(x68951),f2(x68951)),x68952)) % 14.98/14.67 [6896]~P78(x68961)+~P1(f862(f862(f228(x68961),f862(f72(x68961),x68962)),f2(x68961)))+P1(f862(f862(f228(x68961),f2(x68961)),x68962)) % 14.98/14.67 [6910]~P1(f862(f862(f228(a1),a76),x69102))+~P1(f862(f862(f228(a1),x69101),x69102))+P1(f862(f862(f228(a924),f862(f96(a924),x69101)),f862(f96(a924),x69102))) % 14.98/14.67 [7002]~P1(f862(f862(f227(a1),f2(a1)),x70021))+P1(f862(f862(f228(a924),f862(a97,x70021)),x70022))+~P1(f862(f862(f228(a1),x70021),f862(f93(a1),x70022))) % 14.98/14.67 [7007]P1(f862(x70071,x70072))+~P1(f862(x70071,f862(a22,f815(x70071,x70072))))+~P1(f862(f862(f321(a924),x70072),f234(f932(a924,a921)))) % 14.98/14.67 [7018]E(x70181,f2(a1))+E(f38(a1,x70182,x70181),f2(a1))+E(f862(f862(f3(a1),f862(f72(a1),f862(f862(f29(a1),x70182),x70181))),f71(a1)),f862(f862(f29(a1),x70182),f862(f72(a1),x70181))) % 14.98/14.67 [7032]~P1(f862(f862(f227(a1),f2(a1)),x70321))+~P1(f862(f862(f228(a924),f862(a97,x70321)),x70322))+P1(f862(f862(f228(a1),x70321),f862(f93(a1),x70322))) % 14.98/14.67 [7068]~P1(f862(f862(f227(a924),f862(a97,x70681)),f862(a97,x70682)))+~P1(f862(f862(f227(a1),f2(a1)),x70682))+P1(f862(f862(f227(a1),x70681),x70682)) % 14.98/14.67 [7069]~P1(f862(f862(f227(a924),f862(a97,x70691)),f862(a97,x70692)))+~P1(f862(f862(f228(a1),f2(a1)),x70691))+P1(f862(f862(f227(a1),x70691),x70692)) % 14.98/14.67 [7098]P1(f862(f862(f227(a1),x70981),x70982))+~P1(f862(f862(f227(a924),f862(f96(a924),x70981)),f862(f96(a924),x70982)))+P1(f862(f862(f227(a1),x70981),a76)) % 14.98/14.67 [7124]P1(f862(f862(f227(a1),f2(a1)),f38(a1,x71241,x71242)))+~P1(f862(f862(f227(a1),f2(a1)),x71242))+~P1(f862(f862(f227(a1),f2(a1)),x71241)) % 14.98/14.67 [7220]P1(f862(f862(f228(a1),a76),x72201))+~P1(f862(f862(f228(a1),x72202),x72201))+~P1(f862(f862(f228(a924),f862(f96(a924),x72202)),f862(f96(a924),x72201))) % 14.98/14.67 [7275]E(f862(f862(f244(a1,a1),f862(f862(f29(a1),x72751),x72752)),f38(a1,x72751,x72752)),f43(x72751,x72752))+~P1(f862(f862(f228(a1),x72751),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x72752)) % 14.98/14.67 [7295]E(f862(f862(f244(a1,a1),f862(f862(f29(a1),x72951),x72952)),f38(a1,x72951,x72952)),f40(x72951,x72952))+~P1(f862(f862(f227(a1),f2(a1)),x72952))+~P1(f862(f862(f227(a1),f2(a1)),x72951)) % 14.98/14.67 [7349]~P100(x73492)+E(x73491,f106(x73492))+E(f862(f135(x73492,x73492,f74(x73492),f862(f134(x73492),x73491)),f862(f164(x73492),x73491)),f862(f56(x73492,f74(x73492)),f862(f165(x73492),x73491))) % 14.98/14.67 [7467]~E(x74671,f2(a924))+E(f862(f135(a924,a924,f73(a924),x74671),x74672),f2(a924))+P1(f862(f862(f321(a924),f681(x74672,x74671)),f862(f165(a924),x74672))) % 14.98/14.67 [7521]~P1(f862(f862(f227(a1),x75211),f2(a1)))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x75211),x75212)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x75212)) % 14.98/14.67 [7522]~P1(f862(f862(f228(a1),x75222),f2(a1)))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x75221),x75222)),f2(a1)))+~P1(f862(f862(f227(a1),f2(a1)),x75221)) % 14.98/14.67 [7523]~P1(f862(f862(f228(a1),x75232),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f29(a1),x75231),x75232)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x75231)) % 14.98/14.67 [7525]~P1(f862(f862(f228(a1),x75251),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f29(a1),x75251),x75252)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x75252)) % 14.98/14.67 [7532]P1(f862(f862(f321(f932(x75321,a921)),f883(x75322,x75321)),x75322))+~P1(f862(f54(f932(x75321,a921)),x75322))+P1(f862(f54(x75321),f30(f932(x75321,a921),x75322))) % 14.98/14.67 [7623]P22(x76231,x76231,x76232,f234(f932(x76231,a921)))+~E(f862(f302(x76231,x76231,x76232),f234(f932(x76231,a921))),f234(f932(x76231,a921)))+~P1(f862(f54(x76231),f234(f932(x76231,a921)))) % 14.98/14.67 [7744]~P22(x77441,x77441,x77442,f234(f932(x77441,a921)))+E(f862(f302(x77441,x77441,x77442),f234(f932(x77441,a921))),f234(f932(x77441,a921)))+~P1(f862(f54(x77441),f234(f932(x77441,a921)))) % 14.98/14.67 [7885]E(f862(f862(f29(a1),x78851),x78852),f862(f96(a1),a90))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x78851),x78852)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x78851)) % 14.98/14.67 [7941]~P1(f862(f862(f228(a1),x79412),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f29(a1),x79411),x79412)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x79411)) % 14.98/14.67 [7946]E(f862(f862(f73(a1),x79461),x79462),f38(a1,x79461,x79462))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x79461),x79462)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x79461)) % 14.98/14.67 [7949]P1(f862(f862(f228(a1),x79491),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f29(a1),x79491),x79492)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x79492)) % 14.98/14.67 [8654]~P109(x86541)+P11(x86541,x86542)+~P1(f862(f862(f227(x86541),f862(f862(f157(x86541),x86542),f715(x86542,x86541))),f862(f862(f157(x86541),x86542),f716(x86542,x86541)))) % 14.98/14.67 [8655]~P109(x86551)+P11(x86551,x86552)+~P1(f862(f862(f227(x86551),f862(f862(f157(x86551),x86552),f722(x86552,x86551))),f862(f862(f157(x86551),x86552),f727(x86552,x86551)))) % 14.98/14.67 [5872]E(x58721,f2(a1))+~E(f38(a1,x58722,x58721),f2(a1))+E(f862(f862(f29(a1),x58722),f862(f72(a1),x58721)),f862(f72(a1),f862(f862(f29(a1),x58722),x58721))) % 14.98/14.67 [5890]~P38(x58902)+~P38(x58901)+P38(f862(f862(f103(f932(a1,a921)),x58901),x58902)) % 14.98/14.67 [5891]~P38(x58912)+~P38(x58911)+P38(f862(f862(f94(f932(a1,a921)),x58911),x58912)) % 14.98/14.67 [5909]~P64(x59091)+~P98(x59091)+E(f862(f72(x59091),f862(f862(f281(x59091),f71(x59091)),x59092)),f862(f862(f281(x59091),f862(f96(x59091),a90)),x59092)) % 14.98/14.67 [6034]E(x60341,f2(a1))+~E(f38(a1,x60342,x60341),f2(a1))+E(f862(f862(f29(a1),f862(f72(a1),x60342)),x60341),f862(f72(a1),f862(f862(f29(a1),x60342),x60341))) % 14.98/14.67 [6174]~P109(x61741)+P11(x61741,x61742)+P1(f862(f862(f228(a924),f716(x61742,x61741)),f862(f182(f925(x61741)),x61742))) % 14.98/14.67 [6175]~P109(x61751)+P11(x61751,x61752)+P1(f862(f862(f228(a924),f727(x61752,x61751)),f862(f182(f925(x61751)),x61752))) % 14.98/14.67 [6331]~P98(x63311)+~E(f862(f96(x63311),x63312),f2(x63311))+P26(x63311,f862(f96(x63311),f862(f862(f73(a1),x63312),f862(f72(a1),a76)))) % 14.98/14.67 [6332]~P98(x63321)+~E(f862(f96(x63321),x63322),f2(x63321))+P26(x63321,f862(f96(x63321),f862(f862(f73(a1),a76),f862(f72(a1),x63322)))) % 14.98/14.67 [6334]E(f862(a44,f40(f862(f72(a1),x63341),f862(f72(a1),x63342))),f39(x63341,x63342))+P1(f862(f862(f227(a1),f2(a1)),x63341))+P1(f862(f862(f228(a1),f2(a1)),x63342)) % 14.98/14.67 [6460]~E(x64602,f2(a924))+~E(x64601,f2(a924))+P1(f862(f862(f227(a1),f862(f93(a1),x64601)),f862(f72(a1),f862(f93(a1),x64602)))) % 14.98/14.67 [6489]E(f862(f862(f73(a924),f862(f96(a924),x64891)),f862(f96(a924),x64892)),f862(f96(a924),f862(f862(f73(a1),x64891),x64892)))+P1(f862(f862(f228(a1),x64891),a76))+P1(f862(f862(f228(a1),x64892),a76)) % 14.98/14.67 [6625]~P76(x66251)+~P1(f862(f862(f227(x66251),f2(x66251)),x66252))+P1(f862(f862(f227(x66251),f862(f72(x66251),x66252)),x66252)) % 14.98/14.67 [6626]~P76(x66261)+~P1(f862(f862(f228(x66261),f2(x66261)),x66262))+P1(f862(f862(f228(x66261),f862(f72(x66261),x66262)),x66262)) % 14.98/14.67 [6801]E(f862(f862(f3(a924),f862(a97,x68011)),f862(a97,x68012)),f862(a97,f862(f862(f3(a1),x68011),x68012)))+~P1(f862(f862(f227(a1),f2(a1)),x68012))+~P1(f862(f862(f227(a1),x68012),x68011)) % 14.98/14.67 [6833]E(f862(a97,f38(a1,f862(f96(a1),x68331),f862(f96(a1),x68332))),f38(a924,f862(f96(a924),x68331),f862(f96(a924),x68332)))+P1(f862(a186,f862(f96(a1),x68331)))+P1(f862(a186,f862(f96(a1),x68332))) % 14.98/14.67 [6851]~P76(x68511)+P1(f862(f862(f227(x68511),f2(x68511)),x68512))+~P1(f862(f862(f227(x68511),f862(f72(x68511),x68512)),x68512)) % 14.98/14.67 [6852]~P76(x68521)+P1(f862(f862(f228(x68521),f2(x68521)),x68522))+~P1(f862(f862(f228(x68521),f862(f72(x68521),x68522)),x68522)) % 14.98/14.67 [6864]~P76(x68641)+~P1(f862(f862(f227(x68641),f2(x68641)),x68642))+P1(f862(f862(f227(x68641),f2(x68641)),f862(f862(f73(x68641),x68642),x68642))) % 14.98/14.67 [6866]~P76(x68661)+~P1(f862(f862(f228(x68661),f2(x68661)),x68662))+P1(f862(f862(f228(x68661),f2(x68661)),f862(f862(f73(x68661),x68662),x68662))) % 14.98/14.67 [6878]E(f862(f862(f73(a924),f862(a97,x68781)),f862(a97,x68782)),f862(a97,f862(f862(f73(a1),x68781),x68782)))+~P1(f862(f862(f227(a1),f2(a1)),x68782))+~P1(f862(f862(f227(a1),f2(a1)),x68781)) % 14.98/14.67 [6889]E(x68891,f2(a924))+P1(f862(f862(f228(a924),f2(a924)),x68892))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f236(a924),x68892),x68891))) % 14.98/14.67 [6920]~P98(x69201)+E(f862(f96(x69201),x69202),f2(x69201))+~P26(x69201,f862(f96(x69201),f862(f862(f73(a1),a76),f862(f72(a1),x69202)))) % 14.98/14.67 [6921]~P98(x69211)+E(f862(f96(x69211),x69212),f2(x69211))+~P26(x69211,f862(f96(x69211),f862(f862(f73(a1),x69212),f862(f72(a1),a76)))) % 14.98/14.67 [6980]~P1(f862(f54(x69801),x69802))+~P1(f862(f54(x69801),f234(f932(x69801,a921))))+P1(f862(f54(x69801),f862(f72(f932(x69801,a921)),x69802))) % 14.98/14.67 [7003]~P1(f862(f862(f228(a1),f2(a1)),x70032))+~P1(f862(f862(f227(a1),x70032),x70031))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x70031),x70032))) % 14.98/14.67 [7004]~P1(f862(f862(f227(a1),x70041),f2(a1)))+~P1(f862(f862(f228(a1),x70042),f2(a1)))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x70041),x70042))) % 14.98/14.67 [7042]~P1(f862(f862(f227(a1),f2(a1)),x70422))+~P1(f862(f862(f227(a1),f2(a1)),x70421))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f74(a1),x70421),x70422))) % 14.98/14.67 [7043]~P1(f862(f862(f227(a1),f2(a1)),x70432))+~P1(f862(f862(f227(a1),f2(a1)),x70431))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x70431),x70432))) % 14.98/14.67 [7044]~P1(f862(f862(f227(a1),f2(a1)),x70442))+~P1(f862(f862(f227(a1),f2(a1)),x70441))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x70441),x70442))) % 14.98/14.67 [7045]~P1(f862(f862(f227(a1),f2(a1)),x70451))+~P1(f862(f862(f228(a1),f2(a1)),x70452))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x70451),x70452))) % 14.98/14.67 [7046]~P1(f862(f862(f228(a924),f2(a924)),x70462))+~P1(f862(f862(f228(a924),f2(a924)),x70461))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f74(a924),x70461),x70462))) % 14.98/14.67 [7111]E(x71111,f2(a1))+E(f38(a1,x71112,x71111),f2(a1))+E(f862(f862(f3(a1),f862(f72(a1),f862(f862(f29(a1),x71112),x71111))),f71(a1)),f862(f862(f29(a1),f862(f72(a1),x71112)),x71111)) % 14.98/14.67 [7166]P1(f862(f862(f228(a924),f2(a924)),x71661))+P1(f862(f862(f228(a924),f2(a924)),x71662))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f73(a924),x71662),x71661))) % 14.98/14.67 [7170]~P76(x71701)+P1(f862(f862(f227(x71701),f2(x71701)),x71702))+~P1(f862(f862(f227(x71701),f2(x71701)),f862(f862(f73(x71701),x71702),x71702))) % 14.98/14.67 [7171]~P76(x71711)+P1(f862(f862(f228(x71711),f2(x71711)),x71712))+~P1(f862(f862(f228(x71711),f2(x71711)),f862(f862(f73(x71711),x71712),x71712))) % 14.98/14.67 [7221]~P1(f862(f54(x72211),x72212))+P1(f862(f54(x72211),f234(f932(x72211,a921))))+~P1(f862(f54(x72211),f862(f72(f932(x72211,a921)),x72212))) % 14.98/14.67 [7287]P1(f862(f862(f227(a1),x72871),f2(a1)))+~P1(f862(f862(f228(a1),x72872),f2(a1)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x72871),x72872))) % 14.98/14.67 [7293]~P1(f862(f862(f228(a1),f2(a1)),x72931))+P1(f862(f862(f227(a1),x72931),x72932))+~P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x72932),x72931))) % 14.98/14.67 [7294]~P1(f862(f862(f227(a1),f2(a1)),x72942))+P1(f862(f862(f227(a1),x72941),x72942))+~P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x72942),x72941))) % 14.98/14.67 [7324]P1(f862(f862(f227(a1),f2(a1)),x73241))+~P1(f862(f862(f228(a1),f2(a1)),x73242))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x73241),x73242))) % 14.98/14.67 [7325]P1(f862(f862(f228(a1),f2(a1)),x73251))+~P1(f862(f862(f227(a1),f2(a1)),x73252))+~P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x73252),x73251))) % 14.98/14.67 [7776]~P1(f862(f54(x77762),f234(f932(x77762,a921))))+~P1(f862(f54(x77761),f234(f932(x77761,a921))))+P1(f862(f54(f930(x77761,x77762)),f234(f932(f930(x77761,x77762),a921)))) % 14.98/14.67 [7777]~P1(f862(f54(x77772),f234(f932(x77772,a921))))+~P1(f862(f54(x77771),f234(f932(x77771,a921))))+P1(f862(f54(f931(x77771,x77772)),f234(f932(f931(x77771,x77772),a921)))) % 14.98/14.67 [7849]~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x78491))+~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x78492))+P1(f862(f862(f228(a924),x78491),f862(f862(f74(a924),x78492),x78491))) % 14.98/14.67 [7850]~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x78501))+~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x78502))+P1(f862(f862(f228(a924),x78501),f862(f862(f74(a924),x78501),x78502))) % 14.98/14.67 [7884]E(f862(f28(x78841),f234(f932(x78841,a921))),f862(a105,f2(a924)))+P1(f862(f54(x78842),f234(f932(x78842,a921))))+~P1(f862(f54(f932(x78842,x78841)),f234(f932(f932(x78842,x78841),a921)))) % 14.98/14.67 [8010]~P1(f862(f862(f227(a924),f862(a105,f2(a924))),x80101))+~P1(f862(f862(f227(a924),f862(a105,f2(a924))),x80102))+P1(f862(f862(f227(a924),f862(a105,f2(a924))),f862(f862(f74(a924),x80101),x80102))) % 14.98/14.67 [8011]~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x80112))+~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x80111))+P1(f862(f862(f228(a924),f862(a105,f2(a924))),f862(f862(f74(a924),x80111),x80112))) % 14.98/14.67 [8701]E(x87011,f106(x87012))+~P1(f862(f130(x87012),x87011))+E(f170(x87012,f862(f862(f10(a921,a921,x87012),a314),f862(f862(f9(x87012,x87012,a921),a317),f137(x87012,x87011))),x87011),f107(x87012,x87011)) % 14.98/14.67 [8798]~P38(x87982)+~P38(x87981)+E(f862(f302(a924,a1,f93(a1)),f862(f862(f103(f932(a924,a921)),f862(f302(a1,a924,a97),x87981)),f862(f302(a1,a924,a97),x87982))),f862(f862(f103(f932(a1,a921)),x87981),x87982)) % 14.98/14.67 [8799]~P38(x87992)+~P38(x87991)+E(f862(f302(a924,a1,f93(a1)),f862(f862(f94(f932(a924,a921)),f862(f302(a1,a924,a97),x87991)),f862(f302(a1,a924,a97),x87992))),f862(f862(f94(f932(a1,a921)),x87991),x87992)) % 14.98/14.67 [9469]~P98(x94691)+~E(f862(f96(x94691),x94692),f71(x94691))+P26(x94691,f862(f96(x94691),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f72(a1),x94692)))) % 14.98/14.67 [9715]~P98(x97151)+E(f862(f96(x97151),x97152),f71(x97151))+~P26(x97151,f862(f96(x97151),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f72(a1),x97152)))) % 14.98/14.67 [10466]E(x104661,f2(a1))+E(x104662,f2(a1))+E(f862(f250(a1,a1,a1,a1,f25(a1),f862(f74(a1),f75(a1,x104662))),f862(f862(f862(f89(f931(a1,a1)),f862(f862(a317,f75(a1,x104661)),f75(a1,x104662))),f46(x104661,x104662)),f862(f862(f249(a1,a1,f931(a1,a1)),f862(f862(f20(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f20(a1,f931(a1,a1),f931(a1,a1))),f862(f862(f10(f931(a1,a1),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f862(f9(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f862(f862(f10(a921,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f89(f931(a1,a1))),f862(f862(f9(a1,a1,a921),a317),f2(a1))))),f862(f862(f9(a1,a1,f931(a1,a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f72(a1))),f2(a1))))),f862(f862(f9(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f10(a1,f931(a1,a1),a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f862(f9(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f3(a1)),f72(a1))),f71(a1))))),f862(f3(a1),f862(f69(a1),x104662))))),f46(x104661,x104662)))),f39(x104661,x104662)) % 14.98/14.67 [10467]E(x104671,f2(a1))+E(x104672,f2(a1))+E(f862(f250(a1,a1,a1,a1,f25(a1),f862(f74(a1),f75(a1,x104672))),f862(f862(f862(f89(f931(a1,a1)),f862(f862(a319,f862(f862(a318,f862(f862(f228(a1),f2(a1)),x104672)),f862(f862(f227(a1),f2(a1)),x104671))),f862(f862(a318,f862(f862(f228(a1),x104672),f2(a1))),f862(f862(f228(a1),x104671),f2(a1))))),f46(x104671,x104672)),f862(f862(f249(a1,a1,f931(a1,a1)),f862(f862(f20(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f20(a1,f931(a1,a1),f931(a1,a1))),f862(f862(f10(f931(a1,a1),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f862(f9(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f862(f862(f10(a921,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f89(f931(a1,a1))),f862(f862(f9(a1,a1,a921),a317),f2(a1))))),f862(f862(f9(a1,a1,f931(a1,a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f72(a1))),f2(a1))))),f862(f862(f9(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f10(a1,f931(a1,a1),a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f862(f9(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f3(a1)),f72(a1))),f71(a1))))),f862(f3(a1),f862(f69(a1),x104672))))),f46(x104671,x104672)))),f39(x104671,x104672)) % 14.98/14.67 [5898]~P112(x58981)+~P98(x58981)+E(f862(f69(x58981),f862(f862(f236(x58981),f862(f96(x58981),a90)),x58982)),f71(x58981)) % 14.98/14.67 [6402]~P142(x64021)+~P1(f862(f862(f228(a1),x64022),f2(a1)))+E(f862(f72(x64021),f862(f93(x64021),f862(a97,f862(f72(a1),x64022)))),f862(f95(x64021),x64022)) % 14.98/14.67 [6609]P1(f862(f862(f227(a92),x66091),f71(a92)))+E(f862(f862(f73(a92),f71(a92)),f264(x66091,f862(f862(f29(a92),x66092),x66091))),f264(x66091,x66092))+P1(f862(f862(f228(a92),x66092),x66091)) % 14.98/14.67 [7211]~P97(x72111)+~P1(f862(f862(f321(x72111),x72112),f102(x72111)))+~E(f862(f862(f73(x72111),f862(f862(f73(x72111),f71(x72111)),x72112)),x72112),f2(x72111)) % 14.98/14.67 [7326]~P1(f862(f862(f227(a1),x73262),f2(a1)))+~P1(f862(f862(f228(a1),x73261),f2(a1)))+E(f862(f243(a1,a1),f862(a44,f40(f862(f72(a1),x73261),f862(f72(a1),x73262)))),f862(f862(f29(a1),x73261),x73262)) % 14.98/14.67 [7343]~P1(f862(f862(f227(a1),x73432),f2(a1)))+~P1(f862(f862(f228(a1),x73431),f2(a1)))+E(f862(f248(a1,a1),f862(a44,f40(f862(f72(a1),x73431),f862(f72(a1),x73432)))),f38(a1,x73431,x73432)) % 14.98/14.67 [7351]~P1(f862(f862(f228(a1),x73512),f2(a1)))+E(f862(f243(a1,a1),f862(a44,f43(f862(f72(a1),x73511),f862(f72(a1),x73512)))),f862(f862(f29(a1),x73511),x73512))+~P1(f862(f862(f228(a1),f2(a1)),x73511)) % 14.98/14.67 [7369]~P1(f862(f862(f228(a1),x73692),f2(a1)))+E(f862(f248(a1,a1),f862(a44,f43(f862(f72(a1),x73691),f862(f72(a1),x73692)))),f38(a1,x73691,x73692))+~P1(f862(f862(f228(a1),f2(a1)),x73691)) % 14.98/14.67 [7422]E(f862(f862(f29(a1),f862(f862(f236(a1),x74221),x74222)),x74221),f862(f862(f236(a1),x74221),f862(f862(f3(a924),x74222),f862(a105,f2(a924)))))+~P1(f862(f862(f228(a924),f2(a924)),x74222))+~P1(f862(f862(f228(a1),f2(a1)),x74221)) % 14.98/14.67 [7528]~P1(f862(f862(f228(a924),f2(a924)),x75281))+~P1(f862(f862(f228(a924),f2(a924)),x75282))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x75281),x75282)),x75281)) % 14.98/14.67 [7529]~P1(f862(f862(f228(a924),f2(a924)),x75291))+~P1(f862(f862(f228(a924),f71(a924)),x75292))+P1(f862(f862(f228(a924),f862(f862(f29(a924),x75291),x75292)),x75291)) % 14.98/14.67 [7530]~P1(f862(f862(f228(a1),f2(a1)),x75301))+~P1(f862(f862(f228(a1),f71(a1)),x75302))+P1(f862(f862(f228(a1),f862(f862(f29(a1),x75301),x75302)),x75301)) % 14.98/14.67 [7668]E(x76681,f2(a924))+~E(x76682,f2(a1))+~P1(f862(f862(f228(a1),f2(a1)),f862(f862(f236(a1),f862(f69(a1),x76682)),x76681))) % 14.98/14.67 [8090]~E(x80902,f106(f925(x80901)))+E(f862(f182(f925(f925(x80901))),f172(x80901,x80902)),f2(a924))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x80901),a924),f182(f925(x80901))),x80902))) % 14.98/14.67 [8349]P1(f862(x83491,x83492))+~P1(f862(x83491,f862(a100,f569(x83491,x83492))))+~P1(f862(f862(f321(f932(f931(a924,a924),a921)),x83492),a91)) % 14.98/14.67 [8365]E(x83651,f106(f925(x83652)))+E(f862(f182(f925(x83652)),f862(f862(f157(f925(x83652)),x83651),f2(a924))),f862(f182(f925(f925(x83652))),f172(x83652,x83651)))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x83652),a924),f182(f925(x83652))),x83651))) % 14.98/14.67 [8506]~P36(x85061,x85062)+~P37(x85061,x85062)+P36(x85061,f862(f862(f3(f932(f931(x85061,x85061),a921)),x85062),f299(x85061,f181(f932(f931(x85061,x85061),a921))))) % 14.98/14.67 [9086]~P1(f862(f54(x90861),f862(f254(x90861),x90862)))+~P1(f862(f54(x90861),f234(f932(x90861,a921))))+P1(f862(f54(x90861),f862(f254(x90861),f862(f862(f10(a921,a921,x90861),a314),x90862)))) % 14.98/14.67 [9150]E(f862(f862(f244(a924,a924),f862(a105,f862(f862(f29(a924),f862(f862(f3(a924),x91501),x91502)),x91502))),f38(a924,f862(f862(f3(a924),x91501),x91502),x91502)),f78(f931(a924,a924),f41(x91501,x91502)))+~P1(f862(f862(f228(a924),f2(a924)),x91502))+~P1(f862(f862(f227(a924),x91502),x91501)) % 14.98/14.67 [9434]~P1(f862(f54(x94341),f862(f254(x94341),x94342)))+P1(f862(f54(x94341),f234(f932(x94341,a921))))+~P1(f862(f54(x94341),f862(f254(x94341),f862(f862(f10(a921,a921,x94341),a314),x94342)))) % 14.98/14.67 [10159]P24(x101591,x101592)+~P35(x101591,f862(f243(f932(f931(x101591,x101591),a921),f932(f931(x101591,x101591),a921)),x101592))+~P1(f862(f862(f227(f932(f931(x101591,x101591),a921)),f862(f862(f280(x101591,x101591,x101591),f862(f243(f932(f931(x101591,x101591),a921),f932(f931(x101591,x101591),a921)),x101592)),f862(f248(f932(f931(x101591,x101591),a921),f932(f931(x101591,x101591),a921)),x101592))),f862(f243(f932(f931(x101591,x101591),a921),f932(f931(x101591,x101591),a921)),x101592))) % 14.98/14.67 [7453]~P1(f862(f862(f228(a924),f2(a924)),x74532))+P1(f862(f862(f228(a924),x74531),x74532))+E(f862(a105,f862(f862(f29(a924),f862(f862(f3(a924),x74531),x74532)),x74532)),f862(f862(f29(a924),x74531),x74532)) % 14.98/14.67 [7596]~P1(f862(f862(f228(a924),f2(a924)),x75962))+~P1(f862(f862(f227(a924),x75962),x75961))+E(f862(a105,f862(f862(f29(a924),f862(f862(f3(a924),x75961),x75962)),x75962)),f862(f862(f29(a924),x75961),x75962)) % 14.98/14.67 [8570]~P98(x85701)+~P97(x85701)+~P26(x85701,f862(f96(x85701),f862(f862(f3(a1),f862(f862(f73(a1),x85702),x85702)),a90))) % 14.98/14.67 [9341]E(x93411,f2(a924))+E(f862(f862(f249(a924,a924,f931(a924,a924)),f862(f862(f10(a924,f932(a924,f931(a924,a924)),a924),f244(a924,a924)),a105)),f78(f931(a924,a924),f41(f862(f862(f3(a924),x93412),x93411),x93411))),f78(f931(a924,a924),f41(x93412,x93411)))+P1(f862(f862(f228(a924),x93412),x93411)) % 14.98/14.67 [9521]~P36(x95211,x95212)+~P49(x95211,x95212)+P1(f862(f862(f227(f932(f931(x95211,x95211),a921)),f862(f862(f280(x95211,x95211,x95211),f862(f277(x95211,x95211),x95212)),x95212)),x95212)) % 14.98/14.67 [9779]P1(f862(x97792,f649(x97792,x97791)))+P1(f862(x97791,f649(x97792,x97791)))+E(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97791)),f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97792))) % 14.98/14.67 [9783]~P1(f862(x97832,f649(x97832,x97831)))+~P1(f862(x97831,f649(x97832,x97831)))+E(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97831)),f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97832))) % 14.98/14.67 [10327]~P1(f862(f862(f278(a924),x103272),x103271))+P1(f862(f862(f278(a924),x103271),x103272))+P1(f862(f862(f321(a924),x103271),f285(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103272))) % 14.98/14.67 [10328]~P1(f862(f862(f278(a924),x103282),x103281))+P1(f862(f862(f278(a924),x103281),x103282))+P1(f862(f862(f321(a924),x103282),f289(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103281))) % 14.98/14.67 [7807]~P65(x78071)+~P98(x78071)+E(f862(f862(f281(x78071),x78072),f862(f96(x78071),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),x78072) % 14.98/14.67 [9468]~P98(x94681)+~E(f862(f96(x94681),x94682),f71(x94681))+P26(x94681,f862(f96(x94681),f862(f862(f73(a1),x94682),f862(f72(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.67 [9655]~P141(x96551)+~E(x96552,f71(x96551))+E(f862(f862(f236(x96551),x96552),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(x96551)) % 14.98/14.67 [9656]~P141(x96561)+~E(x96562,f2(x96561))+E(f862(f862(f236(x96561),x96562),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(x96561)) % 14.98/14.67 [9671]~P141(x96711)+~E(x96712,f862(f72(x96711),f71(x96711)))+E(f862(f862(f236(x96711),x96712),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(x96711)) % 14.98/14.67 [9716]~P98(x97161)+E(f862(f96(x97161),x97162),f71(x97161))+~P26(x97161,f862(f96(x97161),f862(f862(f73(a1),x97162),f862(f72(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.67 [10103]~P112(x101032)+E(x101031,f2(x101032))+P1(f862(f862(f228(x101032),f2(x101032)),f862(f862(f236(x101032),x101031),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.67 [10158]~P112(x101582)+~E(x101581,f2(x101582))+~P1(f862(f862(f228(x101582),f2(x101582)),f862(f862(f236(x101582),x101581),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.67 [10184]P1(f862(f862(f227(a1),x101841),f2(a1)))+P1(f862(f862(f228(a1),x101842),x101841))+E(f862(f36(x101841),f40(x101842,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101841))),f40(x101842,x101841)) % 14.98/14.67 [10185]~P1(f862(f862(f228(a1),f2(a1)),x101851))+P1(f862(f862(f228(a1),x101852),x101851))+E(f862(f36(x101851),f40(x101852,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101851))),f40(x101852,x101851)) % 14.98/14.67 [10186]P1(f862(f862(f227(a1),x101861),f2(a1)))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x101862),x101861)))+E(f862(f36(x101861),f43(x101862,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101861))),f43(x101862,x101861)) % 14.98/14.67 [10187]~P1(f862(f862(f228(a1),f2(a1)),x101871))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x101872),x101871)))+E(f862(f36(x101871),f43(x101872,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101871))),f43(x101872,x101871)) % 14.98/14.67 [10188]~P147(x101881)+~P1(f862(f862(f227(a1),f2(a1)),x101882))+E(f862(f93(x101881),f862(a97,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101882))),f862(f862(f73(x101881),f862(f93(x101881),f862(a97,x101882))),f862(f93(x101881),f862(a97,x101882)))) % 14.98/14.67 [5226]~P148(x52261,x52263,x52262)+~E(x52263,f2(a1))+P1(f862(x52261,x52262)) % 14.98/14.67 [5350]~P109(x53501)+~P11(x53501,x53503)+P11(x53501,f163(x53501,x53502,x53503)) % 14.98/14.67 [5351]~P109(x53511)+~P11(x53511,x53513)+P11(x53511,f170(x53511,x53512,x53513)) % 14.98/14.67 [4911]~P68(x49112)+~E(x49113,f862(f72(x49112),x49111))+E(x49111,f862(f72(x49112),x49113)) % 14.98/14.67 [4913]~P68(x49131)+~E(f862(f72(x49131),x49133),x49132)+E(f862(f72(x49131),x49132),x49133) % 14.98/14.67 [4993]~P109(x49933)+E(x49931,x49932)+~E(f862(f293(x49933),x49931),f862(f293(x49933),x49932)) % 14.98/14.67 [4994]~P109(x49943)+E(x49941,x49942)+~E(f862(f294(x49943),x49941),f862(f294(x49943),x49942)) % 14.98/14.67 [4995]~P109(x49953)+E(x49951,x49952)+~E(f862(f274(x49953),x49951),f862(f274(x49953),x49952)) % 14.98/14.67 [4996]~P109(x49963)+E(x49961,x49962)+~E(f862(f292(x49963),x49961),f862(f292(x49963),x49962)) % 14.98/14.67 [4997]~P96(x49973)+E(x49971,x49972)+~E(f862(f72(x49973),x49971),f862(f72(x49973),x49972)) % 14.98/14.67 [4998]~P68(x49983)+E(x49981,x49982)+~E(f862(f72(x49983),x49981),f862(f72(x49983),x49982)) % 14.98/14.67 [4999]~P105(x49993)+E(x49991,x49992)+~E(f862(f93(x49993),x49991),f862(f93(x49993),x49992)) % 14.98/14.67 [5000]~P97(x50003)+E(x50001,x50002)+~E(f862(f95(x50003),x50001),f862(f95(x50003),x50002)) % 14.98/14.67 [5102]~P63(x51021)+~P1(f862(x51022,x51023))+P1(f862(f49(x51021),x51022)) % 14.98/14.67 [5142]~P63(x51423)+P1(f862(x51421,x51422))+~P1(f862(f50(x51423),x51421)) % 14.98/14.67 [5246]~P149(x52461,x52462,x52463)+~E(x52462,f2(a1))+P1(f862(x52461,f2(a1))) % 14.98/14.67 [5286]~E(x52861,f2(a924))+E(f327(x52861,x52862,x52863),f181(f932(x52863,a921)))+~E(f862(f28(x52863),x52862),f862(a105,x52861)) % 14.98/14.67 [5437]~E(x54372,f2(a924))+E(f862(f243(a924,a924),x54371),f2(a924))+~P1(f862(f41(x54373,x54372),x54371)) % 14.98/14.67 [5476]P1(f862(x54761,x54762))+~E(x54763,f862(f93(a1),x54762))+~P1(f862(x54761,f862(a97,x54763))) % 14.98/14.67 [5962]~E(x59623,f2(a924))+~P1(f862(x59621,x59622))+P1(f862(x59621,f38(a924,x59622,x59623))) % 14.98/14.67 [6202]~P106(x62022)+~P106(x62021)+E(f124(x62021,x62022,f125(x62021,x62023),f125(x62022,x62023)),f125(f931(x62021,x62022),x62023)) % 14.98/14.67 [6383]~E(x63833,f2(a924))+P1(f862(x63831,x63832))+~P1(f862(x63831,f38(a924,x63832,x63833))) % 14.98/14.67 [7067]E(x70671,f2(a924))+~P1(f862(x70672,f429(x70671,x70673,x70672)))+P1(f862(x70672,f38(a924,x70673,x70671))) % 14.98/14.67 [7176]~P3(x71761)+~P1(f862(f862(f227(x71761),x71762),f368(x71763,x71762,x71761)))+P1(f862(f862(f227(x71761),x71762),f31(x71761,x71763))) % 14.98/14.67 [7177]~P3(x71771)+~P1(f862(f862(f227(x71771),x71772),f498(x71772,x71773,x71771)))+P1(f862(f862(f227(x71771),x71772),f31(x71771,x71773))) % 14.98/14.67 [7179]~P1(f862(x71791,x71792))+~P1(f862(x71791,f429(x71793,x71792,x71791)))+P1(f862(x71791,f38(a924,x71792,x71793))) % 14.98/14.67 [7281]E(x72811,f106(x72812))+E(f862(f862(f144(x72812),f696(x72813,x72811,x72812)),f699(x72813,x72811,x72812)),x72811)+~P1(f862(f862(f321(f925(x72812)),x72811),f154(x72812,x72813))) % 14.98/14.67 [7312]~P142(x73121)+~P1(f862(f862(f321(x73121),x73122),f102(x73121)))+P1(f862(f862(f321(x73121),f862(f862(f236(x73121),x73122),x73123)),f102(x73121))) % 14.98/14.67 [7641]P35(x76411,x76412)+~P1(f862(f862(f321(x76411),x76413),f610(x76412,x76411)))+P1(f862(f862(f321(x76411),f620(x76412,x76411,x76413)),f610(x76412,x76411))) % 14.98/14.67 [7911]E(x79111,f106(x79112))+~P1(f862(f862(f321(f925(x79112)),x79111),f154(x79112,x79113)))+P1(f862(f862(f321(f925(x79112)),f699(x79113,x79111,x79112)),f154(x79112,x79113))) % 14.98/14.67 [7963]E(x79631,f2(a924))+E(f862(f862(f73(a924),f862(f862(f74(a924),x79631),f430(x79631,x79632,x79633))),f429(x79631,x79632,x79633)),x79632)+P1(f862(x79633,f38(a924,x79632,x79631))) % 14.98/14.67 [8005]~P1(f862(x80053,x80052))+E(f862(f862(f73(a924),f862(f862(f74(a924),x80051),f430(x80051,x80052,x80053))),f429(x80051,x80052,x80053)),x80052)+P1(f862(x80053,f38(a924,x80052,x80051))) % 14.98/14.67 [8147]P1(f862(f862(f228(a1),x81471),f416(x81472,x81473,x81471)))+P1(f862(f862(x81473,f862(f862(f29(a1),x81472),x81471)),f38(a1,x81472,x81471)))+~P1(f862(f862(f228(a1),x81471),f2(a1))) % 14.98/14.67 [8421]P1(f862(f862(x84212,f862(f862(f29(a1),x84211),x84213)),f38(a1,x84211,x84213)))+~P1(f862(f862(f228(a1),x84213),f2(a1)))+P1(f862(f862(f227(a1),f416(x84211,x84212,x84213)),f2(a1))) % 14.98/14.67 [8605]E(f862(f862(f73(a1),f862(f862(f74(a1),x86051),f412(x86052,x86053,x86051))),f416(x86052,x86053,x86051)),x86052)+P1(f862(f862(x86053,f862(f862(f29(a1),x86052),x86051)),f38(a1,x86052,x86051)))+~P1(f862(f862(f228(a1),x86051),f2(a1))) % 14.98/14.67 [8846]~P1(f862(f862(x88461,f412(x88462,x88461,x88463)),f416(x88462,x88461,x88463)))+P1(f862(f862(x88461,f862(f862(f29(a1),x88462),x88463)),f38(a1,x88462,x88463)))+~P1(f862(f862(f228(a1),x88463),f2(a1))) % 14.98/14.67 [9099]~P109(x90991)+~P11(x90991,x90993)+P11(x90991,f142(x90991,x90991,f7(x90991),x90992,x90993)) % 14.98/14.67 [9601]~P128(x96012)+E(x96011,f2(x96012))+~P1(f862(f862(f227(x96012),f862(f862(f73(x96012),f862(f862(f74(x96012),x96013),x96013)),f862(f862(f74(x96012),x96011),x96011))),f2(x96012))) % 14.98/14.67 [9602]~P128(x96022)+E(x96021,f2(x96022))+~P1(f862(f862(f227(x96022),f862(f862(f73(x96022),f862(f862(f74(x96022),x96021),x96021)),f862(f862(f74(x96022),x96023),x96023))),f2(x96022))) % 14.98/14.67 [10401]~P112(x104011)+~P1(f862(f862(f228(x104011),x104012),f2(x104011)))+P1(f862(f862(f228(x104011),f862(f862(f236(x104011),x104012),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x104013)))),f2(x104011))) % 14.98/14.67 [10410]~P112(x104102)+E(x104101,f2(x104102))+~P1(f862(f862(f227(x104102),f862(f862(f73(x104102),f862(f862(f236(x104102),x104103),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x104102),x104101),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f2(x104102))) % 14.98/14.67 [10411]~P112(x104112)+E(x104111,f2(x104112))+~P1(f862(f862(f227(x104112),f862(f862(f73(x104112),f862(f862(f236(x104112),x104111),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x104112),x104113),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f2(x104112))) % 14.98/14.67 [4948]~E(x49482,x49483)+~P59(x49481)+E(f862(f862(f3(x49481),x49482),x49483),f2(x49481)) % 14.98/14.67 [4949]~E(x49492,x49493)+~P68(x49491)+E(f862(f862(f3(x49491),x49492),x49493),f2(x49491)) % 14.98/14.67 [4962]~P144(x49621)+~E(x49623,f2(x49621))+E(f862(f862(f73(x49621),x49622),x49623),x49622) % 14.98/14.67 [4979]~P143(x49791)+~E(x49793,f2(x49791))+E(f862(f862(f74(x49791),x49792),x49793),f2(x49791)) % 14.98/14.67 [4980]~P143(x49801)+~E(x49802,f2(x49801))+E(f862(f862(f74(x49801),x49802),x49803),f2(x49801)) % 14.98/14.67 [5002]~E(x50023,f106(x50021))+~E(x50022,f106(x50021))+E(f862(f862(f127(x50021),x50022),x50023),f106(x50021)) % 14.98/14.67 [5092]~P144(x50922)+E(x50921,f2(x50922))+~E(f862(f862(f73(x50922),x50923),x50921),x50923) % 14.98/14.67 [5093]~P68(x50931)+~E(x50932,f862(f72(x50931),x50933))+E(f862(f862(f73(x50931),x50932),x50933),f2(x50931)) % 14.98/14.67 [5100]E(x51001,f106(x51002))+E(x51003,f2(a924))+~E(f862(f862(f168(x51002),x51003),x51001),f106(x51002)) % 14.98/14.67 [5110]~P59(x51103)+E(x51101,x51102)+~E(f862(f862(f3(x51103),x51101),x51102),f2(x51103)) % 14.98/14.67 [5111]~P68(x51113)+E(x51111,x51112)+~E(f862(f862(f3(x51113),x51111),x51112),f2(x51113)) % 14.98/14.67 [5124]~P141(x51242)+E(x51241,f2(x51242))+~E(f862(f862(f236(x51242),x51241),x51243),f2(x51242)) % 14.98/14.67 [5125]~P95(x51252)+E(x51251,f181(x51252))+~E(f862(f862(f103(x51252),x51253),x51251),f181(x51252)) % 14.98/14.67 [5126]~P95(x51262)+E(x51261,f181(x51262))+~E(f862(f862(f103(x51262),x51261),x51263),f181(x51262)) % 14.98/14.67 [5127]~P94(x51272)+E(x51271,f234(x51272))+~E(f862(f862(f94(x51272),x51273),x51271),f234(x51272)) % 14.98/14.67 [5128]~P94(x51282)+E(x51281,f234(x51282))+~E(f862(f862(f94(x51282),x51281),x51283),f234(x51282)) % 14.98/14.67 [5199]~P68(x51992)+E(x51991,f862(f72(x51992),x51993))+~E(f862(f862(f73(x51992),x51991),x51993),f2(x51992)) % 14.98/14.67 [5200]~P68(x52001)+E(f862(f72(x52001),x52002),x52003)+~E(f862(f862(f73(x52001),x52002),x52003),f2(x52001)) % 14.98/14.67 [5201]~E(x52012,x52013)+~P2(x52011)+P1(f862(f862(f84(x52011),x52012),x52013)) % 14.98/14.67 [5203]~E(x52032,x52033)+~P91(x52031)+P1(f862(f862(f227(x52031),x52032),x52033)) % 14.98/14.67 [5205]~E(x52052,x52053)+~P110(x52051)+P1(f862(f862(f227(x52051),x52052),x52053)) % 14.98/14.67 [5303]~P113(x53031)+~E(x53032,f862(f72(x53031),x53033))+E(f862(f862(f74(x53031),x53032),x53032),f862(f862(f74(x53031),x53033),x53033)) % 14.98/14.67 [5311]~P109(x53111)+~P11(x53111,x53113)+P11(x53111,f862(f862(f168(x53111),x53112),x53113)) % 14.98/14.67 [5312]~P109(x53121)+~P11(x53121,x53123)+P11(x53121,f862(f862(f131(x53121),x53122),x53123)) % 14.98/14.67 [5348]E(x53481,x53482)+E(x53483,f2(a924))+~E(f862(f862(f74(a924),x53483),x53481),f862(f862(f74(a924),x53483),x53482)) % 14.98/14.67 [5349]E(x53491,x53492)+E(x53493,f2(a924))+~E(f862(f862(f74(a924),x53491),x53493),f862(f862(f74(a924),x53492),x53493)) % 14.98/14.67 [5429]~E(x54292,x54293)+~P110(x54291)+E(f296(x54291,x54292,x54293),f862(f862(f301(x54291),x54292),f181(f932(x54291,a921)))) % 14.98/14.67 [5462]E(x54621,x54622)+~P2(x54623)+~P1(f862(f862(f84(x54623),x54621),x54622)) % 14.98/14.67 [5473]~E(x54731,x54732)+~P109(x54733)+~P1(f862(f862(f228(x54733),x54731),x54732)) % 14.98/14.67 [5474]~E(x54741,x54742)+~P110(x54743)+~P1(f862(f862(f228(x54743),x54741),x54742)) % 14.98/14.67 [5487]~P110(x54871)+E(f862(f295(x54871,x54872),x54873),f181(f932(x54871,a921)))+P1(f862(f862(f228(x54871),x54872),x54873)) % 14.98/14.67 [5535]~P110(x55351)+E(f297(x55351,x55352,x55353),f181(f932(x55351,a921)))+P1(f862(f862(f228(x55351),x55352),x55353)) % 14.98/14.67 [5536]~P110(x55361)+E(f296(x55361,x55362,x55363),f181(f932(x55361,a921)))+P1(f862(f862(f227(x55361),x55362),x55363)) % 14.98/14.67 [5537]~P110(x55371)+E(f181(f932(x55371,a921)),f297(x55371,x55372,x55373))+P1(f862(f862(f228(x55371),x55372),x55373)) % 14.98/14.67 [5538]~P110(x55381)+E(f181(f932(x55381,a921)),f296(x55381,x55382,x55383))+P1(f862(f862(f227(x55381),x55382),x55383)) % 14.98/14.67 [5547]~P103(x55471)+~E(f862(f862(f103(x55471),x55472),x55473),x55473)+P1(f862(f862(f227(x55471),x55472),x55473)) % 14.98/14.67 [5548]~P104(x55481)+~E(f862(f862(f94(x55481),x55482),x55483),x55482)+P1(f862(f862(f227(x55481),x55482),x55483)) % 14.98/14.67 [5549]~P109(x55491)+~E(f862(f862(f225(x55491),x55492),x55493),x55492)+P1(f862(f862(f227(x55491),x55492),x55493)) % 14.98/14.67 [5550]~P109(x55501)+~E(f862(f862(f226(x55501),x55502),x55503),x55503)+P1(f862(f862(f227(x55501),x55502),x55503)) % 14.98/14.67 [5569]~P109(x55691)+P11(x55691,x55692)+~P11(x55691,f862(f862(f144(x55691),x55693),x55692)) % 14.98/14.67 [5570]~P109(x55701)+P11(x55701,x55702)+~P11(x55701,f862(f862(f127(x55701),x55703),x55702)) % 14.98/14.67 [5571]~P109(x55711)+P11(x55711,x55712)+~P11(x55711,f862(f862(f127(x55711),x55712),x55713)) % 14.98/14.67 [5576]~P61(x55761)+~E(f38(x55761,x55763,x55762),f2(x55761))+P1(f862(f862(f278(x55761),x55762),x55763)) % 14.98/14.67 [5638]~P109(x56381)+P1(f862(f862(f227(x56381),x56383),x56382))+P1(f862(f862(f227(x56381),x56382),x56383)) % 14.98/14.67 [5643]~P109(x56431)+P1(f862(f862(f228(x56431),x56433),x56432))+P1(f862(f862(f227(x56431),x56432),x56433)) % 14.98/14.67 [5680]~P103(x56801)+E(f862(f862(f103(x56801),x56802),x56803),x56802)+~P1(f862(f862(f227(x56801),x56803),x56802)) % 14.98/14.67 [5682]~P103(x56821)+E(f862(f862(f103(x56821),x56822),x56823),x56823)+~P1(f862(f862(f227(x56821),x56822),x56823)) % 14.98/14.67 [5683]~P104(x56831)+E(f862(f862(f94(x56831),x56832),x56833),x56833)+~P1(f862(f862(f227(x56831),x56833),x56832)) % 14.98/14.67 [5685]~P104(x56851)+E(f862(f862(f94(x56851),x56852),x56853),x56852)+~P1(f862(f862(f227(x56851),x56852),x56853)) % 14.98/14.67 [5686]~P109(x56861)+E(f862(f862(f225(x56861),x56862),x56863),x56863)+~P1(f862(f862(f227(x56861),x56863),x56862)) % 14.98/14.67 [5688]~P109(x56881)+E(f862(f862(f225(x56881),x56882),x56883),x56882)+~P1(f862(f862(f227(x56881),x56882),x56883)) % 14.98/14.67 [5689]~P109(x56891)+E(f862(f862(f226(x56891),x56892),x56893),x56892)+~P1(f862(f862(f227(x56891),x56893),x56892)) % 14.98/14.67 [5691]~P109(x56911)+E(f862(f862(f226(x56911),x56912),x56913),x56913)+~P1(f862(f862(f227(x56911),x56912),x56913)) % 14.98/14.67 [5698]~P121(x56982)+E(x56981,f2(x56982))+E(f862(f862(f281(x56982),f862(f72(x56982),x56983)),f862(f72(x56982),x56981)),f862(f862(f281(x56982),x56983),x56981)) % 14.98/14.67 [5705]~P61(x57051)+E(f38(x57051,x57052,x57053),f2(x57051))+~P1(f862(f862(f278(x57051),x57053),x57052)) % 14.98/14.67 [5753]~P110(x57531)+E(f862(f295(x57531,x57532),x57533),f181(f932(x57531,a921)))+~P1(f862(f862(f227(x57531),x57533),x57532)) % 14.98/14.67 [5787]~P110(x57871)+E(f298(x57871,x57872,x57873),f181(f932(x57871,a921)))+~P1(f862(f862(f227(x57871),x57873),x57872)) % 14.98/14.67 [5788]~P110(x57881)+E(f297(x57881,x57882,x57883),f181(f932(x57881,a921)))+~P1(f862(f862(f227(x57881),x57883),x57882)) % 14.98/14.67 [5789]~P110(x57891)+E(f296(x57891,x57892,x57893),f181(f932(x57891,a921)))+~P1(f862(f862(f228(x57891),x57893),x57892)) % 14.98/14.67 [5841]~E(f862(f862(f3(a924),x58411),x58413),x58412)+E(x58411,f862(f862(f73(a924),x58412),x58413))+~P1(f862(f862(f227(a924),x58413),x58411)) % 14.98/14.67 [5842]~E(x58421,f862(f862(f73(a924),x58423),x58422))+E(f862(f862(f3(a924),x58421),x58422),x58423)+~P1(f862(f862(f227(a924),x58422),x58421)) % 14.98/14.67 [5887]~P1(f862(x58871,x58873))+P1(f862(x58871,f331(x58871,x58872)))+~P1(f862(f862(f227(a924),x58873),x58872)) % 14.98/14.67 [5888]~P1(f862(x58881,x58883))+P1(f862(x58881,f343(x58881,x58882)))+~P1(f862(f862(f228(a924),x58883),x58882)) % 14.98/14.67 [5896]~P110(x58961)+~E(f862(f295(x58961,x58962),x58963),f181(f932(x58961,a921)))+~P1(f862(f862(f228(x58961),x58962),x58963)) % 14.98/14.67 [5901]~P91(x59011)+~P1(f862(f862(f228(x59011),x59012),x59013))+P1(f862(f862(f227(x59011),x59012),x59013)) % 14.98/14.67 [5903]~P110(x59031)+~P1(f862(f862(f228(x59031),x59032),x59033))+P1(f862(f862(f227(x59031),x59032),x59033)) % 14.98/14.67 [6019]~P110(x60191)+~E(f297(x60191,x60192,x60193),f181(f932(x60191,a921)))+~P1(f862(f862(f228(x60191),x60192),x60193)) % 14.98/14.67 [6020]~P110(x60201)+~E(f296(x60201,x60202,x60203),f181(f932(x60201,a921)))+~P1(f862(f862(f227(x60201),x60202),x60203)) % 14.98/14.67 [6021]~P110(x60211)+~E(f181(f932(x60211,a921)),f297(x60211,x60212,x60213))+~P1(f862(f862(f228(x60211),x60212),x60213)) % 14.98/14.67 [6022]~P110(x60221)+~E(f181(f932(x60221,a921)),f296(x60221,x60222,x60223))+~P1(f862(f862(f227(x60221),x60222),x60223)) % 14.98/14.67 [6032]P1(f862(x60321,x60322))+~P1(f862(x60321,f344(x60321,x60323)))+~P1(f862(f862(f227(a924),x60322),x60323)) % 14.98/14.67 [6033]P1(f862(x60331,x60332))+~P1(f862(x60331,f347(x60331,x60333)))+~P1(f862(f862(f228(a924),x60332),x60333)) % 14.98/14.67 [6041]~E(x60411,f862(a105,x60413))+P1(f862(f862(f228(a924),x60411),f862(a105,x60412)))+~P1(f862(f862(f228(a924),x60413),x60412)) % 14.98/14.67 [6060]E(x60601,x60602)+~E(f862(f862(f74(a924),x60603),x60601),f862(f862(f74(a924),x60603),x60602))+~P1(f862(f862(f228(a924),f2(a924)),x60603)) % 14.98/14.67 [6120]E(f862(x61201,f335(x61201,x61202,x61203)),f71(a924))+~E(f862(f862(f8(x61203,a924),x61201),x61202),f71(a924))+~P1(f862(f54(x61203),x61202)) % 14.98/14.67 [6137]~P3(x61371)+P1(f862(f862(f227(x61371),x61372),f30(x61371,x61373)))+~P1(f862(f862(f321(x61371),x61372),x61373)) % 14.98/14.67 [6160]~P91(x61601)+~P1(f862(f862(f228(x61601),x61603),x61602))+~P1(f862(f862(f227(x61601),x61602),x61603)) % 14.98/14.67 [6164]~P91(x61641)+~P1(f862(f862(f228(x61641),x61643),x61642))+~P1(f862(f862(f228(x61641),x61642),x61643)) % 14.98/14.67 [6167]~P109(x61671)+~P1(f862(f862(f228(x61671),x61673),x61672))+~P1(f862(f862(f227(x61671),x61672),x61673)) % 14.98/14.67 [6168]~P109(x61681)+~P1(f862(f862(f228(x61681),x61683),x61682))+~P1(f862(f862(f228(x61681),x61682),x61683)) % 14.98/14.67 [6169]~P110(x61691)+~P1(f862(f862(f228(x61691),x61693),x61692))+~P1(f862(f862(f228(x61691),x61692),x61693)) % 14.98/14.67 [6194]~E(f862(x61942,f336(x61942,x61943,x61941)),f2(a924))+E(f862(f862(f8(x61941,a924),x61942),x61943),f2(a924))+~P1(f862(f54(x61941),x61943)) % 14.98/14.67 [6195]~E(f862(x61952,f914(x61952,x61953,x61951)),f71(a924))+E(f862(f862(f11(x61951,a924),x61952),x61953),f71(a924))+~P1(f862(f54(x61951),x61953)) % 14.98/14.67 [6211]~P108(x62111)+~P1(f862(f862(f228(x62111),x62113),x62112))+P1(f862(f862(f321(x62111),x62112),f862(f293(x62111),x62113))) % 14.98/14.67 [6212]~P108(x62121)+~P1(f862(f862(f227(x62121),x62123),x62122))+P1(f862(f862(f321(x62121),x62122),f862(f274(x62121),x62123))) % 14.98/14.67 [6213]~P108(x62131)+~P1(f862(f862(f227(x62131),x62132),x62133))+P1(f862(f862(f321(x62131),x62132),f862(f294(x62131),x62133))) % 14.98/14.67 [6214]~P108(x62141)+~P1(f862(f862(f228(x62141),x62142),x62143))+P1(f862(f862(f321(x62141),x62142),f862(f292(x62141),x62143))) % 14.98/14.67 [6227]E(f862(x62271,f333(x62271,x62272,x62273)),f862(a105,f2(a924)))+~E(f862(f862(f8(x62273,a924),x62271),x62272),f862(a105,f2(a924)))+~P1(f862(f54(x62273),x62272)) % 14.98/14.67 [6308]~P3(x63081)+~P1(f862(f862(f321(x63081),x63083),x63082))+P1(f862(f862(f227(x63081),f31(x63081,x63082)),x63083)) % 14.98/14.67 [6328]~P1(f862(f862(f227(a924),x63281),x63283))+P1(f862(f862(f227(a924),x63281),x63282))+~P1(f862(f862(f227(a924),x63283),x63282)) % 14.98/14.67 [6329]~P1(f862(f862(f227(a1),x63291),x63293))+P1(f862(f862(f227(a1),x63291),x63292))+~P1(f862(f862(f227(a1),x63293),x63292)) % 14.98/14.67 [6349]~P108(x63491)+~P1(f862(f862(f321(x63491),x63493),f862(f274(x63491),x63492)))+P1(f862(f862(f227(x63491),x63492),x63493)) % 14.98/14.67 [6350]~P108(x63501)+~P1(f862(f862(f321(x63501),x63502),f862(f294(x63501),x63503)))+P1(f862(f862(f227(x63501),x63502),x63503)) % 14.98/14.67 [6351]~P108(x63511)+~P1(f862(f862(f321(x63511),x63513),f862(f293(x63511),x63512)))+P1(f862(f862(f228(x63511),x63512),x63513)) % 14.98/14.67 [6352]~P108(x63521)+~P1(f862(f862(f321(x63521),x63522),f862(f292(x63521),x63523)))+P1(f862(f862(f228(x63521),x63522),x63523)) % 14.98/14.67 [6427]~P1(f862(x64271,x64272))+P1(f862(x64271,f792(x64271)))+~P1(f862(f862(f321(x64273),x64272),f234(f932(x64273,a921)))) % 14.98/14.67 [6571]~P66(x65711)+P1(f862(f862(f228(x65711),f2(x65711)),f363(x65713,x65712,x65711)))+P1(f862(f862(f227(x65711),x65712),x65713)) % 14.98/14.67 [6572]~P67(x65721)+P1(f862(f862(f228(x65721),f2(x65721)),f436(x65723,x65722,x65721)))+P1(f862(f862(f227(x65721),x65722),x65723)) % 14.98/14.67 [6642]~P78(x66421)+~P1(f862(f862(f227(x66421),x66423),f862(f72(x66421),x66422)))+P1(f862(f862(f227(x66421),x66422),f862(f72(x66421),x66423))) % 14.98/14.67 [6644]~P78(x66441)+~P1(f862(f862(f228(x66441),x66443),f862(f72(x66441),x66442)))+P1(f862(f862(f228(x66441),x66442),f862(f72(x66441),x66443))) % 14.98/14.67 [6656]~P1(f862(f862(f228(a924),x66561),x66563))+~P1(f862(f862(f228(a924),x66563),x66562))+P1(f862(f862(f228(a924),f862(a105,x66561)),x66562)) % 14.98/14.67 [6684]~P127(x66841)+P1(f862(f862(f227(x66841),f862(f93(x66841),x66842)),f862(f93(x66841),x66843)))+~P1(f862(f862(f227(a924),x66842),x66843)) % 14.98/14.67 [6685]~P112(x66851)+P1(f862(f862(f227(x66851),f862(f95(x66851),x66852)),f862(f95(x66851),x66853)))+~P1(f862(f862(f227(a1),x66852),x66853)) % 14.98/14.67 [6687]~P112(x66871)+P1(f862(f862(f228(x66871),f862(f95(x66871),x66872)),f862(f95(x66871),x66873)))+~P1(f862(f862(f228(a1),x66872),x66873)) % 14.98/14.67 [6688]~P127(x66881)+P1(f862(f862(f228(x66881),f862(f93(x66881),x66882)),f862(f93(x66881),x66883)))+~P1(f862(f862(f228(a924),x66882),x66883)) % 14.98/14.67 [6694]~P109(x66941)+E(f862(f862(f103(f932(x66941,a921)),f862(f292(x66941),x66942)),f862(f295(x66941,x66942),x66943)),f862(f292(x66941),x66943))+~P1(f862(f862(f227(x66941),x66942),x66943)) % 14.98/14.67 [6725]~P78(x67251)+~P1(f862(f862(f227(x67251),x67253),x67252))+P1(f862(f862(f227(x67251),f862(f72(x67251),x67252)),f862(f72(x67251),x67253))) % 14.98/14.67 [6727]~P96(x67271)+~P1(f862(f862(f227(x67271),x67273),x67272))+P1(f862(f862(f227(x67271),f862(f72(x67271),x67272)),f862(f72(x67271),x67273))) % 14.98/14.67 [6728]~P78(x67281)+~P1(f862(f862(f228(x67281),x67283),x67282))+P1(f862(f862(f228(x67281),f862(f72(x67281),x67282)),f862(f72(x67281),x67283))) % 14.98/14.67 [6761]~P109(x67611)+E(f862(f862(f103(f932(x67611,a921)),f862(f294(x67611),x67612)),f298(x67611,x67612,x67613)),f862(f292(x67611),x67613))+~P1(f862(f862(f228(x67611),x67612),x67613)) % 14.98/14.67 [6762]~P109(x67621)+E(f862(f862(f103(f932(x67621,a921)),f862(f294(x67621),x67622)),f297(x67621,x67622,x67623)),f862(f294(x67621),x67623))+~P1(f862(f862(f227(x67621),x67622),x67623)) % 14.98/14.67 [6763]~P109(x67631)+E(f862(f862(f103(f932(x67631,a921)),f862(f292(x67631),x67632)),f296(x67631,x67632,x67633)),f862(f294(x67631),x67633))+~P1(f862(f862(f227(x67631),x67632),x67633)) % 14.98/14.67 [6796]~P109(x67961)+E(f862(f862(f103(f932(x67961,a921)),f862(f295(x67961,x67962),x67963)),f862(f274(x67961),x67963)),f862(f274(x67961),x67962))+~P1(f862(f862(f227(x67961),x67962),x67963)) % 14.98/14.67 [6949]~P109(x69491)+E(f862(f862(f103(f932(x69491,a921)),f298(x69491,x69492,x69493)),f862(f274(x69491),x69493)),f862(f293(x69491),x69492))+~P1(f862(f862(f228(x69491),x69492),x69493)) % 14.98/14.67 [6950]~P109(x69501)+E(f862(f862(f103(f932(x69501,a921)),f297(x69501,x69502,x69503)),f862(f293(x69501),x69503)),f862(f293(x69501),x69502))+~P1(f862(f862(f227(x69501),x69502),x69503)) % 14.98/14.67 [6951]~P109(x69511)+E(f862(f862(f103(f932(x69511,a921)),f296(x69511,x69512,x69513)),f862(f293(x69511),x69513)),f862(f274(x69511),x69512))+~P1(f862(f862(f227(x69511),x69512),x69513)) % 14.98/14.67 [6971]P1(f862(x69711,x69712))+~P1(f862(f862(f227(a924),x69712),x69713))+P1(f862(f862(f321(a924),f344(x69711,x69713)),f296(a924,f2(a924),x69713))) % 14.98/14.67 [7005]E(x70051,x70052)+~E(f862(f862(f157(x70053),x70051),f658(x70053,x70052,x70051)),f862(f862(f157(x70053),x70052),f658(x70053,x70052,x70051)))+~E(f862(f182(f925(x70053)),x70051),f862(f182(f925(x70053)),x70052)) % 14.98/14.67 [7010]~E(x70103,f862(f862(f29(a924),x70101),x70102))+~P1(f862(f862(f228(a924),f2(a924)),x70102))+P1(f862(f862(f228(a924),x70101),f862(f862(f74(a924),x70102),f862(a105,x70103)))) % 14.98/14.67 [7026]~P1(f862(x70261,x70263))+~P1(f862(f862(f227(a924),x70263),x70262))+P1(f862(f862(f321(a924),f331(x70261,x70262)),f296(a924,f2(a924),x70262))) % 14.98/14.67 [7065]~P1(f862(x70651,x70653))+P1(f862(x70651,f345(x70651,x70652)))+~P1(f862(f862(f321(a924),x70653),f296(a924,f2(a924),x70652))) % 14.98/14.67 [7084]~P127(x70843)+~P1(f862(f862(f227(x70843),f862(f93(x70843),x70841)),f862(f93(x70843),x70842)))+P1(f862(f862(f227(a924),x70841),x70842)) % 14.98/14.67 [7085]~P112(x70853)+~P1(f862(f862(f227(x70853),f862(f95(x70853),x70851)),f862(f95(x70853),x70852)))+P1(f862(f862(f227(a1),x70851),x70852)) % 14.98/14.67 [7087]~P127(x70873)+~P1(f862(f862(f228(x70873),f862(f93(x70873),x70871)),f862(f93(x70873),x70872)))+P1(f862(f862(f228(a924),x70871),x70872)) % 14.98/14.67 [7088]~P112(x70883)+~P1(f862(f862(f228(x70883),f862(f95(x70883),x70881)),f862(f95(x70883),x70882)))+P1(f862(f862(f228(a1),x70881),x70882)) % 14.98/14.67 [7104]~P127(x71041)+~P1(f862(f862(f228(x71041),f71(x71041)),x71042))+P1(f862(f862(f228(x71041),f71(x71041)),f862(f862(f236(x71041),x71042),f862(a105,x71043)))) % 14.98/14.67 [7107]~P78(x71071)+~P1(f862(f862(f227(x71071),f862(f72(x71071),x71073)),f862(f72(x71071),x71072)))+P1(f862(f862(f227(x71071),x71072),x71073)) % 14.98/14.67 [7108]~P96(x71081)+~P1(f862(f862(f227(x71081),f862(f72(x71081),x71083)),f862(f72(x71081),x71082)))+P1(f862(f862(f227(x71081),x71082),x71083)) % 14.98/14.67 [7109]~P78(x71091)+~P1(f862(f862(f228(x71091),f862(f72(x71091),x71093)),f862(f72(x71091),x71092)))+P1(f862(f862(f228(x71091),x71092),x71093)) % 14.98/14.67 [7133]P1(f862(x71331,x71332))+~P1(f862(x71331,f346(x71331,x71333)))+~P1(f862(f862(f321(a924),x71332),f296(a924,f2(a924),x71333))) % 14.98/14.67 [7153]~P66(x71531)+P1(f862(f862(f228(x71531),f363(x71533,x71532,x71531)),f71(x71531)))+P1(f862(f862(f227(x71531),x71532),x71533)) % 14.98/14.67 [7173]~E(f38(a924,x71733,x71732),f38(a924,x71731,x71732))+E(f862(f862(f73(a924),x71731),f862(f862(f74(a924),x71732),f438(x71731,x71732,x71733))),x71733)+~P1(f862(f862(f227(a924),x71731),x71733)) % 14.98/14.67 [7228]E(f862(f862(f8(x72281,a924),x72282),x72283),f2(a924))+~P1(f862(f54(x72281),x72283))+P1(f862(f862(f321(x72281),f336(x72282,x72283,x72281)),x72283)) % 14.98/14.67 [7229]E(f862(f862(f11(x72291,a924),x72292),x72293),f71(a924))+~P1(f862(f54(x72291),x72293))+P1(f862(f862(f321(x72291),f914(x72292,x72293,x72291)),x72293)) % 14.98/14.67 [7251]~P109(x72511)+~P1(f862(f862(f227(x72511),x72513),x72512))+P1(f862(f862(f227(f932(x72511,a921)),f862(f293(x72511),x72512)),f862(f293(x72511),x72513))) % 14.98/14.67 [7252]~P110(x72521)+~P1(f862(f862(f227(x72521),x72522),x72523))+P1(f862(f862(f227(f932(x72521,a921)),f862(f294(x72521),x72522)),f862(f294(x72521),x72523))) % 14.98/14.67 [7253]~P110(x72531)+~P1(f862(f862(f227(x72531),x72533),x72532))+P1(f862(f862(f227(f932(x72531,a921)),f862(f274(x72531),x72532)),f862(f274(x72531),x72533))) % 14.98/14.67 [7254]~P109(x72541)+~P1(f862(f862(f227(x72541),x72542),x72543))+P1(f862(f862(f227(f932(x72541,a921)),f862(f292(x72541),x72542)),f862(f292(x72541),x72543))) % 14.98/14.67 [7255]~P109(x72551)+~P1(f862(f862(f228(x72551),x72552),x72553))+P1(f862(f862(f228(f932(x72551,a921)),f862(f292(x72551),x72552)),f862(f292(x72551),x72553))) % 14.98/14.67 [7266]~P3(x72661)+P1(f862(f862(f227(x72661),x72662),f31(x72661,x72663)))+P1(f862(f862(f321(x72661),f368(x72663,x72662,x72661)),x72663)) % 14.98/14.67 [7267]~P3(x72671)+P1(f862(f862(f227(x72671),x72672),f31(x72671,x72673)))+P1(f862(f862(f321(x72671),f498(x72672,x72673,x72671)),x72673)) % 14.98/14.67 [7273]~P78(x72731)+P1(f862(f862(f227(x72731),f862(f862(f3(x72731),x72732),x72733)),f2(x72731)))+~P1(f862(f862(f227(x72731),x72732),x72733)) % 14.98/14.67 [7274]~P78(x72741)+P1(f862(f862(f228(x72741),f862(f862(f3(x72741),x72742),x72743)),f2(x72741)))+~P1(f862(f862(f228(x72741),x72742),x72743)) % 14.98/14.67 [7316]P1(f862(x73161,x73162))+P1(f862(f862(f227(a924),f346(x73161,x73163)),x73163))+~P1(f862(f862(f321(a924),x73162),f296(a924,f2(a924),x73163))) % 14.98/14.67 [7358]~E(f862(f862(f8(x73581,a924),x73582),x73583),f71(a924))+~P1(f862(f54(x73581),x73583))+P1(f862(f862(f321(x73581),f335(x73582,x73583,x73581)),x73583)) % 14.98/14.67 [7359]~P1(f862(x73591,x73593))+P1(f862(f862(f227(a924),f345(x73591,x73592)),x73592))+~P1(f862(f862(f321(a924),x73593),f296(a924,f2(a924),x73592))) % 14.98/14.67 [7398]~P3(x73981)+P1(f862(f862(f321(x73981),f375(x73983,x73982,x73981)),x73982))+P1(f862(f862(f227(x73981),f30(x73981,x73982)),x73983)) % 14.98/14.67 [7399]~P3(x73991)+P1(f862(f862(f321(x73991),f502(x73993,x73992,x73991)),x73992))+P1(f862(f862(f227(x73991),f30(x73991,x73992)),x73993)) % 14.98/14.67 [7433]~E(f862(f862(f8(x74331,a924),x74332),x74333),f862(a105,f2(a924)))+~P1(f862(f54(x74331),x74333))+P1(f862(f862(f321(x74331),f333(x74332,x74333,x74331)),x74333)) % 14.98/14.67 [7445]E(x74451,f2(a924))+P1(f862(x74452,f38(a924,x74453,x74451)))+P1(f862(f862(f228(a924),f429(x74451,x74453,x74452)),x74451)) % 14.98/14.67 [7559]~P1(f862(x75591,x75592))+P1(f862(x75591,f38(a924,x75592,x75593)))+P1(f862(f862(f228(a924),f429(x75593,x75592,x75591)),x75593)) % 14.98/14.67 [7672]E(x76721,f106(x76722))+~P1(f862(f862(f321(f925(x76722)),x76721),f154(x76722,x76723)))+P1(f862(f862(f321(x76722),f696(x76723,x76721,x76722)),x76723)) % 14.98/14.67 [7696]~P109(x76961)+E(f862(f862(f103(f932(x76961,a921)),f862(f862(f301(x76961),x76962),f181(f932(x76961,a921)))),f298(x76961,x76962,x76963)),f862(f295(x76961,x76962),x76963))+~P1(f862(f862(f228(x76961),x76962),x76963)) % 14.98/14.67 [7717]~P109(x77171)+E(f862(f862(f103(f932(x77171,a921)),f862(f862(f301(x77171),x77172),f181(f932(x77171,a921)))),f297(x77171,x77172,x77173)),f296(x77171,x77172,x77173))+~P1(f862(f862(f227(x77171),x77172),x77173)) % 14.98/14.67 [7829]~P109(x78291)+P1(f862(f862(f227(x78291),x78292),x78293))+~P1(f862(f862(f227(f932(x78291,a921)),f862(f293(x78291),x78293)),f862(f293(x78291),x78292))) % 14.98/14.67 [7830]~P110(x78301)+P1(f862(f862(f227(x78301),x78302),x78303))+~P1(f862(f862(f227(f932(x78301,a921)),f862(f274(x78301),x78303)),f862(f274(x78301),x78302))) % 14.98/14.67 [7831]~P109(x78311)+P1(f862(f862(f227(x78311),x78312),x78313))+~P1(f862(f862(f227(f932(x78311,a921)),f862(f292(x78311),x78312)),f862(f292(x78311),x78313))) % 14.98/14.67 [7832]~P110(x78321)+P1(f862(f862(f227(x78321),x78322),x78323))+~P1(f862(f862(f227(f932(x78321,a921)),f862(f294(x78321),x78322)),f862(f294(x78321),x78323))) % 14.98/14.67 [7833]~P109(x78331)+P1(f862(f862(f228(x78331),x78332),x78333))+~P1(f862(f862(f228(f932(x78331,a921)),f862(f292(x78331),x78332)),f862(f292(x78331),x78333))) % 14.98/14.67 [7856]~P78(x78561)+~P1(f862(f862(f227(x78561),f862(f862(f3(x78561),x78562),x78563)),f2(x78561)))+P1(f862(f862(f227(x78561),x78562),x78563)) % 14.98/14.67 [7857]~P78(x78571)+~P1(f862(f862(f228(x78571),f862(f862(f3(x78571),x78572),x78573)),f2(x78571)))+P1(f862(f862(f228(x78571),x78572),x78573)) % 14.98/14.67 [8012]E(x80121,f2(a924))+~E(f862(f135(a924,a924,f73(a924),x80122),x80123),f2(a924))+~P1(f862(f862(f321(a924),x80121),f862(f165(a924),x80123))) % 14.98/14.67 [8016]~P3(x80161)+~P1(f862(f862(f227(x80161),f375(x80163,x80162,x80161)),x80163))+P1(f862(f862(f227(x80161),f30(x80161,x80162)),x80163)) % 14.98/14.67 [8017]~P3(x80171)+~P1(f862(f862(f227(x80171),f502(x80173,x80172,x80171)),x80173))+P1(f862(f862(f227(x80171),f30(x80171,x80172)),x80173)) % 14.98/14.67 [8174]P1(f862(f862(f227(a1),f2(a1)),f417(x81741,x81742,x81743)))+P1(f862(f862(x81742,f862(f862(f29(a1),x81741),x81743)),f38(a1,x81741,x81743)))+~P1(f862(f862(f228(a1),f2(a1)),x81743)) % 14.98/14.67 [8263]E(x82631,x82632)+~E(f862(f182(f925(x82633)),x82631),f862(f182(f925(x82633)),x82632))+~P1(f862(f862(f249(x82633,x82633,a921),a317),f670(x82633,x82631,x82632))) % 14.98/14.67 [8336]~P35(x83362,x83363)+E(x83361,f181(f932(x83362,a921)))+~P1(f862(f862(f227(f932(x83362,a921)),x83361),f862(f276(x83362,x83362,x83363),x83361))) % 14.98/14.67 [8367]~P67(x83671)+~P1(f862(f862(f227(x83671),x83672),f862(f862(f73(x83671),x83673),f436(x83673,x83672,x83671))))+P1(f862(f862(f227(x83671),x83672),x83673)) % 14.98/14.67 [8403]P50(x84031,x84032,x84033)+P1(f862(f862(f321(x84031),f579(x84033,x84032,x84031)),x84032))+P1(f862(f862(f321(f931(x84031,x84031)),f580(x84033,x84032,x84031)),x84033)) % 14.98/14.67 [8424]P1(f862(f862(x84242,f862(f862(f29(a1),x84241),x84243)),f38(a1,x84241,x84243)))+~P1(f862(f862(f228(a1),f2(a1)),x84243))+P1(f862(f862(f228(a1),f417(x84241,x84242,x84243)),x84243)) % 14.98/14.67 [8448]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x84481)),f862(f295(a924,x84482),x84483)),f181(f932(a924,a921)))+P1(f862(f862(f228(a924),x84481),x84483))+P1(f862(f862(f228(a924),x84482),x84483)) % 14.98/14.67 [8559]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x85591)),f862(f295(a924,x85592),x85593)),f862(f862(f301(a924),f2(a924)),f181(f932(a924,a921))))+P1(f862(f862(f228(a924),x85591),x85593))+~P1(f862(f862(f228(a924),x85592),x85593)) % 14.98/14.67 [8573]~P109(x85731)+E(f142(x85731,x85731,f7(x85731),x85732,x85733),x85733)+~P1(f862(f862(f321(x85731),x85732),f862(f165(x85731),x85733))) % 14.98/14.67 [8586]P22(x85861,x85861,x85862,x85863)+~P1(f862(f54(x85861),x85863))+~P1(f862(f862(f227(f932(x85861,a921)),x85863),f862(f302(x85861,x85861,x85862),x85863))) % 14.98/14.67 [8613]E(f862(f862(f73(a1),f862(f862(f74(a1),x86131),f418(x86132,x86133,x86131))),f417(x86132,x86133,x86131)),x86132)+P1(f862(f862(x86133,f862(f862(f29(a1),x86132),x86131)),f38(a1,x86132,x86131)))+~P1(f862(f862(f228(a1),f2(a1)),x86131)) % 14.98/14.67 [8853]~P1(f862(f862(x88531,f418(x88532,x88531,x88533)),f417(x88532,x88531,x88533)))+P1(f862(f862(x88531,f862(f862(f29(a1),x88532),x88533)),f38(a1,x88532,x88533)))+~P1(f862(f862(f228(a1),f2(a1)),x88533)) % 14.98/14.67 [9747]~P1(f862(f54(x97471),x97472))+~P1(f862(f862(f321(x97471),x97473),x97472))+P1(f862(f862(f228(a924),f862(f28(x97471),f862(f862(f3(f932(x97471,a921)),x97472),f862(f862(f301(x97471),x97473),f181(f932(x97471,a921)))))),f862(f28(x97471),x97472))) % 14.98/14.67 [10101]P1(f862(x101011,x101012))+~P1(f862(x101011,f862(f87(x101013),f773(x101011,x101012,x101013))))+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x101013,f932(a920,a921))),f930(a920,x101013)),a921)),x101012),f862(f254(f932(f922(f930(a919,f932(x101013,f932(a920,a921))),f930(a920,x101013)),a921)),f88(x101013)))) % 14.98/14.67 [10341]P50(x103411,x103412,x103413)+~P1(f862(f862(f249(x103411,x103411,a921),f862(f862(f9(x103411,f932(x103411,a921),f932(x103411,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x103411,a921),f932(x103411,a921)),x103411),f10(a921,a921,x103411)),f862(f862(f10(a921,f932(a921,a921),x103411),a318),f862(f862(f9(x103411,f932(x103411,a921),a921),f321(x103411)),x103412)))),f862(f862(f9(x103411,f932(x103411,a921),a921),f321(x103411)),x103412))),f580(x103413,x103412,x103411)))+P1(f862(f862(f321(x103411),f579(x103413,x103412,x103411)),x103412)) % 14.98/14.67 [5660]~P121(x56602)+E(x56601,f2(x56602))+E(f862(f862(f281(x56602),x56603),f862(f72(x56602),x56601)),f862(f72(x56602),f862(f862(f281(x56602),x56603),x56601))) % 14.98/14.67 [5803]~E(x58033,f181(f932(x58031,a921)))+~E(x58032,f181(f932(x58031,a921)))+E(f862(f862(f103(f932(x58031,a921)),x58032),x58033),f181(f932(x58031,a921))) % 14.98/14.67 [5861]~E(x58613,f2(a924))+~P1(f862(x58611,f2(a924)))+P1(f862(x58611,f862(f862(f29(a924),x58612),x58613))) % 14.98/14.67 [6011]~P67(x60112)+E(x60111,f2(x60112))+E(f862(f862(f281(x60112),f862(f69(x60112),x60113)),f862(f69(x60112),x60111)),f862(f69(x60112),f862(f862(f281(x60112),x60113),x60111))) % 14.98/14.67 [6130]~P61(x61301)+E(f862(f862(f74(x61301),x61302),f862(f862(f29(x61301),x61303),x61302)),x61303)+~P1(f862(f862(f278(x61301),x61302),x61303)) % 14.98/14.67 [6184]~P1(f862(f54(x61841),x61843))+E(f862(f28(x61841),f862(f862(f301(x61841),x61842),x61843)),f862(a105,f862(f28(x61841),x61843)))+P1(f862(f862(f321(x61841),x61842),x61843)) % 14.98/14.67 [6257]~E(x62572,f2(a924))+P1(f862(x62571,f2(a924)))+~P1(f862(x62571,f862(f862(f29(a924),x62573),x62572))) % 14.98/14.67 [6274]~P1(f862(f54(x62741),x62743))+E(f862(f28(x62741),f862(f862(f301(x62741),x62742),x62743)),f862(f28(x62741),x62743))+~P1(f862(f862(f321(x62741),x62742),x62743)) % 14.98/14.67 [6310]~P1(f862(f54(x63101),x63103))+E(f862(f28(x63101),f862(f862(f301(x63101),x63102),x63103)),f862(f862(f73(a924),f71(a924)),f862(f28(x63101),x63103)))+P1(f862(f862(f321(x63101),x63102),x63103)) % 14.98/14.67 [6428]E(f862(f862(f73(a924),x64281),f339(x64281,x64282,x64283)),x64282)+~P1(f862(x64283,f2(a924)))+P1(f862(x64283,f862(f862(f3(a924),x64282),x64281))) % 14.98/14.67 [6429]E(f862(f862(f73(a924),x64291),f340(x64291,x64292,x64293)),x64292)+~P1(f862(x64293,f2(a924)))+P1(f862(x64293,f862(f862(f3(a924),x64292),x64291))) % 14.98/14.67 [6475]~P3(x64751)+~P1(f862(f54(x64751),x64753))+E(f862(f862(f57(x64751,x64751,f103(x64751)),x64752),x64753),f862(f862(f103(x64751),x64752),f30(x64751,x64753))) % 14.98/14.67 [6476]~P3(x64761)+~P1(f862(f54(x64761),x64763))+E(f862(f862(f57(x64761,x64761,f94(x64761)),x64762),x64763),f862(f862(f94(x64761),x64762),f31(x64761,x64763))) % 14.98/14.67 [6482]~P98(x64821)+~E(f862(f96(x64821),x64822),f862(f96(x64821),x64823))+P26(x64821,f862(f96(x64821),f862(f862(f73(a1),x64822),f862(f72(a1),x64823)))) % 14.98/14.67 [6491]~P142(x64911)+E(f862(f862(f3(x64911),f862(f93(x64911),x64912)),f862(f93(x64911),x64913)),f862(f93(x64911),f862(f862(f3(a924),x64912),x64913)))+~P1(f862(f862(f227(a924),x64913),x64912)) % 14.98/14.67 [6582]E(f862(f862(f73(a924),x65821),f339(x65821,x65822,x65823)),x65822)+P1(f862(f862(f228(a924),x65822),x65821))+P1(f862(x65823,f862(f862(f3(a924),x65822),x65821))) % 14.98/14.67 [6583]E(f862(f862(f73(a924),x65831),f340(x65831,x65832,x65833)),x65832)+P1(f862(f862(f228(a924),x65832),x65831))+P1(f862(x65833,f862(f862(f3(a924),x65832),x65831))) % 14.98/14.67 [6600]~P112(x66001)+E(f862(f862(f74(x66001),f862(f69(x66001),x66002)),x66003),f862(f69(x66001),f862(f862(f74(x66001),x66002),x66003)))+~P1(f862(f862(f227(x66001),f2(x66001)),x66003)) % 14.98/14.67 [6601]~P66(x66011)+E(f862(f862(f281(x66011),f862(f69(x66011),x66012)),x66013),f862(f69(x66011),f862(f862(f281(x66011),x66012),x66013)))+~P1(f862(f862(f228(x66011),f2(x66011)),x66013)) % 14.98/14.67 [6610]~P93(x66101)+~P1(f862(f54(x66101),x66103))+E(f862(f862(f57(x66101,x66101,f94(x66101)),x66102),x66103),f12(x66101,f862(f862(f301(x66101),x66102),x66103))) % 14.98/14.67 [6611]~P93(x66111)+~P1(f862(f54(x66111),x66113))+E(f862(f862(f57(x66111,x66111,f103(x66111)),x66112),x66113),f15(x66111,f862(f862(f301(x66111),x66112),x66113))) % 14.98/14.67 [6612]~P109(x66121)+~P1(f862(f54(x66121),x66123))+E(f862(f862(f57(x66121,x66121,f225(x66121)),x66122),x66123),f16(x66121,f862(f862(f301(x66121),x66122),x66123))) % 14.98/14.67 [6613]~P109(x66131)+~P1(f862(f54(x66131),x66133))+E(f862(f862(f57(x66131,x66131,f226(x66131)),x66132),x66133),f17(x66131,f862(f862(f301(x66131),x66132),x66133))) % 14.98/14.67 [6658]E(x66581,f106(x66582))+~E(f172(x66582,x66583),f106(f925(x66582)))+~P1(f862(f862(f321(f925(x66582)),x66581),f862(f165(f925(x66582)),x66583))) % 14.98/14.67 [6702]~P1(f862(f130(x67021),x67023))+P1(f862(f862(f321(x67021),x67022),f862(f165(x67021),x67023)))+P1(f862(f130(x67021),f862(f862(f144(x67021),x67022),x67023))) % 14.98/14.67 [6713]~P100(x67131)+~P1(f862(f54(x67131),x67133))+E(f862(f56(x67131,f74(x67131)),f862(f862(f301(x67131),x67132),x67133)),f862(f862(f57(x67131,x67131,f74(x67131)),x67132),x67133)) % 14.98/14.67 [6736]~P109(x67361)+~P1(f862(f54(x67361),x67363))+E(f13(x67361,f225(x67361),f862(f862(f301(x67361),x67362),x67363)),f862(f862(f57(x67361,x67361,f225(x67361)),x67362),x67363)) % 14.98/14.67 [6737]~P109(x67371)+~P1(f862(f54(x67371),x67373))+E(f14(x67371,f226(x67371),f862(f862(f301(x67371),x67372),x67373)),f862(f862(f57(x67371,x67371,f226(x67371)),x67372),x67373)) % 14.98/14.67 [6739]P1(f862(x67391,f2(a924)))+~P1(f862(f862(f228(a924),x67392),x67393))+~P1(f862(x67391,f862(f862(f3(a924),x67392),x67393))) % 14.98/14.67 [6759]~P86(x67591)+P1(f862(f862(f227(x67591),x67592),x67593))+~P1(f862(f862(f227(x67591),f862(f69(x67591),x67592)),x67593)) % 14.98/14.67 [6760]~P112(x67601)+P1(f862(f862(f228(x67601),x67602),x67603))+~P1(f862(f862(f228(x67601),f862(f69(x67601),x67602)),x67603)) % 14.98/14.67 [6777]E(x67771,f106(x67772))+E(f862(f134(x67772),f862(f862(f131(x67772),x67773),x67771)),f862(f862(f157(x67772),x67771),x67773))+~P1(f862(f862(f228(a924),x67773),f862(f182(f925(x67772)),x67771))) % 14.98/14.67 [6827]~P1(f862(x68271,x68273))+P1(f862(x68271,f349(x68271,x68272)))+~P1(f862(f862(f321(a924),x68273),f862(f295(a924,f2(a924)),x68272))) % 14.98/14.67 [6848]P1(f862(x68481,x68482))+~P1(f862(f862(f228(a924),x68482),x68483))+P1(f862(f862(f321(a924),f347(x68481,x68483)),f862(f295(a924,f2(a924)),x68483))) % 14.98/14.67 [6863]~P127(x68631)+~P1(f862(f862(f227(x68631),f71(x68631)),x68632))+P1(f862(f862(f227(x68631),f71(x68631)),f862(f862(f236(x68631),x68632),x68633))) % 14.98/14.67 [6865]~P127(x68651)+~P1(f862(f862(f227(x68651),f2(x68651)),x68652))+P1(f862(f862(f227(x68651),f2(x68651)),f862(f862(f236(x68651),x68652),x68653))) % 14.98/14.67 [6867]~P127(x68671)+~P1(f862(f862(f228(x68671),f2(x68671)),x68672))+P1(f862(f862(f228(x68671),f2(x68671)),f862(f862(f236(x68671),x68672),x68673))) % 14.98/14.67 [6891]~P1(f862(x68911,x68913))+~P1(f862(f862(f228(a924),x68913),x68912))+P1(f862(f862(f321(a924),f343(x68911,x68912)),f862(f295(a924,f2(a924)),x68912))) % 14.98/14.67 [6899]P1(f862(f54(x68991),x68992))+~P1(f862(f54(x68991),x68993))+~P1(f862(f862(f227(f932(x68991,a921)),x68992),x68993)) % 14.98/14.67 [6906]P1(f862(x69061,x69062))+~P1(f862(x69061,f350(x69061,x69063)))+~P1(f862(f862(f321(a924),x69062),f862(f295(a924,f2(a924)),x69063))) % 14.98/14.67 [6917]E(x69171,f2(a924))+P1(f862(x69172,f420(x69171,x69173,x69172)))+~P1(f862(x69172,f862(f862(f29(a924),x69173),x69171))) % 14.98/14.67 [6924]~P128(x69242)+E(x69241,f2(x69242))+~E(f862(f862(f73(x69242),f862(f862(f74(x69242),x69243),x69243)),f862(f862(f74(x69242),x69241),x69241)),f2(x69242)) % 14.98/14.67 [6925]~P128(x69252)+E(x69251,f2(x69252))+~E(f862(f862(f73(x69252),f862(f862(f74(x69252),x69251),x69251)),f862(f862(f74(x69252),x69253),x69253)),f2(x69252)) % 14.98/14.67 [6972]E(x69721,f2(a924))+~P1(f862(x69722,f421(x69721,x69723,x69722)))+P1(f862(x69722,f862(f862(f29(a924),x69723),x69721))) % 14.98/14.67 [6977]~P109(x69771)+~P11(x69771,x69773)+P11(x69771,f862(f862(f141(x69771,x69771,f7(x69771)),x69772),x69773)) % 14.98/14.67 [7019]P1(f862(x70191,f420(x70192,x70193,x70191)))+P1(f862(x70191,f2(a924)))+~P1(f862(x70191,f862(f862(f29(a924),x70193),x70192))) % 14.98/14.67 [7025]~P98(x70251)+E(f862(f96(x70251),x70252),f862(f96(x70251),x70253))+~P26(x70251,f862(f96(x70251),f862(f862(f73(a1),x70252),f862(f72(a1),x70253)))) % 14.98/14.67 [7091]E(x70911,f2(a1))+E(x70912,f2(a1))+~P1(f862(f42(x70912,x70912),f862(f862(f244(a1,a1),x70913),x70911))) % 14.98/14.67 [7092]E(x70921,f71(a1))+E(x70922,f2(a1))+~P1(f862(f42(x70922,x70922),f862(f862(f244(a1,a1),x70921),x70923))) % 14.98/14.67 [7106]P1(f862(x71061,x71062))+P1(f862(f862(f228(a924),f350(x71061,x71063)),x71063))+~P1(f862(f862(f321(a924),x71062),f862(f295(a924,f2(a924)),x71063))) % 14.98/14.67 [7129]~P1(f862(x71291,f339(x71293,x71292,x71291)))+~P1(f862(x71291,f2(a924)))+P1(f862(x71291,f862(f862(f3(a924),x71292),x71293))) % 14.98/14.67 [7130]~P1(f862(x71301,f340(x71303,x71302,x71301)))+~P1(f862(x71301,f2(a924)))+P1(f862(x71301,f862(f862(f3(a924),x71302),x71303))) % 14.98/14.67 [7131]~P1(f862(x71311,f421(x71313,x71312,x71311)))+~P1(f862(x71311,f2(a924)))+P1(f862(x71311,f862(f862(f29(a924),x71312),x71313))) % 14.98/14.67 [7149]~P1(f862(x71491,x71493))+P1(f862(f862(f228(a924),f349(x71491,x71492)),x71492))+~P1(f862(f862(f321(a924),x71493),f862(f295(a924,f2(a924)),x71492))) % 14.98/14.67 [7150]E(f862(f862(f3(a924),f862(f862(f3(a924),x71501),x71502)),f862(f862(f3(a924),x71503),x71502)),f862(f862(f3(a924),x71501),x71503))+~P1(f862(f862(f227(a924),x71502),x71501))+~P1(f862(f862(f227(a924),x71502),x71503)) % 14.98/14.67 [7187]~P78(x71871)+~P1(f862(f862(f227(x71871),f862(f72(x71871),x71873)),x71872))+P1(f862(f862(f227(x71871),f862(f72(x71871),x71872)),x71873)) % 14.98/14.67 [7189]~P86(x71891)+~P1(f862(f862(f227(x71891),f862(f69(x71891),x71892)),x71893))+P1(f862(f862(f227(x71891),f862(f72(x71891),x71892)),x71893)) % 14.98/14.67 [7191]~P78(x71911)+~P1(f862(f862(f228(x71911),f862(f72(x71911),x71913)),x71912))+P1(f862(f862(f228(x71911),f862(f72(x71911),x71912)),x71913)) % 14.98/14.67 [7192]~P112(x71921)+~P1(f862(f862(f228(x71921),f862(f69(x71921),x71922)),x71923))+P1(f862(f862(f228(x71921),f862(f72(x71921),x71922)),x71923)) % 14.98/14.67 [7223]~P1(f862(x72233,f339(x72232,x72231,x72233)))+P1(f862(f862(f228(a924),x72231),x72232))+P1(f862(x72233,f862(f862(f3(a924),x72231),x72232))) % 14.98/14.67 [7224]~P1(f862(x72243,f340(x72242,x72241,x72243)))+P1(f862(f862(f228(a924),x72241),x72242))+P1(f862(x72243,f862(f862(f3(a924),x72241),x72242))) % 14.98/14.67 [7277]~E(f711(x72773,x72772,x72771),f703(x72773,x72772,x72771))+E(f862(f862(f94(f932(x72771,a921)),x72772),f30(f932(x72771,a921),x72773)),f181(f932(x72771,a921)))+P1(f862(f862(f321(f932(x72771,a921)),x72772),x72773)) % 14.98/14.67 [7285]~P1(f862(f54(x72851),x72853))+P1(f862(f54(x72851),f31(f932(x72851,a921),x72852)))+~P1(f862(f862(f321(f932(x72851,a921)),x72853),x72852)) % 14.98/14.67 [7345]~P109(x73451)+E(f862(f862(f103(f932(x73451,a921)),f862(f295(x73451,x73452),x73453)),f862(f862(f301(x73451),x73453),f181(f932(x73451,a921)))),f296(x73451,x73452,x73453))+~P1(f862(f862(f227(x73451),x73452),x73453)) % 14.98/14.67 [7348]E(x73481,f2(a924))+P1(f862(f862(f228(a924),f422(x73481,x73483,x73482)),x73481))+P1(f862(x73482,f862(f862(f29(a924),x73483),x73481))) % 14.98/14.67 [7377]P1(f862(f862(f228(a924),f862(f182(f925(x73771)),x73772)),f789(x73773,x73771)))+~P1(f862(f54(f925(x73771)),x73773))+~P1(f862(f862(f321(f925(x73771)),x73772),x73773)) % 14.98/14.67 [7383]E(x73831,x73832)+~P1(f862(f862(f227(f932(x73833,a921)),x73831),x73832))+P1(f862(f862(f228(f932(x73833,a921)),x73831),x73832)) % 14.98/14.67 [7395]E(x73951,x73952)+~E(f862(f182(f925(x73953)),x73951),f862(f182(f925(x73953)),x73952))+P1(f862(f862(f228(a924),f658(x73953,x73951,x73952)),f862(f182(f925(x73953)),x73952))) % 14.98/14.67 [7446]P6(x74461,x74462,x74463)+~E(f862(f256(x74461,x74461),x74463),x74462)+~E(f862(f862(f280(x74461,x74461,x74461),f862(f277(x74461,x74461),x74463)),x74463),x74463) % 14.98/14.67 [7527]~P1(f862(x75271,f2(a924)))+P1(f862(f862(f228(a924),f422(x75273,x75272,x75271)),x75273))+P1(f862(x75271,f862(f862(f29(a924),x75272),x75273))) % 14.98/14.67 [7537]~P109(x75371)+E(f862(f862(f103(f932(x75371,a921)),f298(x75371,x75372,x75373)),f862(f862(f301(x75371),x75373),f181(f932(x75371,a921)))),f297(x75371,x75372,x75373))+~P1(f862(f862(f228(x75371),x75372),x75373)) % 14.98/14.67 [7630]~P1(f862(f54(x76301),x76303))+P1(f862(f862(f227(a924),f862(f28(x76301),x76302)),f862(f28(x76301),x76303)))+~P1(f862(f862(f227(f932(x76301,a921)),x76302),x76303)) % 14.98/14.67 [7631]~P1(f862(f54(x76311),x76313))+P1(f862(f862(f228(a924),f862(f28(x76311),x76312)),f862(f28(x76311),x76313)))+~P1(f862(f862(f228(f932(x76311,a921)),x76312),x76313)) % 14.98/14.67 [7764]E(x77641,x77642)+~P1(f862(f862(f227(f932(x77643,a921)),x77642),x77641))+~P1(f862(f862(f227(f932(x77643,a921)),x77641),x77642)) % 14.98/14.67 [7767]~P109(x77671)+P11(x77671,x77672)+~P11(x77671,f862(f862(f141(x77671,x77671,f7(x77671)),x77673),x77672)) % 14.98/14.67 [7838]~P1(f862(f862(f228(a924),x78383),x78382))+~P1(f862(f862(f228(a924),x78383),x78381))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x78381),x78382)),f862(f862(f3(a924),x78381),x78383))) % 14.98/14.67 [7839]~P1(f862(f862(f227(a924),x78392),x78391))+~P1(f862(f862(f228(a924),x78391),x78393))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x78391),x78392)),f862(f862(f3(a924),x78393),x78392))) % 14.98/14.67 [7854]~P1(f862(f862(f228(a1),x78542),f2(a1)))+~P1(f862(f862(f227(a1),x78543),x78541))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x78541),x78542)),f862(f862(f29(a1),x78543),x78542))) % 14.98/14.67 [7871]~P1(f862(f862(f228(a924),f2(a924)),x78713))+~P1(f862(f862(f227(a924),x78713),x78712))+P1(f862(f862(f227(a924),f862(f862(f29(a924),x78711),x78712)),f862(f862(f29(a924),x78711),x78713))) % 14.98/14.67 [7872]~P1(f862(f862(f228(a1),f2(a1)),x78722))+~P1(f862(f862(f227(a1),x78721),x78723))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x78721),x78722)),f862(f862(f29(a1),x78723),x78722))) % 14.98/14.67 [7876]~P1(f862(f862(f228(a924),f2(a924)),x78762))+~P1(f862(f862(f228(a924),x78761),x78763))+P1(f862(f862(f228(a924),f862(f862(f74(a924),x78761),x78762)),f862(f862(f74(a924),x78763),x78762))) % 14.98/14.67 [7877]~P1(f862(f862(f228(a924),f2(a924)),x78771))+~P1(f862(f862(f228(a924),x78772),x78773))+P1(f862(f862(f228(a924),f862(f862(f74(a924),x78771),x78772)),f862(f862(f74(a924),x78771),x78773))) % 14.98/14.67 [7878]~P1(f862(f862(f228(a1),f2(a1)),x78781))+~P1(f862(f862(f228(a1),x78782),x78783))+P1(f862(f862(f228(a1),f862(f862(f74(a1),x78781),x78782)),f862(f862(f74(a1),x78781),x78783))) % 14.98/14.67 [7926]E(x79261,f2(a924))+E(f862(f862(f73(a924),f862(f862(f74(a924),x79261),f421(x79261,x79262,x79263))),f422(x79261,x79262,x79263)),x79262)+P1(f862(x79263,f862(f862(f29(a924),x79262),x79261))) % 14.98/14.67 [7985]E(f862(f862(f73(a924),f862(f862(f74(a924),x79851),f421(x79851,x79852,x79853))),f422(x79851,x79852,x79853)),x79852)+~P1(f862(x79853,f2(a924)))+P1(f862(x79853,f862(f862(f29(a924),x79852),x79851))) % 14.98/14.67 [8003]~P1(f862(f54(x80031),x80033))+P1(f862(f862(f321(x80031),f338(x80032,x80033,x80031)),x80033))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x80031,a924),x80032),x80033))) % 14.98/14.67 [8004]~P1(f862(f54(x80041),x80043))+P1(f862(f862(f321(x80041),f369(x80042,x80043,x80041)),x80043))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x80041,a924),x80042),x80043))) % 14.98/14.67 [8106]E(x81061,f2(a924))+P1(f862(f862(f278(a924),x81062),x81063))+~P1(f862(f862(f278(a924),f862(f862(f74(a924),x81061),x81062)),f862(f862(f74(a924),x81061),x81063))) % 14.98/14.67 [8301]E(x83011,f181(f932(x83012,a921)))+E(x83011,f862(f862(f301(x83012),x83013),f181(f932(x83012,a921))))+~P1(f862(f862(f227(f932(x83012,a921)),x83011),f862(f862(f301(x83012),x83013),f181(f932(x83012,a921))))) % 14.98/14.67 [8337]~P1(f862(f862(f228(a924),f71(a924)),x83373))+P1(f862(f862(f227(a924),x83371),x83372))+~P1(f862(f862(f278(a924),f862(f862(f236(a924),x83373),x83371)),f862(f862(f236(a924),x83373),x83372))) % 14.98/14.67 [8339]~P1(f862(f862(f228(a924),f2(a924)),x83393))+P1(f862(f862(f227(a924),x83391),x83392))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x83393),x83391)),f862(f862(f74(a924),x83393),x83392))) % 14.98/14.67 [8340]~P1(f862(f862(f228(a924),f2(a924)),x83403))+P1(f862(f862(f227(a924),x83401),x83402))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x83401),x83403)),f862(f862(f74(a924),x83402),x83403))) % 14.98/14.67 [8342]~P1(f862(f862(f228(a924),f2(a924)),x83423))+P1(f862(f862(f228(a924),x83421),x83422))+~P1(f862(f862(f228(a924),f862(f862(f236(a924),x83423),x83421)),f862(f862(f236(a924),x83423),x83422))) % 14.98/14.67 [8344]~P1(f862(f862(f228(a924),f2(a924)),x83443))+P1(f862(f862(f278(a924),x83441),x83442))+~P1(f862(f862(f278(a924),f862(f862(f74(a924),x83443),x83441)),f862(f862(f74(a924),x83443),x83442))) % 14.98/14.67 [8384]~E(f862(f862(f94(f932(x83841,a921)),f703(x83843,x83842,x83841)),f711(x83843,x83842,x83841)),f181(f932(x83841,a921)))+E(f862(f862(f94(f932(x83841,a921)),x83842),f30(f932(x83841,a921),x83843)),f181(f932(x83841,a921)))+P1(f862(f862(f321(f932(x83841,a921)),x83842),x83843)) % 14.98/14.67 [8398]E(x83981,f106(x83982))+~E(f862(f135(f925(x83982),f925(x83982),f127(x83982),f106(x83982)),x83983),f106(x83982))+~P1(f862(f862(f321(f925(x83982)),x83981),f862(f165(f925(x83982)),x83983))) % 14.98/14.67 [8453]E(x84531,f181(f932(f932(x84532,a921),a921)))+P1(f862(f862(f321(f932(x84532,a921)),f472(x84533,x84531,x84532)),x84531))+P1(f862(f862(f227(f932(x84532,a921)),f31(f932(x84532,a921),x84531)),x84533)) % 14.98/14.67 [8459]~P71(x84591)+~P72(x84591)+E(f862(f862(f8(a1,x84591),f862(f862(f10(a924,x84591,a1),x84592),a97)),f862(f302(a924,a1,f93(a1)),x84593)),f862(f862(f8(a924,x84591),x84592),x84593)) % 14.98/14.67 [8460]~P71(x84601)+~P72(x84601)+E(f862(f862(f11(a1,x84601),f862(f862(f10(a924,x84601,a1),x84602),a97)),f862(f302(a924,a1,f93(a1)),x84603)),f862(f862(f11(a924,x84601),x84602),x84603)) % 14.98/14.67 [8502]~P1(f862(f54(x85021),x85023))+~P1(f862(f862(f228(a924),f2(a924)),f862(x85022,f338(x85022,x85023,x85021))))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x85021,a924),x85022),x85023))) % 14.98/14.67 [8503]~P1(f862(f54(x85031),x85033))+~P1(f862(f862(f228(a924),f2(a924)),f862(x85032,f369(x85032,x85033,x85031))))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x85031,a924),x85032),x85033))) % 14.98/14.67 [8539]~P65(x85392)+E(x85391,f71(x85392))+E(f862(f862(f281(x85392),f862(f862(f3(x85392),f862(f862(f236(x85392),x85391),x85393)),f71(x85392))),f862(f862(f3(x85392),x85391),f71(x85392))),f862(f862(f8(a924,x85392),f862(f236(x85392),x85391)),f862(f295(a924,f2(a924)),x85393))) % 14.98/14.67 [8597]E(x85971,f2(a924))+~P1(f862(x85973,f862(f862(f29(a924),x85972),x85971)))+P1(f862(f862(f228(a924),x85972),f862(f862(f74(a924),x85971),f862(a105,f420(x85971,x85972,x85973))))) % 14.98/14.67 [8617]P1(f862(x86171,f2(a924)))+~P1(f862(x86171,f862(f862(f29(a924),x86172),x86173)))+P1(f862(f862(f228(a924),x86172),f862(f862(f74(a924),x86173),f862(a105,f420(x86173,x86172,x86171))))) % 14.98/14.67 [8656]E(x86561,f2(a924))+~P1(f862(x86563,f862(f862(f29(a924),x86562),x86561)))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x86561),f420(x86561,x86562,x86563))),x86562)) % 14.98/14.67 [8687]P1(f862(x86871,f2(a924)))+~P1(f862(x86871,f862(f862(f29(a924),x86873),x86872)))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x86872),f420(x86872,x86873,x86871))),x86873)) % 14.98/14.67 [8695]~P109(x86951)+E(f862(f862(f141(x86951,x86951,f7(x86951)),x86952),x86953),f142(x86951,x86951,f7(x86951),x86952,x86953))+P1(f862(f862(f321(x86951),x86952),f862(f165(x86951),x86953))) % 14.98/14.67 [8731]~E(f862(x87313,f595(x87312,x87313,x87311)),f862(x87313,f597(x87312,x87313,x87311)))+~P57(x87311,f862(x87313,f596(x87312,x87313,x87311)))+P57(x87311,f862(f862(f33(x87312,f932(x87311,f932(x87311,a921))),f234(f932(x87312,a921))),x87313)) % 14.98/14.67 [8740]E(x87401,f181(f932(f932(x87402,a921),a921)))+~P1(f862(f862(f227(f932(x87402,a921)),f472(x87403,x87401,x87402)),x87403))+P1(f862(f862(f227(f932(x87402,a921)),f31(f932(x87402,a921),x87401)),x87403)) % 14.98/14.67 [8801]~P67(x88011)+~P1(f862(f862(f228(x88011),x88012),x88013))+P1(f862(f862(f228(x88011),x88012),f862(f862(f281(x88011),f862(f862(f73(x88011),x88012),x88013)),f862(f862(f73(x88011),f71(x88011)),f71(x88011))))) % 14.98/14.67 [8859]~P1(f862(f862(x88591,f499(x88591,x88593,x88592)),f500(x88591,x88593,x88592)))+P1(f862(f862(x88591,x88592),x88593))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x88592),x88593))) % 14.98/14.67 [8860]~P1(f862(f862(x88601,f501(x88601,x88603,x88602)),f503(x88601,x88603,x88602)))+P1(f862(f862(x88601,x88602),x88603))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x88602),x88603))) % 14.98/14.67 [8861]~P1(f862(f862(x88611,f504(x88611,x88613,x88612)),f507(x88611,x88613,x88612)))+P1(f862(f862(x88611,x88612),x88613))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x88612),x88613))) % 14.98/14.67 [8862]~P1(f862(f862(x88621,f508(x88621,x88623,x88622)),f510(x88621,x88623,x88622)))+P1(f862(f862(x88621,x88622),x88623))+~P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),x88622),x88623))) % 14.98/14.67 [8863]~P1(f862(f862(x88631,f683(x88631,x88633,x88632)),f685(x88631,x88633,x88632)))+P1(f862(f862(x88631,x88632),x88633))+~P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),x88632),x88633))) % 14.98/14.67 [8864]~P1(f862(f862(x88641,f779(x88641,x88643,x88642)),f780(x88641,x88643,x88642)))+P1(f862(f862(x88641,x88642),x88643))+~P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),x88642),x88643))) % 14.98/14.67 [9140]P1(f862(f862(x91401,x91402),x91403))+P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),f508(x91401,x91403,x91402)),f510(x91401,x91403,x91402))))+~P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),x91402),x91403))) % 14.98/14.67 [9141]P1(f862(f862(x91411,x91412),x91413))+P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),f499(x91411,x91413,x91412)),f500(x91411,x91413,x91412))))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x91412),x91413))) % 14.98/14.67 [9142]P1(f862(f862(x91421,x91422),x91423))+P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),f501(x91421,x91423,x91422)),f503(x91421,x91423,x91422))))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x91422),x91423))) % 14.98/14.67 [9143]P1(f862(f862(x91431,x91432),x91433))+P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),f504(x91431,x91433,x91432)),f507(x91431,x91433,x91432))))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x91432),x91433))) % 14.98/14.67 [9144]P1(f862(f862(x91441,x91442),x91443))+P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),f683(x91441,x91443,x91442)),f685(x91441,x91443,x91442))))+~P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),x91442),x91443))) % 14.98/14.67 [9145]P1(f862(f862(x91451,x91452),x91453))+P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),f779(x91451,x91453,x91452)),f780(x91451,x91453,x91452))))+~P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),x91452),x91453))) % 14.98/14.67 [9481]~P1(f862(f54(x94811),x94813))+P1(f862(f862(f321(f931(f932(x94811,a921),f932(x94811,a921))),f862(f862(f244(f932(x94811,a921),f932(x94811,a921)),x94812),x94813)),f306(x94811)))+~P1(f862(f862(f228(f932(x94811,a921)),x94812),x94813)) % 14.98/14.67 [9555]~P57(x95551,f862(x95553,f596(x95552,x95553,x95551)))+P57(x95551,f862(f862(f33(x95552,f932(x95551,f932(x95551,a921))),f234(f932(x95552,a921))),x95553))+~E(f862(f862(f94(f932(x95551,a921)),f241(x95551,x95551,f862(x95553,f595(x95552,x95553,x95551)))),f242(x95551,x95551,f862(x95553,f597(x95552,x95553,x95551)))),f181(f932(x95551,a921))) % 14.98/14.67 [9760]P50(x97601,x97602,x97603)+P1(f862(f862(f321(f931(x97601,x97601)),f580(x97603,x97602,x97601)),x97603))+~P1(f862(f862(f321(f931(x97601,x97601)),f862(f862(f244(x97601,x97601),f579(x97603,x97602,x97601)),f579(x97603,x97602,x97601))),x97603)) % 14.98/14.67 [10344]P50(x103441,x103442,x103443)+~P1(f862(f862(f249(x103441,x103441,a921),f862(f862(f9(x103441,f932(x103441,a921),f932(x103441,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x103441,a921),f932(x103441,a921)),x103441),f10(a921,a921,x103441)),f862(f862(f10(a921,f932(a921,a921),x103441),a318),f862(f862(f9(x103441,f932(x103441,a921),a921),f321(x103441)),x103442)))),f862(f862(f9(x103441,f932(x103441,a921),a921),f321(x103441)),x103442))),f580(x103443,x103442,x103441)))+~P1(f862(f862(f321(f931(x103441,x103441)),f862(f862(f244(x103441,x103441),f579(x103443,x103442,x103441)),f579(x103443,x103442,x103441))),x103443)) % 14.98/14.67 [5843]~P61(x58432)+E(x58431,f2(x58432))+E(f862(f862(f29(x58432),f862(f862(f74(x58432),x58433),x58431)),x58431),x58433) % 14.98/14.67 [5844]~P61(x58442)+E(x58441,f2(x58442))+E(f862(f862(f29(x58442),f862(f862(f74(x58442),x58441),x58443)),x58441),x58443) % 14.98/14.67 [6492]~P61(x64921)+E(f862(f862(f74(x64921),f862(f862(f29(x64921),x64922),x64923)),x64923),x64922)+~P1(f862(f862(f278(x64921),x64923),x64922)) % 14.98/14.67 [6657]~P72(x66571)+~E(f862(x66572,f2(a924)),f2(x66571))+E(f862(f862(f8(a924,x66571),x66572),f862(f295(a924,f862(a105,f2(a924))),x66573)),f862(f862(f8(a924,x66571),x66572),f862(f295(a924,f2(a924)),x66573))) % 14.98/14.67 [6789]~P61(x67892)+E(x67891,f2(x67892))+E(f862(f862(f29(x67892),f862(f862(f73(x67892),x67893),x67891)),x67891),f862(f862(f73(x67892),f862(f862(f29(x67892),x67893),x67891)),f71(x67892))) % 14.98/14.67 [6790]~P61(x67902)+E(x67901,f2(x67902))+E(f862(f862(f29(x67902),f862(f862(f73(x67902),x67901),x67903)),x67901),f862(f862(f73(x67902),f862(f862(f29(x67902),x67903),x67901)),f71(x67902))) % 14.98/14.67 [7008]~P1(f862(x70083,f2(a1)))+P1(f862(f862(f227(a924),x70081),x70082))+P1(f862(x70083,f862(f93(a1),f862(f862(f3(a924),x70082),x70081)))) % 14.98/14.67 [7112]P1(f862(f862(f228(a924),x71122),x71121))+P1(f862(f862(f227(a924),x71121),x71122))+P1(f862(x71123,f862(f93(a1),f862(f862(f3(a924),x71122),x71121)))) % 14.98/14.67 [7185]E(f862(f862(f73(a924),f862(f96(a924),x71851)),f862(f862(f73(a924),f862(f96(a924),x71852)),x71853)),f862(f862(f73(a924),f862(f96(a924),x71851)),x71853))+P1(f862(a186,f862(f96(a1),x71851)))+~P1(f862(a186,f862(f96(a1),x71852))) % 14.98/14.67 [7263]~E(x72632,f862(f862(f29(a924),x72633),x72631))+~P1(f862(f862(f228(a924),f2(a924)),x72631))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x72631),x72632)),x72633)) % 14.98/14.67 [7380]~P1(f862(f54(x73801),x73803))+~P1(f862(f54(x73801),x73802))+P1(f862(f54(x73801),f862(f862(f103(f932(x73801,a921)),x73802),x73803))) % 14.98/14.67 [7430]~P36(x74301,x74303)+~P36(x74301,x74302)+P36(x74301,f862(f862(f94(f932(f931(x74301,x74301),a921)),x74302),x74303)) % 14.98/14.67 [7431]~P49(x74311,x74313)+~P49(x74311,x74312)+P49(x74311,f862(f862(f103(f932(f931(x74311,x74311),a921)),x74312),x74313)) % 14.98/14.67 [7432]~P49(x74321,x74323)+~P49(x74321,x74322)+P49(x74321,f862(f862(f94(f932(f931(x74321,x74321),a921)),x74322),x74323)) % 14.98/14.67 [7678]~P109(x76781)+~P1(f862(f54(x76781),x76782))+E(f132(x76781,f862(f862(f3(f932(x76781,a921)),x76782),f862(f862(f301(x76781),x76783),f181(f932(x76781,a921))))),f163(x76781,x76783,f132(x76781,x76782))) % 14.98/14.67 [7742]P1(f862(x77421,f2(a1)))+~P1(f862(f862(f228(a924),x77422),x77423))+~P1(f862(x77421,f862(f93(a1),f862(f862(f3(a924),x77422),x77423)))) % 14.98/14.67 [7761]~P1(f862(f54(x77611),x77612))+E(f862(f28(x77611),f862(f862(f3(f932(x77611,a921)),x77612),f862(f862(f301(x77611),x77613),f181(f932(x77611,a921))))),f862(f28(x77611),x77612))+P1(f862(f862(f321(x77611),x77613),x77612)) % 14.98/14.67 [7894]~P127(x78941)+~P1(f862(f862(f228(x78941),f71(x78941)),x78942))+P1(f862(f862(f228(x78941),f71(x78941)),f862(f862(f74(x78941),x78942),f862(f862(f236(x78941),x78942),x78943)))) % 14.98/14.67 [7936]~P1(f862(f54(x79361),x79363))+E(f862(f862(f3(a924),f862(f28(x79361),x79362)),f862(f28(x79361),x79363)),f862(f28(x79361),f862(f862(f3(f932(x79361,a921)),x79362),x79363)))+~P1(f862(f862(f227(f932(x79361,a921)),x79363),x79362)) % 14.98/14.67 [7993]~P1(f862(f862(f227(a924),x79932),x79933))+~P1(f862(f862(f227(a924),x79931),f862(f862(f3(a924),x79933),x79932)))+P1(f862(f862(f227(a924),f862(f862(f73(a924),x79931),x79932)),x79933)) % 14.98/14.67 [8048]P1(f862(f54(x80481),x80482))+~P1(f862(f54(x80481),x80483))+~P1(f862(f54(x80481),f862(f862(f3(f932(x80481,a921)),x80482),x80483))) % 14.98/14.67 [8054]~P1(f862(f54(x80541),x80542))+E(f862(f28(x80541),f862(f862(f3(f932(x80541,a921)),x80542),f862(f862(f301(x80541),x80543),f181(f932(x80541,a921))))),f862(f862(f3(a924),f862(f28(x80541),x80542)),f71(a924)))+~P1(f862(f862(f321(x80541),x80543),x80542)) % 14.98/14.67 [8131]P57(x81311,x81312)+~P57(x81311,x81313)+~P1(f862(f862(f227(f932(x81311,f932(x81311,a921))),x81312),x81313)) % 14.98/14.67 [8173]~P1(f862(f862(f227(a924),x81733),x81732))+P1(f862(f862(f227(a924),x81731),f862(f862(f3(a924),x81732),x81733)))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x81731),x81733)),x81732)) % 14.98/14.67 [8191]P35(x81911,x81912)+~P35(x81911,x81913)+~P1(f862(f862(f227(f932(f931(x81911,x81911),a921)),x81912),x81913)) % 14.98/14.67 [8192]P55(x81921,x81922)+~P55(x81921,x81923)+~P1(f862(f862(f227(f932(f931(x81921,x81921),a921)),x81922),x81923)) % 14.98/14.67 [8193]P37(x81931,x81932)+~P37(x81931,x81933)+~P1(f862(f862(f227(f932(f931(x81931,x81931),a921)),x81932),x81933)) % 14.98/14.67 [8431]~P127(x84311)+~P1(f862(f862(f228(x84311),f71(x84311)),x84312))+P1(f862(f862(f228(x84311),f862(f862(f236(x84311),x84312),x84313)),f862(f862(f74(x84311),x84312),f862(f862(f236(x84311),x84312),x84313)))) % 14.98/14.67 [8521]~P1(f862(x85211,f2(a1)))+~P1(f862(x85211,f862(f862(f3(a1),f862(f93(a1),x85212)),f862(f93(a1),x85213))))+P1(f862(x85211,f862(f93(a1),f862(f862(f3(a924),x85212),x85213)))) % 14.98/14.67 [8536]~P1(f862(f862(f227(a924),x85363),x85362))+P1(f862(x85361,f862(f862(f3(a1),f862(f93(a1),x85362)),f862(f93(a1),x85363))))+~P1(f862(x85361,f862(f93(a1),f862(f862(f3(a924),x85362),x85363)))) % 14.98/14.67 [8556]P1(f862(f862(f228(a924),x85561),x85562))+~P1(f862(x85563,f862(f862(f3(a1),f862(f93(a1),x85561)),f862(f93(a1),x85562))))+P1(f862(x85563,f862(f93(a1),f862(f862(f3(a924),x85561),x85562)))) % 14.98/14.67 [8610]~P128(x86102)+E(x86101,f2(x86102))+P1(f862(f862(f228(x86102),f2(x86102)),f862(f862(f73(x86102),f862(f862(f74(x86102),x86103),x86103)),f862(f862(f74(x86102),x86101),x86101)))) % 14.98/14.67 [8611]~P128(x86112)+E(x86111,f2(x86112))+P1(f862(f862(f228(x86112),f2(x86112)),f862(f862(f73(x86112),f862(f862(f74(x86112),x86111),x86111)),f862(f862(f74(x86112),x86113),x86113)))) % 14.98/14.67 [8713]~P1(f862(f862(f228(a924),f2(a924)),x87131))+~P1(f862(f862(f228(a1),x87132),x87133))+P1(f862(f862(f228(a1),f862(f862(f74(a1),f862(f93(a1),x87131)),x87132)),f862(f862(f74(a1),f862(f93(a1),x87131)),x87133))) % 14.98/14.67 [8770]E(f862(f862(f94(f932(x87701,a921)),x87702),f30(f932(x87701,a921),x87703)),f181(f932(x87701,a921)))+P1(f862(f862(f321(f932(x87701,a921)),x87702),x87703))+P1(f862(f862(f321(f932(x87701,a921)),f703(x87703,x87702,x87701)),f862(f862(f301(f932(x87701,a921)),x87702),x87703))) % 14.98/14.67 [8771]E(f862(f862(f94(f932(x87711,a921)),x87712),f30(f932(x87711,a921),x87713)),f181(f932(x87711,a921)))+P1(f862(f862(f321(f932(x87711,a921)),x87712),x87713))+P1(f862(f862(f321(f932(x87711,a921)),f711(x87713,x87712,x87711)),f862(f862(f301(f932(x87711,a921)),x87712),x87713))) % 14.98/14.67 [8800]E(x88001,x88002)+~E(f862(f182(f925(x88003)),x88001),f862(f182(f925(x88003)),x88002))+P1(f862(f862(f321(f931(x88003,x88003)),f670(x88003,x88001,x88002)),f862(f165(f931(x88003,x88003)),f862(f862(f174(x88003,x88003),x88002),x88001)))) % 14.98/14.67 [9053]E(f299(x90531,x90532),f299(x90531,x90533))+~P1(f862(f862(f227(f932(f931(x90531,x90531),a921)),x90533),f299(x90531,x90532)))+~P1(f862(f862(f227(f932(f931(x90531,x90531),a921)),x90532),x90533)) % 14.98/14.67 [9120]~P50(x91201,f234(f932(x91201,a921)),x91203)+P1(f862(f862(f227(f932(f931(f925(x91201),f925(x91201)),a921)),f150(x91201,x91202)),f151(x91201,x91203)))+~P1(f862(f862(f227(f932(f931(x91201,x91201),a921)),x91202),x91203)) % 14.98/14.67 [9316]P35(x93161,x93162)+~P1(f862(f862(f321(x93161),x93163),f610(x93162,x93161)))+P1(f862(f862(f321(f931(x93161,x93161)),f862(f862(f244(x93161,x93161),f620(x93162,x93161,x93163)),x93163)),x93162)) % 14.98/14.67 [9352]~P1(f862(f54(x93521),x93522))+P1(f862(f54(f932(x93521,a921)),f862(f862(f53(x93521),x93522),x93523)))+~P1(f862(f862(f227(f932(f931(x93521,x93521),a921)),x93523),f862(f862(f246(x93521,x93521),x93522),f862(f18(f932(x93521,a921),x93521),x93522)))) % 14.98/14.67 [9388]P50(x93881,x93882,x93883)+P1(f862(f862(f321(x93881),f582(x93883,x93882,x93881)),x93882))+~P1(f862(f862(f227(f932(f931(x93881,x93881),a921)),x93883),f862(f862(f246(x93881,x93881),x93882),f862(f18(f932(x93881,a921),x93881),x93882)))) % 14.98/14.67 [9389]P50(x93891,x93892,x93893)+P1(f862(f862(f321(x93891),f585(x93892,x93893,x93891)),x93892))+~P1(f862(f862(f227(f932(f931(x93891,x93891),a921)),x93893),f862(f862(f246(x93891,x93891),x93892),f862(f18(f932(x93891,a921),x93891),x93892)))) % 14.98/14.67 [9424]~P67(x94241)+~P1(f862(f862(f228(x94241),x94242),x94243))+P1(f862(f862(f228(x94241),f862(f862(f281(x94241),f862(f862(f73(x94241),x94242),x94243)),f862(f862(f73(x94241),f71(x94241)),f71(x94241)))),x94243)) % 14.98/14.67 [9454]~P66(x94541)+P1(f862(f862(f227(x94541),x94542),x94543))+~P1(f862(f862(f227(x94541),f862(f862(f74(x94541),f363(x94543,x94542,x94541)),x94542)),x94543)) % 14.98/14.67 [9592]E(f862(f182(f925(f925(x95921))),f862(f129(f925(x95921),f862(f862(f10(a924,a921,f925(x95921)),f862(f228(a924),x95922)),f182(f925(x95921)))),f172(x95921,x95923))),f862(f182(f925(x95921)),f862(f862(f157(f925(x95921)),x95923),x95922)))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x95921),a924),f182(f925(x95921))),x95923)))+~P1(f862(f862(f228(a924),x95922),f862(f182(f925(f925(x95921))),x95923))) % 14.98/14.67 [9708]~P35(x97081,x97082)+P24(x97081,f862(f862(f244(f932(f931(x97081,x97081),a921),f932(f931(x97081,x97081),a921)),x97082),x97083))+~P1(f862(f862(f227(f932(f931(x97081,x97081),a921)),f862(f862(f280(x97081,x97081,x97081),x97082),x97083)),x97082)) % 14.98/14.67 [9713]E(f862(f862(f147(f925(x97131),x97131),f862(f862(f9(f925(x97131),a924,x97131),f157(x97131)),x97132)),f862(f129(f925(x97131),f862(f862(f10(a924,a921,f925(x97131)),f862(f228(a924),x97132)),f182(f925(x97131)))),f172(x97131,x97133))),f862(f862(f157(f925(x97131)),x97133),x97132))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x97131),a924),f182(f925(x97131))),x97133)))+~P1(f862(f862(f228(a924),x97132),f862(f182(f925(f925(x97131))),x97133))) % 14.98/14.67 [9848]P50(x98481,x98482,x98483)+~P1(f862(f862(f321(f931(x98481,x98481)),f862(f862(f244(x98481,x98481),f582(x98483,x98482,x98481)),f582(x98483,x98482,x98481))),x98483))+~P1(f862(f862(f227(f932(f931(x98481,x98481),a921)),x98483),f862(f862(f246(x98481,x98481),x98482),f862(f18(f932(x98481,a921),x98481),x98482)))) % 14.98/14.67 [9849]P50(x98491,x98492,x98493)+~P1(f862(f862(f321(f931(x98491,x98491)),f862(f862(f244(x98491,x98491),f585(x98492,x98493,x98491)),f585(x98492,x98493,x98491))),x98493))+~P1(f862(f862(f227(f932(f931(x98491,x98491),a921)),x98493),f862(f862(f246(x98491,x98491),x98492),f862(f18(f932(x98491,a921),x98491),x98492)))) % 14.98/14.67 [10020]~P142(x100201)+~P124(x100201)+E(f862(f862(f281(x100201),f862(f95(x100201),f862(f862(f66(f931(a1,a1),a1,x100202,f243(a1,a1)),f205(x100202)),x100203))),f862(f95(x100201),f862(f862(f66(f931(a1,a1),a1,x100202,f248(a1,a1)),f205(x100202)),x100203))),f215(x100202,x100201,x100203)) % 14.98/14.67 [10216]~E(x102163,f2(a924))+~E(f862(f182(f925(x102161)),f862(f862(f157(f925(x102161)),x102162),f718(x102163,x102161,x102162))),x102163)+E(f862(f862(f147(a924,f925(x102161)),f862(f862(f9(a924,f925(a924),f925(x102161)),f862(f862(f10(f932(a924,x102161),f932(f925(a924),f925(x102161)),a924),f147(a924,x102161)),f862(f9(a924,a924,x102161),f862(f862(f10(f925(x102161),f932(a924,x102161),a924),f157(x102161)),f862(f157(f925(x102161)),x102162))))),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(f925(x102161))),x102162))))),f132(a924,f862(f295(a924,f2(a924)),x102163))),f172(x102161,x102162)) % 14.98/14.67 [10217]E(x102171,f106(f925(x102172)))+~E(f862(f182(f925(x102172)),f862(f862(f157(f925(x102172)),x102171),f718(x102173,x102172,x102171))),x102173)+E(f862(f862(f147(a924,f925(x102172)),f862(f862(f9(a924,f925(a924),f925(x102172)),f862(f862(f10(f932(a924,x102172),f932(f925(a924),f925(x102172)),a924),f147(a924,x102172)),f862(f9(a924,a924,x102172),f862(f862(f10(f925(x102172),f932(a924,x102172),a924),f157(x102172)),f862(f157(f925(x102172)),x102171))))),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(f925(x102172))),x102171))))),f132(a924,f862(f295(a924,f2(a924)),x102173))),f172(x102172,x102171)) % 14.98/14.67 [10218]~E(x102183,f2(a924))+E(f862(f862(f147(a924,f925(x102181)),f862(f862(f9(a924,f925(a924),f925(x102181)),f862(f862(f10(f932(a924,x102181),f932(f925(a924),f925(x102181)),a924),f147(a924,x102181)),f862(f9(a924,a924,x102181),f862(f862(f10(f925(x102181),f932(a924,x102181),a924),f157(x102181)),f862(f157(f925(x102181)),x102182))))),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(f925(x102181))),x102182))))),f132(a924,f862(f295(a924,f2(a924)),x102183))),f172(x102181,x102182))+P1(f862(f862(f228(a924),f718(x102183,x102181,x102182)),f862(f182(f925(f925(x102181))),x102182))) % 14.98/14.67 [10219]E(x102191,f106(f925(x102192)))+E(f862(f862(f147(a924,f925(x102192)),f862(f862(f9(a924,f925(a924),f925(x102192)),f862(f862(f10(f932(a924,x102192),f932(f925(a924),f925(x102192)),a924),f147(a924,x102192)),f862(f9(a924,a924,x102192),f862(f862(f10(f925(x102192),f932(a924,x102192),a924),f157(x102192)),f862(f157(f925(x102192)),x102191))))),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(f925(x102192))),x102191))))),f132(a924,f862(f295(a924,f2(a924)),x102193))),f172(x102192,x102191))+P1(f862(f862(f228(a924),f718(x102193,x102192,x102191)),f862(f182(f925(f925(x102192))),x102191))) % 14.98/14.67 [7933]E(f862(f862(f73(a924),f862(f96(a924),x79331)),f862(f862(f73(a924),f862(f96(a924),x79332)),x79333)),f862(f862(f73(a924),f862(f96(a924),f862(f862(f73(a1),x79331),x79332))),x79333))+P1(f862(a186,f862(f96(a1),x79331)))+P1(f862(a186,f862(f96(a1),x79332))) % 14.98/14.67 [8704]~P1(f862(f54(x87041),x87042))+~P1(f862(f862(f321(x87041),x87043),x87042))+E(f862(a105,f862(f28(x87041),f862(f862(f3(f932(x87041,a921)),x87042),f862(f862(f301(x87041),x87043),f181(f932(x87041,a921)))))),f862(f28(x87041),x87042)) % 14.98/14.67 [8721]~P1(f862(f54(x87211),x87212))+~P1(f862(f862(f321(x87211),x87213),x87212))+E(f862(f862(f73(a924),f71(a924)),f862(f28(x87211),f862(f862(f3(f932(x87211,a921)),x87212),f862(f862(f301(x87211),x87213),f181(f932(x87211,a921)))))),f862(f28(x87211),x87212)) % 14.98/14.67 [8809]~P109(x88091)+~P1(f862(f54(x88091),x88093))+E(f862(f862(f141(x88091,x88091,f7(x88091)),x88092),f132(x88091,f862(f862(f3(f932(x88091,a921)),x88093),f862(f862(f301(x88091),x88092),f181(f932(x88091,a921)))))),f132(x88091,f862(f862(f301(x88091),x88092),x88093))) % 14.98/14.67 [8976]~P1(f862(f54(x89761),x89763))+~P1(f862(f54(x89761),x89762))+E(f862(f862(f73(a924),f862(f28(x89761),f862(f862(f103(f932(x89761,a921)),x89762),x89763))),f862(f28(x89761),f862(f862(f94(f932(x89761,a921)),x89762),x89763))),f862(f862(f73(a924),f862(f28(x89761),x89762)),f862(f28(x89761),x89763))) % 14.98/14.67 [10164]~P22(x101641,f932(f932(x101641,a921),a921),f862(f862(f9(x101641,f932(f931(x101641,x101641),a921),f932(f932(x101641,a921),a921)),f862(f862(f10(f932(x101641,a921),f932(f932(f931(x101641,x101641),a921),f932(f932(x101641,a921),a921)),x101641),f53(x101641)),f862(f862(f9(x101641,f932(x101641,a921),f932(x101641,a921)),f301(x101641)),f181(f932(x101641,a921))))),x101643),x101642)+~P1(f862(f54(x101641),x101642))+E(f862(f28(f932(x101641,a921)),f862(f862(f53(x101641),x101642),x101643)),f862(f28(x101641),x101642)) % 14.98/14.67 [8206]~P98(x82061)+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x82063)))+E(f862(f862(f236(x82061),x82062),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x82063),x82063)),a90))),f71(x82061)) % 14.98/14.67 [9693]~P98(x96931)+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x96933)))+E(f862(f862(f236(x96931),x96932),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x96933),x96933)),a90))),f862(f862(f79(x96931,x96931),f862(f862(f236(x96931),x96932),f862(f96(a924),x96933))),f862(f862(f20(x96931,x96931,x96931),f862(f862(f10(x96931,f932(x96931,x96931),x96931),f74(x96931)),f862(f74(x96931),x96932))),f7(x96931)))) % 14.98/14.67 [10082]~P1(f862(f130(x100821),x100823))+~P1(f862(f862(f321(x100821),x100822),f862(f165(x100821),x100823)))+E(f862(f862(f131(x100821),f862(f182(f925(x100821)),f170(x100821,f862(f862(f10(a921,a921,x100821),a314),f862(f862(f9(x100821,x100821,a921),a317),x100822)),f862(f161(x100821),x100823)))),f862(f161(x100821),x100823)),f862(f862(f144(x100821),x100822),f862(f161(x100821),f170(x100821,f862(f862(f10(a921,a921,x100821),a314),f862(f862(f9(x100821,x100821,a921),a317),x100822)),x100823)))) % 14.98/14.67 [10145]P1(f862(f862(f227(f932(f931(x101451,x101451),a921)),f299(x101451,x101452)),x101453))+~P1(f862(f862(f227(f932(f931(x101451,x101451),a921)),f299(x101451,f181(f932(f931(x101451,x101451),a921)))),x101453))+~P1(f862(f862(f227(f932(f931(x101451,x101451),a921)),f862(f862(f280(x101451,x101451,x101451),f862(f862(f94(f932(f931(x101451,x101451),a921)),f299(x101451,x101452)),x101453)),x101452)),x101453)) % 14.98/14.67 [9999]~P1(f862(f54(x99991),f862(f254(x99991),x99993)))+~P1(f862(f54(x99991),f862(f254(x99991),x99992)))+P1(f862(f54(x99991),f862(f254(x99991),f862(f862(f20(x99991,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99991),a319),x99992)),x99993)))) % 14.98/14.67 [10279]P1(f862(f862(f227(f932(f931(x102791,x102791),a921)),f862(f862(f280(x102791,x102791,x102791),x102792),f299(x102791,x102792))),x102793))+~P1(f862(f862(f227(f932(f931(x102791,x102791),a921)),x102792),x102793))+~P1(f862(f862(f227(f932(f931(x102791,x102791),a921)),f862(f862(f280(x102791,x102791,x102791),f862(f862(f94(f932(f931(x102791,x102791),a921)),f862(f862(f280(x102791,x102791,x102791),x102792),f299(x102791,x102792))),x102793)),x102792)),x102793)) % 14.98/14.67 [10232]~P112(x102322)+E(x102321,f2(x102322))+~E(f862(f862(f73(x102322),f862(f862(f236(x102322),x102323),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102322),x102321),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f2(x102322)) % 14.98/14.67 [10233]~P112(x102332)+E(x102331,f2(x102332))+~E(f862(f862(f73(x102332),f862(f862(f236(x102332),x102331),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102332),x102333),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f2(x102332)) % 14.98/14.67 [10239]~P1(f862(f130(x102391),x102393))+~P1(f862(f862(f321(x102391),x102392),f862(f165(x102391),x102393)))+E(f862(f161(x102391),f862(f164(x102391),f862(f862(f131(x102391),f862(f182(f925(x102391)),f170(x102391,f862(f862(f10(a921,a921,x102391),a314),f862(f862(f9(x102391,x102391,a921),a317),x102392)),x102393))),x102393))),f170(x102391,f862(f862(f10(a921,a921,x102391),a314),f862(f862(f9(x102391,x102391,a921),a317),x102392)),f862(f161(x102391),x102393))) % 14.98/14.67 [10324]~P112(x103242)+E(x103241,f2(x103242))+P1(f862(f862(f228(x103242),f2(x103242)),f862(f862(f73(x103242),f862(f862(f236(x103242),x103243),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103242),x103241),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))) % 14.98/14.67 [10325]~P112(x103252)+E(x103251,f2(x103252))+P1(f862(f862(f228(x103252),f2(x103252)),f862(f862(f73(x103252),f862(f862(f236(x103252),x103251),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103252),x103253),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))) % 14.98/14.67 [10386]~P112(x103861)+P1(f862(f862(f227(x103861),f2(x103861)),x103862))+~P1(f862(f862(f227(x103861),f2(x103861)),f862(f862(f236(x103861),x103862),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103863))))) % 14.98/14.67 [5134]~E(x51342,f83(x51343,x51341))+P1(f862(x51341,x51342))+~P1(f862(x51341,x51344)) % 14.98/14.67 [5383]E(f61(x53833,x53832,x53834),x53832)+E(x53831,f744(x53832,x53833,x53834))+~P1(f862(x53834,x53831)) % 14.98/14.67 [6714]E(f61(x67141,x67142,x67143),f78(x67141,x67143))+~E(f782(x67142,x67141,x67143,x67144),x67144)+~P1(f862(x67143,x67144)) % 14.98/14.67 [6918]~P35(x69182,x69184)+~P35(x69181,x69183)+P35(f931(x69181,x69182),f311(x69181,x69182,x69183,x69184)) % 14.98/14.67 [6919]~P36(x69192,x69194)+~P36(x69191,x69193)+P36(f931(x69191,x69192),f311(x69191,x69192,x69193,x69194)) % 14.98/14.67 [5322]~P5(x53224,x53221)+~E(f862(x53221,x53222),f862(x53221,x53223))+P1(f862(f862(x53221,x53222),x53223)) % 14.98/14.67 [5484]~P5(x54844,x54841)+E(f862(x54841,x54842),f862(x54841,x54843))+~P1(f862(f862(x54841,x54842),x54843)) % 14.98/14.67 [5485]~P13(x54854,x54851)+E(f862(x54851,x54852),f862(x54851,x54853))+~P1(f862(f862(x54851,x54852),x54853)) % 14.98/14.67 [5579]~P16(x55793,x55794,x55791)+E(f862(x55791,x55792),f862(f56(x55793,x55794),x55792))+~P1(f862(f54(x55793),x55792)) % 14.98/14.67 [5580]~P7(x55803,x55804,x55801)+E(f862(x55801,x55802),f862(f56(x55803,x55804),x55802))+~P1(f862(f54(x55803),x55802)) % 14.98/14.67 [5707]~P5(x57074,x57071)+~P1(f862(f862(x57071,x57073),x57072))+P1(f862(f862(x57071,x57072),x57073)) % 14.98/14.67 [5708]~P48(x57084,x57081)+~P1(f862(f862(x57081,x57083),x57082))+P1(f862(f862(x57081,x57082),x57083)) % 14.98/14.67 [5709]~P13(x57094,x57091)+~P1(f862(f862(x57091,x57093),x57092))+P1(f862(f862(x57091,x57092),x57093)) % 14.98/14.67 [5710]~P13(x57103,x57101)+P1(f862(f862(x57101,x57102),x57102))+~P1(f862(f862(x57101,x57104),x57102)) % 14.98/14.67 [5711]~P13(x57113,x57111)+P1(f862(f862(x57111,x57112),x57112))+~P1(f862(f862(x57111,x57112),x57114)) % 14.98/14.67 [5784]E(x57841,x57842)+~E(f862(f243(x57843,x57844),x57841),f862(f243(x57843,x57844),x57842))+~E(f862(f248(x57843,x57844),x57841),f862(f248(x57843,x57844),x57842)) % 14.98/14.67 [5812]E(x58121,x58122)+~P1(f862(f41(x58123,x58124),x58122))+~P1(f862(f41(x58123,x58124),x58121)) % 14.98/14.67 [6010]~P72(x60102)+E(f224(x60101,x60102,x60103,x60104),f2(x60102))+P1(f862(f54(x60101),x60104)) % 14.98/14.67 [6058]~P5(x60583,x60582)+~P1(f862(x60581,x60584))+P1(f862(x60581,f824(x60581,x60582,x60583))) % 14.98/14.67 [6155]~P1(f862(f307(x61551,x61552),x61554))+P1(f862(f307(x61551,x61552),x61553))+~P1(f862(f862(x61552,x61553),x61554)) % 14.98/14.67 [6954]~P27(x69541,x69543,x69544)+P1(f862(x69541,x69542))+~P1(f862(f862(f321(a1),x69542),f296(a1,x69543,x69544))) % 14.98/14.67 [7146]~P5(x71461,x71463)+~P1(f862(x71462,x71464))+P1(f862(f862(f321(x71461),f824(x71462,x71463,x71461)),f262(x71461,x71463))) % 14.98/14.67 [8043]E(x80431,f2(a924))+~P1(f862(x80432,x80433))+P1(f862(x80432,f777(x80432,x80433,x80431,x80434))) % 14.98/14.67 [8126]~P109(x81262)+~P1(f862(f130(x81261),x81264))+P1(f862(f130(x81261),f143(x81261,x81262,x81263,x81264))) % 14.98/14.67 [8172]E(f61(x81721,x81722,x81723),f78(x81721,x81723))+~P1(f862(x81723,x81724))+P1(f862(x81723,f782(x81722,x81721,x81723,x81724))) % 14.98/14.67 [8357]~P1(f862(f54(x83572),x83574))+~P1(f862(f54(x83571),x83573))+P1(f862(f54(f930(x83571,x83572)),f305(x83571,x83572,x83573,x83574))) % 14.98/14.67 [8358]~P1(f862(f130(x83582),x83584))+~P1(f862(f130(x83581),x83583))+P1(f862(f130(f931(x83581,x83582)),f52(x83581,x83582,x83583,x83584))) % 14.98/14.67 [8361]P1(f862(f862(f321(f925(x83611)),f862(f862(f127(x83611),x83612),x83613)),f154(x83611,x83614)))+~P1(f862(f862(f321(f925(x83611)),x83613),f154(x83611,x83614)))+~P1(f862(f862(f321(f925(x83611)),x83612),f154(x83611,x83614))) % 14.98/14.67 [8641]E(x86411,f2(a924))+P1(f862(x86412,x86413))+~P1(f862(x86412,f778(x86412,x86413,x86411,x86414))) % 14.98/14.67 [8679]~P109(x86793)+~P1(f862(f130(x86791),f143(x86791,x86793,x86794,x86792)))+P1(f862(f130(x86791),x86792)) % 14.98/14.67 [8965]~P1(f862(f862(f321(f931(x89651,x89651)),f862(f862(f244(x89651,x89651),x89652),x89654)),f299(x89651,x89653)))+P1(f862(f862(f321(x89651),x89652),f308(x89651,x89653)))+~P1(f862(f862(f321(x89651),x89654),f308(x89651,x89653))) % 14.98/14.67 [5306]~P72(x53062)+E(f862(f862(f8(x53061,x53062),x53063),x53064),f2(x53062))+P1(f862(f54(x53061),x53064)) % 14.98/14.67 [5309]~P71(x53092)+E(f862(f862(f11(x53091,x53092),x53093),x53094),f71(x53092))+P1(f862(f54(x53091),x53094)) % 14.98/14.67 [5447]~P73(x54473)+E(x54471,x54472)+~E(f862(f862(f73(x54473),x54474),x54471),f862(f862(f73(x54473),x54474),x54472)) % 14.98/14.67 [5448]~P74(x54483)+E(x54481,x54482)+~E(f862(f862(f73(x54483),x54484),x54481),f862(f862(f73(x54483),x54484),x54482)) % 14.98/14.67 [5450]~P73(x54503)+E(x54501,x54502)+~E(f862(f862(f73(x54503),x54501),x54504),f862(f862(f73(x54503),x54502),x54504)) % 14.98/14.67 [5546]~P120(x55461)+~E(x55463,f862(f862(f74(x55461),x55462),x55464))+P1(f862(f862(f278(x55461),x55462),x55463)) % 14.98/14.67 [5574]~P3(x55743)+E(x55741,f181(f932(x55742,a921)))+E(f862(f862(f32(x55742,x55743),x55741),f862(f18(x55743,x55742),x55744)),x55744) % 14.98/14.67 [5575]~P3(x55753)+E(x55751,f181(f932(x55752,a921)))+E(f862(f862(f33(x55752,x55753),x55751),f862(f18(x55753,x55752),x55754)),x55754) % 14.98/14.67 [5728]~E(x57284,f181(f932(x57281,a921)))+~E(x57284,f862(f862(f301(x57281),x57282),x57283))+P1(f862(f862(f321(x57281),x57282),x57283)) % 14.98/14.67 [5798]~P110(x57983)+E(x57981,x57982)+~E(f296(x57983,x57984,x57981),f862(f862(f301(x57983),x57982),f181(f932(x57983,a921)))) % 14.98/14.67 [5799]~P110(x57993)+E(x57991,x57992)+~E(f296(x57993,x57991,x57992),f862(f862(f301(x57993),x57994),f181(f932(x57993,a921)))) % 14.98/14.67 [5859]~P33(x58593,x58591,x58594)+P33(x58593,x58591,f862(f862(f144(x58593),x58592),x58594))+P1(f862(x58591,x58592)) % 14.98/14.67 [5961]~P29(x59611,x59612,x59614)+~P1(f862(x59612,x59613))+P29(x59611,x59612,f862(f862(f144(x59611),x59613),x59614)) % 14.98/14.67 [6110]P1(f862(x61101,x61102))+~P1(f862(f240(x61103,x61101),x61104))+~P1(f862(f862(f321(x61103),x61102),x61104)) % 14.98/14.67 [6119]~P29(x61191,x61192,x61194)+~P29(x61191,x61192,x61193)+P29(x61191,x61192,f862(f862(f127(x61191),x61193),x61194)) % 14.98/14.67 [6134]P31(x61341,x61342,x61343)+~P31(x61341,x61342,f862(f862(f144(x61341),x61344),x61343))+P1(f862(x61342,x61344)) % 14.98/14.67 [6135]P33(x61351,x61352,x61353)+~P33(x61351,x61352,f862(f862(f144(x61351),x61354),x61353))+P1(f862(x61352,x61354)) % 14.98/14.67 [6208]P31(x62081,x62082,x62083)+P31(x62081,x62082,x62084)+~P31(x62081,x62082,f862(f862(f127(x62081),x62084),x62083)) % 14.98/14.67 [6228]~P72(x62281)+E(f862(f862(f8(a924,x62281),x62282),f862(f295(a924,x62283),f862(a105,x62284))),f2(x62281))+~P1(f862(f862(f228(a924),x62284),x62283)) % 14.98/14.67 [6233]~P62(x62331)+~E(f38(x62331,x62332,x62333),f38(x62331,x62334,x62333))+E(f38(x62331,f862(f72(x62331),x62332),x62333),f38(x62331,f862(f72(x62331),x62334),x62333)) % 14.98/14.67 [6299]P1(f862(x62991,x62992))+~E(f862(f129(x62993,x62991),x62994),x62994)+~P1(f862(f862(f321(x62993),x62992),f862(f165(x62993),x62994))) % 14.98/14.67 [6318]~E(f862(f862(f73(a924),x63183),x63182),f862(f862(f73(a924),x63181),x63184))+~P1(f862(f862(f228(a924),x63183),x63184))+P1(f862(f862(f228(a924),x63181),x63182)) % 14.98/14.67 [6324]P31(x63241,x63242,x63243)+~P1(f862(x63242,x63244))+~P1(f862(f862(f321(x63241),x63244),f862(f165(x63241),x63243))) % 14.98/14.67 [6327]~P61(x63271)+E(f38(x63271,f38(x63271,x63272,x63273),x63274),f38(x63271,x63272,x63274))+~P1(f862(f862(f278(x63271),x63274),x63273)) % 14.98/14.67 [6364]~P29(x63643,x63641,x63644)+P1(f862(x63641,x63642))+~P1(f862(f862(f321(x63643),x63642),f862(f165(x63643),x63644))) % 14.98/14.67 [6366]~E(f862(f129(x63661,x63662),x63663),f106(x63661))+~P1(f862(x63662,x63664))+~P1(f862(f862(f321(x63661),x63664),f862(f165(x63661),x63663))) % 14.98/14.67 [6367]~E(f170(x63673,x63671,x63674),x63674)+P1(f862(x63671,x63672))+~P1(f862(f862(f321(x63673),x63672),f862(f165(x63673),x63674))) % 14.98/14.67 [6395]~E(x63954,f181(f932(x63952,a921)))+~E(x63953,f181(f932(x63951,a921)))+E(f305(x63951,x63952,x63953,x63954),f181(f932(f930(x63951,x63952),a921))) % 14.98/14.67 [6543]P1(f862(x65431,x65432))+~P1(f862(f153(x65433,x65431),x65434))+~P1(f862(f862(f321(x65433),x65432),f862(f165(x65433),x65434))) % 14.98/14.67 [6586]~P1(f862(x65861,x65864))+P1(f862(x65861,f348(x65861,x65862,x65863)))+~P1(f862(f862(f321(x65863),x65864),x65862)) % 14.98/14.67 [6683]~P28(x66831,x66833,x66834)+P1(f862(x66831,x66832))+~P1(f862(f862(f321(a924),x66832),f862(f295(a924,x66833),x66834))) % 14.98/14.67 [6817]~P72(x68171)+E(f862(f862(f8(a924,x68171),x68172),f296(a924,x68173,f862(a105,x68174))),f2(x68171))+~P1(f862(f862(f228(a924),f862(a105,x68174)),x68173)) % 14.98/14.67 [6957]~P109(x69571)+E(f862(f862(f3(f932(x69571,a921)),f862(f295(x69571,x69572),x69573)),f862(f295(x69571,x69572),x69574)),f862(f295(x69571,x69574),x69573))+~P1(f862(f862(f227(x69571),x69572),x69574)) % 14.98/14.67 [7029]~E(x70293,x70294)+E(x70291,f2(a924))+P1(f862(f862(f321(x70292),x70293),f862(f165(x70292),f162(x70292,x70291,x70294)))) % 14.98/14.67 [7310]~P1(f862(f862(f321(f925(x73101)),x73104),f154(x73101,x73103)))+P1(f862(f862(f321(x73101),x73102),x73103))+~P1(f862(f862(f321(x73101),x73102),f862(f165(x73101),x73104))) % 14.98/14.67 [7317]~P35(x73171,x73172)+P1(f862(f862(f321(x73171),f611(x73172,x73171,x73173)),x73173))+~P1(f862(f862(f321(x73171),x73174),x73173)) % 14.98/14.67 [7374]~P72(x73741)+E(f862(f862(f862(f58(x73741,x73742,f73(x73741)),x73743),f2(x73741)),x73744),f862(f862(f8(x73742,x73741),x73743),x73744))+~P1(f862(f54(x73742),x73744)) % 14.98/14.67 [7376]~P71(x73761)+E(f862(f862(f862(f58(x73761,x73762,f74(x73761)),x73763),f71(x73761)),x73764),f862(f862(f11(x73762,x73761),x73763),x73764))+~P1(f862(f54(x73762),x73764)) % 14.98/14.67 [7391]~P1(f862(x73912,x73914))+~P1(f862(f862(f321(x73911),x73914),x73913))+P1(f862(f862(f321(x73911),f348(x73912,x73913,x73911)),x73913)) % 14.98/14.67 [7405]P22(x74051,x74052,x74053,x74054)+~E(f862(f28(x74052),f862(f302(x74051,x74052,x74053),x74054)),f862(f28(x74051),x74054))+~P1(f862(f54(x74051),x74054)) % 14.98/14.67 [7602]~P72(x76021)+E(f862(f862(f73(x76021),f862(x76022,x76023)),f862(f862(f8(a924,x76021),x76022),f297(a924,x76023,x76024))),f862(f862(f8(a924,x76021),x76022),f296(a924,x76023,x76024)))+~P1(f862(f862(f227(a924),x76023),x76024)) % 14.98/14.67 [7611]~P72(x76111)+~P22(x76112,x76111,x76113,x76114)+E(f862(f862(f8(x76111,x76111),f25(x76111)),f862(f302(x76112,x76111,x76113),x76114)),f862(f862(f8(x76112,x76111),x76113),x76114)) % 14.98/14.67 [7612]~P71(x76121)+~P22(x76122,x76121,x76123,x76124)+E(f862(f862(f11(x76121,x76121),f25(x76121)),f862(f302(x76122,x76121,x76123),x76124)),f862(f862(f11(x76122,x76121),x76123),x76124)) % 14.98/14.67 [7660]E(f862(f28(f930(x76601,x76602)),f305(x76601,x76602,x76603,x76604)),f862(f862(f73(a924),f862(f28(x76601),x76603)),f862(f28(x76602),x76604)))+~P1(f862(f54(x76602),x76604))+~P1(f862(f54(x76601),x76603)) % 14.98/14.67 [7743]E(x77431,x77432)+P1(f862(f862(f321(x77433),x77431),f862(f165(x77433),f163(x77433,x77432,x77434))))+~P1(f862(f862(f321(x77433),x77431),f862(f165(x77433),x77434))) % 14.98/14.67 [7972]~P72(x79721)+E(f862(f862(f73(x79721),f862(f862(f8(a924,x79721),x79722),f862(f295(a924,x79723),x79724))),f862(x79722,x79724)),f862(f862(f8(a924,x79721),x79722),f862(f295(a924,x79723),f862(a105,x79724))))+P1(f862(f862(f228(a924),x79724),x79723)) % 14.98/14.67 [8023]~P22(x80231,x80232,x80233,f234(f932(x80231,a921)))+~P1(f862(f54(x80232),x80234))+P1(f862(f54(x80231),f862(f303(x80231,x80232,x80233),x80234))) % 14.98/14.67 [8141]P1(f862(f862(f321(f925(x81411)),f862(f862(f144(x81411),x81412),x81413)),f154(x81411,x81414)))+~P1(f862(f862(f321(f925(x81411)),x81413),f154(x81411,x81414)))+~P1(f862(f862(f321(x81411),x81412),x81414)) % 14.98/14.67 [8230]~E(f862(f302(x82303,x82301,x82304),f234(f932(x82303,a921))),f234(f932(x82301,a921)))+P1(f862(f54(x82301),x82302))+~P1(f862(f54(x82303),f862(f303(x82303,x82301,x82304),x82302))) % 14.98/14.67 [8294]~P1(f862(x82941,x82944))+P1(f862(x82941,f364(x82942,x82943,x82944,x82941)))+~P1(f862(f862(f321(x82943),x82944),x82942)) % 14.98/14.67 [8327]~P22(x83271,x83273,x83274,x83272)+P1(f862(f54(x83271),x83272))+~P1(f862(f54(x83273),f862(f302(x83271,x83273,x83274),x83272))) % 14.98/14.67 [8351]~E(x83512,x83513)+P1(f862(f862(f321(f931(x83511,x83511)),f862(f862(f244(x83511,x83511),x83512),x83513)),f255(x83511,x83514)))+~P1(f862(f862(f321(x83511),x83512),x83514)) % 14.98/14.67 [8385]~P72(x83851)+E(f862(f862(f73(x83851),f862(f862(f8(a924,x83851),x83852),f296(a924,x83853,x83854))),f862(x83852,f862(a105,x83854))),f862(f862(f8(a924,x83851),x83852),f296(a924,x83853,f862(a105,x83854))))+P1(f862(f862(f228(a924),f862(a105,x83854)),x83853)) % 14.98/14.67 [8445]P1(f862(x84451,x84452))+~P1(f862(x84451,f862(f862(f157(x84453),x84454),f667(x84451,x84454,x84453))))+~P1(f862(f862(f321(x84453),x84452),f862(f165(x84453),x84454))) % 14.98/14.67 [8585]~P1(f862(f862(f321(x85851),x85852),f308(x85851,x85854)))+P1(f862(f862(f321(f925(x85851)),f862(f862(f144(x85851),x85852),x85853)),f308(f925(x85851),f150(x85851,x85854))))+~P1(f862(f862(f321(f925(x85851)),x85853),f308(f925(x85851),f150(x85851,x85854)))) % 14.98/14.67 [8600]~P22(x86002,x86003,x86004,f560(x86004,x86003,x86002,x86001))+P22(x86002,x86003,x86004,f31(f932(x86002,a921),x86001))+E(x86001,f181(f932(f932(x86002,a921),a921))) % 14.98/14.67 [8754]P1(f862(x87541,x87542))+~P1(f862(x87541,f341(x87542,x87541,x87543,x87544)))+~P1(f862(f862(f321(x87544),x87542),x87543)) % 14.98/14.67 [8873]E(x88731,x88732)+~P1(f862(f862(f321(f931(x88733,x88733)),f862(f862(f244(x88733,x88733),x88731),x88732)),f299(x88733,x88734)))+P1(f862(f862(f321(x88733),x88731),f862(f256(x88733,x88733),x88734))) % 14.98/14.67 [9026]P1(f862(x90261,x90262))+P1(f862(f862(f321(x90263),f341(x90262,x90261,x90264,x90263)),x90264))+~P1(f862(f862(f321(x90263),x90262),x90264)) % 14.98/14.67 [9038]~P1(f862(x90384,x90383))+~P1(f862(f862(f321(x90381),x90383),x90382))+P1(f862(f862(f321(x90381),f364(x90382,x90381,x90383,x90384)),x90382)) % 14.98/14.67 [9154]E(x91541,f2(a924))+P1(f862(x91542,x91543))+P1(f862(f862(f321(x91544),f778(x91542,x91543,x91541,x91544)),f862(f165(x91544),f162(x91544,x91541,x91543)))) % 14.98/14.67 [9166]E(x91661,f2(a924))+~P1(f862(x91663,x91664))+P1(f862(f862(f321(x91662),f777(x91663,x91664,x91661,x91662)),f862(f165(x91662),f162(x91662,x91661,x91664)))) % 14.98/14.67 [9168]~P23(x91681,x91682,x91683,f234(f932(x91681,a921)),f234(f932(x91682,a921)))+~P1(f862(f54(x91682),x91684))+P1(f862(f54(x91681),f862(f303(x91681,x91682,x91683),x91684))) % 14.98/14.67 [9171]P22(x91712,x91713,x91714,f31(f932(x91712,a921),x91711))+E(x91711,f181(f932(f932(x91712,a921),a921)))+P1(f862(f862(f321(f932(x91712,a921)),f560(x91714,x91713,x91712,x91711)),x91711)) % 14.98/14.67 [9286]~P23(x92863,x92861,x92864,f234(f932(x92863,a921)),f234(f932(x92861,a921)))+P1(f862(f54(x92861),x92862))+~P1(f862(f54(x92863),f862(f303(x92863,x92861,x92864),x92862))) % 14.98/14.67 [9304]P1(f862(f54(x93041),x93042))+~P1(f862(f54(x93044),f862(f302(x93041,x93044,x93043),x93042)))+P1(f862(f862(f321(x93041),f581(x93043,x93044,x93042,x93041)),x93042)) % 14.98/14.67 [9400]~P3(x94002)+E(f862(f862(f57(x94001,x94002,f862(f862(f10(x94002,f932(x94002,x94002),x94001),f94(x94002)),x94003)),f234(x94002)),x94004),f862(f862(f32(x94001,x94002),x94004),x94003))+~P1(f862(f54(x94001),x94004)) % 14.98/14.67 [9401]~P3(x94012)+E(f862(f862(f57(x94011,x94012,f862(f862(f10(x94012,f932(x94012,x94012),x94011),f103(x94012)),x94013)),f181(x94012)),x94014),f862(f862(f33(x94011,x94012),x94014),x94013))+~P1(f862(f54(x94011),x94014)) % 14.98/14.67 [9443]~P1(f862(f862(f278(a924),x94432),x94434))+~P1(f862(f862(f278(a924),x94433),x94431))+P1(f862(f862(f227(f932(a924,a921)),f287(a924,f278(a924),x94431,x94432)),f287(a924,f278(a924),x94433,x94434))) % 14.98/14.67 [9484]P1(f862(x94841,x94842))+~P1(f862(x94841,f862(f862(f157(x94843),x94844),f704(x94842,x94841,x94844,x94843))))+~P1(f862(f862(f321(x94843),x94842),f862(f165(x94843),x94844))) % 14.98/14.67 [9505]E(x95051,x95052)+~P1(f862(f862(f321(f931(x95053,x95053)),f862(f862(f244(x95053,x95053),x95051),x95052)),f299(x95053,x95054)))+P1(f862(f862(f321(f931(x95053,x95053)),f862(f862(f244(x95053,x95053),x95051),x95052)),f862(f862(f280(x95053,x95053,x95053),x95054),f299(x95053,x95054)))) % 14.98/14.67 [9556]~E(f862(f182(f925(x95561)),x95562),f862(f182(f925(x95561)),x95563))+~P1(f862(f862(f321(f931(f925(x95561),f925(x95561))),f862(f862(f244(f925(x95561),f925(x95561)),x95562),x95563)),f140(x95561,x95564)))+P1(f862(f862(f321(f931(f925(x95561),f925(x95561))),f862(f862(f244(f925(x95561),f925(x95561)),x95562),x95563)),f138(x95561,x95564))) % 14.98/14.67 [9680]P1(f862(f862(f278(a924),x96801),x96802))+~P1(f862(f862(f278(a924),x96803),x96801))+~P1(f862(f862(f227(f932(a924,a921)),f287(a924,f278(a924),x96803,x96801)),f287(a924,f278(a924),x96804,x96802))) % 14.98/14.67 [9681]P1(f862(f862(f278(a924),x96811),x96812))+~P1(f862(f862(f278(a924),x96812),x96813))+~P1(f862(f862(f227(f932(a924,a921)),f287(a924,f278(a924),x96812,x96813)),f287(a924,f278(a924),x96811,x96814))) % 14.98/14.67 [9796]P29(x97961,f862(f862(f20(x97961,a921,a921),f862(f862(f10(a921,f932(a921,a921),x97961),a319),f862(f862(f10(a921,a921,x97961),a314),x97962))),f862(a317,x97963)),x97964)+~P1(f862(x97962,x97963))+~P33(x97961,x97962,f862(f862(f144(x97961),x97963),x97964)) % 14.98/14.67 [9962]~P29(x99621,f862(f862(f20(x99621,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99621),a319),f862(f862(f10(a921,a921,x99621),a314),x99622))),f862(a317,x99623)),x99624)+~P1(f862(x99622,x99623))+P33(x99621,x99622,f862(f862(f144(x99621),x99623),x99624)) % 14.98/14.67 [9966]~P33(x99661,x99662,x99664)+~P29(x99661,f862(f862(f20(x99661,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99661),a319),f862(f862(f10(a921,a921,x99661),a314),x99662))),f862(a317,x99663)),x99664)+P33(x99661,x99662,f862(f862(f144(x99661),x99663),x99664)) % 14.98/14.67 [10000]~P59(x100001)+E(f862(f862(f8(a924,x100001),f862(f862(f20(a924,x100001,x100001),f862(f862(f10(x100001,f932(x100001,x100001),a924),f3(x100001)),x100002)),f862(f862(f10(a924,x100001,a924),x100002),f862(f862(f9(a924,a924,a924),f73(a924)),f71(a924))))),f296(a924,x100003,x100004)),f2(x100001))+P1(f862(f862(f227(a924),x100003),x100004)) % 14.98/14.67 [10231]~P35(x102312,x102314)+~P22(x102312,x102311,x102313,f234(f932(x102312,a921)))+P35(x102311,f862(f302(f931(x102312,x102312),f931(x102311,x102311),f250(x102312,x102311,x102312,x102311,x102313,x102313)),x102314)) % 14.98/14.67 [10421]~E(f862(f182(f925(x104211)),x104213),f862(f182(f925(x104211)),x104212))+P1(f862(f862(f321(f931(f925(x104211),f925(x104211))),f862(f862(f244(f925(x104211),f925(x104211)),x104212),x104213)),f151(x104211,x104214)))+~P1(f862(f862(f249(x104211,x104211,a921),f862(f862(f9(x104211,f932(f931(x104211,x104211),a921),f932(x104211,a921)),f862(f862(f10(f932(x104211,f932(f932(f931(x104211,x104211),a921),a921)),f932(f932(f931(x104211,x104211),a921),f932(x104211,a921)),x104211),f9(x104211,f932(f931(x104211,x104211),a921),a921)),f862(f862(f10(f932(x104211,f931(x104211,x104211)),f932(x104211,f932(f932(f931(x104211,x104211),a921),a921)),x104211),f862(f10(f931(x104211,x104211),f932(f932(f931(x104211,x104211),a921),a921),x104211),f321(f931(x104211,x104211)))),f244(x104211,x104211)))),x104214)),f671(x104214,x104213,x104212,x104211))) % 14.98/14.67 [6280]~P61(x62801)+~E(x62802,f2(x62801))+E(f862(f862(f29(x62801),f862(f862(f74(x62801),x62802),x62803)),f862(f862(f74(x62801),x62802),x62804)),f2(x62801)) % 14.98/14.67 [6321]E(x63211,f106(x63212))+E(x63213,f862(f862(f3(a924),f862(f182(f925(x63212)),x63211)),f71(a924)))+E(f137(x63212,f862(f862(f152(x63212,x63211),x63213),x63214)),f137(x63212,x63211)) % 14.98/14.67 [6355]E(x63551,x63552)+P1(f862(x63553,x63552))+~P1(f862(f862(f862(f301(x63554),x63551),x63553),x63552)) % 14.98/14.67 [6371]~P72(x63711)+~P1(f862(f130(x63712),x63714))+E(f862(f158(x63711),f862(f862(f147(x63712,x63711),x63713),x63714)),f862(f862(f8(x63712,x63711),x63713),f862(f165(x63712),x63714))) % 14.98/14.67 [6388]~P71(x63882)+~P1(f862(f54(x63881),x63884))+E(f862(f862(f11(x63881,x63882),f862(f18(x63882,x63881),x63883)),x63884),f862(f862(f236(x63882),x63883),f862(f28(x63881),x63884))) % 14.98/14.67 [6441]~P64(x64412)+E(x64411,f2(x64412))+E(f862(f862(f281(x64412),f862(f862(f74(x64412),x64413),x64411)),f862(f862(f74(x64412),x64414),x64411)),f862(f862(f281(x64412),x64413),x64414)) % 14.98/14.67 [6442]~P64(x64422)+E(x64421,f2(x64422))+E(f862(f862(f281(x64422),f862(f862(f74(x64422),x64421),x64423)),f862(f862(f74(x64422),x64421),x64424)),f862(f862(f281(x64422),x64423),x64424)) % 14.98/14.67 [6443]~P61(x64432)+E(x64431,f2(x64432))+E(f862(f862(f29(x64432),f862(f862(f74(x64432),x64433),x64431)),f862(f862(f74(x64432),x64434),x64431)),f862(f862(f29(x64432),x64433),x64434)) % 14.98/14.67 [6445]~P61(x64452)+E(x64451,f2(x64452))+E(f862(f862(f29(x64452),f862(f862(f74(x64452),x64451),x64453)),f862(f862(f74(x64452),x64451),x64454)),f862(f862(f29(x64452),x64453),x64454)) % 14.98/14.67 [6511]P1(f862(x65111,x65112))+~E(x65113,f862(f862(f73(a924),x65114),x65112))+~P1(f862(x65111,f862(f862(f3(a924),x65113),x65114))) % 14.98/14.67 [6599]~P1(f862(x65992,x65993))+~P1(f862(f153(x65991,x65992),x65994))+P1(f862(f153(x65991,x65992),f862(f862(f144(x65991),x65993),x65994))) % 14.98/14.67 [6640]E(x66401,f106(x66402))+~E(x66403,f862(f862(f3(a924),f862(f182(f925(x66402)),x66401)),f71(a924)))+E(f137(x66402,f862(f862(f152(x66402,x66401),x66403),x66404)),x66404) % 14.98/14.67 [6663]~P103(x66631)+~P1(f862(f862(f227(x66631),x66632),x66634))+P1(f862(f862(f227(x66631),x66632),f862(f862(f103(x66631),x66633),x66634))) % 14.98/14.67 [6664]~P103(x66641)+~P1(f862(f862(f227(x66641),x66642),x66643))+P1(f862(f862(f227(x66641),x66642),f862(f862(f103(x66641),x66643),x66644))) % 14.98/14.67 [6666]~P109(x66661)+~P1(f862(f862(f227(x66661),x66662),x66664))+P1(f862(f862(f227(x66661),x66662),f862(f862(f226(x66661),x66663),x66664))) % 14.98/14.67 [6668]~P109(x66681)+~P1(f862(f862(f227(x66681),x66682),x66683))+P1(f862(f862(f227(x66681),x66682),f862(f862(f226(x66681),x66683),x66684))) % 14.98/14.67 [6669]~P103(x66691)+~P1(f862(f862(f228(x66691),x66692),x66694))+P1(f862(f862(f228(x66691),x66692),f862(f862(f103(x66691),x66693),x66694))) % 14.98/14.67 [6670]~P103(x66701)+~P1(f862(f862(f228(x66701),x66702),x66703))+P1(f862(f862(f228(x66701),x66702),f862(f862(f103(x66701),x66703),x66704))) % 14.98/14.67 [6672]~P109(x66721)+~P1(f862(f862(f228(x66721),x66722),x66724))+P1(f862(f862(f228(x66721),x66722),f862(f862(f226(x66721),x66723),x66724))) % 14.98/14.67 [6674]~P109(x66741)+~P1(f862(f862(f228(x66741),x66742),x66743))+P1(f862(f862(f228(x66741),x66742),f862(f862(f226(x66741),x66743),x66744))) % 14.98/14.67 [6675]~P119(x66751)+~P1(f862(f862(f278(x66751),x66752),x66754))+P1(f862(f862(f278(x66751),x66752),f862(f862(f74(x66751),x66753),x66754))) % 14.98/14.67 [6676]~P119(x66761)+~P1(f862(f862(f278(x66761),x66762),x66763))+P1(f862(f862(f278(x66761),x66762),f862(f862(f74(x66761),x66763),x66764))) % 14.98/14.67 [6764]~E(f862(f862(f157(x67641),x67642),x67643),x67644)+E(f862(f862(f152(x67641,x67642),x67643),x67644),x67642)+~P1(f862(f862(f228(a924),x67643),f862(f182(f925(x67641)),x67642))) % 14.98/14.67 [6803]P1(f862(x68031,x68032))+~P1(f862(x68033,x68032))+~P1(f862(f862(f227(f932(x68034,a921)),x68033),x68031)) % 14.98/14.67 [6834]~E(f862(f862(f152(x68341,x68342),x68343),x68344),x68342)+E(f862(f862(f157(x68341),x68342),x68343),x68344)+~P1(f862(f862(f228(a924),x68343),f862(f182(f925(x68341)),x68342))) % 14.98/14.67 [6849]~P1(f862(f153(x68491,x68492),x68494))+~P1(f862(f153(x68491,x68492),x68493))+P1(f862(f153(x68491,x68492),f862(f862(f127(x68491),x68493),x68494))) % 14.98/14.67 [6953]E(x69531,f181(f932(x69532,a921)))+E(x69533,f181(f932(x69534,a921)))+~E(f862(f862(f246(x69534,x69532),x69533),f862(f18(f932(x69532,a921),x69534),x69531)),f181(f932(f931(x69534,x69532),a921))) % 14.98/14.67 [6974]E(x69741,x69742)+P1(f862(f862(f321(x69743),x69741),x69744))+~P1(f862(f862(f321(x69743),x69741),f862(f862(f301(x69743),x69742),x69744))) % 14.98/14.67 [6991]~P109(x69911)+P1(f862(f862(f227(x69911),x69912),x69913))+~P1(f862(f862(f227(x69911),x69912),f862(f862(f225(x69911),x69914),x69913))) % 14.98/14.67 [6993]~P109(x69931)+P1(f862(f862(f227(x69931),x69932),x69933))+~P1(f862(f862(f227(x69931),x69932),f862(f862(f225(x69931),x69933),x69934))) % 14.98/14.67 [6995]~P104(x69951)+P1(f862(f862(f227(x69951),x69952),x69953))+~P1(f862(f862(f227(x69951),x69952),f862(f862(f94(x69951),x69954),x69953))) % 14.98/14.67 [6997]~P104(x69971)+P1(f862(f862(f227(x69971),x69972),x69973))+~P1(f862(f862(f227(x69971),x69972),f862(f862(f94(x69971),x69973),x69974))) % 14.98/14.67 [6998]~P109(x69981)+P1(f862(f862(f228(x69981),x69982),x69983))+~P1(f862(f862(f228(x69981),x69982),f862(f862(f225(x69981),x69984),x69983))) % 14.98/14.67 [6999]~P109(x69991)+P1(f862(f862(f228(x69991),x69992),x69993))+~P1(f862(f862(f228(x69991),x69992),f862(f862(f225(x69991),x69993),x69994))) % 14.98/14.67 [7020]~E(f862(f862(f157(x70201),x70203),x70204),x70202)+P1(f862(f862(f321(x70201),x70202),f862(f165(x70201),x70203)))+~P1(f862(f862(f228(a924),x70204),f862(f182(f925(x70201)),x70203))) % 14.98/14.67 [7030]~P109(x70301)+~P11(x70301,f862(f862(f144(x70301),x70302),f862(f862(f144(x70301),x70303),x70304)))+P1(f862(f862(f227(x70301),x70302),x70303)) % 14.98/14.67 [7174]~P29(x71742,x71741,x71743)+P1(f862(x71741,f862(f862(f157(x71742),x71743),x71744)))+~P1(f862(f862(f228(a924),x71744),f862(f182(f925(x71742)),x71743))) % 14.98/14.67 [7193]E(x71931,f2(a1))+E(f862(f862(f29(a1),x71932),x71931),x71933)+~P1(f862(f42(x71932,x71931),f862(f862(f244(a1,a1),x71933),x71934))) % 14.98/14.67 [7214]E(f38(a1,x72142,x72141),x72143)+E(x72141,f2(a1))+~P1(f862(f42(x72142,x72141),f862(f862(f244(a1,a1),x72144),x72143))) % 14.98/14.67 [7334]P1(f862(f862(f321(x73341),x73342),x73343))+~P1(f862(f862(f321(x73341),x73342),x73344))+~P1(f862(f862(f228(f932(x73341,a921)),x73344),x73343)) % 14.98/14.67 [7335]P1(f862(f862(f321(x73351),x73352),x73353))+~P1(f862(f862(f321(x73351),x73352),x73354))+~P1(f862(f862(f227(f932(x73351,a921)),x73354),x73353)) % 14.98/14.67 [7346]~P113(x73461)+~E(x73463,f2(x73461))+P1(f862(f862(f278(x73461),f862(f862(f74(x73461),x73462),x73463)),f862(f862(f74(x73461),x73464),x73463))) % 14.98/14.67 [7347]~P113(x73471)+~E(x73472,f2(x73471))+P1(f862(f862(f278(x73471),f862(f862(f74(x73471),x73472),x73473)),f862(f862(f74(x73471),x73472),x73474))) % 14.98/14.67 [7450]P31(x74501,x74502,x74503)+~P1(f862(x74502,f862(f862(f157(x74501),x74503),x74504)))+~P1(f862(f862(f228(a924),x74504),f862(f182(f925(x74501)),x74503))) % 14.98/14.67 [7567]~P108(x75672)+~P1(f862(f862(f228(f932(x75671,x75672)),x75673),x75674))+P1(f862(f862(f227(f932(x75671,x75672)),x75673),x75674)) % 14.98/14.67 [7692]~P1(f862(f862(f321(x76921),x76922),x76924))+P1(f862(f862(f321(x76921),x76922),f30(f932(x76921,a921),x76923)))+~P1(f862(f862(f321(f932(x76921,a921)),x76924),x76923)) % 14.98/14.67 [7694]~P119(x76941)+~P1(f862(f862(f227(a924),x76943),x76944))+P1(f862(f862(f278(x76941),f862(f862(f236(x76941),x76942),x76943)),f862(f862(f236(x76941),x76942),x76944))) % 14.98/14.67 [7720]~P84(x77201)+~P1(f862(f862(f227(x77201),x77203),x77204))+P1(f862(f862(f227(x77201),f862(f862(f73(x77201),x77202),x77203)),f862(f862(f73(x77201),x77202),x77204))) % 14.98/14.67 [7721]~P85(x77211)+~P1(f862(f862(f227(x77211),x77213),x77214))+P1(f862(f862(f227(x77211),f862(f862(f73(x77211),x77212),x77213)),f862(f862(f73(x77211),x77212),x77214))) % 14.98/14.67 [7722]~P84(x77221)+~P1(f862(f862(f227(x77221),x77222),x77224))+P1(f862(f862(f227(x77221),f862(f862(f73(x77221),x77222),x77223)),f862(f862(f73(x77221),x77224),x77223))) % 14.98/14.67 [7723]~P85(x77231)+~P1(f862(f862(f227(x77231),x77232),x77234))+P1(f862(f862(f227(x77231),f862(f862(f73(x77231),x77232),x77233)),f862(f862(f73(x77231),x77234),x77233))) % 14.98/14.67 [7724]~P83(x77241)+~P1(f862(f862(f228(x77241),x77243),x77244))+P1(f862(f862(f228(x77241),f862(f862(f73(x77241),x77242),x77243)),f862(f862(f73(x77241),x77242),x77244))) % 14.98/14.67 [7725]~P84(x77251)+~P1(f862(f862(f228(x77251),x77253),x77254))+P1(f862(f862(f228(x77251),f862(f862(f73(x77251),x77252),x77253)),f862(f862(f73(x77251),x77252),x77254))) % 14.98/14.67 [7726]~P83(x77261)+~P1(f862(f862(f228(x77261),x77262),x77264))+P1(f862(f862(f228(x77261),f862(f862(f73(x77261),x77262),x77263)),f862(f862(f73(x77261),x77264),x77263))) % 14.98/14.67 [7727]~P84(x77271)+~P1(f862(f862(f228(x77271),x77272),x77274))+P1(f862(f862(f228(x77271),f862(f862(f73(x77271),x77272),x77273)),f862(f862(f73(x77271),x77274),x77273))) % 14.98/14.67 [7728]~P113(x77281)+~P1(f862(f862(f278(x77281),x77283),x77284))+P1(f862(f862(f278(x77281),f862(f862(f74(x77281),x77282),x77283)),f862(f862(f74(x77281),x77282),x77284))) % 14.98/14.67 [7729]~P113(x77291)+~P1(f862(f862(f278(x77291),x77292),x77294))+P1(f862(f862(f278(x77291),f862(f862(f74(x77291),x77292),x77293)),f862(f862(f74(x77291),x77294),x77293))) % 14.98/14.67 [7730]~P119(x77301)+~P1(f862(f862(f278(x77301),x77302),x77304))+P1(f862(f862(f278(x77301),f862(f862(f236(x77301),x77302),x77303)),f862(f862(f236(x77301),x77304),x77303))) % 14.98/14.67 [7737]~P125(x77371)+~P99(x77371)+E(f862(f862(f3(x77371),f862(f862(f74(x77371),x77372),f862(f96(x77371),x77373))),f862(f862(f74(x77371),x77374),f862(f96(x77371),x77373))),f862(f862(f74(x77371),f862(f862(f3(x77371),x77372),x77374)),f862(f96(x77371),x77373))) % 14.98/14.67 [7738]~P140(x77381)+~P99(x77381)+E(f862(f862(f73(x77381),f862(f862(f74(x77381),x77382),f862(f96(x77381),x77383))),f862(f862(f74(x77381),x77384),f862(f96(x77381),x77383))),f862(f862(f74(x77381),f862(f862(f73(x77381),x77382),x77384)),f862(f96(x77381),x77383))) % 14.98/14.67 [7775]~P72(x77751)+E(f862(f862(f73(x77751),f862(x77752,x77753)),f862(f862(f8(a924,x77751),x77752),f296(a924,f862(a105,x77753),x77754))),f862(f862(f8(a924,x77751),x77752),f296(a924,x77753,x77754)))+~P1(f862(f862(f227(a924),x77753),x77754)) % 14.98/14.67 [7787]~P22(x77872,x77871,x77873,f862(f165(x77872),x77874))+~P1(f862(f130(x77872),x77874))+P1(f862(f130(x77871),f862(f862(f147(x77872,x77871),x77873),x77874))) % 14.98/14.67 [7836]~P1(f862(f862(f227(a924),x78362),x78364))+~P1(f862(f862(f227(a924),x78361),x78363))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x78361),x78362)),f862(f862(f74(a924),x78363),x78364))) % 14.98/14.67 [7837]~P1(f862(f862(f227(a924),x78372),x78374))+~P1(f862(f862(f227(a924),x78371),x78373))+P1(f862(f862(f227(a924),f862(f862(f73(a924),x78371),x78372)),f862(f862(f73(a924),x78373),x78374))) % 14.98/14.67 [7840]~P1(f862(f862(f228(a924),x78402),x78404))+~P1(f862(f862(f228(a924),x78401),x78403))+P1(f862(f862(f228(a924),f862(f862(f73(a924),x78401),x78402)),f862(f862(f73(a924),x78403),x78404))) % 14.98/14.67 [7841]~P1(f862(f862(f227(a1),x78412),x78414))+~P1(f862(f862(f228(a1),x78411),x78413))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x78411),x78412)),f862(f862(f73(a1),x78413),x78414))) % 14.98/14.67 [7889]P1(f862(f862(f321(x78891),x78892),x78893))+~P1(f862(f862(f321(x78891),x78892),f31(f932(x78891,a921),x78894)))+~P1(f862(f862(f321(f932(x78891,a921)),x78893),x78894)) % 14.98/14.67 [7905]~P1(f862(x79051,f665(x79051,x79053,x79052)))+P1(f862(x79051,f862(f862(f157(x79052),x79053),x79054)))+~P1(f862(f862(f228(a924),x79054),f862(f182(f925(x79052)),x79053))) % 14.98/14.67 [7910]P1(f862(x79101,x79102))+~P1(f862(f862(f321(x79104),x79102),f862(f165(x79104),x79103)))+P1(f862(f862(f228(a924),f667(x79101,x79103,x79104)),f862(f182(f925(x79104)),x79103))) % 14.98/14.67 [7957]~P108(x79571)+~P1(f862(f862(f228(f932(x79572,x79571)),x79574),x79573))+~P1(f862(f862(f227(f932(x79572,x79571)),x79573),x79574)) % 14.98/14.67 [8001]~P1(f862(x80014,x80012))+~P1(f862(f862(f321(x80011),x80012),x80013))+P1(f862(f862(f321(x80011),x80012),f862(f862(f94(f932(x80011,a921)),x80013),f862(f254(x80011),x80014)))) % 14.98/14.67 [8148]~P1(f862(f862(f321(x81481),x81483),x81484))+~P1(f862(f862(f228(f932(x81481,a921)),x81482),x81484))+P1(f862(f862(f228(f932(x81481,a921)),x81482),f862(f862(f301(x81481),x81483),x81484))) % 14.98/14.67 [8150]E(f862(f862(f94(f932(x81501,a921)),x81502),x81503),f181(f932(x81501,a921)))+~E(f862(f862(f94(f932(x81501,a921)),f30(f932(x81501,a921),x81504)),x81503),f181(f932(x81501,a921)))+~P1(f862(f862(f321(f932(x81501,a921)),x81502),x81504)) % 14.98/14.67 [8226]P1(f862(f862(f321(x82261),x82262),x82263))+~P1(f862(f862(f227(f932(x82261,a921)),x82263),f862(f862(f301(x82261),x82262),x82264)))+P1(f862(f862(f227(f932(x82261,a921)),x82263),x82264)) % 14.98/14.67 [8243]P1(f862(f862(f321(x82432),f665(x82431,x82433,x82432)),f862(f165(x82432),x82433)))+P1(f862(x82431,f862(f862(f157(x82432),x82433),x82434)))+~P1(f862(f862(f228(a924),x82434),f862(f182(f925(x82432)),x82433))) % 14.98/14.67 [8251]~P1(f862(f862(f227(f932(x82511,a921)),x82512),x82514))+P1(f862(f862(f227(f932(x82511,a921)),x82512),x82513))+~P1(f862(f862(f227(f932(x82511,a921)),x82514),x82513)) % 14.98/14.67 [8252]~P1(f862(f862(f228(f932(x82521,a921)),x82522),x82524))+~P1(f862(f862(f227(f932(x82521,a921)),x82524),x82523))+P1(f862(f862(f228(f932(x82521,a921)),x82522),x82523)) % 14.98/14.67 [8253]~P1(f862(f862(f227(f932(x82531,a921)),x82532),x82534))+~P1(f862(f862(f228(f932(x82531,a921)),x82534),x82533))+P1(f862(f862(f228(f932(x82531,a921)),x82532),x82533)) % 14.98/14.67 [8254]~P1(f862(f862(f228(f932(x82541,a921)),x82542),x82544))+P1(f862(f862(f228(f932(x82541,a921)),x82542),x82543))+~P1(f862(f862(f228(f932(x82541,a921)),x82544),x82543)) % 14.98/14.67 [8300]~P1(f862(f862(f321(x83001),x83004),x83003))+~P1(f862(f862(f228(f932(x83001,a921)),x83002),f862(f862(f301(x83001),x83004),x83003)))+P1(f862(f862(f228(f932(x83001,a921)),x83002),x83003)) % 14.98/14.67 [8311]~P84(x83111)+P1(f862(f862(f227(x83111),x83112),x83113))+~P1(f862(f862(f227(x83111),f862(f862(f73(x83111),x83114),x83112)),f862(f862(f73(x83111),x83114),x83113))) % 14.98/14.67 [8313]~P84(x83131)+P1(f862(f862(f227(x83131),x83132),x83133))+~P1(f862(f862(f227(x83131),f862(f862(f73(x83131),x83132),x83134)),f862(f862(f73(x83131),x83133),x83134))) % 14.98/14.67 [8315]~P84(x83151)+P1(f862(f862(f228(x83151),x83152),x83153))+~P1(f862(f862(f228(x83151),f862(f862(f73(x83151),x83154),x83152)),f862(f862(f73(x83151),x83154),x83153))) % 14.98/14.67 [8317]~P84(x83171)+P1(f862(f862(f228(x83171),x83172),x83173))+~P1(f862(f862(f228(x83171),f862(f862(f73(x83171),x83172),x83174)),f862(f862(f73(x83171),x83173),x83174))) % 14.98/14.67 [8368]P1(f862(x83681,x83682))+~E(f862(f862(f131(x83683),f862(f182(f925(x83683)),f170(x83683,x83681,x83684))),x83684),f106(x83683))+~P1(f862(f862(f321(x83683),x83682),f862(f165(x83683),x83684))) % 14.98/14.67 [8487]P1(f862(x84871,x84872))+~P1(f862(f862(f321(x84873),x84872),f862(f165(x84873),x84874)))+P1(f862(f862(f228(a924),f862(f182(f925(x84873)),f862(f129(x84873,x84871),x84874))),f862(f182(f925(x84873)),x84874))) % 14.98/14.67 [8981]~P1(f862(x89811,f759(x89811,x89813,x89812,x89814)))+P1(f862(x89811,f862(f862(f157(x89812),x89813),x89814)))+~P1(f862(f862(f228(a924),x89814),f862(f182(f925(x89812)),x89813))) % 14.98/14.67 [9005]~P22(x90054,x90053,x90051,f234(f932(x90054,a921)))+E(f862(x90051,f539(x90052,x90051,x90053,x90054)),x90052)+~P1(f862(f862(f321(x90053),x90052),f862(f302(x90054,x90053,x90051),f234(f932(x90054,a921))))) % 14.98/14.67 [9075]E(f170(x90751,x90752,x90753),f862(f862(f168(x90751),x90754),x90753))+P1(f862(f862(f228(a924),f729(x90752,x90753,x90751,x90754)),x90754))+P1(f862(f862(f228(a924),x90754),f862(f182(f925(x90751)),x90753))) % 14.98/14.67 [9078]E(f170(x90781,x90782,x90783),f862(f862(f168(x90781),x90784),x90783))+P1(f862(f862(f228(a924),f729(x90782,x90783,x90781,x90784)),x90784))+P1(f862(x90782,f862(f862(f157(x90781),x90783),x90784))) % 14.98/14.67 [9113]P1(f862(x91131,x91132))+~P1(f862(f862(f321(x91134),x91132),f862(f165(x91134),x91133)))+P1(f862(f862(f228(a924),f704(x91132,x91131,x91133,x91134)),f862(f182(f925(x91134)),x91133))) % 14.98/14.67 [9115]E(f170(x91151,x91152,x91153),f862(f862(f168(x91151),x91154),x91153))+P1(f862(f862(f228(a924),x91154),f862(f182(f925(x91151)),x91153)))+P1(f862(f862(f228(a924),f729(x91152,x91153,x91151,x91154)),f862(f182(f925(x91151)),x91153))) % 14.98/14.67 [9122]E(f170(x91221,x91222,x91223),f862(f862(f168(x91221),x91224),x91223))+P1(f862(x91222,f862(f862(f157(x91221),x91223),x91224)))+P1(f862(f862(f228(a924),f729(x91222,x91223,x91221,x91224)),f862(f182(f925(x91221)),x91223))) % 14.98/14.67 [9147]~P127(x91474)+P1(f862(f862(f321(x91471),f445(x91472,x91473,x91471,x91474)),x91473))+P1(f862(f862(f228(x91474),f2(x91474)),f862(f862(f11(x91471,x91474),x91472),x91473))) % 14.98/14.67 [9148]~P127(x91484)+P1(f862(f862(f321(x91481),f446(x91482,x91483,x91481,x91484)),x91483))+P1(f862(f862(f227(x91484),f2(x91484)),f862(f862(f11(x91481,x91484),x91482),x91483))) % 14.98/14.67 [9173]~P1(f862(f54(x91731),x91734))+P1(f862(f862(f321(x91731),f571(x91732,x91733,x91734,x91731)),x91734))+P1(f862(f54(f931(x91731,x91733)),f862(f862(f246(x91731,x91733),x91734),x91732))) % 14.98/14.67 [9205]P1(f862(f862(f321(x92052),f759(x92051,x92053,x92052,x92054)),f862(f165(x92052),x92053)))+P1(f862(x92051,f862(f862(f157(x92052),x92053),x92054)))+~P1(f862(f862(f228(a924),x92054),f862(f182(f925(x92052)),x92053))) % 14.98/14.67 [9336]P1(f862(f862(f227(a924),x93364),f862(f182(f925(x93362)),f170(x93362,x93363,x93361))))+P1(f862(f862(f228(a924),f730(x93361,x93362,x93363,x93364)),x93364))+~P1(f862(f862(f227(a924),x93364),f862(f182(f925(x93362)),x93361))) % 14.98/14.67 [9488]E(f170(x94881,x94882,x94883),f862(f862(f168(x94881),x94884),x94883))+~P1(f862(x94882,f862(f862(f157(x94881),x94883),f729(x94882,x94883,x94881,x94884))))+P1(f862(f862(f228(a924),x94884),f862(f182(f925(x94881)),x94883))) % 14.98/14.67 [9495]E(f170(x94951,x94952,x94953),f862(f862(f168(x94951),x94954),x94953))+~P1(f862(x94952,f862(f862(f157(x94951),x94953),f729(x94952,x94953,x94951,x94954))))+P1(f862(x94952,f862(f862(f157(x94951),x94953),x94954))) % 14.98/14.67 [9499]~P1(f862(f54(x94991),x94993))+~P1(f862(f54(x94992),f862(x94994,f571(x94994,x94992,x94993,x94991))))+P1(f862(f54(f931(x94991,x94992)),f862(f862(f246(x94991,x94992),x94993),x94994))) % 14.98/14.67 [9507]~P127(x95071)+~P1(f862(f862(f227(x95071),f2(x95071)),f862(x95073,f446(x95073,x95074,x95072,x95071))))+P1(f862(f862(f227(x95071),f2(x95071)),f862(f862(f11(x95072,x95071),x95073),x95074))) % 14.98/14.67 [9508]~P127(x95081)+~P1(f862(f862(f228(x95081),f2(x95081)),f862(x95083,f445(x95083,x95084,x95082,x95081))))+P1(f862(f862(f228(x95081),f2(x95081)),f862(f862(f11(x95082,x95081),x95083),x95084))) % 14.98/14.67 [9516]~E(f862(f182(f925(x95164)),x95162),f862(f182(f925(x95164)),x95163))+P1(f862(f862(f321(f931(f925(x95164),f925(x95164))),f862(f862(f244(f925(x95164),f925(x95164)),x95163),x95162)),f151(x95164,x95161)))+P1(f862(f862(f228(a924),f659(x95161,x95162,x95163,x95164)),f862(f182(f925(x95164)),x95163))) % 14.98/14.67 [9570]~P1(f862(x95703,f862(f862(f157(x95702),x95704),f730(x95704,x95702,x95703,x95701))))+P1(f862(f862(f227(a924),x95701),f862(f182(f925(x95702)),f170(x95702,x95703,x95704))))+~P1(f862(f862(f227(a924),x95701),f862(f182(f925(x95702)),x95704))) % 14.98/14.67 [9652]E(f862(f862(f168(x96521),f666(x96522,x96523,x96524,x96521)),x96523),f862(f862(f168(x96521),f666(x96522,x96523,x96524,x96521)),x96524))+~P1(f862(f862(f321(f931(f925(x96521),f925(x96521))),f862(f862(f244(f925(x96521),f925(x96521)),x96524),x96523)),f140(x96521,x96522)))+P1(f862(f862(f228(a924),f862(f182(f925(x96521)),x96524)),f862(f182(f925(x96521)),x96523))) % 14.98/14.67 [9710]~P1(f862(f862(f228(a924),f2(a924)),x97103))+~P1(f862(f862(f228(a924),x97104),x97101))+P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x97101),f38(a924,x97102,x97103))),x97104)),f862(f862(f74(a924),x97101),x97103))) % 14.98/14.67 [9901]~P108(x99012)+~P1(f862(f862(f227(x99012),f862(x99013,f435(x99014,x99013,x99011,x99012))),f862(x99014,f435(x99014,x99013,x99011,x99012))))+P1(f862(f862(f227(f932(x99011,x99012)),x99013),x99014)) % 14.98/14.67 [9902]~P108(x99022)+~P1(f862(f862(f227(x99022),f862(x99023,f568(x99021,x99024,x99023,x99022))),f862(x99024,f568(x99021,x99024,x99023,x99022))))+P1(f862(f862(f227(f932(x99021,x99022)),x99023),x99024)) % 14.98/14.67 [10006]~P59(x100061)+E(f862(f862(f8(a924,x100061),f862(f862(f20(a924,x100061,x100061),f862(f862(f10(x100061,f932(x100061,x100061),a924),f3(x100061)),x100062)),f862(f862(f10(a924,x100061,a924),x100062),f862(f862(f9(a924,a924,a924),f73(a924)),f71(a924))))),f296(a924,x100063,x100064)),f862(f862(f3(x100061),f862(x100062,x100063)),f862(x100062,f862(f862(f73(a924),x100064),f71(a924)))))+~P1(f862(f862(f227(a924),x100063),x100064)) % 14.98/14.67 [10081]~P35(x100813,f862(f862(f280(x100813,x100813,x100813),x100812),f299(x100813,x100812)))+~P1(f862(f862(f321(f931(x100813,x100813)),f862(f862(f244(x100813,x100813),f862(x100811,f862(a105,f841(x100812,x100811,x100813)))),f862(x100811,f841(x100812,x100811,x100813)))),f299(x100813,x100812)))+E(f862(x100811,f862(f862(f73(a924),f840(x100812,x100811,x100813)),x100814)),f862(x100811,f840(x100812,x100811,x100813))) % 14.98/14.67 [6936]~P61(x69361)+E(f862(f862(f29(x69361),f862(f862(f74(x69361),x69362),x69363)),x69364),f862(f862(f74(x69361),x69362),f862(f862(f29(x69361),x69363),x69364)))+~P1(f862(f862(f278(x69361),x69364),x69363)) % 14.98/14.67 [7024]E(f862(f862(f127(x70241),x70242),x70243),x70244)+~E(x70243,f862(f862(f131(x70241),f862(f182(f925(x70241)),x70242)),x70244))+~E(f862(f862(f168(x70241),f862(f182(f925(x70241)),x70242)),x70244),x70242) % 14.98/14.67 [7080]~P65(x70802)+E(x70801,f2(x70802))+E(f862(f862(f281(x70802),f862(f862(f236(x70802),x70803),x70804)),f862(f862(f236(x70802),x70801),x70804)),f862(f862(f236(x70802),f862(f862(f281(x70802),x70803),x70801)),x70804)) % 14.98/14.67 [7222]~P61(x72221)+E(f862(f862(f29(x72221),f862(f862(f74(x72221),x72222),x72223)),x72224),f862(f862(f74(x72221),f862(f862(f29(x72221),x72222),x72224)),x72223))+~P1(f862(f862(f278(x72221),x72224),x72222)) % 14.98/14.67 [7230]~P104(x72301)+~P1(f862(f862(f227(x72301),x72303),x72304))+P1(f862(f862(f227(x72301),f862(f862(f94(x72301),x72302),x72303)),x72304)) % 14.98/14.67 [7231]~P104(x72311)+~P1(f862(f862(f227(x72311),x72312),x72314))+P1(f862(f862(f227(x72311),f862(f862(f94(x72311),x72312),x72313)),x72314)) % 14.98/14.67 [7233]~P109(x72331)+~P1(f862(f862(f227(x72331),x72333),x72334))+P1(f862(f862(f227(x72331),f862(f862(f225(x72331),x72332),x72333)),x72334)) % 14.98/14.67 [7235]~P109(x72351)+~P1(f862(f862(f227(x72351),x72352),x72354))+P1(f862(f862(f227(x72351),f862(f862(f225(x72351),x72352),x72353)),x72354)) % 14.98/14.67 [7236]~P104(x72361)+~P1(f862(f862(f228(x72361),x72363),x72364))+P1(f862(f862(f228(x72361),f862(f862(f94(x72361),x72362),x72363)),x72364)) % 14.98/14.67 [7237]~P104(x72371)+~P1(f862(f862(f228(x72371),x72372),x72374))+P1(f862(f862(f228(x72371),f862(f862(f94(x72371),x72372),x72373)),x72374)) % 14.98/14.67 [7239]~P109(x72391)+~P1(f862(f862(f228(x72391),x72393),x72394))+P1(f862(f862(f228(x72391),f862(f862(f225(x72391),x72392),x72393)),x72394)) % 14.98/14.67 [7241]~P109(x72411)+~P1(f862(f862(f228(x72411),x72412),x72414))+P1(f862(f862(f228(x72411),f862(f862(f225(x72411),x72412),x72413)),x72414)) % 14.98/14.67 [7264]~P1(f862(x72643,x72644))+~P1(f862(x72642,x72644))+P1(f862(f862(f862(f94(f932(x72641,a921)),x72642),x72643),x72644)) % 14.98/14.67 [7531]~P61(x75311)+E(f862(f862(f29(x75311),f862(f862(f236(x75311),x75312),x75313)),f862(f862(f236(x75311),x75314),x75313)),f862(f862(f236(x75311),f862(f862(f29(x75311),x75312),x75314)),x75313))+~P1(f862(f862(f278(x75311),x75314),x75312)) % 14.98/14.67 [7765]~P72(x77651)+E(f862(f862(f73(x77651),f862(x77652,x77653)),f862(f862(f8(a924,x77651),x77652),f862(f295(a924,f862(a105,x77653)),x77654))),f862(f862(f8(a924,x77651),x77652),f862(f295(a924,x77653),x77654)))+~P1(f862(f862(f228(a924),x77653),x77654)) % 14.98/14.67 [7783]E(x77831,x77832)+P1(f862(f862(f165(x77833),x77834),x77832))+~P1(f862(f862(f165(x77833),f862(f862(f144(x77833),x77831),x77834)),x77832)) % 14.98/14.67 [7795]~P109(x77951)+P1(f862(f862(f227(x77951),x77952),x77953))+~P1(f862(f862(f227(x77951),f862(f862(f226(x77951),x77954),x77952)),x77953)) % 14.98/14.67 [7797]~P109(x77971)+P1(f862(f862(f227(x77971),x77972),x77973))+~P1(f862(f862(f227(x77971),f862(f862(f226(x77971),x77972),x77974)),x77973)) % 14.98/14.67 [7799]~P103(x77991)+P1(f862(f862(f227(x77991),x77992),x77993))+~P1(f862(f862(f227(x77991),f862(f862(f103(x77991),x77994),x77992)),x77993)) % 14.98/14.67 [7801]~P103(x78011)+P1(f862(f862(f227(x78011),x78012),x78013))+~P1(f862(f862(f227(x78011),f862(f862(f103(x78011),x78012),x78014)),x78013)) % 14.98/14.67 [7802]~P109(x78021)+P1(f862(f862(f228(x78021),x78022),x78023))+~P1(f862(f862(f228(x78021),f862(f862(f226(x78021),x78024),x78022)),x78023)) % 14.98/14.67 [7803]~P109(x78031)+P1(f862(f862(f228(x78031),x78032),x78033))+~P1(f862(f862(f228(x78031),f862(f862(f226(x78031),x78032),x78034)),x78033)) % 14.98/14.67 [7804]~P119(x78041)+P1(f862(f862(f278(x78041),x78042),x78043))+~P1(f862(f862(f278(x78041),f862(f862(f74(x78041),x78044),x78042)),x78043)) % 14.98/14.67 [7805]~P119(x78051)+P1(f862(f862(f278(x78051),x78052),x78053))+~P1(f862(f862(f278(x78051),f862(f862(f74(x78051),x78052),x78054)),x78053)) % 14.98/14.67 [7881]~P1(f862(f862(f321(x78811),x78812),x78814))+P1(f862(f862(f321(x78811),x78812),x78813))+P1(f862(f862(f321(x78811),x78812),f862(f862(f3(f932(x78811,a921)),x78814),x78813))) % 14.98/14.67 [7964]P1(f862(x79641,x79642))+P1(f862(x79643,x79642))+~P1(f862(f862(f862(f103(f932(x79644,a921)),x79643),x79641),x79642)) % 14.98/14.67 [7975]~P1(f862(f862(f321(x79751),x79752),x79754))+~P1(f862(f862(f321(x79751),x79752),x79753))+P1(f862(f862(f321(x79751),x79752),f862(f862(f94(f932(x79751,a921)),x79753),x79754))) % 14.98/14.67 [8024]~P103(x80241)+~P1(f862(f54(x80241),x80244))+E(f862(f862(f57(x80241,x80241,f103(x80241)),x80242),f862(f862(f301(x80241),x80243),x80244)),f862(f862(f103(x80241),x80243),f862(f862(f57(x80241,x80241,f103(x80241)),x80242),x80244))) % 14.98/14.67 [8025]~P104(x80251)+~P1(f862(f54(x80251),x80254))+E(f862(f862(f57(x80251,x80251,f94(x80251)),x80252),f862(f862(f301(x80251),x80253),x80254)),f862(f862(f94(x80251),x80253),f862(f862(f57(x80251,x80251,f94(x80251)),x80252),x80254))) % 14.98/14.67 [8026]~P109(x80261)+~P1(f862(f54(x80261),x80264))+E(f862(f862(f57(x80261,x80261,f225(x80261)),x80262),f862(f862(f301(x80261),x80263),x80264)),f862(f862(f225(x80261),x80263),f862(f862(f57(x80261,x80261,f225(x80261)),x80262),x80264))) % 14.98/14.67 [8027]~P109(x80271)+~P1(f862(f54(x80271),x80274))+E(f862(f862(f57(x80271,x80271,f226(x80271)),x80272),f862(f862(f301(x80271),x80273),x80274)),f862(f862(f226(x80271),x80273),f862(f862(f57(x80271,x80271,f226(x80271)),x80272),x80274))) % 14.98/14.67 [8029]~P125(x80291)+~P99(x80291)+E(f862(f862(f3(x80291),f862(f862(f74(x80291),f862(f96(x80291),x80292)),x80293)),f862(f862(f74(x80291),f862(f96(x80291),x80292)),x80294)),f862(f862(f74(x80291),f862(f96(x80291),x80292)),f862(f862(f3(x80291),x80293),x80294))) % 14.98/14.67 [8030]~P140(x80301)+~P99(x80301)+E(f862(f862(f73(x80301),f862(f862(f74(x80301),f862(f96(x80301),x80302)),x80303)),f862(f862(f74(x80301),f862(f96(x80301),x80302)),x80304)),f862(f862(f74(x80301),f862(f96(x80301),x80302)),f862(f862(f73(x80301),x80303),x80304))) % 14.98/14.67 [8146]E(x81461,x81462)+P1(f862(f862(f321(x81463),x81461),f862(f165(x81463),x81464)))+~P1(f862(f862(f321(x81463),x81461),f862(f165(x81463),f862(f862(f144(x81463),x81462),x81464)))) % 14.98/14.67 [8322]P52(x83221,x83222,x83223)+~P52(x83221,x83222,x83224)+~P1(f862(f862(f227(f932(f931(x83221,x83222),a921)),x83223),x83224)) % 14.98/14.67 [8370]P1(f862(f862(f321(x83701),x83702),x83703))+P1(f862(f862(f321(x83701),x83702),x83704))+~P1(f862(f862(f321(x83701),x83702),f862(f862(f103(f932(x83701,a921)),x83704),x83703))) % 14.98/14.67 [8381]~P50(x83811,x83814,x83813)+~P1(f862(f862(f321(x83811),x83812),x83814))+P1(f862(f862(f321(f931(x83811,x83811)),f862(f862(f244(x83811,x83811),x83812),x83812)),x83813)) % 14.98/14.67 [8393]~P1(f862(f54(x83932),x83934))+~P1(f862(f54(x83931),x83933))+P1(f862(f54(f931(x83931,x83932)),f862(f862(f246(x83931,x83932),x83933),f862(f18(f932(x83932,a921),x83931),x83934)))) % 14.98/14.67 [8394]~P1(f862(f862(f321(x83941),x83942),x83944))+~P1(f862(f862(f227(f932(x83941,a921)),x83943),x83944))+P1(f862(f862(f227(f932(x83941,a921)),f862(f862(f301(x83941),x83942),x83943)),x83944)) % 14.98/14.67 [8401]~P71(x84012)+~P147(x84012)+E(f862(f862(f11(x84011,x84012),f862(f862(f10(a924,x84012,x84011),f93(x84012)),x84013)),x84014),f862(f93(x84012),f862(f862(f11(x84011,a924),x84013),x84014))) % 14.98/14.67 [8402]~P71(x84022)+~P142(x84022)+E(f862(f862(f11(x84021,x84022),f862(f862(f10(a1,x84022,x84021),f95(x84022)),x84023)),x84024),f862(f95(x84022),f862(f862(f11(x84021,a1),x84023),x84024))) % 14.98/14.67 [8426]E(f862(f862(f3(f932(x84261,a921)),x84262),f862(f862(f3(f932(x84261,a921)),x84263),x84264)),x84264)+~P1(f862(f862(f227(f932(x84261,a921)),x84262),x84263))+~P1(f862(f862(f227(f932(x84261,a921)),x84264),x84262)) % 14.98/14.67 [8522]~P1(f862(f54(x85221),x85224))+E(f862(f862(f3(a924),f862(f862(f8(x85221,a924),x85222),x85223)),f862(f862(f8(x85221,a924),x85222),x85224)),f862(f862(f8(x85221,a924),x85222),f862(f862(f3(f932(x85221,a921)),x85223),x85224)))+~P1(f862(f862(f227(f932(x85221,a921)),x85224),x85223)) % 14.98/14.67 [8676]~P6(x86761,x86764,x86763)+~P1(f862(f862(f321(x86761),x86762),x86764))+P1(f862(f862(f321(x86761),x86762),f862(f276(x86761,x86761,x86763),f862(f862(f301(x86761),x86762),f181(f932(x86761,a921)))))) % 14.98/14.67 [8738]~P1(f862(f862(f227(f932(x87381,a921)),x87382),x87383))+~P1(f862(f862(f227(f932(x87381,a921)),x87382),x87384))+P1(f862(f862(f227(f932(x87381,a921)),x87382),f862(f862(f94(f932(x87381,a921)),x87383),x87384))) % 14.98/14.67 [8841]E(x88411,f181(f932(x88412,a921)))+P1(f862(f54(x88413),x88414))+~P1(f862(f54(f931(x88413,x88412)),f862(f862(f246(x88413,x88412),x88414),f862(f18(f932(x88412,a921),x88413),x88411)))) % 14.98/14.67 [8842]E(x88421,f181(f932(x88422,a921)))+P1(f862(f54(x88423),x88424))+~P1(f862(f54(f931(x88422,x88423)),f862(f862(f246(x88422,x88423),x88421),f862(f18(f932(x88423,a921),x88422),x88424)))) % 14.98/14.67 [8916]P1(f862(f862(f321(x89161),x89162),f308(x89161,x89163)))+~P1(f862(f862(f321(x89161),x89164),f308(x89161,x89163)))+~P1(f862(f862(f321(f931(x89161,x89161)),f862(f862(f244(x89161,x89161),x89162),x89164)),x89163)) % 14.98/14.67 [8973]~P35(x89731,x89734)+P1(f862(f862(f321(f931(x89731,x89731)),f862(f862(f244(x89731,x89731),x89733),x89732)),f299(x89731,x89734)))+P35(x89731,f862(f862(f301(f931(x89731,x89731)),f862(f862(f244(x89731,x89731),x89732),x89733)),x89734)) % 14.98/14.67 [8974]~P55(x89741,x89744)+P1(f862(f862(f321(f931(x89741,x89741)),f862(f862(f244(x89741,x89741),x89743),x89742)),f299(x89741,x89744)))+P55(x89741,f862(f862(f301(f931(x89741,x89741)),f862(f862(f244(x89741,x89741),x89742),x89743)),x89744)) % 14.98/14.67 [9058]~E(x90582,x90583)+~P1(f862(f862(f321(x90581),x90582),f862(f165(x90581),x90584)))+P1(f862(f862(f321(f931(x90581,x90581)),f862(f862(f244(x90581,x90581),x90582),x90583)),f862(f165(f931(x90581,x90581)),f862(f862(f174(x90581,x90581),x90584),x90584)))) % 14.98/14.67 [9146]~E(x91463,x91464)+P1(f862(f862(f249(x91461,x91461,a921),a317),x91462))+~P1(f862(f862(f321(f931(x91461,x91461)),x91462),f862(f165(f931(x91461,x91461)),f862(f862(f174(x91461,x91461),x91463),x91464)))) % 14.98/14.67 [9190]P1(f862(f862(f321(f931(f925(x91901),f925(x91901))),f862(f862(f244(f925(x91901),f925(x91901)),x91902),x91903)),f140(x91901,x91904)))+~E(f862(f862(f168(x91901),f862(f182(f925(x91901)),x91902)),x91903),x91902)+~P1(f862(f862(f228(a924),f862(f182(f925(x91901)),x91902)),f862(f182(f925(x91901)),x91903))) % 14.98/14.67 [9193]~P49(x91931,x91934)+~P1(f862(f862(f321(f931(x91931,x91931)),f862(f862(f244(x91931,x91931),x91933),x91932)),x91934))+P1(f862(f862(f321(f931(x91931,x91931)),f862(f862(f244(x91931,x91931),x91932),x91933)),x91934)) % 14.98/14.67 [9284]~P1(f862(f54(x92841),x92844))+P1(f862(f862(f321(x92841),f878(x92842,x92843,x92844,x92841)),x92844))+P1(f862(f54(x92843),f862(f862(f33(x92841,f932(x92843,a921)),x92844),x92842))) % 14.98/14.67 [9285]~P1(f862(f54(x92851),x92854))+P1(f862(f862(f321(x92851),f594(x92852,x92853,x92854,x92851)),x92854))+P1(f862(f54(x92853),f862(f862(f33(x92851,f932(x92853,a921)),x92854),x92852))) % 14.98/14.67 [9372]P1(f862(f862(f321(f931(x93721,x93721)),x93722),f862(f862(f280(x93721,x93721,x93721),x93723),f299(x93721,x93723))))+~P1(f862(f862(f228(a924),f2(a924)),x93724))+~P1(f862(f862(f321(f931(x93721,x93721)),x93722),f862(f862(f176(f931(x93721,x93721),a921),x93724),x93723))) % 14.98/14.67 [9380]~P35(x93801,x93802)+~P1(f862(f862(f321(f931(x93801,x93801)),f862(f862(f244(x93801,x93801),x93804),x93803)),x93802))+~P1(f862(f862(f321(f931(x93801,x93801)),f862(f862(f244(x93801,x93801),x93803),x93804)),x93802)) % 14.98/14.67 [9506]~P1(f862(f54(x95061),x95064))+E(f862(f862(f8(x95061,a924),f862(f862(f10(f932(x95062,a921),a924,x95061),f28(x95062)),x95063)),x95064),f862(f28(f931(x95061,x95062)),f862(f862(f246(x95061,x95062),x95064),x95063)))+P1(f862(f862(f321(x95061),f572(x95063,x95062,x95064,x95061)),x95064)) % 14.98/14.67 [9510]~P1(f862(f130(x95101),x95102))+P1(f862(f130(x95101),f862(f862(f152(x95101,x95102),x95103),x95104)))+P1(f862(f862(f321(x95101),x95104),f862(f862(f3(f932(x95101,a921)),f862(f165(x95101),x95102)),f862(f862(f301(x95101),f862(f862(f157(x95101),x95102),x95103)),f181(f932(x95101,a921)))))) % 14.98/14.67 [9527]~P1(f862(f54(x95272),x95273))+~P1(f862(f54(x95271),f862(x95274,f878(x95274,x95271,x95273,x95272))))+P1(f862(f54(x95271),f862(f862(f33(x95272,f932(x95271,a921)),x95273),x95274))) % 14.98/14.67 [9528]~P1(f862(f54(x95282),x95283))+~P1(f862(f54(x95281),f862(x95284,f594(x95284,x95281,x95283,x95282))))+P1(f862(f54(x95281),f862(f862(f33(x95282,f932(x95281,a921)),x95283),x95284))) % 14.98/14.67 [9609]~P1(f862(f862(f321(f931(x96091,x96091)),x96092),f862(f862(f280(x96091,x96091,x96091),x96094),f299(x96091,x96094))))+P1(f862(f862(f321(f931(x96091,x96091)),x96092),f862(f862(f280(x96091,x96091,x96091),x96093),f299(x96091,x96093))))+~P1(f862(f862(f227(f932(f931(x96091,x96091),a921)),x96094),x96093)) % 14.98/14.67 [9619]E(f862(f862(f168(x96191),f666(x96194,x96193,x96192,x96191)),x96193),f862(f862(f168(x96191),f666(x96194,x96193,x96192,x96191)),x96192))+~P1(f862(f862(f321(f931(f925(x96191),f925(x96191))),f862(f862(f244(f925(x96191),f925(x96191)),x96192),x96193)),f140(x96191,x96194)))+E(f862(f862(f168(x96191),f862(f182(f925(x96191)),x96192)),x96193),x96192) % 14.98/14.67 [9635]~P1(f862(f54(x96351),x96354))+E(f862(f862(f8(x96351,a924),f862(f862(f10(f932(x96352,a921),a924,x96351),f28(x96352)),x96353)),x96354),f862(f28(f931(x96351,x96352)),f862(f862(f246(x96351,x96352),x96354),x96353)))+~P1(f862(f54(x96352),f862(x96353,f572(x96353,x96352,x96354,x96351)))) % 14.98/14.67 [9639]~E(f862(f182(f925(x96391)),x96393),f862(f182(f925(x96391)),x96392))+P1(f862(f862(f321(f931(f925(x96391),f925(x96391))),f862(f862(f244(f925(x96391),f925(x96391)),x96392),x96393)),f151(x96391,x96394)))+P1(f862(f862(f321(f931(x96391,x96391)),f671(x96394,x96393,x96392,x96391)),f862(f165(f931(x96391,x96391)),f862(f862(f174(x96391,x96391),x96392),x96393)))) % 14.98/14.67 [9721]~P1(f862(f862(f321(f931(f925(x97211),f925(x97211))),f862(f862(f244(f925(x97211),f925(x97211)),x97212),x97213)),f140(x97211,x97214)))+E(f862(f862(f168(x97211),f862(f182(f925(x97211)),x97212)),x97213),x97212)+P1(f862(f862(f228(a924),f666(x97214,x97213,x97212,x97211)),f862(f862(f225(a924),f862(f182(f925(x97211)),x97212)),f862(f182(f925(x97211)),x97213)))) % 14.98/14.67 [9745]~P1(f862(f862(f321(f931(f925(x97451),f925(x97451))),f862(f862(f244(f925(x97451),f925(x97451)),x97452),x97453)),f140(x97451,x97454)))+P1(f862(f862(f228(a924),f862(f182(f925(x97451)),x97452)),f862(f182(f925(x97451)),x97453)))+P1(f862(f862(f228(a924),f666(x97454,x97453,x97452,x97451)),f862(f862(f225(a924),f862(f182(f925(x97451)),x97452)),f862(f182(f925(x97451)),x97453)))) % 14.98/14.67 [10151]~P1(f862(f862(f321(f931(f925(x101511),f925(x101511))),f862(f862(f244(f925(x101511),f925(x101511)),x101512),x101513)),f140(x101511,x101514)))+E(f862(f862(f168(x101511),f862(f182(f925(x101511)),x101512)),x101513),x101512)+P1(f862(f862(f321(f931(x101511,x101511)),f862(f862(f244(x101511,x101511),f862(f862(f157(x101511),x101512),f666(x101514,x101513,x101512,x101511))),f862(f862(f157(x101511),x101513),f666(x101514,x101513,x101512,x101511)))),x101514)) % 14.98/14.67 [10152]~P1(f862(f862(f321(f931(f925(x101521),f925(x101521))),f862(f862(f244(f925(x101521),f925(x101521)),x101522),x101523)),f140(x101521,x101524)))+P1(f862(f862(f228(a924),f862(f182(f925(x101521)),x101522)),f862(f182(f925(x101521)),x101523)))+P1(f862(f862(f321(f931(x101521,x101521)),f862(f862(f244(x101521,x101521),f862(f862(f157(x101521),x101522),f666(x101524,x101523,x101522,x101521))),f862(f862(f157(x101521),x101523),f666(x101524,x101523,x101522,x101521)))),x101524)) % 14.98/14.67 [10209]~E(f862(f182(f925(x102091)),x102092),f862(f182(f925(x102091)),x102093))+P1(f862(f862(f321(f931(f925(x102091),f925(x102091))),f862(f862(f244(f925(x102091),f925(x102091)),x102092),x102093)),f151(x102091,x102094)))+~P1(f862(f862(f321(f931(x102091,x102091)),f862(f862(f244(x102091,x102091),f862(f862(f157(x102091),x102092),f659(x102094,x102093,x102092,x102091))),f862(f862(f157(x102091),x102093),f659(x102094,x102093,x102092,x102091)))),x102094)) % 14.98/14.67 [10355]~P72(x103551)+~P1(f862(f54(x103552),x103554))+E(f862(f158(x103551),f862(f862(f147(x103552,x103551),x103553),f83(f925(x103552),f862(f862(f20(f925(x103552),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x103552)),a318),f862(f862(f9(f925(x103552),f932(x103552,a921),a921),f862(f862(f10(f932(x103552,a921),f932(f932(x103552,a921),a921),f925(x103552)),a317),f165(x103552))),x103554))),f130(x103552))))),f224(x103552,x103551,x103553,x103554)) % 14.98/14.67 [7613]~P64(x76132)+E(x76131,f2(x76132))+E(f862(f862(f281(x76132),f862(f862(f73(x76132),x76133),f862(f862(f74(x76132),x76134),x76131))),x76131),f862(f862(f73(x76132),x76134),f862(f862(f281(x76132),x76133),x76131))) % 14.98/14.67 [7614]~P61(x76142)+E(x76141,f2(x76142))+E(f862(f862(f29(x76142),f862(f862(f73(x76142),x76143),f862(f862(f74(x76142),x76144),x76141))),x76141),f862(f862(f73(x76142),x76144),f862(f862(f29(x76142),x76143),x76141))) % 14.98/14.67 [7615]~P61(x76152)+E(x76151,f2(x76152))+E(f862(f862(f29(x76152),f862(f862(f73(x76152),x76153),f862(f862(f74(x76152),x76151),x76154))),x76151),f862(f862(f73(x76152),x76154),f862(f862(f29(x76152),x76153),x76151))) % 14.98/14.67 [7844]~P65(x78442)+E(x78441,f2(x78442))+E(f862(f862(f281(x78442),f862(f862(f3(x78442),x78443),f862(f862(f74(x78442),x78441),x78444))),x78441),f862(f862(f3(x78442),f862(f862(f281(x78442),x78443),x78441)),x78444)) % 14.98/14.67 [7845]~P64(x78452)+E(x78451,f2(x78452))+E(f862(f862(f281(x78452),f862(f862(f73(x78452),x78453),f862(f862(f74(x78452),x78454),x78451))),x78451),f862(f862(f73(x78452),f862(f862(f281(x78452),x78453),x78451)),x78454)) % 14.98/14.67 [7846]~P65(x78462)+E(x78461,f2(x78462))+E(f862(f862(f281(x78462),f862(f862(f73(x78462),x78463),f862(f862(f74(x78462),x78461),x78464))),x78461),f862(f862(f73(x78462),f862(f862(f281(x78462),x78463),x78461)),x78464)) % 14.98/14.67 [8554]~P1(f862(f153(x85541,x85543),x85544))+~P1(f862(f153(x85541,x85542),x85544))+P1(f862(f153(x85541,f862(f862(f94(f932(x85541,a921)),x85542),x85543)),x85544)) % 14.98/14.67 [8931]~E(f862(f862(f280(x89311,x89311,x89311),x89312),x89314),f181(f932(f931(x89311,x89311),a921)))+~E(f862(f862(f280(x89311,x89311,x89311),x89312),x89313),f181(f932(f931(x89311,x89311),a921)))+E(f862(f862(f280(x89311,x89311,x89311),x89312),f862(f862(f103(f932(f931(x89311,x89311),a921)),x89313),x89314)),f181(f932(f931(x89311,x89311),a921))) % 14.98/14.67 [9059]~P1(f862(f862(f227(f932(x90591,a921)),x90593),x90594))+~P1(f862(f862(f227(f932(x90591,a921)),x90592),x90594))+P1(f862(f862(f227(f932(x90591,a921)),f862(f862(f103(f932(x90591,a921)),x90592),x90593)),x90594)) % 14.98/14.67 [9435]~P1(f862(f54(x94351),x94354))+~P1(f862(f54(x94351),x94353))+E(f862(f862(f3(a924),f862(f862(f73(a924),f862(f862(f8(x94351,a924),x94352),x94353)),f862(f862(f8(x94351,a924),x94352),x94354))),f862(f862(f8(x94351,a924),x94352),f862(f862(f94(f932(x94351,a921)),x94353),x94354))),f862(f862(f8(x94351,a924),x94352),f862(f862(f103(f932(x94351,a921)),x94353),x94354))) % 14.98/14.67 [9524]~P1(f862(f862(f321(x95241),x95243),x95242))+~P1(f862(f862(f227(f932(x95241,a921)),x95242),f862(f862(f301(x95241),x95243),x95244)))+P1(f862(f862(f227(f932(x95241,a921)),f862(f862(f3(f932(x95241,a921)),x95242),f862(f862(f301(x95241),x95243),f181(f932(x95241,a921))))),x95244)) % 14.98/14.67 [9697]~P1(f862(f862(f321(x96971),x96973),x96972))+P1(f862(f862(f227(f932(x96971,a921)),x96972),f862(f862(f301(x96971),x96973),x96974)))+~P1(f862(f862(f227(f932(x96971,a921)),f862(f862(f3(f932(x96971,a921)),x96972),f862(f862(f301(x96971),x96973),f181(f932(x96971,a921))))),x96974)) % 14.98/14.67 [9785]~P1(f862(f862(f227(a924),x97851),x97853))+~P1(f862(f862(f228(a924),x97852),x97854))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97851),x97852)),f862(f862(f244(a924,a924),x97853),x97854))),a26)) % 14.98/14.67 [9786]~P1(f862(f862(f227(a924),x97862),x97864))+~P1(f862(f862(f227(a924),x97861),x97863))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97861),x97862)),f862(f862(f244(a924,a924),x97863),x97864))),a64)) % 14.98/14.67 [10079]~P1(f862(f862(f321(f925(x100791)),x100794),f154(x100791,x100793)))+~P1(f862(f862(f321(f925(x100791)),x100794),f154(x100791,x100792)))+P1(f862(f153(x100791,f862(f862(f94(f932(x100791,a921)),f862(f862(f9(x100791,f932(x100791,a921),a921),f321(x100791)),x100792)),f862(f862(f9(x100791,f932(x100791,a921),a921),f321(x100791)),x100793))),x100794)) % 14.98/14.67 [10174]~P22(x101741,f932(f932(x101741,a921),a921),f862(f862(f9(x101741,f932(f931(x101741,x101741),a921),f932(f932(x101741,a921),a921)),f862(f862(f10(f932(x101741,a921),f932(f932(f931(x101741,x101741),a921),f932(f932(x101741,a921),a921)),x101741),f53(x101741)),f862(f862(f9(x101741,f932(x101741,a921),f932(x101741,a921)),f301(x101741)),f181(f932(x101741,a921))))),x101743),x101742)+~P1(f862(f862(f321(x101741),x101744),x101742))+E(f862(f862(f3(f932(f932(x101741,a921),a921)),f862(f862(f53(x101741),x101742),x101743)),f862(f862(f53(x101741),f862(f862(f301(x101741),x101744),f181(f932(x101741,a921)))),x101743)),f862(f862(f53(x101741),f862(f862(f3(f932(x101741,a921)),x101742),f862(f862(f301(x101741),x101744),f181(f932(x101741,a921))))),x101743)) % 14.98/14.67 [10309]~P50(x103091,x103092,x103094)+~P1(f862(f862(f321(f931(x103091,x103091)),x103093),x103094))+P1(f862(f862(f249(x103091,x103091,a921),f862(f862(f9(x103091,f932(x103091,a921),f932(x103091,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x103091,a921),f932(x103091,a921)),x103091),f10(a921,a921,x103091)),f862(f862(f10(a921,f932(a921,a921),x103091),a318),f862(f862(f9(x103091,f932(x103091,a921),a921),f321(x103091)),x103092)))),f862(f862(f9(x103091,f932(x103091,a921),a921),f321(x103091)),x103092))),x103093)) % 14.98/14.67 [10321]P1(f862(f54(x103211),x103212))+~P1(f862(f54(x103213),f862(f302(x103211,x103213,x103214),x103212)))+~P1(f862(f54(x103211),f862(f254(x103211),f862(f862(f20(x103211,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103211),a318),f862(f862(f9(x103211,f932(x103211,a921),a921),f321(x103211)),x103212))),f862(f862(f9(x103211,x103213,a921),f862(f862(f10(x103213,f932(x103213,a921),x103211),a317),x103214)),f862(x103214,f581(x103214,x103213,x103212,x103211))))))) % 14.98/14.67 [8306]~P65(x83062)+E(x83061,f2(x83062))+E(f862(f862(f281(x83062),f862(f862(f3(x83062),f862(f862(f74(x83062),x83061),x83063)),x83064)),x83061),f862(f862(f3(x83062),x83063),f862(f862(f281(x83062),x83064),x83061))) % 14.98/14.67 [8307]~P65(x83072)+E(x83071,f2(x83072))+E(f862(f862(f281(x83072),f862(f862(f73(x83072),f862(f862(f74(x83072),x83071),x83073)),x83074)),x83071),f862(f862(f73(x83072),x83073),f862(f862(f281(x83072),x83074),x83071))) % 14.98/14.67 [9219]~E(f862(f862(f280(x92191,x92191,x92191),x92193),x92194),f181(f932(f931(x92191,x92191),a921)))+~E(f862(f862(f280(x92191,x92191,x92191),x92192),x92194),f181(f932(f931(x92191,x92191),a921)))+E(f862(f862(f280(x92191,x92191,x92191),f862(f862(f103(f932(f931(x92191,x92191),a921)),x92192),x92193)),x92194),f181(f932(f931(x92191,x92191),a921))) % 14.98/14.67 [9995]~P1(f862(f153(x99951,x99953),x99954))+~P1(f862(f153(x99951,x99952),x99954))+P1(f862(f153(x99951,f862(f862(f20(x99951,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99951),a318),x99952)),x99953)),x99954)) % 14.98/14.67 [10245]P1(f862(x102451,f511(x102452,x102453,x102451,x102454)))+~P1(f862(f54(x102454),f862(f254(x102454),x102451)))+P1(f862(f54(x102453),f862(f254(x102453),f862(f862(f10(f932(x102454,a921),a921,x102453),f80(x102454)),f862(f862(f10(f932(x102454,a921),f932(x102454,a921),x102453),f862(f20(x102454,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102454),a318),x102451))),x102452))))) % 14.98/14.67 [10263]~P1(f862(f54(x102632),f862(f254(x102632),x102633)))+~P1(f862(f54(x102631),f862(f254(x102631),f862(f862(f9(x102631,x102632,a921),x102634),f511(x102634,x102631,x102633,x102632)))))+P1(f862(f54(x102631),f862(f254(x102631),f862(f862(f10(f932(x102632,a921),a921,x102631),f80(x102632)),f862(f862(f10(f932(x102632,a921),f932(x102632,a921),x102631),f862(f20(x102632,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102632),a318),x102633))),x102634))))) % 14.98/14.67 [10334]~P1(f862(f54(x103341),x103344))+P1(f862(f862(f321(x103341),f800(x103342,x103343,x103344,x103341)),x103344))+P1(f862(f54(x103343),f862(f254(x103343),f862(f862(f10(f932(x103341,a921),a921,x103343),f80(x103341)),f862(f862(f10(f932(x103341,a921),f932(x103341,a921),x103343),f862(f20(x103341,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103341),a318),f862(f862(f9(x103341,f932(x103341,a921),a921),f321(x103341)),x103344)))),x103342))))) % 14.98/14.67 [10340]~P1(f862(f54(x103402),x103403))+~P1(f862(f54(x103401),f862(f254(x103401),f862(f862(f9(x103401,x103402,a921),x103404),f800(x103404,x103401,x103403,x103402)))))+P1(f862(f54(x103401),f862(f254(x103401),f862(f862(f10(f932(x103402,a921),a921,x103401),f80(x103402)),f862(f862(f10(f932(x103402,a921),f932(x103402,a921),x103401),f862(f20(x103402,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103402),a318),f862(f862(f9(x103402,f932(x103402,a921),a921),f321(x103402)),x103403)))),x103404))))) % 14.98/14.67 [5214]~E(x52142,x52144)+E(f162(x52141,x52142,x52143),f162(x52141,x52144,x52145))+~E(x52142,f2(a924)) % 14.98/14.67 [5465]E(x54651,x54652)+~E(f162(x54654,x54653,x54651),f162(x54654,x54655,x54652))+E(x54653,f2(a924)) % 14.98/14.67 [6744]E(x67441,x67442)+~E(f862(x67443,x67441),f862(x67443,x67442))+~P22(x67444,x67445,x67443,f234(f932(x67444,a921))) % 14.98/14.67 [7645]E(x76451,x76452)+~P22(x76453,x76454,x76455,f234(f932(x76453,a921)))+~E(f862(f302(x76453,x76454,x76455),x76451),f862(f302(x76453,x76454,x76455),x76452)) % 14.98/14.67 [7898]P22(x78982,x78983,f535(x78984,x78983,x78982,x78981),x78981)+~E(f862(f302(x78983,x78982,x78985),x78984),x78981)+E(x78981,f181(f932(x78982,a921))) % 14.98/14.67 [8437]~P1(f862(f862(x84373,x84372),x84375))+~P1(f862(f862(x84373,x84374),x84372))+P1(f862(f862(f321(x84371),x84372),f287(x84371,x84373,x84374,x84375))) % 14.98/14.67 [8438]~P1(f862(f862(x84383,x84382),x84385))+~P1(f862(f862(x84383,x84384),x84382))+P1(f862(f862(f321(x84381),x84382),f290(x84381,x84383,x84384,x84385))) % 14.98/14.67 [8746]~P22(x87461,x87462,x87463,x87464)+P23(x87461,x87462,x87463,x87464,x87465)+~E(f862(f302(x87461,x87462,x87463),x87464),x87465) % 14.98/14.67 [8880]~P23(x88801,x88803,x88804,x88802,x88805)+~P1(f862(f54(x88803),x88805))+P1(f862(f54(x88801),x88802)) % 14.98/14.67 [8881]~P23(x88813,x88811,x88814,x88815,x88812)+~P1(f862(f54(x88813),x88815))+P1(f862(f54(x88811),x88812)) % 14.98/14.67 [9014]~P22(x90141,x90143,x90145,f234(f932(x90141,a921)))+~P22(x90143,x90142,x90144,f234(f932(x90143,a921)))+P22(x90141,x90142,f862(f66(x90143,x90142,x90141,x90144),x90145),f234(f932(x90141,a921))) % 14.98/14.67 [9586]P1(f862(f862(f321(f931(x95861,x95861)),f862(f862(f244(x95861,x95861),x95862),x95863)),f299(x95861,x95864)))+~P1(f862(f862(f321(f931(x95861,x95861)),f862(f862(f244(x95861,x95861),x95862),x95865)),f299(x95861,x95864)))+~P1(f862(f862(f321(f931(x95861,x95861)),f862(f862(f244(x95861,x95861),x95865),x95863)),f299(x95861,x95864))) % 14.98/14.67 [9626]~P109(x96262)+~P1(f862(f130(x96261),x96265))+P1(f862(f130(x96261),f142(x96261,x96262,x96263,x96264,x96265))) % 14.98/14.67 [5540]~E(x55402,f106(x55401))+E(f862(f862(f127(x55401),x55402),x55403),f862(f862(f144(x55401),x55404),x55405))+~E(x55403,f862(f862(f144(x55401),x55404),x55405)) % 14.98/14.67 [5541]~E(x55412,f106(x55411))+E(f862(f862(f127(x55411),x55412),x55413),f862(f862(f144(x55411),x55414),x55415))+~E(f862(f862(f144(x55411),x55414),x55415),x55413) % 14.98/14.67 [6700]~E(f862(f182(f925(x67001)),x67005),f862(f182(f925(x67002)),x67004))+E(f862(f862(f147(f931(x67001,x67002),x67002),f248(x67001,x67002)),x67003),x67004)+~E(f862(f862(f174(x67001,x67002),x67005),x67004),x67003) % 14.98/14.67 [6701]~E(f862(f182(f925(x67011)),x67014),f862(f182(f925(x67012)),x67015))+E(f862(f862(f147(f931(x67011,x67012),x67011),f243(x67011,x67012)),x67013),x67014)+~E(f862(f862(f174(x67011,x67012),x67014),x67015),x67013) % 14.98/14.67 [7175]~P109(x71751)+~P11(x71751,f862(f862(f147(x71752,x71751),x71753),x71755))+P11(x71751,f862(f862(f147(x71752,x71751),x71753),f862(f129(x71752,x71754),x71755))) % 14.98/14.67 [7318]~P109(x73181)+P11(x73181,f862(f862(f147(x73182,x73181),x73183),f163(x73182,x73184,x73185)))+~P11(x73181,f862(f862(f147(x73182,x73181),x73183),x73185)) % 14.98/14.67 [7341]~P52(x73413,x73412,x73415)+~P52(x73411,x73413,x73414)+P52(x73411,x73412,f862(f862(f280(x73411,x73413,x73412),x73414),x73415)) % 14.98/14.67 [7438]E(x74381,x74382)+~P22(x74383,x74384,x74385,f234(f932(x74383,a921)))+~E(f862(f862(f147(x74383,x74384),x74385),x74381),f862(f862(f147(x74383,x74384),x74385),x74382)) % 14.98/14.67 [7600]~P1(f862(f862(f227(a924),x76001),f862(x76003,x76005)))+P1(f862(f862(f227(a924),x76001),f148(x76002,x76003,x76004)))+~P1(f862(f862(f321(x76002),x76005),f862(f165(x76002),x76004))) % 14.98/14.67 [7601]~P1(f862(f862(f228(a924),x76011),f862(x76013,x76015)))+P1(f862(f862(f228(a924),x76011),f148(x76012,x76013,x76014)))+~P1(f862(f862(f321(x76012),x76015),f862(f165(x76012),x76014))) % 14.98/14.67 [7994]P1(f862(x79941,x79942))+~P1(f862(x79941,x79943))+~P1(f862(f862(f321(x79944),x79942),f862(f165(x79944),f162(x79944,x79945,x79943)))) % 14.98/14.67 [7995]P1(f862(x79951,x79952))+~P1(f862(x79951,x79953))+~P1(f862(f862(f321(x79954),x79953),f862(f165(x79954),f162(x79954,x79955,x79952)))) % 14.98/14.67 [8000]~P110(x80001)+P1(f862(f862(f227(f932(x80001,a921)),f296(x80001,x80002,x80003)),f296(x80001,x80004,x80005)))+P1(f862(f862(f227(x80001),x80002),x80003)) % 14.98/14.67 [8022]~P3(x80221)+P1(f862(f862(f227(x80221),f862(f862(f32(x80222,x80221),x80223),x80224)),f862(x80224,x80225)))+~P1(f862(f862(f321(x80222),x80225),x80223)) % 14.98/14.67 [8091]~P22(x80911,x80912,x80914,x80913)+E(f862(f70(x80911,x80912,x80913,x80914),f862(x80914,x80915)),x80915)+~P1(f862(f862(f321(x80911),x80915),x80913)) % 14.98/14.67 [8092]~P22(x80921,x80922,x80924,x80923)+E(f862(f86(x80921,x80922,x80923,x80924),f862(x80924,x80925)),x80925)+~P1(f862(f862(f321(x80921),x80925),x80923)) % 14.98/14.67 [8295]~P1(f862(x82951,x82955))+P1(f862(x82951,f628(x82951,x82952,x82953,x82954)))+~P1(f862(f862(f321(x82954),x82955),x82953)) % 14.98/14.67 [8296]~P1(f862(x82961,x82965))+P1(f862(x82961,f628(x82961,x82962,x82963,x82964)))+~P1(f862(f862(f321(x82964),x82965),x82962)) % 14.98/14.67 [8391]P1(f862(f54(x83911),x83912))+~P1(f862(f54(x83913),x83914))+~P1(f862(f862(f227(f932(x83911,a921)),x83912),f862(f302(x83913,x83911,x83915),x83914))) % 14.98/14.67 [8558]E(x85581,x85582)+~P22(x85583,x85584,x85585,f862(f862(f103(f932(x85583,a921)),f862(f165(x85583),x85581)),f862(f165(x85583),x85582)))+~E(f862(f862(f147(x85583,x85584),x85585),x85581),f862(f862(f147(x85583,x85584),x85585),x85582)) % 14.98/14.67 [8612]~P110(x86121)+~P1(f862(f862(f228(f932(x86121,a921)),f296(x86121,x86124,x86125)),f296(x86121,x86122,x86123)))+P1(f862(f862(f227(x86121),x86122),x86123)) % 14.98/14.67 [8675]~P22(x86751,x86754,x86755,f234(f932(x86751,a921)))+~P1(f862(f862(f321(x86754),f862(x86755,x86752)),f862(f302(x86751,x86754,x86755),x86753)))+P1(f862(f862(f321(x86751),x86752),x86753)) % 14.98/14.67 [8752]P1(f862(x87521,x87522))+~P1(f862(x87521,f591(x87521,x87523,x87524,x87525)))+~P1(f862(f862(f321(x87525),x87522),x87524)) % 14.98/14.67 [8753]P1(f862(x87531,x87532))+~P1(f862(x87531,f591(x87531,x87533,x87534,x87535)))+~P1(f862(f862(f321(x87535),x87532),x87533)) % 14.98/14.67 [9056]~P22(x90562,x90563,x90561,x90564)+E(f862(x90561,f862(f70(x90562,x90563,x90564,x90561),x90565)),x90565)+~P1(f862(f862(f321(x90563),x90565),f862(f302(x90562,x90563,x90561),x90564))) % 14.98/14.67 [9159]E(x91591,f106(x91592))+E(f862(f862(f144(x91592),x91593),f686(x91594,x91593,x91595,x91591,x91592)),x91591)+~E(f862(f862(f127(x91592),x91591),x91595),f862(f862(f144(x91592),x91593),x91594)) % 14.98/14.67 [9160]E(x91601,f106(x91602))+E(f862(f862(f144(x91602),x91603),f687(x91604,x91601,x91605,x91603,x91602)),x91601)+~E(f862(f862(f127(x91602),x91601),x91604),f862(f862(f144(x91602),x91603),x91605)) % 14.98/14.67 [9178]E(f862(f862(f144(x91782),x91783),f686(x91784,x91783,x91781,x91785,x91782)),x91785)+~E(f862(f862(f127(x91782),x91785),x91781),f862(f862(f144(x91782),x91783),x91784))+E(x91781,f862(f862(f144(x91782),x91783),x91784)) % 14.98/14.67 [9179]E(f862(f862(f144(x91791),x91792),f687(x91794,x91795,x91793,x91792,x91791)),x91795)+~E(f862(f862(f127(x91791),x91795),x91794),f862(f862(f144(x91791),x91792),x91793))+E(f862(f862(f144(x91791),x91792),x91793),x91794) % 14.98/14.67 [9255]~E(f862(f302(x92553,x92552,x92554),f234(f932(x92553,a921))),f234(f932(x92552,a921)))+~E(f862(f302(x92551,x92553,x92555),f234(f932(x92551,a921))),f234(f932(x92553,a921)))+E(f862(f302(x92551,x92552,f862(f66(x92553,x92552,x92551,x92554),x92555)),f234(f932(x92551,a921))),f234(f932(x92552,a921))) % 14.98/14.67 [9632]E(x96321,f106(x96322))+~E(f862(f862(f127(x96322),x96321),x96323),f862(f862(f144(x96322),x96325),x96324))+E(f862(f862(f127(x96322),f687(x96323,x96321,x96324,x96325,x96322)),x96323),x96324) % 14.98/14.67 [9633]E(x96331,f106(x96332))+~E(f862(f862(f127(x96332),x96331),x96335),f862(f862(f144(x96332),x96334),x96333))+E(f862(f862(f127(x96332),f686(x96333,x96334,x96335,x96331,x96332)),x96335),x96333) % 14.98/14.67 [9640]E(f862(f862(f127(x96402),f686(x96404,x96403,x96401,x96405,x96402)),x96401),x96404)+~E(f862(f862(f127(x96402),x96405),x96401),f862(f862(f144(x96402),x96403),x96404))+E(x96401,f862(f862(f144(x96402),x96403),x96404)) % 14.98/14.67 [9641]~E(f862(f862(f127(x96411),x96415),x96414),f862(f862(f144(x96411),x96412),x96413))+E(f862(f862(f127(x96411),f687(x96414,x96415,x96413,x96412,x96411)),x96414),x96413)+E(f862(f862(f144(x96411),x96412),x96413),x96414) % 14.98/14.67 [9642]E(f862(f862(f127(x96421),x96425),f689(x96423,x96422,x96424,x96425,x96421)),x96422)+E(f862(f862(f127(x96421),x96422),f688(x96423,x96422,x96424,x96425,x96421)),x96425)+~E(f862(f862(f127(x96421),x96425),x96424),f862(f862(f127(x96421),x96422),x96423)) % 14.98/14.67 [9678]~P109(x96781)+P11(x96781,f862(f862(f147(x96782,x96781),x96783),f142(x96782,x96781,x96783,x96784,x96785)))+~P11(x96781,f862(f862(f147(x96782,x96781),x96783),x96785)) % 14.98/14.67 [9694]~P56(x96945,x96941,x96944,x96943)+P1(f862(f862(x96941,x96942),f551(x96943,x96944,x96941,x96945,x96942)))+~P1(f862(f862(f321(x96945),x96942),x96944)) % 14.98/14.67 [9695]~P56(x96955,x96951,x96954,x96953)+P1(f862(f862(x96951,x96952),f805(x96953,x96954,x96951,x96955,x96952)))+~P1(f862(f862(f321(x96955),x96952),x96954)) % 14.98/14.67 [9797]~P1(f862(f862(f321(f931(x97971,x97971)),f862(f862(f244(x97971,x97971),x97975),x97973)),f299(x97971,x97974)))+P1(f862(f862(f321(f931(x97971,x97971)),f862(f862(f244(x97971,x97971),x97972),x97973)),f862(f862(f280(x97971,x97971,x97971),x97974),f299(x97971,x97974))))+~P1(f862(f862(f321(f931(x97971,x97971)),f862(f862(f244(x97971,x97971),x97972),x97975)),f862(f862(f280(x97971,x97971,x97971),x97974),f299(x97971,x97974)))) % 14.98/14.67 [9798]~P1(f862(f862(f321(f931(x97981,x97981)),f862(f862(f244(x97981,x97981),x97982),x97985)),f299(x97981,x97984)))+P1(f862(f862(f321(f931(x97981,x97981)),f862(f862(f244(x97981,x97981),x97982),x97983)),f862(f862(f280(x97981,x97981,x97981),x97984),f299(x97981,x97984))))+~P1(f862(f862(f321(f931(x97981,x97981)),f862(f862(f244(x97981,x97981),x97985),x97983)),f862(f862(f280(x97981,x97981,x97981),x97984),f299(x97981,x97984)))) % 14.98/14.67 [9800]P1(f862(f862(f321(f931(f925(x98001),f925(x98001))),f862(f862(f244(f925(x98001),f925(x98001)),x98002),x98003)),f151(x98001,f299(x98001,x98004))))+~P1(f862(f862(f321(f931(f925(x98001),f925(x98001))),f862(f862(f244(f925(x98001),f925(x98001)),x98002),x98005)),f151(x98001,f299(x98001,x98004))))+~P1(f862(f862(f321(f931(f925(x98001),f925(x98001))),f862(f862(f244(f925(x98001),f925(x98001)),x98005),x98003)),f151(x98001,f299(x98001,x98004)))) % 14.98/14.67 [9804]E(f862(f862(f127(x98041),x98042),f688(x98043,x98042,x98044,x98045,x98041)),x98045)+E(f862(f862(f127(x98041),f689(x98043,x98042,x98044,x98045,x98041)),x98043),x98044)+~E(f862(f862(f127(x98041),x98042),x98043),f862(f862(f127(x98041),x98045),x98044)) % 14.98/14.67 [9805]E(f862(f862(f127(x98051),x98052),f689(x98053,x98054,x98055,x98052,x98051)),x98054)+E(f862(f862(f127(x98051),f688(x98053,x98054,x98055,x98052,x98051)),x98055),x98053)+~E(f862(f862(f127(x98051),x98052),x98055),f862(f862(f127(x98051),x98054),x98053)) % 14.98/14.67 [9859]P1(f862(f862(f321(f931(x98591,x98591)),f862(f862(f244(x98591,x98591),x98592),x98593)),f862(f862(f280(x98591,x98591,x98591),x98594),f299(x98591,x98594))))+~P1(f862(f862(f321(f931(x98591,x98591)),f862(f862(f244(x98591,x98591),x98592),x98595)),f862(f862(f280(x98591,x98591,x98591),x98594),f299(x98591,x98594))))+~P1(f862(f862(f321(f931(x98591,x98591)),f862(f862(f244(x98591,x98591),x98595),x98593)),f862(f862(f280(x98591,x98591,x98591),x98594),f299(x98591,x98594)))) % 14.98/14.67 [9886]P32(x98861,x98862,x98863,x98864,x98865)+~E(f862(f182(f925(x98861)),x98864),f862(f182(f925(x98862)),x98865))+~P1(f862(f862(f249(x98861,x98862,a921),x98863),f705(x98865,x98864,x98863,x98862,x98861))) % 14.98/14.67 [9887]P32(x98871,x98872,x98873,x98874,x98875)+~E(f862(f182(f925(x98871)),x98874),f862(f182(f925(x98872)),x98875))+~P1(f862(f862(f249(x98871,x98872,a921),x98873),f706(x98873,x98875,x98874,x98872,x98871))) % 14.98/14.67 [9892]E(f862(f862(f127(x98921),f688(x98922,x98923,x98924,x98925,x98921)),x98924),x98922)+~E(f862(f862(f127(x98921),x98923),x98922),f862(f862(f127(x98921),x98925),x98924))+E(f862(f862(f127(x98921),f689(x98922,x98923,x98924,x98925,x98921)),x98922),x98924) % 14.98/14.67 [9908]~P109(x99082)+E(f862(f862(f141(x99081,x99082,x99083),x99084),x99085),f862(f862(f144(x99081),x99084),x99085))+P1(f862(f862(f321(x99081),f750(x99084,x99083,x99085,x99081,x99082)),f862(f165(x99081),x99085))) % 14.98/14.67 [9912]~P56(x99121,x99124,x99123,x99122)+~P1(f862(f862(f321(x99121),x99125),x99123))+P1(f862(f862(f321(x99121),f551(x99122,x99123,x99124,x99121,x99125)),x99122)) % 14.98/14.67 [9913]~P56(x99131,x99134,x99133,x99132)+~P1(f862(f862(f321(x99131),x99135),x99133))+P1(f862(f862(f321(x99131),f805(x99132,x99133,x99134,x99131,x99135)),x99132)) % 14.98/14.67 [10029]~P1(f862(f862(f321(f931(f932(x100291,a921),f932(x100291,a921))),f862(f862(f244(f932(x100291,a921),f932(x100291,a921)),x100294),x100293)),f310(x100291,x100292)))+~P1(f862(f862(f321(x100291),x100295),x100294))+P1(f862(f862(f321(x100291),f616(x100292,x100293,x100294,x100291,x100295)),x100293)) % 14.98/14.67 [10039]~P109(x100392)+E(f862(f862(f141(x100391,x100392,x100393),x100394),x100395),f862(f862(f144(x100391),x100394),x100395))+~P1(f862(f862(f227(x100392),f862(x100393,x100394)),f862(x100393,f750(x100394,x100393,x100395,x100391,x100392)))) % 14.98/14.67 [10088]~P22(x100883,x100884,x100885,f234(f932(x100883,a921)))+P1(f862(x100881,x100882))+~P1(f862(x100881,f862(f86(x100883,x100884,f234(f932(x100883,a921)),x100885),f818(x100882,x100881,x100885,x100884,x100883)))) % 14.98/14.67 [10226]P32(x102261,x102262,x102263,x102264,x102265)+~E(f862(f182(f925(x102261)),x102264),f862(f182(f925(x102262)),x102265))+~P1(f862(f862(x102263,f862(f862(f157(x102261),x102264),f707(x102265,x102264,x102263,x102262,x102261))),f862(f862(f157(x102262),x102265),f707(x102265,x102264,x102263,x102262,x102261)))) % 14.98/14.67 [10227]P32(x102271,x102272,x102273,x102274,x102275)+~E(f862(f182(f925(x102271)),x102274),f862(f182(f925(x102272)),x102275))+~P1(f862(f862(x102273,f862(f862(f157(x102271),x102274),f742(x102273,x102275,x102272,x102274,x102271))),f862(f862(f157(x102272),x102275),f742(x102273,x102275,x102272,x102274,x102271)))) % 14.98/14.67 [6773]~P15(x67732,x67735,x67731)+~P1(f862(f54(x67732),x67734))+E(f862(x67731,f862(f862(f301(x67732),x67733),x67734)),f862(f862(f57(x67732,x67732,x67735),x67733),x67734)) % 14.98/14.67 [6774]~E(x67743,x67744)+~E(x67742,x67745)+E(f862(f862(f301(x67741),x67742),f862(f862(f301(x67741),x67743),f181(f932(x67741,a921)))),f862(f862(f301(x67741),x67744),f862(f862(f301(x67741),x67745),f181(f932(x67741,a921))))) % 14.98/14.67 [6784]P1(f862(x67842,x67845))+E(f170(x67841,x67842,f862(f862(f127(x67841),x67843),x67844)),f170(x67841,x67842,x67843))+~P1(f862(f862(f321(x67841),x67845),f862(f165(x67841),x67843))) % 14.98/14.67 [6820]E(f862(x68201,x68202),f181(f932(x68203,a921)))+~E(f862(f862(f33(x68204,f932(x68203,a921)),x68205),x68201),f181(f932(x68203,a921)))+~P1(f862(f862(f321(x68204),x68202),x68205)) % 14.98/14.67 [6821]E(f862(x68211,x68212),f234(f932(x68213,a921)))+~E(f862(f862(f32(x68214,f932(x68213,a921)),x68215),x68211),f234(f932(x68213,a921)))+~P1(f862(f862(f321(x68214),x68212),x68215)) % 14.98/14.67 [7328]~E(x73282,x73284)+~P144(x73281)+E(f862(f862(f73(x73281),f862(f862(f74(x73281),x73282),x73283)),f862(f862(f74(x73281),x73284),x73285)),f862(f862(f73(x73281),f862(f862(f74(x73281),x73282),x73285)),f862(f862(f74(x73281),x73284),x73283))) % 14.98/14.67 [7390]~P3(x73901)+~P1(f862(f862(f321(x73904),x73903),x73905))+P1(f862(f862(f227(x73901),f862(x73902,x73903)),f862(f862(f33(x73904,x73901),x73905),x73902))) % 14.98/14.67 [7444]~P108(x74441)+P1(f862(f862(f227(x74441),f862(x74442,x74443)),f862(x74444,x74443)))+~P1(f862(f862(f227(f932(x74445,x74441)),x74442),x74444)) % 14.98/14.67 [7568]E(x75681,x75682)+E(x75683,x75681)+~E(f862(f862(f301(x75684),x75681),f862(f862(f301(x75684),x75685),f181(f932(x75684,a921)))),f862(f862(f301(x75684),x75682),f862(f862(f301(x75684),x75683),f181(f932(x75684,a921))))) % 14.98/14.67 [7569]E(x75691,x75692)+E(x75693,x75691)+~E(f862(f862(f301(x75694),x75693),f862(f862(f301(x75694),x75692),f181(f932(x75694,a921)))),f862(f862(f301(x75694),x75695),f862(f862(f301(x75694),x75691),f181(f932(x75694,a921))))) % 14.98/14.67 [7570]E(x75701,x75702)+E(x75701,x75703)+~E(f862(f862(f301(x75704),x75703),f862(f862(f301(x75704),x75702),f181(f932(x75704,a921)))),f862(f862(f301(x75704),x75705),f862(f862(f301(x75704),x75701),f181(f932(x75704,a921))))) % 14.98/14.67 [7571]E(x75711,x75712)+E(x75711,x75713)+~E(f862(f862(f301(x75714),x75711),f862(f862(f301(x75714),x75715),f181(f932(x75714,a921)))),f862(f862(f301(x75714),x75712),f862(f862(f301(x75714),x75713),f181(f932(x75714,a921))))) % 14.98/14.67 [8102]P22(x81021,x81022,x81023,x81024)+~P22(x81021,x81022,x81023,x81025)+~P1(f862(f862(f227(f932(x81021,a921)),x81024),x81025)) % 14.98/14.67 [8132]~E(f862(x81323,x81325),x81324)+~P22(x81321,x81322,x81323,f234(f932(x81321,a921)))+E(f862(f86(x81321,x81322,f234(f932(x81321,a921)),x81323),x81324),x81325) % 14.98/14.67 [8281]E(x82811,x82812)+~E(f862(f302(x82813,x82814,x82815),x82811),f862(f302(x82813,x82814,x82815),x82812))+~P22(x82813,x82814,x82815,f862(f862(f103(f932(x82813,a921)),x82811),x82812)) % 14.98/14.67 [8360]P1(f862(x83602,x83604))+E(f862(f862(f131(x83601),f862(f182(f925(x83601)),f170(x83601,x83602,x83603))),x83603),f862(f862(f144(x83601),x83604),x83605))+~E(f862(f862(f127(x83601),f170(x83601,x83602,x83603)),f862(f862(f144(x83601),x83604),x83605)),x83603) % 14.98/14.67 [8389]~P22(x83891,x83892,x83893,x83895)+~P22(x83891,x83892,x83893,x83894)+P22(x83891,x83892,x83893,f862(f862(f94(f932(x83891,a921)),x83894),x83895)) % 14.98/14.67 [8496]~P72(x84961)+E(f862(f862(f73(x84961),f862(x84962,x84963)),f862(f158(x84961),f862(f862(f147(x84964,x84961),x84962),f163(x84964,x84963,x84965)))),f862(f158(x84961),f862(f862(f147(x84964,x84961),x84962),x84965)))+~P1(f862(f862(f321(x84964),x84963),f862(f165(x84964),x84965))) % 14.98/14.67 [8584]~P109(x85841)+~P11(x85841,f862(f862(f147(x85842,x85841),x85843),x85845))+P11(x85841,f862(f862(f147(x85842,x85841),x85843),f862(f862(f141(x85842,x85841,x85843),x85844),x85845))) % 14.98/14.67 [8671]~P3(x86711)+P1(f862(f862(f227(x86711),f862(f862(f32(x86712,x86711),x86713),x86714)),f862(f862(f32(x86712,x86711),x86715),x86714)))+~P1(f862(f862(f227(f932(x86712,a921)),x86715),x86713)) % 14.98/14.67 [8672]~P3(x86721)+P1(f862(f862(f227(x86721),f862(f862(f33(x86722,x86721),x86723),x86724)),f862(f862(f33(x86722,x86721),x86725),x86724)))+~P1(f862(f862(f227(f932(x86722,a921)),x86723),x86725)) % 14.98/14.67 [8706]~P109(x87063)+P1(f862(f130(x87061),x87062))+~P1(f862(f130(x87061),f862(f862(f141(x87061,x87063,x87064),x87065),x87062))) % 14.98/14.67 [8852]~P109(x88521)+~P1(f862(f862(f321(x88522),x88523),f862(f165(x88522),x88524)))+~P1(f862(f130(x88522),f862(f862(f141(x88522,x88521,x88525),x88523),x88524))) % 14.98/14.67 [8943]~P109(x89431)+P11(x89431,f862(f862(f147(x89432,x89431),x89433),x89434))+~P11(x89431,f862(f862(f147(x89432,x89431),x89433),f862(f862(f141(x89432,x89431,x89433),x89435),x89434))) % 14.98/14.67 [8989]~P22(x89892,x89891,x89894,x89893)+E(f862(f302(x89891,x89892,f86(x89892,x89891,x89893,x89894)),f862(f302(x89892,x89891,x89894),x89895)),x89895)+~P1(f862(f862(f227(f932(x89892,a921)),x89895),x89893)) % 14.98/14.67 [9044]~P109(x90442)+E(f862(f862(f141(x90441,x90442,x90443),x90444),x90445),f142(x90441,x90442,x90443,x90444,x90445))+P1(f862(f862(f321(x90442),f862(x90443,x90444)),f862(f302(x90441,x90442,x90443),f862(f165(x90441),x90445)))) % 14.98/14.67 [9125]~P109(x91252)+E(f142(x91251,x91252,x91253,x91254,x91255),x91255)+~P1(f862(f862(f321(x91252),f862(x91253,x91254)),f862(f302(x91251,x91252,x91253),f862(f165(x91251),x91255)))) % 14.98/14.67 [9139]~P22(x91392,x91391,x91393,x91395)+P1(f862(f862(f228(f932(x91391,a921)),f862(f302(x91392,x91391,x91393),x91394)),f862(f302(x91392,x91391,x91393),x91395)))+~P1(f862(f862(f228(f932(x91392,a921)),x91394),x91395)) % 14.98/14.67 [9297]~P22(x92971,x92972,x92973,f234(f932(x92971,a921)))+~P1(f862(f862(f227(f932(x92972,a921)),x92974),f862(f302(x92971,x92972,x92973),x92975)))+P1(f862(f862(f227(f932(x92971,a921)),f862(f303(x92971,x92972,x92973),x92974)),x92975)) % 14.98/14.67 [9320]~E(f862(f302(x93203,x93201,x93204),f234(f932(x93203,a921))),f234(f932(x93201,a921)))+P1(f862(f862(f227(f932(x93201,a921)),x93202),f862(f302(x93203,x93201,x93204),x93205)))+~P1(f862(f862(f227(f932(x93203,a921)),f862(f303(x93203,x93201,x93204),x93202)),x93205)) % 14.98/14.67 [9428]~P22(x94281,x94284,x94285,f234(f932(x94281,a921)))+~P1(f862(f862(f227(f932(x94284,a921)),f862(f302(x94281,x94284,x94285),x94282)),f862(f302(x94281,x94284,x94285),x94283)))+P1(f862(f862(f227(f932(x94281,a921)),x94282),x94283)) % 14.98/14.67 [9552]~P81(x95521)+~E(f862(x95523,f726(x95523,x95524,x95525,x95522,x95521)),f2(x95521))+E(f862(f158(x95521),f862(f862(f147(x95522,x95521),x95523),f862(f129(x95522,x95524),x95525))),f862(f158(x95521),f862(f862(f147(x95522,x95521),x95523),x95525))) % 14.98/14.67 [9581]~P23(x95811,x95812,x95813,f234(f932(x95811,a921)),f234(f932(x95812,a921)))+~P1(f862(f862(f227(f932(x95812,a921)),x95814),f862(f302(x95811,x95812,x95813),x95815)))+P1(f862(f862(f227(f932(x95811,a921)),f862(f303(x95811,x95812,x95813),x95814)),x95815)) % 14.98/14.67 [9610]~P23(x96103,x96101,x96104,f234(f932(x96103,a921)),f234(f932(x96101,a921)))+P1(f862(f862(f227(f932(x96101,a921)),x96102),f862(f302(x96103,x96101,x96104),x96105)))+~P1(f862(f862(f227(f932(x96103,a921)),f862(f303(x96103,x96101,x96104),x96102)),x96105)) % 14.98/14.67 [9738]~P14(x97381,x97382,x97383)+~P1(f862(f54(x97381),x97385))+P1(f862(f59(x97381,x97382,x97383,x97384,x97385),f862(f862(f57(x97381,x97382,x97383),x97384),x97385))) % 14.98/14.67 [9817]~P23(x98172,x98171,x98174,f234(f932(x98172,a921)),f234(f932(x98171,a921)))+~P23(x98171,x98173,x98175,f234(f932(x98171,a921)),f234(f932(x98173,a921)))+E(f862(f66(x98171,x98172,x98173,f86(x98172,x98171,f234(f932(x98172,a921)),x98174)),f86(x98171,x98173,f234(f932(x98171,a921)),x98175)),f86(x98172,x98173,f234(f932(x98172,a921)),f862(f66(x98171,x98173,x98172,x98175),x98174))) % 14.98/14.67 [9818]P1(f862(x98181,f694(x98182,x98181,x98183,x98184,x98185)))+~P1(f862(f862(f227(f932(x98185,a921)),x98184),x98183))+P1(f862(f862(f227(f932(x98185,a921)),f862(f862(f94(f932(x98185,a921)),x98184),f862(f254(x98185),x98181))),f862(f862(f94(f932(x98185,a921)),x98183),f862(f254(x98185),x98182)))) % 14.98/14.67 [9832]~P81(x98321)+~P1(f862(x98324,f726(x98323,x98324,x98325,x98322,x98321)))+E(f862(f158(x98321),f862(f862(f147(x98322,x98321),x98323),f862(f129(x98322,x98324),x98325))),f862(f158(x98321),f862(f862(f147(x98322,x98321),x98323),x98325))) % 14.98/14.67 [9910]~P3(x99105)+P1(f862(f862(f321(x99101),f478(x99102,x99103,x99101,x99104,x99105)),x99103))+P1(f862(f862(f227(x99105),x99104),f862(f862(f32(x99101,x99105),x99103),x99102))) % 14.98/14.67 [9914]~P81(x99141)+E(f862(f158(x99141),f862(f862(f147(x99142,x99141),x99143),f862(f129(x99142,x99144),x99145))),f862(f158(x99141),f862(f862(f147(x99142,x99141),x99143),x99145)))+P1(f862(f862(f321(x99142),f726(x99143,x99144,x99145,x99142,x99141)),f862(f165(x99142),x99145))) % 14.98/14.67 [9924]~P1(f862(x99245,f694(x99245,x99243,x99244,x99242,x99241)))+~P1(f862(f862(f227(f932(x99241,a921)),x99242),x99244))+P1(f862(f862(f227(f932(x99241,a921)),f862(f862(f94(f932(x99241,a921)),x99242),f862(f254(x99241),x99243))),f862(f862(f94(f932(x99241,a921)),x99244),f862(f254(x99241),x99245)))) % 14.98/14.67 [9940]~P22(x99405,x99403,x99404,f234(f932(x99405,a921)))+P1(f862(x99401,x99402))+P1(f862(f862(f321(x99403),f818(x99402,x99401,x99404,x99403,x99405)),f862(f302(x99405,x99403,x99404),f234(f932(x99405,a921))))) % 14.98/14.67 [9963]P32(x99631,x99632,x99633,x99634,x99635)+~E(f862(f182(f925(x99632)),x99635),f862(f182(f925(x99631)),x99634))+P1(f862(f862(f228(a924),f707(x99635,x99634,x99633,x99632,x99631)),f862(f182(f925(x99631)),x99634))) % 14.98/14.67 [9964]P32(x99641,x99642,x99643,x99644,x99645)+~E(f862(f182(f925(x99642)),x99645),f862(f182(f925(x99641)),x99644))+P1(f862(f862(f228(a924),f742(x99643,x99645,x99642,x99644,x99641)),f862(f182(f925(x99641)),x99644))) % 14.98/14.67 [9996]P1(f862(f862(f321(x99961),f694(x99962,x99963,x99964,x99965,x99961)),x99965))+~P1(f862(f862(f227(f932(x99961,a921)),x99965),x99964))+P1(f862(f862(f227(f932(x99961,a921)),f862(f862(f94(f932(x99961,a921)),x99965),f862(f254(x99961),x99963))),f862(f862(f94(f932(x99961,a921)),x99964),f862(f254(x99961),x99962)))) % 14.98/14.67 [10040]~P3(x100401)+~P1(f862(f862(f227(x100401),x100402),f862(x100405,f478(x100405,x100404,x100403,x100402,x100401))))+P1(f862(f862(f227(x100401),x100402),f862(f862(f32(x100403,x100401),x100404),x100405))) % 14.98/14.67 [10077]~P71(x100771)+~P1(f862(f54(x100772),x100775))+E(f862(f862(f862(f58(x100771,x100772,f74(x100771)),f862(f862(f20(x100772,x100771,x100771),f862(f862(f10(x100771,f932(x100771,x100771),x100772),f74(x100771)),x100773)),x100774)),f71(x100771)),x100775),f862(f862(f74(x100771),f862(f862(f862(f58(x100771,x100772,f74(x100771)),x100773),f71(x100771)),x100775)),f862(f862(f862(f58(x100771,x100772,f74(x100771)),x100774),f71(x100771)),x100775))) % 14.98/14.67 [10135]~P1(f862(f862(f321(f931(f932(x101351,a921),f932(x101351,a921))),f862(f862(f244(f932(x101351,a921),f932(x101351,a921)),x101355),x101354)),f310(x101351,x101353)))+~P1(f862(f862(f321(x101351),x101352),x101355))+P1(f862(f862(f321(f931(x101351,x101351)),f862(f862(f244(x101351,x101351),x101352),f616(x101353,x101354,x101355,x101351,x101352))),x101353)) % 14.98/14.67 [10260]~P1(f862(f862(f321(f931(f925(x102601),f925(x102601))),f862(f862(f244(f925(x102601),f925(x102601)),f862(f862(f127(x102601),x102605),x102602)),f862(f862(f127(x102601),x102605),x102603))),f140(x102601,x102604)))+P1(f862(f862(f321(f931(f925(x102601),f925(x102601))),f862(f862(f244(f925(x102601),f925(x102601)),x102602),x102603)),f140(x102601,x102604)))+P1(f862(f862(f321(f931(x102601,x102601)),f862(f862(f244(x102601,x102601),f695(x102604,x102603,x102602,x102605,x102601)),f695(x102604,x102603,x102602,x102605,x102601))),x102604)) % 14.98/14.67 [7447]~E(x74473,x74475)+E(f862(f862(f157(x74471),f862(f862(f152(x74471,x74472),x74473),x74474)),x74475),x74474)+~P1(f862(f862(f228(a924),x74473),f862(f182(f925(x74471)),x74472))) % 14.98/14.67 [7565]~E(f862(f862(f127(x75651),x75652),x75654),f862(f862(f127(x75651),x75653),x75655))+E(f862(f862(f168(x75651),f862(f182(f925(x75651)),x75652)),x75653),x75652)+P1(f862(f862(f227(a924),f862(f182(f925(x75651)),x75653)),f862(f182(f925(x75651)),x75652))) % 14.98/14.67 [8062]~E(f862(f862(f127(x80621),x80622),x80624),f862(f862(f127(x80621),x80623),x80625))+E(f862(f862(f168(x80621),f862(f182(f925(x80621)),x80622)),x80623),x80622)+~P1(f862(f862(f227(a924),f862(f182(f925(x80621)),x80622)),f862(f182(f925(x80621)),x80623))) % 14.98/14.67 [8086]~P1(f862(f54(x80861),f862(x80864,x80865)))+~P1(f862(f862(f321(x80862),x80865),x80863))+P1(f862(f54(x80861),f862(f862(f32(x80862,f932(x80861,a921)),x80863),x80864))) % 14.98/14.67 [8265]~P50(x82651,x82653,x82655)+~P50(x82651,x82652,x82654)+P50(x82651,f862(f862(f103(f932(x82651,a921)),x82652),x82653),f862(f862(f103(f932(f931(x82651,x82651),a921)),x82654),x82655)) % 14.98/14.67 [8266]~P50(x82661,x82663,x82665)+~P50(x82661,x82662,x82664)+P50(x82661,f862(f862(f94(f932(x82661,a921)),x82662),x82663),f862(f862(f94(f932(f931(x82661,x82661),a921)),x82664),x82665)) % 14.98/14.67 [8625]E(f862(f862(f244(x86251,x86252),f862(f862(f157(x86251),x86253),x86254)),f862(f862(f157(x86252),x86255),x86254)),f862(f862(f157(f931(x86251,x86252)),f862(f862(f174(x86251,x86252),x86253),x86255)),x86254))+~P1(f862(f862(f228(a924),x86254),f862(f182(f925(x86251)),x86253)))+~P1(f862(f862(f228(a924),x86254),f862(f182(f925(x86252)),x86255))) % 14.98/14.67 [8781]~P50(x87811,x87813,x87814)+P1(f862(f862(f321(x87811),x87812),x87813))+~P1(f862(f862(f321(f931(x87811,x87811)),f862(f862(f244(x87811,x87811),x87815),x87812)),x87814)) % 14.98/14.67 [8782]~P50(x87821,x87823,x87824)+P1(f862(f862(f321(x87821),x87822),x87823))+~P1(f862(f862(f321(f931(x87821,x87821)),f862(f862(f244(x87821,x87821),x87822),x87825)),x87824)) % 14.98/14.67 [8783]~P6(x87831,x87833,x87834)+P1(f862(f862(f321(x87831),x87832),x87833))+~P1(f862(f862(f321(f931(x87831,x87831)),f862(f862(f244(x87831,x87831),x87835),x87832)),x87834)) % 14.98/14.67 [8784]~P6(x87841,x87843,x87844)+P1(f862(f862(f321(x87841),x87842),x87843))+~P1(f862(f862(f321(f931(x87841,x87841)),f862(f862(f244(x87841,x87841),x87842),x87845)),x87844)) % 14.98/14.67 [9068]~P6(x90681,x90685,x90682)+E(f862(f276(x90681,x90681,x90682),f862(f862(f301(x90681),x90683),f181(f932(x90681,a921)))),f862(f276(x90681,x90681,x90682),f862(f862(f301(x90681),x90684),f181(f932(x90681,a921)))))+~P1(f862(f862(f321(f931(x90681,x90681)),f862(f862(f244(x90681,x90681),x90683),x90684)),x90682)) % 14.98/14.67 [9252]P1(f862(x92521,x92522))+~P1(f862(f862(f321(x92523),x92522),x92525))+P1(f862(f862(f321(x92523),f591(x92521,x92524,x92525,x92523)),f862(f862(f103(f932(x92523,a921)),x92525),x92524))) % 14.98/14.67 [9253]P1(f862(x92531,x92532))+~P1(f862(f862(f321(x92533),x92532),x92534))+P1(f862(f862(f321(x92533),f591(x92531,x92534,x92535,x92533)),f862(f862(f103(f932(x92533,a921)),x92535),x92534))) % 14.98/14.67 [9261]~P1(f862(x92612,x92615))+~P1(f862(f862(f321(x92611),x92615),x92614))+P1(f862(f862(f321(x92611),f628(x92612,x92613,x92614,x92611)),f862(f862(f103(f932(x92611,a921)),x92614),x92613))) % 14.98/14.67 [9262]~P1(f862(x92622,x92625))+~P1(f862(f862(f321(x92621),x92625),x92623))+P1(f862(f862(f321(x92621),f628(x92622,x92623,x92624,x92621)),f862(f862(f103(f932(x92621,a921)),x92624),x92623))) % 14.98/14.67 [9277]~P1(f862(f862(f227(f932(x92771,a921)),x92773),x92775))+~P1(f862(f862(f227(f932(x92771,a921)),x92772),x92774))+P1(f862(f862(f227(f932(x92771,a921)),f862(f862(f103(f932(x92771,a921)),x92772),x92773)),f862(f862(f103(f932(x92771,a921)),x92774),x92775))) % 14.98/14.67 [9278]~P1(f862(f862(f227(f932(x92781,a921)),x92783),x92785))+~P1(f862(f862(f227(f932(x92781,a921)),x92782),x92784))+P1(f862(f862(f227(f932(x92781,a921)),f862(f862(f94(f932(x92781,a921)),x92782),x92783)),f862(f862(f94(f932(x92781,a921)),x92784),x92785))) % 14.98/14.67 [9279]~P1(f862(f862(f227(f932(x92791,a921)),x92795),x92793))+~P1(f862(f862(f227(f932(x92791,a921)),x92792),x92794))+P1(f862(f862(f227(f932(x92791,a921)),f862(f862(f3(f932(x92791,a921)),x92792),x92793)),f862(f862(f3(f932(x92791,a921)),x92794),x92795))) % 14.98/14.67 [9375]P1(f862(f862(f321(f931(x93751,x93751)),f862(f862(f244(x93751,x93751),x93752),x93753)),f313(x93751,x93754,x93755)))+~P1(f862(f862(f227(a924),f862(x93754,x93752)),f862(x93754,x93753)))+~P1(f862(f862(f321(f931(x93751,x93751)),f862(f862(f244(x93751,x93751),x93752),x93753)),x93755)) % 14.98/14.67 [9562]P1(f862(f862(f321(f931(x95621,x95621)),f862(f862(f244(x95621,x95621),x95622),x95623)),f299(x95621,x95624)))+~P1(f862(f862(f321(f931(x95621,x95621)),f862(f862(f244(x95621,x95621),x95622),x95625)),f299(x95621,x95624)))+~P1(f862(f862(f321(f931(x95621,x95621)),f862(f862(f244(x95621,x95621),x95625),x95623)),x95624)) % 14.98/14.67 [9563]P1(f862(f862(f321(f931(x95631,x95631)),f862(f862(f244(x95631,x95631),x95632),x95633)),f299(x95631,x95634)))+~P1(f862(f862(f321(f931(x95631,x95631)),f862(f862(f244(x95631,x95631),x95635),x95633)),f299(x95631,x95634)))+~P1(f862(f862(f321(f931(x95631,x95631)),f862(f862(f244(x95631,x95631),x95632),x95635)),x95634)) % 14.98/14.67 [9665]E(x96651,x96652)+E(f862(a105,f633(x96653,x96654,x96651,x96652,x96655)),x96654)+~P1(f862(f862(f321(f931(x96655,x96655)),f862(f862(f244(x96655,x96655),x96652),x96651)),f862(f862(f176(f931(x96655,x96655),a921),x96654),x96653))) % 14.98/14.67 [9666]E(x96661,x96662)+E(f862(a105,f636(x96663,x96664,x96661,x96662,x96665)),x96664)+~P1(f862(f862(f321(f931(x96665,x96665)),f862(f862(f244(x96665,x96665),x96662),x96661)),f862(f862(f176(f931(x96665,x96665),a921),x96664),x96663))) % 14.98/14.67 [9667]E(x96671,f2(a924))+E(f862(a105,f633(x96672,x96671,x96673,x96674,x96675)),x96671)+~P1(f862(f862(f321(f931(x96675,x96675)),f862(f862(f244(x96675,x96675),x96674),x96673)),f862(f862(f176(f931(x96675,x96675),a921),x96671),x96672))) % 14.98/14.67 [9668]E(x96681,f2(a924))+E(f862(a105,f636(x96682,x96681,x96683,x96684,x96685)),x96681)+~P1(f862(f862(f321(f931(x96685,x96685)),f862(f862(f244(x96685,x96685),x96684),x96683)),f862(f862(f176(f931(x96685,x96685),a921),x96681),x96682))) % 14.98/14.67 [9691]P1(f862(f862(f321(f931(x96911,x96911)),f862(f862(f244(x96911,x96911),x96912),x96913)),f862(f862(f280(x96911,x96911,x96911),x96914),f299(x96911,x96914))))+~P1(f862(f862(f321(f931(x96911,x96911)),f862(f862(f244(x96911,x96911),x96912),x96915)),x96914))+~P1(f862(f862(f321(f931(x96911,x96911)),f862(f862(f244(x96911,x96911),x96915),x96913)),x96914)) % 14.98/14.67 [9698]~P1(f862(f862(f321(f931(x96981,x96981)),f862(f862(f244(x96981,x96981),x96982),x96985)),f299(x96981,x96984)))+P1(f862(f862(f321(f931(x96981,x96981)),f862(f862(f244(x96981,x96981),x96982),x96983)),f862(f862(f280(x96981,x96981,x96981),x96984),f299(x96981,x96984))))+~P1(f862(f862(f321(f931(x96981,x96981)),f862(f862(f244(x96981,x96981),x96985),x96983)),x96984)) % 14.98/14.67 [9732]~P6(x97321,x97325,x97322)+~P1(f862(f862(f321(f931(x97321,x97321)),f862(f862(f244(x97321,x97321),x97323),x97324)),x97322))+P1(f862(f862(f227(f932(x97321,a921)),f862(f276(x97321,x97321,x97322),f862(f862(f301(x97321),x97323),f181(f932(x97321,a921))))),f862(f276(x97321,x97321,x97322),f862(f862(f301(x97321),x97324),f181(f932(x97321,a921)))))) % 14.98/14.67 [9790]P1(f862(f862(f321(f931(x97901,x97901)),f862(f862(f244(x97901,x97901),x97902),x97903)),f862(f862(f280(x97901,x97901,x97901),x97904),f299(x97901,x97904))))+~P1(f862(f862(f321(f931(x97901,x97901)),f862(f862(f244(x97901,x97901),x97902),x97905)),f862(f862(f280(x97901,x97901,x97901),x97904),f299(x97901,x97904))))+~P1(f862(f862(f321(f931(x97901,x97901)),f862(f862(f244(x97901,x97901),x97905),x97903)),x97904)) % 14.98/14.67 [9791]P1(f862(f862(f321(f931(x97911,x97911)),f862(f862(f244(x97911,x97911),x97912),x97913)),f862(f862(f280(x97911,x97911,x97911),x97914),f299(x97911,x97914))))+~P1(f862(f862(f321(f931(x97911,x97911)),f862(f862(f244(x97911,x97911),x97915),x97913)),f862(f862(f280(x97911,x97911,x97911),x97914),f299(x97911,x97914))))+~P1(f862(f862(f321(f931(x97911,x97911)),f862(f862(f244(x97911,x97911),x97912),x97915)),x97914)) % 14.98/14.67 [9841]~P1(f862(f59(x98411,x98411,x98414,x98412,x98413),x98415))+P1(f862(f862(f321(x98411),x98412),x98413))+P1(f862(f55(x98411,x98414,f862(f862(f301(x98411),x98412),x98413)),x98415)) % 14.98/14.67 [9879]~E(f862(f302(x98793,x98792,x98795),x98794),x98791)+E(x98791,f181(f932(x98792,a921)))+P1(f862(f862(f227(f932(x98793,a921)),f862(f302(x98792,x98793,f535(x98794,x98793,x98792,x98791)),x98791)),x98794)) % 14.98/14.67 [9927]~P3(x99275)+P1(f862(f862(f321(x99271),f481(x99272,x99273,x99274,x99271,x99275)),x99274))+P1(f862(f862(f227(x99275),f862(f862(f33(x99271,x99275),x99274),x99273)),x99272)) % 14.98/14.67 [9983]P32(x99831,x99832,x99833,x99834,x99835)+~E(f862(f182(f925(x99831)),x99834),f862(f182(f925(x99832)),x99835))+P1(f862(f862(f321(f931(x99831,x99832)),f705(x99835,x99834,x99833,x99832,x99831)),f862(f165(f931(x99831,x99832)),f862(f862(f174(x99831,x99832),x99834),x99835)))) % 14.98/14.67 [9984]P32(x99841,x99842,x99843,x99844,x99845)+~E(f862(f182(f925(x99841)),x99844),f862(f182(f925(x99842)),x99845))+P1(f862(f862(f321(f931(x99841,x99842)),f706(x99843,x99845,x99844,x99842,x99841)),f862(f165(f931(x99841,x99842)),f862(f862(f174(x99841,x99842),x99844),x99845)))) % 14.98/14.67 [10114]E(x101141,x101142)+P1(f862(f862(f321(f931(x101143,x101143)),f862(f862(f244(x101143,x101143),x101141),f634(x101144,x101145,x101142,x101141,x101143))),x101144))+~P1(f862(f862(f321(f931(x101143,x101143)),f862(f862(f244(x101143,x101143),x101141),x101142)),f862(f862(f176(f931(x101143,x101143),a921),x101145),x101144))) % 14.98/14.67 [10115]E(x101151,f2(a924))+P1(f862(f862(f321(f931(x101152,x101152)),f862(f862(f244(x101152,x101152),x101153),f634(x101154,x101151,x101155,x101153,x101152))),x101154))+~P1(f862(f862(f321(f931(x101152,x101152)),f862(f862(f244(x101152,x101152),x101153),x101155)),f862(f862(f176(f931(x101152,x101152),a921),x101151),x101154))) % 14.98/14.67 [10154]~P3(x101541)+~P1(f862(f862(f227(x101541),f862(x101544,f481(x101545,x101544,x101543,x101542,x101541))),x101545))+P1(f862(f862(f227(x101541),f862(f862(f33(x101542,x101541),x101543),x101544)),x101545)) % 14.98/14.67 [10196]E(x101961,x101962)+P1(f862(f862(f321(f931(x101963,x101963)),f862(f862(f244(x101963,x101963),f635(x101964,x101965,x101961,x101962,x101963)),x101961)),x101964))+~P1(f862(f862(f321(f931(x101963,x101963)),f862(f862(f244(x101963,x101963),x101962),x101961)),f862(f862(f176(f931(x101963,x101963),a921),x101965),x101964))) % 14.98/14.67 [10197]E(x101971,f2(a924))+P1(f862(f862(f321(f931(x101972,x101972)),f862(f862(f244(x101972,x101972),f635(x101973,x101971,x101974,x101975,x101972)),x101974)),x101973))+~P1(f862(f862(f321(f931(x101972,x101972)),f862(f862(f244(x101972,x101972),x101975),x101974)),f862(f862(f176(f931(x101972,x101972),a921),x101971),x101973))) % 14.98/14.67 [10201]E(x102011,x102012)+P1(f862(f862(f321(f931(x102013,x102013)),f862(f862(f244(x102013,x102013),x102011),f635(x102014,x102015,x102012,x102011,x102013))),f862(f862(f176(f931(x102013,x102013),a921),f636(x102014,x102015,x102012,x102011,x102013)),x102014)))+~P1(f862(f862(f321(f931(x102013,x102013)),f862(f862(f244(x102013,x102013),x102011),x102012)),f862(f862(f176(f931(x102013,x102013),a921),x102015),x102014))) % 14.98/14.67 [10202]E(x102021,f2(a924))+P1(f862(f862(f321(f931(x102022,x102022)),f862(f862(f244(x102022,x102022),x102023),f635(x102024,x102021,x102025,x102023,x102022))),f862(f862(f176(f931(x102022,x102022),a921),f636(x102024,x102021,x102025,x102023,x102022)),x102024)))+~P1(f862(f862(f321(f931(x102022,x102022)),f862(f862(f244(x102022,x102022),x102023),x102025)),f862(f862(f176(f931(x102022,x102022),a921),x102021),x102024))) % 14.98/14.67 [10251]E(x102511,x102512)+P1(f862(f862(f321(f931(x102513,x102513)),f862(f862(f244(x102513,x102513),f634(x102514,x102515,x102511,x102512,x102513)),x102511)),f862(f862(f176(f931(x102513,x102513),a921),f633(x102514,x102515,x102511,x102512,x102513)),x102514)))+~P1(f862(f862(f321(f931(x102513,x102513)),f862(f862(f244(x102513,x102513),x102512),x102511)),f862(f862(f176(f931(x102513,x102513),a921),x102515),x102514))) % 14.98/14.67 [10252]E(x102521,f2(a924))+P1(f862(f862(f321(f931(x102522,x102522)),f862(f862(f244(x102522,x102522),f634(x102523,x102521,x102524,x102525,x102522)),x102524)),f862(f862(f176(f931(x102522,x102522),a921),f633(x102523,x102521,x102524,x102525,x102522)),x102523)))+~P1(f862(f862(f321(f931(x102522,x102522)),f862(f862(f244(x102522,x102522),x102525),x102524)),f862(f862(f176(f931(x102522,x102522),a921),x102521),x102523))) % 14.98/14.67 [10287]~P72(x102872)+~P1(f862(f54(x102871),x102875))+E(f862(f862(f8(x102871,x102872),f862(f862(f9(x102871,x102872,x102872),f862(f862(f20(x102871,x102872,f932(x102872,x102872)),f862(f862(f10(a921,f932(x102872,f932(x102872,x102872)),x102871),f89(x102872)),f862(f862(f9(x102871,f932(x102871,a921),a921),f321(x102871)),x102873))),x102874)),f2(x102872))),x102875),f862(f862(f8(x102871,x102872),x102874),f862(f862(f94(f932(x102871,a921)),x102875),x102873))) % 14.98/14.67 [8849]~P72(x88491)+~P1(f862(f54(x88494),x88495))+E(f862(f862(f73(x88491),f862(x88492,x88493)),f862(f862(f8(x88494,x88491),x88492),f862(f862(f3(f932(x88494,a921)),x88495),f862(f862(f301(x88494),x88493),f181(f932(x88494,a921)))))),f862(f862(f8(x88494,x88491),x88492),f862(f862(f301(x88494),x88493),x88495))) % 14.98/14.67 [8850]~P71(x88501)+~P1(f862(f54(x88504),x88505))+E(f862(f862(f74(x88501),f862(x88502,x88503)),f862(f862(f11(x88504,x88501),x88502),f862(f862(f3(f932(x88504,a921)),x88505),f862(f862(f301(x88504),x88503),f181(f932(x88504,a921)))))),f862(f862(f11(x88504,x88501),x88502),f862(f862(f301(x88504),x88503),x88505))) % 14.98/14.67 [9185]~P109(x91852)+~P11(x91852,f862(f161(x91852),f862(f862(f147(x91851,x91852),x91854),x91855)))+E(f862(f129(x91851,f862(f862(f10(x91852,a921,x91851),f862(f228(x91852),x91853)),x91854)),x91855),f170(x91851,f862(f862(f10(x91852,a921,x91851),f862(f228(x91852),x91853)),x91854),x91855)) % 14.98/14.67 [9209]~P72(x92091)+E(f862(f862(f73(x92091),f862(f862(f8(a924,x92091),x92092),f296(a924,x92093,x92094))),f862(f862(f8(a924,x92091),x92092),f296(a924,f862(f862(f73(a924),x92094),f71(a924)),f862(f862(f73(a924),x92094),x92095)))),f862(f862(f8(a924,x92091),x92092),f296(a924,x92093,f862(f862(f73(a924),x92094),x92095))))+~P1(f862(f862(f227(a924),x92093),f862(f862(f73(a924),x92094),f71(a924)))) % 14.98/14.67 [9210]~P1(f862(f862(f321(x92101),x92104),x92105))+~P1(f862(f862(f227(f932(x92101,a921)),f862(f165(x92101),x92102)),x92105))+P1(f862(f862(f227(f932(x92101,a921)),f862(f165(x92101),f862(f862(f152(x92101,x92102),x92103),x92104))),x92105)) % 14.98/14.67 [9436]~P3(x94362)+~P1(f862(f54(x94361),x94365))+E(f862(f862(f57(x94361,x94362,f862(f862(f10(x94362,f932(x94362,x94362),x94361),f103(x94362)),x94363)),x94364),x94365),f862(f862(f103(x94362),x94364),f862(f862(f33(x94361,x94362),x94365),x94363))) % 14.98/14.67 [9437]~P3(x94372)+~P1(f862(f54(x94371),x94375))+E(f862(f862(f57(x94371,x94372,f862(f862(f10(x94372,f932(x94372,x94372),x94371),f94(x94372)),x94373)),x94374),x94375),f862(f862(f94(x94372),x94374),f862(f862(f32(x94371,x94372),x94375),x94373))) % 14.98/14.67 [9486]E(f862(x94861,x94862),f862(x94861,x94863))+P1(f862(f862(f228(a924),f862(x94861,x94862)),f862(x94861,x94863)))+~P1(f862(f862(f321(f931(x94864,x94864)),f862(f862(f244(x94864,x94864),x94862),x94863)),f146(x94864,f862(f862(f144(f932(x94864,a924)),x94861),x94865)))) % 14.98/14.67 [9519]~E(f862(x95194,x95192),f862(x95194,x95193))+~P1(f862(f862(f321(f931(x95191,x95191)),f862(f862(f244(x95191,x95191),x95192),x95193)),f146(x95191,x95195)))+P1(f862(f862(f321(f931(x95191,x95191)),f862(f862(f244(x95191,x95191),x95192),x95193)),f146(x95191,f862(f862(f144(f932(x95191,a924)),x95194),x95195)))) % 14.98/14.67 [9539]~P22(x95391,x95392,x95393,x95395)+P22(x95391,x95392,x95393,f862(f862(f301(x95391),x95394),x95395))+P1(f862(f862(f321(x95392),f862(x95393,x95394)),f862(f302(x95391,x95392,x95393),f862(f862(f3(f932(x95391,a921)),x95395),f862(f862(f301(x95391),x95394),f181(f932(x95391,a921))))))) % 14.98/14.67 [9542]P1(f862(x95422,x95425))+~P1(f862(f862(f321(x95421),x95425),f862(f165(x95421),x95423)))+E(f862(f862(f131(x95421),f862(f182(f925(x95421)),f170(x95421,x95422,f862(f862(f127(x95421),x95423),x95424)))),f862(f862(f127(x95421),x95423),x95424)),f862(f862(f127(x95421),f862(f862(f131(x95421),f862(f182(f925(x95421)),f170(x95421,x95422,x95423))),x95423)),x95424)) % 14.98/14.67 [9548]~P1(f862(f862(f321(f931(x95481,x95481)),f862(f862(f244(x95481,x95481),x95482),x95483)),f146(x95481,x95485)))+~P1(f862(f862(f227(a924),f862(x95484,x95482)),f862(x95484,x95483)))+P1(f862(f862(f321(f931(x95481,x95481)),f862(f862(f244(x95481,x95481),x95482),x95483)),f146(x95481,f862(f862(f144(f932(x95481,a924)),x95484),x95485)))) % 14.98/14.67 [9617]P1(f862(f862(f321(f931(x96174,x96174)),f862(f862(f244(x96174,x96174),x96172),x96173)),f146(x96174,x96175)))+P1(f862(f862(f228(a924),f862(x96171,x96172)),f862(x96171,x96173)))+~P1(f862(f862(f321(f931(x96174,x96174)),f862(f862(f244(x96174,x96174),x96172),x96173)),f146(x96174,f862(f862(f144(f932(x96174,a924)),x96171),x96175)))) % 14.98/14.67 [9762]~P1(f862(f862(f321(f931(f925(x97621),f925(x97621))),f862(f862(f244(f925(x97621),f925(x97621)),x97622),x97624)),f151(x97621,x97625)))+~P1(f862(f862(f228(a924),x97623),f862(f182(f925(x97621)),x97622)))+P1(f862(f862(f321(f931(x97621,x97621)),f862(f862(f244(x97621,x97621),f862(f862(f157(x97621),x97622),x97623)),f862(f862(f157(x97621),x97624),x97623))),x97625)) % 14.98/14.67 [10007]E(x100071,f2(a1))+~P1(f862(f42(x100073,x100071),f862(f862(f244(a1,a1),x100074),x100075)))+P1(f862(f42(f862(f862(f74(a1),x100072),x100073),x100071),f862(f862(f244(a1,a1),f862(f862(f73(a1),f862(f862(f74(a1),x100072),x100074)),f862(f862(f29(a1),f862(f862(f74(a1),x100072),x100075)),x100071))),f38(a1,f862(f862(f74(a1),x100072),x100075),x100071)))) % 14.98/14.67 [10008]~P1(f862(f862(f228(a924),f2(a924)),x100083))+~P1(f862(f41(x100082,x100083),f862(f862(f244(a924,a924),x100084),x100085)))+P1(f862(f41(f862(f862(f74(a924),x100081),x100082),x100083),f862(f862(f244(a924,a924),f862(f862(f73(a924),f862(f862(f74(a924),x100081),x100084)),f862(f862(f29(a924),f862(f862(f74(a924),x100081),x100085)),x100083))),f38(a924,f862(f862(f74(a924),x100081),x100085),x100083)))) % 14.98/14.67 [10310]~P72(x103102)+~P1(f862(f54(x103101),x103104))+E(f862(f862(f8(x103101,x103102),x103103),f862(f254(x103101),f862(f862(f20(x103101,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103101),a318),f862(f862(f9(x103101,f932(x103101,a921),a921),f321(x103101)),x103104))),f862(f862(f9(x103101,f932(x103101,a921),a921),f321(x103101)),x103105)))),f862(f862(f8(x103101,x103102),f862(f862(f9(x103101,x103102,x103102),f862(f862(f20(x103101,x103102,f932(x103102,x103102)),f862(f862(f10(a921,f932(x103102,f932(x103102,x103102)),x103101),f89(x103102)),f862(f862(f9(x103101,f932(x103101,a921),a921),f321(x103101)),x103105))),x103103)),f2(x103102))),x103104)) % 14.98/14.67 [8475]~E(f862(f862(f127(x84751),x84752),x84755),f862(f862(f127(x84751),x84753),x84754))+E(f862(f862(f127(x84751),f862(f862(f131(x84751),f862(f182(f925(x84751)),x84752)),x84753)),x84754),x84755)+P1(f862(f862(f227(a924),f862(f182(f925(x84751)),x84753)),f862(f182(f925(x84751)),x84752))) % 14.98/14.67 [8674]~E(f862(f862(f127(x86742),x86743),x86741),f862(f862(f127(x86742),x86744),x86745))+E(x86741,f862(f862(f127(x86742),f862(f862(f131(x86742),f862(f182(f925(x86742)),x86743)),x86744)),x86745))+~P1(f862(f862(f227(a924),f862(f182(f925(x86742)),x86743)),f862(f182(f925(x86742)),x86744))) % 14.98/14.67 [8764]~E(f862(f862(f73(a924),f862(f862(f74(a924),x87643),x87644)),x87641),f862(f862(f73(a924),f862(f862(f74(a924),x87642),x87644)),x87645))+~P1(f862(f862(f227(a924),x87643),x87642))+E(x87641,f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x87642),x87643)),x87644)),x87645)) % 14.98/14.67 [8765]~E(f862(f862(f73(a924),f862(f862(f74(a924),x87651),x87653)),x87654),f862(f862(f73(a924),f862(f862(f74(a924),x87652),x87653)),x87655))+~P1(f862(f862(f227(a924),x87652),x87651))+E(f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x87651),x87652)),x87653)),x87654),x87655) % 14.98/14.67 [8934]E(f862(f862(f73(a924),f862(f862(f74(a924),x89341),x89342)),x89343),f862(f862(f73(a924),f862(f862(f74(a924),x89344),x89342)),x89345))+~P1(f862(f862(f227(a924),x89344),x89341))+~E(x89345,f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x89341),x89344)),x89342)),x89343)) % 14.98/14.67 [8935]E(f862(f862(f73(a924),f862(f862(f74(a924),x89351),x89352)),x89353),f862(f862(f73(a924),f862(f862(f74(a924),x89354),x89352)),x89355))+~P1(f862(f862(f227(a924),x89354),x89351))+~E(f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x89351),x89354)),x89352)),x89353),x89355) % 14.98/14.67 [9816]~P64(x98162)+~P1(f862(f54(x98161),x98165))+E(f862(f862(f11(x98161,x98162),f862(f862(f20(x98161,x98162,x98162),f862(f862(f10(x98162,f932(x98162,x98162),x98161),f281(x98162)),x98163)),x98164)),x98165),f862(f862(f281(x98162),f862(f862(f11(x98161,x98162),x98163),x98165)),f862(f862(f11(x98161,x98162),x98164),x98165))) % 14.98/14.67 [9946]~E(f638(x99465,x99464,x99463,x99462,x99461),f639(x99465,x99464,x99463,x99462,x99461))+P1(f862(f862(f321(f931(x99461,x99461)),f862(f862(f244(x99461,x99461),x99462),x99463)),f299(x99461,x99464)))+~P1(f862(f862(f321(f931(x99461,x99461)),f862(f862(f244(x99461,x99461),x99462),x99463)),f299(x99461,f862(f862(f103(f932(f931(x99461,x99461),a921)),x99464),x99465)))) % 14.98/14.67 [9947]~E(f640(x99475,x99474,x99473,x99472,x99471),f641(x99475,x99474,x99473,x99472,x99471))+P1(f862(f862(f321(f931(x99471,x99471)),f862(f862(f244(x99471,x99471),x99472),x99473)),f299(x99471,x99474)))+~P1(f862(f862(f321(f931(x99471,x99471)),f862(f862(f244(x99471,x99471),x99472),x99473)),f299(x99471,f862(f862(f103(f932(f931(x99471,x99471),a921)),x99474),x99475)))) % 14.98/14.67 [10144]P1(f862(f862(f321(f931(x101441,x101441)),f862(f862(f244(x101441,x101441),x101442),f639(x101445,x101444,x101443,x101442,x101441))),f299(x101441,x101444)))+P1(f862(f862(f321(f931(x101441,x101441)),f862(f862(f244(x101441,x101441),x101442),x101443)),f299(x101441,x101444)))+~P1(f862(f862(f321(f931(x101441,x101441)),f862(f862(f244(x101441,x101441),x101442),x101443)),f299(x101441,f862(f862(f103(f932(f931(x101441,x101441),a921)),x101444),x101445)))) % 14.98/14.67 [10223]P1(f862(f862(f321(f931(x102231,x102231)),f862(f862(f244(x102231,x102231),f641(x102235,x102234,x102233,x102232,x102231)),x102233)),f299(x102231,x102234)))+P1(f862(f862(f321(f931(x102231,x102231)),f862(f862(f244(x102231,x102231),x102232),x102233)),f299(x102231,x102234)))+~P1(f862(f862(f321(f931(x102231,x102231)),f862(f862(f244(x102231,x102231),x102232),x102233)),f299(x102231,f862(f862(f103(f932(f931(x102231,x102231),a921)),x102234),x102235)))) % 14.98/14.67 [10258]P1(f862(f862(f321(f931(x102581,x102581)),f862(f862(f244(x102581,x102581),x102582),x102583)),f299(x102581,x102584)))+P1(f862(f862(f321(f931(x102581,x102581)),f862(f862(f244(x102581,x102581),f639(x102585,x102584,x102583,x102582,x102581)),f638(x102585,x102584,x102583,x102582,x102581))),x102585))+~P1(f862(f862(f321(f931(x102581,x102581)),f862(f862(f244(x102581,x102581),x102582),x102583)),f299(x102581,f862(f862(f103(f932(f931(x102581,x102581),a921)),x102584),x102585)))) % 14.98/14.67 [10259]P1(f862(f862(f321(f931(x102591,x102591)),f862(f862(f244(x102591,x102591),x102592),x102593)),f299(x102591,x102594)))+P1(f862(f862(f321(f931(x102591,x102591)),f862(f862(f244(x102591,x102591),f640(x102595,x102594,x102593,x102592,x102591)),f641(x102595,x102594,x102593,x102592,x102591))),x102595))+~P1(f862(f862(f321(f931(x102591,x102591)),f862(f862(f244(x102591,x102591),x102592),x102593)),f299(x102591,f862(f862(f103(f932(f931(x102591,x102591),a921)),x102594),x102595)))) % 14.98/14.67 [10408]~P1(f862(f862(f321(f931(f925(x104081),f925(x104081))),f862(f862(f244(f925(x104081),f925(x104081)),x104084),x104085)),f151(x104081,x104082)))+~P1(f862(f862(f321(f931(x104081,x104081)),x104083),f862(f165(f931(x104081,x104081)),f862(f862(f174(x104081,x104081),x104084),x104085))))+P1(f862(f862(f249(x104081,x104081,a921),f862(f862(f9(x104081,f932(f931(x104081,x104081),a921),f932(x104081,a921)),f862(f862(f10(f932(x104081,f932(f932(f931(x104081,x104081),a921),a921)),f932(f932(f931(x104081,x104081),a921),f932(x104081,a921)),x104081),f9(x104081,f932(f931(x104081,x104081),a921),a921)),f862(f862(f10(f932(x104081,f931(x104081,x104081)),f932(x104081,f932(f932(f931(x104081,x104081),a921),a921)),x104081),f862(f10(f931(x104081,x104081),f932(f932(f931(x104081,x104081),a921),a921),x104081),f321(f931(x104081,x104081)))),f244(x104081,x104081)))),x104082)),x104083)) % 14.98/14.67 [9845]~P1(f862(f862(f227(a924),x98453),x98452))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),x98453),x98454)),x98451)),f862(f862(f73(a924),f862(f862(f74(a924),x98452),x98454)),x98455)))+P1(f862(f862(f227(a924),x98451),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x98452),x98453)),x98454)),x98455))) % 14.98/14.67 [9846]~P1(f862(f862(f227(a924),x98463),x98462))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x98463),x98464)),x98461)),f862(f862(f73(a924),f862(f862(f74(a924),x98462),x98464)),x98465)))+P1(f862(f862(f228(a924),x98461),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x98462),x98463)),x98464)),x98465))) % 14.98/14.67 [9863]~P1(f862(f862(f227(a924),x98631),x98634))+P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),x98631),x98632)),x98633)),f862(f862(f73(a924),f862(f862(f74(a924),x98634),x98632)),x98635)))+~P1(f862(f862(f227(a924),x98633),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x98634),x98631)),x98632)),x98635))) % 14.98/14.67 [9864]~P1(f862(f862(f227(a924),x98641),x98644))+P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x98641),x98642)),x98643)),f862(f862(f73(a924),f862(f862(f74(a924),x98644),x98642)),x98645)))+~P1(f862(f862(f228(a924),x98643),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x98644),x98641)),x98642)),x98645))) % 14.98/14.67 [9981]~P1(f862(f862(f227(a924),x99812),x99811))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),x99811),x99813)),x99814)),f862(f862(f73(a924),f862(f862(f74(a924),x99812),x99813)),x99815)))+P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x99811),x99812)),x99813)),x99814)),x99815)) % 14.98/14.67 [9982]~P1(f862(f862(f227(a924),x99822),x99821))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x99821),x99823)),x99824)),f862(f862(f73(a924),f862(f862(f74(a924),x99822),x99823)),x99825)))+P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x99821),x99822)),x99823)),x99824)),x99825)) % 14.98/14.67 [10026]~P1(f862(f862(f227(a924),x100264),x100261))+P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),x100261),x100262)),x100263)),f862(f862(f73(a924),f862(f862(f74(a924),x100264),x100262)),x100265)))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x100261),x100264)),x100262)),x100263)),x100265)) % 14.98/14.67 [10027]~P1(f862(f862(f227(a924),x100274),x100271))+P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x100271),x100272)),x100273)),f862(f862(f73(a924),f862(f862(f74(a924),x100274),x100272)),x100275)))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x100271),x100274)),x100272)),x100273)),x100275)) % 14.98/14.67 [10246]~P9(x102461,x102462,x102465,x102463)+~P1(f862(f862(f321(f931(x102461,x102461)),x102464),x102465))+P1(f862(f862(f249(x102461,x102461,a921),f862(f862(f9(x102461,f932(x102461,x102462),f932(x102461,a921)),f862(f862(f10(f932(x102462,a921),f932(f932(x102461,x102462),f932(x102461,a921)),x102461),f10(x102462,a921,x102461)),f862(f862(f10(x102462,f932(x102462,a921),x102461),a317),x102463))),x102463)),x102464)) % 14.98/14.67 [8637]~P17(x86376,x86371,x86372,x86374)+E(f862(f66(x86371,x86371,x86371,f862(x86372,x86373)),f862(x86374,x86375)),f862(f66(x86371,x86371,x86371,f862(x86374,x86375)),f862(x86372,x86373)))+~P1(f862(f54(x86376),x86375)) % 14.98/14.67 [9080]~P22(x90801,x90803,x90805,x90806)+~P22(x90803,x90802,x90804,f862(f302(x90801,x90803,x90805),x90806))+P22(x90801,x90802,f862(f66(x90803,x90802,x90801,x90804),x90805),x90806) % 14.98/14.67 [9649]~P1(f862(f862(x96493,x96492),x96496))+~P1(f862(f862(x96494,x96495),x96492))+P1(f862(f862(f321(x96491),x96492),f291(x96491,x96493,x96494,x96495,x96496))) % 14.98/14.67 [9650]~P1(f862(f862(x96504,x96502),x96506))+~P1(f862(f862(x96503,x96505),x96502))+P1(f862(f862(f321(x96501),x96502),f288(x96501,x96503,x96504,x96505,x96506))) % 14.98/14.67 [9763]E(x97631,x97632)+E(x97633,x97634)+~P1(f862(f862(f321(f931(f925(x97635),f925(x97635))),f862(f862(f244(f925(x97635),f925(x97635)),f862(f862(f144(x97635),x97633),x97631)),f862(f862(f144(x97635),x97634),x97632))),f150(x97635,x97636))) % 14.98/14.67 [9772]~E(x97722,x97724)+P1(f862(f862(f321(f931(f925(x97721),f925(x97721))),f862(f862(f244(f925(x97721),f925(x97721)),f862(f862(f144(x97721),x97722),x97723)),f862(f862(f144(x97721),x97724),x97725))),f138(x97721,x97726)))+~P1(f862(f862(f321(f931(f925(x97721),f925(x97721))),f862(f862(f244(f925(x97721),f925(x97721)),x97723),x97725)),f138(x97721,x97726))) % 14.98/14.67 [9773]~E(x97732,x97734)+P1(f862(f862(f321(f931(f925(x97731),f925(x97731))),f862(f862(f244(f925(x97731),f925(x97731)),f862(f862(f144(x97731),x97732),x97733)),f862(f862(f144(x97731),x97734),x97735))),f140(x97731,x97736)))+~P1(f862(f862(f321(f931(f925(x97731),f925(x97731))),f862(f862(f244(f925(x97731),f925(x97731)),x97733),x97735)),f140(x97731,x97736))) % 14.98/14.67 [9774]~E(x97742,x97744)+P1(f862(f862(f321(f931(f925(x97741),f925(x97741))),f862(f862(f244(f925(x97741),f925(x97741)),f862(f862(f144(x97741),x97742),x97743)),f862(f862(f144(x97741),x97744),x97745))),f150(x97741,x97746)))+~P1(f862(f862(f321(f931(f925(x97741),f925(x97741))),f862(f862(f244(f925(x97741),f925(x97741)),x97743),x97745)),f150(x97741,x97746))) % 14.98/14.67 [9775]~E(x97752,x97754)+P1(f862(f862(f321(f931(f925(x97751),f925(x97751))),f862(f862(f244(f925(x97751),f925(x97751)),f862(f862(f127(x97751),x97752),x97753)),f862(f862(f127(x97751),x97754),x97755))),f150(x97751,x97756)))+~P1(f862(f862(f321(f931(f925(x97751),f925(x97751))),f862(f862(f244(f925(x97751),f925(x97751)),x97753),x97755)),f150(x97751,x97756))) % 14.98/14.67 [9776]~E(x97763,x97765)+P1(f862(f862(f321(f931(f925(x97761),f925(x97761))),f862(f862(f244(f925(x97761),f925(x97761)),f862(f862(f127(x97761),x97762),x97763)),f862(f862(f127(x97761),x97764),x97765))),f150(x97761,x97766)))+~P1(f862(f862(f321(f931(f925(x97761),f925(x97761))),f862(f862(f244(f925(x97761),f925(x97761)),x97762),x97764)),f150(x97761,x97766))) % 14.98/14.67 [9833]E(x98331,x98332)+P1(f862(f862(f321(f931(f925(x98333),f925(x98333))),f862(f862(f244(f925(x98333),f925(x98333)),x98331),x98332)),f150(x98333,x98334)))+~P1(f862(f862(f321(f931(f925(x98333),f925(x98333))),f862(f862(f244(f925(x98333),f925(x98333)),f862(f862(f144(x98333),x98335),x98331)),f862(f862(f144(x98333),x98336),x98332))),f150(x98333,x98334))) % 14.98/14.67 [9985]~E(x99853,x99855)+P1(f862(f862(f321(f931(f925(x99851),f925(x99851))),f862(f862(f244(f925(x99851),f925(x99851)),f862(f862(f127(x99851),x99852),f862(f862(f144(x99851),x99853),f106(x99851)))),f862(f862(f127(x99851),x99854),f862(f862(f144(x99851),x99855),f106(x99851))))),f150(x99851,x99856)))+~P1(f862(f862(f321(f931(f925(x99851),f925(x99851))),f862(f862(f244(f925(x99851),f925(x99851)),x99852),x99854)),f150(x99851,x99856))) % 14.98/14.67 [10030]E(x100301,x100302)+E(x100303,x100304)+~P1(f862(f862(f321(f931(f925(x100305),f925(x100305))),f862(f862(f244(f925(x100305),f925(x100305)),f862(f862(f127(x100305),x100303),f862(f862(f144(x100305),x100301),f106(x100305)))),f862(f862(f127(x100305),x100304),f862(f862(f144(x100305),x100302),f106(x100305))))),f150(x100305,x100306))) % 14.98/14.67 [10056]E(x100561,x100562)+~P1(f862(f862(f321(f931(f925(x100563),f925(x100563))),f862(f862(f244(f925(x100563),f925(x100563)),f862(f862(f127(x100563),x100561),f862(f862(f144(x100563),x100565),f106(x100563)))),f862(f862(f127(x100563),x100562),f862(f862(f144(x100563),x100566),f106(x100563))))),f150(x100563,x100564)))+P1(f862(f862(f321(f931(f925(x100563),f925(x100563))),f862(f862(f244(f925(x100563),f925(x100563)),x100561),x100562)),f150(x100563,x100564))) % 14.98/14.67 [10096]~P1(f862(f862(f321(f931(f932(x100961,a921),f932(x100961,a921))),f862(f862(f244(f932(x100961,a921),f932(x100961,a921)),x100962),x100964)),f310(x100961,x100966)))+~P1(f862(f862(f321(f931(f932(x100961,a921),f932(x100961,a921))),f862(f862(f244(f932(x100961,a921),f932(x100961,a921)),x100963),x100965)),f310(x100961,x100966)))+P1(f862(f862(f321(f931(f932(x100961,a921),f932(x100961,a921))),f862(f862(f244(f932(x100961,a921),f932(x100961,a921)),f862(f862(f103(f932(x100961,a921)),x100962),x100963)),f862(f862(f103(f932(x100961,a921)),x100964),x100965))),f310(x100961,x100966))) % 14.98/14.67 [5851]~E(f862(f862(f127(x58511),x58516),x58513),x58515)+E(f862(f862(f127(x58511),x58512),x58513),f862(f862(f144(x58511),x58514),x58515))+~E(x58512,f862(f862(f144(x58511),x58514),x58516)) % 14.98/14.67 [5852]~E(f862(f862(f127(x58521),x58526),x58523),x58525)+E(f862(f862(f127(x58521),x58522),x58523),f862(f862(f127(x58521),x58524),x58525))+~E(x58522,f862(f862(f127(x58521),x58524),x58526)) % 14.98/14.67 [5854]E(f862(f862(f127(x58541),x58542),x58543),f862(f862(f144(x58541),x58544),x58545))+~E(f862(f862(f144(x58541),x58544),x58546),x58542)+~E(x58545,f862(f862(f127(x58541),x58546),x58543)) % 14.98/14.67 [5856]~E(f862(f862(f127(x58561),x58562),x58566),x58564)+E(f862(f862(f127(x58561),x58562),x58563),f862(f862(f127(x58561),x58564),x58565))+~E(x58563,f862(f862(f127(x58561),x58566),x58565)) % 14.98/14.67 [7006]E(f862(x70061,x70062),f862(x70063,x70062))+~E(f862(f862(f147(x70064,x70065),x70061),x70066),f862(f862(f147(x70064,x70065),x70063),x70066))+~P1(f862(f862(f321(x70064),x70062),f862(f165(x70064),x70066))) % 14.98/14.67 [7392]~P17(x73924,x73925,x73926,x73921)+E(f862(f862(x73921,x73922),x73923),f862(f862(f57(x73924,x73925,x73926),x73923),x73922))+~P1(f862(f54(x73924),x73922)) % 14.98/14.67 [7465]~E(x74652,f862(x74654,x74656))+~P1(f862(f862(f321(x74653),x74656),x74655))+P1(f862(f862(f321(x74651),x74652),f862(f302(x74653,x74651,x74654),x74655))) % 14.98/14.67 [7466]~E(f862(x74664,x74662),x74666)+~P1(f862(f862(f321(x74663),x74666),x74665))+P1(f862(f862(f321(x74661),x74662),f862(f303(x74661,x74663,x74664),x74665))) % 14.98/14.67 [7919]~P30(x79191,x79192,x79194,x79196)+P30(x79191,x79192,f862(f862(f144(x79191),x79193),x79194),f862(f862(f144(x79191),x79195),x79196))+~P1(f862(f862(x79192,x79193),x79195)) % 14.98/14.67 [8944]~P54(x89444,x89445,x89441,x89442,x89446)+E(f862(x89441,f862(x89442,x89443)),x89443)+~P1(f862(f862(f321(x89445),x89443),x89446)) % 14.98/14.67 [9446]~P23(x94462,x94461,x94465,x94464,x94463)+E(f862(f86(x94461,x94462,x94463,f86(x94462,x94461,x94464,x94465)),x94466),f862(x94465,x94466))+~P1(f862(f862(f321(x94462),x94466),x94464)) % 14.98/14.67 [9457]~P22(x94571,x94572,x94573,x94576)+P22(x94571,x94572,f68(x94571,x94572,x94573,x94574,x94575),x94576)+P1(f862(f862(f321(x94572),x94575),f862(f302(x94571,x94572,x94573),x94576))) % 14.98/14.67 [9579]~P54(x95796,x95795,x95791,x95794,x95793)+E(f862(x95791,f915(x95792,x95793,x95794,x95791,x95795)),x95792)+~P1(f862(f862(f321(x95795),x95792),x95793)) % 14.98/14.67 [9765]E(x97651,x97652)+E(f862(f182(f925(x97653)),x97654),f862(f182(f925(x97653)),x97655))+~P1(f862(f862(f321(f931(f925(x97653),f925(x97653))),f862(f862(f244(f925(x97653),f925(x97653)),f862(f862(f144(x97653),x97651),x97654)),f862(f862(f144(x97653),x97652),x97655))),f138(x97653,x97656))) % 14.98/14.67 [9828]~P14(x98281,x98282,x98283)+E(f862(f862(f57(x98281,x98282,x98283),x98284),x98285),x98286)+~P1(f862(f59(x98281,x98282,x98283,x98284,x98285),x98286)) % 14.98/14.67 [9836]E(f862(f182(f925(x98361)),x98362),f862(f182(f925(x98361)),x98363))+P1(f862(f862(f321(f931(f925(x98361),f925(x98361))),f862(f862(f244(f925(x98361),f925(x98361)),x98362),x98363)),f138(x98361,x98364)))+~P1(f862(f862(f321(f931(f925(x98361),f925(x98361))),f862(f862(f244(f925(x98361),f925(x98361)),f862(f862(f144(x98361),x98365),x98362)),f862(f862(f144(x98361),x98366),x98363))),f138(x98361,x98364))) % 14.98/14.67 [9857]~P1(f862(f862(f321(f931(x98571,x98571)),f862(f862(f244(x98571,x98571),x98572),x98574)),f299(x98571,x98576)))+P1(f862(f862(f321(f931(f925(x98571),f925(x98571))),f862(f862(f244(f925(x98571),f925(x98571)),f862(f862(f144(x98571),x98572),x98573)),f862(f862(f144(x98571),x98574),x98575))),f299(f925(x98571),f150(x98571,x98576))))+~P1(f862(f862(f321(f931(f925(x98571),f925(x98571))),f862(f862(f244(f925(x98571),f925(x98571)),x98573),x98575)),f299(f925(x98571),f150(x98571,x98576)))) % 14.98/14.67 [10036]~P1(f862(x100362,x100366))+~E(f862(f129(x100361,x100362),x100363),f862(f862(f144(x100361),x100364),x100365))+~P1(f862(f862(f321(x100361),x100366),f862(f165(x100361),f749(x100365,x100364,x100363,x100362,x100361)))) % 14.98/14.67 [10037]~P1(f862(x100374,x100376))+~E(f862(f862(f144(x100371),x100372),x100373),f862(f129(x100371,x100374),x100375))+~P1(f862(f862(f321(x100371),x100376),f862(f165(x100371),f753(x100375,x100374,x100373,x100372,x100371)))) % 14.98/14.67 [10345]~P72(x103452)+E(f862(f862(f8(x103451,x103452),f862(f862(f10(f932(x103453,a921),x103452,x103451),f862(f8(x103453,x103452),x103454)),f862(f862(f10(f932(x103453,a921),f932(x103453,a921),x103451),f254(x103453)),f862(f862(f10(f932(x103453,a921),f932(x103453,a921),x103451),f862(f20(x103453,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103453),a318),f862(f862(f9(x103453,f932(x103453,a921),a921),f321(x103453)),x103455)))),f862(f9(x103453,x103451,a921),f862(f862(f10(x103451,f932(x103451,a921),x103453),a317),x103456)))))),f862(f302(x103453,x103451,x103456),x103455)),f862(f862(f8(x103453,x103452),x103454),x103455))+~P1(f862(f54(x103453),x103455)) % 14.98/14.67 [7064]~P109(x70643)+P1(f862(x70642,x70645))+E(f862(f129(x70641,x70642),f862(f862(f141(x70641,x70643,x70644),x70645),x70646)),f862(f129(x70641,x70642),x70646)) % 14.98/14.67 [7066]P1(f862(x70661,x70662))+~E(f159(x70663,x70661,x70664),f862(f862(f244(f925(x70663),f925(x70663)),x70665),x70666))+~P1(f862(f862(f321(x70663),x70662),f862(f165(x70663),x70665))) % 14.98/14.67 [7110]~P1(f862(x71102,x71106))+~E(f159(x71101,x71102,x71103),f862(f862(f244(f925(x71101),f925(x71101)),x71104),x71105))+~P1(f862(f862(f321(x71101),x71106),f862(f165(x71101),x71105))) % 14.98/14.67 [7782]~P12(x77821,x77822,x77823)+~P1(f862(f54(x77821),x77826))+E(f862(f862(f57(x77821,x77822,x77823),x77824),f862(f862(f301(x77821),x77825),x77826)),f862(f862(f57(x77821,x77822,x77823),f862(f862(x77823,x77825),x77824)),x77826)) % 14.98/14.67 [7835]~P109(x78352)+~P1(f862(f862(f227(x78352),f862(x78353,x78354)),f862(x78353,x78355)))+E(f862(f862(f141(x78351,x78352,x78353),x78354),f862(f862(f144(x78351),x78355),x78356)),f862(f862(f144(x78351),x78354),f862(f862(f144(x78351),x78355),x78356))) % 14.98/14.67 [7947]E(x79471,x79472)+~E(f862(f862(f246(x79473,x79474),x79471),f862(f18(f932(x79474,a921),x79473),x79475)),f862(f862(f246(x79473,x79474),x79472),f862(f18(f932(x79474,a921),x79473),x79475)))+~P1(f862(f862(f321(x79474),x79476),x79475)) % 14.98/14.67 [8013]~P12(x80131,x80132,x80133)+~P1(f862(f54(x80131),x80136))+E(f862(f862(f57(x80131,x80132,x80133),x80134),f862(f862(f301(x80131),x80135),x80136)),f862(f862(x80133,x80135),f862(f862(f57(x80131,x80132,x80133),x80134),x80136))) % 14.98/14.67 [8133]~P14(x81331,x81332,x81333)+~P1(f862(f54(x81331),x81336))+E(f862(f862(f57(x81331,x81332,x81333),f862(f862(x81333,x81334),x81335)),x81336),f862(f862(x81333,x81334),f862(f862(f57(x81331,x81332,x81333),x81335),x81336))) % 14.98/14.67 [8204]~P18(x82042,x82045,x82046,x82041)+~P1(f862(f54(x82042),x82044))+E(f862(x82041,f862(f862(f301(x82042),x82043),x82044)),f862(f66(x82045,x82045,x82045,f862(x82041,x82044)),f862(x82046,x82043))) % 14.98/14.67 [8236]~P109(x82362)+P1(f862(f862(f227(x82362),f862(x82363,x82364)),f862(x82363,x82365)))+E(f862(f862(f141(x82361,x82362,x82363),x82364),f862(f862(f144(x82361),x82365),x82366)),f862(f862(f144(x82361),x82365),f862(f862(f141(x82361,x82362,x82363),x82364),x82366))) % 14.98/14.67 [8382]~E(f862(f182(f925(x83821)),x83825),f862(f182(f925(x83822)),x83826))+~E(f862(f182(f925(x83821)),x83823),f862(f182(f925(x83822)),x83824))+E(f862(f862(f127(f931(x83821,x83822)),f862(f862(f174(x83821,x83822),x83823),x83824)),f862(f862(f174(x83821,x83822),x83825),x83826)),f862(f862(f174(x83821,x83822),f862(f862(f127(x83821),x83823),x83825)),f862(f862(f127(x83822),x83824),x83826))) % 14.98/14.67 [8493]~E(x84932,f862(f302(x84933,x84931,x84934),x84936))+P1(f862(f862(f227(f932(x84931,a921)),x84932),f862(f302(x84933,x84931,x84934),x84935)))+~P1(f862(f862(f227(f932(x84933,a921)),x84936),x84935)) % 14.98/14.67 [8595]~P109(x85955)+E(f862(x85951,x85952),f862(x85951,x85953))+E(f862(f862(f141(x85954,x85955,x85951),x85952),f862(f862(f141(x85954,x85955,x85951),x85953),x85956)),f862(f862(f141(x85954,x85955,x85951),x85953),f862(f862(f141(x85954,x85955,x85951),x85952),x85956))) % 14.98/14.67 [8773]~P1(f862(f862(f321(x87732),x87734),f862(x87736,x87733)))+~P1(f862(f862(f321(x87731),x87733),x87735))+P1(f862(f862(f321(f931(x87731,x87732)),f862(f862(f244(x87731,x87732),x87733),x87734)),f862(f862(f246(x87731,x87732),x87735),x87736))) % 14.98/14.67 [9250]~P72(x92502)+~P22(x92504,x92501,x92505,x92506)+E(f862(f862(f8(x92501,x92502),x92503),f862(f302(x92504,x92501,x92505),x92506)),f862(f862(f8(x92504,x92502),f862(f66(x92501,x92502,x92504,x92503),x92505)),x92506)) % 14.98/14.67 [9251]~P71(x92512)+~P22(x92514,x92511,x92515,x92516)+E(f862(f862(f11(x92511,x92512),x92513),f862(f302(x92514,x92511,x92515),x92516)),f862(f862(f11(x92514,x92512),f862(f66(x92511,x92512,x92514,x92513),x92515)),x92516)) % 14.98/14.67 [9299]~P32(x92992,x92995,x92991,x92993,x92996)+P1(f862(f862(x92991,f862(f862(f157(x92992),x92993),x92994)),f862(f862(f157(x92995),x92996),x92994)))+~P1(f862(f862(f228(a924),x92994),f862(f182(f925(x92995)),x92996))) % 14.98/14.67 [9300]~P32(x93002,x93005,x93001,x93003,x93006)+P1(f862(f862(x93001,f862(f862(f157(x93002),x93003),x93004)),f862(f862(f157(x93005),x93006),x93004)))+~P1(f862(f862(f228(a924),x93004),f862(f182(f925(x93002)),x93003))) % 14.98/14.67 [9311]~E(f862(f302(x93111,x93112,x93113),x93114),x93116)+E(f862(f302(x93111,x93112,x93113),f862(f302(x93112,x93111,f86(x93111,x93112,x93114,x93113)),x93115)),x93115)+~P1(f862(f862(f227(f932(x93112,a921)),x93115),x93116)) % 14.98/14.67 [9514]~P17(x95143,x95141,x95146,x95142)+~P1(f862(f54(x95143),x95144))+E(f862(f66(x95141,x95141,x95141,f862(x95142,f862(f862(f3(f932(x95143,a921)),x95144),f862(f862(f301(x95143),x95145),f181(f932(x95143,a921)))))),f862(x95146,x95145)),f862(x95142,f862(f862(f301(x95143),x95145),x95144))) % 14.98/14.67 [10126]~E(f862(f302(x101262,x101264,x101266),f234(f932(x101262,a921))),f234(f932(x101264,a921)))+~E(f862(f302(x101261,x101263,x101265),f234(f932(x101261,a921))),f234(f932(x101263,a921)))+E(f862(f302(f931(x101261,x101262),f931(x101263,x101264),f250(x101261,x101263,x101262,x101264,x101265,x101266)),f234(f932(f931(x101261,x101262),a921))),f234(f932(f931(x101263,x101264),a921))) % 14.98/14.67 [10172]~P22(x101723,x101724,x101725,f862(x101726,f586(x101726,x101725,x101724,x101723,x101722,x101721)))+P22(x101723,x101724,x101725,f862(f862(f32(x101722,f932(x101723,a921)),x101721),x101726))+E(x101721,f181(f932(x101722,a921))) % 14.98/14.67 [10230]P22(x102306,x102305,x102304,f862(f862(f32(x102302,f932(x102306,a921)),x102301),x102303))+E(x102301,f181(f932(x102302,a921)))+P1(f862(f862(f321(x102302),f586(x102303,x102304,x102305,x102306,x102302,x102301)),x102301)) % 14.98/14.67 [10236]P1(f862(f862(f321(x102361),f613(x102362,x102363,x102364,x102365,x102366,x102361)),x102366))+P1(f862(f862(f227(f932(f931(x102361,x102364),a921)),f862(f862(f246(x102361,x102364),x102366),x102363)),f862(f862(f246(x102361,x102364),x102365),x102362)))+~P1(f862(f862(f227(f932(x102361,a921)),x102366),x102365)) % 14.98/14.67 [10363]~P1(f862(f862(f227(f932(x103632,a921)),f862(x103634,f613(x103636,x103634,x103632,x103635,x103633,x103631))),f862(x103636,f613(x103636,x103634,x103632,x103635,x103633,x103631))))+~P1(f862(f862(f227(f932(x103631,a921)),x103633),x103635))+P1(f862(f862(f227(f932(f931(x103631,x103632),a921)),f862(f862(f246(x103631,x103632),x103633),x103634)),f862(f862(f246(x103631,x103632),x103635),x103636))) % 14.98/14.67 [7969]~P1(f862(x79691,x79695))+~P1(f862(x79696,x79694))+P1(f862(x79691,f862(f248(x79692,x79693),f862(f862(f244(x79692,x79693),x79694),x79695)))) % 14.98/14.67 [7970]~P1(f862(x79701,x79704))+~P1(f862(x79706,x79705))+P1(f862(x79701,f862(f243(x79702,x79703),f862(f862(f244(x79702,x79703),x79704),x79705)))) % 14.98/14.67 [8019]~P1(f862(f862(x80194,x80196),x80195))+~P1(f862(f862(f321(x80191),x80196),x80193))+P1(f862(f862(f862(f33(x80191,f932(x80192,a921)),x80193),x80194),x80195)) % 14.98/14.67 [8331]~P1(f862(f862(f321(x83311),x83312),f862(x83315,x83316)))+~P1(f862(f862(f321(x83313),x83316),x83314))+P1(f862(f862(f321(x83311),x83312),f862(f862(f33(x83313,f932(x83311,a921)),x83314),x83315))) % 14.98/14.67 [8375]P1(f862(f862(x83751,x83752),x83753))+~P1(f862(f862(x83754,x83752),x83753))+~P1(f862(f862(f227(f932(x83755,f932(x83756,a921))),x83754),x83751)) % 14.98/14.67 [8516]P1(f862(f862(x85161,x85162),x85163))+~P1(f862(f862(f321(x85164),x85162),x85165))+~P1(f862(f862(f862(f32(x85164,f932(x85166,a921)),x85165),x85161),x85163)) % 14.98/14.67 [8653]P1(f862(f862(f321(x86531),x86532),f862(x86533,x86534)))+~P1(f862(f862(f321(x86535),x86534),x86536))+~P1(f862(f862(f321(x86531),x86532),f862(f862(f32(x86535,f932(x86531,a921)),x86536),x86533))) % 14.98/14.67 [8923]~P9(x89234,x89235,x89236,x89231)+E(f862(x89231,x89232),f862(x89231,x89233))+~P1(f862(f862(f321(f931(x89234,x89234)),f862(f862(f244(x89234,x89234),x89232),x89233)),x89236)) % 14.98/14.67 [8958]P1(f862(f862(f227(f932(x89581,a921)),x89582),f862(x89583,x89584)))+~P1(f862(f862(f321(x89585),x89584),x89586))+~P1(f862(f862(f227(f932(x89581,a921)),x89582),f862(f862(f32(x89585,f932(x89581,a921)),x89586),x89583))) % 14.98/14.67 [8991]~P52(x89913,x89914,f862(f277(x89914,x89913),x89915))+E(x89911,f181(f932(x89912,a921)))+E(f862(f862(f32(x89912,f932(x89913,a921)),x89911),f862(f862(f10(f932(x89914,a921),f932(x89913,a921),x89912),f276(x89914,x89913,x89915)),x89916)),f862(f276(x89914,x89913,x89915),f862(f862(f32(x89912,f932(x89914,a921)),x89911),x89916))) % 14.98/14.67 [9071]P1(f862(f862(f321(x90711),x90712),f862(f276(x90713,x90711,x90714),x90715)))+~P1(f862(f862(f321(x90713),x90716),x90715))+~P1(f862(f862(f321(f931(x90713,x90711)),f862(f862(f244(x90713,x90711),x90716),x90712)),x90714)) % 14.98/14.67 [9377]P1(f862(f862(f227(f932(x93771,a921)),f862(f276(x93772,x93771,x93773),x93774)),f862(f276(x93772,x93771,x93775),x93776)))+~P1(f862(f862(f227(f932(x93772,a921)),x93774),x93776))+~P1(f862(f862(f227(f932(f931(x93772,x93771),a921)),x93773),x93775)) % 14.98/14.67 [9564]~P1(f862(f862(f321(x95642),x95646),x95644))+~P1(f862(f862(f227(f932(x95641,a921)),x95643),x95645))+P1(f862(f862(f227(f932(f931(x95641,x95642),a921)),f862(f862(f246(x95641,x95642),x95643),f862(f18(f932(x95642,a921),x95641),x95644))),f862(f862(f246(x95641,x95642),x95645),f862(f18(f932(x95642,a921),x95641),x95644)))) % 14.98/14.67 [9577]~P32(x95771,x95772,x95773,x95775,x95776)+P1(f862(f862(f249(x95771,x95772,a921),x95773),x95774))+~P1(f862(f862(f321(f931(x95771,x95772)),x95774),f862(f165(f931(x95771,x95772)),f862(f862(f174(x95771,x95772),x95775),x95776)))) % 14.98/14.67 [9719]~E(x97193,x97195)+P1(f862(f862(f321(f931(f925(x97191),f925(x97191))),f862(f862(f244(f925(x97191),f925(x97191)),f862(f862(f144(x97191),x97192),x97193)),f862(f862(f144(x97191),x97194),x97195))),f150(x97191,x97196)))+~P1(f862(f862(f321(f931(x97191,x97191)),f862(f862(f244(x97191,x97191),x97192),x97194)),x97196)) % 14.98/14.67 [9725]~E(f862(f182(f925(x97251)),x97253),f862(f182(f925(x97251)),x97255))+P1(f862(f862(f321(f931(f925(x97251),f925(x97251))),f862(f862(f244(f925(x97251),f925(x97251)),f862(f862(f144(x97251),x97252),x97253)),f862(f862(f144(x97251),x97254),x97255))),f138(x97251,x97256)))+~P1(f862(f862(f321(f931(x97251,x97251)),f862(f862(f244(x97251,x97251),x97252),x97254)),x97256)) % 14.98/14.67 [9757]P1(f862(f862(f321(f931(x97571,x97571)),f862(f862(f244(x97571,x97571),x97572),x97573)),f862(f862(f176(f931(x97571,x97571),a921),f862(a105,x97574)),x97575)))+~P1(f862(f862(f321(f931(x97571,x97571)),f862(f862(f244(x97571,x97571),x97576),x97573)),x97575))+~P1(f862(f862(f321(f931(x97571,x97571)),f862(f862(f244(x97571,x97571),x97572),x97576)),f862(f862(f176(f931(x97571,x97571),a921),x97574),x97575))) % 14.98/14.67 [9758]P1(f862(f862(f321(f931(x97581,x97581)),f862(f862(f244(x97581,x97581),x97582),x97583)),f862(f862(f176(f931(x97581,x97581),a921),f862(a105,x97584)),x97585)))+~P1(f862(f862(f321(f931(x97581,x97581)),f862(f862(f244(x97581,x97581),x97582),x97586)),x97585))+~P1(f862(f862(f321(f931(x97581,x97581)),f862(f862(f244(x97581,x97581),x97586),x97583)),f862(f862(f176(f931(x97581,x97581),a921),x97584),x97585))) % 14.98/14.67 [9761]~P1(f862(f862(f321(x97614),x97615),x97616))+P1(f862(f862(f227(f932(x97611,a921)),x97612),x97613))+~P1(f862(f862(f227(f932(f931(x97611,x97614),a921)),f862(f862(f246(x97611,x97614),x97612),f862(f18(f932(x97614,a921),x97611),x97616))),f862(f862(f246(x97611,x97614),x97613),f862(f18(f932(x97614,a921),x97611),x97616)))) % 14.98/14.67 [9806]E(x98061,x98062)+~P1(f862(f862(f321(f931(f925(x98063),f925(x98063))),f862(f862(f244(f925(x98063),f925(x98063)),f862(f862(f144(x98063),x98061),x98065)),f862(f862(f144(x98063),x98062),x98066))),f138(x98063,x98064)))+P1(f862(f862(f321(f931(x98063,x98063)),f862(f862(f244(x98063,x98063),x98061),x98062)),x98064)) % 14.98/14.67 [9807]E(x98071,x98072)+~P1(f862(f862(f321(f931(f925(x98073),f925(x98073))),f862(f862(f244(f925(x98073),f925(x98073)),f862(f862(f144(x98073),x98071),x98075)),f862(f862(f144(x98073),x98072),x98076))),f140(x98073,x98074)))+P1(f862(f862(f321(f931(x98073,x98073)),f862(f862(f244(x98073,x98073),x98071),x98072)),x98074)) % 14.98/14.67 [9808]E(x98081,x98082)+~P1(f862(f862(f321(f931(f925(x98083),f925(x98083))),f862(f862(f244(f925(x98083),f925(x98083)),f862(f862(f144(x98083),x98081),x98085)),f862(f862(f144(x98083),x98082),x98086))),f150(x98083,x98084)))+P1(f862(f862(f321(f931(x98083,x98083)),f862(f862(f244(x98083,x98083),x98081),x98082)),x98084)) % 14.98/14.67 [9844]P1(f862(f862(f321(f931(f925(x98441),f925(x98441))),f862(f862(f244(f925(x98441),f925(x98441)),f862(f862(f144(x98441),x98442),x98443)),f862(f862(f144(x98441),x98444),x98445))),f151(x98441,x98446)))+~P1(f862(f862(f321(f931(f925(x98441),f925(x98441))),f862(f862(f244(f925(x98441),f925(x98441)),x98443),x98445)),f151(x98441,x98446)))+~P1(f862(f862(f321(f931(x98441,x98441)),f862(f862(f244(x98441,x98441),x98442),x98444)),x98446)) % 14.98/14.67 [9861]P1(f862(x98611,x98612))+~P1(f862(x98611,f887(x98611,x98613,x98614,x98615,x98616)))+~P1(f862(f862(f321(x98616),x98612),f862(f862(f33(x98615,f932(x98616,a921)),x98614),x98613))) % 14.98/14.67 [9866]~P1(f862(f862(f321(f931(f925(x98661),f925(x98661))),f862(f862(f244(f925(x98661),f925(x98661)),f862(f862(f144(x98661),x98662),x98665)),f862(f862(f144(x98661),x98663),x98666))),f138(x98661,x98664)))+P1(f862(f862(f321(f931(f925(x98661),f925(x98661))),f862(f862(f244(f925(x98661),f925(x98661)),x98665),x98666)),f138(x98661,x98664)))+P1(f862(f862(f321(f931(x98661,x98661)),f862(f862(f244(x98661,x98661),x98662),x98663)),x98664)) % 14.98/14.67 [9867]~P1(f862(f862(f321(f931(f925(x98671),f925(x98671))),f862(f862(f244(f925(x98671),f925(x98671)),f862(f862(f144(x98671),x98672),x98675)),f862(f862(f144(x98671),x98673),x98676))),f140(x98671,x98674)))+P1(f862(f862(f321(f931(f925(x98671),f925(x98671))),f862(f862(f244(f925(x98671),f925(x98671)),x98675),x98676)),f140(x98671,x98674)))+P1(f862(f862(f321(f931(x98671,x98671)),f862(f862(f244(x98671,x98671),x98672),x98673)),x98674)) % 14.98/14.67 [9868]~P1(f862(f862(f321(f931(f925(x98681),f925(x98681))),f862(f862(f244(f925(x98681),f925(x98681)),f862(f862(f144(x98681),x98682),x98685)),f862(f862(f144(x98681),x98683),x98686))),f150(x98681,x98684)))+P1(f862(f862(f321(f931(f925(x98681),f925(x98681))),f862(f862(f244(f925(x98681),f925(x98681)),x98685),x98686)),f150(x98681,x98684)))+P1(f862(f862(f321(f931(x98681,x98681)),f862(f862(f244(x98681,x98681),x98682),x98683)),x98684)) % 14.98/14.67 [9957]P1(f862(x99571,x99572))+P1(f862(f862(f321(x99573),f888(x99571,x99574,x99575,x99573,x99576)),x99575))+~P1(f862(f862(f321(x99576),x99572),f862(f862(f33(x99573,f932(x99576,a921)),x99575),x99574))) % 14.98/14.67 [9968]~E(x99682,x99684)+P1(f862(f862(f321(f931(f925(x99681),f925(x99681))),f862(f862(f244(f925(x99681),f925(x99681)),f862(f862(f127(x99681),x99682),f862(f862(f144(x99681),x99683),f106(x99681)))),f862(f862(f127(x99681),x99684),f862(f862(f144(x99681),x99685),f106(x99681))))),f150(x99681,x99686)))+~P1(f862(f862(f321(f931(x99681,x99681)),f862(f862(f244(x99681,x99681),x99683),x99685)),x99686)) % 14.98/14.67 [10044]E(x100441,x100442)+~P1(f862(f862(f321(f931(f925(x100443),f925(x100443))),f862(f862(f244(f925(x100443),f925(x100443)),f862(f862(f127(x100443),x100445),f862(f862(f144(x100443),x100441),f106(x100443)))),f862(f862(f127(x100443),x100446),f862(f862(f144(x100443),x100442),f106(x100443))))),f150(x100443,x100444)))+P1(f862(f862(f321(f931(x100443,x100443)),f862(f862(f244(x100443,x100443),x100441),x100442)),x100444)) % 14.98/14.67 [10075]~P1(f862(f862(f321(f931(f925(x100751),f925(x100751))),f862(f862(f244(f925(x100751),f925(x100751)),f862(f862(f127(x100751),x100755),f862(f862(f144(x100751),x100752),f106(x100751)))),f862(f862(f127(x100751),x100756),f862(f862(f144(x100751),x100753),f106(x100751))))),f150(x100751,x100754)))+P1(f862(f862(f321(f931(f925(x100751),f925(x100751))),f862(f862(f244(f925(x100751),f925(x100751)),x100755),x100756)),f150(x100751,x100754)))+P1(f862(f862(f321(f931(x100751,x100751)),f862(f862(f244(x100751,x100751),x100752),x100753)),x100754)) % 14.98/14.67 [10097]P1(f862(x100971,x100972))+P1(f862(f862(f321(x100973),f887(x100971,x100974,x100975,x100976,x100973)),f862(x100974,f888(x100971,x100974,x100975,x100976,x100973))))+~P1(f862(f862(f321(x100973),x100972),f862(f862(f33(x100976,f932(x100973,a921)),x100975),x100974))) % 14.98/14.67 [10240]P1(f862(f862(f321(x102401),f842(x102402,x102403,x102404,x102405,x102406,x102401)),x102405))+~P1(f862(f862(f227(f932(x102401,a921)),x102406),x102405))+P1(f862(f862(f227(f932(x102404,a921)),f862(f862(f32(x102401,f932(x102404,a921)),x102405),x102403)),f862(f862(f32(x102401,f932(x102404,a921)),x102405),x102402))) % 14.98/14.67 [10364]~P1(f862(f862(f227(f932(x103641,a921)),f862(x103644,f842(x103645,x103644,x103641,x103643,x103646,x103642))),f862(x103645,f842(x103645,x103644,x103641,x103643,x103646,x103642))))+~P1(f862(f862(f227(f932(x103642,a921)),x103646),x103643))+P1(f862(f862(f227(f932(x103641,a921)),f862(f862(f32(x103642,f932(x103641,a921)),x103643),x103644)),f862(f862(f32(x103642,f932(x103641,a921)),x103643),x103645))) % 14.98/14.67 [9091]~P14(x90913,x90914,x90911)+~P1(f862(f54(x90913),x90916))+E(f862(f862(x90911,x90912),f862(f862(f57(x90913,x90914,x90911),x90915),f862(f862(f3(f932(x90913,a921)),x90916),f862(f862(f301(x90913),x90912),f181(f932(x90913,a921)))))),f862(f862(f57(x90913,x90914,x90911),x90915),f862(f862(f301(x90913),x90912),x90916))) % 14.98/14.67 [9386]~P1(f862(f862(f321(x93865),x93863),x93866))+P1(f862(f862(f227(f932(x93861,a921)),f862(x93862,x93863)),x93864))+~P1(f862(f862(f227(f932(x93861,a921)),f862(f862(f33(x93865,f932(x93861,a921)),x93866),x93862)),x93864)) % 14.98/14.67 [10019]~P6(x100191,x100195,x100194)+P1(f862(f862(f321(f931(x100191,x100191)),f862(f862(f244(x100191,x100191),x100192),x100193)),x100194))+~P1(f862(f862(f321(x100191),x100196),f862(f862(f94(f932(x100191,a921)),f862(f276(x100191,x100191,x100194),f862(f862(f301(x100191),x100192),f181(f932(x100191,a921))))),f862(f276(x100191,x100191,x100194),f862(f862(f301(x100191),x100193),f181(f932(x100191,a921))))))) % 14.98/14.67 [8810]~P125(x88102)+~E(f862(f862(f73(x88102),f862(f862(f74(x88102),x88104),x88105)),x88101),f862(f862(f73(x88102),f862(f862(f74(x88102),x88103),x88105)),x88106))+E(x88101,f862(f862(f73(x88102),f862(f862(f74(x88102),f862(f862(f3(x88102),x88103),x88104)),x88105)),x88106)) % 14.98/14.67 [8811]~P125(x88111)+~E(f862(f862(f73(x88111),f862(f862(f74(x88111),x88112),x88114)),x88115),f862(f862(f73(x88111),f862(f862(f74(x88111),x88113),x88114)),x88116))+E(f862(f862(f73(x88111),f862(f862(f74(x88111),f862(f862(f3(x88111),x88112),x88113)),x88114)),x88115),x88116) % 14.98/14.67 [8994]~P125(x89941)+E(f862(f862(f73(x89941),f862(f862(f74(x89941),x89942),x89943)),x89944),f862(f862(f73(x89941),f862(f862(f74(x89941),x89945),x89943)),x89946))+~E(x89946,f862(f862(f73(x89941),f862(f862(f74(x89941),f862(f862(f3(x89941),x89942),x89945)),x89943)),x89944)) % 14.98/14.67 [8995]~P125(x89951)+E(f862(f862(f73(x89951),f862(f862(f74(x89951),x89952),x89953)),x89954),f862(f862(f73(x89951),f862(f862(f74(x89951),x89955),x89953)),x89956))+~E(f862(f862(f73(x89951),f862(f862(f74(x89951),f862(f862(f3(x89951),x89952),x89955)),x89953)),x89954),x89956) % 14.98/14.67 [9322]~P1(f862(f862(x93224,x93225),x93226))+~P1(f862(f862(x93223,x93225),x93226))+P1(f862(f862(f862(f862(f94(f932(x93221,f932(x93222,a921))),x93223),x93224),x93225),x93226)) % 14.98/14.67 [9587]P1(f862(f862(x95871,x95872),x95873))+P1(f862(f862(x95874,x95872),x95873))+~P1(f862(f862(f862(f862(f103(f932(x95875,f932(x95876,a921))),x95874),x95871),x95872),x95873)) % 14.98/14.67 [9881]~P126(x98811)+~P1(f862(f862(f227(x98811),f862(f862(f73(x98811),f862(f862(f74(x98811),x98814),x98815)),x98812)),f862(f862(f73(x98811),f862(f862(f74(x98811),x98813),x98815)),x98816)))+P1(f862(f862(f227(x98811),x98812),f862(f862(f73(x98811),f862(f862(f74(x98811),f862(f862(f3(x98811),x98813),x98814)),x98815)),x98816))) % 14.98/14.67 [9882]~P126(x98821)+~P1(f862(f862(f228(x98821),f862(f862(f73(x98821),f862(f862(f74(x98821),x98824),x98825)),x98822)),f862(f862(f73(x98821),f862(f862(f74(x98821),x98823),x98825)),x98826)))+P1(f862(f862(f228(x98821),x98822),f862(f862(f73(x98821),f862(f862(f74(x98821),f862(f862(f3(x98821),x98823),x98824)),x98825)),x98826))) % 14.98/14.67 [9906]~P126(x99061)+P1(f862(f862(f227(x99061),f862(f862(f73(x99061),f862(f862(f74(x99061),x99062),x99063)),x99064)),f862(f862(f73(x99061),f862(f862(f74(x99061),x99065),x99063)),x99066)))+~P1(f862(f862(f227(x99061),x99064),f862(f862(f73(x99061),f862(f862(f74(x99061),f862(f862(f3(x99061),x99065),x99062)),x99063)),x99066))) % 14.98/14.67 [9907]~P126(x99071)+P1(f862(f862(f228(x99071),f862(f862(f73(x99071),f862(f862(f74(x99071),x99072),x99073)),x99074)),f862(f862(f73(x99071),f862(f862(f74(x99071),x99075),x99073)),x99076)))+~P1(f862(f862(f228(x99071),x99074),f862(f862(f73(x99071),f862(f862(f74(x99071),f862(f862(f3(x99071),x99075),x99072)),x99073)),x99076))) % 14.98/14.67 [10011]~P126(x100111)+~P1(f862(f862(f227(x100111),f862(f862(f73(x100111),f862(f862(f74(x100111),x100112),x100114)),x100115)),f862(f862(f73(x100111),f862(f862(f74(x100111),x100113),x100114)),x100116)))+P1(f862(f862(f227(x100111),f862(f862(f73(x100111),f862(f862(f74(x100111),f862(f862(f3(x100111),x100112),x100113)),x100114)),x100115)),x100116)) % 14.98/14.67 [10012]~P126(x100121)+~P1(f862(f862(f228(x100121),f862(f862(f73(x100121),f862(f862(f74(x100121),x100122),x100124)),x100125)),f862(f862(f73(x100121),f862(f862(f74(x100121),x100123),x100124)),x100126)))+P1(f862(f862(f228(x100121),f862(f862(f73(x100121),f862(f862(f74(x100121),f862(f862(f3(x100121),x100122),x100123)),x100124)),x100125)),x100126)) % 14.98/14.67 [10058]~P126(x100581)+P1(f862(f862(f227(x100581),f862(f862(f73(x100581),f862(f862(f74(x100581),x100582),x100583)),x100584)),f862(f862(f73(x100581),f862(f862(f74(x100581),x100585),x100583)),x100586)))+~P1(f862(f862(f227(x100581),f862(f862(f73(x100581),f862(f862(f74(x100581),f862(f862(f3(x100581),x100582),x100585)),x100583)),x100584)),x100586)) % 14.98/14.67 [10059]~P126(x100591)+P1(f862(f862(f228(x100591),f862(f862(f73(x100591),f862(f862(f74(x100591),x100592),x100593)),x100594)),f862(f862(f73(x100591),f862(f862(f74(x100591),x100595),x100593)),x100596)))+~P1(f862(f862(f228(x100591),f862(f862(f73(x100591),f862(f862(f74(x100591),f862(f862(f3(x100591),x100592),x100595)),x100593)),x100594)),x100596)) % 14.98/14.67 [10224]~P72(x102242)+~P1(f862(f54(x102241),x102246))+E(f862(f862(f8(x102241,x102242),f862(f862(f20(x102241,x102242,x102242),f862(f862(f20(x102241,x102242,f932(x102242,x102242)),f862(f862(f10(a921,f932(x102242,f932(x102242,x102242)),x102241),f89(x102242)),x102243)),x102244)),x102245)),x102246),f862(f862(f73(x102242),f862(f862(f8(x102241,x102242),x102244),f862(f862(f94(f932(x102241,a921)),x102246),f862(f254(x102241),x102243)))),f862(f862(f8(x102241,x102242),x102245),f862(f862(f94(f932(x102241,a921)),x102246),f862(f72(f932(x102241,a921)),f862(f254(x102241),x102243)))))) % 14.98/14.67 [10283]P1(f862(f862(f321(x102832),x102834),x102836))+P1(f862(f862(f321(x102832),x102835),x102836))+E(f862(f303(x102831,x102832,f862(f862(f9(x102831,x102832,x102832),f862(f862(f9(x102831,x102832,f932(x102832,x102832)),f862(f862(f10(a921,f932(x102832,f932(x102832,x102832)),x102831),f89(x102832)),f862(f862(f9(x102831,f932(x102831,a921),a921),f321(x102831)),x102833))),x102834)),x102835)),x102836),f181(f932(x102831,a921))) % 14.98/14.67 [10284]P1(f862(f862(f321(x102842),x102845),x102846))+~P1(f862(f862(f321(x102842),x102844),x102846))+E(f862(f303(x102841,x102842,f862(f862(f9(x102841,x102842,x102842),f862(f862(f9(x102841,x102842,f932(x102842,x102842)),f862(f862(f10(a921,f932(x102842,f932(x102842,x102842)),x102841),f89(x102842)),f862(f862(f9(x102841,f932(x102841,a921),a921),f321(x102841)),x102843))),x102844)),x102845)),x102846),x102843) % 14.98/14.67 [10285]P1(f862(f862(f321(x102852),x102854),x102856))+~P1(f862(f862(f321(x102852),x102855),x102856))+E(f862(f303(x102851,x102852,f862(f862(f9(x102851,x102852,x102852),f862(f862(f9(x102851,x102852,f932(x102852,x102852)),f862(f862(f10(a921,f932(x102852,f932(x102852,x102852)),x102851),f89(x102852)),f862(f862(f9(x102851,f932(x102851,a921),a921),f321(x102851)),x102853))),x102854)),x102855)),x102856),f862(f72(f932(x102851,a921)),x102853)) % 14.98/14.67 [10286]~P1(f862(f862(f321(x102862),x102864),x102866))+~P1(f862(f862(f321(x102862),x102865),x102866))+E(f862(f303(x102861,x102862,f862(f862(f9(x102861,x102862,x102862),f862(f862(f9(x102861,x102862,f932(x102862,x102862)),f862(f862(f10(a921,f932(x102862,f932(x102862,x102862)),x102861),f89(x102862)),f862(f862(f9(x102861,f932(x102861,a921),a921),f321(x102861)),x102863))),x102864)),x102865)),x102866),f234(f932(x102861,a921))) % 14.98/14.67 [8843]E(x88431,x88432)+~P54(x88434,x88435,x88433,x88436,x88437)+~E(f862(x88433,x88431),f862(x88433,x88432)) % 14.98/14.67 [8872]~P8(x88726,x88725,x88727,x88724,x88721)+E(f862(f862(x88721,x88722),x88723),x88724)+P1(f862(f54(x88725),x88723)) % 14.98/14.67 [9748]P40(x97481,x97482,x97483,x97484,x97485,f862(f862(x97483,x97486),x97487))+~E(f862(f862(x97483,x97486),x97487),x97484)+~E(x97485,f181(f932(x97481,a921))) % 14.98/14.67 [9928]~P1(f862(x99286,x99283))+~P1(f862(f862(f321(f931(x99282,x99282)),f862(f862(f244(x99282,x99282),x99284),x99285)),f862(x99287,x99283)))+P1(f862(f862(f321(f931(f931(x99281,x99282),f931(x99281,x99282))),f862(f862(f244(f931(x99281,x99282),f931(x99281,x99282)),f862(f862(f244(x99281,x99282),x99283),x99284)),f862(f862(f244(x99281,x99282),x99283),x99285))),f272(x99281,x99282,x99286,x99287))) % 14.98/14.67 [10348]~P40(x103482,x103487,x103483,x103486,x103481,f862(f862(x103483,x103485),x103484))+E(f862(f862(x103483,f751(x103484,x103485,x103481,x103486,x103483,x103487,x103482)),f761(x103484,x103485,x103481,x103486,x103483,x103487,x103482)),f862(f862(x103483,x103485),x103484))+E(x103481,f181(f932(x103482,a921))) % 14.98/14.67 [10349]~P40(x103497,x103496,x103491,x103494,x103495,f862(f862(x103491,x103492),x103493))+E(f862(f862(x103491,f751(x103493,x103492,x103495,x103494,x103491,x103496,x103497)),f761(x103493,x103492,x103495,x103494,x103491,x103496,x103497)),f862(f862(x103491,x103492),x103493))+E(f862(f862(x103491,x103492),x103493),x103494) % 14.98/14.67 [9420]~P32(x94201,x94202,x94203,x94205,x94207)+P32(x94201,x94202,x94203,f862(f862(f144(x94201),x94204),x94205),f862(f862(f144(x94202),x94206),x94207))+~P1(f862(f862(x94203,x94204),x94206)) % 14.98/14.67 [9438]P32(x94381,x94382,x94383,x94384,x94385)+~P32(x94381,x94382,x94383,f862(f862(f127(x94381),x94386),x94384),f862(f862(f127(x94382),x94387),x94385))+~E(f862(f182(f925(x94381)),x94386),f862(f182(f925(x94382)),x94387)) % 14.98/14.67 [9439]P32(x94391,x94392,x94393,x94394,x94395)+~P32(x94391,x94392,x94393,f862(f862(f127(x94391),x94394),x94396),f862(f862(f127(x94392),x94395),x94397))+~E(f862(f182(f925(x94391)),x94394),f862(f182(f925(x94392)),x94395)) % 14.98/14.67 [9653]~P32(x96531,x96532,x96533,x96535,x96537)+~P32(x96531,x96532,x96533,x96534,x96536)+P32(x96531,x96532,x96533,f862(f862(f127(x96531),x96534),x96535),f862(f862(f127(x96532),x96536),x96537)) % 14.98/14.67 [10003]~P1(f862(f59(x100031,x100034,x100035,x100036,x100033),x100037))+P1(f862(f59(x100031,x100034,x100035,x100036,f862(f862(f301(x100031),x100032),x100033)),f862(f862(x100035,x100032),x100037)))+P1(f862(f862(f321(x100031),x100032),x100033)) % 14.98/14.67 [10235]~P54(x102357,x102353,x102356,x102355,x102354)+P1(f862(x102351,x102352))+P1(f862(f862(f321(x102353),f901(x102352,x102351,x102354,x102355,x102356,x102353)),x102354)) % 14.98/14.67 [10275]~P54(x102753,x102754,x102755,x102756,x102757)+P1(f862(x102751,x102752))+~P1(f862(x102751,f862(x102756,f901(x102752,x102751,x102757,x102756,x102755,x102754)))) % 14.98/14.67 [10380]~P40(x103802,x103807,x103806,x103805,x103801,f862(f862(x103806,x103804),x103803))+E(x103801,f181(f932(x103802,a921)))+P1(f862(f862(f321(x103802),f751(x103803,x103804,x103801,x103805,x103806,x103807,x103802)),x103801)) % 14.98/14.67 [10381]~P40(x103815,x103817,x103811,x103814,x103816,f862(f862(x103811,x103812),x103813))+E(f862(f862(x103811,x103812),x103813),x103814)+P1(f862(f862(f321(x103815),f751(x103813,x103812,x103816,x103814,x103811,x103817,x103815)),x103816)) % 14.98/14.67 [10468]E(f862(f862(f244(x104681,x104682),x104683),x104684),f862(f862(f244(x104681,x104682),x104685),x104686))+P1(f862(f862(f321(f931(f931(x104681,x104682),f931(x104681,x104682))),f862(f862(f244(f931(x104681,x104682),f931(x104681,x104682)),f862(f862(f244(x104681,x104682),f849(x104687,x104684,x104683,x104686,x104685,x104682,x104681)),f850(x104687,x104684,x104683,x104686,x104685,x104682,x104681))),f862(f862(f244(x104681,x104682),x104683),x104684))),f299(f931(x104681,x104682),x104687)))+~P1(f862(f862(f321(f931(f931(x104681,x104682),f931(x104681,x104682))),f862(f862(f244(f931(x104681,x104682),f931(x104681,x104682)),f862(f862(f244(x104681,x104682),x104685),x104686)),f862(f862(f244(x104681,x104682),x104683),x104684))),f299(f931(x104681,x104682),x104687))) % 14.98/14.67 [9116]~P19(x91164,x91165,x91166,x91167,x91161)+~P1(f862(f54(x91165),x91163))+E(f862(f862(x91161,x91162),x91163),f862(f862(f862(f58(x91164,x91165,x91166),x91162),x91167),x91163)) % 14.98/14.67 [9117]~P8(x91174,x91175,x91176,x91177,x91171)+~P1(f862(f54(x91175),x91173))+E(f862(f862(x91171,x91172),x91173),f862(f862(f862(f58(x91174,x91175,x91176),x91172),x91177),x91173)) % 14.98/14.67 [9900]~P21(x99003,x99004,x99005,x99007,x99006,x99001)+~P1(f862(f54(x99004),x99002))+E(f862(x99001,x99002),f862(f862(f862(f58(x99003,x99004,x99005),x99006),x99007),x99002)) % 14.98/14.67 [10053]P40(x100531,x100532,x100533,x100534,x100535,f862(f862(x100533,x100536),x100537))+~P40(x100531,x100532,x100533,x100534,f862(f862(f3(f932(x100531,a921)),x100535),f862(f862(f301(x100531),x100536),f181(f932(x100531,a921)))),x100537)+~P1(f862(f862(f321(x100531),x100536),x100535)) % 14.98/14.67 [10404]P1(f862(f862(x104047,f795(x104044,x104045,x104041,x104046,x104043,x104042,x104047)),f796(x104044,x104045,x104041,x104046,x104043,x104042,x104047)))+~P1(f862(f862(x104047,f862(f248(x104042,x104043),x104046)),f862(f243(x104042,x104043),x104046)))+P1(f862(x104041,f862(f862(f249(x104042,x104043,x104044),x104045),x104046))) % 14.98/14.67 [10414]~P40(x104142,x104143,x104144,x104145,x104141,f862(f862(x104144,x104147),x104146))+P40(x104142,x104143,x104144,x104145,f862(f862(f3(f932(x104142,a921)),x104141),f862(f862(f301(x104142),f751(x104146,x104147,x104141,x104145,x104144,x104143,x104142)),f181(f932(x104142,a921)))),f761(x104146,x104147,x104141,x104145,x104144,x104143,x104142))+E(x104141,f181(f932(x104142,a921))) % 14.98/14.67 [10415]~P40(x104155,x104156,x104151,x104154,x104157,f862(f862(x104151,x104152),x104153))+P40(x104155,x104156,x104151,x104154,f862(f862(f3(f932(x104155,a921)),x104157),f862(f862(f301(x104155),f751(x104153,x104152,x104157,x104154,x104151,x104156,x104155)),f181(f932(x104155,a921)))),f761(x104153,x104152,x104157,x104154,x104151,x104156,x104155))+E(f862(f862(x104151,x104152),x104153),x104154) % 14.98/14.67 [10435]~P1(f862(x104351,f862(f862(x104355,f796(x104354,x104355,x104351,x104356,x104353,x104352,x104357)),f795(x104354,x104355,x104351,x104356,x104353,x104352,x104357))))+~P1(f862(f862(x104357,f862(f248(x104352,x104353),x104356)),f862(f243(x104352,x104353),x104356)))+P1(f862(x104351,f862(f862(f249(x104352,x104353,x104354),x104355),x104356))) % 14.98/14.67 [9733]P1(f862(f862(f227(f932(f931(x97331,x97332),a921)),f862(f862(f280(x97331,x97333,x97332),x97334),x97335)),f862(f862(f280(x97331,x97333,x97332),x97336),x97337)))+~P1(f862(f862(f227(f932(f931(x97333,x97332),a921)),x97335),x97337))+~P1(f862(f862(f227(f932(f931(x97331,x97333),a921)),x97334),x97336)) % 14.98/14.67 [10462]E(f862(f862(f244(x104621,x104622),x104623),x104624),f862(f862(f244(x104621,x104622),x104625),x104626))+~P1(f862(f862(f321(f931(f931(x104621,x104622),f931(x104621,x104622))),f862(f862(f244(f931(x104621,x104622),f931(x104621,x104622)),f862(f862(f244(x104621,x104622),x104623),x104624)),f862(f862(f244(x104621,x104622),x104625),x104626))),f299(f931(x104621,x104622),x104627)))+P1(f862(f862(f321(f931(f931(x104621,x104622),f931(x104621,x104622))),f862(f862(f244(f931(x104621,x104622),f931(x104621,x104622)),f862(f862(f244(x104621,x104622),x104623),x104624)),f862(f862(f244(x104621,x104622),f849(x104627,x104626,x104625,x104624,x104623,x104622,x104621)),f850(x104627,x104626,x104625,x104624,x104623,x104622,x104621)))),x104627)) % 14.98/14.67 [10064]~P1(f862(f862(f321(x100641),x100646),x100645))+P1(f862(f59(x100641,x100642,x100643,x100644,x100645),f862(f862(x100643,x100646),x100647)))+~P1(f862(f59(x100641,x100642,x100643,x100644,f862(f862(f3(f932(x100641,a921)),x100645),f862(f862(f301(x100641),x100646),f181(f932(x100641,a921))))),x100647)) % 14.98/14.67 [10475]~P146(x104751)+~P22(f931(x104752,x104753),x104751,f862(f249(x104752,x104753,x104751),f862(f862(f9(x104752,f932(x104753,x104751),f932(x104753,x104751)),f862(f862(f10(f932(x104751,x104751),f932(f932(x104753,x104751),f932(x104753,x104751)),x104752),f10(x104751,x104751,x104753)),f862(f862(f10(x104751,f932(x104751,x104751),x104752),f74(x104751)),x104754))),x104755)),f862(f862(f246(x104752,x104753),x104756),f862(f18(f932(x104753,a921),x104752),x104757)))+E(f862(f862(f8(x104751,x104751),f25(x104751)),f862(f254(x104751),f862(f862(f10(f932(x104752,a921),a921,x104751),f80(x104752)),f862(f862(f10(f932(x104752,f932(x104753,a921)),f932(x104752,a921),x104751),f862(f10(f932(x104753,a921),a921,x104752),f80(x104753))),f862(f862(f9(x104751,f932(x104752,f932(x104753,a921)),f932(x104752,f932(x104753,a921))),f862(f862(f10(f932(x104752,f932(f932(x104753,a921),f932(x104753,a921))),f932(f932(x104752,f932(x104753,a921)),f932(x104752,f932(x104753,a921))),x104751),f20(x104752,f932(x104753,a921),f932(x104753,a921))),f862(f862(f10(f932(x104752,f932(x104753,f932(a921,a921))),f932(x104752,f932(f932(x104753,a921),f932(x104753,a921))),x104751),f862(f10(f932(x104753,f932(a921,a921)),f932(f932(x104753,a921),f932(x104753,a921)),x104752),f20(x104753,a921,a921))),f862(f862(f10(f932(x104752,f932(x104753,a921)),f932(x104752,f932(x104753,f932(a921,a921))),x104751),f862(f10(f932(x104753,a921),f932(x104753,f932(a921,a921)),x104752),f862(f10(a921,f932(a921,a921),x104753),a318))),f862(f862(f9(x104751,f932(x104752,f932(x104753,x104751)),f932(x104752,f932(x104753,a921))),f862(f862(f10(f932(f932(x104753,x104751),f932(x104753,a921)),f932(f932(x104752,f932(x104753,x104751)),f932(x104752,f932(x104753,a921))),x104751),f10(f932(x104753,x104751),f932(x104753,a921),x104752)),f862(f862(f10(f932(x104751,a921),f932(f932(x104753,x104751),f932(x104753,a921)),x104751),f10(x104751,a921,x104753)),a317))),f862(f862(f9(x104752,f932(x104753,x104751),f932(x104753,x104751)),f862(f862(f10(f932(x104751,x104751),f932(f932(x104753,x104751),f932(x104753,x104751)),x104752),f10(x104751,x104751,x104753)),f862(f862(f10(x104751,f932(x104751,x104751),x104752),f74(x104751)),x104754))),x104755)))))),f862(f862(f9(x104752,f932(x104753,a921),f932(x104753,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104753,a921),f932(x104753,a921)),x104752),f10(a921,a921,x104753)),f862(f862(f10(a921,f932(a921,a921),x104752),a318),f862(f862(f9(x104752,f932(x104752,a921),a921),f321(x104752)),x104756)))),f862(f862(f9(x104753,f932(x104753,a921),a921),f321(x104753)),x104757))))))),f862(f862(f74(x104751),f862(f862(f8(x104752,x104751),x104754),x104756)),f862(f862(f8(x104753,x104751),x104755),x104757))) % 14.98/14.67 [9737]~P23(x97371,x97373,x97375,x97376,x97378)+~P23(x97373,x97372,x97374,x97378,x97377)+P23(x97371,x97372,f862(f66(x97373,x97372,x97371,x97374),x97375),x97376,x97377) % 14.98/14.67 [9766]P23(x97661,x97662,x97663,x97664,x97665)+~P23(x97666,x97661,x97667,x97668,x97664)+~P23(x97666,x97662,f862(f66(x97661,x97662,x97666,x97663),x97667),x97668,x97665) % 14.98/14.67 [9898]~P1(f862(f862(x98984,x98986),x98988))+~P1(f862(f862(x98985,x98988),x98987))+P1(f862(f862(f245(x98981,x98982,x98983,x98984,x98985),x98986),x98987)) % 14.98/14.67 [9491]~P17(x94918,x94911,x94913,x94915)+~P1(f862(f54(x94918),x94916))+E(f862(f66(x94911,x94911,x94912,f862(x94913,x94914)),f862(f66(x94911,x94911,x94912,f862(x94915,x94916)),x94917)),f862(f66(x94911,x94911,x94912,f862(x94915,x94916)),f862(f66(x94911,x94911,x94912,f862(x94913,x94914)),x94917))) % 14.98/14.67 [9888]~P20(x98887,x98882,x98885,x98888,x98886,x98881)+~P1(f862(f54(x98882),x98884))+E(f862(x98881,f862(f862(f301(x98882),x98883),x98884)),f862(f862(x98885,f862(x98886,x98883)),f862(x98881,x98884))) % 14.98/14.67 [10009]~P22(x100092,x100094,x100096,x100098)+~P22(x100091,x100093,x100095,x100097)+P22(f931(x100091,x100092),f931(x100093,x100094),f250(x100091,x100093,x100092,x100094,x100095,x100096),f862(f862(f246(x100091,x100092),x100097),f862(f18(f932(x100092,a921),x100091),x100098))) % 14.98/14.67 [9679]P1(f862(f862(f321(f931(x96791,x96792)),f862(f862(f244(x96791,x96792),x96793),x96794)),f862(f862(f280(x96791,x96795,x96792),x96796),x96797)))+~P1(f862(f862(f321(f931(x96791,x96795)),f862(f862(f244(x96791,x96795),x96793),x96798)),x96796))+~P1(f862(f862(f321(f931(x96795,x96792)),f862(f862(f244(x96795,x96792),x96798),x96794)),x96797)) % 14.98/14.67 [9869]~P1(f862(f862(f227(f932(f931(x98693,x98692),a921)),x98695),f862(f862(f246(x98693,x98692),x98698),f862(f18(f932(x98692,a921),x98693),x98697))))+~P1(f862(f862(f227(f932(f931(x98691,x98693),a921)),x98694),f862(f862(f246(x98691,x98693),x98696),f862(f18(f932(x98693,a921),x98691),x98698))))+P1(f862(f862(f227(f932(f931(x98691,x98692),a921)),f862(f862(f280(x98691,x98693,x98692),x98694),x98695)),f862(f862(f246(x98691,x98692),x98696),f862(f18(f932(x98692,a921),x98691),x98697)))) % 14.98/14.67 [9923]~E(x99233,x99235)+P1(f862(f862(f321(f931(f931(x99231,x99232),f931(x99231,x99232))),f862(f862(f244(f931(x99231,x99232),f931(x99231,x99232)),f862(f862(f244(x99231,x99232),x99233),x99234)),f862(f862(f244(x99231,x99232),x99235),x99236))),f311(x99231,x99232,x99237,x99238)))+~P1(f862(f862(f321(f931(x99232,x99232)),f862(f862(f244(x99232,x99232),x99234),x99236)),x99238)) % 14.98/14.67 [10028]E(x100281,x100282)+~P1(f862(f862(f321(f931(f931(x100283,x100285),f931(x100283,x100285))),f862(f862(f244(f931(x100283,x100285),f931(x100283,x100285)),f862(f862(f244(x100283,x100285),x100281),x100286)),f862(f862(f244(x100283,x100285),x100282),x100287))),f311(x100283,x100285,x100284,x100288)))+P1(f862(f862(f321(f931(x100283,x100283)),f862(f862(f244(x100283,x100283),x100281),x100282)),x100284)) % 14.98/14.67 [10043]~P1(f862(f862(f321(f931(f931(x100431,x100435),f931(x100431,x100435))),f862(f862(f244(f931(x100431,x100435),f931(x100431,x100435)),f862(f862(f244(x100431,x100435),x100432),x100436)),f862(f862(f244(x100431,x100435),x100433),x100437))),f311(x100431,x100435,x100434,x100438)))+P1(f862(f862(f321(f931(x100431,x100431)),f862(f862(f244(x100431,x100431),x100432),x100433)),x100434))+P1(f862(f862(f321(f931(x100435,x100435)),f862(f862(f244(x100435,x100435),x100436),x100437)),x100438)) % 14.98/14.67 [9958]~P21(x99587,x99585,x99581,x99588,x99582,x99584)+~P1(f862(f54(x99585),x99586))+E(f862(f862(x99581,f862(x99582,x99583)),f862(x99584,f862(f862(f3(f932(x99585,a921)),x99586),f862(f862(f301(x99585),x99583),f181(f932(x99585,a921)))))),f862(x99584,f862(f862(f301(x99585),x99583),x99586))) % 14.98/14.67 [9445]~P1(f862(f862(f862(x94455,x94458),x94456),x94457))+~P1(f862(f862(f321(x94451),x94458),x94454))+P1(f862(f862(f862(f862(f33(x94451,f932(x94452,f932(x94453,a921))),x94454),x94455),x94456),x94457)) % 14.98/14.67 [9664]P1(f862(f862(f862(x96641,x96642),x96643),x96644))+~P1(f862(f862(f321(x96645),x96642),x96646))+~P1(f862(f862(f862(f862(f32(x96645,f932(x96647,f932(x96648,a921))),x96646),x96641),x96643),x96644)) % 14.98/14.67 [9862]~P19(x98623,x98622,x98624,x98628,x98621)+~P1(f862(f54(x98622),x98627))+E(f862(f862(x98621,f862(f862(f20(x98622,x98623,x98623),f862(f862(f10(x98623,f932(x98623,x98623),x98622),x98624),x98625)),x98626)),x98627),f862(f862(x98624,f862(f862(x98621,x98625),x98627)),f862(f862(x98621,x98626),x98627))) % 14.98/14.67 [10132]~E(f862(f302(x101322,x101324,x101326),x101328),x1013210)+~E(f862(f302(x101321,x101323,x101325),x101327),x101329)+E(f862(f302(f931(x101321,x101322),f931(x101323,x101324),f250(x101321,x101323,x101322,x101324,x101325,x101326)),f862(f862(f246(x101321,x101322),x101327),f862(f18(f932(x101322,a921),x101321),x101328))),f862(f862(f246(x101323,x101324),x101329),f862(f18(f932(x101324,a921),x101323),x1013210))) % 14.98/14.67 [5052]~P46(x50521,x50522)+~P47(x50521,x50522)+~P48(x50521,x50522)+P5(x50521,x50522) % 14.98/14.67 [5008]~P109(x50082)+~P11(x50082,x50081)+P11(x50082,f107(x50082,x50081))+E(x50081,f106(x50082)) % 14.98/14.67 [5009]~P109(x50092)+~P11(x50092,x50091)+P11(x50092,f714(x50091,x50092))+E(x50091,f106(x50092)) % 14.98/14.67 [5258]~P3(x52582)+E(f12(x52582,x52581),f31(x52582,x52581))+E(x52581,f181(f932(x52582,a921)))+~P1(f862(f54(x52582),x52581)) % 14.98/14.67 [5259]~P3(x52592)+E(f15(x52592,x52591),f30(x52592,x52591))+E(x52591,f181(f932(x52592,a921)))+~P1(f862(f54(x52592),x52591)) % 14.98/14.67 [5418]~P109(x54182)+~P11(x54182,x54181)+E(x54181,f106(x54182))+E(f862(f862(f144(x54182),f733(x54181,x54182)),f714(x54181,x54182)),x54181) % 14.98/14.67 [6239]~P93(x62392)+E(x62391,f181(f932(x62392,a921)))+P1(f862(f862(f227(x62392),f12(x62392,x62391)),f15(x62392,x62391)))+~P1(f862(f54(x62392),x62391)) % 14.98/14.67 [6248]~P38(x62482)+~P38(x62481)+E(x62481,x62482)+~E(f862(f302(a1,a924,a97),x62481),f862(f302(a1,a924,a97),x62482)) % 14.98/14.67 [9301]~P112(x93011)+~P1(f862(f862(f321(x93011),x93012),f102(x93011)))+P1(f862(f862(f228(x93011),f862(f862(f73(x93011),f862(f862(f73(x93011),f71(x93011)),x93012)),x93012)),f2(x93011)))+~P1(f862(f862(f228(x93011),x93012),f2(x93011))) % 14.98/14.67 [9545]~P112(x95451)+~P1(f862(f862(f321(x95451),x95452),f102(x95451)))+~P1(f862(f862(f228(x95451),f862(f862(f73(x95451),f862(f862(f73(x95451),f71(x95451)),x95452)),x95452)),f2(x95451)))+P1(f862(f862(f228(x95451),x95452),f2(x95451))) % 14.98/14.67 [5067]~P116(x50672)+~P146(x50672)+E(x50671,f2(a924))+E(f862(f862(f236(x50672),f2(x50672)),x50671),f2(x50672)) % 14.98/14.67 [5070]~P116(x50701)+~P146(x50701)+~E(x50702,f2(a924))+E(f862(f862(f236(x50701),f2(x50701)),x50702),f71(x50701)) % 14.98/14.67 [5244]~P141(x52442)+E(x52441,f71(x52442))+E(x52441,f862(f72(x52442),f71(x52442)))+~E(f862(f862(f74(x52442),x52441),x52441),f71(x52442)) % 14.98/14.67 [5495]~P88(x54952)+E(x54951,f2(x54952))+E(f75(x54952,x54951),f862(f72(x54952),f71(x54952)))+P1(f862(f862(f228(x54952),f2(x54952)),x54951)) % 14.98/14.67 [5739]~P88(x57392)+E(f75(x57392,x57391),f71(x57392))+E(x57391,f2(x57392))+~P1(f862(f862(f228(x57392),f2(x57392)),x57391)) % 14.98/14.67 [5749]E(x57491,x57492)+~E(f862(f96(a924),x57491),f862(f96(a924),x57492))+P1(f862(a186,f862(f96(a1),x57492)))+P1(f862(a186,f862(f96(a1),x57491))) % 14.98/14.67 [5801]~P97(x58011)+~E(x58012,f2(x58011))+E(f862(f862(f73(x58011),x58012),x58012),f2(x58011))+~P1(f862(f862(f321(x58011),x58012),f102(x58011))) % 14.98/14.67 [5840]E(x58401,f2(a1))+~E(f862(f862(f29(a1),x58402),x58401),f2(a1))+P1(f862(f862(f228(a1),x58401),x58402))+P1(f862(f862(f228(a1),x58402),x58401)) % 14.98/14.67 [5870]E(x58701,f2(a1))+~E(f862(f862(f29(a1),x58702),x58701),f2(a1))+P1(f862(f862(f227(a1),x58702),f2(a1)))+P1(f862(f862(f228(a1),x58702),x58701)) % 14.98/14.67 [5904]E(x59041,f2(a1))+~E(f862(f862(f29(a1),x59042),x59041),f2(a1))+P1(f862(f862(f227(a1),f2(a1)),x59042))+P1(f862(f862(f228(a1),x59041),x59042)) % 14.98/14.67 [5939]~P97(x59392)+E(x59391,f2(x59392))+~E(f862(f862(f73(x59392),x59391),x59391),f2(x59392))+~P1(f862(f862(f321(x59392),x59391),f102(x59392))) % 14.98/14.67 [6008]E(f862(f96(a924),x60081),f862(f96(a924),x60082))+~E(f862(f96(a1),x60082),f2(a1))+P1(f862(a186,f862(f96(a1),x60082)))+~P1(f862(a186,f862(f96(a1),x60081))) % 14.98/14.67 [6037]~E(f862(f96(a924),x60372),f862(f96(a924),x60371))+E(f862(f96(a1),x60371),f2(a1))+P1(f862(a186,f862(f96(a1),x60371)))+~P1(f862(a186,f862(f96(a1),x60372))) % 14.98/14.67 [6047]~P109(x60472)+E(x60471,f181(f932(x60472,a921)))+~P1(f862(f54(x60472),x60471))+P1(f862(f862(f321(x60472),f16(x60472,x60471)),x60471)) % 14.98/14.67 [6048]~P109(x60482)+E(x60481,f181(f932(x60482,a921)))+~P1(f862(f54(x60482),x60481))+P1(f862(f862(f321(x60482),f17(x60482,x60481)),x60481)) % 14.98/14.67 [6216]~P112(x62161)+~P98(x62161)+P1(f862(f862(f227(x62161),f2(x62161)),f862(f96(x62161),x62162)))+~P1(f862(f862(f227(a1),a76),x62162)) % 14.98/14.67 [6217]~P112(x62171)+~P98(x62171)+P1(f862(f862(f228(x62171),f2(x62171)),f862(f96(x62171),x62172)))+~P1(f862(f862(f228(a1),a76),x62172)) % 14.98/14.67 [6238]~P112(x62381)+~P98(x62381)+E(f862(f69(x62381),f862(f96(x62381),x62382)),f862(f96(x62381),x62382))+P1(f862(f862(f228(x62381),f862(f96(x62381),x62382)),f2(x62381))) % 14.98/14.67 [6272]E(x62721,x62722)+~E(f862(a97,x62721),f862(a97,x62722))+~P1(f862(f862(f227(a1),f2(a1)),x62722))+~P1(f862(f862(f227(a1),f2(a1)),x62721)) % 14.98/14.67 [6467]~P98(x64672)+~P112(x64672)+~P1(f862(f862(f227(x64672),f2(x64672)),f862(f96(x64672),x64671)))+P1(f862(f862(f227(a1),a76),x64671)) % 14.98/14.67 [6468]~P98(x64682)+~P112(x64682)+~P1(f862(f862(f228(x64682),f2(x64682)),f862(f96(x64682),x64681)))+P1(f862(f862(f228(a1),a76),x64681)) % 14.98/14.67 [6473]~P112(x64731)+~P98(x64731)+P1(f862(f862(f227(x64731),f862(f96(x64731),x64732)),f2(x64731)))+~P1(f862(f862(f227(a1),x64732),a76)) % 14.98/14.67 [6474]~P112(x64741)+~P98(x64741)+P1(f862(f862(f228(x64741),f862(f96(x64741),x64742)),f2(x64741)))+~P1(f862(f862(f228(a1),x64742),a76)) % 14.98/14.67 [6794]~P98(x67942)+~P112(x67942)+~P1(f862(f862(f227(x67942),f862(f96(x67942),x67941)),f2(x67942)))+P1(f862(f862(f227(a1),x67941),a76)) % 14.98/14.67 [6795]~P98(x67952)+~P112(x67952)+~P1(f862(f862(f228(x67952),f862(f96(x67952),x67951)),f2(x67952)))+P1(f862(f862(f228(a1),x67951),a76)) % 14.98/14.67 [6885]~P112(x68851)+~P98(x68851)+E(f862(f69(x68851),f862(f96(x68851),x68852)),f862(f72(x68851),f862(f96(x68851),x68852)))+~P1(f862(f862(f228(x68851),f862(f96(x68851),x68852)),f2(x68851))) % 14.98/14.67 [6903]E(f862(f96(a924),x69031),f862(f96(a924),x69032))+~E(f862(f96(a1),x69032),f2(a1))+~P1(f862(f862(f227(a1),f862(f96(a1),x69031)),f2(a1)))+~P1(f862(a186,f862(f96(a1),x69031))) % 14.98/14.67 [7789]~P109(x77892)+E(x77891,f181(f932(x77892,a921)))+~P1(f862(f54(x77892),x77891))+P1(f862(f862(f227(x77892),f13(x77892,f225(x77892),x77891)),f14(x77892,f226(x77892),x77891))) % 14.98/14.67 [8109]~P4(x81091)+~P38(x81092)+P1(f862(f862(f321(a1),x81091),x81092))+~P1(f862(f862(f321(a924),f862(a97,x81091)),f862(f302(a1,a924,a97),x81092))) % 14.98/14.67 [6043]~P142(x60432)+E(x60431,f2(a1))+E(f862(f72(x60432),f862(f95(x60432),f862(f72(a1),x60431))),f862(f95(x60432),x60431))+~P1(f862(f862(f228(a1),x60431),f2(a1))) % 14.98/14.67 [6121]~P97(x61211)+~P98(x61211)+~P26(x61211,f862(f96(x61211),x61212))+P26(x61211,f862(f96(x61211),f862(f862(f73(a1),x61212),x61212))) % 14.98/14.67 [6456]~P76(x64562)+E(x64561,f181(f932(x64562,a921)))+E(f17(x64562,f862(f302(x64562,x64562,f72(x64562)),x64561)),f862(f72(x64562),f16(x64562,x64561)))+~P1(f862(f54(x64562),x64561)) % 14.98/14.67 [6457]~P76(x64572)+E(x64571,f181(f932(x64572,a921)))+E(f16(x64572,f862(f302(x64572,x64572,f72(x64572)),x64571)),f862(f72(x64572),f17(x64572,x64571)))+~P1(f862(f54(x64572),x64571)) % 14.98/14.67 [6490]~P97(x64901)+~P98(x64901)+P26(x64901,f862(f96(x64901),x64902))+~P26(x64901,f862(f96(x64901),f862(f862(f73(a1),x64902),x64902))) % 14.98/14.67 [6584]E(x65841,f2(a1))+E(f862(a44,f43(f862(f72(a1),x65841),f862(f72(a1),x65842))),f39(x65841,x65842))+P1(f862(f862(f227(a1),f2(a1)),x65842))+~P1(f862(f862(f227(a1),f2(a1)),x65841)) % 14.98/14.67 [8901]~P38(x89012)+~P38(x89011)+P1(f862(f862(f228(f932(a924,a921)),f862(f302(a1,a924,a97),x89011)),f862(f302(a1,a924,a97),x89012)))+~P1(f862(f862(f228(f932(a1,a921)),x89011),x89012)) % 14.98/14.67 [9134]~E(f737(x91342,x91341),f738(x91342,x91341))+~P1(f862(f130(x91341),f736(x91342,x91341)))+~P1(f862(f130(f925(x91341)),x91342))+P1(f862(f130(x91341),f862(f135(f925(x91341),f925(x91341),f127(x91341),f106(x91341)),x91342))) % 14.98/14.67 [9220]~P38(x92202)+~P38(x92201)+~P1(f862(f862(f227(f932(a924,a921)),f862(f302(a1,a924,a97),x92201)),f862(f302(a1,a924,a97),x92202)))+P1(f862(f862(f227(f932(a1,a921)),x92201),x92202)) % 14.98/14.67 [9221]~P38(x92212)+~P38(x92211)+~P1(f862(f862(f228(f932(a924,a921)),f862(f302(a1,a924,a97),x92211)),f862(f302(a1,a924,a97),x92212)))+P1(f862(f862(f228(f932(a1,a921)),x92211),x92212)) % 14.98/14.67 [9227]~E(f737(x92272,x92271),f738(x92272,x92271))+~P1(f862(f130(f925(x92271)),x92272))+P1(f862(f130(x92271),f862(f135(f925(x92271),f925(x92271),f127(x92271),f106(x92271)),x92272)))+P1(f862(f862(f321(f925(x92271)),f736(x92272,x92271)),f862(f165(f925(x92271)),x92272))) % 14.98/14.67 [9268]~P1(f862(f130(x92681),f736(x92682,x92681)))+~P1(f862(f130(f925(x92681)),x92682))+P1(f862(f130(x92681),f862(f135(f925(x92681),f925(x92681),f127(x92681),f106(x92681)),x92682)))+P1(f862(f862(f321(f925(x92681)),f738(x92682,x92681)),f862(f165(f925(x92681)),x92682))) % 14.98/14.67 [9269]~P1(f862(f130(x92691),f736(x92692,x92691)))+~P1(f862(f130(f925(x92691)),x92692))+P1(f862(f130(x92691),f862(f135(f925(x92691),f925(x92691),f127(x92691),f106(x92691)),x92692)))+P1(f862(f862(f321(f925(x92691)),f737(x92692,x92691)),f862(f165(f925(x92691)),x92692))) % 14.98/14.67 [9348]~P1(f862(f130(f925(x93481)),x93482))+P1(f862(f130(x93481),f862(f135(f925(x93481),f925(x93481),f127(x93481),f106(x93481)),x93482)))+P1(f862(f862(f321(f925(x93481)),f738(x93482,x93481)),f862(f165(f925(x93481)),x93482)))+P1(f862(f862(f321(f925(x93481)),f736(x93482,x93481)),f862(f165(f925(x93481)),x93482))) % 14.98/14.67 [9349]~P1(f862(f130(f925(x93491)),x93492))+P1(f862(f130(x93491),f862(f135(f925(x93491),f925(x93491),f127(x93491),f106(x93491)),x93492)))+P1(f862(f862(f321(f925(x93491)),f737(x93492,x93491)),f862(f165(f925(x93491)),x93492)))+P1(f862(f862(f321(f925(x93491)),f736(x93492,x93491)),f862(f165(f925(x93491)),x93492))) % 14.98/14.67 [9363]~E(f862(f862(f94(f932(x93631,a921)),f862(f165(x93631),f738(x93632,x93631))),f862(f165(x93631),f737(x93632,x93631))),f181(f932(x93631,a921)))+~P1(f862(f130(x93631),f736(x93632,x93631)))+~P1(f862(f130(f925(x93631)),x93632))+P1(f862(f130(x93631),f862(f135(f925(x93631),f925(x93631),f127(x93631),f106(x93631)),x93632))) % 14.98/14.67 [9426]~E(f862(f862(f94(f932(x94261,a921)),f862(f165(x94261),f738(x94262,x94261))),f862(f165(x94261),f737(x94262,x94261))),f181(f932(x94261,a921)))+~P1(f862(f130(f925(x94261)),x94262))+P1(f862(f130(x94261),f862(f135(f925(x94261),f925(x94261),f127(x94261),f106(x94261)),x94262)))+P1(f862(f862(f321(f925(x94261)),f736(x94262,x94261)),f862(f165(f925(x94261)),x94262))) % 14.98/14.67 [9706]E(x97061,f2(a1))+E(x97062,f2(a1))+E(f862(f862(f79(a1,f931(a1,a1)),f862(f862(a210,x97062),x97061)),f862(f862(f20(a1,a1,f931(a1,a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f29(a1),x97062))),f862(f29(a1),x97061))),f208(x97062,x97061))+P1(f862(f862(f228(a1),x97061),f2(a1))) % 14.98/14.67 [8441]~P98(x84412)+~P112(x84412)+~P1(f862(f862(f227(x84412),f862(f96(x84412),x84411)),f71(x84412)))+P1(f862(f862(f227(a1),x84411),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))) % 14.98/14.67 [8442]~P98(x84422)+~P112(x84422)+~P1(f862(f862(f228(x84422),f862(f96(x84422),x84421)),f71(x84422)))+P1(f862(f862(f228(a1),x84421),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))) % 14.98/14.67 [8715]~P112(x87151)+~P98(x87151)+P1(f862(f862(f227(x87151),f862(f96(x87151),x87152)),f71(x87151)))+~P1(f862(f862(f227(a1),x87152),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))) % 14.98/14.67 [8716]~P112(x87161)+~P98(x87161)+P1(f862(f862(f228(x87161),f862(f96(x87161),x87162)),f71(x87161)))+~P1(f862(f862(f228(a1),x87162),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))) % 14.98/14.67 [8929]~P98(x89292)+~P112(x89292)+~P1(f862(f862(f227(x89292),f71(x89292)),f862(f96(x89292),x89291)))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x89291)) % 14.98/14.67 [8930]~P98(x89302)+~P112(x89302)+~P1(f862(f862(f228(x89302),f71(x89302)),f862(f96(x89302),x89301)))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x89301)) % 14.98/14.67 [9307]~P112(x93071)+~P98(x93071)+P1(f862(f862(f227(x93071),f71(x93071)),f862(f96(x93071),x93072)))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x93072)) % 14.98/14.67 [9308]~P112(x93081)+~P98(x93081)+P1(f862(f862(f228(x93081),f71(x93081)),f862(f96(x93081),x93082)))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x93082)) % 14.98/14.67 [9835]~P141(x98352)+E(x98351,f71(x98352))+E(x98351,f862(f72(x98352),f71(x98352)))+~E(f862(f862(f236(x98352),x98351),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(x98352)) % 14.98/14.67 [10108]~P66(x101081)+~P98(x101081)+~P1(f862(f862(f228(x101081),f2(x101081)),x101082))+P1(f862(f862(f228(x101081),f2(x101081)),f862(f862(f281(x101081),x101082),f862(f96(x101081),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.67 [10160]~P66(x101601)+~P98(x101601)+P1(f862(f862(f228(x101601),f2(x101601)),x101602))+~P1(f862(f862(f228(x101601),f2(x101601)),f862(f862(f281(x101601),x101602),f862(f96(x101601),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.67 [10442]~P142(x104422)+E(x104421,f2(a1))+P1(f862(f862(f228(a1),x104421),f2(a1)))+E(f862(f862(f249(a1,a1,x104422),f862(f862(f9(a1,f932(a1,f932(x104422,x104422)),f932(a1,x104422)),f862(f862(f10(f932(f932(x104422,x104422),x104422),f932(f932(a1,f932(x104422,x104422)),f932(a1,x104422)),a1),f10(f932(x104422,x104422),x104422,a1)),f862(f862(f10(x104422,f932(f932(x104422,x104422),x104422),a1),f79(x104422,x104422)),f95(x104422)))),f862(f862(f9(a1,f932(x104422,x104422),f932(x104422,x104422)),f862(f862(f10(f932(x104422,f932(x104422,x104422)),f932(f932(x104422,x104422),f932(x104422,x104422)),a1),f20(x104422,x104422,x104422)),f862(f862(f9(a1,f932(x104422,x104422),f932(x104422,f932(x104422,x104422))),f862(f862(f10(f932(x104422,f932(x104422,x104422)),f932(f932(x104422,x104422),f932(x104422,f932(x104422,x104422))),a1),f10(x104422,f932(x104422,x104422),x104422)),f862(f862(f10(a921,f932(x104422,f932(x104422,x104422)),a1),f89(x104422)),f862(f862(f9(a1,a1,a921),a317),f2(a1))))),f862(f862(f20(x104422,x104422,x104422),f73(x104422)),f7(x104422))))),f862(f862(f9(x104422,x104422,x104422),f862(f862(f10(x104422,f932(x104422,x104422),x104422),f73(x104422)),f862(f862(f20(x104422,x104422,x104422),f73(x104422)),f7(x104422)))),f71(x104422))))),f39(x104421,f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f95(x104422),x104421)) % 14.98/14.67 [5504]~P36(x55041,x55043)+~P49(x55041,x55043)+~P50(x55041,x55042,x55043)+P6(x55041,x55042,x55043) % 14.98/14.67 [5036]~P97(x50363)+~P98(x50363)+E(x50361,x50362)+~E(f862(f96(x50363),x50361),f862(f96(x50363),x50362)) % 14.98/14.67 [5514]~P47(x55141,x55142)+~P48(x55141,x55142)+P13(x55141,x55142)+~P1(f862(f862(x55142,x55143),x55143)) % 14.98/14.67 [6023]P13(x60232,x60231)+E(f862(x60231,f811(x60231)),f862(x60231,f813(x60231)))+P1(f862(f862(x60231,f811(x60231)),f813(x60231)))+~P1(f862(f862(x60231,x60233),x60233)) % 14.98/14.67 [6226]~P1(f862(x62261,x62262))+~P1(f862(x62261,x62263))+~P1(f862(f862(f227(a924),x62263),f360(x62262,x62261)))+P1(f862(x62261,f2(a924))) % 14.98/14.67 [6291]P13(x62911,x62912)+P1(f862(f862(x62912,f811(x62912)),f811(x62912)))+P1(f862(f862(x62912,f811(x62912)),f813(x62912)))+~P1(f862(f862(x62912,x62913),x62913)) % 14.98/14.67 [6292]P13(x62921,x62922)+P1(f862(f862(x62922,f811(x62922)),f813(x62922)))+P1(f862(f862(x62922,f813(x62922)),f813(x62922)))+~P1(f862(f862(x62922,x62923),x62923)) % 14.98/14.67 [6650]P149(x66502,x66501,x66503)+E(x66501,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f868(x66503,x66501,x66502)))+P1(f862(f862(f228(a1),x66501),f2(a1))) % 14.98/14.67 [6651]P148(x66512,x66511,x66513)+E(x66511,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f873(x66513,x66511,x66512)))+P1(f862(f862(f228(a1),x66511),f2(a1))) % 14.98/14.67 [6775]P148(x67751,x67752,x67753)+~P1(f862(x67751,x67753))+P1(f862(f862(f227(a1),f2(a1)),f873(x67753,x67752,x67751)))+P1(f862(f862(f228(a1),x67752),f2(a1))) % 14.98/14.67 [6800]P149(x68001,x68002,x68003)+P1(f862(f862(f227(a1),f2(a1)),f868(x68003,x68002,x68001)))+~P1(f862(x68001,f2(a1)))+P1(f862(f862(f228(a1),x68002),f2(a1))) % 14.98/14.67 [6828]P149(x68282,x68281,x68283)+E(x68281,f2(a1))+~P1(f862(x68282,f869(x68283,x68281,x68282)))+P1(f862(f862(f228(a1),x68281),f2(a1))) % 14.98/14.67 [6829]P148(x68292,x68291,x68293)+E(x68291,f2(a1))+~P1(f862(x68292,f873(x68293,x68291,x68292)))+P1(f862(f862(f228(a1),x68291),f2(a1))) % 14.98/14.67 [6927]~P3(x69271)+~P109(x69271)+~P1(f862(f862(f228(x69271),x69272),f30(x69271,x69273)))+P1(f862(f862(f228(x69271),x69272),f724(x69273,x69272,x69271))) % 14.98/14.67 [6937]P148(x69371,x69372,x69373)+~P1(f862(x69371,x69373))+~P1(f862(x69371,f873(x69373,x69372,x69371)))+P1(f862(f862(f228(a1),x69372),f2(a1))) % 14.98/14.67 [6970]P149(x69701,x69702,x69703)+~P1(f862(x69701,f869(x69703,x69702,x69701)))+~P1(f862(x69701,f2(a1)))+P1(f862(f862(f228(a1),x69702),f2(a1))) % 14.98/14.67 [7218]P149(x72182,x72181,x72183)+E(x72181,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f868(x72183,x72181,x72182)))+P1(f862(f862(f228(a1),x72181),f867(x72183,x72181,x72182))) % 14.98/14.67 [7219]P148(x72192,x72191,x72193)+E(x72191,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f873(x72193,x72191,x72192)))+P1(f862(f862(f228(a1),x72191),f872(x72193,x72191,x72192))) % 14.98/14.67 [7340]P148(x73401,x73402,x73403)+~P1(f862(x73401,x73403))+P1(f862(f862(f227(a1),f2(a1)),f873(x73403,x73402,x73401)))+P1(f862(f862(f228(a1),x73402),f872(x73403,x73402,x73401))) % 14.98/14.67 [7361]P149(x73611,x73612,x73613)+P1(f862(f862(f227(a1),f2(a1)),f868(x73613,x73612,x73611)))+P1(f862(f862(f228(a1),x73612),f867(x73613,x73612,x73611)))+~P1(f862(x73611,f2(a1))) % 14.98/14.67 [7393]P149(x73932,x73931,x73933)+E(x73931,f2(a1))+~P1(f862(x73932,f869(x73933,x73931,x73932)))+P1(f862(f862(f228(a1),x73931),f867(x73933,x73931,x73932))) % 14.98/14.67 [7394]P148(x73942,x73941,x73943)+E(x73941,f2(a1))+~P1(f862(x73942,f873(x73943,x73941,x73942)))+P1(f862(f862(f228(a1),x73941),f872(x73943,x73941,x73942))) % 14.98/14.67 [7439]P149(x74392,x74391,x74393)+E(x74391,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f868(x74393,x74391,x74392)))+~P1(f862(x74392,f871(x74393,x74391,x74392))) % 14.98/14.67 [7440]P148(x74402,x74401,x74403)+E(x74401,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f873(x74403,x74401,x74402)))+~P1(f862(x74402,f872(x74403,x74401,x74402))) % 14.98/14.67 [7539]P148(x75391,x75392,x75393)+~P1(f862(x75391,x75393))+~P1(f862(x75391,f873(x75393,x75392,x75391)))+P1(f862(f862(f228(a1),x75392),f872(x75393,x75392,x75391))) % 14.98/14.67 [7555]P149(x75551,x75552,x75553)+~P1(f862(x75551,f869(x75553,x75552,x75551)))+P1(f862(f862(f228(a1),x75552),f867(x75553,x75552,x75551)))+~P1(f862(x75551,f2(a1))) % 14.98/14.67 [7558]P148(x75581,x75582,x75583)+~P1(f862(x75581,x75583))+P1(f862(f862(f227(a1),f2(a1)),f873(x75583,x75582,x75581)))+~P1(f862(x75581,f872(x75583,x75582,x75581))) % 14.98/14.67 [7574]P149(x75741,x75742,x75743)+P1(f862(f862(f227(a1),f2(a1)),f868(x75743,x75742,x75741)))+~P1(f862(x75741,f871(x75743,x75742,x75741)))+~P1(f862(x75741,f2(a1))) % 14.98/14.67 [7598]P149(x75982,x75981,x75983)+E(x75981,f2(a1))+~P1(f862(x75982,f869(x75983,x75981,x75982)))+~P1(f862(x75982,f871(x75983,x75981,x75982))) % 14.98/14.67 [7599]P148(x75992,x75991,x75993)+E(x75991,f2(a1))+~P1(f862(x75992,f873(x75993,x75991,x75992)))+~P1(f862(x75992,f872(x75993,x75991,x75992))) % 14.98/14.67 [7684]P148(x76841,x76842,x76843)+~P1(f862(x76841,x76843))+~P1(f862(x76841,f873(x76843,x76842,x76841)))+~P1(f862(x76841,f872(x76843,x76842,x76841))) % 14.98/14.67 [7702]P149(x77021,x77022,x77023)+~P1(f862(x77021,f869(x77023,x77022,x77021)))+~P1(f862(x77021,f871(x77023,x77022,x77021)))+~P1(f862(x77021,f2(a1))) % 14.98/14.67 [7748]P149(x77482,x77481,x77483)+E(x77481,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f868(x77483,x77481,x77482)))+P1(f862(f862(f227(a1),f867(x77483,x77481,x77482)),f2(a1))) % 14.98/14.67 [7749]P148(x77492,x77491,x77493)+E(x77491,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f873(x77493,x77491,x77492)))+P1(f862(f862(f227(a1),f872(x77493,x77491,x77492)),f2(a1))) % 14.98/14.67 [7750]~P142(x77501)+~P1(f862(f862(f321(x77501),x77503),f102(x77501)))+~P1(f862(f862(f321(x77501),x77502),f102(x77501)))+P1(f862(f862(f321(x77501),f862(f862(f3(x77501),x77502),x77503)),f102(x77501))) % 14.98/14.67 [7751]~P142(x77511)+~P1(f862(f862(f321(x77511),x77513),f102(x77511)))+~P1(f862(f862(f321(x77511),x77512),f102(x77511)))+P1(f862(f862(f321(x77511),f862(f862(f74(x77511),x77512),x77513)),f102(x77511))) % 14.98/14.67 [7752]~P147(x77521)+~P1(f862(f862(f321(x77521),x77523),f179(x77521)))+~P1(f862(f862(f321(x77521),x77522),f179(x77521)))+P1(f862(f862(f321(x77521),f862(f862(f74(x77521),x77522),x77523)),f179(x77521))) % 14.98/14.67 [7753]~P142(x77531)+~P1(f862(f862(f321(x77531),x77533),f102(x77531)))+~P1(f862(f862(f321(x77531),x77532),f102(x77531)))+P1(f862(f862(f321(x77531),f862(f862(f73(x77531),x77532),x77533)),f102(x77531))) % 14.98/14.67 [7754]~P147(x77541)+~P1(f862(f862(f321(x77541),x77543),f179(x77541)))+~P1(f862(f862(f321(x77541),x77542),f179(x77541)))+P1(f862(f862(f321(x77541),f862(f862(f73(x77541),x77542),x77543)),f179(x77541))) % 14.98/14.67 [7755]~P87(x77551)+~P1(f862(f862(f227(x77551),x77553),f2(x77551)))+~P1(f862(f862(f227(x77551),x77552),f2(x77551)))+P1(f862(f862(f227(x77551),f862(f862(f73(x77551),x77552),x77553)),f2(x77551))) % 14.98/14.67 [7756]~P87(x77561)+~P1(f862(f862(f227(x77561),x77563),f2(x77561)))+~P1(f862(f862(f228(x77561),x77562),f2(x77561)))+P1(f862(f862(f228(x77561),f862(f862(f73(x77561),x77562),x77563)),f2(x77561))) % 14.98/14.67 [7757]~P87(x77571)+~P1(f862(f862(f227(x77571),x77572),f2(x77571)))+~P1(f862(f862(f228(x77571),x77573),f2(x77571)))+P1(f862(f862(f228(x77571),f862(f862(f73(x77571),x77572),x77573)),f2(x77571))) % 14.98/14.67 [7758]~P87(x77581)+~P1(f862(f862(f228(x77581),x77583),f2(x77581)))+~P1(f862(f862(f228(x77581),x77582),f2(x77581)))+P1(f862(f862(f228(x77581),f862(f862(f73(x77581),x77582),x77583)),f2(x77581))) % 14.98/14.67 [7785]P149(x77853,x77851,x77852)+E(x77851,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x77851),f869(x77852,x77851,x77853))),f868(x77852,x77851,x77853)),x77852)+P1(f862(f862(f228(a1),x77851),f2(a1))) % 14.98/14.67 [7786]P148(x77863,x77861,x77862)+E(x77861,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x77861),f874(x77862,x77861,x77863))),f873(x77862,x77861,x77863)),x77862)+P1(f862(f862(f228(a1),x77861),f2(a1))) % 14.98/14.67 [7869]P148(x78691,x78692,x78693)+~P1(f862(x78691,x78693))+P1(f862(f862(f227(a1),f2(a1)),f873(x78693,x78692,x78691)))+P1(f862(f862(f227(a1),f872(x78693,x78692,x78691)),f2(a1))) % 14.98/14.67 [7899]P149(x78991,x78992,x78993)+P1(f862(f862(f227(a1),f2(a1)),f868(x78993,x78992,x78991)))+~P1(f862(x78991,f2(a1)))+P1(f862(f862(f227(a1),f867(x78993,x78992,x78991)),f2(a1))) % 14.98/14.67 [7908]P148(x79083,x79081,x79082)+~P1(f862(x79083,x79082))+E(f862(f862(f73(a1),f862(f862(f74(a1),x79081),f874(x79082,x79081,x79083))),f873(x79082,x79081,x79083)),x79082)+P1(f862(f862(f228(a1),x79081),f2(a1))) % 14.98/14.67 [7914]P149(x79142,x79141,x79143)+E(x79141,f2(a1))+~P1(f862(x79142,f869(x79143,x79141,x79142)))+P1(f862(f862(f227(a1),f867(x79143,x79141,x79142)),f2(a1))) % 14.98/14.67 [7915]P148(x79152,x79151,x79153)+E(x79151,f2(a1))+~P1(f862(x79152,f873(x79153,x79151,x79152)))+P1(f862(f862(f227(a1),f872(x79153,x79151,x79152)),f2(a1))) % 14.98/14.67 [7920]P149(x79203,x79201,x79202)+E(f862(f862(f73(a1),f862(f862(f74(a1),x79201),f869(x79202,x79201,x79203))),f868(x79202,x79201,x79203)),x79202)+~P1(f862(x79203,f2(a1)))+P1(f862(f862(f228(a1),x79201),f2(a1))) % 14.98/14.67 [7976]P148(x79761,x79762,x79763)+~P1(f862(x79761,x79763))+~P1(f862(x79761,f873(x79763,x79762,x79761)))+P1(f862(f862(f227(a1),f872(x79763,x79762,x79761)),f2(a1))) % 14.98/14.67 [7980]P149(x79801,x79802,x79803)+~P1(f862(x79801,f869(x79803,x79802,x79801)))+~P1(f862(x79801,f2(a1)))+P1(f862(f862(f227(a1),f867(x79803,x79802,x79801)),f2(a1))) % 14.98/14.67 [8049]~P128(x80491)+~P1(f862(f862(f227(x80491),f862(f862(f74(x80491),x80493),x80492)),f2(x80491)))+P1(f862(f862(f227(x80491),x80492),f2(x80491)))+P1(f862(f862(f227(x80491),x80493),f2(x80491))) % 14.98/14.67 [8050]~P66(x80501)+~P1(f862(f862(f227(x80501),f862(f862(f281(x80501),x80503),x80502)),f2(x80501)))+P1(f862(f862(f227(x80501),x80502),f2(x80501)))+P1(f862(f862(f227(x80501),x80503),f2(x80501))) % 14.98/14.67 [8051]~P66(x80511)+~P1(f862(f862(f228(x80511),f862(f862(f281(x80511),x80513),x80512)),f2(x80511)))+P1(f862(f862(f228(x80511),x80512),f2(x80511)))+P1(f862(f862(f228(x80511),x80513),f2(x80511))) % 14.98/14.67 [8166]P149(x81663,x81661,x81662)+E(x81661,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x81661),f869(x81662,x81661,x81663))),f868(x81662,x81661,x81663)),x81662)+P1(f862(f862(f228(a1),x81661),f867(x81662,x81661,x81663))) % 14.98/14.67 [8167]P148(x81673,x81671,x81672)+E(x81671,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x81671),f874(x81672,x81671,x81673))),f873(x81672,x81671,x81673)),x81672)+P1(f862(f862(f228(a1),x81671),f872(x81672,x81671,x81673))) % 14.98/14.67 [8180]P149(x81803,x81801,x81802)+E(x81801,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x81801),f871(x81802,x81801,x81803))),f867(x81802,x81801,x81803)),x81802)+P1(f862(f862(f227(a1),f2(a1)),f868(x81802,x81801,x81803))) % 14.98/14.67 [8181]P148(x81813,x81811,x81812)+E(x81811,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x81811),f875(x81812,x81811,x81813))),f872(x81812,x81811,x81813)),x81812)+P1(f862(f862(f227(a1),f2(a1)),f873(x81812,x81811,x81813))) % 14.98/14.67 [8224]P148(x82243,x82241,x82242)+~P1(f862(x82243,x82242))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82241),f874(x82242,x82241,x82243))),f873(x82242,x82241,x82243)),x82242)+P1(f862(f862(f228(a1),x82241),f872(x82242,x82241,x82243))) % 14.98/14.67 [8233]P149(x82333,x82331,x82332)+E(f862(f862(f73(a1),f862(f862(f74(a1),x82331),f869(x82332,x82331,x82333))),f868(x82332,x82331,x82333)),x82332)+P1(f862(f862(f228(a1),x82331),f867(x82332,x82331,x82333)))+~P1(f862(x82333,f2(a1))) % 14.98/14.67 [8239]P148(x82393,x82391,x82392)+~P1(f862(x82393,x82392))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82391),f875(x82392,x82391,x82393))),f872(x82392,x82391,x82393)),x82392)+P1(f862(f862(f227(a1),f2(a1)),f873(x82392,x82391,x82393))) % 14.98/14.67 [8245]P149(x82453,x82451,x82452)+E(f862(f862(f73(a1),f862(f862(f74(a1),x82451),f871(x82452,x82451,x82453))),f867(x82452,x82451,x82453)),x82452)+P1(f862(f862(f227(a1),f2(a1)),f868(x82452,x82451,x82453)))+~P1(f862(x82453,f2(a1))) % 14.98/14.67 [8256]P149(x82563,x82561,x82562)+E(x82561,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82561),f869(x82562,x82561,x82563))),f868(x82562,x82561,x82563)),x82562)+~P1(f862(x82563,f871(x82562,x82561,x82563))) % 14.98/14.67 [8257]P148(x82573,x82571,x82572)+E(x82571,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82571),f874(x82572,x82571,x82573))),f873(x82572,x82571,x82573)),x82572)+~P1(f862(x82573,f872(x82572,x82571,x82573))) % 14.98/14.67 [8258]P149(x82583,x82581,x82582)+E(x82581,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82581),f871(x82582,x82581,x82583))),f867(x82582,x82581,x82583)),x82582)+~P1(f862(x82583,f869(x82582,x82581,x82583))) % 14.98/14.67 [8259]P148(x82593,x82591,x82592)+E(x82591,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82591),f875(x82592,x82591,x82593))),f872(x82592,x82591,x82593)),x82592)+~P1(f862(x82593,f873(x82592,x82591,x82593))) % 14.98/14.67 [8320]P148(x83203,x83201,x83202)+~P1(f862(x83203,x83202))+E(f862(f862(f73(a1),f862(f862(f74(a1),x83201),f874(x83202,x83201,x83203))),f873(x83202,x83201,x83203)),x83202)+~P1(f862(x83203,f872(x83202,x83201,x83203))) % 14.98/14.67 [8321]P148(x83213,x83211,x83212)+~P1(f862(x83213,x83212))+E(f862(f862(f73(a1),f862(f862(f74(a1),x83211),f875(x83212,x83211,x83213))),f872(x83212,x83211,x83213)),x83212)+~P1(f862(x83213,f873(x83212,x83211,x83213))) % 14.98/14.67 [8334]P149(x83343,x83341,x83342)+E(f862(f862(f73(a1),f862(f862(f74(a1),x83341),f869(x83342,x83341,x83343))),f868(x83342,x83341,x83343)),x83342)+~P1(f862(x83343,f871(x83342,x83341,x83343)))+~P1(f862(x83343,f2(a1))) % 14.98/14.67 [8335]P149(x83353,x83351,x83352)+E(f862(f862(f73(a1),f862(f862(f74(a1),x83351),f871(x83352,x83351,x83353))),f867(x83352,x83351,x83353)),x83352)+~P1(f862(x83353,f869(x83352,x83351,x83353)))+~P1(f862(x83353,f2(a1))) % 14.98/14.67 [8434]P149(x84343,x84341,x84342)+E(x84341,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84341),f869(x84342,x84341,x84343))),f868(x84342,x84341,x84343)),x84342)+P1(f862(f862(f227(a1),f867(x84342,x84341,x84343)),f2(a1))) % 14.98/14.67 [8435]P148(x84353,x84351,x84352)+E(x84351,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84351),f874(x84352,x84351,x84353))),f873(x84352,x84351,x84353)),x84352)+P1(f862(f862(f227(a1),f872(x84352,x84351,x84353)),f2(a1))) % 14.98/14.67 [8474]P148(x84743,x84741,x84742)+~P1(f862(x84743,x84742))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84741),f874(x84742,x84741,x84743))),f873(x84742,x84741,x84743)),x84742)+P1(f862(f862(f227(a1),f872(x84742,x84741,x84743)),f2(a1))) % 14.98/14.67 [8479]P149(x84793,x84791,x84792)+E(f862(f862(f73(a1),f862(f862(f74(a1),x84791),f869(x84792,x84791,x84793))),f868(x84792,x84791,x84793)),x84792)+~P1(f862(x84793,f2(a1)))+P1(f862(f862(f227(a1),f867(x84792,x84791,x84793)),f2(a1))) % 14.98/14.67 [8615]P149(x86153,x86151,x86152)+E(x86151,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x86151),f871(x86152,x86151,x86153))),f867(x86152,x86151,x86153)),x86152)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86151),f869(x86152,x86151,x86153))),f868(x86152,x86151,x86153)),x86152) % 14.98/14.67 [8616]P148(x86163,x86161,x86162)+E(x86161,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x86161),f875(x86162,x86161,x86163))),f872(x86162,x86161,x86163)),x86162)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86161),f874(x86162,x86161,x86163))),f873(x86162,x86161,x86163)),x86162) % 14.98/14.67 [8636]P148(x86363,x86361,x86362)+~P1(f862(x86363,x86362))+E(f862(f862(f73(a1),f862(f862(f74(a1),x86361),f875(x86362,x86361,x86363))),f872(x86362,x86361,x86363)),x86362)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86361),f874(x86362,x86361,x86363))),f873(x86362,x86361,x86363)),x86362) % 14.98/14.67 [8648]P149(x86483,x86481,x86482)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86481),f871(x86482,x86481,x86483))),f867(x86482,x86481,x86483)),x86482)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86481),f869(x86482,x86481,x86483))),f868(x86482,x86481,x86483)),x86482)+~P1(f862(x86483,f2(a1))) % 14.98/14.67 [9315]~P128(x93151)+~E(x93153,f2(x93151))+~E(x93152,f2(x93151))+P1(f862(f862(f227(x93151),f862(f862(f73(x93151),f862(f862(f74(x93151),x93152),x93152)),f862(f862(f74(x93151),x93153),x93153))),f2(x93151))) % 14.98/14.67 [10383]~P112(x103831)+~E(x103833,f2(x103831))+~E(x103832,f2(x103831))+P1(f862(f862(f227(x103831),f862(f862(f73(x103831),f862(f862(f236(x103831),x103832),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103831),x103833),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f2(x103831))) % 14.98/14.67 [4984]~E(x49843,x49841)+~P121(x49842)+E(x49841,f2(x49842))+E(f862(f862(f281(x49842),x49843),x49841),f71(x49842)) % 14.98/14.67 [5037]~P95(x50371)+~E(x50373,f181(x50371))+~E(x50372,f181(x50371))+E(f862(f862(f103(x50371),x50372),x50373),f181(x50371)) % 14.98/14.67 [5038]~P94(x50381)+~E(x50383,f234(x50381))+~E(x50382,f234(x50381))+E(f862(f862(f94(x50381),x50382),x50383),f234(x50381)) % 14.98/14.67 [5135]~P121(x51353)+E(x51351,x51352)+E(x51352,f2(x51353))+~E(f862(f862(f281(x51353),x51351),x51352),f71(x51353)) % 14.98/14.67 [5153]~P133(x51532)+E(x51531,f2(x51532))+E(x51533,f2(x51532))+~E(f862(f862(f74(x51532),x51533),x51531),f2(x51532)) % 14.98/14.67 [5154]~P143(x51542)+E(x51541,f2(x51542))+E(x51543,f2(x51542))+~E(f862(f862(f74(x51542),x51543),x51541),f2(x51542)) % 14.98/14.67 [5533]~P113(x55333)+E(x55331,x55332)+E(x55331,f862(f72(x55333),x55332))+~E(f862(f862(f74(x55333),x55331),x55331),f862(f862(f74(x55333),x55332),x55332)) % 14.98/14.67 [5573]~P96(x55731)+E(f862(f72(x55731),x55732),x55733)+~E(f862(f862(f103(x55731),x55732),x55733),f234(x55731))+~E(f862(f862(f94(x55731),x55732),x55733),f181(x55731)) % 14.98/14.67 [5654]~P112(x56543)+E(x56541,x56542)+P1(f862(f862(f228(x56543),x56542),x56541))+P1(f862(f862(f228(x56543),x56541),x56542)) % 14.98/14.67 [5655]~P109(x56553)+E(x56551,x56552)+P1(f862(f862(f228(x56553),x56552),x56551))+P1(f862(f862(f228(x56553),x56551),x56552)) % 14.98/14.67 [5656]~E(x56562,x56563)+~P109(x56561)+P1(f862(f862(f228(x56561),x56562),x56563))+P1(f862(f862(f227(x56561),x56562),x56563)) % 14.98/14.67 [5920]~P110(x59203)+E(x59201,x59202)+~P1(f862(f862(f227(x59203),x59202),x59201))+P1(f862(f862(f228(x59203),x59202),x59201)) % 14.98/14.67 [5922]~P109(x59223)+E(x59221,x59222)+~P1(f862(f862(f227(x59223),x59221),x59222))+P1(f862(f862(f228(x59223),x59221),x59222)) % 14.98/14.67 [5928]~P110(x59283)+E(x59281,x59282)+~P1(f862(f862(f227(x59283),x59281),x59282))+P1(f862(f862(f228(x59283),x59281),x59282)) % 14.98/14.67 [6040]P148(x60401,x60402,x60403)+~P1(f862(x60401,x60403))+P1(f862(f862(f228(a1),x60402),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x60402)) % 14.98/14.67 [6094]P149(x60941,x60942,x60943)+~P1(f862(x60941,f2(a1)))+P1(f862(f862(f228(a1),x60942),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x60942)) % 14.98/14.67 [6099]~P93(x60991)+E(f862(f862(f103(x60991),x60992),f12(x60991,x60993)),x60992)+~P1(f862(f54(x60991),x60993))+~P1(f862(f862(f321(x60991),x60992),x60993)) % 14.98/14.67 [6100]~P93(x61001)+E(f862(f862(f94(x61001),x61002),f15(x61001,x61003)),x61002)+~P1(f862(f54(x61001),x61003))+~P1(f862(f862(f321(x61001),x61002),x61003)) % 14.98/14.67 [6138]~P93(x61381)+E(f862(f862(f103(x61381),x61382),f15(x61381,x61383)),f15(x61381,x61383))+~P1(f862(f54(x61381),x61383))+~P1(f862(f862(f321(x61381),x61382),x61383)) % 14.98/14.67 [6139]~P93(x61391)+E(f862(f862(f94(x61391),x61392),f12(x61391,x61393)),f12(x61391,x61393))+~P1(f862(f54(x61391),x61393))+~P1(f862(f862(f321(x61391),x61392),x61393)) % 14.98/14.67 [6140]~P109(x61401)+E(f862(f862(f225(x61401),x61402),f16(x61401,x61403)),f16(x61401,x61403))+~P1(f862(f54(x61401),x61403))+~P1(f862(f862(f321(x61401),x61402),x61403)) % 14.98/14.67 [6141]~P109(x61411)+E(f862(f862(f226(x61411),x61412),f17(x61411,x61413)),f17(x61411,x61413))+~P1(f862(f54(x61411),x61413))+~P1(f862(f862(f321(x61411),x61412),x61413)) % 14.98/14.67 [6179]E(x61791,x61792)+~P110(x61793)+~P1(f862(f862(f227(x61793),x61792),x61791))+~P1(f862(f862(f227(x61793),x61791),x61792)) % 14.98/14.67 [6319]~P91(x63191)+P1(f862(f862(f228(x63191),x63193),x63192))+~P1(f862(f862(f227(x63191),x63193),x63192))+P1(f862(f862(f227(x63191),x63192),x63193)) % 14.98/14.67 [6346]~P109(x63461)+~P1(f862(f54(x63461),x63463))+P1(f862(f862(f227(x63461),x63462),f17(x63461,x63463)))+~P1(f862(f862(f321(x63461),x63462),x63463)) % 14.98/14.67 [6393]~P109(x63931)+E(f862(f862(f225(x63931),x63932),f14(x63931,f226(x63931),x63933)),x63932)+~P1(f862(f54(x63931),x63933))+~P1(f862(f862(f321(x63931),x63932),x63933)) % 14.98/14.67 [6394]~P109(x63941)+E(f862(f862(f226(x63941),x63942),f13(x63941,f225(x63941),x63943)),x63942)+~P1(f862(f54(x63941),x63943))+~P1(f862(f862(f321(x63941),x63942),x63943)) % 14.98/14.67 [6536]E(x65361,x65362)+~E(f862(f862(f3(a924),x65361),x65363),f862(f862(f3(a924),x65362),x65363))+~P1(f862(f862(f227(a924),x65363),x65361))+~P1(f862(f862(f227(a924),x65363),x65362)) % 14.98/14.67 [6563]~P109(x65631)+~P1(f862(f54(x65631),x65632))+~P1(f862(f862(f321(x65631),x65633),x65632))+P1(f862(f862(f227(x65631),f16(x65631,x65632)),x65633)) % 14.98/14.67 [6629]P149(x66292,x66291,x66293)+E(x66291,f2(a1))+P1(f862(f862(f228(a1),x66291),f867(x66293,x66291,x66292)))+P1(f862(f862(f228(a1),f2(a1)),x66291)) % 14.98/14.67 [6630]P148(x66302,x66301,x66303)+E(x66301,f2(a1))+P1(f862(f862(f228(a1),x66301),f872(x66303,x66301,x66302)))+P1(f862(f862(f228(a1),f2(a1)),x66301)) % 14.98/14.67 [6631]~P109(x66311)+E(f862(f862(f225(x66311),x66312),f13(x66311,f225(x66311),x66313)),f13(x66311,f225(x66311),x66313))+~P1(f862(f54(x66311),x66313))+~P1(f862(f862(f321(x66311),x66312),x66313)) % 14.98/14.67 [6632]~P109(x66321)+E(f862(f862(f226(x66321),x66322),f14(x66321,f226(x66321),x66323)),f14(x66321,f226(x66321),x66323))+~P1(f862(f54(x66321),x66323))+~P1(f862(f862(f321(x66321),x66322),x66323)) % 14.98/14.67 [6637]~P1(f862(x66371,x66372))+P1(f862(x66371,f437(x66372,x66371,x66373)))+P1(f862(x66371,f2(a924)))+~P1(f862(f862(f228(a924),x66372),x66373)) % 14.98/14.67 [6695]~P1(f862(x66951,x66952))+~P1(f862(f54(x66953),x66952))+P1(f862(x66951,f876(x66951,x66952,x66953)))+P1(f862(x66951,f181(f932(x66953,a921)))) % 14.98/14.67 [6708]~P112(x67081)+~P98(x67081)+P1(f862(f862(f227(x67081),f862(f96(x67081),x67082)),f862(f96(x67081),x67083)))+~P1(f862(f862(f227(a1),x67082),x67083)) % 14.98/14.67 [6709]~P112(x67091)+~P98(x67091)+P1(f862(f862(f228(x67091),f862(f96(x67091),x67092)),f862(f96(x67091),x67093)))+~P1(f862(f862(f228(a1),x67092),x67093)) % 14.98/14.67 [6712]~P1(f862(x67121,x67123))+~P1(f862(f54(x67122),x67123))+P1(f862(f54(x67122),f876(x67121,x67123,x67122)))+P1(f862(x67121,f181(f932(x67122,a921)))) % 14.98/14.67 [6746]P148(x67461,x67462,x67463)+~P1(f862(x67461,x67463))+P1(f862(f862(f228(a1),x67462),f872(x67463,x67462,x67461)))+P1(f862(f862(f228(a1),f2(a1)),x67462)) % 14.98/14.67 [6781]P149(x67811,x67812,x67813)+P1(f862(f862(f228(a1),x67812),f867(x67813,x67812,x67811)))+~P1(f862(x67811,f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x67812)) % 14.98/14.67 [6811]~P108(x68111)+~P99(x68111)+E(f862(f862(f225(x68111),f862(f96(x68111),x68112)),f862(f96(x68111),x68113)),f862(f96(x68111),x68113))+P1(f862(f862(f227(x68111),f862(f96(x68111),x68112)),f862(f96(x68111),x68113))) % 14.98/14.67 [6812]~P108(x68121)+~P99(x68121)+E(f862(f862(f226(x68121),f862(f96(x68121),x68122)),f862(f96(x68121),x68123)),f862(f96(x68121),x68122))+P1(f862(f862(f227(x68121),f862(f96(x68121),x68122)),f862(f96(x68121),x68123))) % 14.98/14.67 [6869]P149(x68692,x68691,x68693)+E(x68691,f2(a1))+~P1(f862(x68692,f871(x68693,x68691,x68692)))+P1(f862(f862(f228(a1),f2(a1)),x68691)) % 14.98/14.67 [6870]P148(x68702,x68701,x68703)+E(x68701,f2(a1))+~P1(f862(x68702,f872(x68703,x68701,x68702)))+P1(f862(f862(f228(a1),f2(a1)),x68701)) % 14.98/14.67 [6874]P1(f862(x68741,x68742))+~P1(f862(f54(x68743),x68742))+P1(f862(x68741,f441(x68741,x68742,x68743)))+~P1(f862(x68741,f181(f932(x68743,a921)))) % 14.98/14.67 [6894]P1(f862(x68941,x68942))+P1(f862(f54(x68943),f441(x68941,x68942,x68943)))+~P1(f862(f54(x68943),x68942))+~P1(f862(x68941,f181(f932(x68943,a921)))) % 14.98/14.67 [6958]P148(x69581,x69582,x69583)+~P1(f862(x69581,x69583))+~P1(f862(x69581,f872(x69583,x69582,x69581)))+P1(f862(f862(f228(a1),f2(a1)),x69582)) % 14.98/14.67 [6989]P149(x69891,x69892,x69893)+~P1(f862(x69891,f871(x69893,x69892,x69891)))+~P1(f862(x69891,f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x69892)) % 14.98/14.67 [7096]~P98(x70963)+~P112(x70963)+~P1(f862(f862(f227(x70963),f862(f96(x70963),x70961)),f862(f96(x70963),x70962)))+P1(f862(f862(f227(a1),x70961),x70962)) % 14.98/14.67 [7097]~P98(x70973)+~P112(x70973)+~P1(f862(f862(f228(x70973),f862(f96(x70973),x70971)),f862(f96(x70973),x70972)))+P1(f862(f862(f228(a1),x70971),x70972)) % 14.98/14.67 [7125]~P109(x71251)+~P11(x71251,x71253)+P11(x71251,f862(f862(f144(x71251),x71252),x71253))+~P1(f862(f862(f227(x71251),x71252),f717(x71253,x71252,x71251))) % 14.98/14.67 [7126]~P109(x71261)+~P11(x71261,x71263)+P11(x71261,f862(f862(f144(x71261),x71262),x71263))+~P1(f862(f862(f227(x71261),x71262),f719(x71263,x71262,x71261))) % 14.98/14.67 [7127]~P109(x71271)+~P11(x71271,x71273)+P11(x71271,f862(f862(f144(x71271),x71272),x71273))+~P1(f862(f862(f227(x71271),x71272),f758(x71272,x71273,x71271))) % 14.98/14.67 [7212]P149(x72122,x72121,x72123)+E(x72121,f2(a1))+P1(f862(f862(f228(a1),x72121),f2(a1)))+P1(f862(f862(f228(a1),f868(x72123,x72121,x72122)),x72121)) % 14.98/14.67 [7213]P148(x72132,x72131,x72133)+E(x72131,f2(a1))+P1(f862(f862(f228(a1),x72131),f2(a1)))+P1(f862(f862(f228(a1),f873(x72133,x72131,x72132)),x72131)) % 14.98/14.67 [7249]P149(x72492,x72491,x72493)+E(x72491,f2(a1))+P1(f862(f862(f227(a1),f867(x72493,x72491,x72492)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x72491)) % 14.98/14.67 [7250]P148(x72502,x72501,x72503)+E(x72501,f2(a1))+P1(f862(f862(f227(a1),f872(x72503,x72501,x72502)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x72501)) % 14.98/14.67 [7276]~P109(x72761)+~P11(x72761,x72763)+E(f862(f862(f141(x72761,x72761,f7(x72761)),x72762),f163(x72761,x72762,x72763)),x72763)+~P1(f862(f862(f321(x72761),x72762),f862(f165(x72761),x72763))) % 14.98/14.67 [7323]P148(x73231,x73232,x73233)+~P1(f862(x73231,x73233))+P1(f862(f862(f228(a1),x73232),f2(a1)))+P1(f862(f862(f228(a1),f873(x73233,x73232,x73231)),x73232)) % 14.98/14.67 [7329]~P108(x73291)+~P99(x73291)+E(f862(f862(f225(x73291),f862(f96(x73291),x73292)),f862(f96(x73291),x73293)),f862(f96(x73291),x73292))+~P1(f862(f862(f227(x73291),f862(f96(x73291),x73292)),f862(f96(x73291),x73293))) % 14.98/14.67 [7330]~P108(x73301)+~P99(x73301)+E(f862(f862(f226(x73301),f862(f96(x73301),x73302)),f862(f96(x73301),x73303)),f862(f96(x73301),x73303))+~P1(f862(f862(f227(x73301),f862(f96(x73301),x73302)),f862(f96(x73301),x73303))) % 14.98/14.67 [7344]P149(x73441,x73442,x73443)+~P1(f862(x73441,f2(a1)))+P1(f862(f862(f228(a1),x73442),f2(a1)))+P1(f862(f862(f228(a1),f868(x73443,x73442,x73441)),x73442)) % 14.98/14.67 [7354]P148(x73541,x73542,x73543)+~P1(f862(x73541,x73543))+P1(f862(f862(f227(a1),f872(x73543,x73542,x73541)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x73542)) % 14.98/14.67 [7378]P149(x73781,x73782,x73783)+~P1(f862(x73781,f2(a1)))+P1(f862(f862(f227(a1),f867(x73783,x73782,x73781)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x73782)) % 14.98/14.67 [7406]~P1(f862(x74061,x74062))+P1(f862(x74061,f2(a924)))+~P1(f862(f862(f228(a924),x74062),x74063))+P1(f862(f862(f228(a924),f437(x74062,x74061,x74063)),x74063)) % 14.98/14.67 [7423]~P109(x74231)+~P11(x74231,x74233)+P11(x74231,f862(f862(f144(x74231),x74232),x74233))+P1(f862(f862(f321(x74231),f717(x74233,x74232,x74231)),f862(f165(x74231),x74233))) % 14.98/14.67 [7424]~P109(x74241)+~P11(x74241,x74243)+P11(x74241,f862(f862(f144(x74241),x74242),x74243))+P1(f862(f862(f321(x74241),f719(x74243,x74242,x74241)),f862(f165(x74241),x74243))) % 14.98/14.67 [7425]~P109(x74251)+~P11(x74251,x74253)+P11(x74251,f862(f862(f144(x74251),x74252),x74253))+P1(f862(f862(f321(x74251),f758(x74252,x74253,x74251)),f862(f165(x74251),x74253))) % 14.98/14.67 [7543]~P3(x75431)+~P109(x75431)+~P1(f862(f862(f228(x75431),x75433),f30(x75431,x75432)))+P1(f862(f862(f321(x75431),f724(x75432,x75433,x75431)),x75432)) % 14.98/14.67 [7700]~P3(x77001)+~P109(x77001)+~P1(f862(f862(f228(x77001),f31(x77001,x77003)),x77002))+P1(f862(f862(f321(x77001),f734(x77002,x77003,x77001)),x77003)) % 14.98/14.67 [7701]~P3(x77011)+~P109(x77011)+~P1(f862(f862(f228(x77011),f31(x77011,x77013)),x77012))+P1(f862(f862(f228(x77011),f734(x77012,x77013,x77011)),x77012)) % 14.98/14.67 [7712]P149(x77122,x77121,x77123)+E(x77121,f2(a1))+P1(f862(f862(f228(a1),x77121),f867(x77123,x77121,x77122)))+P1(f862(f862(f228(a1),f868(x77123,x77121,x77122)),x77121)) % 14.98/14.67 [7713]P148(x77132,x77131,x77133)+E(x77131,f2(a1))+P1(f862(f862(f228(a1),x77131),f872(x77133,x77131,x77132)))+P1(f862(f862(f228(a1),f873(x77133,x77131,x77132)),x77131)) % 14.98/14.67 [7808]P149(x78083,x78081,x78082)+E(x78081,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x78081),f871(x78082,x78081,x78083))),f867(x78082,x78081,x78083)),x78082)+P1(f862(f862(f228(a1),f2(a1)),x78081)) % 14.98/14.67 [7809]P148(x78093,x78091,x78092)+E(x78091,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x78091),f875(x78092,x78091,x78093))),f872(x78092,x78091,x78093)),x78092)+P1(f862(f862(f228(a1),f2(a1)),x78091)) % 14.98/14.67 [7812]~P136(x78121)+~P1(f862(f862(f227(x78121),x78123),f2(x78121)))+P1(f862(f862(f227(x78121),f862(f862(f74(x78121),x78122),x78123)),f2(x78121)))+~P1(f862(f862(f227(x78121),f2(x78121)),x78122)) % 14.98/14.67 [7814]~P136(x78141)+~P1(f862(f862(f227(x78141),x78142),f2(x78141)))+P1(f862(f862(f227(x78141),f862(f862(f74(x78141),x78142),x78143)),f2(x78141)))+~P1(f862(f862(f227(x78141),f2(x78141)),x78143)) % 14.98/14.67 [7815]~P128(x78151)+~P1(f862(f862(f227(x78151),x78153),f2(x78151)))+P1(f862(f862(f227(x78151),f862(f862(f74(x78151),x78152),x78153)),f2(x78151)))+~P1(f862(f862(f227(x78151),f2(x78151)),x78152)) % 14.98/14.67 [7816]~P128(x78161)+~P1(f862(f862(f227(x78161),x78162),f2(x78161)))+P1(f862(f862(f227(x78161),f862(f862(f74(x78161),x78162),x78163)),f2(x78161)))+~P1(f862(f862(f227(x78161),f2(x78161)),x78163)) % 14.98/14.67 [7817]~P66(x78171)+~P1(f862(f862(f227(x78171),x78173),f2(x78171)))+P1(f862(f862(f227(x78171),f862(f862(f281(x78171),x78172),x78173)),f2(x78171)))+~P1(f862(f862(f227(x78171),f2(x78171)),x78172)) % 14.98/14.67 [7818]~P66(x78181)+~P1(f862(f862(f227(x78181),x78182),f2(x78181)))+P1(f862(f862(f227(x78181),f862(f862(f281(x78181),x78182),x78183)),f2(x78181)))+~P1(f862(f862(f227(x78181),f2(x78181)),x78183)) % 14.98/14.67 [7819]~P67(x78191)+~P1(f862(f862(f227(x78191),x78192),f2(x78191)))+P1(f862(f862(f227(x78191),f862(f862(f281(x78191),x78192),x78193)),f2(x78191)))+~P1(f862(f862(f228(x78191),f2(x78191)),x78193)) % 14.98/14.67 [7820]~P67(x78201)+~P1(f862(f862(f228(x78201),x78203),f2(x78201)))+P1(f862(f862(f227(x78201),f862(f862(f281(x78201),x78202),x78203)),f2(x78201)))+~P1(f862(f862(f227(x78201),f2(x78201)),x78202)) % 14.98/14.67 [7822]~P135(x78221)+~P1(f862(f862(f228(x78221),x78223),f2(x78221)))+P1(f862(f862(f228(x78221),f862(f862(f74(x78221),x78222),x78223)),f2(x78221)))+~P1(f862(f862(f228(x78221),f2(x78221)),x78222)) % 14.98/14.67 [7823]~P135(x78231)+~P1(f862(f862(f228(x78231),x78232),f2(x78231)))+P1(f862(f862(f228(x78231),f862(f862(f74(x78231),x78232),x78233)),f2(x78231)))+~P1(f862(f862(f228(x78231),f2(x78231)),x78233)) % 14.98/14.67 [7824]~P66(x78241)+~P1(f862(f862(f228(x78241),x78243),f2(x78241)))+P1(f862(f862(f228(x78241),f862(f862(f281(x78241),x78242),x78243)),f2(x78241)))+~P1(f862(f862(f228(x78241),f2(x78241)),x78242)) % 14.98/14.67 [7825]~P66(x78251)+~P1(f862(f862(f228(x78251),x78252),f2(x78251)))+P1(f862(f862(f228(x78251),f862(f862(f281(x78251),x78252),x78253)),f2(x78251)))+~P1(f862(f862(f228(x78251),f2(x78251)),x78253)) % 14.98/14.67 [7826]~P67(x78261)+~P1(f862(f862(f228(x78261),x78263),f2(x78261)))+P1(f862(f862(f228(x78261),f862(f862(f281(x78261),x78262),x78263)),f2(x78261)))+~P1(f862(f862(f228(x78261),f2(x78261)),x78262)) % 14.98/14.67 [7827]~P67(x78271)+~P1(f862(f862(f228(x78271),x78272),f2(x78271)))+P1(f862(f862(f228(x78271),f862(f862(f281(x78271),x78272),x78273)),f2(x78271)))+~P1(f862(f862(f228(x78271),f2(x78271)),x78273)) % 14.98/14.67 [7842]P148(x78421,x78422,x78423)+~P1(f862(x78421,x78423))+P1(f862(f862(f228(a1),x78422),f872(x78423,x78422,x78421)))+P1(f862(f862(f228(a1),f873(x78423,x78422,x78421)),x78422)) % 14.98/14.67 [7855]P149(x78551,x78552,x78553)+P1(f862(f862(f228(a1),x78552),f867(x78553,x78552,x78551)))+~P1(f862(x78551,f2(a1)))+P1(f862(f862(f228(a1),f868(x78553,x78552,x78551)),x78552)) % 14.98/14.67 [7906]P149(x79062,x79061,x79063)+E(x79061,f2(a1))+~P1(f862(x79062,f871(x79063,x79061,x79062)))+P1(f862(f862(f228(a1),f868(x79063,x79061,x79062)),x79061)) % 14.98/14.67 [7907]P148(x79072,x79071,x79073)+E(x79071,f2(a1))+~P1(f862(x79072,f872(x79073,x79071,x79072)))+P1(f862(f862(f228(a1),f873(x79073,x79071,x79072)),x79071)) % 14.98/14.67 [7917]P148(x79173,x79171,x79172)+~P1(f862(x79173,x79172))+E(f862(f862(f73(a1),f862(f862(f74(a1),x79171),f875(x79172,x79171,x79173))),f872(x79172,x79171,x79173)),x79172)+P1(f862(f862(f228(a1),f2(a1)),x79171)) % 14.98/14.67 [7932]P149(x79323,x79321,x79322)+E(f862(f862(f73(a1),f862(f862(f74(a1),x79321),f871(x79322,x79321,x79323))),f867(x79322,x79321,x79323)),x79322)+~P1(f862(x79323,f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x79321)) % 14.98/14.67 [7960]~P1(f862(x79601,x79603))+~P1(f862(f54(x79602),x79603))+P1(f862(f862(f321(x79602),f877(x79601,x79603,x79602)),f876(x79601,x79603,x79602)))+P1(f862(x79601,f181(f932(x79602,a921)))) % 14.98/14.67 [7971]P148(x79711,x79712,x79713)+~P1(f862(x79711,x79713))+~P1(f862(x79711,f872(x79713,x79712,x79711)))+P1(f862(f862(f228(a1),f873(x79713,x79712,x79711)),x79712)) % 14.98/14.67 [7977]P149(x79771,x79772,x79773)+~P1(f862(x79771,f871(x79773,x79772,x79771)))+~P1(f862(x79771,f2(a1)))+P1(f862(f862(f228(a1),f868(x79773,x79772,x79771)),x79772)) % 14.98/14.67 [8080]~P128(x80801)+~P1(f862(f862(f227(x80801),f862(f862(f74(x80801),x80803),x80802)),f2(x80801)))+P1(f862(f862(f227(x80801),x80802),f2(x80801)))+P1(f862(f862(f227(x80801),f2(x80801)),x80802)) % 14.98/14.67 [8081]~P128(x80811)+~P1(f862(f862(f227(x80811),f862(f862(f74(x80811),x80812),x80813)),f2(x80811)))+P1(f862(f862(f227(x80811),x80812),f2(x80811)))+P1(f862(f862(f227(x80811),f2(x80811)),x80812)) % 14.98/14.67 [8082]~P66(x80821)+~P1(f862(f862(f227(x80821),f862(f862(f281(x80821),x80823),x80822)),f2(x80821)))+P1(f862(f862(f227(x80821),x80822),f2(x80821)))+P1(f862(f862(f227(x80821),f2(x80821)),x80822)) % 14.98/14.67 [8083]~P66(x80831)+~P1(f862(f862(f227(x80831),f862(f862(f281(x80831),x80832),x80833)),f2(x80831)))+P1(f862(f862(f227(x80831),x80832),f2(x80831)))+P1(f862(f862(f227(x80831),f2(x80831)),x80832)) % 14.98/14.67 [8084]~P66(x80841)+~P1(f862(f862(f228(x80841),f862(f862(f281(x80841),x80843),x80842)),f2(x80841)))+P1(f862(f862(f228(x80841),x80842),f2(x80841)))+P1(f862(f862(f228(x80841),f2(x80841)),x80842)) % 14.98/14.67 [8085]~P66(x80851)+~P1(f862(f862(f228(x80851),f862(f862(f281(x80851),x80852),x80853)),f2(x80851)))+P1(f862(f862(f228(x80851),x80852),f2(x80851)))+P1(f862(f862(f228(x80851),f2(x80851)),x80852)) % 14.98/14.67 [8110]~P128(x81101)+~P1(f862(f862(f227(x81101),f862(f862(f74(x81101),x81102),x81103)),f2(x81101)))+P1(f862(f862(f227(x81101),f2(x81101)),x81102))+P1(f862(f862(f227(x81101),f2(x81101)),x81103)) % 14.98/14.67 [8111]~P66(x81111)+~P1(f862(f862(f227(x81111),f862(f862(f281(x81111),x81112),x81113)),f2(x81111)))+P1(f862(f862(f227(x81111),f2(x81111)),x81112))+P1(f862(f862(f227(x81111),f2(x81111)),x81113)) % 14.98/14.67 [8112]~P66(x81121)+~P1(f862(f862(f228(x81121),f862(f862(f281(x81121),x81122),x81123)),f2(x81121)))+P1(f862(f862(f228(x81121),f2(x81121)),x81122))+P1(f862(f862(f228(x81121),f2(x81121)),x81123)) % 14.98/14.67 [8134]P149(x81342,x81341,x81343)+E(x81341,f2(a1))+P1(f862(f862(f227(a1),f867(x81343,x81341,x81342)),f2(a1)))+P1(f862(f862(f228(a1),f868(x81343,x81341,x81342)),x81341)) % 14.98/14.67 [8135]P148(x81352,x81351,x81353)+E(x81351,f2(a1))+P1(f862(f862(f227(a1),f872(x81353,x81351,x81352)),f2(a1)))+P1(f862(f862(f228(a1),f873(x81353,x81351,x81352)),x81351)) % 14.98/14.67 [8142]~P127(x81421)+~P1(f862(f862(f228(x81421),x81422),f71(x81421)))+P1(f862(f862(f228(x81421),f862(f862(f236(x81421),x81422),f862(a105,x81423))),f71(x81421)))+~P1(f862(f862(f228(x81421),f2(x81421)),x81422)) % 14.98/14.67 [8197]~P109(x81971)+~E(x81973,f106(x81971))+~P11(x81971,f862(f161(x81971),x81973))+E(f862(f135(x81971,x81971,f862(f9(x81971,x81971,x81971),f226(x81971)),x81972),f862(f161(x81971),x81973)),x81972) % 14.98/14.67 [8201]P148(x82011,x82012,x82013)+~P1(f862(x82011,x82013))+P1(f862(f862(f227(a1),f872(x82013,x82012,x82011)),f2(a1)))+P1(f862(f862(f228(a1),f873(x82013,x82012,x82011)),x82012)) % 14.98/14.67 [8208]P149(x82081,x82082,x82083)+~P1(f862(x82081,f2(a1)))+P1(f862(f862(f227(a1),f867(x82083,x82082,x82081)),f2(a1)))+P1(f862(f862(f228(a1),f868(x82083,x82082,x82081)),x82082)) % 14.98/14.67 [8429]P149(x84293,x84291,x84292)+E(x84291,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84291),f871(x84292,x84291,x84293))),f867(x84292,x84291,x84293)),x84292)+P1(f862(f862(f228(a1),f868(x84292,x84291,x84293)),x84291)) % 14.98/14.67 [8430]P148(x84303,x84301,x84302)+E(x84301,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84301),f875(x84302,x84301,x84303))),f872(x84302,x84301,x84303)),x84302)+P1(f862(f862(f228(a1),f873(x84302,x84301,x84303)),x84301)) % 14.98/14.67 [8465]P148(x84653,x84651,x84652)+~P1(f862(x84653,x84652))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84651),f875(x84652,x84651,x84653))),f872(x84652,x84651,x84653)),x84652)+P1(f862(f862(f228(a1),f873(x84652,x84651,x84653)),x84651)) % 14.98/14.67 [8466]~P71(x84661)+~P72(x84661)+~P38(x84663)+E(f862(f862(f8(a924,x84661),f862(f862(f10(a1,x84661,a924),x84662),f93(a1))),f862(f302(a1,a924,a97),x84663)),f862(f862(f8(a1,x84661),x84662),x84663)) % 14.98/14.67 [8467]~P71(x84671)+~P72(x84671)+~P38(x84673)+E(f862(f862(f11(a924,x84671),f862(f862(f10(a1,x84671,a924),x84672),f93(a1))),f862(f302(a1,a924,a97),x84673)),f862(f862(f11(a1,x84671),x84672),x84673)) % 14.98/14.67 [8476]P149(x84763,x84761,x84762)+E(f862(f862(f73(a1),f862(f862(f74(a1),x84761),f871(x84762,x84761,x84763))),f867(x84762,x84761,x84763)),x84762)+~P1(f862(x84763,f2(a1)))+P1(f862(f862(f228(a1),f868(x84762,x84761,x84763)),x84761)) % 14.98/14.67 [8498]~E(x84982,f2(a924))+~E(f862(f243(a924,a924),x84983),f2(a924))+~E(x84981,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x84983)),x84982)),f862(f248(a924,a924),x84983)))+P1(f862(f41(x84981,x84982),x84983)) % 14.98/14.67 [8555]P1(f862(x85551,x85552))+~P1(f862(f862(f321(x85553),f442(x85551,x85552,x85553)),f441(x85551,x85552,x85553)))+~P1(f862(f54(x85553),x85552))+~P1(f862(x85551,f181(f932(x85553,a921)))) % 14.98/14.67 [9186]P1(f862(x91861,x91862))+~P1(f862(f54(x91863),x91862))+~P1(f862(x91861,f862(f862(f301(x91863),f442(x91861,x91862,x91863)),f441(x91861,x91862,x91863))))+~P1(f862(x91861,f181(f932(x91863,a921)))) % 14.98/14.67 [9419]P1(f862(f862(f227(a1),x94191),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f74(a1),x94193),x94191)),x94192)),f2(a1)))+~P1(f862(f862(f227(a1),f2(a1)),x94192))+~P1(f862(f862(f228(a1),f2(a1)),x94193)) % 14.98/14.67 [10177]E(x101771,x101772)+~E(f862(f85(x101773),x101771),f862(f85(x101773),x101772))+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x101773,f932(a920,a921))),f930(a920,x101773)),a921)),x101771),f862(f254(f932(f922(f930(a919,f932(x101773,f932(a920,a921))),f930(a920,x101773)),a921)),f88(x101773))))+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x101773,f932(a920,a921))),f930(a920,x101773)),a921)),x101772),f862(f254(f932(f922(f930(a919,f932(x101773,f932(a920,a921))),f930(a920,x101773)),a921)),f88(x101773)))) % 14.98/14.67 [5990]~P93(x59902)+E(x59901,f181(f932(x59902,a921)))+~P1(f862(f54(x59902),x59901))+E(f12(x59902,f862(f862(f301(x59902),x59903),x59901)),f862(f862(f94(x59902),x59903),f12(x59902,x59901))) % 14.98/14.67 [5991]~P93(x59912)+E(x59911,f181(f932(x59912,a921)))+~P1(f862(f54(x59912),x59911))+E(f15(x59912,f862(f862(f301(x59912),x59913),x59911)),f862(f862(f103(x59912),x59913),f15(x59912,x59911))) % 14.98/14.67 [5992]~P109(x59922)+E(x59921,f181(f932(x59922,a921)))+~P1(f862(f54(x59922),x59921))+E(f16(x59922,f862(f862(f301(x59922),x59923),x59921)),f862(f862(f225(x59922),x59923),f16(x59922,x59921))) % 14.98/14.67 [5993]~P109(x59932)+E(x59931,f181(f932(x59932,a921)))+~P1(f862(f54(x59932),x59931))+E(f17(x59932,f862(f862(f301(x59932),x59933),x59931)),f862(f862(f226(x59932),x59933),f17(x59932,x59931))) % 14.98/14.67 [6316]~P128(x63161)+~E(x63163,f2(x63161))+~E(x63162,f2(x63161))+E(f862(f862(f73(x63161),f862(f862(f74(x63161),x63162),x63162)),f862(f862(f74(x63161),x63163),x63163)),f2(x63161)) % 14.98/14.67 [6386]~P100(x63862)+E(x63861,f181(f932(x63862,a921)))+~P1(f862(f54(x63862),x63861))+E(f862(f56(x63862,f74(x63862)),f862(f862(f301(x63862),x63863),x63861)),f862(f862(f74(x63862),x63863),f862(f56(x63862,f74(x63862)),x63861))) % 14.98/14.67 [6512]~P109(x65122)+E(x65121,f181(f932(x65122,a921)))+~P1(f862(f54(x65122),x65121))+E(f13(x65122,f225(x65122),f862(f862(f301(x65122),x65123),x65121)),f862(f862(f225(x65122),x65123),f13(x65122,f225(x65122),x65121))) % 14.98/14.67 [6513]~P109(x65132)+E(x65131,f181(f932(x65132,a921)))+~P1(f862(f54(x65132),x65131))+E(f14(x65132,f226(x65132),f862(f862(f301(x65132),x65133),x65131)),f862(f862(f226(x65132),x65133),f14(x65132,f226(x65132),x65131))) % 14.98/14.67 [7023]~P69(x70231)+~P1(f862(f54(x70231),x70233))+E(f862(f56(x70231,f74(x70231)),f862(f862(f301(x70231),x70232),x70233)),f862(f862(f57(x70231,x70231,f74(x70231)),x70232),x70233))+P1(f862(f862(f321(x70231),x70232),x70233)) % 14.98/14.67 [7103]~E(f862(f862(f73(a1),x71032),f862(f862(f74(a1),x71033),x71031)),x71033)+~P1(f862(f862(f228(a1),f2(a1)),x71033))+P1(f862(f862(f227(a1),f71(a1)),x71031))+~P1(f862(f862(f228(a1),x71032),x71033)) % 14.98/14.67 [7132]~E(f862(f862(f73(a1),x71322),f862(f862(f74(a1),x71323),x71321)),x71323)+P1(f862(f862(f227(a1),x71321),f71(a1)))+~P1(f862(f862(f227(a1),f2(a1)),x71322))+~P1(f862(f862(f228(a1),f2(a1)),x71323)) % 14.98/14.67 [7148]E(x71481,f2(a924))+~P1(f862(f41(x71483,x71481),x71482))+~P1(f862(f862(f228(a924),f2(a924)),x71481))+P1(f862(f862(f228(a924),f862(f248(a924,a924),x71482)),x71481)) % 14.98/14.67 [7180]~P139(x71801)+~P1(f862(f862(f227(x71801),x71802),f2(x71801)))+~P1(f862(f862(f227(x71801),x71803),f2(x71801)))+E(f862(f862(f74(x71801),f862(f69(x71801),x71802)),f862(f69(x71801),x71803)),f862(f69(x71801),f862(f862(f74(x71801),x71802),x71803))) % 14.98/14.67 [7226]~P139(x72261)+~P1(f862(f862(f227(x72261),x72262),f2(x72261)))+E(f862(f862(f74(x72261),f862(f69(x72261),x72262)),f862(f69(x72261),x72263)),f862(f69(x72261),f862(f862(f74(x72261),x72262),x72263)))+~P1(f862(f862(f227(x72261),f2(x72261)),x72263)) % 14.98/14.67 [7227]~P139(x72271)+~P1(f862(f862(f227(x72271),x72273),f2(x72271)))+E(f862(f862(f74(x72271),f862(f69(x72271),x72272)),f862(f69(x72271),x72273)),f862(f69(x72271),f862(f862(f74(x72271),x72272),x72273)))+~P1(f862(f862(f227(x72271),f2(x72271)),x72272)) % 14.98/14.67 [7284]~P139(x72841)+E(f862(f862(f74(x72841),f862(f69(x72841),x72842)),f862(f69(x72841),x72843)),f862(f69(x72841),f862(f862(f74(x72841),x72842),x72843)))+~P1(f862(f862(f227(x72841),f2(x72841)),x72842))+~P1(f862(f862(f227(x72841),f2(x72841)),x72843)) % 14.98/14.67 [7301]~P126(x73011)+~P1(f862(f862(f227(x73011),x73013),f2(x73011)))+~P1(f862(f862(f227(x73011),x73012),f2(x73011)))+P1(f862(f862(f227(x73011),f2(x73011)),f862(f862(f74(x73011),x73012),x73013))) % 14.98/14.67 [7302]~P128(x73021)+~P1(f862(f862(f227(x73021),x73023),f2(x73021)))+~P1(f862(f862(f227(x73021),x73022),f2(x73021)))+P1(f862(f862(f227(x73021),f2(x73021)),f862(f862(f74(x73021),x73022),x73023))) % 14.98/14.67 [7303]~P66(x73031)+~P1(f862(f862(f227(x73031),x73033),f2(x73031)))+~P1(f862(f862(f227(x73031),x73032),f2(x73031)))+P1(f862(f862(f227(x73031),f2(x73031)),f862(f862(f281(x73031),x73032),x73033))) % 14.98/14.67 [7304]~P67(x73041)+~P1(f862(f862(f228(x73041),x73043),f2(x73041)))+~P1(f862(f862(f227(x73041),x73042),f2(x73041)))+P1(f862(f862(f227(x73041),f2(x73041)),f862(f862(f281(x73041),x73042),x73043))) % 14.98/14.67 [7305]~P128(x73051)+~P1(f862(f862(f228(x73051),x73053),f2(x73051)))+~P1(f862(f862(f228(x73051),x73052),f2(x73051)))+P1(f862(f862(f228(x73051),f2(x73051)),f862(f862(f74(x73051),x73052),x73053))) % 14.98/14.67 [7306]~P66(x73061)+~P1(f862(f862(f228(x73061),x73063),f2(x73061)))+~P1(f862(f862(f228(x73061),x73062),f2(x73061)))+P1(f862(f862(f228(x73061),f2(x73061)),f862(f862(f281(x73061),x73062),x73063))) % 14.98/14.67 [7307]~P67(x73071)+~P1(f862(f862(f228(x73071),x73073),f2(x73071)))+~P1(f862(f862(f228(x73071),x73072),f2(x73071)))+P1(f862(f862(f228(x73071),f2(x73071)),f862(f862(f281(x73071),x73072),x73073))) % 14.98/14.67 [7308]~P127(x73081)+~P1(f862(f862(f228(a924),f2(a924)),x73083))+~P1(f862(f862(f228(x73081),f71(x73081)),x73082))+P1(f862(f862(f228(x73081),f71(x73081)),f862(f862(f236(x73081),x73082),x73083))) % 14.98/14.67 [7407]~P126(x74071)+~P1(f862(f862(f227(x74071),f2(x74071)),x74073))+~P1(f862(f862(f227(x74071),f2(x74071)),x74072))+P1(f862(f862(f227(x74071),f2(x74071)),f862(f862(f74(x74071),x74072),x74073))) % 14.98/14.67 [7408]~P136(x74081)+~P1(f862(f862(f227(x74081),f2(x74081)),x74083))+~P1(f862(f862(f227(x74081),f2(x74081)),x74082))+P1(f862(f862(f227(x74081),f2(x74081)),f862(f862(f74(x74081),x74082),x74083))) % 14.98/14.67 [7409]~P128(x74091)+~P1(f862(f862(f227(x74091),f2(x74091)),x74093))+~P1(f862(f862(f227(x74091),f2(x74091)),x74092))+P1(f862(f862(f227(x74091),f2(x74091)),f862(f862(f74(x74091),x74092),x74093))) % 14.98/14.67 [7411]~P66(x74111)+~P1(f862(f862(f227(x74111),f2(x74111)),x74113))+~P1(f862(f862(f227(x74111),f2(x74111)),x74112))+P1(f862(f862(f227(x74111),f2(x74111)),f862(f862(f281(x74111),x74112),x74113))) % 14.98/14.67 [7412]~P67(x74121)+~P1(f862(f862(f228(x74121),f2(x74121)),x74123))+~P1(f862(f862(f227(x74121),f2(x74121)),x74122))+P1(f862(f862(f227(x74121),f2(x74121)),f862(f862(f281(x74121),x74122),x74123))) % 14.98/14.67 [7413]~P127(x74131)+~P1(f862(f862(f228(x74131),f71(x74131)),x74133))+~P1(f862(f862(f228(x74131),f71(x74131)),x74132))+P1(f862(f862(f228(x74131),f71(x74131)),f862(f862(f74(x74131),x74132),x74133))) % 14.98/14.67 [7414]~P135(x74141)+~P1(f862(f862(f228(x74141),f2(x74141)),x74143))+~P1(f862(f862(f228(x74141),f2(x74141)),x74142))+P1(f862(f862(f228(x74141),f2(x74141)),f862(f862(f74(x74141),x74142),x74143))) % 14.98/14.67 [7417]~P87(x74171)+~P1(f862(f862(f228(x74171),f2(x74171)),x74173))+~P1(f862(f862(f228(x74171),f2(x74171)),x74172))+P1(f862(f862(f228(x74171),f2(x74171)),f862(f862(f73(x74171),x74172),x74173))) % 14.98/14.67 [7418]~P66(x74181)+~P1(f862(f862(f228(x74181),f2(x74181)),x74183))+~P1(f862(f862(f228(x74181),f2(x74181)),x74182))+P1(f862(f862(f228(x74181),f2(x74181)),f862(f862(f281(x74181),x74182),x74183))) % 14.98/14.67 [7419]~P67(x74191)+~P1(f862(f862(f228(x74191),f2(x74191)),x74193))+~P1(f862(f862(f228(x74191),f2(x74191)),x74192))+P1(f862(f862(f228(x74191),f2(x74191)),f862(f862(f281(x74191),x74192),x74193))) % 14.98/14.67 [7500]~P93(x75001)+~P1(f862(f54(x75001),x75003))+E(f12(x75001,f862(f862(f301(x75001),x75002),x75003)),x75002)+~E(f862(f862(f3(f932(x75001,a921)),x75003),f862(f862(f301(x75001),x75002),f181(f932(x75001,a921)))),f181(f932(x75001,a921))) % 14.98/14.67 [7501]~P93(x75011)+~P1(f862(f54(x75011),x75013))+E(f15(x75011,f862(f862(f301(x75011),x75012),x75013)),x75012)+~E(f862(f862(f3(f932(x75011,a921)),x75013),f862(f862(f301(x75011),x75012),f181(f932(x75011,a921)))),f181(f932(x75011,a921))) % 14.98/14.67 [7502]~P109(x75021)+~P1(f862(f54(x75021),x75023))+E(f16(x75021,f862(f862(f301(x75021),x75022),x75023)),x75022)+~E(f862(f862(f3(f932(x75021,a921)),x75023),f862(f862(f301(x75021),x75022),f181(f932(x75021,a921)))),f181(f932(x75021,a921))) % 14.98/14.67 [7503]~P109(x75031)+~P1(f862(f54(x75031),x75033))+E(f17(x75031,f862(f862(f301(x75031),x75032),x75033)),x75032)+~E(f862(f862(f3(f932(x75031,a921)),x75033),f862(f862(f301(x75031),x75032),f181(f932(x75031,a921)))),f181(f932(x75031,a921))) % 14.98/14.67 [7505]~P128(x75051)+P1(f862(f862(f227(x75051),x75052),f2(x75051)))+P1(f862(f862(f227(x75051),f2(x75051)),x75053))+~P1(f862(f862(f227(x75051),f2(x75051)),f862(f862(f74(x75051),x75053),x75052))) % 14.98/14.67 [7506]~P128(x75061)+P1(f862(f862(f227(x75061),x75062),f2(x75061)))+P1(f862(f862(f227(x75061),f2(x75061)),x75063))+~P1(f862(f862(f227(x75061),f2(x75061)),f862(f862(f74(x75061),x75062),x75063))) % 14.98/14.67 [7507]~P66(x75071)+P1(f862(f862(f227(x75071),x75072),f2(x75071)))+P1(f862(f862(f227(x75071),f2(x75071)),x75073))+~P1(f862(f862(f227(x75071),f2(x75071)),f862(f862(f281(x75071),x75073),x75072))) % 14.98/14.67 [7508]~P66(x75081)+P1(f862(f862(f227(x75081),x75082),f2(x75081)))+P1(f862(f862(f227(x75081),f2(x75081)),x75083))+~P1(f862(f862(f227(x75081),f2(x75081)),f862(f862(f281(x75081),x75082),x75083))) % 14.98/14.67 [7509]~P128(x75091)+P1(f862(f862(f227(x75091),x75092),f2(x75091)))+P1(f862(f862(f227(x75091),f2(x75091)),x75092))+~P1(f862(f862(f227(x75091),f2(x75091)),f862(f862(f74(x75091),x75093),x75092))) % 14.98/14.67 [7510]~P128(x75101)+P1(f862(f862(f227(x75101),x75102),f2(x75101)))+P1(f862(f862(f227(x75101),f2(x75101)),x75102))+~P1(f862(f862(f227(x75101),f2(x75101)),f862(f862(f74(x75101),x75102),x75103))) % 14.98/14.67 [7511]~P66(x75111)+P1(f862(f862(f227(x75111),x75112),f2(x75111)))+P1(f862(f862(f227(x75111),f2(x75111)),x75112))+~P1(f862(f862(f227(x75111),f2(x75111)),f862(f862(f281(x75111),x75113),x75112))) % 14.98/14.67 [7512]~P66(x75121)+P1(f862(f862(f227(x75121),x75122),f2(x75121)))+P1(f862(f862(f227(x75121),f2(x75121)),x75122))+~P1(f862(f862(f227(x75121),f2(x75121)),f862(f862(f281(x75121),x75122),x75123))) % 14.98/14.67 [7513]~P66(x75131)+P1(f862(f862(f228(x75131),x75132),f2(x75131)))+P1(f862(f862(f228(x75131),f2(x75131)),x75133))+~P1(f862(f862(f228(x75131),f2(x75131)),f862(f862(f281(x75131),x75133),x75132))) % 14.98/14.67 [7514]~P66(x75141)+P1(f862(f862(f228(x75141),x75142),f2(x75141)))+P1(f862(f862(f228(x75141),f2(x75141)),x75143))+~P1(f862(f862(f228(x75141),f2(x75141)),f862(f862(f281(x75141),x75142),x75143))) % 14.98/14.67 [7515]~P66(x75151)+P1(f862(f862(f228(x75151),x75152),f2(x75151)))+P1(f862(f862(f228(x75151),f2(x75151)),x75152))+~P1(f862(f862(f228(x75151),f2(x75151)),f862(f862(f281(x75151),x75153),x75152))) % 14.98/14.67 [7516]~P66(x75161)+P1(f862(f862(f228(x75161),x75162),f2(x75161)))+P1(f862(f862(f228(x75161),f2(x75161)),x75162))+~P1(f862(f862(f228(x75161),f2(x75161)),f862(f862(f281(x75161),x75162),x75163))) % 14.98/14.67 [7589]~P1(f862(f862(f278(a924),x75891),x75893))+P1(f862(f862(f278(a924),x75891),x75892))+~P1(f862(f862(f227(a924),x75892),x75893))+~P1(f862(f862(f278(a924),x75891),f862(f862(f3(a924),x75893),x75892))) % 14.98/14.67 [7590]~P1(f862(f862(f278(a924),x75901),x75903))+P1(f862(f862(f278(a924),x75901),x75902))+~P1(f862(f862(f227(a924),x75903),x75902))+~P1(f862(f862(f278(a924),x75901),f862(f862(f3(a924),x75902),x75903))) % 14.98/14.67 [7606]~E(f862(f862(f94(f932(x76061,a921)),f862(f165(x76061),x76062)),f862(f165(x76061),x76063)),f181(f932(x76061,a921)))+~P1(f862(f130(x76061),x76063))+~P1(f862(f130(x76061),x76062))+P1(f862(f130(x76061),f862(f862(f127(x76061),x76062),x76063))) % 14.98/14.67 [7607]~P109(x76071)+~P1(f862(f54(x76071),x76073))+E(f13(x76071,f225(x76071),f862(f862(f301(x76071),x76072),x76073)),x76072)+~E(f862(f862(f3(f932(x76071,a921)),x76073),f862(f862(f301(x76071),x76072),f181(f932(x76071,a921)))),f181(f932(x76071,a921))) % 14.98/14.67 [7608]~P109(x76081)+~P1(f862(f54(x76081),x76083))+E(f14(x76081,f226(x76081),f862(f862(f301(x76081),x76082),x76083)),x76082)+~E(f862(f862(f3(f932(x76081,a921)),x76083),f862(f862(f301(x76081),x76082),f181(f932(x76081,a921)))),f181(f932(x76081,a921))) % 14.98/14.67 [7621]~P86(x76211)+~P1(f862(f862(f227(x76211),x76212),x76213))+~P1(f862(f862(f227(x76211),f862(f72(x76211),x76212)),x76213))+P1(f862(f862(f227(x76211),f862(f69(x76211),x76212)),x76213)) % 14.98/14.67 [7622]~P112(x76221)+~P1(f862(f862(f228(x76221),x76222),x76223))+~P1(f862(f862(f228(x76221),f862(f72(x76221),x76222)),x76223))+P1(f862(f862(f228(x76221),f862(f69(x76221),x76222)),x76223)) % 14.98/14.67 [7689]~P135(x76891)+P1(f862(f862(f228(x76891),f2(x76891)),x76892))+~P1(f862(f862(f228(x76891),f2(x76891)),x76893))+~P1(f862(f862(f228(x76891),f2(x76891)),f862(f862(f74(x76891),x76893),x76892))) % 14.98/14.67 [7690]~P135(x76901)+P1(f862(f862(f228(x76901),f2(x76901)),x76902))+~P1(f862(f862(f228(x76901),f2(x76901)),x76903))+~P1(f862(f862(f228(x76901),f2(x76901)),f862(f862(f74(x76901),x76902),x76903))) % 14.98/14.67 [7991]E(x79911,x79912)+~P1(f862(f54(x79913),x79911))+~P1(f862(f862(f227(a924),f862(f28(x79913),x79911)),f862(f28(x79913),x79912)))+~P1(f862(f862(f227(f932(x79913,a921)),x79912),x79911)) % 14.98/14.67 [8139]~P1(f862(f862(f228(a1),x81391),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x81392))+~P1(f862(f862(f227(a1),x81392),x81393))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x81391),x81392)),f862(f862(f29(a1),x81391),x81393))) % 14.98/14.67 [8149]~P1(f862(f862(f227(a1),f2(a1)),x81491))+~P1(f862(f862(f228(a1),f2(a1)),x81493))+~P1(f862(f862(f227(a1),x81493),x81492))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x81491),x81492)),f862(f862(f29(a1),x81491),x81493))) % 14.98/14.67 [8286]E(f862(x82861,f433(x82862,x82861,x82863)),x82862)+~P1(f862(f862(f227(a1),x82862),f862(x82861,x82863)))+P1(f862(f862(f228(a924),f434(x82862,x82861,x82863)),x82863))+~P1(f862(f862(f227(a1),f862(x82861,f2(a924))),x82862)) % 14.98/14.67 [8287]E(f862(x82871,f439(x82872,x82871,x82873)),x82872)+~P1(f862(f862(f227(a1),x82872),f862(x82871,x82873)))+P1(f862(f862(f228(a924),f440(x82872,x82871,x82873)),x82873))+~P1(f862(f862(f227(a1),f862(x82871,f2(a924))),x82872)) % 14.98/14.67 [8392]~P1(f862(f54(x83921),x83923))+~P1(f862(f862(f228(a924),f862(f28(x83921),x83922)),f862(f28(x83921),x83923)))+~P1(f862(f862(f227(f932(x83921,a921)),x83922),x83923))+P1(f862(f862(f228(f932(x83921,a921)),x83922),x83923)) % 14.98/14.67 [8419]E(f862(f862(f73(a1),f385(x84193,x84191,x84192)),f386(x84193,x84191,x84192)),x84191)+E(f862(f862(f3(a1),x84191),x84192),x84191)+~P1(f862(f862(f228(a1),f2(a1)),x84192))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x84191),f71(a1))),x84193)) % 14.98/14.67 [8420]E(f862(f862(f3(a1),f393(x84203,x84201,x84202)),f394(x84203,x84201,x84202)),x84201)+E(f862(f862(f73(a1),x84201),x84202),x84201)+~P1(f862(f862(f228(a1),f2(a1)),x84202))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x84201),f71(a1))),x84203)) % 14.98/14.67 [8471]~P1(f862(f862(f227(a924),x84713),x84711))+P1(f862(f862(f227(a924),x84711),x84712))+~P1(f862(f862(f227(a924),x84713),x84712))+~P1(f862(f862(f227(a924),f862(f862(f3(a924),x84711),x84713)),f862(f862(f3(a924),x84712),x84713))) % 14.98/14.67 [8472]~P1(f862(f862(f227(a924),x84723),x84721))+P1(f862(f862(f228(a924),x84721),x84722))+~P1(f862(f862(f227(a924),x84723),x84722))+~P1(f862(f862(f228(a924),f862(f862(f3(a924),x84721),x84723)),f862(f862(f3(a924),x84722),x84723))) % 14.98/14.67 [8491]~P109(x84912)+E(x84911,f106(x84912))+~P11(x84912,f862(f161(x84912),x84911))+E(f862(f135(x84912,x84912,f862(f9(x84912,x84912,x84912),f226(x84912)),x84913),f862(f161(x84912),x84911)),f862(f862(f226(x84912),f862(f862(f157(x84912),x84911),f2(a924))),x84913)) % 14.98/14.67 [8560]E(f862(f862(f3(a1),x85601),x85602),x85601)+~P1(f862(f862(f228(a1),f2(a1)),x85602))+P1(f862(f862(f321(a1),f385(x85603,x85601,x85602)),x85603))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x85601),f71(a1))),x85603)) % 14.98/14.67 [8561]E(f862(f862(f73(a1),x85611),x85612),x85611)+~P1(f862(f862(f228(a1),f2(a1)),x85612))+P1(f862(f862(f321(a1),f393(x85613,x85611,x85612)),x85613))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x85611),f71(a1))),x85613)) % 14.98/14.67 [8634]~P1(f862(f862(f227(a1),x86341),f862(x86342,x86343)))+P1(f862(f862(f228(a924),f434(x86341,x86342,x86343)),x86343))+P1(f862(f862(f227(a924),f433(x86341,x86342,x86343)),x86343))+~P1(f862(f862(f227(a1),f862(x86342,f2(a924))),x86341)) % 14.98/14.67 [8635]~P1(f862(f862(f227(a1),x86351),f862(x86352,x86353)))+P1(f862(f862(f228(a924),f440(x86351,x86352,x86353)),x86353))+P1(f862(f862(f227(a924),f439(x86351,x86352,x86353)),x86353))+~P1(f862(f862(f227(a1),f862(x86352,f2(a924))),x86351)) % 14.98/14.67 [8709]E(f862(f862(f3(a1),x87091),x87092),x87091)+~P1(f862(f862(f228(a1),f2(a1)),x87092))+P1(f862(f862(f321(a1),f386(x87093,x87091,x87092)),f296(a1,f71(a1),x87092)))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x87091),f71(a1))),x87093)) % 14.98/14.67 [8710]E(f862(f862(f73(a1),x87101),x87102),x87101)+~P1(f862(f862(f228(a1),f2(a1)),x87102))+P1(f862(f862(f321(a1),f394(x87103,x87101,x87102)),f296(a1,f71(a1),x87102)))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x87101),f71(a1))),x87103)) % 14.98/14.67 [8844]~P127(x88441)+~P1(f862(f862(f228(x88441),x88442),f71(x88441)))+~P1(f862(f862(f228(x88441),f2(x88441)),x88442))+P1(f862(f862(f228(x88441),f862(f862(f74(x88441),x88442),f862(f862(f236(x88441),x88442),x88443))),f862(f862(f236(x88441),x88442),x88443))) % 14.98/14.67 [8938]~P1(f862(x89381,x89382))+P1(f862(x89381,f2(a924)))+~P1(f862(f862(f228(a924),x89382),x89383))+~P1(f862(x89381,f38(a924,f862(a105,f437(x89382,x89381,x89383)),x89383))) % 14.98/14.67 [9092]E(f510(x90921,x90922,x90923),f2(a924))+P1(f862(f862(x90921,x90923),x90922))+P1(f862(f862(x90921,f510(x90921,x90922,x90923)),f38(a924,f508(x90921,x90922,x90923),f510(x90921,x90922,x90923))))+~P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),x90923),x90922))) % 14.98/14.67 [9128]~P22(x91281,x91281,x91282,x91283)+E(f862(f302(x91281,x91281,x91282),x91283),x91283)+~P1(f862(f54(x91281),x91283))+~P1(f862(f862(f227(f932(x91281,a921)),f862(f302(x91281,x91281,x91282),x91283)),x91283)) % 14.98/14.67 [9345]P1(f862(f862(x93451,x93452),x93453))+P1(f862(f862(f228(a1),f779(x93451,x93453,x93452)),f780(x93451,x93453,x93452)))+P1(f862(f862(x93451,f779(x93451,x93453,x93452)),f862(f862(f73(a1),f780(x93451,x93453,x93452)),f71(a1))))+~P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),x93452),x93453))) % 14.98/14.67 [9362]P1(f862(f862(x93621,x93622),x93623))+~P1(f862(f862(f228(a1),f507(x93621,x93623,x93622)),f2(a1)))+P1(f862(f862(x93621,f862(f72(a1),f504(x93621,x93623,x93622))),f862(f72(a1),f507(x93621,x93623,x93622))))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x93622),x93623))) % 14.98/14.67 [9551]P1(f862(f862(x95511,x95512),x95513))+P1(f862(f862(x95511,f862(f862(f73(a1),f683(x95511,x95513,x95512)),f71(a1))),f685(x95511,x95513,x95512)))+~P1(f862(f862(f227(a1),f683(x95511,x95513,x95512)),f685(x95511,x95513,x95512)))+~P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),x95512),x95513))) % 14.98/14.67 [9990]~P63(x99902)+~P63(x99901)+~P1(f862(f49(f931(x99901,x99902)),x99903))+P1(f862(f49(x99901),f862(f862(f10(f932(x99902,a921),a921,x99901),f49(x99902)),f862(f862(f10(f932(x99902,f931(x99901,x99902)),f932(x99902,a921),x99901),f862(f10(f931(x99901,x99902),a921,x99902),x99903)),f244(x99901,x99902))))) % 14.98/14.67 [9991]~P63(x99912)+~P63(x99911)+~P1(f862(f50(f931(x99911,x99912)),x99913))+P1(f862(f50(x99911),f862(f862(f10(f932(x99912,a921),a921,x99911),f50(x99912)),f862(f862(f10(f932(x99912,f931(x99911,x99912)),f932(x99912,a921),x99911),f862(f10(f931(x99911,x99912),a921,x99912),x99913)),f244(x99911,x99912))))) % 14.98/14.67 [10086]~P63(x100862)+~P63(x100861)+P1(f862(f49(f931(x100861,x100862)),x100863))+~P1(f862(f49(x100861),f862(f862(f10(f932(x100862,a921),a921,x100861),f49(x100862)),f862(f862(f10(f932(x100862,f931(x100861,x100862)),f932(x100862,a921),x100861),f862(f10(f931(x100861,x100862),a921,x100862),x100863)),f244(x100861,x100862))))) % 14.98/14.67 [10087]~P63(x100872)+~P63(x100871)+P1(f862(f50(f931(x100871,x100872)),x100873))+~P1(f862(f50(x100871),f862(f862(f10(f932(x100872,a921),a921,x100871),f50(x100872)),f862(f862(f10(f932(x100872,f931(x100871,x100872)),f932(x100872,a921),x100871),f862(f10(f931(x100871,x100872),a921,x100872),x100873)),f244(x100871,x100872))))) % 14.98/14.67 [10249]E(f862(x102491,f433(x102492,x102491,x102493)),x102492)+~P1(f862(f862(f227(a1),x102492),f862(x102491,x102493)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x102491,f862(f862(f73(a924),f434(x102492,x102491,x102493)),f71(a924)))),f862(x102491,f434(x102492,x102491,x102493))))),f71(a1)))+~P1(f862(f862(f227(a1),f862(x102491,f2(a924))),x102492)) % 14.98/14.67 [10250]E(f862(x102501,f439(x102502,x102501,x102503)),x102502)+~P1(f862(f862(f227(a1),x102502),f862(x102501,x102503)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x102501,f862(f862(f73(a924),f440(x102502,x102501,x102503)),f71(a924)))),f862(x102501,f440(x102502,x102501,x102503))))),f71(a1)))+~P1(f862(f862(f227(a1),f862(x102501,f2(a924))),x102502)) % 14.98/14.67 [10253]~P1(f862(f862(f227(a1),x102531),f862(x102532,x102533)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x102532,f862(f862(f73(a924),f434(x102531,x102532,x102533)),f71(a924)))),f862(x102532,f434(x102531,x102532,x102533))))),f71(a1)))+P1(f862(f862(f227(a924),f433(x102531,x102532,x102533)),x102533))+~P1(f862(f862(f227(a1),f862(x102532,f2(a924))),x102531)) % 14.98/14.67 [10254]~P1(f862(f862(f227(a1),x102541),f862(x102542,x102543)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x102542,f862(f862(f73(a924),f440(x102541,x102542,x102543)),f71(a924)))),f862(x102542,f440(x102541,x102542,x102543))))),f71(a1)))+P1(f862(f862(f227(a924),f439(x102541,x102542,x102543)),x102543))+~P1(f862(f862(f227(a1),f862(x102542,f2(a924))),x102541)) % 14.98/14.67 [10313]E(x103131,x103132)+~E(f862(f135(f925(x103133),f925(x103133),f127(x103133),f106(x103133)),x103131),f862(f135(f925(x103133),f925(x103133),f127(x103133),f106(x103133)),x103132))+~E(f862(f182(f925(f925(x103133))),x103131),f862(f182(f925(f925(x103133))),x103132))+~P1(f862(f862(f249(f925(x103133),f925(x103133),a921),f862(f862(f9(f925(x103133),f932(f925(x103133),a924),f932(f925(x103133),a921)),f862(f862(f10(f932(a924,a921),f932(f932(f925(x103133),a924),f932(f925(x103133),a921)),f925(x103133)),f10(a924,a921,f925(x103133))),f862(f862(f10(a924,f932(a924,a921),f925(x103133)),a317),f182(f925(x103133))))),f182(f925(x103133)))),f709(x103132,x103131,x103133))) % 14.98/14.67 [10314]E(x103141,x103142)+~E(f862(f135(f925(x103143),f925(x103143),f127(x103143),f106(x103143)),x103141),f862(f135(f925(x103143),f925(x103143),f127(x103143),f106(x103143)),x103142))+~E(f862(f182(f925(f925(x103143))),x103141),f862(f182(f925(f925(x103143))),x103142))+~P1(f862(f862(f249(f925(x103143),f925(x103143),a921),f862(f862(f9(f925(x103143),f932(f925(x103143),a924),f932(f925(x103143),a921)),f862(f862(f10(f932(a924,a921),f932(f932(f925(x103143),a924),f932(f925(x103143),a921)),f925(x103143)),f10(a924,a921,f925(x103143))),f862(f862(f10(a924,f932(a924,a921),f925(x103143)),a317),f182(f925(x103143))))),f182(f925(x103143)))),f710(x103141,x103142,x103143))) % 14.98/14.67 [7011]~E(f71(a924),f2(a924))+~P1(f862(f54(x70111),x70113))+~P1(f862(f54(x70111),x70112))+E(f862(f862(f73(a924),f862(f28(x70111),x70112)),f862(f28(x70111),x70113)),f862(f28(x70111),f862(f862(f103(f932(x70111,a921)),x70112),x70113))) % 14.98/14.67 [7426]~P104(x74261)+~P1(f862(f54(x74261),x74262))+~P1(f862(f862(f321(x74261),x74263),x74262))+P1(f862(f862(f227(x74261),f862(f56(x74261,f94(x74261)),x74262)),x74263)) % 14.98/14.67 [7427]~P109(x74271)+~P1(f862(f54(x74271),x74272))+~P1(f862(f862(f321(x74271),x74273),x74272))+P1(f862(f862(f227(x74271),f862(f56(x74271,f225(x74271)),x74272)),x74273)) % 14.98/14.67 [7682]~P1(f862(f54(x76821),x76823))+~P1(f862(f54(x76821),x76822))+~E(f862(f862(f94(f932(x76821,a921)),x76822),x76823),f181(f932(x76821,a921)))+E(f862(f862(f73(a924),f862(f28(x76821),x76822)),f862(f28(x76821),x76823)),f862(f28(x76821),f862(f862(f103(f932(x76821,a921)),x76822),x76823))) % 14.98/14.67 [8477]~P35(x84771,x84773)+~P35(x84771,x84772)+~E(f862(f862(f94(f932(x84771,a921)),f862(f256(x84771,x84771),x84772)),f862(f275(x84771,x84771),x84773)),f181(f932(x84771,a921)))+P35(x84771,f862(f862(f103(f932(f931(x84771,x84771),a921)),x84772),x84773)) % 14.98/14.67 [8572]E(x85721,f862(f862(f29(a924),x85722),x85723))+~P1(f862(f862(f228(a924),f2(a924)),x85723))+~P1(f862(f862(f228(a924),x85722),f862(f862(f74(a924),x85723),f862(a105,x85721))))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x85723),x85721)),x85722)) % 14.98/14.67 [8707]~P1(f862(f54(x87071),x87072))+~P1(f862(f54(x87071),x87073))+E(f862(f862(f73(a924),f862(f28(x87071),x87072)),f862(f28(x87071),x87073)),f862(f28(x87071),f862(f862(f103(f932(x87071,a921)),x87072),x87073)))+P1(f862(f862(f321(x87071),f352(x87073,x87072,x87071)),f862(f862(f94(f932(x87071,a921)),x87072),x87073))) % 14.98/14.67 [9104]~P128(x91042)+~E(x91041,f2(x91042))+~E(x91043,f2(x91042))+~P1(f862(f862(f228(x91042),f2(x91042)),f862(f862(f73(x91042),f862(f862(f74(x91042),x91043),x91043)),f862(f862(f74(x91042),x91041),x91041)))) % 14.98/14.67 [9634]~P35(x96341,x96343)+~P35(x96341,x96342)+P35(x96341,f862(f862(f103(f932(f931(x96341,x96341),a921)),x96342),x96343))+~P1(f862(f862(f227(f932(f931(x96341,x96341),a921)),f862(f862(f280(x96341,x96341,x96341),x96342),x96343)),x96342)) % 14.98/14.67 [9764]~P1(f862(x97641,x97643))+~P1(f862(f54(x97642),x97643))+P1(f862(x97641,f181(f932(x97642,a921))))+~P1(f862(x97641,f862(f862(f3(f932(x97642,a921)),f876(x97641,x97643,x97642)),f862(f862(f301(x97642),f877(x97641,x97643,x97642)),f181(f932(x97642,a921)))))) % 14.98/14.67 [8884]~P1(f862(f862(f228(a1),f2(a1)),x88843))+P1(f862(f862(f227(a1),f2(a1)),x88841))+~P1(f862(f862(f228(a1),x88842),x88843))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f862(f862(f74(a1),x88843),x88841)),x88842))) % 14.98/14.67 [8909]~P93(x89091)+~P1(f862(f54(x89091),x89092))+E(f862(f862(f3(f932(x89091,a921)),x89092),f862(f862(f301(x89091),x89093),f181(f932(x89091,a921)))),f181(f932(x89091,a921)))+E(f862(f862(f94(x89091),x89093),f12(x89091,f862(f862(f3(f932(x89091,a921)),x89092),f862(f862(f301(x89091),x89093),f181(f932(x89091,a921)))))),f12(x89091,f862(f862(f301(x89091),x89093),x89092))) % 14.98/14.67 [8910]~P93(x89101)+~P1(f862(f54(x89101),x89102))+E(f862(f862(f3(f932(x89101,a921)),x89102),f862(f862(f301(x89101),x89103),f181(f932(x89101,a921)))),f181(f932(x89101,a921)))+E(f862(f862(f103(x89101),x89103),f15(x89101,f862(f862(f3(f932(x89101,a921)),x89102),f862(f862(f301(x89101),x89103),f181(f932(x89101,a921)))))),f15(x89101,f862(f862(f301(x89101),x89103),x89102))) % 14.98/14.67 [8911]~P109(x89111)+~P1(f862(f54(x89111),x89112))+E(f862(f862(f3(f932(x89111,a921)),x89112),f862(f862(f301(x89111),x89113),f181(f932(x89111,a921)))),f181(f932(x89111,a921)))+E(f862(f862(f225(x89111),x89113),f16(x89111,f862(f862(f3(f932(x89111,a921)),x89112),f862(f862(f301(x89111),x89113),f181(f932(x89111,a921)))))),f16(x89111,f862(f862(f301(x89111),x89113),x89112))) % 14.98/14.67 [8912]~P109(x89121)+~P1(f862(f54(x89121),x89122))+E(f862(f862(f3(f932(x89121,a921)),x89122),f862(f862(f301(x89121),x89123),f181(f932(x89121,a921)))),f181(f932(x89121,a921)))+E(f862(f862(f226(x89121),x89123),f17(x89121,f862(f862(f3(f932(x89121,a921)),x89122),f862(f862(f301(x89121),x89123),f181(f932(x89121,a921)))))),f17(x89121,f862(f862(f301(x89121),x89123),x89122))) % 14.98/14.67 [8984]~P109(x89841)+~P1(f862(f54(x89841),x89842))+E(f862(f862(f3(f932(x89841,a921)),x89842),f862(f862(f301(x89841),x89843),f181(f932(x89841,a921)))),f181(f932(x89841,a921)))+E(f862(f862(f225(x89841),x89843),f13(x89841,f225(x89841),f862(f862(f3(f932(x89841,a921)),x89842),f862(f862(f301(x89841),x89843),f181(f932(x89841,a921)))))),f13(x89841,f225(x89841),f862(f862(f301(x89841),x89843),x89842))) % 14.98/14.67 [8985]~P109(x89851)+~P1(f862(f54(x89851),x89852))+E(f862(f862(f3(f932(x89851,a921)),x89852),f862(f862(f301(x89851),x89853),f181(f932(x89851,a921)))),f181(f932(x89851,a921)))+E(f862(f862(f226(x89851),x89853),f14(x89851,f226(x89851),f862(f862(f3(f932(x89851,a921)),x89852),f862(f862(f301(x89851),x89853),f181(f932(x89851,a921)))))),f14(x89851,f226(x89851),f862(f862(f301(x89851),x89853),x89852))) % 14.98/14.67 [9571]E(x95711,x95712)+~E(f862(f135(f925(x95713),f925(x95713),f127(x95713),f106(x95713)),x95711),f862(f135(f925(x95713),f925(x95713),f127(x95713),f106(x95713)),x95712))+~E(f862(f182(f925(f925(x95713))),x95711),f862(f182(f925(f925(x95713))),x95712))+P1(f862(f862(f321(f931(f925(x95713),f925(x95713))),f709(x95712,x95711,x95713)),f862(f165(f931(f925(x95713),f925(x95713))),f862(f862(f174(f925(x95713),f925(x95713)),x95711),x95712)))) % 14.98/14.67 [9572]E(x95721,x95722)+~E(f862(f135(f925(x95723),f925(x95723),f127(x95723),f106(x95723)),x95721),f862(f135(f925(x95723),f925(x95723),f127(x95723),f106(x95723)),x95722))+~E(f862(f182(f925(f925(x95723))),x95721),f862(f182(f925(f925(x95723))),x95722))+P1(f862(f862(f321(f931(f925(x95723),f925(x95723))),f710(x95721,x95722,x95723)),f862(f165(f931(f925(x95723),f925(x95723))),f862(f862(f174(f925(x95723),f925(x95723)),x95722),x95721)))) % 14.98/14.67 [10422]~P102(x104222)+E(x104221,f181(f932(x104222,a921)))+~P1(f862(f54(x104222),x104221))+E(f12(x104222,f862(f254(x104222),f862(f862(f10(f932(x104222,a921),a921,x104222),f80(x104222)),f862(f862(f9(x104222,f932(x104222,a921),f932(x104222,a921)),f862(f862(f10(f932(x104222,f932(a921,a921)),f932(f932(x104222,a921),f932(x104222,a921)),x104222),f20(x104222,a921,a921)),f862(f862(f10(f932(x104222,a921),f932(x104222,f932(a921,a921)),x104222),f862(f10(a921,f932(a921,a921),x104222),a318)),f862(f862(f9(x104222,f932(x104222,x104222),f932(x104222,a921)),f862(f862(f10(f932(x104222,a921),f932(f932(x104222,x104222),f932(x104222,a921)),x104222),f10(x104222,a921,x104222)),a317)),f862(f103(x104222),x104223))))),f862(f862(f9(x104222,f932(x104222,a921),a921),f321(x104222)),x104221))))),f862(f862(f103(x104222),x104223),f12(x104222,x104221))) % 14.98/14.67 [10423]~P102(x104232)+E(x104231,f181(f932(x104232,a921)))+~P1(f862(f54(x104232),x104231))+E(f15(x104232,f862(f254(x104232),f862(f862(f10(f932(x104232,a921),a921,x104232),f80(x104232)),f862(f862(f9(x104232,f932(x104232,a921),f932(x104232,a921)),f862(f862(f10(f932(x104232,f932(a921,a921)),f932(f932(x104232,a921),f932(x104232,a921)),x104232),f20(x104232,a921,a921)),f862(f862(f10(f932(x104232,a921),f932(x104232,f932(a921,a921)),x104232),f862(f10(a921,f932(a921,a921),x104232),a318)),f862(f862(f9(x104232,f932(x104232,x104232),f932(x104232,a921)),f862(f862(f10(f932(x104232,a921),f932(f932(x104232,x104232),f932(x104232,a921)),x104232),f10(x104232,a921,x104232)),a317)),f862(f94(x104232),x104233))))),f862(f862(f9(x104232,f932(x104232,a921),a921),f321(x104232)),x104231))))),f862(f862(f94(x104232),x104233),f15(x104232,x104231))) % 14.98/14.67 [10424]~P77(x104242)+E(x104241,f181(f932(x104242,a921)))+~P1(f862(f54(x104242),x104241))+E(f16(x104242,f862(f254(x104242),f862(f862(f10(f932(x104242,a921),a921,x104242),f80(x104242)),f862(f862(f9(x104242,f932(x104242,a921),f932(x104242,a921)),f862(f862(f10(f932(x104242,f932(a921,a921)),f932(f932(x104242,a921),f932(x104242,a921)),x104242),f20(x104242,a921,a921)),f862(f862(f10(f932(x104242,a921),f932(x104242,f932(a921,a921)),x104242),f862(f10(a921,f932(a921,a921),x104242),a318)),f862(f862(f9(x104242,f932(x104242,x104242),f932(x104242,a921)),f862(f862(f10(f932(x104242,a921),f932(f932(x104242,x104242),f932(x104242,a921)),x104242),f10(x104242,a921,x104242)),a317)),f862(f73(x104242),x104243))))),f862(f862(f9(x104242,f932(x104242,a921),a921),f321(x104242)),x104241))))),f862(f862(f73(x104242),x104243),f16(x104242,x104241))) % 14.98/14.67 [10425]~P77(x104252)+E(x104251,f181(f932(x104252,a921)))+~P1(f862(f54(x104252),x104251))+E(f17(x104252,f862(f254(x104252),f862(f862(f10(f932(x104252,a921),a921,x104252),f80(x104252)),f862(f862(f9(x104252,f932(x104252,a921),f932(x104252,a921)),f862(f862(f10(f932(x104252,f932(a921,a921)),f932(f932(x104252,a921),f932(x104252,a921)),x104252),f20(x104252,a921,a921)),f862(f862(f10(f932(x104252,a921),f932(x104252,f932(a921,a921)),x104252),f862(f10(a921,f932(a921,a921),x104252),a318)),f862(f862(f9(x104252,f932(x104252,x104252),f932(x104252,a921)),f862(f862(f10(f932(x104252,a921),f932(f932(x104252,x104252),f932(x104252,a921)),x104252),f10(x104252,a921,x104252)),a317)),f862(f73(x104252),x104253))))),f862(f862(f9(x104252,f932(x104252,a921),a921),f321(x104252)),x104251))))),f862(f862(f73(x104252),x104253),f17(x104252,x104251))) % 14.98/14.67 [10426]~P109(x104262)+E(x104261,f181(f932(x104262,a921)))+~P1(f862(f54(x104262),x104261))+E(f14(x104262,f226(x104262),f862(f254(x104262),f862(f862(f10(f932(x104262,a921),a921,x104262),f80(x104262)),f862(f862(f9(x104262,f932(x104262,a921),f932(x104262,a921)),f862(f862(f10(f932(x104262,f932(a921,a921)),f932(f932(x104262,a921),f932(x104262,a921)),x104262),f20(x104262,a921,a921)),f862(f862(f10(f932(x104262,a921),f932(x104262,f932(a921,a921)),x104262),f862(f10(a921,f932(a921,a921),x104262),a318)),f862(f862(f9(x104262,f932(x104262,x104262),f932(x104262,a921)),f862(f862(f10(f932(x104262,a921),f932(f932(x104262,x104262),f932(x104262,a921)),x104262),f10(x104262,a921,x104262)),a317)),f862(f225(x104262),x104263))))),f862(f862(f9(x104262,f932(x104262,a921),a921),f321(x104262)),x104261))))),f862(f862(f225(x104262),x104263),f14(x104262,f226(x104262),x104261))) % 14.98/14.67 [10427]~P109(x104272)+E(x104271,f181(f932(x104272,a921)))+~P1(f862(f54(x104272),x104271))+E(f13(x104272,f225(x104272),f862(f254(x104272),f862(f862(f10(f932(x104272,a921),a921,x104272),f80(x104272)),f862(f862(f9(x104272,f932(x104272,a921),f932(x104272,a921)),f862(f862(f10(f932(x104272,f932(a921,a921)),f932(f932(x104272,a921),f932(x104272,a921)),x104272),f20(x104272,a921,a921)),f862(f862(f10(f932(x104272,a921),f932(x104272,f932(a921,a921)),x104272),f862(f10(a921,f932(a921,a921),x104272),a318)),f862(f862(f9(x104272,f932(x104272,x104272),f932(x104272,a921)),f862(f862(f10(f932(x104272,a921),f932(f932(x104272,x104272),f932(x104272,a921)),x104272),f10(x104272,a921,x104272)),a317)),f862(f226(x104272),x104273))))),f862(f862(f9(x104272,f932(x104272,a921),a921),f321(x104272)),x104271))))),f862(f862(f226(x104272),x104273),f13(x104272,f225(x104272),x104271))) % 14.98/14.67 [10153]~P112(x101531)+~E(x101533,f2(x101531))+~E(x101532,f2(x101531))+E(f862(f862(f73(x101531),f862(f862(f236(x101531),x101532),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x101531),x101533),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f2(x101531)) % 14.98/14.67 [10294]~P127(x102941)+~P1(f862(f862(f227(x102941),f2(x102941)),x102943))+P1(f862(f862(f227(x102941),x102942),x102943))+~P1(f862(f862(f227(x102941),f862(f862(f236(x102941),x102942),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102941),x102943),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))) % 14.98/14.67 [10351]~P112(x103512)+~E(x103511,f2(x103512))+~E(x103513,f2(x103512))+~P1(f862(f862(f228(x103512),f2(x103512)),f862(f862(f73(x103512),f862(f862(f236(x103512),x103513),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103512),x103511),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))) % 14.98/14.67 [6892]~P5(x68923,x68922)+~P1(f862(x68921,x68924))+~P1(f862(f862(f321(x68923),x68924),f262(x68923,x68922)))+P1(f862(x68921,f825(x68921,x68922,x68923))) % 14.98/14.67 [8819]P23(x88191,x88192,f829(x88193,x88192,x88194,x88191),x88194,x88193)+~E(f862(f28(x88191),x88194),f862(f28(x88192),x88193))+~P1(f862(f54(x88192),x88193))+~P1(f862(f54(x88191),x88194)) % 14.98/14.67 [9532]E(x95321,x95322)+~E(f650(x95321,x95322,x95324,x95323),f655(x95321,x95322,x95324,x95323))+P1(f862(f862(f321(f931(f925(x95323),f925(x95323))),f862(f862(f244(f925(x95323),f925(x95323)),x95322),x95321)),f140(x95323,x95324)))+P1(f862(f862(f321(f931(f925(x95323),f925(x95323))),f862(f862(f244(f925(x95323),f925(x95323)),x95321),x95322)),f140(x95323,x95324))) % 14.98/14.67 [5022]~P64(x50222)+~E(x50224,f2(x50222))+~E(x50221,f2(x50222))+E(x50221,f862(f862(f281(x50222),x50223),x50224)) % 14.98/14.67 [5023]~P64(x50231)+~E(x50233,f2(x50231))+~E(x50234,f2(x50231))+E(f862(f862(f281(x50231),x50232),x50233),x50234) % 14.98/14.67 [5143]~P64(x51432)+E(x51431,f2(x51432))+~E(x51433,f2(x51432))+~E(x51431,f862(f862(f281(x51432),x51434),x51433)) % 14.98/14.67 [5144]~P64(x51442)+E(x51441,f2(x51442))+~E(x51443,f2(x51442))+~E(f862(f862(f281(x51442),x51444),x51443),x51441) % 14.98/14.67 [5329]~P121(x53292)+E(x53291,f2(x53292))+~E(f862(f862(f281(x53292),x53293),x53291),x53294)+E(x53293,f862(f862(f74(x53292),x53294),x53291)) % 14.98/14.67 [5331]~P121(x53312)+E(x53311,f2(x53312))+~E(f862(f862(f74(x53312),x53313),x53311),x53314)+E(x53313,f862(f862(f281(x53312),x53314),x53311)) % 14.98/14.67 [5332]~P64(x53322)+E(x53321,f2(x53322))+~E(f862(f862(f281(x53322),x53323),x53321),x53324)+E(x53323,f862(f862(f74(x53322),x53324),x53321)) % 14.98/14.67 [5333]~P64(x53332)+E(x53331,f2(x53332))+~E(f862(f862(f74(x53332),x53333),x53331),x53334)+E(x53333,f862(f862(f281(x53332),x53334),x53331)) % 14.98/14.67 [5334]~P121(x53342)+E(x53341,f2(x53342))+~E(x53343,f862(f862(f281(x53342),x53344),x53341))+E(f862(f862(f74(x53342),x53343),x53341),x53344) % 14.98/14.67 [5336]~P121(x53362)+E(x53361,f2(x53362))+~E(x53363,f862(f862(f74(x53362),x53364),x53361))+E(f862(f862(f281(x53362),x53363),x53361),x53364) % 14.98/14.67 [5337]~P64(x53372)+E(x53371,f2(x53372))+~E(x53373,f862(f862(f281(x53372),x53374),x53371))+E(f862(f862(f74(x53372),x53373),x53371),x53374) % 14.98/14.67 [5338]~P64(x53382)+E(x53381,f2(x53382))+~E(x53383,f862(f862(f74(x53382),x53384),x53381))+E(f862(f862(f281(x53382),x53383),x53381),x53384) % 14.98/14.67 [5362]~P64(x53622)+~E(x53621,f2(x53622))+~E(f862(f862(f74(x53622),x53621),x53624),x53623)+E(x53621,f862(f862(f281(x53622),x53623),x53624)) % 14.98/14.67 [5363]~P64(x53631)+~E(x53634,f2(x53631))+~E(x53632,f862(f862(f74(x53631),x53634),x53633))+E(f862(f862(f281(x53631),x53632),x53633),x53634) % 14.98/14.67 [5440]~E(x54403,x54404)+~E(x54402,x54403)+~P110(x54401)+E(f296(x54401,x54402,x54403),f862(f862(f301(x54401),x54404),f181(f932(x54401,a921)))) % 14.98/14.67 [5644]~E(f107(x56442,x56441),x56443)+~E(f137(x56442,x56441),x56444)+E(x56441,f106(x56442))+E(f862(f862(f127(x56442),x56443),f862(f862(f144(x56442),x56444),f106(x56442))),x56441) % 14.98/14.67 [6282]~P127(x62823)+E(x62821,x62822)+~E(f862(f862(f236(x62823),x62824),x62821),f862(f862(f236(x62823),x62824),x62822))+~P1(f862(f862(f228(x62823),f71(x62823)),x62824)) % 14.98/14.67 [6283]E(x62831,x62832)+~E(f862(f862(f301(x62833),x62834),x62831),f862(f862(f301(x62833),x62834),x62832))+P1(f862(f862(f321(x62833),x62834),x62832))+P1(f862(f862(f321(x62833),x62834),x62831)) % 14.98/14.67 [6325]E(f862(x63251,x63252),f71(a924))+~E(f862(f862(f11(x63253,a924),x63251),x63254),f71(a924))+~P1(f862(f54(x63253),x63254))+~P1(f862(f862(f321(x63253),x63252),x63254)) % 14.98/14.67 [6326]E(f862(x63261,x63262),f2(a924))+~E(f862(f862(f8(x63263,a924),x63261),x63264),f2(a924))+~P1(f862(f54(x63263),x63264))+~P1(f862(f862(f321(x63263),x63262),x63264)) % 14.98/14.67 [6547]~P110(x65471)+~P1(f862(f862(f227(x65471),x65474),x65473))+P1(f862(f862(f227(x65471),x65472),x65473))+~P1(f862(f862(f227(x65471),x65472),x65474)) % 14.98/14.67 [6548]~P91(x65481)+~P1(f862(f862(f227(x65481),x65482),x65484))+P1(f862(f862(f227(x65481),x65482),x65483))+~P1(f862(f862(f227(x65481),x65484),x65483)) % 14.98/14.67 [6549]~P110(x65491)+~P1(f862(f862(f228(x65491),x65494),x65493))+P1(f862(f862(f228(x65491),x65492),x65493))+~P1(f862(f862(f227(x65491),x65492),x65494)) % 14.98/14.67 [6550]~P110(x65501)+~P1(f862(f862(f228(x65501),x65502),x65504))+P1(f862(f862(f228(x65501),x65502),x65503))+~P1(f862(f862(f227(x65501),x65504),x65503)) % 14.98/14.67 [6551]~P110(x65511)+~P1(f862(f862(f228(x65511),x65514),x65513))+P1(f862(f862(f228(x65511),x65512),x65513))+~P1(f862(f862(f228(x65511),x65512),x65514)) % 14.98/14.67 [6552]~P91(x65521)+~P1(f862(f862(f228(x65521),x65522),x65524))+P1(f862(f862(f228(x65521),x65522),x65523))+~P1(f862(f862(f227(x65521),x65524),x65523)) % 14.98/14.67 [6553]~P91(x65531)+~P1(f862(f862(f228(x65531),x65534),x65533))+P1(f862(f862(f228(x65531),x65532),x65533))+~P1(f862(f862(f227(x65531),x65532),x65534)) % 14.98/14.67 [6554]~P91(x65541)+~P1(f862(f862(f228(x65541),x65542),x65544))+P1(f862(f862(f228(x65541),x65542),x65543))+~P1(f862(f862(f228(x65541),x65544),x65543)) % 14.98/14.67 [6555]~P119(x65551)+~P1(f862(f862(f278(x65551),x65552),x65554))+P1(f862(f862(f278(x65551),x65552),x65553))+~P1(f862(f862(f278(x65551),x65554),x65553)) % 14.98/14.67 [6638]~P33(x66384,x66383,x66382)+E(x66381,f764(x66382,x66383,x66384))+~P1(f862(x66383,x66381))+~P1(f862(f862(f321(x66384),x66381),f862(f165(x66384),x66382))) % 14.98/14.67 [6639]~P33(x66394,x66393,x66392)+E(x66391,f775(x66392,x66393,x66394))+~P1(f862(x66393,x66391))+~P1(f862(f862(f321(x66394),x66391),f862(f165(x66394),x66392))) % 14.98/14.67 [6787]~P3(x67871)+~P1(f862(f862(f227(x67871),x67872),f31(x67871,x67874)))+P1(f862(f862(f227(x67871),x67872),x67873))+~P1(f862(f862(f321(x67871),x67873),x67874)) % 14.98/14.67 [6930]~P109(x69301)+~P11(x69301,f862(f862(f144(x69301),x69302),x69304))+~P1(f862(f862(f321(x69301),x69303),f862(f165(x69301),x69304)))+P1(f862(f862(f227(x69301),x69302),x69303)) % 14.98/14.67 [7021]~P3(x70211)+~P1(f862(f862(f227(x70211),f30(x70211,x70214)),x70213))+P1(f862(f862(f227(x70211),x70212),x70213))+~P1(f862(f862(f321(x70211),x70212),x70214)) % 14.98/14.67 [7162]~P61(x71621)+P1(f862(f862(f278(x71621),x71622),f38(x71621,x71623,x71624)))+~P1(f862(f862(f278(x71621),x71622),x71624))+~P1(f862(f862(f278(x71621),x71622),x71623)) % 14.98/14.67 [7429]~P109(x74291)+E(f862(f862(f103(f932(x74291,a921)),f862(f295(x74291,x74292),x74293)),f862(f295(x74291,x74293),x74294)),f862(f295(x74291,x74292),x74294))+~P1(f862(f862(f227(x74291),x74293),x74294))+~P1(f862(f862(f227(x74291),x74292),x74293)) % 14.98/14.67 [7474]P33(x74741,x74742,x74743)+~E(f776(x74743,x74742,x74741,x74744),x74744)+~P1(f862(x74742,x74744))+~P1(f862(f862(f321(x74741),x74744),f862(f165(x74741),x74743))) % 14.98/14.67 [7475]P33(x74751,x74752,x74753)+~E(f783(x74753,x74752,x74751,x74754),x74754)+~P1(f862(x74752,x74754))+~P1(f862(f862(f321(x74751),x74754),f862(f165(x74751),x74753))) % 14.98/14.67 [7519]~P61(x75191)+~P1(f862(f862(f278(x75191),x75192),f38(x75191,x75193,x75194)))+P1(f862(f862(f278(x75191),x75192),x75193))+~P1(f862(f862(f278(x75191),x75192),x75194)) % 14.98/14.67 [7554]~P109(x75541)+E(f862(f862(f103(f932(x75541,a921)),f862(f295(x75541,x75542),x75543)),f296(x75541,x75543,x75544)),f296(x75541,x75542,x75544))+~P1(f862(f862(f227(x75541),x75543),x75544))+~P1(f862(f862(f227(x75541),x75542),x75543)) % 14.98/14.67 [7616]~P109(x76161)+E(f862(f862(f103(f932(x76161,a921)),f298(x76161,x76162,x76163)),f862(f295(x76161,x76163),x76164)),f298(x76161,x76162,x76164))+~P1(f862(f862(f227(x76161),x76163),x76164))+~P1(f862(f862(f228(x76161),x76162),x76163)) % 14.98/14.67 [7633]~P109(x76331)+E(f862(f862(f103(f932(x76331,a921)),f296(x76331,x76332,x76333)),f298(x76331,x76333,x76334)),f862(f295(x76331,x76332),x76334))+~P1(f862(f862(f227(x76331),x76332),x76333))+~P1(f862(f862(f228(x76331),x76333),x76334)) % 14.98/14.67 [7663]~P109(x76631)+E(f862(f862(f103(f932(x76631,a921)),f298(x76631,x76632,x76633)),f296(x76631,x76633,x76634)),f297(x76631,x76632,x76634))+~P1(f862(f862(f227(x76631),x76633),x76634))+~P1(f862(f862(f228(x76631),x76632),x76633)) % 14.98/14.67 [7664]~P109(x76641)+E(f862(f862(f103(f932(x76641,a921)),f297(x76641,x76642,x76643)),f298(x76641,x76643,x76644)),f298(x76641,x76642,x76644))+~P1(f862(f862(f227(x76641),x76642),x76643))+~P1(f862(f862(f228(x76641),x76643),x76644)) % 14.98/14.67 [7665]~P109(x76651)+E(f862(f862(f103(f932(x76651,a921)),f297(x76651,x76652,x76653)),f297(x76651,x76653,x76654)),f297(x76651,x76652,x76654))+~P1(f862(f862(f227(x76651),x76653),x76654))+~P1(f862(f862(f227(x76651),x76652),x76653)) % 14.98/14.67 [7666]~P109(x76661)+E(f862(f862(f103(f932(x76661,a921)),f296(x76661,x76662,x76663)),f297(x76661,x76663,x76664)),f296(x76661,x76662,x76664))+~P1(f862(f862(f227(x76661),x76663),x76664))+~P1(f862(f862(f227(x76661),x76662),x76663)) % 14.98/14.67 [8461]P22(x84611,x84612,f543(x84613,x84612,x84614,x84611),x84614)+~P1(f862(f54(x84612),x84613))+~P1(f862(f54(x84611),x84614))+~P1(f862(f862(f227(a924),f862(f28(x84611),x84614)),f862(f28(x84612),x84613))) % 14.98/14.67 [8482]P33(x84821,x84822,x84823)+~P1(f862(x84822,x84824))+P1(f862(x84822,f776(x84823,x84822,x84821,x84824)))+~P1(f862(f862(f321(x84821),x84824),f862(f165(x84821),x84823))) % 14.98/14.67 [8483]P33(x84831,x84832,x84833)+~P1(f862(x84832,x84834))+P1(f862(x84832,f783(x84833,x84832,x84831,x84834)))+~P1(f862(f862(f321(x84831),x84834),f862(f165(x84831),x84833))) % 14.98/14.67 [8537]~P71(x85371)+~E(f862(x85373,f374(x85373,x85374,x85372,x85371)),f71(x85371))+E(f862(f862(f862(f58(x85371,x85372,f74(x85371)),x85373),f71(x85371)),x85374),f71(x85371))+~P1(f862(f54(x85372),x85374)) % 14.98/14.67 [8808]~P127(x88081)+~P1(f862(f862(f227(x88081),f2(x88081)),x88083))+P1(f862(f862(f227(x88081),x88082),x88083))+~P1(f862(f862(f227(x88081),f862(f862(f236(x88081),x88082),f862(a105,x88084))),f862(f862(f236(x88081),x88083),f862(a105,x88084)))) % 14.98/14.67 [9129]P33(x91291,x91292,x91293)+~P1(f862(x91292,x91294))+~P1(f862(f862(f321(x91291),x91294),f862(f165(x91291),x91293)))+P1(f862(f862(f321(x91291),f776(x91293,x91292,x91291,x91294)),f862(f165(x91291),x91293))) % 14.98/14.67 [9130]P33(x91301,x91302,x91303)+~P1(f862(x91302,x91304))+~P1(f862(f862(f321(x91301),x91304),f862(f165(x91301),x91303)))+P1(f862(f862(f321(x91301),f783(x91303,x91302,x91301,x91304)),f862(f165(x91301),x91303))) % 14.98/14.67 [9206]~P71(x92061)+E(f862(f862(f862(f58(x92061,x92062,f74(x92061)),x92063),f71(x92061)),x92064),f71(x92061))+~P1(f862(f54(x92062),x92064))+P1(f862(f862(f321(x92062),f374(x92063,x92064,x92062,x92061)),x92064)) % 14.98/14.67 [9707]~P1(f862(f862(f227(a1),x97074),f2(a1)))+P1(f862(f862(f227(a1),f862(f862(f73(a1),f862(f862(f74(a1),x97071),f38(a1,x97072,x97073))),x97074)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x97073))+~P1(f862(f862(f228(a1),x97071),x97074)) % 14.98/14.67 [10146]~P1(f862(f54(x101461),x101462))+~P1(f862(f862(f321(x101461),x101464),x101462))+~P1(f862(f862(f321(x101461),x101463),x101462))+P1(f862(f862(f228(a924),f862(f28(x101461),f862(f862(f3(f932(x101461,a921)),f862(f862(f3(f932(x101461,a921)),x101462),f862(f862(f301(x101461),x101463),f181(f932(x101461,a921))))),f862(f862(f301(x101461),x101464),f181(f932(x101461,a921)))))),f862(f28(x101461),x101462))) % 14.98/14.67 [7079]~P146(x70793)+~P120(x70793)+P1(f862(x70791,f858(x70792,x70791,x70793)))+~P1(f862(x70791,f862(f862(f74(x70793),x70792),x70794))) % 14.98/14.67 [7136]~P104(x71361)+~P1(f862(f862(f227(x71361),x71362),x71364))+~P1(f862(f862(f227(x71361),x71362),x71363))+P1(f862(f862(f227(x71361),x71362),f862(f862(f94(x71361),x71363),x71364))) % 14.98/14.67 [7139]~P109(x71391)+~P1(f862(f862(f227(x71391),x71392),x71394))+~P1(f862(f862(f227(x71391),x71392),x71393))+P1(f862(f862(f227(x71391),x71392),f862(f862(f225(x71391),x71393),x71394))) % 14.98/14.67 [7140]~P109(x71401)+~P1(f862(f862(f228(x71401),x71402),x71404))+~P1(f862(f862(f228(x71401),x71402),x71403))+P1(f862(f862(f228(x71401),x71402),f862(f862(f225(x71401),x71403),x71404))) % 14.98/14.67 [7160]~P65(x71602)+E(x71601,f2(x71602))+E(f862(f862(f281(x71602),f862(f862(f236(x71602),x71601),x71603)),f862(f862(f236(x71602),x71601),x71604)),f862(f862(f236(x71602),x71601),f862(f862(f3(a924),x71603),x71604)))+~P1(f862(f862(f227(a924),x71604),x71603)) % 14.98/14.67 [7206]~P109(x72061)+~P11(x72061,f862(f862(f144(x72061),x72063),x72064))+P11(x72061,f862(f862(f144(x72061),x72062),f862(f862(f144(x72061),x72063),x72064)))+~P1(f862(f862(f227(x72061),x72062),x72063)) % 14.98/14.67 [7242]~P87(x72421)+~P1(f862(f862(f227(x72421),f2(x72421)),x72424))+~P1(f862(f862(f227(x72421),x72422),x72423))+P1(f862(f862(f227(x72421),x72422),f862(f862(f73(x72421),x72423),x72424))) % 14.98/14.67 [7243]~P87(x72431)+~P1(f862(f862(f227(x72431),f2(x72431)),x72433))+~P1(f862(f862(f227(x72431),x72432),x72434))+P1(f862(f862(f227(x72431),x72432),f862(f862(f73(x72431),x72433),x72434))) % 14.98/14.67 [7244]~P127(x72441)+~P1(f862(f862(f228(x72441),f2(x72441)),x72443))+~P1(f862(f862(f228(x72441),x72442),x72444))+P1(f862(f862(f228(x72441),x72442),f862(f862(f73(x72441),x72443),x72444))) % 14.98/14.67 [7245]~P87(x72451)+~P1(f862(f862(f227(x72451),x72452),x72454))+~P1(f862(f862(f228(x72451),f2(x72451)),x72453))+P1(f862(f862(f228(x72451),x72452),f862(f862(f73(x72451),x72453),x72454))) % 14.98/14.67 [7246]~P87(x72461)+~P1(f862(f862(f227(x72461),f2(x72461)),x72463))+~P1(f862(f862(f228(x72461),x72462),x72464))+P1(f862(f862(f228(x72461),x72462),f862(f862(f73(x72461),x72463),x72464))) % 14.98/14.67 [7288]~P109(x72881)+P1(f862(f862(f227(x72881),x72882),x72883))+P1(f862(f862(f227(x72881),x72882),x72884))+~P1(f862(f862(f227(x72881),x72882),f862(f862(f226(x72881),x72884),x72883))) % 14.98/14.67 [7289]~P109(x72891)+P1(f862(f862(f228(x72891),x72892),x72893))+P1(f862(f862(f228(x72891),x72892),x72894))+~P1(f862(f862(f228(x72891),x72892),f862(f862(f226(x72891),x72894),x72893))) % 14.98/14.67 [7587]~P110(x75872)+~P63(x75871)+~P1(f862(f862(f228(f932(x75871,x75872)),x75873),x75874))+P1(f862(f862(f227(f932(x75871,x75872)),x75873),x75874)) % 14.98/14.67 [7953]~P67(x79531)+~P1(f862(f862(f228(x79531),x79534),f2(x79531)))+~P1(f862(f862(f227(x79531),x79533),f862(f862(f281(x79531),x79532),x79534)))+P1(f862(f862(f227(x79531),x79532),f862(f862(f74(x79531),x79533),x79534))) % 14.98/14.67 [7954]~P67(x79541)+~P1(f862(f862(f228(x79541),x79544),f2(x79541)))+~P1(f862(f862(f227(x79541),x79543),f862(f862(f74(x79541),x79542),x79544)))+P1(f862(f862(f227(x79541),x79542),f862(f862(f281(x79541),x79543),x79544))) % 14.98/14.67 [7955]~P67(x79551)+~P1(f862(f862(f228(x79551),x79554),f2(x79551)))+~P1(f862(f862(f228(x79551),x79553),f862(f862(f281(x79551),x79552),x79554)))+P1(f862(f862(f228(x79551),x79552),f862(f862(f74(x79551),x79553),x79554))) % 14.98/14.67 [7956]~P67(x79561)+~P1(f862(f862(f228(x79561),x79564),f2(x79561)))+~P1(f862(f862(f228(x79561),x79563),f862(f862(f74(x79561),x79562),x79564)))+P1(f862(f862(f228(x79561),x79562),f862(f862(f281(x79561),x79563),x79564))) % 14.98/14.67 [8063]~P126(x80631)+~P1(f862(f862(f227(x80631),x80632),f2(x80631)))+~P1(f862(f862(f227(x80631),x80634),x80633))+P1(f862(f862(f227(x80631),f862(f862(f74(x80631),x80632),x80633)),f862(f862(f74(x80631),x80632),x80634))) % 14.98/14.67 [8064]~P128(x80641)+~P1(f862(f862(f228(x80641),x80642),f2(x80641)))+~P1(f862(f862(f227(x80641),x80644),x80643))+P1(f862(f862(f227(x80641),f862(f862(f74(x80641),x80642),x80643)),f862(f862(f74(x80641),x80642),x80644))) % 14.98/14.67 [8065]~P126(x80651)+~P1(f862(f862(f227(x80651),x80653),f2(x80651)))+~P1(f862(f862(f227(x80651),x80654),x80652))+P1(f862(f862(f227(x80651),f862(f862(f74(x80651),x80652),x80653)),f862(f862(f74(x80651),x80654),x80653))) % 14.98/14.67 [8066]~P66(x80661)+~P1(f862(f862(f227(x80661),x80663),f2(x80661)))+~P1(f862(f862(f227(x80661),x80664),x80662))+P1(f862(f862(f227(x80661),f862(f862(f281(x80661),x80662),x80663)),f862(f862(f281(x80661),x80664),x80663))) % 14.98/14.67 [8070]~P128(x80701)+~P1(f862(f862(f228(x80701),x80703),f2(x80701)))+~P1(f862(f862(f228(x80701),x80704),x80702))+P1(f862(f862(f228(x80701),f862(f862(f74(x80701),x80702),x80703)),f862(f862(f74(x80701),x80704),x80703))) % 14.98/14.67 [8071]~P128(x80711)+~P1(f862(f862(f228(x80711),x80712),f2(x80711)))+~P1(f862(f862(f228(x80711),x80714),x80713))+P1(f862(f862(f228(x80711),f862(f862(f74(x80711),x80712),x80713)),f862(f862(f74(x80711),x80712),x80714))) % 14.98/14.67 [8072]~P67(x80721)+~P1(f862(f862(f228(x80721),x80723),f2(x80721)))+~P1(f862(f862(f228(x80721),x80724),x80722))+P1(f862(f862(f228(x80721),f862(f862(f281(x80721),x80722),x80723)),f862(f862(f281(x80721),x80724),x80723))) % 14.98/14.67 [8073]~P127(x80731)+~P1(f862(f862(f228(x80731),f71(x80731)),x80732))+~P1(f862(f862(f227(a924),x80733),x80734))+P1(f862(f862(f227(x80731),f862(f862(f236(x80731),x80732),x80733)),f862(f862(f236(x80731),x80732),x80734))) % 14.98/14.67 [8074]~P127(x80741)+~P1(f862(f862(f227(x80741),f71(x80741)),x80742))+~P1(f862(f862(f227(a924),x80743),x80744))+P1(f862(f862(f227(x80741),f862(f862(f236(x80741),x80742),x80743)),f862(f862(f236(x80741),x80742),x80744))) % 14.98/14.67 [8076]~P127(x80761)+~P1(f862(f862(f228(x80761),f71(x80761)),x80762))+~P1(f862(f862(f228(a924),x80763),x80764))+P1(f862(f862(f228(x80761),f862(f862(f236(x80761),x80762),x80763)),f862(f862(f236(x80761),x80762),x80764))) % 14.98/14.67 [8104]P1(f862(f862(f228(a924),f2(a924)),f862(x81041,x81042)))+~P1(f862(f54(x81043),x81044))+~P1(f862(f862(f321(x81043),x81042),x81044))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x81043,a924),x81041),x81044))) % 14.98/14.67 [8113]~P138(x81131)+~P1(f862(f862(f227(x81131),x81133),x81134))+~P1(f862(f862(f227(x81131),f2(x81131)),x81132))+P1(f862(f862(f227(x81131),f862(f862(f74(x81131),x81132),x81133)),f862(f862(f74(x81131),x81132),x81134))) % 14.98/14.67 [8114]~P137(x81141)+~P1(f862(f862(f227(x81141),x81143),x81144))+~P1(f862(f862(f227(x81141),f2(x81141)),x81142))+P1(f862(f862(f227(x81141),f862(f862(f74(x81141),x81142),x81143)),f862(f862(f74(x81141),x81142),x81144))) % 14.98/14.67 [8115]~P128(x81151)+~P1(f862(f862(f228(x81151),f2(x81151)),x81152))+~P1(f862(f862(f227(x81151),x81153),x81154))+P1(f862(f862(f227(x81151),f862(f862(f74(x81151),x81152),x81153)),f862(f862(f74(x81151),x81152),x81154))) % 14.98/14.67 [8116]~P138(x81161)+~P1(f862(f862(f227(x81161),x81162),x81164))+~P1(f862(f862(f227(x81161),f2(x81161)),x81163))+P1(f862(f862(f227(x81161),f862(f862(f74(x81161),x81162),x81163)),f862(f862(f74(x81161),x81164),x81163))) % 14.98/14.67 [8117]~P66(x81171)+~P1(f862(f862(f227(x81171),x81172),x81174))+~P1(f862(f862(f227(x81171),f2(x81171)),x81173))+P1(f862(f862(f227(x81171),f862(f862(f281(x81171),x81172),x81173)),f862(f862(f281(x81171),x81174),x81173))) % 14.98/14.67 [8118]~P127(x81181)+~P1(f862(f862(f227(x81181),x81182),x81184))+~P1(f862(f862(f227(x81181),f2(x81181)),x81182))+P1(f862(f862(f227(x81181),f862(f862(f236(x81181),x81182),x81183)),f862(f862(f236(x81181),x81184),x81183))) % 14.98/14.67 [8120]~P123(x81201)+~P1(f862(f862(f228(x81201),x81203),x81204))+~P1(f862(f862(f228(x81201),f2(x81201)),x81202))+P1(f862(f862(f228(x81201),f862(f862(f74(x81201),x81202),x81203)),f862(f862(f74(x81201),x81202),x81204))) % 14.98/14.67 [8121]~P135(x81211)+~P1(f862(f862(f228(x81211),x81213),x81214))+~P1(f862(f862(f228(x81211),f2(x81211)),x81212))+P1(f862(f862(f228(x81211),f862(f862(f74(x81211),x81212),x81213)),f862(f862(f74(x81211),x81212),x81214))) % 14.98/14.67 [8122]~P128(x81221)+~P1(f862(f862(f228(x81221),x81222),x81224))+~P1(f862(f862(f228(x81221),f2(x81221)),x81223))+P1(f862(f862(f228(x81221),f862(f862(f74(x81221),x81222),x81223)),f862(f862(f74(x81221),x81224),x81223))) % 14.98/14.67 [8123]~P135(x81231)+~P1(f862(f862(f228(x81231),x81232),x81234))+~P1(f862(f862(f228(x81231),f2(x81231)),x81233))+P1(f862(f862(f228(x81231),f862(f862(f74(x81231),x81232),x81233)),f862(f862(f74(x81231),x81234),x81233))) % 14.98/14.67 [8124]~P128(x81241)+~P1(f862(f862(f228(x81241),x81243),x81244))+~P1(f862(f862(f228(x81241),f2(x81241)),x81242))+P1(f862(f862(f228(x81241),f862(f862(f74(x81241),x81242),x81243)),f862(f862(f74(x81241),x81242),x81244))) % 14.98/14.67 [8125]~P67(x81251)+~P1(f862(f862(f228(x81251),x81252),x81254))+~P1(f862(f862(f228(x81251),f2(x81251)),x81253))+P1(f862(f862(f228(x81251),f862(f862(f281(x81251),x81252),x81253)),f862(f862(f281(x81251),x81254),x81253))) % 14.98/14.67 [8169]~P108(x81692)+P1(f862(f862(f228(f932(x81691,x81692)),x81694),x81693))+~P1(f862(f862(f227(f932(x81691,x81692)),x81694),x81693))+P1(f862(f862(f227(f932(x81691,x81692)),x81693),x81694)) % 14.98/14.67 [8210]P1(f862(f862(f321(x82101),x82102),x82103))+P1(f862(f862(f321(x82101),x82102),x82104))+~P1(f862(f862(f227(f932(x82101,a921)),x82104),x82103))+P1(f862(f862(f228(f932(x82101,a921)),x82104),f862(f862(f301(x82101),x82102),x82103))) % 14.98/14.67 [8323]~P113(x83232)+E(x83231,f2(x83232))+P1(f862(f862(f278(x83232),x83233),x83234))+~P1(f862(f862(f278(x83232),f862(f862(f74(x83232),x83233),x83231)),f862(f862(f74(x83232),x83234),x83231))) % 14.98/14.67 [8324]~P113(x83242)+E(x83241,f2(x83242))+P1(f862(f862(f278(x83242),x83243),x83244))+~P1(f862(f862(f278(x83242),f862(f862(f74(x83242),x83241),x83243)),f862(f862(f74(x83242),x83241),x83244))) % 14.98/14.67 [8373]P1(f862(f862(f321(x83731),x83732),x83733))+P1(f862(f862(f321(x83731),x83732),x83734))+~P1(f862(f862(f228(f932(x83731,a921)),x83734),f862(f862(f301(x83731),x83732),x83733)))+P1(f862(f862(f227(f932(x83731,a921)),x83734),x83733)) % 14.98/14.67 [8439]~P128(x84391)+P1(f862(f862(f228(x84391),x84393),x84392))+P1(f862(f862(f228(x84391),x84392),x84393))+~P1(f862(f862(f228(x84391),f862(f862(f74(x84391),x84394),x84392)),f862(f862(f74(x84391),x84394),x84393))) % 14.98/14.67 [8440]~P128(x84401)+P1(f862(f862(f228(x84401),x84403),x84402))+P1(f862(f862(f228(x84401),x84402),x84403))+~P1(f862(f862(f228(x84401),f862(f862(f74(x84401),x84402),x84404)),f862(f862(f74(x84401),x84403),x84404))) % 14.98/14.67 [8451]~P128(x84511)+P1(f862(f862(f228(x84511),x84514),f2(x84511)))+P1(f862(f862(f228(x84511),x84512),x84513))+~P1(f862(f862(f228(x84511),f862(f862(f74(x84511),x84512),x84514)),f862(f862(f74(x84511),x84513),x84514))) % 14.98/14.67 [8452]~P128(x84521)+P1(f862(f862(f228(x84521),x84524),f2(x84521)))+P1(f862(f862(f228(x84521),x84522),x84523))+~P1(f862(f862(f228(x84521),f862(f862(f74(x84521),x84524),x84522)),f862(f862(f74(x84521),x84524),x84523))) % 14.98/14.67 [8455]~P128(x84551)+P1(f862(f862(f228(x84551),x84552),x84553))+P1(f862(f862(f228(x84551),f2(x84551)),x84554))+~P1(f862(f862(f228(x84551),f862(f862(f74(x84551),x84554),x84553)),f862(f862(f74(x84551),x84554),x84552))) % 14.98/14.67 [8456]~P128(x84561)+P1(f862(f862(f228(x84561),x84562),x84563))+P1(f862(f862(f228(x84561),f2(x84561)),x84564))+~P1(f862(f862(f228(x84561),f862(f862(f74(x84561),x84563),x84564)),f862(f862(f74(x84561),x84562),x84564))) % 14.98/14.67 [8469]~P128(x84691)+P1(f862(f862(f228(x84691),x84692),f2(x84691)))+P1(f862(f862(f228(x84691),f2(x84691)),x84692))+~P1(f862(f862(f228(x84691),f862(f862(f74(x84691),x84693),x84692)),f862(f862(f74(x84691),x84694),x84692))) % 14.98/14.67 [8470]~P128(x84701)+P1(f862(f862(f228(x84701),x84702),f2(x84701)))+P1(f862(f862(f228(x84701),f2(x84701)),x84702))+~P1(f862(f862(f228(x84701),f862(f862(f74(x84701),x84702),x84703)),f862(f862(f74(x84701),x84702),x84704))) % 14.98/14.67 [8499]~P128(x84991)+~P1(f862(f862(f228(x84991),x84994),f2(x84991)))+P1(f862(f862(f227(x84991),x84992),x84993))+~P1(f862(f862(f227(x84991),f862(f862(f74(x84991),x84994),x84993)),f862(f862(f74(x84991),x84994),x84992))) % 14.98/14.67 [8500]~P128(x85001)+~P1(f862(f862(f228(x85001),x85004),f2(x85001)))+P1(f862(f862(f228(x85001),x85002),x85003))+~P1(f862(f862(f228(x85001),f862(f862(f74(x85001),x85004),x85003)),f862(f862(f74(x85001),x85004),x85002))) % 14.98/14.67 [8511]~P127(x85113)+~P1(f862(f862(f228(x85113),f71(x85113)),x85114))+P1(f862(f862(f227(a924),x85111),x85112))+~P1(f862(f862(f227(x85113),f862(f862(f236(x85113),x85114),x85111)),f862(f862(f236(x85113),x85114),x85112))) % 14.98/14.67 [8513]~P127(x85133)+~P1(f862(f862(f228(x85133),f71(x85133)),x85134))+P1(f862(f862(f228(a924),x85131),x85132))+~P1(f862(f862(f228(x85133),f862(f862(f236(x85133),x85134),x85131)),f862(f862(f236(x85133),x85134),x85132))) % 14.98/14.67 [8523]~P128(x85231)+P1(f862(f862(f227(x85231),x85232),x85233))+~P1(f862(f862(f228(x85231),f2(x85231)),x85234))+~P1(f862(f862(f227(x85231),f862(f862(f74(x85231),x85234),x85232)),f862(f862(f74(x85231),x85234),x85233))) % 14.98/14.67 [8524]~P135(x85241)+P1(f862(f862(f227(x85241),x85242),x85243))+~P1(f862(f862(f228(x85241),f2(x85241)),x85244))+~P1(f862(f862(f227(x85241),f862(f862(f74(x85241),x85244),x85242)),f862(f862(f74(x85241),x85244),x85243))) % 14.98/14.67 [8525]~P135(x85251)+P1(f862(f862(f227(x85251),x85252),x85253))+~P1(f862(f862(f228(x85251),f2(x85251)),x85254))+~P1(f862(f862(f227(x85251),f862(f862(f74(x85251),x85252),x85254)),f862(f862(f74(x85251),x85253),x85254))) % 14.98/14.67 [8526]~P128(x85261)+P1(f862(f862(f228(x85261),x85262),x85263))+~P1(f862(f862(f228(x85261),f2(x85261)),x85264))+~P1(f862(f862(f228(x85261),f862(f862(f74(x85261),x85264),x85262)),f862(f862(f74(x85261),x85264),x85263))) % 14.98/14.67 [8527]~P135(x85271)+P1(f862(f862(f228(x85271),x85272),x85273))+~P1(f862(f862(f227(x85271),f2(x85271)),x85274))+~P1(f862(f862(f228(x85271),f862(f862(f74(x85271),x85274),x85272)),f862(f862(f74(x85271),x85274),x85273))) % 14.98/14.67 [8528]~P131(x85281)+P1(f862(f862(f228(x85281),x85282),x85283))+~P1(f862(f862(f227(x85281),f2(x85281)),x85284))+~P1(f862(f862(f228(x85281),f862(f862(f74(x85281),x85284),x85282)),f862(f862(f74(x85281),x85284),x85283))) % 14.98/14.67 [8529]~P127(x85291)+~P1(f862(f862(f227(x85291),f2(x85291)),x85293))+P1(f862(f862(f228(x85291),x85292),x85293))+~P1(f862(f862(f228(x85291),f862(f862(f236(x85291),x85292),x85294)),f862(f862(f236(x85291),x85293),x85294))) % 14.98/14.67 [8530]~P135(x85301)+P1(f862(f862(f228(x85301),x85302),x85303))+~P1(f862(f862(f227(x85301),f2(x85301)),x85304))+~P1(f862(f862(f228(x85301),f862(f862(f74(x85301),x85302),x85304)),f862(f862(f74(x85301),x85303),x85304))) % 14.98/14.67 [8531]~P131(x85311)+P1(f862(f862(f228(x85311),x85312),x85313))+~P1(f862(f862(f227(x85311),f2(x85311)),x85314))+~P1(f862(f862(f228(x85311),f862(f862(f74(x85311),x85312),x85314)),f862(f862(f74(x85311),x85313),x85314))) % 14.98/14.67 [8575]P1(f862(f862(f321(x85751),x85752),x85753))+~P1(f862(f862(f227(f932(x85751,a921)),x85753),x85754))+~P1(f862(f862(f228(f932(x85751,a921)),x85753),x85754))+P1(f862(f862(f228(f932(x85751,a921)),x85753),f862(f862(f301(x85751),x85752),x85754))) % 14.98/14.67 [8608]~P146(x86081)+~P120(x86081)+P1(f862(f862(f278(x86081),x86082),f862(f862(f73(x86081),f858(x86082,x86083,x86081)),f2(x86081))))+~P1(f862(x86083,f862(f862(f74(x86081),x86082),x86084))) % 14.98/14.67 [8959]E(f862(f862(f3(a1),f376(x89591,x89592,x89593,x89594)),f377(x89591,x89592,x89593,x89594)),x89594)+~P1(f862(f862(f228(a1),f2(a1)),x89593))+~P1(f862(f862(f227(a1),x89591),x89594))+P1(f862(f862(f227(a1),x89591),f862(f862(f73(a1),x89594),x89593))) % 14.98/14.67 [8960]E(f862(f862(f3(a1),f402(x89601,x89602,x89603,x89604)),f403(x89601,x89602,x89603,x89604)),x89604)+~P1(f862(f862(f228(a1),f2(a1)),x89603))+~P1(f862(f862(f228(a1),x89601),x89604))+P1(f862(f862(f228(a1),x89601),f862(f862(f73(a1),x89604),x89603))) % 14.98/14.67 [9112]~E(f862(f862(f157(x91121),x91123),f684(x91124,x91123,x91121,x91122)),f862(f862(f157(x91121),x91124),f684(x91124,x91123,x91121,x91122)))+E(f862(f862(f168(x91121),x91122),x91123),f862(f862(f168(x91121),x91122),x91124))+~P1(f862(f862(f227(a924),x91122),f862(f182(f925(x91121)),x91123)))+~P1(f862(f862(f227(a924),x91122),f862(f182(f925(x91121)),x91124))) % 14.98/14.67 [9174]~P1(f862(f862(f228(a1),f2(a1)),x91743))+~P1(f862(f862(f227(a1),x91741),x91744))+P1(f862(f862(f321(a1),f376(x91741,x91742,x91743,x91744)),x91742))+P1(f862(f862(f227(a1),x91741),f862(f862(f73(a1),x91744),x91743))) % 14.98/14.67 [9175]~P1(f862(f862(f228(a1),f2(a1)),x91753))+~P1(f862(f862(f228(a1),x91751),x91754))+P1(f862(f862(f321(a1),f402(x91751,x91752,x91753,x91754)),x91752))+P1(f862(f862(f228(a1),x91751),f862(f862(f73(a1),x91754),x91753))) % 14.98/14.67 [9215]~P104(x92151)+~P1(f862(f54(x92151),x92153))+~P1(f862(f862(f321(x92151),x92154),x92153))+P1(f862(f862(f227(x92151),f862(f862(f57(x92151,x92151,f94(x92151)),x92152),x92153)),f862(f862(f94(x92151),x92154),x92152))) % 14.98/14.67 [9216]~P109(x92161)+~P1(f862(f54(x92161),x92163))+~P1(f862(f862(f321(x92161),x92164),x92163))+P1(f862(f862(f227(x92161),f862(f862(f57(x92161,x92161,f225(x92161)),x92162),x92163)),f862(f862(f225(x92161),x92164),x92162))) % 14.98/14.67 [9260]E(f862(f862(f168(x92601),x92602),x92603),f862(f862(f168(x92601),x92602),x92604))+P1(f862(f862(f228(a924),f684(x92603,x92604,x92601,x92602)),x92602))+~P1(f862(f862(f227(a924),x92602),f862(f182(f925(x92601)),x92603)))+~P1(f862(f862(f227(a924),x92602),f862(f182(f925(x92601)),x92604))) % 14.98/14.67 [9265]~P1(f862(f862(f228(a1),f2(a1)),x92653))+~P1(f862(f862(f227(a1),x92651),x92652))+P1(f862(f862(f321(a1),f377(x92651,x92654,x92653,x92652)),f296(a1,f71(a1),x92653)))+P1(f862(f862(f227(a1),x92651),f862(f862(f73(a1),x92652),x92653))) % 14.98/14.67 [9266]~P1(f862(f862(f228(a1),f2(a1)),x92663))+~P1(f862(f862(f228(a1),x92661),x92662))+P1(f862(f862(f321(a1),f403(x92661,x92664,x92663,x92662)),f296(a1,f71(a1),x92663)))+P1(f862(f862(f228(a1),x92661),f862(f862(f73(a1),x92662),x92663))) % 14.98/14.67 [9593]~P103(x95931)+~P1(f862(f54(x95931),x95934))+P1(f862(f862(f321(x95931),f909(x95932,x95933,x95934,x95931)),x95934))+P1(f862(f862(f227(x95931),f862(f862(f57(x95931,x95931,f103(x95931)),x95932),x95934)),f862(f862(f103(x95931),x95933),x95932))) % 14.98/14.67 [9594]~P109(x95941)+~P1(f862(f54(x95941),x95944))+P1(f862(f862(f321(x95941),f477(x95942,x95943,x95944,x95941)),x95944))+P1(f862(f862(f227(x95941),f862(f862(f57(x95941,x95941,f226(x95941)),x95942),x95944)),f862(f862(f226(x95941),x95943),x95942))) % 14.98/14.67 [9723]~P103(x97231)+~P1(f862(f54(x97231),x97233))+~P1(f862(f862(f227(x97231),f909(x97232,x97234,x97233,x97231)),x97234))+P1(f862(f862(f227(x97231),f862(f862(f57(x97231,x97231,f103(x97231)),x97232),x97233)),f862(f862(f103(x97231),x97234),x97232))) % 14.98/14.67 [9724]~P109(x97241)+~P1(f862(f54(x97241),x97243))+~P1(f862(f862(f227(x97241),f477(x97242,x97244,x97243,x97241)),x97244))+P1(f862(f862(f227(x97241),f862(f862(f57(x97241,x97241,f226(x97241)),x97242),x97243)),f862(f862(f226(x97241),x97244),x97242))) % 14.98/14.67 [9726]~P1(f862(f862(f227(a1),f2(a1)),x97264))+~P1(f862(f862(f228(a1),f2(a1)),x97263))+~P1(f862(f862(f228(a1),x97264),x97261))+P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f74(a1),x97261),f38(a1,x97262,x97263))),x97264)),f862(f862(f74(a1),x97261),x97263))) % 14.98/14.67 [10118]E(x101181,x101182)+P1(f862(f862(f321(f931(f925(x101183),f925(x101183))),f862(f862(f244(f925(x101183),f925(x101183)),x101182),x101181)),f140(x101183,x101184)))+P1(f862(f862(f321(f931(f925(x101183),f925(x101183))),f862(f862(f244(f925(x101183),f925(x101183)),x101181),x101182)),f140(x101183,x101184)))+~P1(f862(f862(f321(f931(x101183,x101183)),f862(f862(f244(x101183,x101183),f650(x101181,x101182,x101184,x101183)),f655(x101181,x101182,x101184,x101183))),x101184)) % 14.98/14.67 [10119]E(x101191,x101192)+P1(f862(f862(f321(f931(f925(x101193),f925(x101193))),f862(f862(f244(f925(x101193),f925(x101193)),x101192),x101191)),f140(x101193,x101194)))+P1(f862(f862(f321(f931(f925(x101193),f925(x101193))),f862(f862(f244(f925(x101193),f925(x101193)),x101191),x101192)),f140(x101193,x101194)))+~P1(f862(f862(f321(f931(x101193,x101193)),f862(f862(f244(x101193,x101193),f655(x101191,x101192,x101194,x101193)),f650(x101191,x101192,x101194,x101193))),x101194)) % 14.98/14.67 [7654]~P103(x76541)+~P1(f862(f862(f227(x76541),x76543),x76544))+~P1(f862(f862(f227(x76541),x76542),x76544))+P1(f862(f862(f227(x76541),f862(f862(f103(x76541),x76542),x76543)),x76544)) % 14.98/14.67 [7657]~P109(x76571)+~P1(f862(f862(f227(x76571),x76573),x76574))+~P1(f862(f862(f227(x76571),x76572),x76574))+P1(f862(f862(f227(x76571),f862(f862(f226(x76571),x76572),x76573)),x76574)) % 14.98/14.67 [7658]~P109(x76581)+~P1(f862(f862(f228(x76581),x76583),x76584))+~P1(f862(f862(f228(x76581),x76582),x76584))+P1(f862(f862(f228(x76581),f862(f862(f226(x76581),x76582),x76583)),x76584)) % 14.98/14.67 [7978]~E(x79781,x79783)+E(f132(a924,f862(f295(a924,x79781),x79782)),f862(f862(f144(a924),x79783),x79784))+~E(f132(a924,f862(f295(a924,f862(f862(f73(a924),x79781),f71(a924))),x79782)),x79784)+~P1(f862(f862(f228(a924),x79781),x79782)) % 14.98/14.67 [7986]~P109(x79861)+P1(f862(f862(f227(x79861),x79862),x79863))+P1(f862(f862(f227(x79861),x79864),x79863))+~P1(f862(f862(f227(x79861),f862(f862(f225(x79861),x79864),x79862)),x79863)) % 14.98/14.67 [7987]~P109(x79871)+P1(f862(f862(f228(x79871),x79872),x79873))+P1(f862(f862(f228(x79871),x79874),x79873))+~P1(f862(f862(f228(x79871),f862(f862(f225(x79871),x79874),x79872)),x79873)) % 14.98/14.67 [8268]~P66(x82681)+~P1(f862(f862(f228(x82681),f2(x82681)),x82683))+~P1(f862(f862(f227(x82681),x82682),f862(f862(f281(x82681),x82684),x82683)))+P1(f862(f862(f227(x82681),f862(f862(f74(x82681),x82682),x82683)),x82684)) % 14.98/14.67 [8269]~P67(x82691)+~P1(f862(f862(f228(x82691),f2(x82691)),x82693))+~P1(f862(f862(f227(x82691),x82692),f862(f862(f281(x82691),x82694),x82693)))+P1(f862(f862(f227(x82691),f862(f862(f74(x82691),x82692),x82693)),x82694)) % 14.98/14.67 [8270]~P66(x82701)+~P1(f862(f862(f228(x82701),f2(x82701)),x82703))+~P1(f862(f862(f227(x82701),x82702),f862(f862(f74(x82701),x82704),x82703)))+P1(f862(f862(f227(x82701),f862(f862(f281(x82701),x82702),x82703)),x82704)) % 14.98/14.67 [8272]~P67(x82721)+~P1(f862(f862(f228(x82721),f2(x82721)),x82723))+~P1(f862(f862(f227(x82721),x82722),f862(f862(f74(x82721),x82724),x82723)))+P1(f862(f862(f227(x82721),f862(f862(f281(x82721),x82722),x82723)),x82724)) % 14.98/14.67 [8273]~P66(x82731)+~P1(f862(f862(f228(x82731),f2(x82731)),x82733))+~P1(f862(f862(f228(x82731),x82732),f862(f862(f281(x82731),x82734),x82733)))+P1(f862(f862(f228(x82731),f862(f862(f74(x82731),x82732),x82733)),x82734)) % 14.98/14.67 [8274]~P67(x82741)+~P1(f862(f862(f228(x82741),f2(x82741)),x82743))+~P1(f862(f862(f228(x82741),x82742),f862(f862(f281(x82741),x82744),x82743)))+P1(f862(f862(f228(x82741),f862(f862(f74(x82741),x82742),x82743)),x82744)) % 14.98/14.67 [8275]~P66(x82751)+~P1(f862(f862(f228(x82751),f2(x82751)),x82753))+~P1(f862(f862(f228(x82751),x82752),f862(f862(f74(x82751),x82754),x82753)))+P1(f862(f862(f228(x82751),f862(f862(f281(x82751),x82752),x82753)),x82754)) % 14.98/14.67 [8277]~P67(x82771)+~P1(f862(f862(f228(x82771),f2(x82771)),x82773))+~P1(f862(f862(f228(x82771),x82772),f862(f862(f74(x82771),x82774),x82773)))+P1(f862(f862(f228(x82771),f862(f862(f281(x82771),x82772),x82773)),x82774)) % 14.98/14.67 [8409]~P66(x84091)+~P1(f862(f862(f228(x84091),f2(x84091)),x84094))+P1(f862(f862(f227(x84091),x84092),f862(f862(f74(x84091),x84093),x84094)))+~P1(f862(f862(f227(x84091),f862(f862(f281(x84091),x84092),x84094)),x84093)) % 14.98/14.67 [8410]~P66(x84101)+~P1(f862(f862(f228(x84101),f2(x84101)),x84104))+P1(f862(f862(f227(x84101),x84102),f862(f862(f281(x84101),x84103),x84104)))+~P1(f862(f862(f227(x84101),f862(f862(f74(x84101),x84102),x84104)),x84103)) % 14.98/14.67 [8412]~P67(x84121)+~P1(f862(f862(f228(x84121),f2(x84121)),x84124))+P1(f862(f862(f227(x84121),x84122),f862(f862(f74(x84121),x84123),x84124)))+~P1(f862(f862(f227(x84121),f862(f862(f281(x84121),x84122),x84124)),x84123)) % 14.98/14.67 [8413]~P67(x84131)+~P1(f862(f862(f228(x84131),f2(x84131)),x84134))+P1(f862(f862(f227(x84131),x84132),f862(f862(f281(x84131),x84133),x84134)))+~P1(f862(f862(f227(x84131),f862(f862(f74(x84131),x84132),x84134)),x84133)) % 14.98/14.67 [8414]~P66(x84141)+~P1(f862(f862(f228(x84141),f2(x84141)),x84144))+P1(f862(f862(f228(x84141),x84142),f862(f862(f74(x84141),x84143),x84144)))+~P1(f862(f862(f228(x84141),f862(f862(f281(x84141),x84142),x84144)),x84143)) % 14.98/14.67 [8415]~P66(x84151)+~P1(f862(f862(f228(x84151),f2(x84151)),x84154))+P1(f862(f862(f228(x84151),x84152),f862(f862(f281(x84151),x84153),x84154)))+~P1(f862(f862(f228(x84151),f862(f862(f74(x84151),x84152),x84154)),x84153)) % 14.98/14.67 [8417]~P67(x84171)+~P1(f862(f862(f228(x84171),f2(x84171)),x84174))+P1(f862(f862(f228(x84171),x84172),f862(f862(f74(x84171),x84173),x84174)))+~P1(f862(f862(f228(x84171),f862(f862(f281(x84171),x84172),x84174)),x84173)) % 14.98/14.67 [8418]~P67(x84181)+~P1(f862(f862(f228(x84181),f2(x84181)),x84184))+P1(f862(f862(f228(x84181),x84182),f862(f862(f281(x84181),x84183),x84184)))+~P1(f862(f862(f228(x84181),f862(f862(f74(x84181),x84182),x84184)),x84183)) % 14.98/14.67 [8578]~P67(x85781)+~P1(f862(f862(f228(x85781),x85783),f2(x85781)))+~P1(f862(f862(f227(x85781),f862(f862(f281(x85781),x85784),x85783)),x85782))+P1(f862(f862(f227(x85781),f862(f862(f74(x85781),x85782),x85783)),x85784)) % 14.98/14.67 [8579]~P67(x85791)+~P1(f862(f862(f228(x85791),x85793),f2(x85791)))+~P1(f862(f862(f227(x85791),f862(f862(f74(x85791),x85794),x85793)),x85792))+P1(f862(f862(f227(x85791),f862(f862(f281(x85791),x85792),x85793)),x85794)) % 14.98/14.67 [8580]~P67(x85801)+~P1(f862(f862(f228(x85801),x85803),f2(x85801)))+~P1(f862(f862(f228(x85801),f862(f862(f281(x85801),x85804),x85803)),x85802))+P1(f862(f862(f228(x85801),f862(f862(f74(x85801),x85802),x85803)),x85804)) % 14.98/14.67 [8581]~P67(x85811)+~P1(f862(f862(f228(x85811),x85813),f2(x85811)))+~P1(f862(f862(f228(x85811),f862(f862(f74(x85811),x85814),x85813)),x85812))+P1(f862(f862(f228(x85811),f862(f862(f281(x85811),x85812),x85813)),x85814)) % 14.98/14.67 [8593]~P1(f862(x85931,x85934))+~P1(f862(f862(f228(a924),x85932),f862(f862(f74(a924),x85933),f862(a105,x85934))))+P1(f862(x85931,f862(f862(f29(a924),x85932),x85933)))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x85933),x85934)),x85932)) % 14.98/14.67 [8806]~P103(x88061)+~P1(f862(f54(x88061),x88064))+~P1(f862(f862(f321(x88061),x88062),x88064))+P1(f862(f862(f227(x88061),f862(f862(f103(x88061),x88062),x88063)),f862(f862(f57(x88061,x88061,f103(x88061)),x88063),x88064))) % 14.98/14.67 [8807]~P109(x88071)+~P1(f862(f54(x88071),x88074))+~P1(f862(f862(f321(x88071),x88072),x88074))+P1(f862(f862(f227(x88071),f862(f862(f226(x88071),x88072),x88073)),f862(f862(f57(x88071,x88071,f226(x88071)),x88073),x88074))) % 14.98/14.67 [8961]~P1(f862(f54(x89611),x89612))+E(f862(f28(x89611),f862(f862(f3(f932(x89611,a921)),x89612),f862(f862(f301(x89611),x89613),x89614))),f862(f862(f3(a924),f862(f28(x89611),f862(f862(f3(f932(x89611,a921)),x89612),x89614))),f71(a924)))+P1(f862(f862(f321(x89611),x89613),x89614))+~P1(f862(f862(f321(x89611),x89613),x89612)) % 14.98/14.67 [9040]E(f862(f862(f73(a1),f378(x90401,x90402,x90403,x90404)),f379(x90401,x90402,x90403,x90404)),x90404)+~P1(f862(f862(f228(a1),f2(a1)),x90403))+~P1(f862(f862(f227(a1),x90404),x90401))+P1(f862(f862(f227(a1),f862(f862(f3(a1),x90404),x90403)),x90401)) % 14.98/14.67 [9041]E(f862(f862(f73(a1),f404(x90411,x90412,x90413,x90414)),f405(x90411,x90412,x90413,x90414)),x90414)+~P1(f862(f862(f228(a1),f2(a1)),x90413))+~P1(f862(f862(f228(a1),x90414),x90411))+P1(f862(f862(f228(a1),f862(f862(f3(a1),x90414),x90413)),x90411)) % 14.98/14.67 [9245]~P1(f862(f862(f228(a1),f2(a1)),x92453))+~P1(f862(f862(f227(a1),x92454),x92451))+P1(f862(f862(f321(a1),f378(x92451,x92452,x92453,x92454)),x92452))+P1(f862(f862(f227(a1),f862(f862(f3(a1),x92454),x92453)),x92451)) % 14.98/14.67 [9246]~P1(f862(f862(f228(a1),f2(a1)),x92463))+~P1(f862(f862(f228(a1),x92464),x92461))+P1(f862(f862(f321(a1),f404(x92461,x92462,x92463,x92464)),x92462))+P1(f862(f862(f228(a1),f862(f862(f3(a1),x92464),x92463)),x92461)) % 14.98/14.67 [9334]~P1(f862(f862(f228(a1),f2(a1)),x93342))+~P1(f862(f862(f227(a1),x93341),x93343))+P1(f862(f862(f321(a1),f379(x93343,x93344,x93342,x93341)),f296(a1,f71(a1),x93342)))+P1(f862(f862(f227(a1),f862(f862(f3(a1),x93341),x93342)),x93343)) % 14.98/14.67 [9335]~P1(f862(f862(f228(a1),f2(a1)),x93352))+~P1(f862(f862(f228(a1),x93351),x93353))+P1(f862(f862(f321(a1),f405(x93353,x93354,x93352,x93351)),f296(a1,f71(a1),x93352)))+P1(f862(f862(f228(a1),f862(f862(f3(a1),x93351),x93352)),x93353)) % 14.98/14.67 [9353]~P1(f862(f862(f227(a1),f2(a1)),x93534))+~P1(f862(f862(f228(a1),f2(a1)),x93533))+~P1(f862(f862(f228(a1),x93534),x93531))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f862(f862(f74(a1),x93531),f38(a1,x93532,x93533))),x93534))) % 14.98/14.67 [9382]E(x93821,x93822)+~P37(x93823,x93824)+~P1(f862(f862(f321(f931(x93823,x93823)),f862(f862(f244(x93823,x93823),x93822),x93821)),x93824))+~P1(f862(f862(f321(f931(x93823,x93823)),f862(f862(f244(x93823,x93823),x93821),x93822)),x93824)) % 14.98/14.67 [9415]~P104(x94151)+~P1(f862(f54(x94151),x94154))+~P1(f862(f862(f227(x94151),x94152),f906(x94153,x94152,x94154,x94151)))+P1(f862(f862(f227(x94151),f862(f862(f94(x94151),x94152),x94153)),f862(f862(f57(x94151,x94151,f94(x94151)),x94153),x94154))) % 14.98/14.67 [9416]~P109(x94161)+~P1(f862(f54(x94161),x94164))+~P1(f862(f862(f227(x94161),x94162),f463(x94163,x94162,x94164,x94161)))+P1(f862(f862(f227(x94161),f862(f862(f225(x94161),x94162),x94163)),f862(f862(f57(x94161,x94161,f225(x94161)),x94163),x94164))) % 14.98/14.67 [9432]~P1(f862(f862(f227(a1),x94324),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x94322))+~P1(f862(f862(f228(a1),x94321),x94324))+P1(f862(f862(f228(a1),f862(f862(f74(a1),x94321),x94322)),f862(f862(f73(a1),f862(f862(f74(a1),x94321),f38(a1,x94323,x94322))),x94324))) % 14.98/14.67 [9458]P1(f862(f54(x94581),x94582))+~P1(f862(f54(x94581),x94583))+~P1(f862(f862(f321(f932(x94581,a921)),x94582),f862(f862(f53(x94581),x94583),x94584)))+~P1(f862(f862(f227(f932(f931(x94581,x94581),a921)),x94584),f862(f862(f246(x94581,x94581),x94583),f862(f18(f932(x94581,a921),x94581),x94583)))) % 14.98/14.67 [9482]~P104(x94821)+~P1(f862(f54(x94821),x94824))+P1(f862(f862(f321(x94821),f906(x94822,x94823,x94824,x94821)),x94824))+P1(f862(f862(f227(x94821),f862(f862(f94(x94821),x94823),x94822)),f862(f862(f57(x94821,x94821,f94(x94821)),x94822),x94824))) % 14.98/14.67 [9483]~P109(x94831)+~P1(f862(f54(x94831),x94834))+P1(f862(f862(f321(x94831),f463(x94832,x94833,x94834,x94831)),x94834))+P1(f862(f862(f227(x94831),f862(f862(f225(x94831),x94833),x94832)),f862(f862(f57(x94831,x94831,f225(x94831)),x94832),x94834))) % 14.98/14.67 [9890]~P1(f862(f54(x98902),x98904))+~P1(f862(f54(x98901),x98903))+~P1(f862(f862(f227(a924),f862(f28(x98902),x98904)),f862(f28(x98901),x98903)))+P1(f862(f862(f227(f932(x98901,a921)),f862(f302(x98902,x98901,f543(x98903,x98901,x98904,x98902)),x98904)),x98903)) % 14.98/14.67 [9531]~P1(f862(f862(f321(x95311),x95312),x95314))+P1(f862(f862(f321(x95311),x95312),x95313))+~P1(f862(f862(f228(f932(x95311,a921)),x95314),f862(f862(f301(x95311),x95312),x95313)))+P1(f862(f862(f228(f932(x95311,a921)),f862(f862(f3(f932(x95311,a921)),x95314),f862(f862(f301(x95311),x95312),f181(f932(x95311,a921))))),x95313)) % 14.98/14.67 [9704]~P1(f862(f862(f321(x97041),x97042),x97044))+P1(f862(f862(f321(x97041),x97042),x97043))+P1(f862(f862(f228(f932(x97041,a921)),x97044),f862(f862(f301(x97041),x97042),x97043)))+~P1(f862(f862(f228(f932(x97041,a921)),f862(f862(f3(f932(x97041,a921)),x97044),f862(f862(f301(x97041),x97042),f181(f932(x97041,a921))))),x97043)) % 14.98/14.67 [9729]P1(f862(f862(f321(x97291),x97292),x97293))+~P1(f862(f862(f227(f932(x97291,a921)),x97294),x97293))+P1(f862(f862(f228(f932(x97291,a921)),x97294),f862(f862(f301(x97291),x97292),x97293)))+~P1(f862(f862(f228(f932(x97291,a921)),f862(f862(f3(f932(x97291,a921)),x97294),f862(f862(f301(x97291),x97292),f181(f932(x97291,a921))))),x97293)) % 14.98/14.67 [9734]~P1(f862(f862(f321(x97341),x97343),x97342))+~P1(f862(f862(f228(f932(x97341,a921)),x97342),x97344))+P1(f862(f862(f228(f932(x97341,a921)),x97342),f862(f862(f301(x97341),x97343),x97344)))+~P1(f862(f862(f228(f932(x97341,a921)),f862(f862(f3(f932(x97341,a921)),x97342),f862(f862(f301(x97341),x97343),f181(f932(x97341,a921))))),x97344)) % 14.98/14.67 [9750]~P1(f862(f862(f227(f932(x97501,a921)),x97502),x97504))+~P1(f862(f862(f228(f932(x97501,a921)),x97502),x97504))+P1(f862(f862(f228(f932(x97501,a921)),x97502),f862(f862(f301(x97501),x97503),x97504)))+~P1(f862(f862(f228(f932(x97501,a921)),f862(f862(f3(f932(x97501,a921)),x97502),f862(f862(f301(x97501),x97503),f181(f932(x97501,a921))))),x97504)) % 14.98/14.67 [9795]~P110(x97952)+~P63(x97951)+~P1(f862(f862(f227(f932(x97951,x97952)),x97953),x97954))+P1(f862(f50(x97951),f862(f862(f20(x97951,x97952,a921),f862(f862(f10(x97952,f932(x97952,a921),x97951),f227(x97952)),x97953)),x97954))) % 14.98/14.67 [9939]~P110(x99392)+~P63(x99391)+P1(f862(f862(f227(f932(x99391,x99392)),x99393),x99394))+~P1(f862(f50(x99391),f862(f862(f20(x99391,x99392,a921),f862(f862(f10(x99392,f932(x99392,a921),x99391),f227(x99392)),x99393)),x99394))) % 14.98/14.67 [10109]E(f862(f862(f157(x101091),f862(f862(f157(f925(x101091)),f172(x101091,x101092)),x101093)),x101094),f862(f862(f157(x101091),f862(f862(f157(f925(x101091)),x101092),x101094)),x101093))+~P1(f862(f862(f228(a924),x101093),f862(f182(f925(f925(x101091))),f172(x101091,x101092))))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x101091),a924),f182(f925(x101091))),x101092)))+~P1(f862(f862(f228(a924),x101094),f862(f182(f925(f925(x101091))),f862(f129(f925(x101091),f862(f862(f10(a924,a921,f925(x101091)),f862(f228(a924),x101093)),f182(f925(x101091)))),x101092)))) % 14.98/14.67 [10130]~P1(f862(f862(f321(f931(a924,a924)),x101304),x101301))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x101304),x101302)),a64))+~P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101301),x101303)),a65))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101301),f862(f862(f301(f931(a924,a924)),x101302),x101303))),a65)) % 14.98/14.67 [10131]~P1(f862(f862(f321(f931(a924,a924)),x101314),x101311))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x101314),x101312)),a26))+~P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101311),x101313)),a62))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101311),f862(f862(f301(f931(a924,a924)),x101312),x101313))),a62)) % 14.98/14.67 [10018]~P110(x100182)+~P63(x100181)+~P1(f862(f862(f228(f932(x100181,x100182)),x100183),x100184))+P1(f862(f49(x100181),f862(f862(f10(a921,a921,x100181),a314),f862(f862(f20(x100181,x100182,a921),f862(f862(f10(x100182,f932(x100182,a921),x100181),a317),x100183)),x100184)))) % 14.98/14.67 [10142]~P1(f862(f862(f321(f931(a924,a924)),x101424),x101423))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x101421),x101424)),a26))+~P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101422),x101423)),a27))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f862(f862(f301(f931(a924,a924)),x101421),x101422)),x101423)),a27)) % 14.98/14.67 [10143]~P1(f862(f862(f321(f931(a924,a924)),x101434),x101433))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x101431),x101434)),a64))+~P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101432),x101433)),a63))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f862(f862(f301(f931(a924,a924)),x101431),x101432)),x101433)),a63)) % 14.98/14.67 [6235]~P5(x62354,x62351)+~P1(f862(f862(x62351,x62352),x62355))+P1(f862(f862(x62351,x62352),x62353))+~P1(f862(f862(x62351,x62355),x62353)) % 14.98/14.67 [6236]~P47(x62364,x62361)+~P1(f862(f862(x62361,x62362),x62365))+P1(f862(f862(x62361,x62362),x62363))+~P1(f862(f862(x62361,x62365),x62363)) % 14.98/14.67 [6237]~P13(x62374,x62371)+~P1(f862(f862(x62371,x62372),x62375))+P1(f862(f862(x62371,x62372),x62373))+~P1(f862(f862(x62371,x62375),x62373)) % 14.98/14.67 [8946]~P5(x89464,x89463)+~P1(f862(x89461,x89465))+P1(f862(x89462,f837(x89462,x89461,x89463,x89464)))+P1(f862(x89461,f836(x89462,x89461,x89463,x89464))) % 14.98/14.67 [9182]~P5(x91824,x91823)+~P1(f862(x91822,x91825))+~P1(f862(x91821,f836(x91821,x91822,x91823,x91824)))+P1(f862(x91821,f837(x91821,x91822,x91823,x91824))) % 14.98/14.67 [9366]~P5(x93664,x93663)+~P1(f862(x93661,x93665))+P1(f862(f862(f321(x93664),f837(x93662,x93661,x93663,x93664)),f262(x93664,x93663)))+P1(f862(x93661,f836(x93662,x93661,x93663,x93664))) % 14.98/14.67 [9489]~P5(x94891,x94894)+~P1(f862(x94893,x94895))+~P1(f862(x94892,f836(x94892,x94893,x94894,x94891)))+P1(f862(f862(f321(x94891),f837(x94892,x94893,x94894,x94891)),f262(x94891,x94894))) % 14.98/14.67 [9784]~P36(x97841,x97844)+P1(f862(f862(f321(f931(f925(x97841),f925(x97841))),f862(f862(f244(f925(x97841),f925(x97841)),x97842),x97843)),f140(x97841,x97844)))+~P1(f862(f862(f321(f931(f925(x97841),f925(x97841))),f862(f862(f244(f925(x97841),f925(x97841)),x97842),x97845)),f140(x97841,x97844)))+~P1(f862(f862(f321(f931(f925(x97841),f925(x97841))),f862(f862(f244(f925(x97841),f925(x97841)),x97845),x97843)),f140(x97841,x97844))) % 14.98/14.67 [5464]~P59(x54645)+E(x54641,x54642)+~E(x54643,x54644)+~E(f862(f862(f3(x54645),x54643),x54644),f862(f862(f3(x54645),x54641),x54642)) % 14.98/14.67 [6347]~P15(x63475,x63471,x63473)+E(f862(f862(x63471,x63472),f862(x63473,x63474)),f862(x63473,x63474))+~P1(f862(f54(x63475),x63474))+~P1(f862(f862(f321(x63475),x63472),x63474)) % 14.98/14.67 [6538]~P78(x65381)+~E(f862(f862(f3(x65381),x65384),x65385),f862(f862(f3(x65381),x65382),x65383))+~P1(f862(f862(f227(x65381),x65384),x65385))+P1(f862(f862(f227(x65381),x65382),x65383)) % 14.98/14.67 [6540]~P78(x65401)+~E(f862(f862(f3(x65401),x65404),x65405),f862(f862(f3(x65401),x65402),x65403))+~P1(f862(f862(f228(x65401),x65404),x65405))+P1(f862(f862(f228(x65401),x65402),x65403)) % 14.98/14.67 [7520]~E(x75202,f862(f862(f144(x75201),x75204),x75205))+P1(f862(f862(f321(f925(x75201)),x75202),f154(x75201,x75203)))+~P1(f862(f862(f321(f925(x75201)),x75205),f154(x75201,x75203)))+~P1(f862(f862(f321(x75201),x75204),x75203)) % 14.98/14.67 [7927]~E(f862(f182(f925(x79271)),x79273),f862(f182(f925(x79272)),x79274))+~E(f862(f862(f147(f931(x79271,x79272),x79272),f248(x79271,x79272)),x79275),x79274)+~E(f862(f862(f147(f931(x79271,x79272),x79271),f243(x79271,x79272)),x79275),x79273)+E(f862(f862(f174(x79271,x79272),x79273),x79274),x79275) % 14.98/14.67 [8264]~P110(x82641)+P1(f862(f862(f228(f932(x82641,a921)),f296(x82641,x82642,x82643)),f296(x82641,x82644,x82645)))+~P1(f862(f862(f227(x82641),x82644),x82645))+P1(f862(f862(f227(x82641),x82642),x82643)) % 14.98/14.67 [8366]~P110(x83661)+P1(f862(f862(f227(f932(x83661,a921)),f296(x83661,x83662,x83663)),f296(x83661,x83664,x83665)))+~P1(f862(f862(f227(x83661),x83663),x83665))+~P1(f862(f862(f227(x83661),x83664),x83662)) % 14.98/14.67 [8485]~P109(x84851)+P1(f862(f862(f227(x84851),x84852),x84853))+P1(f862(f862(f227(x84851),x84854),x84853))+~P1(f862(f862(f227(f932(x84851,a921)),f862(f295(x84851,x84853),x84852)),f862(f295(x84851,x84854),x84855))) % 14.98/14.67 [8486]~P109(x84861)+P1(f862(f862(f227(x84861),x84862),x84863))+P1(f862(f862(f227(x84861),x84862),x84864))+~P1(f862(f862(f227(f932(x84861,a921)),f862(f295(x84861,x84863),x84862)),f862(f295(x84861,x84865),x84864))) % 14.98/14.67 [8722]~P110(x87221)+~P1(f862(f862(f227(f932(x87221,a921)),f296(x87221,x87224,x87222)),f296(x87221,x87225,x87223)))+P1(f862(f862(f227(x87221),x87222),x87223))+~P1(f862(f862(f227(x87221),x87224),x87222)) % 14.98/14.67 [8723]~P110(x87231)+~P1(f862(f862(f228(f932(x87231,a921)),f296(x87231,x87234,x87232)),f296(x87231,x87235,x87233)))+P1(f862(f862(f227(x87231),x87232),x87233))+~P1(f862(f862(f227(x87231),x87234),x87232)) % 14.98/14.67 [8724]~P110(x87241)+~P1(f862(f862(f227(f932(x87241,a921)),f296(x87241,x87243,x87244)),f296(x87241,x87242,x87245)))+P1(f862(f862(f227(x87241),x87242),x87243))+~P1(f862(f862(f227(x87241),x87243),x87244)) % 14.98/14.67 [8725]~P110(x87251)+~P1(f862(f862(f228(f932(x87251,a921)),f296(x87251,x87253,x87254)),f296(x87251,x87252,x87255)))+P1(f862(f862(f227(x87251),x87252),x87253))+~P1(f862(f862(f227(x87251),x87253),x87254)) % 14.98/14.67 [6234]~P15(x62342,x62345,x62343)+E(x62341,f181(f932(x62342,a921)))+~P1(f862(f54(x62342),x62341))+E(f862(x62343,f862(f862(f301(x62342),x62344),x62341)),f862(f862(x62345,x62344),f862(x62343,x62341))) % 14.98/14.67 [7009]~E(x70091,x70092)+~E(f862(f862(f94(f932(x70093,a921)),x70094),x70095),f181(f932(x70093,a921)))+~P1(f862(f862(f321(x70093),x70092),x70095))+~P1(f862(f862(f321(x70093),x70091),x70094)) % 14.98/14.67 [7090]~P16(x70902,x70905,x70901)+~P1(f862(f54(x70902),x70904))+E(f862(x70901,f862(f862(f301(x70902),x70903),x70904)),f862(f862(f57(x70902,x70902,x70905),x70903),x70904))+P1(f862(f862(f321(x70902),x70903),x70904)) % 14.98/14.67 [7156]~P72(x71562)+~P1(f862(f54(x71561),x71565))+E(f862(f862(f8(x71561,x71562),x71563),f862(f862(f301(x71561),x71564),x71565)),f862(f862(f73(x71562),f862(x71563,x71564)),f862(f862(f8(x71561,x71562),x71563),x71565)))+P1(f862(f862(f321(x71561),x71564),x71565)) % 14.98/14.67 [7158]~P71(x71582)+~P1(f862(f54(x71581),x71585))+E(f862(f862(f11(x71581,x71582),x71583),f862(f862(f301(x71581),x71584),x71585)),f862(f862(f74(x71582),f862(x71583,x71584)),f862(f862(f11(x71581,x71582),x71583),x71585)))+P1(f862(f862(f321(x71581),x71584),x71585)) % 14.98/14.67 [7667]~P16(x76672,x76675,x76671)+~P1(f862(f54(x76672),x76674))+E(f862(x76671,f862(f862(f301(x76672),x76673),x76674)),x76673)+~E(f862(f862(f3(f932(x76672,a921)),x76674),f862(f862(f301(x76672),x76673),f181(f932(x76672,a921)))),f181(f932(x76672,a921))) % 14.98/14.67 [7999]~P119(x79991)+~P1(f862(f862(f278(x79991),x79992),x79994))+~P1(f862(f862(f227(a924),x79993),x79995))+P1(f862(f862(f278(x79991),f862(f862(f236(x79991),x79992),x79993)),f862(f862(f236(x79991),x79994),x79995))) % 14.98/14.67 [8028]~P61(x80281)+E(f862(f862(f29(x80281),f862(f862(f74(x80281),x80282),x80283)),f862(f862(f74(x80281),x80284),x80285)),f862(f862(f74(x80281),f862(f862(f29(x80281),x80282),x80284)),f862(f862(f29(x80281),x80283),x80285)))+~P1(f862(f862(f278(x80281),x80285),x80283))+~P1(f862(f862(f278(x80281),x80284),x80282)) % 14.98/14.67 [8032]~P103(x80321)+~P1(f862(f862(f227(x80321),x80323),x80325))+~P1(f862(f862(f227(x80321),x80322),x80324))+P1(f862(f862(f227(x80321),f862(f862(f103(x80321),x80322),x80323)),f862(f862(f103(x80321),x80324),x80325))) % 14.98/14.67 [8033]~P104(x80331)+~P1(f862(f862(f227(x80331),x80333),x80335))+~P1(f862(f862(f227(x80331),x80332),x80334))+P1(f862(f862(f227(x80331),f862(f862(f94(x80331),x80332),x80333)),f862(f862(f94(x80331),x80334),x80335))) % 14.98/14.67 [8034]~P85(x80341)+~P1(f862(f862(f227(x80341),x80343),x80345))+~P1(f862(f862(f227(x80341),x80342),x80344))+P1(f862(f862(f227(x80341),f862(f862(f73(x80341),x80342),x80343)),f862(f862(f73(x80341),x80344),x80345))) % 14.98/14.67 [8035]~P109(x80351)+~P1(f862(f862(f227(x80351),x80353),x80355))+~P1(f862(f862(f227(x80351),x80352),x80354))+P1(f862(f862(f227(x80351),f862(f862(f225(x80351),x80352),x80353)),f862(f862(f225(x80351),x80354),x80355))) % 14.98/14.67 [8036]~P109(x80361)+~P1(f862(f862(f227(x80361),x80363),x80365))+~P1(f862(f862(f227(x80361),x80362),x80364))+P1(f862(f862(f227(x80361),f862(f862(f226(x80361),x80362),x80363)),f862(f862(f226(x80361),x80364),x80365))) % 14.98/14.67 [8037]~P83(x80371)+~P1(f862(f862(f227(x80371),x80373),x80375))+~P1(f862(f862(f228(x80371),x80372),x80374))+P1(f862(f862(f228(x80371),f862(f862(f73(x80371),x80372),x80373)),f862(f862(f73(x80371),x80374),x80375))) % 14.98/14.67 [8038]~P83(x80381)+~P1(f862(f862(f227(x80381),x80382),x80384))+~P1(f862(f862(f228(x80381),x80383),x80385))+P1(f862(f862(f228(x80381),f862(f862(f73(x80381),x80382),x80383)),f862(f862(f73(x80381),x80384),x80385))) % 14.98/14.67 [8039]~P83(x80391)+~P1(f862(f862(f228(x80391),x80393),x80395))+~P1(f862(f862(f228(x80391),x80392),x80394))+P1(f862(f862(f228(x80391),f862(f862(f73(x80391),x80392),x80393)),f862(f862(f73(x80391),x80394),x80395))) % 14.98/14.67 [8040]~P119(x80401)+~P1(f862(f862(f278(x80401),x80403),x80405))+~P1(f862(f862(f278(x80401),x80402),x80404))+P1(f862(f862(f278(x80401),f862(f862(f74(x80401),x80402),x80403)),f862(f862(f74(x80401),x80404),x80405))) % 14.98/14.67 [8179]~P144(x81795)+E(x81791,x81792)+E(x81793,x81794)+~E(f862(f862(f73(x81795),f862(f862(f74(x81795),x81793),x81791)),f862(f862(f74(x81795),x81794),x81792)),f862(f862(f73(x81795),f862(f862(f74(x81795),x81793),x81792)),f862(f862(f74(x81795),x81794),x81791))) % 14.98/14.67 [8387]~P109(x83874)+~P1(f862(f130(x83871),x83873))+P1(f862(f862(f321(x83871),x83872),f862(f165(x83871),x83873)))+P1(f862(f130(x83871),f862(f862(f141(x83871,x83874,x83875),x83872),x83873))) % 14.98/14.67 [8532]~P59(x85321)+E(f862(f862(f3(x85321),f862(f862(f8(a924,x85321),x85322),f862(f295(a924,x85323),x85324))),f862(f862(f8(a924,x85321),x85322),f862(f295(a924,x85323),x85325))),f862(f862(f8(a924,x85321),x85322),f862(f295(a924,x85325),x85324)))+~P1(f862(f862(f227(a924),x85325),x85324))+~P1(f862(f862(f227(a924),x85323),x85325)) % 14.98/14.67 [8533]~P72(x85331)+E(f862(f862(f73(x85331),f862(f862(f8(a924,x85331),x85332),f862(f295(a924,x85333),x85334))),f862(f862(f8(a924,x85331),x85332),f862(f295(a924,x85334),x85335))),f862(f862(f8(a924,x85331),x85332),f862(f295(a924,x85333),x85335)))+~P1(f862(f862(f227(a924),x85334),x85335))+~P1(f862(f862(f227(a924),x85333),x85334)) % 14.98/14.67 [8866]~P65(x88662)+E(x88661,f2(x88662))+E(x88663,f2(x88662))+E(f862(f862(f281(x88662),f862(f862(f3(x88662),f862(f862(f74(x88662),x88664),x88661)),f862(f862(f74(x88662),x88665),x88663))),f862(f862(f74(x88662),x88663),x88661)),f862(f862(f3(x88662),f862(f862(f281(x88662),x88664),x88663)),f862(f862(f281(x88662),x88665),x88661))) % 14.98/14.67 [8867]~P65(x88672)+E(x88671,f2(x88672))+E(x88673,f2(x88672))+E(f862(f862(f281(x88672),f862(f862(f73(x88672),f862(f862(f74(x88672),x88674),x88671)),f862(f862(f74(x88672),x88675),x88673))),f862(f862(f74(x88672),x88673),x88671)),f862(f862(f73(x88672),f862(f862(f281(x88672),x88674),x88673)),f862(f862(f281(x88672),x88675),x88671))) % 14.98/14.67 [8876]~E(x88762,f862(x88763,x88761))+E(x88761,f539(x88762,x88763,x88764,x88765))+~P22(x88765,x88764,x88763,f234(f932(x88765,a921)))+~P1(f862(f862(f321(x88764),x88762),f862(f302(x88765,x88764,x88763),f234(f932(x88765,a921))))) % 14.98/14.67 [9096]~P112(x90961)+~P1(f862(f862(f228(x90961),f862(f69(x90961),x90962)),x90964))+P1(f862(f862(f228(x90961),f862(f862(f74(x90961),f862(f69(x90961),x90962)),f862(f69(x90961),x90963))),f862(f862(f74(x90961),x90964),x90965)))+~P1(f862(f862(f228(x90961),f862(f69(x90961),x90963)),x90965)) % 14.98/14.67 [9207]~P22(x92071,x92073,x92075,x92072)+~P1(f862(f54(x92073),x92074))+P1(f862(f862(f227(a924),f862(f28(x92071),x92072)),f862(f28(x92073),x92074)))+~P1(f862(f862(f227(f932(x92073,a921)),f862(f302(x92071,x92073,x92075),x92072)),x92074)) % 14.98/14.67 [9274]~P72(x92742)+~P22(x92741,x92741,x92744,x92745)+~P1(f862(f54(x92741),x92745))+E(f862(f862(f8(x92741,x92742),f862(f66(x92741,x92742,x92741,x92743),x92744)),x92745),f862(f862(f8(x92741,x92742),x92743),f862(f302(x92741,x92741,x92744),x92745))) % 14.98/14.67 [9275]~P71(x92752)+~P22(x92751,x92751,x92754,x92755)+~P1(f862(f54(x92751),x92755))+E(f862(f862(f11(x92751,x92752),f862(f66(x92751,x92752,x92751,x92753),x92754)),x92755),f862(f862(f11(x92751,x92752),x92753),f862(f302(x92751,x92751,x92754),x92755))) % 14.98/14.67 [9395]~P35(x93951,x93952)+~P1(f862(f862(f321(x93951),x93953),x93954))+~P1(f862(f862(f321(x93951),x93955),x93954))+~P1(f862(f862(f321(f931(x93951,x93951)),f862(f862(f244(x93951,x93951),x93955),f611(x93952,x93951,x93954))),x93952)) % 14.98/14.67 [9431]~P22(x94312,x94313,x94315,x94311)+E(x94311,f181(f932(x94312,a921)))+E(f862(f302(x94313,x94312,f541(x94314,x94313,x94312,x94311)),x94314),x94311)+~P1(f862(f862(f227(f932(x94313,a921)),f862(f302(x94312,x94313,x94315),x94311)),x94314)) % 14.98/14.67 [9920]~P3(x99205)+~P109(x99205)+P1(f862(f862(f321(x99201),f479(x99202,x99203,x99201,x99204,x99205)),x99203))+~P1(f862(f862(f228(x99205),x99204),f862(f862(f33(x99201,x99205),x99203),x99202))) % 14.98/14.67 [9925]~P3(x99251)+~P109(x99251)+P1(f862(f862(f228(x99251),x99252),f862(x99253,f479(x99253,x99254,x99255,x99252,x99251))))+~P1(f862(f862(f228(x99251),x99252),f862(f862(f33(x99255,x99251),x99254),x99253))) % 14.98/14.67 [10005]~P69(x100051)+~P1(f862(f59(x100051,x100051,f74(x100051),x100052,x100053),x100055))+P1(f862(f862(f321(x100051),x100052),x100053))+P1(f862(f59(x100051,x100051,f74(x100051),x100054,f862(f862(f301(x100051),x100052),x100053)),f862(f862(f74(x100051),x100054),x100055))) % 14.98/14.67 [10210]~P72(x102102)+~P1(f862(f54(x102101),x102105))+E(f862(f862(f8(x102101,x102102),f862(f862(f9(x102101,x102102,x102102),f862(f862(f20(x102101,x102102,f932(x102102,x102102)),f862(f862(f10(a921,f932(x102102,f932(x102102,x102102)),x102101),f89(x102102)),f862(a317,x102103))),x102104)),f2(x102102))),x102105),f2(x102102))+P1(f862(f862(f321(x102101),x102103),x102105)) % 14.98/14.67 [10211]~P71(x102112)+~P1(f862(f54(x102111),x102115))+E(f862(f862(f11(x102111,x102112),f862(f862(f9(x102111,x102112,x102112),f862(f862(f20(x102111,x102112,f932(x102112,x102112)),f862(f862(f10(a921,f932(x102112,f932(x102112,x102112)),x102111),f89(x102112)),f862(a317,x102113))),x102114)),f71(x102112))),x102115),f71(x102112))+P1(f862(f862(f321(x102111),x102113),x102115)) % 14.98/14.67 [10212]~P72(x102122)+~P1(f862(f54(x102121),x102125))+E(f862(f862(f8(x102121,x102122),f862(f862(f9(x102121,x102122,x102122),f862(f862(f20(x102121,x102122,f932(x102122,x102122)),f862(f862(f10(a921,f932(x102122,f932(x102122,x102122)),x102121),f89(x102122)),f862(a317,x102123))),x102124)),f2(x102122))),x102125),f862(x102124,x102123))+~P1(f862(f862(f321(x102121),x102123),x102125)) % 14.98/14.67 [10213]~P71(x102132)+~P1(f862(f54(x102131),x102135))+E(f862(f862(f11(x102131,x102132),f862(f862(f9(x102131,x102132,x102132),f862(f862(f20(x102131,x102132,f932(x102132,x102132)),f862(f862(f10(a921,f932(x102132,f932(x102132,x102132)),x102131),f89(x102132)),f862(a317,x102133))),x102134)),f71(x102132))),x102135),f862(x102134,x102133))+~P1(f862(f862(f321(x102131),x102133),x102135)) % 14.98/14.67 [10267]~P72(x102672)+~P1(f862(f54(x102671),x102675))+E(f862(f862(f8(x102671,x102672),f862(f862(f9(x102671,x102672,x102672),f862(f862(f20(x102671,x102672,f932(x102672,x102672)),f862(f862(f10(a921,f932(x102672,f932(x102672,x102672)),x102671),f89(x102672)),f862(f862(f9(x102671,x102671,a921),a317),x102673))),x102674)),f2(x102672))),x102675),f2(x102672))+P1(f862(f862(f321(x102671),x102673),x102675)) % 14.98/14.67 [10268]~P71(x102682)+~P1(f862(f54(x102681),x102685))+E(f862(f862(f11(x102681,x102682),f862(f862(f9(x102681,x102682,x102682),f862(f862(f20(x102681,x102682,f932(x102682,x102682)),f862(f862(f10(a921,f932(x102682,f932(x102682,x102682)),x102681),f89(x102682)),f862(f862(f9(x102681,x102681,a921),a317),x102683))),x102684)),f71(x102682))),x102685),f71(x102682))+P1(f862(f862(f321(x102681),x102683),x102685)) % 14.98/14.67 [10270]~P72(x102702)+~P1(f862(f54(x102701),x102705))+E(f862(f862(f8(x102701,x102702),f862(f862(f9(x102701,x102702,x102702),f862(f862(f20(x102701,x102702,f932(x102702,x102702)),f862(f862(f10(a921,f932(x102702,f932(x102702,x102702)),x102701),f89(x102702)),f862(f862(f9(x102701,x102701,a921),a317),x102703))),x102704)),f2(x102702))),x102705),f862(x102704,x102703))+~P1(f862(f862(f321(x102701),x102703),x102705)) % 14.98/14.67 [10271]~P71(x102712)+~P1(f862(f54(x102711),x102715))+E(f862(f862(f11(x102711,x102712),f862(f862(f9(x102711,x102712,x102712),f862(f862(f20(x102711,x102712,f932(x102712,x102712)),f862(f862(f10(a921,f932(x102712,f932(x102712,x102712)),x102711),f89(x102712)),f862(f862(f9(x102711,x102711,a921),a317),x102713))),x102714)),f71(x102712))),x102715),f862(x102714,x102713))+~P1(f862(f862(f321(x102711),x102713),x102715)) % 14.98/14.67 [8031]~P59(x80312)+~P1(f862(f54(x80311),x80314))+E(f862(f862(f8(x80311,x80312),x80313),f862(f862(f3(f932(x80311,a921)),x80314),f862(f862(f301(x80311),x80315),f181(f932(x80311,a921))))),f862(f862(f8(x80311,x80312),x80313),x80314))+P1(f862(f862(f321(x80311),x80315),x80314)) % 14.98/14.67 [8540]~P125(x85402)+~P1(f862(f54(x85401),x85404))+E(f862(f862(f8(x85401,x85402),x85403),f862(f862(f3(f932(x85401,a921)),x85404),f862(f862(f301(x85401),x85405),f181(f932(x85401,a921))))),f862(f862(f3(x85402),f862(f862(f8(x85401,x85402),x85403),x85404)),f862(x85403,x85405)))+~P1(f862(f862(f321(x85401),x85405),x85404)) % 14.98/14.67 [8541]~P59(x85412)+~P1(f862(f54(x85411),x85414))+E(f862(f862(f8(x85411,x85412),x85413),f862(f862(f3(f932(x85411,a921)),x85414),f862(f862(f301(x85411),x85415),f181(f932(x85411,a921))))),f862(f862(f3(x85412),f862(f862(f8(x85411,x85412),x85413),x85414)),f862(x85413,x85415)))+~P1(f862(f862(f321(x85411),x85415),x85414)) % 14.98/14.67 [8553]~P119(x85531)+~P1(f862(f862(f227(a924),x85533),x85535))+~P1(f862(f862(f278(x85531),f862(f862(f236(x85531),x85532),x85535)),x85534))+P1(f862(f862(f278(x85531),f862(f862(f236(x85531),x85532),x85533)),x85534)) % 14.98/14.67 [8571]~P59(x85711)+~P1(f862(f54(x85712),x85714))+E(f862(f862(f3(x85711),f862(f862(f8(x85712,x85711),x85713),x85714)),f862(f862(f8(x85712,x85711),x85713),x85715)),f862(f862(f8(x85712,x85711),x85713),f862(f862(f3(f932(x85712,a921)),x85714),x85715)))+~P1(f862(f862(f227(f932(x85712,a921)),x85715),x85714)) % 14.98/14.67 [8590]P1(f862(f54(x85901),f862(x85902,x85903)))+~P1(f862(f54(x85904),x85905))+~P1(f862(f862(f321(x85904),x85903),x85905))+~P1(f862(f54(x85901),f862(f862(f33(x85904,f932(x85901,a921)),x85905),x85902))) % 14.98/14.67 [9052]~P6(x90521,x90525,x90524)+~E(f862(f276(x90521,x90521,x90524),f862(f862(f301(x90521),x90522),f181(f932(x90521,a921)))),f862(f276(x90521,x90521,x90524),f862(f862(f301(x90521),x90523),f181(f932(x90521,a921)))))+~P1(f862(f862(f321(x90521),x90523),x90525))+P1(f862(f862(f321(f931(x90521,x90521)),f862(f862(f244(x90521,x90521),x90522),x90523)),x90524)) % 14.98/14.67 [9351]~P1(f862(x93511,x93515))+P1(f862(x93511,f632(x93511,x93512,x93513,x93514)))+P1(f862(x93511,f622(x93511,x93512,x93513,x93514)))+~P1(f862(f862(f321(x93514),x93515),f862(f862(f103(f932(x93514,a921)),x93513),x93512))) % 14.98/14.67 [9536]~P1(f862(x95361,x95365))+P1(f862(x95361,f622(x95361,x95362,x95363,x95364)))+P1(f862(f862(f321(x95364),f632(x95361,x95362,x95363,x95364)),x95362))+~P1(f862(f862(f321(x95364),x95365),f862(f862(f103(f932(x95364,a921)),x95363),x95362))) % 14.98/14.67 [9537]~P1(f862(x95371,x95375))+P1(f862(x95371,f632(x95371,x95372,x95373,x95374)))+P1(f862(f862(f321(x95374),f622(x95371,x95372,x95373,x95374)),x95373))+~P1(f862(f862(f321(x95374),x95375),f862(f862(f103(f932(x95374,a921)),x95373),x95372))) % 14.98/14.67 [9541]P1(f862(x95411,x95412))+~P1(f862(x95411,f615(x95411,x95413,x95414,x95415)))+~P1(f862(x95411,f598(x95411,x95413,x95414,x95415)))+~P1(f862(f862(f321(x95415),x95412),f862(f862(f103(f932(x95415,a921)),x95414),x95413))) % 14.98/14.67 [9547]~P36(x95471,x95474)+~P1(f862(f862(f321(f931(x95471,x95471)),f862(f862(f244(x95471,x95471),x95472),x95475)),x95474))+P1(f862(f862(f321(f931(x95471,x95471)),f862(f862(f244(x95471,x95471),x95472),x95473)),x95474))+~P1(f862(f862(f321(f931(x95471,x95471)),f862(f862(f244(x95471,x95471),x95475),x95473)),x95474)) % 14.98/14.67 [9588]E(x95881,x95882)+~P1(f862(f862(f321(f931(x95883,x95883)),f862(f862(f244(x95883,x95883),x95881),x95882)),f299(x95883,x95885)))+P1(f862(f862(f321(x95883),x95881),x95884))+~P1(f862(f862(f227(f932(f931(x95883,x95883),a921)),x95885),f862(f862(f246(x95883,x95883),x95884),f862(f18(f932(x95883,a921),x95883),x95884)))) % 14.98/14.67 [9606]P1(f862(x96061,x96062))+~P1(f862(x96061,f598(x96061,x96064,x96065,x96063)))+P1(f862(f862(f321(x96063),f615(x96061,x96064,x96065,x96063)),x96064))+~P1(f862(f862(f321(x96063),x96062),f862(f862(f103(f932(x96063,a921)),x96065),x96064))) % 14.98/14.67 [9607]P1(f862(x96071,x96072))+~P1(f862(x96071,f615(x96071,x96074,x96075,x96073)))+P1(f862(f862(f321(x96073),f598(x96071,x96074,x96075,x96073)),x96075))+~P1(f862(f862(f321(x96073),x96072),f862(f862(f103(f932(x96073,a921)),x96075),x96074))) % 14.98/14.67 [9674]P1(f862(x96741,x96742))+P1(f862(f862(f321(x96743),f615(x96741,x96744,x96745,x96743)),x96744))+P1(f862(f862(f321(x96743),f598(x96741,x96744,x96745,x96743)),x96745))+~P1(f862(f862(f321(x96743),x96742),f862(f862(f103(f932(x96743,a921)),x96745),x96744))) % 14.98/14.67 [9676]~P1(f862(x96762,x96765))+P1(f862(f862(f321(x96761),f632(x96762,x96763,x96764,x96761)),x96763))+P1(f862(f862(f321(x96761),f622(x96762,x96763,x96764,x96761)),x96764))+~P1(f862(f862(f321(x96761),x96765),f862(f862(f103(f932(x96761,a921)),x96764),x96763))) % 14.98/14.67 [9826]~P6(x98261,x98265,x98264)+~P1(f862(f862(f321(x98261),x98263),x98265))+P1(f862(f862(f321(f931(x98261,x98261)),f862(f862(f244(x98261,x98261),x98262),x98263)),x98264))+~P1(f862(f862(f227(f932(x98261,a921)),f862(f276(x98261,x98261,x98264),f862(f862(f301(x98261),x98263),f181(f932(x98261,a921))))),f862(f276(x98261,x98261,x98264),f862(f862(f301(x98261),x98262),f181(f932(x98261,a921)))))) % 14.98/14.67 [9954]~P3(x99545)+~P109(x99545)+P1(f862(f862(f321(x99541),f480(x99542,x99543,x99544,x99541,x99545)),x99544))+~P1(f862(f862(f228(x99545),f862(f862(f32(x99541,x99545),x99544),x99543)),x99542)) % 14.98/14.67 [9987]~P85(x99875)+~P81(x99875)+P1(f862(f862(f321(x99871),f701(x99872,x99873,x99874,x99871,x99875)),f862(f165(x99871),x99874)))+P1(f862(f862(f227(x99875),f862(f158(x99875),f862(f862(f147(x99871,x99875),x99873),x99874))),f862(f158(x99875),f862(f862(f147(x99871,x99875),x99872),x99874)))) % 14.98/14.67 [10098]~P3(x100981)+~P109(x100981)+P1(f862(f862(f228(x100981),f862(x100982,f480(x100983,x100982,x100984,x100985,x100981))),x100983))+~P1(f862(f862(f228(x100981),f862(f862(f32(x100985,x100981),x100984),x100982)),x100983)) % 14.98/14.67 [10228]~P85(x102281)+~P81(x102281)+~P1(f862(f862(f227(x102281),f862(x102283,f701(x102285,x102283,x102284,x102282,x102281))),f862(x102285,f701(x102285,x102283,x102284,x102282,x102281))))+P1(f862(f862(f227(x102281),f862(f158(x102281),f862(f862(f147(x102282,x102281),x102283),x102284))),f862(f158(x102281),f862(f862(f147(x102282,x102281),x102285),x102284)))) % 14.98/14.67 [8889]~P72(x88891)+~P1(f862(f54(x88894),x88895))+~P1(f862(f862(f321(x88894),x88893),x88895))+E(f862(f862(f73(x88891),f862(x88892,x88893)),f862(f862(f8(x88894,x88891),x88892),f862(f862(f3(f932(x88894,a921)),x88895),f862(f862(f301(x88894),x88893),f181(f932(x88894,a921)))))),f862(f862(f8(x88894,x88891),x88892),x88895)) % 14.98/14.67 [8890]~P71(x88901)+~P1(f862(f54(x88904),x88905))+~P1(f862(f862(f321(x88904),x88903),x88905))+E(f862(f862(f74(x88901),f862(x88902,x88903)),f862(f862(f11(x88904,x88901),x88902),f862(f862(f3(f932(x88904,a921)),x88905),f862(f862(f301(x88904),x88903),f181(f932(x88904,a921)))))),f862(f862(f11(x88904,x88901),x88902),x88905)) % 14.98/14.67 [8951]~P16(x89511,x89514,x89515)+~P1(f862(f54(x89511),x89512))+E(f862(f862(f3(f932(x89511,a921)),x89512),f862(f862(f301(x89511),x89513),f181(f932(x89511,a921)))),f181(f932(x89511,a921)))+E(f862(f862(x89514,x89513),f862(x89515,f862(f862(f3(f932(x89511,a921)),x89512),f862(f862(f301(x89511),x89513),f181(f932(x89511,a921)))))),f862(x89515,f862(f862(f301(x89511),x89513),x89512))) % 14.98/14.67 [9330]~P71(x93301)+~P1(f862(f54(x93302),x93305))+~P1(f862(f54(x93302),x93304))+E(f862(f862(f74(x93301),f862(f862(f11(x93302,x93301),x93303),f862(f862(f103(f932(x93302,a921)),x93304),x93305))),f862(f862(f11(x93302,x93301),x93303),f862(f862(f94(f932(x93302,a921)),x93304),x93305))),f862(f862(f74(x93301),f862(f862(f11(x93302,x93301),x93303),x93304)),f862(f862(f11(x93302,x93301),x93303),x93305))) % 14.98/14.67 [9331]~P72(x93311)+~P1(f862(f54(x93312),x93315))+~P1(f862(f54(x93312),x93314))+E(f862(f862(f73(x93311),f862(f862(f8(x93312,x93311),x93313),f862(f862(f103(f932(x93312,a921)),x93314),x93315))),f862(f862(f8(x93312,x93311),x93313),f862(f862(f94(f932(x93312,a921)),x93314),x93315))),f862(f862(f73(x93311),f862(f862(f8(x93312,x93311),x93313),x93314)),f862(f862(f8(x93312,x93311),x93313),x93315))) % 14.98/14.67 [9471]~P59(x94711)+~P1(f862(f54(x94712),x94715))+~P1(f862(f54(x94712),x94714))+E(f862(f862(f3(x94711),f862(f862(f73(x94711),f862(f862(f8(x94712,x94711),x94713),x94714)),f862(f862(f8(x94712,x94711),x94713),x94715))),f862(f862(f8(x94712,x94711),x94713),f862(f862(f94(f932(x94712,a921)),x94714),x94715))),f862(f862(f8(x94712,x94711),x94713),f862(f862(f103(f932(x94712,a921)),x94714),x94715))) % 14.98/14.67 [9688]~P22(x96881,x96882,x96883,x96885)+~P22(x96881,x96882,x96883,x96884)+P22(x96881,x96882,x96883,f862(f862(f103(f932(x96881,a921)),x96884),x96885))+~E(f862(f862(f94(f932(x96882,a921)),f862(f302(x96881,x96882,x96883),f862(f862(f3(f932(x96881,a921)),x96884),x96885))),f862(f302(x96881,x96882,x96883),f862(f862(f3(f932(x96881,a921)),x96885),x96884))),f181(f932(x96882,a921))) % 14.98/14.67 [9801]E(x98011,f2(a1))+~P1(f862(f862(f228(a1),f2(a1)),x98013))+~P1(f862(f42(x98012,x98011),f862(f862(f244(a1,a1),x98014),x98015)))+P1(f862(f42(x98012,f862(f862(f74(a1),x98011),x98013)),f862(f862(f244(a1,a1),f862(f862(f29(a1),x98014),x98013)),f862(f862(f73(a1),f862(f862(f74(a1),x98011),f38(a1,x98014,x98013))),x98015)))) % 14.98/14.67 [9809]~P1(f862(f862(f228(a924),f2(a924)),x98093))+~P1(f862(f862(f228(a924),f2(a924)),x98092))+~P1(f862(f41(x98091,x98092),f862(f862(f244(a924,a924),x98094),x98095)))+P1(f862(f41(x98091,f862(f862(f74(a924),x98092),x98093)),f862(f862(f244(a924,a924),f862(f862(f29(a924),x98094),x98093)),f862(f862(f73(a924),f862(f862(f74(a924),x98092),f38(a924,x98094,x98093))),x98095)))) % 14.98/14.67 [9858]~P71(x98581)+~P1(f862(f54(x98582),x98585))+~P1(f862(f54(x98582),x98584))+E(f862(f862(f74(x98581),f862(f862(f862(f58(x98581,x98582,f74(x98581)),x98583),f71(x98581)),f862(f862(f103(f932(x98582,a921)),x98584),x98585))),f862(f862(f862(f58(x98581,x98582,f74(x98581)),x98583),f71(x98581)),f862(f862(f94(f932(x98582,a921)),x98584),x98585))),f862(f862(f74(x98581),f862(f862(f862(f58(x98581,x98582,f74(x98581)),x98583),f71(x98581)),x98584)),f862(f862(f862(f58(x98581,x98582,f74(x98581)),x98583),f71(x98581)),x98585))) % 14.98/14.67 [9860]~E(f862(f862(f168(x98601),x98605),x98602),f862(f862(f168(x98601),x98605),x98603))+P1(f862(f862(f321(f931(f925(x98601),f925(x98601))),f862(f862(f244(f925(x98601),f925(x98601)),x98602),x98603)),f140(x98601,x98604)))+~P1(f862(f862(f228(a924),x98605),f862(f862(f225(a924),f862(f182(f925(x98601)),x98602)),f862(f182(f925(x98601)),x98603))))+~P1(f862(f862(f321(f931(x98601,x98601)),f862(f862(f244(x98601,x98601),f862(f862(f157(x98601),x98602),x98605)),f862(f862(f157(x98601),x98603),x98605))),x98604)) % 14.98/14.67 [9976]~P85(x99765)+~P147(x99765)+P1(f862(f862(f321(x99761),f413(x99762,x99763,x99764,x99761,x99765)),x99764))+P1(f862(f862(f227(x99765),f862(f862(f8(x99761,x99765),x99763),x99764)),f862(f862(f74(x99765),f862(f93(x99765),f862(f28(x99761),x99764))),x99762))) % 14.98/14.67 [10156]~P85(x101561)+~P147(x101561)+~P1(f862(f862(f227(x101561),f862(x101563,f413(x101565,x101563,x101564,x101562,x101561))),x101565))+P1(f862(f862(f227(x101561),f862(f862(f8(x101562,x101561),x101563),x101564)),f862(f862(f74(x101561),f862(f93(x101561),f862(f28(x101562),x101564))),x101565))) % 14.98/14.67 [8919]E(f862(f862(f127(x89191),x89192),x89193),f862(f862(f127(x89191),x89194),x89195))+~E(f862(f862(f168(x89191),f862(f182(f925(x89191)),x89192)),x89194),x89192)+~E(f862(f862(f127(x89191),f862(f862(f131(x89191),f862(f182(f925(x89191)),x89192)),x89194)),x89195),x89193)+P1(f862(f862(f227(a924),f862(f182(f925(x89191)),x89194)),f862(f182(f925(x89191)),x89192))) % 14.98/14.67 [9051]E(f862(f862(f127(x90511),x90512),x90513),f862(f862(f127(x90511),x90514),x90515))+~E(f862(f862(f168(x90511),f862(f182(f925(x90511)),x90512)),x90514),x90512)+~E(x90513,f862(f862(f127(x90511),f862(f862(f131(x90511),f862(f182(f925(x90511)),x90512)),x90514)),x90515))+~P1(f862(f862(f227(a924),f862(f182(f925(x90511)),x90512)),f862(f182(f925(x90511)),x90514))) % 14.98/14.67 [10290]~P1(f862(x102905,x102904))+~P1(f862(f54(x102902),f862(f254(x102902),x102905)))+P1(f862(f54(x102901),f862(f254(x102901),f862(f862(f9(x102901,x102902,a921),x102903),x102904))))+~P1(f862(f54(x102901),f862(f254(x102901),f862(f862(f10(f932(x102902,a921),a921,x102901),f80(x102902)),f862(f862(f10(f932(x102902,a921),f932(x102902,a921),x102901),f862(f20(x102902,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102902),a318),x102905))),x102903))))) % 14.98/14.67 [10366]~P1(f862(f54(x103662),x103665))+~P1(f862(f862(f321(x103662),x103664),x103665))+P1(f862(f54(x103661),f862(f254(x103661),f862(f862(f9(x103661,x103662,a921),x103663),x103664))))+~P1(f862(f54(x103661),f862(f254(x103661),f862(f862(f10(f932(x103662,a921),a921,x103661),f80(x103662)),f862(f862(f10(f932(x103662,a921),f932(x103662,a921),x103661),f862(f20(x103662,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103662),a318),f862(f862(f9(x103662,f932(x103662,a921),a921),f321(x103662)),x103665)))),x103663))))) % 14.98/14.67 [8702]~P17(x87025,x87021,x87026,x87022)+E(f862(f66(x87021,x87021,x87021,f862(x87022,x87023)),f862(x87022,x87024)),f862(f66(x87021,x87021,x87021,f862(x87022,x87024)),f862(x87022,x87023)))+~P1(f862(f54(x87025),x87024))+~P1(f862(f54(x87025),x87023)) % 14.98/14.67 [8087]~P22(x80871,x80872,x80874,x80873)+~E(f862(x80874,x80876),x80875)+E(f862(f70(x80871,x80872,x80873,x80874),x80875),x80876)+~P1(f862(f862(f321(x80871),x80876),x80873)) % 14.98/14.67 [8088]~P22(x80881,x80882,x80884,x80883)+~E(f862(x80884,x80886),x80885)+E(f862(f86(x80881,x80882,x80883,x80884),x80885),x80886)+~P1(f862(f862(f321(x80881),x80886),x80883)) % 14.98/14.67 [8285]~P18(x82856,x82851,x82854,x82852)+E(f862(f66(x82851,x82851,x82851,f862(x82852,x82853)),f862(x82854,x82855)),f862(x82852,x82853))+~P1(f862(f54(x82856),x82853))+~P1(f862(f862(f321(x82856),x82855),x82853)) % 14.98/14.67 [9423]E(x94231,x94232)+~E(f862(f86(x94233,x94234,x94235,x94236),x94231),f862(f86(x94233,x94234,x94235,x94236),x94232))+~P1(f862(f862(f321(x94234),x94232),f862(f302(x94233,x94234,x94236),x94235)))+~P1(f862(f862(f321(x94234),x94231),f862(f302(x94233,x94234,x94236),x94235))) % 14.98/14.67 [9520]~P17(x95203,x95201,x95206,x95202)+E(f862(f66(x95201,x95201,x95201,f862(x95202,f862(f862(f3(f932(x95203,a921)),x95204),f862(f862(f301(x95203),x95205),f181(f932(x95203,a921)))))),f862(x95206,x95205)),f862(x95202,x95204))+~P1(f862(f54(x95203),x95204))+~P1(f862(f862(f321(x95203),x95205),x95204)) % 14.98/14.67 [7163]~P62(x71631)+~E(f38(x71631,x71633,x71634),f38(x71631,x71636,x71634))+~E(f38(x71631,x71632,x71634),f38(x71631,x71635,x71634))+E(f38(x71631,f862(f862(f3(x71631),x71632),x71633),x71634),f38(x71631,f862(f862(f3(x71631),x71635),x71636),x71634)) % 14.98/14.67 [7164]~P61(x71641)+~E(f38(x71641,x71643,x71644),f38(x71641,x71646,x71644))+~E(f38(x71641,x71642,x71644),f38(x71641,x71645,x71644))+E(f38(x71641,f862(f862(f74(x71641),x71642),x71643),x71644),f38(x71641,f862(f862(f74(x71641),x71645),x71646),x71644)) % 14.98/14.67 [7165]~P61(x71651)+~E(f38(x71651,x71653,x71654),f38(x71651,x71656,x71654))+~E(f38(x71651,x71652,x71654),f38(x71651,x71655,x71654))+E(f38(x71651,f862(f862(f73(x71651),x71652),x71653),x71654),f38(x71651,f862(f862(f73(x71651),x71655),x71656),x71654)) % 14.98/14.67 [7981]~P14(x79811,x79812,x79813)+~P1(f862(f54(x79811),x79816))+E(f862(f862(f57(x79811,x79812,x79813),x79814),f862(f862(f301(x79811),x79815),x79816)),f862(f862(f57(x79811,x79812,x79813),f862(f862(x79813,x79815),x79814)),x79816))+P1(f862(f862(f321(x79811),x79815),x79816)) % 14.98/14.67 [8046]~P3(x80461)+P1(f862(f862(f227(x80461),x80462),f862(x80463,x80464)))+~P1(f862(f862(f321(x80465),x80464),x80466))+~P1(f862(f862(f227(x80461),x80462),f862(f862(f32(x80465,x80461),x80466),x80463))) % 14.98/14.67 [8207]~P14(x82071,x82072,x82073)+~P1(f862(f54(x82071),x82076))+E(f862(f862(f57(x82071,x82072,x82073),x82074),f862(f862(f301(x82071),x82075),x82076)),f862(f862(x82073,x82075),f862(f862(f57(x82071,x82072,x82073),x82074),x82076)))+P1(f862(f862(f321(x82071),x82075),x82076)) % 14.98/14.67 [8305]~P109(x83053)+~P1(f862(x83052,x83055))+~P11(x83053,f862(f862(f147(x83051,x83053),x83054),x83056))+E(f862(f129(x83051,x83052),f862(f862(f141(x83051,x83053,x83054),x83055),x83056)),f862(f862(f141(x83051,x83053,x83054),x83055),f862(f129(x83051,x83052),x83056))) % 14.98/14.67 [8328]E(x83281,x83282)+E(x83283,f2(a1))+~P1(f862(f42(x83284,x83283),f862(f862(f244(a1,a1),x83285),x83282)))+~P1(f862(f42(x83284,x83283),f862(f862(f244(a1,a1),x83286),x83281))) % 14.98/14.67 [8329]E(x83291,x83292)+E(x83293,f2(a1))+~P1(f862(f42(x83294,x83293),f862(f862(f244(a1,a1),x83292),x83295)))+~P1(f862(f42(x83294,x83293),f862(f862(f244(a1,a1),x83291),x83296))) % 14.98/14.67 [8352]~P17(x83522,x83525,x83526,x83521)+~P1(f862(f54(x83522),x83524))+E(f862(x83521,f862(f862(f301(x83522),x83523),x83524)),f862(f66(x83525,x83525,x83525,f862(x83521,x83524)),f862(x83526,x83523)))+P1(f862(f862(f321(x83522),x83523),x83524)) % 14.98/14.67 [8574]~P18(x85745,x85741,x85746,x85742)+E(f862(f66(x85741,x85741,x85741,f862(x85742,x85743)),f862(x85742,x85744)),f862(x85742,x85743))+~P1(f862(f54(x85745),x85743))+~P1(f862(f862(f227(f932(x85745,a921)),x85744),x85743)) % 14.98/14.67 [9731]~P22(x97311,x97312,x97314,x97313)+~P1(f862(f862(f321(x97312),x97315),f862(f302(x97311,x97312,x97314),x97313)))+P1(f862(f862(f321(x97311),f862(f70(x97311,x97312,x97313,x97314),x97315)),x97316))+~P1(f862(f862(f227(f932(x97311,a921)),x97313),x97316)) % 14.98/14.67 [10110]~P72(x101102)+~E(f602(x101101,x101103,x101105,x101106,x101104,x101102),f603(x101101,x101103,x101105,x101106,x101104,x101102))+~P1(f862(f54(x101104),x101106))+E(f862(f862(f8(x101101,x101102),x101103),f862(f302(x101104,x101101,x101105),x101106)),f862(f862(f8(x101104,x101102),f862(f66(x101101,x101102,x101104,x101103),x101105)),x101106)) % 14.98/14.67 [10138]~P72(x101386)+E(f862(x101381,f602(x101382,x101383,x101381,x101384,x101385,x101386)),f862(x101381,f603(x101382,x101383,x101381,x101384,x101385,x101386)))+E(f862(f862(f8(x101382,x101386),x101383),f862(f302(x101385,x101382,x101381),x101384)),f862(f862(f8(x101385,x101386),f862(f66(x101382,x101386,x101385,x101383),x101381)),x101384))+~P1(f862(f54(x101385),x101384)) % 14.98/14.67 [10178]~P72(x101782)+~E(f862(x101783,f862(x101785,f603(x101781,x101783,x101785,x101786,x101784,x101782))),f2(x101782))+~P1(f862(f54(x101784),x101786))+E(f862(f862(f8(x101781,x101782),x101783),f862(f302(x101784,x101781,x101785),x101786)),f862(f862(f8(x101784,x101782),f862(f66(x101781,x101782,x101784,x101783),x101785)),x101786)) % 14.98/14.67 [10237]~P72(x102372)+~P1(f862(f54(x102374),x102376))+E(f862(f862(f8(x102371,x102372),x102373),f862(f302(x102374,x102371,x102375),x102376)),f862(f862(f8(x102374,x102372),f862(f66(x102371,x102372,x102374,x102373),x102375)),x102376))+P1(f862(f862(f321(x102374),f603(x102371,x102373,x102375,x102376,x102374,x102372)),x102376)) % 14.98/14.67 [10238]~P72(x102382)+~P1(f862(f54(x102384),x102386))+E(f862(f862(f8(x102381,x102382),x102383),f862(f302(x102384,x102381,x102385),x102386)),f862(f862(f8(x102384,x102382),f862(f66(x102381,x102382,x102384,x102383),x102385)),x102386))+P1(f862(f862(f321(x102384),f602(x102381,x102383,x102385,x102386,x102384,x102382)),x102386)) % 14.98/14.67 [10365]~P71(x103651)+~P1(f862(f54(x103652),x103656))+E(f862(f862(f862(f58(x103651,x103652,f74(x103651)),f862(f862(f20(x103652,f932(x103653,a921),x103651),f862(f862(f9(x103652,x103651,f932(f932(x103653,a921),x103651)),f862(f862(f10(f932(x103653,x103651),f932(x103651,f932(f932(x103653,a921),x103651)),x103652),f58(x103651,x103653,f74(x103651))),x103654)),f71(x103651))),x103655)),f71(x103651)),x103656),f862(f862(f862(f58(x103651,f931(x103652,x103653),f74(x103651)),f862(f249(x103652,x103653,x103651),x103654)),f71(x103651)),f862(f862(f246(x103652,x103653),x103656),x103655)))+P1(f862(f862(f321(x103652),f575(x103654,x103655,x103653,x103656,x103652,x103651)),x103656)) % 14.98/14.67 [10387]~P71(x103871)+~P1(f862(f54(x103872),x103876))+E(f862(f862(f862(f58(x103871,x103872,f74(x103871)),f862(f862(f20(x103872,f932(x103873,a921),x103871),f862(f862(f9(x103872,x103871,f932(f932(x103873,a921),x103871)),f862(f862(f10(f932(x103873,x103871),f932(x103871,f932(f932(x103873,a921),x103871)),x103872),f58(x103871,x103873,f74(x103871))),x103874)),f71(x103871))),x103875)),f71(x103871)),x103876),f862(f862(f862(f58(x103871,f931(x103872,x103873),f74(x103871)),f862(f249(x103872,x103873,x103871),x103874)),f71(x103871)),f862(f862(f246(x103872,x103873),x103876),x103875)))+~P1(f862(f54(x103873),f862(x103875,f575(x103874,x103875,x103873,x103876,x103872,x103871)))) % 14.98/14.67 [8484]~P18(x84842,x84845,x84846,x84841)+~P1(f862(f54(x84842),x84844))+~P1(f862(f54(x84842),x84843))+E(f862(x84841,f862(f862(f103(f932(x84842,a921)),x84843),x84844)),f862(f66(x84845,x84845,x84845,f862(x84841,x84843)),f862(x84841,x84844))) % 14.98/14.67 [8703]~P3(x87031)+P1(f862(f862(f227(x87031),f862(x87032,x87033)),x87034))+~P1(f862(f862(f321(x87035),x87033),x87036))+~P1(f862(f862(f227(x87031),f862(f862(f33(x87035,x87031),x87036),x87032)),x87034)) % 14.98/14.67 [9137]~P22(x91372,x91371,x91373,x91376)+E(f862(f862(f94(f932(x91371,a921)),f862(f302(x91372,x91371,x91373),x91374)),f862(f302(x91372,x91371,x91373),x91375)),f862(f302(x91372,x91371,x91373),f862(f862(f94(f932(x91372,a921)),x91374),x91375)))+~P1(f862(f862(f227(f932(x91372,a921)),x91375),x91376))+~P1(f862(f862(f227(f932(x91372,a921)),x91374),x91376)) % 14.98/14.67 [9138]~P22(x91382,x91381,x91383,x91386)+E(f862(f862(f3(f932(x91381,a921)),f862(f302(x91382,x91381,x91383),x91384)),f862(f302(x91382,x91381,x91383),x91385)),f862(f302(x91382,x91381,x91383),f862(f862(f3(f932(x91382,a921)),x91384),x91385)))+~P1(f862(f862(f227(f932(x91382,a921)),x91385),x91386))+~P1(f862(f862(f227(f932(x91382,a921)),x91384),x91386)) % 14.98/14.67 [9397]E(x93971,x93972)+~P52(x93973,x93974,x93975)+~P1(f862(f862(f321(f931(x93973,x93974)),f862(f862(f244(x93973,x93974),x93976),x93972)),x93975))+~P1(f862(f862(f321(f931(x93973,x93974)),f862(f862(f244(x93973,x93974),x93976),x93971)),x93975)) % 14.98/14.67 [10173]~P69(x101731)+~E(f862(x101733,f384(x101734,x101736,x101733,x101735,x101732,x101731)),f862(x101736,f384(x101734,x101736,x101733,x101735,x101732,x101731)))+~P1(f862(f54(x101732),x101735))+E(f862(f862(f862(f58(x101731,x101732,f74(x101731)),x101733),x101734),x101735),f862(f862(f862(f58(x101731,x101732,f74(x101731)),x101736),x101734),x101735)) % 14.98/14.67 [10234]~P69(x102341)+~P1(f862(f54(x102342),x102345))+E(f862(f862(f862(f58(x102341,x102342,f74(x102341)),x102343),x102344),x102345),f862(f862(f862(f58(x102341,x102342,f74(x102341)),x102346),x102344),x102345))+P1(f862(f862(f321(x102342),f384(x102344,x102343,x102346,x102345,x102342,x102341)),x102345)) % 14.98/14.67 [8933]~P69(x89331)+~P1(f862(f54(x89332),x89336))+P1(f862(f862(f321(x89332),x89335),x89336))+E(f862(f862(f862(f58(x89331,x89332,f74(x89331)),x89333),x89334),f862(f862(f301(x89332),x89335),x89336)),f862(f862(f74(x89331),f862(x89333,x89335)),f862(f862(f862(f58(x89331,x89332,f74(x89331)),x89333),x89334),x89336))) % 14.98/14.67 [8986]~P6(x89861,x89866,x89863)+~P9(x89861,f932(x89862,a921),x89863,x89865)+~P1(f862(f862(f321(x89861),x89864),x89866))+E(f862(f862(f33(x89861,f932(x89862,a921)),f862(f276(x89861,x89861,x89863),f862(f862(f301(x89861),x89864),f181(f932(x89861,a921))))),x89865),f862(x89865,x89864)) % 14.98/14.67 [9114]~P14(x91143,x91144,x91141)+~P1(f862(f54(x91143),x91146))+~P1(f862(f862(f321(x91143),x91142),x91146))+E(f862(f862(x91141,x91142),f862(f862(f57(x91143,x91144,x91141),x91145),f862(f862(f3(f932(x91143,a921)),x91146),f862(f862(f301(x91143),x91142),f181(f932(x91143,a921)))))),f862(f862(f57(x91143,x91144,x91141),x91145),x91146)) % 14.98/14.67 [9407]~P17(x94073,x94071,x94076,x94072)+~P1(f862(f54(x94073),x94075))+~P1(f862(f54(x94073),x94074))+E(f862(f66(x94071,x94071,x94071,f862(x94072,f862(f862(f103(f932(x94073,a921)),x94074),x94075))),f862(x94072,f862(f862(f94(f932(x94073,a921)),x94074),x94075))),f862(f66(x94071,x94071,x94071,f862(x94072,x94074)),f862(x94072,x94075))) % 14.98/14.67 [9754]~E(x97543,f862(f862(f152(x97541,x97542),x97545),x97546))+P1(f862(f862(f321(f931(f925(x97541),f925(x97541))),f862(f862(f244(f925(x97541),f925(x97541)),x97542),x97543)),f150(x97541,x97544)))+~P1(f862(f862(f228(a924),x97545),f862(f182(f925(x97541)),x97542)))+~P1(f862(f862(f321(f931(x97541,x97541)),f862(f862(f244(x97541,x97541),f862(f862(f157(x97541),x97542),x97545)),x97546)),x97544)) % 14.98/14.67 [10247]~P72(x102472)+~P1(f862(f54(x102471),x102476))+P1(f862(f862(f321(x102471),f573(x102474,x102475,x102473,x102476,x102471,x102472)),x102476))+E(f862(f862(f8(x102471,x102472),f862(f862(f20(x102471,f932(x102473,a921),x102472),f862(f862(f10(f932(x102473,x102472),f932(f932(x102473,a921),x102472),x102471),f8(x102473,x102472)),x102474)),x102475)),x102476),f862(f862(f8(f931(x102471,x102473),x102472),f862(f249(x102471,x102473,x102472),x102474)),f862(f862(f246(x102471,x102473),x102476),x102475))) % 14.98/14.67 [10248]~P71(x102482)+~P1(f862(f54(x102481),x102486))+P1(f862(f862(f321(x102481),f574(x102484,x102485,x102483,x102486,x102481,x102482)),x102486))+E(f862(f862(f11(x102481,x102482),f862(f862(f20(x102481,f932(x102483,a921),x102482),f862(f862(f10(f932(x102483,x102482),f932(f932(x102483,a921),x102482),x102481),f11(x102483,x102482)),x102484)),x102485)),x102486),f862(f862(f11(f931(x102481,x102483),x102482),f862(f249(x102481,x102483,x102482),x102484)),f862(f862(f246(x102481,x102483),x102486),x102485))) % 14.98/14.67 [10288]~P72(x102882)+~P1(f862(f54(x102881),x102886))+~P1(f862(f54(x102883),f862(x102885,f573(x102884,x102885,x102883,x102886,x102881,x102882))))+E(f862(f862(f8(x102881,x102882),f862(f862(f20(x102881,f932(x102883,a921),x102882),f862(f862(f10(f932(x102883,x102882),f932(f932(x102883,a921),x102882),x102881),f8(x102883,x102882)),x102884)),x102885)),x102886),f862(f862(f8(f931(x102881,x102883),x102882),f862(f249(x102881,x102883,x102882),x102884)),f862(f862(f246(x102881,x102883),x102886),x102885))) % 14.98/14.67 [10289]~P71(x102892)+~P1(f862(f54(x102891),x102896))+~P1(f862(f54(x102893),f862(x102895,f574(x102894,x102895,x102893,x102896,x102891,x102892))))+E(f862(f862(f11(x102891,x102892),f862(f862(f20(x102891,f932(x102893,a921),x102892),f862(f862(f10(f932(x102893,x102892),f932(f932(x102893,a921),x102892),x102891),f11(x102893,x102892)),x102894)),x102895)),x102896),f862(f862(f11(f931(x102891,x102893),x102892),f862(f249(x102891,x102893,x102892),x102894)),f862(f862(f246(x102891,x102893),x102896),x102895))) % 14.98/14.67 [10269]~P71(x102692)+~P1(f862(f54(x102691),x102696))+P1(f862(f862(f321(x102691),x102693),x102696))+E(f862(f862(f11(x102691,x102692),f862(f862(f9(x102691,x102692,x102692),f862(f862(f20(x102691,x102692,f932(x102692,x102692)),f862(f862(f10(a921,f932(x102692,f932(x102692,x102692)),x102691),f89(x102692)),f862(f862(f9(x102691,x102691,a921),a317),x102693))),x102694)),x102695)),x102696),f862(f862(f236(x102692),x102695),f862(f28(x102691),x102696))) % 14.98/14.67 [10272]~P71(x102722)+~P1(f862(f54(x102721),x102726))+~P1(f862(f862(f321(x102721),x102723),x102726))+E(f862(f862(f11(x102721,x102722),f862(f862(f9(x102721,x102722,x102722),f862(f862(f20(x102721,x102722,f932(x102722,x102722)),f862(f862(f10(a921,f932(x102722,f932(x102722,x102722)),x102721),f89(x102722)),f862(f862(f9(x102721,x102721,a921),a317),x102723))),x102724)),x102725)),x102726),f862(f862(f74(x102722),f862(x102724,x102723)),f862(f862(f236(x102722),x102725),f862(f862(f3(a924),f862(f28(x102721),x102726)),f71(a924))))) % 14.98/14.67 [10352]~P1(f862(f54(x103521),x103525))+~P1(f862(f54(x103522),x103523))+P1(f862(f862(f321(x103522),f512(x103526,x103524,x103523,x103522,x103525,x103521)),x103523))+E(f862(f862(f8(x103521,a924),f862(f862(f10(f932(x103522,a921),a924,x103521),f28(x103522)),f862(f862(f10(f932(x103522,a921),f932(x103522,a921),x103521),f254(x103522)),f862(f862(f10(f932(x103522,a921),f932(x103522,a921),x103521),f862(f20(x103522,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103522),a318),f862(f862(f9(x103522,f932(x103522,a921),a921),f321(x103522)),x103523)))),x103524)))),x103525),f862(f862(f74(a924),x103526),f862(f28(x103522),x103523))) % 14.98/14.67 [10353]~P1(f862(f54(x103531),x103535))+~P1(f862(f54(x103532),x103533))+P1(f862(f862(f321(x103532),f519(x103536,x103534,x103533,x103532,x103535,x103531)),x103533))+E(f862(f862(f8(x103531,a924),f862(f862(f10(f932(x103532,a921),a924,x103531),f28(x103532)),f862(f862(f10(f932(x103532,a921),f932(x103532,a921),x103531),f254(x103532)),f862(f862(f10(f932(x103532,a921),f932(x103532,a921),x103531),f862(f20(x103532,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103532),a318),f862(f862(f9(x103532,f932(x103532,a921),a921),f321(x103532)),x103533)))),x103534)))),x103535),f862(f862(f8(x103532,a924),x103536),x103533)) % 14.98/14.67 [10400]~P1(f862(f54(x104002),x104003))+~P1(f862(f54(x104001),x104005))+~E(f862(f28(x104001),f862(f254(x104001),f862(f862(f20(x104001,a921,a921),f862(f862(f10(a921,f932(a921,a921),x104001),a318),f862(f862(f9(x104001,f932(x104001,a921),a921),f321(x104001)),x104005))),f862(f862(f9(x104001,x104002,a921),x104004),f512(x104006,x104004,x104003,x104002,x104005,x104001))))),x104006)+E(f862(f862(f8(x104001,a924),f862(f862(f10(f932(x104002,a921),a924,x104001),f28(x104002)),f862(f862(f10(f932(x104002,a921),f932(x104002,a921),x104001),f254(x104002)),f862(f862(f10(f932(x104002,a921),f932(x104002,a921),x104001),f862(f20(x104002,a921,a921),f862(f862(f10(a921,f932(a921,a921),x104002),a318),f862(f862(f9(x104002,f932(x104002,a921),a921),f321(x104002)),x104003)))),x104004)))),x104005),f862(f862(f74(a924),x104006),f862(f28(x104002),x104003))) % 14.98/14.67 [10402]~P1(f862(f54(x104022),x104023))+~P1(f862(f54(x104021),x104025))+~E(f862(f28(x104021),f862(f254(x104021),f862(f862(f20(x104021,a921,a921),f862(f862(f10(a921,f932(a921,a921),x104021),a318),f862(f862(f9(x104021,f932(x104021,a921),a921),f321(x104021)),x104025))),f862(f862(f9(x104021,x104022,a921),x104024),f519(x104026,x104024,x104023,x104022,x104025,x104021))))),f862(x104026,f519(x104026,x104024,x104023,x104022,x104025,x104021)))+E(f862(f862(f8(x104021,a924),f862(f862(f10(f932(x104022,a921),a924,x104021),f28(x104022)),f862(f862(f10(f932(x104022,a921),f932(x104022,a921),x104021),f254(x104022)),f862(f862(f10(f932(x104022,a921),f932(x104022,a921),x104021),f862(f20(x104022,a921,a921),f862(f862(f10(a921,f932(a921,a921),x104022),a318),f862(f862(f9(x104022,f932(x104022,a921),a921),f321(x104022)),x104023)))),x104024)))),x104025),f862(f862(f8(x104022,a924),x104026),x104023)) % 14.98/14.67 [10033]E(x100331,x100332)+~P14(x100333,x100334,x100335)+~P1(f862(f59(x100333,x100334,x100335,x100336,x100337),x100332))+~P1(f862(f59(x100333,x100334,x100335,x100336,x100337),x100331)) % 14.98/14.67 [9830]P1(f862(x98301,x98302))+~P1(f862(f862(f321(x98307),x98302),f862(x98306,x98304)))+~P1(f862(x98301,f886(x98301,x98306,x98305,x98303,x98307)))+~P1(f862(f862(f321(x98303),x98304),x98305)) % 14.98/14.67 [10261]~P14(x102617,x102616,x102611)+E(f862(f862(x102611,x102612),f802(x102612,x102613,x102614,x102615,x102611,x102616,x102617)),x102613)+~P1(f862(f59(x102617,x102616,x102611,x102615,x102614),x102613))+~P1(f862(f862(f321(x102617),x102612),x102614)) % 14.98/14.67 [10276]~P54(x102763,x102764,x102765,x102766,x102767)+P1(f862(x102761,x102762))+~P1(f862(f862(f321(x102764),x102762),x102767))+~P1(f862(x102761,f862(x102765,f910(x102761,x102762,x102767,x102766,x102765,x102764)))) % 14.98/14.67 [10330]~P14(x103301,x103302,x103303)+~P1(f862(f59(x103301,x103302,x103303,x103304,x103305),x103307))+P1(f862(f59(x103301,x103302,x103303,x103304,f862(f862(f3(f932(x103301,a921)),x103305),f862(f862(f301(x103301),x103306),f181(f932(x103301,a921))))),f802(x103306,x103307,x103305,x103304,x103303,x103302,x103301)))+~P1(f862(f862(f321(x103301),x103306),x103305)) % 14.98/14.67 [9478]P23(x94781,x94782,x94783,x94784,x94785)+~P23(x94781,x94782,x94783,x94786,x94787)+~E(f862(f302(x94781,x94782,x94783),x94784),x94785)+~P1(f862(f862(f227(f932(x94781,a921)),x94784),x94786)) % 14.98/14.67 [9722]~P23(x97221,x97222,x97223,x97225,x97227)+~P23(x97221,x97222,x97223,x97224,x97226)+P23(x97221,x97222,x97223,f862(f862(f103(f932(x97221,a921)),x97224),x97225),f862(f862(f103(f932(x97222,a921)),x97226),x97227))+~E(f862(f862(f94(f932(x97222,a921)),x97226),x97227),f181(f932(x97222,a921))) % 14.98/14.67 [9727]~P69(x97271)+~P22(x97275,x97272,x97276,x97277)+~P1(f862(f54(x97275),x97277))+E(f862(f862(f862(f58(x97271,x97272,f74(x97271)),x97273),x97274),f862(f302(x97275,x97272,x97276),x97277)),f862(f862(f862(f58(x97271,x97275,f74(x97271)),f862(f66(x97272,x97271,x97275,x97273),x97276)),x97274),x97277)) % 14.98/14.67 [9853]~E(f862(f862(f301(x98531),x98535),x98536),f862(f862(f301(x98531),x98532),x98533))+~P1(f862(f59(x98531,x98531,x98534,x98532,x98533),x98537))+P1(f862(f862(f321(x98531),x98532),x98533))+P1(f862(f55(x98531,x98534,f862(f862(f301(x98531),x98535),x98536)),x98537)) % 14.98/14.67 [9938]P1(f862(x99381,x99382))+~P1(f862(f862(f321(x99383),x99382),f862(x99384,x99387)))+~P1(f862(f862(f321(x99386),x99387),x99385))+P1(f862(f862(f321(x99383),f886(x99381,x99384,x99385,x99386,x99383)),f862(f862(f33(x99386,f932(x99383,a921)),x99385),x99384))) % 14.98/14.67 [9955]~P22(x99552,x99551,x99555,x99554)+~P22(x99551,x99553,x99556,f862(f302(x99552,x99551,x99555),x99554))+E(f862(f862(f66(x99551,x99552,x99553,f70(x99552,x99551,x99554,x99555)),f70(x99551,x99553,f862(f302(x99552,x99551,x99555),x99554),x99556)),x99557),f862(f70(x99552,x99553,x99554,f862(f66(x99551,x99553,x99552,x99556),x99555)),x99557))+~P1(f862(f862(f321(x99553),x99557),f862(f302(x99551,x99553,x99556),f862(f302(x99552,x99551,x99555),x99554)))) % 14.98/14.67 [9956]~P22(x99562,x99561,x99565,x99564)+~P22(x99561,x99563,x99566,f862(f302(x99562,x99561,x99565),x99564))+E(f862(f862(f66(x99561,x99562,x99563,f86(x99562,x99561,x99564,x99565)),f86(x99561,x99563,f862(f302(x99562,x99561,x99565),x99564),x99566)),x99567),f862(f86(x99562,x99563,x99564,f862(f66(x99561,x99563,x99562,x99566),x99565)),x99567))+~P1(f862(f862(f321(x99563),x99567),f862(f302(x99561,x99563,x99566),f862(f302(x99562,x99561,x99565),x99564)))) % 14.98/14.67 [10262]~P14(x102627,x102626,x102621)+E(f862(f862(x102621,x102622),f880(x102623,x102624,x102622,x102625,x102621,x102626,x102627)),x102623)+P1(f862(f862(f321(x102627),x102622),x102624))+~P1(f862(f59(x102627,x102626,x102621,x102625,f862(f862(f301(x102627),x102622),x102624)),x102623)) % 14.98/14.67 [10329]~P14(x103291,x103294,x103295)+P1(f862(f59(x103291,x103294,x103295,x103296,x103293),f880(x103297,x103293,x103292,x103296,x103295,x103294,x103291)))+P1(f862(f862(f321(x103291),x103292),x103293))+~P1(f862(f59(x103291,x103294,x103295,x103296,f862(f862(f301(x103291),x103292),x103293)),x103297)) % 14.98/14.67 [10015]E(x100151,f2(a1))+~P1(f862(f42(x100153,x100151),f862(f862(f244(a1,a1),x100155),x100157)))+~P1(f862(f42(x100152,x100151),f862(f862(f244(a1,a1),x100154),x100156)))+P1(f862(f42(f862(f862(f73(a1),x100152),x100153),x100151),f862(f862(f244(a1,a1),f862(f862(f73(a1),f862(f862(f73(a1),x100154),x100155)),f862(f862(f29(a1),f862(f862(f73(a1),x100156),x100157)),x100151))),f38(a1,f862(f862(f73(a1),x100156),x100157),x100151)))) % 14.98/14.67 [10017]~P1(f862(f862(f228(a924),f2(a924)),x100173))+~P1(f862(f41(x100172,x100173),f862(f862(f244(a924,a924),x100175),x100177)))+~P1(f862(f41(x100171,x100173),f862(f862(f244(a924,a924),x100174),x100176)))+P1(f862(f41(f862(f862(f73(a924),x100171),x100172),x100173),f862(f862(f244(a924,a924),f862(f862(f73(a924),f862(f862(f73(a924),x100174),x100175)),f862(f862(f29(a924),f862(f862(f73(a924),x100176),x100177)),x100173))),f38(a924,f862(f862(f73(a924),x100176),x100177),x100173)))) % 14.98/14.67 [10399]~P72(x103992)+~P1(f862(f54(x103993),x103995))+~P1(f862(f54(x103991),x103997))+E(f862(f862(f8(x103991,x103992),f862(f862(f20(x103991,f932(x103993,a921),x103992),f862(f862(f10(f932(x103993,x103992),f932(f932(x103993,a921),x103992),x103991),f8(x103993,x103992)),x103994)),f862(f862(f10(f932(x103993,a921),f932(x103993,a921),x103991),f254(x103993)),f862(f862(f10(f932(x103993,a921),f932(x103993,a921),x103991),f862(f20(x103993,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103993),a318),f862(f862(f9(x103993,f932(x103993,a921),a921),f321(x103993)),x103995)))),x103996)))),x103997),f862(f862(f8(x103993,x103992),f862(f862(f20(x103993,f932(x103991,a921),x103992),f862(f862(f10(f932(x103991,x103992),f932(f932(x103991,a921),x103992),x103993),f8(x103991,x103992)),f862(f9(x103991,x103993,x103992),x103994))),f862(f862(f10(f932(x103991,a921),f932(x103991,a921),x103993),f254(x103991)),f862(f862(f10(f932(x103991,a921),f932(x103991,a921),x103993),f862(f20(x103991,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103991),a318),f862(f862(f9(x103991,f932(x103991,a921),a921),f321(x103991)),x103997)))),f862(f9(x103991,x103993,a921),x103996))))),x103995)) % 14.98/14.67 [10350]~P19(x103508,x103507,x103506,x103505,x103501)+~E(f862(x103502,f859(x103504,x103502,x103503,x103501,x103505,x103506,x103507)),f862(x103504,f859(x103504,x103502,x103503,x103501,x103505,x103506,x103507)))+E(f862(f862(x103501,x103502),x103503),f862(f862(x103501,x103504),x103503))+~P1(f862(f54(x103507),x103503)) % 14.98/14.67 [9889]~P20(x98897,x98896,x98891,x98898,x98892,x98894)+E(f862(f862(x98891,f862(x98892,x98893)),f862(x98894,x98895)),f862(x98894,x98895))+~P1(f862(f54(x98896),x98895))+~P1(f862(f862(f321(x98896),x98893),x98895)) % 14.98/14.67 [9893]~P10(x98936,x98931,x98932,x98938,x98933,x98934)+~P6(x98936,x98937,x98938)+P9(x98931,x98932,x98933,f862(x98934,x98935))+~P1(f862(f862(f321(x98936),x98935),x98937)) % 14.98/14.67 [10372]~P19(x103728,x103725,x103727,x103726,x103721)+E(f862(f862(x103721,x103722),x103723),f862(f862(x103721,x103724),x103723))+~P1(f862(f54(x103725),x103723))+P1(f862(f862(f321(x103725),f859(x103722,x103724,x103723,x103721,x103726,x103727,x103725)),x103723)) % 14.98/14.67 [10449]~P1(f862(f862(x104491,x104496),x104495))+P1(f862(f862(x104491,f846(x104491,x104494,x104495,x104496,x104493,x104492,x104497,x104498)),f852(x104491,x104494,x104495,x104496,x104493,x104492,x104497,x104498)))+P1(f862(f862(x104491,x104492),x104493))+~P1(f862(f862(f321(f931(f931(x104498,x104497),f931(x104498,x104497))),f862(f862(f244(f931(x104498,x104497),f931(x104498,x104497)),f862(f862(f244(x104498,x104497),x104492),x104493)),f862(f862(f244(x104498,x104497),x104496),x104495))),f299(f931(x104498,x104497),x104494))) % 14.98/14.67 [10450]~P1(f862(f862(x104501,x104506),x104505))+P1(f862(f862(x104501,f843(x104501,x104504,x104503,x104502,x104505,x104506,x104507,x104508)),f844(x104501,x104504,x104503,x104502,x104505,x104506,x104507,x104508)))+P1(f862(f862(x104501,x104502),x104503))+~P1(f862(f862(f321(f931(f931(x104508,x104507),f931(x104508,x104507))),f862(f862(f244(f931(x104508,x104507),f931(x104508,x104507)),f862(f862(f244(x104508,x104507),x104506),x104505)),f862(f862(f244(x104508,x104507),x104502),x104503))),f299(f931(x104508,x104507),x104504))) % 14.98/14.67 [10460]~P1(f862(f862(x104601,f847(x104601,x104606,x104605,x104604,x104603,x104602,x104607,x104608)),f851(x104601,x104606,x104605,x104604,x104603,x104602,x104607,x104608)))+P1(f862(f862(x104601,x104602),x104603))+~P1(f862(f862(x104601,x104604),x104605))+~P1(f862(f862(f321(f931(f931(x104608,x104607),f931(x104608,x104607))),f862(f862(f244(f931(x104608,x104607),f931(x104608,x104607)),f862(f862(f244(x104608,x104607),x104602),x104603)),f862(f862(f244(x104608,x104607),x104604),x104605))),f299(f931(x104608,x104607),x104606))) % 14.98/14.67 [10461]~P1(f862(f862(x104611,f845(x104611,x104616,x104613,x104612,x104615,x104614,x104617,x104618)),f848(x104611,x104616,x104613,x104612,x104615,x104614,x104617,x104618)))+P1(f862(f862(x104611,x104612),x104613))+~P1(f862(f862(x104611,x104614),x104615))+~P1(f862(f862(f321(f931(f931(x104618,x104617),f931(x104618,x104617))),f862(f862(f244(f931(x104618,x104617),f931(x104618,x104617)),f862(f862(f244(x104618,x104617),x104614),x104615)),f862(f862(f244(x104618,x104617),x104612),x104613))),f299(f931(x104618,x104617),x104616))) % 14.98/14.67 [10474]~P1(f862(f862(x104741,x104746),x104747))+P1(f862(f862(x104741,x104742),x104743))+P1(f862(f862(f321(f931(f931(x104744,x104745),f931(x104744,x104745))),f862(f862(f244(f931(x104744,x104745),f931(x104744,x104745)),f862(f862(f244(x104744,x104745),x104746),x104747)),f862(f862(f244(x104744,x104745),f843(x104741,x104748,x104743,x104742,x104747,x104746,x104745,x104744)),f844(x104741,x104748,x104743,x104742,x104747,x104746,x104745,x104744)))),f299(f931(x104744,x104745),x104748)))+~P1(f862(f862(f321(f931(f931(x104744,x104745),f931(x104744,x104745))),f862(f862(f244(f931(x104744,x104745),f931(x104744,x104745)),f862(f862(f244(x104744,x104745),x104746),x104747)),f862(f862(f244(x104744,x104745),x104742),x104743))),f299(f931(x104744,x104745),x104748))) % 14.98/14.67 [10476]~P1(f862(f862(x104761,x104768),x104767))+P1(f862(f862(x104761,x104762),x104763))+P1(f862(f862(f321(f931(f931(x104764,x104765),f931(x104764,x104765))),f862(f862(f244(f931(x104764,x104765),f931(x104764,x104765)),f862(f862(f244(x104764,x104765),f846(x104761,x104766,x104767,x104768,x104763,x104762,x104765,x104764)),f852(x104761,x104766,x104767,x104768,x104763,x104762,x104765,x104764))),f862(f862(f244(x104764,x104765),x104768),x104767))),f299(f931(x104764,x104765),x104766)))+~P1(f862(f862(f321(f931(f931(x104764,x104765),f931(x104764,x104765))),f862(f862(f244(f931(x104764,x104765),f931(x104764,x104765)),f862(f862(f244(x104764,x104765),x104762),x104763)),f862(f862(f244(x104764,x104765),x104768),x104767))),f299(f931(x104764,x104765),x104766))) % 14.98/14.67 [9503]~P17(x95037,x95031,x95038,x95033)+~P1(f862(f54(x95037),x95035))+~P1(f862(f54(x95037),x95034))+E(f862(f66(x95031,x95031,x95032,f862(x95033,x95034)),f862(f66(x95031,x95031,x95032,f862(x95033,x95035)),x95036)),f862(f66(x95031,x95031,x95032,f862(x95033,x95035)),f862(f66(x95031,x95031,x95032,f862(x95033,x95034)),x95036))) % 14.98/14.67 [9512]~P32(x95121,x95122,x95123,x95124,x95127)+P32(x95121,x95122,x95123,f862(f862(f152(x95121,x95124),x95125),x95126),f862(f862(f152(x95122,x95127),x95125),x95128))+~P1(f862(f862(x95123,x95126),x95128))+~P1(f862(f862(f228(a924),x95125),f862(f182(f925(x95121)),x95124))) % 14.98/14.67 [9513]~P32(x95131,x95132,x95133,x95134,x95137)+P32(x95131,x95132,x95133,f862(f862(f152(x95131,x95134),x95135),x95136),f862(f862(f152(x95132,x95137),x95135),x95138))+~P1(f862(f862(x95133,x95136),x95138))+~P1(f862(f862(f228(a924),x95135),f862(f182(f925(x95132)),x95137))) % 14.98/14.67 [9595]~P22(x95952,x95952,x95955,x95956)+~P19(x95953,x95952,x95957,x95958,x95951)+~P1(f862(f54(x95952),x95956))+E(f862(f862(x95951,f862(f66(x95952,x95953,x95952,x95954),x95955)),x95956),f862(f862(x95951,x95954),f862(f302(x95952,x95952,x95955),x95956))) % 14.98/14.67 [9854]P23(x98541,x98542,x98543,x98544,x98545)+~P23(x98542,x98546,x98547,x98545,x98548)+~P23(x98541,x98546,f862(f66(x98542,x98546,x98541,x98547),x98543),x98544,x98548)+~P1(f862(f862(f227(f932(x98542,a921)),f862(f302(x98541,x98542,x98543),x98544)),x98545)) % 14.98/14.67 [9891]~P21(x98917,x98912,x98915,x98918,x98916,x98911)+~P1(f862(f54(x98912),x98914))+E(f862(x98911,f862(f862(f301(x98912),x98913),x98914)),f862(f862(x98915,f862(x98916,x98913)),f862(x98911,x98914)))+P1(f862(f862(f321(x98912),x98913),x98914)) % 14.98/14.67 [9903]~P20(x99036,x99035,x99031,x99037,x99038,x99032)+E(f862(f862(x99031,f862(x99032,x99033)),f862(x99032,x99034)),f862(x99032,x99034))+~P1(f862(f54(x99035),x99034))+~P1(f862(f862(f227(f932(x99035,a921)),x99033),x99034)) % 14.98/14.67 [9490]P1(f862(f862(f321(f931(f925(x94901),f925(x94901))),f862(f862(f244(f925(x94901),f925(x94901)),x94902),x94903)),f150(x94901,x94904)))+~E(x94903,f862(f862(f127(x94901),x94905),f862(f862(f144(x94901),x94906),x94907)))+~E(x94902,f862(f862(f127(x94901),x94905),f862(f862(f144(x94901),x94908),x94907)))+~P1(f862(f862(f321(f931(x94901,x94901)),f862(f862(f244(x94901,x94901),x94908),x94906)),x94904)) % 14.98/14.67 [9896]~P20(x98966,x98962,x98965,x98967,x98968,x98961)+~P1(f862(f54(x98962),x98964))+~P1(f862(f54(x98962),x98963))+E(f862(x98961,f862(f862(f103(f932(x98962,a921)),x98963),x98964)),f862(f862(x98965,f862(x98961,x98963)),f862(x98961,x98964))) % 14.98/14.67 [10439]~P22(x104394,x104392,x104395,x104398)+E(f862(f862(f32(x104391,f932(x104392,a921)),x104393),f862(f862(f10(f932(x104394,a921),f932(x104392,a921),x104391),f302(x104394,x104392,x104395)),x104396)),f862(f302(x104394,x104392,x104395),f862(f862(f32(x104391,f932(x104394,a921)),x104393),x104396)))+~P1(f862(f862(f321(x104391),x104397),x104393))+P1(f862(f862(f321(x104391),f544(x104397,x104396,x104393,x104391,x104398,x104395,x104392,x104394)),x104393)) % 14.98/14.67 [10465]~P22(x104654,x104652,x104655,x104657)+E(f862(f862(f32(x104651,f932(x104652,a921)),x104653),f862(f862(f10(f932(x104654,a921),f932(x104652,a921),x104651),f302(x104654,x104652,x104655)),x104656)),f862(f302(x104654,x104652,x104655),f862(f862(f32(x104651,f932(x104654,a921)),x104653),x104656)))+~P1(f862(f862(f321(x104651),x104658),x104653))+~P1(f862(f862(f227(f932(x104654,a921)),f862(x104656,f544(x104658,x104656,x104653,x104651,x104657,x104655,x104652,x104654))),x104657)) % 14.98/14.67 [10477]~P1(f862(f862(x104771,x104778),x104777))+P1(f862(f862(x104771,x104772),x104773))+~P1(f862(f862(f321(f931(f931(x104774,x104775),f931(x104774,x104775))),f862(f862(f244(f931(x104774,x104775),f931(x104774,x104775)),f862(f862(f244(x104774,x104775),x104772),x104773)),f862(f862(f244(x104774,x104775),x104778),x104777))),f299(f931(x104774,x104775),x104776)))+P1(f862(f862(f321(f931(f931(x104774,x104775),f931(x104774,x104775))),f862(f862(f244(f931(x104774,x104775),f931(x104774,x104775)),f862(f862(f244(x104774,x104775),f847(x104771,x104776,x104777,x104778,x104773,x104772,x104775,x104774)),f851(x104771,x104776,x104777,x104778,x104773,x104772,x104775,x104774))),f862(f862(f244(x104774,x104775),f846(x104771,x104776,x104777,x104778,x104773,x104772,x104775,x104774)),f852(x104771,x104776,x104777,x104778,x104773,x104772,x104775,x104774)))),x104776)) % 14.98/14.67 [10478]~P1(f862(f862(x104781,x104788),x104787))+P1(f862(f862(x104781,x104782),x104783))+~P1(f862(f862(f321(f931(f931(x104784,x104785),f931(x104784,x104785))),f862(f862(f244(f931(x104784,x104785),f931(x104784,x104785)),f862(f862(f244(x104784,x104785),x104788),x104787)),f862(f862(f244(x104784,x104785),x104782),x104783))),f299(f931(x104784,x104785),x104786)))+P1(f862(f862(f321(f931(f931(x104784,x104785),f931(x104784,x104785))),f862(f862(f244(f931(x104784,x104785),f931(x104784,x104785)),f862(f862(f244(x104784,x104785),f843(x104781,x104786,x104783,x104782,x104787,x104788,x104785,x104784)),f844(x104781,x104786,x104783,x104782,x104787,x104788,x104785,x104784))),f862(f862(f244(x104784,x104785),f845(x104781,x104786,x104783,x104782,x104787,x104788,x104785,x104784)),f848(x104781,x104786,x104783,x104782,x104787,x104788,x104785,x104784)))),x104786)) % 14.98/14.67 [9965]~P21(x99657,x99655,x99651,x99658,x99652,x99654)+~P1(f862(f54(x99655),x99656))+~P1(f862(f862(f321(x99655),x99653),x99656))+E(f862(f862(x99651,f862(x99652,x99653)),f862(x99654,f862(f862(f3(f932(x99655,a921)),x99656),f862(f862(f301(x99655),x99653),f181(f932(x99655,a921)))))),f862(x99654,x99656)) % 14.98/14.67 [9973]~P21(x99736,x99733,x99731,x99737,x99738,x99732)+~P1(f862(f54(x99733),x99735))+~P1(f862(f54(x99733),x99734))+E(f862(f862(x99731,f862(x99732,f862(f862(f103(f932(x99733,a921)),x99734),x99735))),f862(x99732,f862(f862(f94(f932(x99733,a921)),x99734),x99735))),f862(f862(x99731,f862(x99732,x99734)),f862(x99732,x99735))) % 14.98/14.67 [10057]P40(x100571,x100572,x100573,x100574,x100575,f862(f862(x100573,x100576),x100577))+~P40(x100571,x100572,x100573,x100574,f862(f862(f3(f932(x100571,a921)),x100575),f862(f862(f301(x100571),x100578),f181(f932(x100571,a921)))),x100579)+~E(f862(f862(x100573,x100576),x100577),f862(f862(x100573,x100578),x100579))+~P1(f862(f862(f321(x100571),x100578),x100575)) % 14.98/14.67 [9998]~P10(x99986,x99987,x99988,x99989,x999810,x99981)+E(f862(f862(x99981,x99982),x99983),f862(f862(x99981,x99984),x99985))+~P1(f862(f862(f321(f931(x99987,x99987)),f862(f862(f244(x99987,x99987),x99983),x99985)),x999810))+~P1(f862(f862(f321(f931(x99986,x99986)),f862(f862(f244(x99986,x99986),x99982),x99984)),x99989)) % 14.98/14.67 [9597]~P93(x95972)+E(x95971,f181(f932(x95972,a921)))+~P1(f862(f54(x95972),x95971))+P1(f862(f862(f321(x95972),f12(x95972,x95971)),x95971))+~P1(f862(f862(f321(x95972),f862(f862(f94(x95972),f885(x95971,x95972)),f889(x95971,x95972))),f862(f862(f301(x95972),f885(x95971,x95972)),f862(f862(f301(x95972),f889(x95971,x95972)),f181(f932(x95972,a921)))))) % 14.98/14.67 [9598]~P93(x95982)+E(x95981,f181(f932(x95982,a921)))+~P1(f862(f54(x95982),x95981))+P1(f862(f862(f321(x95982),f15(x95982,x95981)),x95981))+~P1(f862(f862(f321(x95982),f862(f862(f103(x95982),f890(x95981,x95982)),f891(x95981,x95982))),f862(f862(f301(x95982),f890(x95981,x95982)),f862(f862(f301(x95982),f891(x95981,x95982)),f181(f932(x95982,a921)))))) % 14.98/14.67 [9631]~P69(x96312)+E(x96311,f181(f932(x96312,a921)))+~P1(f862(f54(x96312),x96311))+P1(f862(f862(f321(x96312),f862(f56(x96312,f74(x96312)),x96311)),x96311))+~P1(f862(f862(f321(x96312),f862(f862(f74(x96312),f903(x96311,x96312)),f904(x96311,x96312))),f862(f862(f301(x96312),f903(x96311,x96312)),f862(f862(f301(x96312),f904(x96311,x96312)),f181(f932(x96312,a921)))))) % 14.98/14.67 [9636]~P109(x96362)+E(x96361,f181(f932(x96362,a921)))+~P1(f862(f54(x96362),x96361))+P1(f862(f862(f321(x96362),f13(x96362,f225(x96362),x96361)),x96361))+~P1(f862(f862(f321(x96362),f862(f862(f225(x96362),f456(x96361,x96362)),f457(x96361,x96362))),f862(f862(f301(x96362),f456(x96361,x96362)),f862(f862(f301(x96362),f457(x96361,x96362)),f181(f932(x96362,a921)))))) % 14.98/14.67 [9637]~P109(x96372)+E(x96371,f181(f932(x96372,a921)))+~P1(f862(f54(x96372),x96371))+P1(f862(f862(f321(x96372),f14(x96372,f226(x96372),x96371)),x96371))+~P1(f862(f862(f321(x96372),f862(f862(f226(x96372),f470(x96371,x96372)),f471(x96371,x96372))),f862(f862(f301(x96372),f470(x96371,x96372)),f862(f862(f301(x96372),f471(x96371,x96372)),f181(f932(x96372,a921)))))) % 14.98/14.67 [6732]~P87(x67322)+E(x67321,f2(x67322))+~E(f862(f862(f73(x67322),x67323),x67321),f2(x67322))+~P1(f862(f862(f227(x67322),f2(x67322)),x67323))+~P1(f862(f862(f227(x67322),f2(x67322)),x67321)) % 14.98/14.67 [6733]~P87(x67332)+E(x67331,f2(x67332))+~E(f862(f862(f73(x67332),x67331),x67333),f2(x67332))+~P1(f862(f862(f227(x67332),f2(x67332)),x67333))+~P1(f862(f862(f227(x67332),f2(x67332)),x67331)) % 14.98/14.67 [7262]~P109(x72622)+~P11(x72622,x72621)+E(x72621,f106(x72622))+~P1(f862(f862(f321(x72622),x72623),f862(f165(x72622),f714(x72621,x72622))))+P1(f862(f862(f227(x72622),f733(x72621,x72622)),x72623)) % 14.98/14.67 [7434]~P109(x74341)+E(f16(x74341,x74342),x74343)+~P1(f862(f54(x74341),x74342))+~P1(f862(f862(f227(x74341),x74343),f459(x74343,x74342,x74341)))+~P1(f862(f862(f321(x74341),x74343),x74342)) % 14.98/14.67 [7468]~P109(x74681)+~P11(x74681,x74682)+~P11(x74681,x74683)+P11(x74681,f862(f862(f127(x74681),x74682),x74683))+P1(f862(f862(f321(x74681),f720(x74683,x74682,x74681)),f862(f165(x74681),x74682))) % 14.98/14.67 [7469]~P109(x74691)+~P11(x74691,x74692)+~P11(x74691,x74693)+P11(x74691,f862(f862(f127(x74691),x74692),x74693))+P1(f862(f862(f321(x74691),f721(x74693,x74692,x74691)),f862(f165(x74691),x74693))) % 14.98/14.67 [7533]~P109(x75331)+E(f16(x75331,x75332),x75333)+~P1(f862(f54(x75331),x75332))+P1(f862(f862(f321(x75331),f459(x75333,x75332,x75331)),x75332))+~P1(f862(f862(f321(x75331),x75333),x75332)) % 14.98/14.67 [7534]~P109(x75341)+E(f17(x75341,x75342),x75343)+~P1(f862(f54(x75341),x75342))+P1(f862(f862(f321(x75341),f465(x75343,x75342,x75341)),x75342))+~P1(f862(f862(f321(x75341),x75343),x75342)) % 14.98/14.67 [8108]~P109(x81081)+E(f17(x81081,x81082),x81083)+~P1(f862(f54(x81081),x81082))+~P1(f862(f862(f321(x81081),x81083),x81082))+~P1(f862(f862(f227(x81081),f465(x81083,x81082,x81081)),x81083)) % 14.98/14.67 [8432]~P109(x84321)+~P11(x84321,x84322)+~P11(x84321,x84323)+P11(x84321,f862(f862(f127(x84321),x84322),x84323))+~P1(f862(f862(f227(x84321),f720(x84323,x84322,x84321)),f721(x84323,x84322,x84321))) % 14.98/14.67 [9230]~P93(x92302)+E(x92301,f181(f932(x92302,a921)))+~E(f862(f862(f94(x92302),f862(x92303,f894(x92301,x92303,x92302))),f862(x92303,f895(x92301,x92303,x92302))),f862(x92303,f862(f862(f94(x92302),f894(x92301,x92303,x92302)),f895(x92301,x92303,x92302))))+E(f12(x92302,f862(f302(x92302,x92302,x92303),x92301)),f862(x92303,f12(x92302,x92301)))+~P1(f862(f54(x92302),x92301)) % 14.98/14.67 [9231]~P93(x92312)+E(x92311,f181(f932(x92312,a921)))+~E(f862(f862(f103(x92312),f862(x92313,f896(x92311,x92313,x92312))),f862(x92313,f897(x92311,x92313,x92312))),f862(x92313,f862(f862(f103(x92312),f896(x92311,x92313,x92312)),f897(x92311,x92313,x92312))))+E(f15(x92312,f862(f302(x92312,x92312,x92313),x92311)),f862(x92313,f15(x92312,x92311)))+~P1(f862(f54(x92312),x92311)) % 14.98/14.67 [9232]~P109(x92322)+E(x92321,f181(f932(x92322,a921)))+~E(f862(f862(f225(x92322),f862(x92323,f460(x92321,x92323,x92322))),f862(x92323,f462(x92321,x92323,x92322))),f862(x92323,f862(f862(f225(x92322),f460(x92321,x92323,x92322)),f462(x92321,x92323,x92322))))+E(f16(x92322,f862(f302(x92322,x92322,x92323),x92321)),f862(x92323,f16(x92322,x92321)))+~P1(f862(f54(x92322),x92321)) % 14.98/14.67 [9233]~P109(x92332)+E(x92331,f181(f932(x92332,a921)))+~E(f862(f862(f226(x92332),f862(x92333,f473(x92331,x92333,x92332))),f862(x92333,f476(x92331,x92333,x92332))),f862(x92333,f862(f862(f226(x92332),f473(x92331,x92333,x92332)),f476(x92331,x92333,x92332))))+E(f17(x92332,f862(f302(x92332,x92332,x92333),x92331)),f862(x92333,f17(x92332,x92331)))+~P1(f862(f54(x92332),x92331)) % 14.98/14.67 [9302]~P109(x93022)+E(x93021,f181(f932(x93022,a921)))+~E(f862(f862(f225(x93022),f862(x93023,f454(x93021,x93023,x93022))),f862(x93023,f461(x93021,x93023,x93022))),f862(x93023,f862(f862(f225(x93022),f454(x93021,x93023,x93022)),f461(x93021,x93023,x93022))))+E(f13(x93022,f225(x93022),f862(f302(x93022,x93022,x93023),x93021)),f862(x93023,f13(x93022,f225(x93022),x93021)))+~P1(f862(f54(x93022),x93021)) % 14.98/14.67 [9303]~P109(x93032)+E(x93031,f181(f932(x93032,a921)))+~E(f862(f862(f226(x93032),f862(x93033,f474(x93031,x93033,x93032))),f862(x93033,f475(x93031,x93033,x93032))),f862(x93033,f862(f862(f226(x93032),f474(x93031,x93033,x93032)),f475(x93031,x93033,x93032))))+E(f14(x93032,f226(x93032),f862(f302(x93032,x93032,x93033),x93031)),f862(x93033,f14(x93032,f226(x93032),x93031)))+~P1(f862(f54(x93032),x93031)) % 14.98/14.67 [6748]~P69(x67482)+E(x67481,f181(f932(x67482,a921)))+~P1(f862(f54(x67482),x67481))+E(f862(f56(x67482,f74(x67482)),f862(f862(f301(x67482),x67483),x67481)),f862(f862(f74(x67482),x67483),f862(f56(x67482,f74(x67482)),x67481)))+P1(f862(f862(f321(x67482),x67483),x67481)) % 14.98/14.67 [7269]~P93(x72692)+E(f862(f862(f103(x72692),f15(x72692,x72691)),f15(x72692,x72693)),f15(x72692,x72693))+E(x72691,f181(f932(x72692,a921)))+~P1(f862(f54(x72692),x72693))+~P1(f862(f862(f227(f932(x72692,a921)),x72691),x72693)) % 14.98/14.67 [7270]~P93(x72702)+E(f862(f862(f94(x72702),f12(x72702,x72701)),f12(x72702,x72703)),f12(x72702,x72703))+E(x72701,f181(f932(x72702,a921)))+~P1(f862(f54(x72702),x72703))+~P1(f862(f862(f227(f932(x72702,a921)),x72701),x72703)) % 14.98/14.67 [7271]~P109(x72712)+E(f862(f862(f225(x72712),f16(x72712,x72711)),f16(x72712,x72713)),f16(x72712,x72713))+E(x72711,f181(f932(x72712,a921)))+~P1(f862(f54(x72712),x72713))+~P1(f862(f862(f227(f932(x72712,a921)),x72711),x72713)) % 14.98/14.67 [7272]~P109(x72722)+E(f862(f862(f226(x72722),f17(x72722,x72721)),f17(x72722,x72723)),f17(x72722,x72723))+E(x72721,f181(f932(x72722,a921)))+~P1(f862(f54(x72722),x72723))+~P1(f862(f862(f227(f932(x72722,a921)),x72721),x72723)) % 14.98/14.67 [7581]~P109(x75812)+E(x75811,f181(f932(x75812,a921)))+~P1(f862(f54(x75812),x75813))+P1(f862(f862(f227(x75812),f16(x75812,x75813)),f16(x75812,x75811)))+~P1(f862(f862(f227(f932(x75812,a921)),x75811),x75813)) % 14.98/14.67 [7582]~P109(x75822)+E(x75821,f181(f932(x75822,a921)))+~P1(f862(f54(x75822),x75823))+P1(f862(f862(f227(x75822),f17(x75822,x75821)),f17(x75822,x75823)))+~P1(f862(f862(f227(f932(x75822,a921)),x75821),x75823)) % 14.98/14.67 [7637]~P93(x76371)+E(f12(x76371,x76372),x76373)+~P1(f862(f54(x76371),x76372))+~E(f862(f862(f3(f932(x76371,a921)),x76372),f862(f862(f301(x76371),x76373),f181(f932(x76371,a921)))),f181(f932(x76371,a921)))+~P1(f862(f862(f321(x76371),x76373),x76372)) % 14.98/14.67 [7638]~P93(x76381)+E(f15(x76381,x76382),x76383)+~P1(f862(f54(x76381),x76382))+~E(f862(f862(f3(f932(x76381,a921)),x76382),f862(f862(f301(x76381),x76383),f181(f932(x76381,a921)))),f181(f932(x76381,a921)))+~P1(f862(f862(f321(x76381),x76383),x76382)) % 14.98/14.67 [7639]~P109(x76391)+E(f16(x76391,x76392),x76393)+~P1(f862(f54(x76391),x76392))+~E(f862(f862(f3(f932(x76391,a921)),x76392),f862(f862(f301(x76391),x76393),f181(f932(x76391,a921)))),f181(f932(x76391,a921)))+~P1(f862(f862(f321(x76391),x76393),x76392)) % 14.98/14.67 [7640]~P109(x76401)+E(f17(x76401,x76402),x76403)+~P1(f862(f54(x76401),x76402))+~E(f862(f862(f3(f932(x76401,a921)),x76402),f862(f862(f301(x76401),x76403),f181(f932(x76401,a921)))),f181(f932(x76401,a921)))+~P1(f862(f862(f321(x76401),x76403),x76402)) % 14.98/14.67 [7735]~P109(x77351)+E(f13(x77351,f225(x77351),x77352),x77353)+~P1(f862(f54(x77351),x77352))+~E(f862(f862(f3(f932(x77351,a921)),x77352),f862(f862(f301(x77351),x77353),f181(f932(x77351,a921)))),f181(f932(x77351,a921)))+~P1(f862(f862(f321(x77351),x77353),x77352)) % 14.98/14.67 [7736]~P109(x77361)+E(f14(x77361,f226(x77361),x77362),x77363)+~P1(f862(f54(x77361),x77362))+~E(f862(f862(f3(f932(x77361,a921)),x77362),f862(f862(f301(x77361),x77363),f181(f932(x77361,a921)))),f181(f932(x77361,a921)))+~P1(f862(f862(f321(x77361),x77363),x77362)) % 14.98/14.67 [7772]~P104(x77722)+E(x77721,f181(f932(x77722,a921)))+~P1(f862(f54(x77722),x77721))+~P1(f862(f862(f227(x77722),x77723),f892(x77723,x77721,x77722)))+P1(f862(f862(f227(x77722),x77723),f862(f56(x77722,f94(x77722)),x77721))) % 14.98/14.67 [7773]~P109(x77732)+E(x77731,f181(f932(x77732,a921)))+~P1(f862(f54(x77732),x77731))+~P1(f862(f862(f227(x77732),x77733),f450(x77733,x77731,x77732)))+P1(f862(f862(f227(x77732),x77733),f862(f56(x77732,f225(x77732)),x77731))) % 14.98/14.67 [7774]~P109(x77742)+E(x77741,f181(f932(x77742,a921)))+~P1(f862(f54(x77742),x77741))+~P1(f862(f862(f228(x77742),x77743),f451(x77743,x77741,x77742)))+P1(f862(f862(f228(x77742),x77743),f862(f56(x77742,f225(x77742)),x77741))) % 14.98/14.67 [7861]~P104(x78612)+E(x78611,f181(f932(x78612,a921)))+~P1(f862(f54(x78612),x78611))+P1(f862(f862(f321(x78612),f892(x78613,x78611,x78612)),x78611))+P1(f862(f862(f227(x78612),x78613),f862(f56(x78612,f94(x78612)),x78611))) % 14.98/14.67 [7862]~P109(x78622)+E(x78621,f181(f932(x78622,a921)))+~P1(f862(f54(x78622),x78621))+P1(f862(f862(f321(x78622),f450(x78623,x78621,x78622)),x78621))+P1(f862(f862(f227(x78622),x78623),f862(f56(x78622,f225(x78622)),x78621))) % 14.98/14.67 [7863]~P109(x78632)+E(x78631,f181(f932(x78632,a921)))+~P1(f862(f54(x78632),x78631))+P1(f862(f862(f321(x78632),f451(x78633,x78631,x78632)),x78631))+P1(f862(f862(f228(x78632),x78633),f862(f56(x78632,f225(x78632)),x78631))) % 14.98/14.67 [7983]~P109(x79832)+E(x79831,f181(f932(x79832,a921)))+E(f862(f862(f225(x79832),f13(x79832,f225(x79832),x79831)),f13(x79832,f225(x79832),x79833)),f13(x79832,f225(x79832),x79833))+~P1(f862(f54(x79832),x79833))+~P1(f862(f862(f227(f932(x79832,a921)),x79831),x79833)) % 14.98/14.67 [7984]~P109(x79842)+E(x79841,f181(f932(x79842,a921)))+E(f862(f862(f226(x79842),f14(x79842,f226(x79842),x79841)),f14(x79842,f226(x79842),x79843)),f14(x79842,f226(x79842),x79843))+~P1(f862(f54(x79842),x79843))+~P1(f862(f862(f227(f932(x79842,a921)),x79841),x79843)) % 14.98/14.67 [8187]~E(f370(x81871,x81873,x81872),f371(x81871,x81873,x81872))+~E(f862(f28(x81872),f372(x81871,x81873,x81872)),x81871)+E(f862(f862(f74(a924),x81871),f862(f28(f932(x81872,a921)),x81873)),f862(f28(x81872),f30(f932(x81872,a921),x81873)))+~P1(f862(f54(x81872),f30(f932(x81872,a921),x81873)))+~P1(f862(f54(f932(x81872,a921)),x81873)) % 14.98/14.67 [8371]~P109(x83712)+E(x83711,f181(f932(x83712,a921)))+~P1(f862(f54(x83712),x83713))+P1(f862(f862(f227(x83712),f862(f56(x83712,f225(x83712)),x83713)),f862(f56(x83712,f225(x83712)),x83711)))+~P1(f862(f862(f227(f932(x83712,a921)),x83711),x83713)) % 14.98/14.67 [8673]~E(f370(x86731,x86733,x86732),f371(x86731,x86733,x86732))+E(f862(f862(f74(a924),x86731),f862(f28(f932(x86732,a921)),x86733)),f862(f28(x86732),f30(f932(x86732,a921),x86733)))+P1(f862(f862(f321(f932(x86732,a921)),f372(x86731,x86733,x86732)),x86733))+~P1(f862(f54(x86732),f30(f932(x86732,a921),x86733)))+~P1(f862(f54(f932(x86732,a921)),x86733)) % 14.98/14.67 [8699]~E(f862(f28(x86992),f372(x86991,x86993,x86992)),x86991)+E(f862(f862(f74(a924),x86991),f862(f28(f932(x86992,a921)),x86993)),f862(f28(x86992),f30(f932(x86992,a921),x86993)))+P1(f862(f862(f321(f932(x86992,a921)),f371(x86991,x86993,x86992)),x86993))+~P1(f862(f54(x86992),f30(f932(x86992,a921),x86993)))+~P1(f862(f54(f932(x86992,a921)),x86993)) % 14.98/14.67 [8700]~E(f862(f28(x87002),f372(x87001,x87003,x87002)),x87001)+E(f862(f862(f74(a924),x87001),f862(f28(f932(x87002,a921)),x87003)),f862(f28(x87002),f30(f932(x87002,a921),x87003)))+P1(f862(f862(f321(f932(x87002,a921)),f370(x87001,x87003,x87002)),x87003))+~P1(f862(f54(x87002),f30(f932(x87002,a921),x87003)))+~P1(f862(f54(f932(x87002,a921)),x87003)) % 14.98/14.67 [8726]~E(f862(f28(x87262),f372(x87261,x87263,x87262)),x87261)+~E(f862(f862(f94(f932(x87262,a921)),f371(x87261,x87263,x87262)),f370(x87261,x87263,x87262)),f181(f932(x87262,a921)))+E(f862(f862(f74(a924),x87261),f862(f28(f932(x87262,a921)),x87263)),f862(f28(x87262),f30(f932(x87262,a921),x87263)))+~P1(f862(f54(f932(x87262,a921)),x87263))+~P1(f862(f54(x87262),f30(f932(x87262,a921),x87263))) % 14.98/14.67 [8992]E(f862(f862(f74(a924),x89921),f862(f28(f932(x89922,a921)),x89923)),f862(f28(x89922),f30(f932(x89922,a921),x89923)))+P1(f862(f862(f321(f932(x89922,a921)),f372(x89921,x89923,x89922)),x89923))+P1(f862(f862(f321(f932(x89922,a921)),f371(x89921,x89923,x89922)),x89923))+~P1(f862(f54(f932(x89922,a921)),x89923))+~P1(f862(f54(x89922),f30(f932(x89922,a921),x89923))) % 14.98/14.67 [8993]E(f862(f862(f74(a924),x89931),f862(f28(f932(x89932,a921)),x89933)),f862(f28(x89932),f30(f932(x89932,a921),x89933)))+P1(f862(f862(f321(f932(x89932,a921)),f372(x89931,x89933,x89932)),x89933))+P1(f862(f862(f321(f932(x89932,a921)),f370(x89931,x89933,x89932)),x89933))+~P1(f862(f54(f932(x89932,a921)),x89933))+~P1(f862(f54(x89932),f30(f932(x89932,a921),x89933))) % 14.98/14.67 [9019]~E(f862(f862(f94(f932(x90192,a921)),f371(x90191,x90193,x90192)),f370(x90191,x90193,x90192)),f181(f932(x90192,a921)))+E(f862(f862(f74(a924),x90191),f862(f28(f932(x90192,a921)),x90193)),f862(f28(x90192),f30(f932(x90192,a921),x90193)))+~P1(f862(f54(f932(x90192,a921)),x90193))+P1(f862(f862(f321(f932(x90192,a921)),f372(x90191,x90193,x90192)),x90193))+~P1(f862(f54(x90192),f30(f932(x90192,a921),x90193))) % 14.98/14.67 [9276]~P100(x92762)+E(x92761,f181(f932(x92762,a921)))+~E(f862(f862(f74(x92762),f862(x92763,f902(x92761,x92763,x92762))),f862(x92763,f905(x92761,x92763,x92762))),f862(x92763,f862(f862(f74(x92762),f902(x92761,x92763,x92762)),f905(x92761,x92763,x92762))))+~P1(f862(f54(x92762),x92761))+E(f862(f56(x92762,f74(x92762)),f862(f302(x92762,x92762,x92763),x92761)),f862(x92763,f862(f56(x92762,f74(x92762)),x92761))) % 14.98/14.67 [10208]P1(f862(f862(x102081,x102082),x102083))+P1(f862(f862(f228(a1),f501(x102081,x102083,x102082)),f503(x102081,x102083,x102082)))+P1(f862(f862(f227(a1),f503(x102081,x102083,x102082)),f2(a1)))+P1(f862(f862(x102081,f501(x102081,x102083,x102082)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f503(x102081,x102083,x102082))))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x102082),x102083))) % 14.98/14.67 [10214]P1(f862(f862(x102141,x102142),x102143))+P1(f862(f862(f227(a1),f500(x102141,x102143,x102142)),f2(a1)))+P1(f862(f862(x102141,f499(x102141,x102143,x102142)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f500(x102141,x102143,x102142))))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f499(x102141,x102143,x102142)),f500(x102141,x102143,x102142))))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x102142),x102143))) % 14.98/14.67 [8158]~P112(x81581)+~P1(f862(f862(f227(x81581),x81582),f71(x81581)))+~P1(f862(f862(f227(x81581),f2(x81581)),x81582))+~P1(f862(f862(f227(x81581),f2(x81581)),x81583))+P1(f862(f862(f227(x81581),f862(f862(f74(x81581),x81582),x81583)),x81583)) % 14.98/14.67 [8159]~P112(x81591)+~P1(f862(f862(f227(x81591),x81593),f71(x81591)))+~P1(f862(f862(f227(x81591),f2(x81591)),x81593))+~P1(f862(f862(f227(x81591),f2(x81591)),x81592))+P1(f862(f862(f227(x81591),f862(f862(f74(x81591),x81592),x81593)),x81592)) % 14.98/14.67 [8517]~P109(x85172)+E(x85171,f181(f932(x85172,a921)))+~P1(f862(f54(x85172),x85171))+P1(f862(f862(f321(x85172),f452(x85173,x85171,x85172)),x85171))+~P1(f862(f862(f227(x85172),f862(f56(x85172,f225(x85172)),x85171)),x85173)) % 14.98/14.67 [8518]~P109(x85182)+E(x85181,f181(f932(x85182,a921)))+~P1(f862(f54(x85182),x85181))+P1(f862(f862(f321(x85182),f453(x85183,x85181,x85182)),x85181))+~P1(f862(f862(f228(x85182),f862(f56(x85182,f225(x85182)),x85181)),x85183)) % 14.98/14.67 [8519]~P109(x85192)+E(x85191,f181(f932(x85192,a921)))+~P1(f862(f54(x85192),x85191))+P1(f862(f862(f227(x85192),f452(x85193,x85191,x85192)),x85193))+~P1(f862(f862(f227(x85192),f862(f56(x85192,f225(x85192)),x85191)),x85193)) % 14.98/14.67 [8520]~P109(x85202)+E(x85201,f181(f932(x85202,a921)))+~P1(f862(f54(x85202),x85201))+P1(f862(f862(f228(x85202),f453(x85203,x85201,x85202)),x85203))+~P1(f862(f862(f228(x85202),f862(f56(x85202,f225(x85202)),x85201)),x85203)) % 14.98/14.67 [8607]~P1(f862(x86071,x86073))+P1(f862(x86071,f388(x86071,x86072)))+P1(f862(x86071,f387(x86071,x86072)))+~P1(f862(f862(f228(a1),f2(a1)),x86072))+P1(f862(x86071,f862(f862(f3(a1),f387(x86071,x86072)),f862(f862(f74(a1),f389(x86071,x86072)),x86072)))) % 14.98/14.67 [8828]~P1(f862(x88281,x88283))+P1(f862(x88281,f387(x88281,x88282)))+~P1(f862(f862(f228(a1),f2(a1)),x88282))+P1(f862(f862(f321(a1),f388(x88281,x88282)),f296(a1,f71(a1),x88282)))+P1(f862(x88281,f862(f862(f3(a1),f387(x88281,x88282)),f862(f862(f74(a1),f389(x88281,x88282)),x88282)))) % 14.98/14.67 [9043]~P1(f862(x90431,x90433))+~P1(f862(x90431,f387(x90431,x90432)))+P1(f862(x90431,f388(x90431,x90432)))+~P1(f862(f862(f228(a1),f2(a1)),x90432))+~P1(f862(x90431,f862(f862(f3(a1),f387(x90431,x90432)),f862(f862(f74(a1),f389(x90431,x90432)),x90432)))) % 14.98/14.67 [9167]~P1(f862(x91671,x91673))+~P1(f862(x91671,f387(x91671,x91672)))+~P1(f862(f862(f228(a1),f2(a1)),x91672))+P1(f862(f862(f321(a1),f388(x91671,x91672)),f296(a1,f71(a1),x91672)))+~P1(f862(x91671,f862(f862(f3(a1),f387(x91671,x91672)),f862(f862(f74(a1),f389(x91671,x91672)),x91672)))) % 14.98/14.67 [8947]~P93(x89471)+~P1(f862(f54(x89471),x89472))+E(f862(f862(f3(f932(x89471,a921)),x89472),f862(f862(f301(x89471),x89473),f181(f932(x89471,a921)))),f181(f932(x89471,a921)))+~P1(f862(f862(f321(x89471),x89473),x89472))+E(f862(f862(f94(x89471),x89473),f12(x89471,f862(f862(f3(f932(x89471,a921)),x89472),f862(f862(f301(x89471),x89473),f181(f932(x89471,a921)))))),f12(x89471,x89472)) % 14.98/14.67 [8948]~P93(x89481)+~P1(f862(f54(x89481),x89482))+E(f862(f862(f3(f932(x89481,a921)),x89482),f862(f862(f301(x89481),x89483),f181(f932(x89481,a921)))),f181(f932(x89481,a921)))+~P1(f862(f862(f321(x89481),x89483),x89482))+E(f862(f862(f103(x89481),x89483),f15(x89481,f862(f862(f3(f932(x89481,a921)),x89482),f862(f862(f301(x89481),x89483),f181(f932(x89481,a921)))))),f15(x89481,x89482)) % 14.98/14.67 [8949]~P109(x89491)+~P1(f862(f54(x89491),x89492))+E(f862(f862(f3(f932(x89491,a921)),x89492),f862(f862(f301(x89491),x89493),f181(f932(x89491,a921)))),f181(f932(x89491,a921)))+~P1(f862(f862(f321(x89491),x89493),x89492))+E(f862(f862(f225(x89491),x89493),f16(x89491,f862(f862(f3(f932(x89491,a921)),x89492),f862(f862(f301(x89491),x89493),f181(f932(x89491,a921)))))),f16(x89491,x89492)) % 14.98/14.67 [8950]~P109(x89501)+~P1(f862(f54(x89501),x89502))+E(f862(f862(f3(f932(x89501,a921)),x89502),f862(f862(f301(x89501),x89503),f181(f932(x89501,a921)))),f181(f932(x89501,a921)))+~P1(f862(f862(f321(x89501),x89503),x89502))+E(f862(f862(f226(x89501),x89503),f17(x89501,f862(f862(f3(f932(x89501,a921)),x89502),f862(f862(f301(x89501),x89503),f181(f932(x89501,a921)))))),f17(x89501,x89502)) % 14.98/14.67 [9012]~P109(x90121)+~P1(f862(f54(x90121),x90122))+E(f862(f862(f3(f932(x90121,a921)),x90122),f862(f862(f301(x90121),x90123),f181(f932(x90121,a921)))),f181(f932(x90121,a921)))+~P1(f862(f862(f321(x90121),x90123),x90122))+E(f862(f862(f225(x90121),x90123),f13(x90121,f225(x90121),f862(f862(f3(f932(x90121,a921)),x90122),f862(f862(f301(x90121),x90123),f181(f932(x90121,a921)))))),f13(x90121,f225(x90121),x90122)) % 14.98/14.67 [9013]~P109(x90131)+~P1(f862(f54(x90131),x90132))+E(f862(f862(f3(f932(x90131,a921)),x90132),f862(f862(f301(x90131),x90133),f181(f932(x90131,a921)))),f181(f932(x90131,a921)))+~P1(f862(f862(f321(x90131),x90133),x90132))+E(f862(f862(f226(x90131),x90133),f14(x90131,f226(x90131),f862(f862(f3(f932(x90131,a921)),x90132),f862(f862(f301(x90131),x90133),f181(f932(x90131,a921)))))),f14(x90131,f226(x90131),x90132)) % 14.98/14.67 [9029]~P93(x90291)+~P1(f862(f54(x90291),x90293))+~P1(f862(f54(x90291),x90292))+E(f862(f862(f94(f932(x90291,a921)),x90292),x90293),f181(f932(x90291,a921)))+E(f862(f862(f103(x90291),f15(x90291,f862(f862(f103(f932(x90291,a921)),x90292),x90293))),f15(x90291,f862(f862(f94(f932(x90291,a921)),x90292),x90293))),f862(f862(f103(x90291),f15(x90291,x90292)),f15(x90291,x90293))) % 14.98/14.67 [9030]~P93(x90301)+~P1(f862(f54(x90301),x90303))+~P1(f862(f54(x90301),x90302))+E(f862(f862(f94(f932(x90301,a921)),x90302),x90303),f181(f932(x90301,a921)))+E(f862(f862(f94(x90301),f12(x90301,f862(f862(f103(f932(x90301,a921)),x90302),x90303))),f12(x90301,f862(f862(f94(f932(x90301,a921)),x90302),x90303))),f862(f862(f94(x90301),f12(x90301,x90302)),f12(x90301,x90303))) % 14.98/14.67 [9031]~P109(x90311)+~P1(f862(f54(x90311),x90313))+~P1(f862(f54(x90311),x90312))+E(f862(f862(f94(f932(x90311,a921)),x90312),x90313),f181(f932(x90311,a921)))+E(f862(f862(f225(x90311),f16(x90311,f862(f862(f103(f932(x90311,a921)),x90312),x90313))),f16(x90311,f862(f862(f94(f932(x90311,a921)),x90312),x90313))),f862(f862(f225(x90311),f16(x90311,x90312)),f16(x90311,x90313))) % 14.98/14.67 [9032]~P109(x90321)+~P1(f862(f54(x90321),x90323))+~P1(f862(f54(x90321),x90322))+E(f862(f862(f94(f932(x90321,a921)),x90322),x90323),f181(f932(x90321,a921)))+E(f862(f862(f226(x90321),f17(x90321,f862(f862(f103(f932(x90321,a921)),x90322),x90323))),f17(x90321,f862(f862(f94(f932(x90321,a921)),x90322),x90323))),f862(f862(f226(x90321),f17(x90321,x90322)),f17(x90321,x90323))) % 14.98/14.67 [9248]~P109(x92481)+~P1(f862(f54(x92481),x92483))+~P1(f862(f54(x92481),x92482))+E(f862(f862(f94(f932(x92481,a921)),x92482),x92483),f181(f932(x92481,a921)))+E(f862(f862(f225(x92481),f13(x92481,f225(x92481),f862(f862(f103(f932(x92481,a921)),x92482),x92483))),f13(x92481,f225(x92481),f862(f862(f94(f932(x92481,a921)),x92482),x92483))),f862(f862(f225(x92481),f13(x92481,f225(x92481),x92482)),f13(x92481,f225(x92481),x92483))) % 14.98/14.67 [9249]~P109(x92491)+~P1(f862(f54(x92491),x92493))+~P1(f862(f54(x92491),x92492))+E(f862(f862(f94(f932(x92491,a921)),x92492),x92493),f181(f932(x92491,a921)))+E(f862(f862(f226(x92491),f14(x92491,f226(x92491),f862(f862(f103(f932(x92491,a921)),x92492),x92493))),f14(x92491,f226(x92491),f862(f862(f94(f932(x92491,a921)),x92492),x92493))),f862(f862(f226(x92491),f14(x92491,f226(x92491),x92492)),f14(x92491,f226(x92491),x92493))) % 14.98/14.67 [10054]~P127(x100543)+E(x100541,x100542)+~P1(f862(f862(f227(x100543),f2(x100543)),x100542))+~P1(f862(f862(f227(x100543),f2(x100543)),x100541))+~E(f862(f862(f236(x100543),x100541),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f236(x100543),x100542),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))) % 14.98/14.67 [6078]~P61(x60782)+E(x60781,f2(x60782))+~E(f862(f862(f29(x60782),x60783),x60781),x60784)+E(x60783,f862(f862(f74(x60782),x60784),x60781))+~P1(f862(f862(f278(x60782),x60781),x60783)) % 14.98/14.67 [6079]~P61(x60792)+E(x60791,f2(x60792))+~E(x60793,f862(f862(f74(x60792),x60794),x60791))+E(f862(f862(f29(x60792),x60793),x60791),x60794)+~P1(f862(f862(f278(x60792),x60791),x60793)) % 14.98/14.67 [6542]E(f335(x65421,x65422,x65423),x65424)+E(f862(x65421,x65424),f2(a924))+~E(f862(f862(f8(x65423,a924),x65421),x65422),f71(a924))+~P1(f862(f54(x65423),x65422))+~P1(f862(f862(f321(x65423),x65424),x65422)) % 14.98/14.67 [6608]E(f333(x66081,x66082,x66083),x66084)+E(f862(x66081,x66084),f2(a924))+~E(f862(f862(f8(x66083,a924),x66081),x66082),f862(a105,f2(a924)))+~P1(f862(f54(x66083),x66082))+~P1(f862(f862(f321(x66083),x66084),x66082)) % 14.98/14.67 [6717]~P3(x67171)+~P109(x67171)+P1(f862(f862(f228(x67171),x67172),f30(x67171,x67173)))+~P1(f862(f862(f228(x67171),x67172),x67174))+~P1(f862(f862(f321(x67171),x67174),x67173)) % 14.98/14.67 [6888]~P3(x68881)+~P109(x68881)+~P1(f862(f862(f228(x68881),x68884),x68883))+P1(f862(f862(f228(x68881),f31(x68881,x68882)),x68883))+~P1(f862(f862(f321(x68881),x68884),x68882)) % 14.98/14.67 [7147]~P127(x71473)+E(x71471,x71472)+~E(f862(f862(f236(x71473),x71471),f862(a105,x71474)),f862(f862(f236(x71473),x71472),f862(a105,x71474)))+~P1(f862(f862(f227(x71473),f2(x71473)),x71472))+~P1(f862(f862(f227(x71473),f2(x71473)),x71471)) % 14.98/14.67 [7360]~E(f342(x73602,x73603,x73601,x73604),x73604)+~E(f862(x73602,x73604),f71(a924))+E(f862(f862(f8(x73601,a924),x73602),x73603),f71(a924))+~P1(f862(f54(x73601),x73603))+~P1(f862(f862(f321(x73601),x73604),x73603)) % 14.98/14.67 [7367]~P119(x73674)+~P133(x73674)+E(f862(x73671,f337(x73671,x73672,x73673,x73674)),f2(x73674))+~E(f862(f862(f11(x73673,x73674),x73671),x73672),f2(x73674))+~P1(f862(f54(x73673),x73672)) % 14.98/14.67 [7458]~E(f334(x74582,x74583,x74581,x74584),x74584)+~E(f862(x74582,x74584),f862(a105,f2(a924)))+E(f862(f862(f8(x74581,a924),x74582),x74583),f862(a105,f2(a924)))+~P1(f862(f54(x74581),x74583))+~P1(f862(f862(f321(x74581),x74584),x74583)) % 14.98/14.67 [8200]~E(f862(x82002,x82004),f71(a924))+~E(f862(x82002,f342(x82002,x82003,x82001,x82004)),f2(a924))+E(f862(f862(f8(x82001,a924),x82002),x82003),f71(a924))+~P1(f862(f54(x82001),x82003))+~P1(f862(f862(f321(x82001),x82004),x82003)) % 14.98/14.67 [8238]~E(f862(x82382,x82384),f862(a105,f2(a924)))+~E(f862(x82382,f334(x82382,x82383,x82381,x82384)),f2(a924))+E(f862(f862(f8(x82381,a924),x82382),x82383),f862(a105,f2(a924)))+~P1(f862(f54(x82381),x82383))+~P1(f862(f862(f321(x82381),x82384),x82383)) % 14.98/14.67 [8326]~P146(x83262)+~P120(x83262)+~P1(f862(x83261,x83264))+~P1(f862(f862(f278(x83262),x83263),f862(f862(f73(x83262),x83264),f2(x83262))))+P1(f862(x83261,f862(f862(f74(x83262),x83263),f860(x83263,x83261,x83262)))) % 14.98/14.67 [8795]~P109(x87951)+~P11(x87951,x87954)+P11(x87951,x87952)+~E(x87952,f862(f862(f144(x87951),x87953),x87954))+~P1(f862(f862(f227(x87951),x87953),f735(x87952,x87951,x87954,x87953))) % 14.98/14.67 [8832]E(x88321,x88322)+E(f862(f862(f3(a1),f390(x88323,x88322,x88324,x88321)),f391(x88323,x88322,x88324,x88321)),x88321)+~E(f862(f862(f73(a1),x88321),x88324),x88322)+~P1(f862(f862(f228(a1),f2(a1)),x88324))+~P1(f862(f862(f321(a1),x88322),x88323)) % 14.98/14.67 [8833]E(x88331,x88332)+E(f862(f862(f73(a1),f396(x88333,x88332,x88334,x88331)),f397(x88333,x88332,x88334,x88331)),x88331)+~E(f862(f862(f3(a1),x88331),x88334),x88332)+~P1(f862(f862(f228(a1),f2(a1)),x88334))+~P1(f862(f862(f321(a1),x88332),x88333)) % 14.98/14.67 [9027]E(f862(x90271,f443(x90272,x90271,x90273,x90274)),x90272)+P1(f862(f862(f227(a924),x90274),f444(x90272,x90271,x90273,x90274)))+~P1(f862(f862(f227(a1),x90272),f862(x90271,x90273)))+~P1(f862(f862(f228(a924),x90274),x90273))+~P1(f862(f862(f227(a1),f862(x90271,x90274)),x90272)) % 14.98/14.67 [9028]~P109(x90281)+~P11(x90281,x90283)+P11(x90281,x90282)+~E(x90282,f862(f862(f144(x90281),x90284),x90283))+P1(f862(f862(f321(x90281),f735(x90282,x90281,x90283,x90284)),f862(f165(x90281),x90283))) % 14.98/14.67 [9047]~P119(x90474)+~P133(x90474)+~E(f862(f862(f11(x90471,x90474),x90472),x90473),f2(x90474))+~P1(f862(f54(x90471),x90473))+P1(f862(f862(f321(x90471),f337(x90472,x90473,x90471,x90474)),x90473)) % 14.98/14.67 [9085]~E(f862(x90852,x90854),f71(a924))+E(f862(f862(f8(x90851,a924),x90852),x90853),f71(a924))+~P1(f862(f54(x90851),x90853))+~P1(f862(f862(f321(x90851),x90854),x90853))+P1(f862(f862(f321(x90851),f342(x90852,x90853,x90851,x90854)),x90853)) % 14.98/14.67 [9097]E(x90971,x90972)+~E(f862(f862(f73(a1),x90972),x90974),x90971)+~P1(f862(f862(f228(a1),f2(a1)),x90974))+~P1(f862(f862(f321(a1),x90971),x90973))+P1(f862(f862(f321(a1),f390(x90973,x90971,x90974,x90972)),x90973)) % 14.98/14.67 [9098]E(x90981,x90982)+~E(f862(f862(f3(a1),x90982),x90984),x90981)+~P1(f862(f862(f228(a1),f2(a1)),x90984))+~P1(f862(f862(f321(a1),x90981),x90983))+P1(f862(f862(f321(a1),f396(x90983,x90981,x90984,x90982)),x90983)) % 14.98/14.67 [9100]~E(f862(x91002,x91004),f862(a105,f2(a924)))+E(f862(f862(f8(x91001,a924),x91002),x91003),f862(a105,f2(a924)))+~P1(f862(f54(x91001),x91003))+~P1(f862(f862(f321(x91001),x91004),x91003))+P1(f862(f862(f321(x91001),f334(x91002,x91003,x91001,x91004)),x91003)) % 14.98/14.67 [9105]P56(x91052,x91053,x91054,x91051)+E(x91051,f181(f932(x91052,a921)))+~P1(f862(f54(x91052),x91054))+~P1(f862(f54(x91052),x91051))+P1(f862(f862(f321(x91052),f803(x91053,x91051,x91054,x91052)),x91054)) % 14.98/14.67 [9106]P56(x91062,x91063,x91064,x91061)+E(x91061,f181(f932(x91062,a921)))+~P1(f862(f54(x91062),x91064))+~P1(f862(f54(x91062),x91061))+P1(f862(f862(f321(x91062),f550(x91061,x91064,x91063,x91062)),x91064)) % 14.98/14.67 [9107]P56(x91072,x91073,x91074,x91071)+E(x91071,f181(f932(x91072,a921)))+~P1(f862(f54(x91072),x91074))+~P1(f862(f54(x91072),x91071))+P1(f862(f862(f321(x91072),f804(x91071,x91074,x91073,x91072)),x91074)) % 14.98/14.67 [9180]E(x91801,x91802)+~E(f862(f862(f73(a1),x91802),x91804),x91801)+~P1(f862(f862(f228(a1),f2(a1)),x91804))+~P1(f862(f862(f321(a1),x91801),x91803))+P1(f862(f862(f321(a1),f391(x91803,x91801,x91804,x91802)),f296(a1,f71(a1),x91804))) % 14.98/14.67 [9181]E(x91811,x91812)+~E(f862(f862(f3(a1),x91812),x91814),x91811)+~P1(f862(f862(f228(a1),f2(a1)),x91814))+~P1(f862(f862(f321(a1),x91811),x91813))+P1(f862(f862(f321(a1),f397(x91813,x91811,x91814,x91812)),f296(a1,f71(a1),x91814))) % 14.98/14.67 [9254]P1(f862(f862(f227(a924),x92541),f443(x92542,x92543,x92544,x92541)))+~P1(f862(f862(f227(a1),x92542),f862(x92543,x92544)))+P1(f862(f862(f227(a924),x92541),f444(x92542,x92543,x92544,x92541)))+~P1(f862(f862(f228(a924),x92541),x92544))+~P1(f862(f862(f227(a1),f862(x92543,x92541)),x92542)) % 14.98/14.67 [9370]E(f862(x93701,f443(x93702,x93701,x93703,x93704)),x93702)+~P1(f862(f862(f227(a1),x93702),f862(x93701,x93703)))+P1(f862(f862(f228(a924),f444(x93702,x93701,x93703,x93704)),x93703))+~P1(f862(f862(f228(a924),x93704),x93703))+~P1(f862(f862(f227(a1),f862(x93701,x93704)),x93702)) % 14.98/14.67 [9500]~P1(f862(f862(f227(a1),x95002),f862(x95003,x95004)))+P1(f862(f862(f227(a924),x95001),f444(x95002,x95003,x95004,x95001)))+P1(f862(f862(f227(a924),f443(x95002,x95003,x95004,x95001)),x95004))+~P1(f862(f862(f228(a924),x95001),x95004))+~P1(f862(f862(f227(a1),f862(x95003,x95001)),x95002)) % 14.98/14.67 [9501]~P1(f862(f862(f227(a1),x95012),f862(x95013,x95014)))+P1(f862(f862(f227(a924),x95011),f443(x95012,x95013,x95014,x95011)))+P1(f862(f862(f228(a924),f444(x95012,x95013,x95014,x95011)),x95014))+~P1(f862(f862(f228(a924),x95011),x95014))+~P1(f862(f862(f227(a1),f862(x95013,x95011)),x95012)) % 14.98/14.67 [9612]~P1(f862(f862(f227(a1),x96121),f862(x96122,x96123)))+P1(f862(f862(f228(a924),f444(x96121,x96122,x96123,x96124)),x96123))+~P1(f862(f862(f228(a924),x96124),x96123))+~P1(f862(f862(f227(a1),f862(x96122,x96124)),x96121))+P1(f862(f862(f227(a924),f443(x96121,x96122,x96123,x96124)),x96123)) % 14.98/14.67 [9700]E(x97001,f181(f932(x97002,a921)))+~P1(f862(f54(x97002),x97004))+~P1(f862(f54(x97002),x97001))+P1(f862(f862(f321(f931(f932(x97002,a921),f932(x97002,a921))),f862(f862(f244(f932(x97002,a921),f932(x97002,a921)),x97004),x97001)),f310(x97002,x97003)))+P1(f862(f862(f321(x97002),f559(x97003,x97001,x97004,x97002)),x97004)) % 14.98/14.67 [9701]E(x97011,f181(f932(x97012,a921)))+~P1(f862(f54(x97012),x97014))+~P1(f862(f54(x97012),x97011))+P1(f862(f862(f321(f931(f932(x97012,a921),f932(x97012,a921))),f862(f862(f244(f932(x97012,a921),f932(x97012,a921)),x97014),x97011)),f310(x97012,x97013)))+P1(f862(f862(f321(x97012),f617(x97013,x97011,x97014,x97012)),x97014)) % 14.98/14.67 [10367]E(f862(x103671,f443(x103672,x103671,x103673,x103674)),x103672)+~P1(f862(f862(f227(a1),x103672),f862(x103671,x103673)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x103671,f862(f862(f73(a924),f444(x103672,x103671,x103673,x103674)),f71(a924)))),f862(x103671,f444(x103672,x103671,x103673,x103674))))),f71(a1)))+~P1(f862(f862(f228(a924),x103674),x103673))+~P1(f862(f862(f227(a1),f862(x103671,x103674)),x103672)) % 14.98/14.67 [10368]~P1(f862(f862(f227(a1),x103682),f862(x103683,x103684)))+P1(f862(f862(f227(a924),x103681),f443(x103682,x103683,x103684,x103681)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x103683,f862(f862(f73(a924),f444(x103682,x103683,x103684,x103681)),f71(a924)))),f862(x103683,f444(x103682,x103683,x103684,x103681))))),f71(a1)))+~P1(f862(f862(f228(a924),x103681),x103684))+~P1(f862(f862(f227(a1),f862(x103683,x103681)),x103682)) % 14.98/14.67 [10369]~P1(f862(f862(f227(a1),x103691),f862(x103692,x103693)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x103692,f862(f862(f73(a924),f444(x103691,x103692,x103693,x103694)),f71(a924)))),f862(x103692,f444(x103691,x103692,x103693,x103694))))),f71(a1)))+~P1(f862(f862(f228(a924),x103694),x103693))+~P1(f862(f862(f227(a1),f862(x103692,x103694)),x103691))+P1(f862(f862(f227(a924),f443(x103691,x103692,x103693,x103694)),x103693)) % 14.98/14.67 [7420]~P66(x74201)+P1(f862(f862(f228(x74201),x74202),f2(x74201)))+~P1(f862(f862(f227(x74201),x74203),f2(x74201)))+P1(f862(f862(f228(x74201),f2(x74201)),x74202))+P1(f862(f862(f227(x74201),x74203),f862(f862(f281(x74201),x74204),x74202))) % 14.98/14.67 [7421]~P66(x74211)+P1(f862(f862(f228(x74211),x74212),f2(x74211)))+~P1(f862(f862(f228(x74211),x74213),f2(x74211)))+P1(f862(f862(f228(x74211),f2(x74211)),x74212))+P1(f862(f862(f228(x74211),x74213),f862(f862(f281(x74211),x74214),x74212))) % 14.98/14.67 [7673]~P66(x76731)+P1(f862(f862(f227(x76731),x76732),f2(x76731)))+P1(f862(f862(f228(x76731),x76733),f2(x76731)))+P1(f862(f862(f228(x76731),f2(x76731)),x76733))+~P1(f862(f862(f227(x76731),x76732),f862(f862(f281(x76731),x76734),x76733))) % 14.98/14.67 [7674]~P66(x76741)+P1(f862(f862(f228(x76741),x76742),f2(x76741)))+P1(f862(f862(f228(x76741),x76743),f2(x76741)))+P1(f862(f862(f228(x76741),f2(x76741)),x76743))+~P1(f862(f862(f228(x76741),x76742),f862(f862(f281(x76741),x76744),x76743))) % 14.98/14.67 [7793]E(x77931,x77932)+~E(f862(f862(f157(x77933),x77934),x77931),f862(f862(f157(x77933),x77934),x77932))+~P1(f862(f130(x77933),x77934))+~P1(f862(f862(f228(a924),x77932),f862(f182(f925(x77933)),x77934)))+~P1(f862(f862(f228(a924),x77931),f862(f182(f925(x77933)),x77934))) % 14.98/14.67 [8160]~P66(x81601)+~P1(f862(f862(f227(x81601),x81603),f2(x81601)))+P1(f862(f862(f228(x81601),f2(x81601)),x81602))+~P1(f862(f862(f227(x81601),x81604),f862(f862(f74(x81601),x81603),x81602)))+P1(f862(f862(f227(x81601),x81603),f862(f862(f281(x81601),x81604),x81602))) % 14.98/14.67 [8161]~P66(x81611)+~P1(f862(f862(f228(x81611),x81613),f2(x81611)))+P1(f862(f862(f228(x81611),f2(x81611)),x81612))+~P1(f862(f862(f228(x81611),x81614),f862(f862(f74(x81611),x81613),x81612)))+P1(f862(f862(f228(x81611),x81613),f862(f862(f281(x81611),x81614),x81612))) % 14.98/14.67 [8162]~P66(x81621)+~P1(f862(f862(f228(x81621),x81622),f2(x81621)))+P1(f862(f862(f228(x81621),f2(x81621)),x81622))+~P1(f862(f862(f227(x81621),x81624),f862(f862(f74(x81621),x81623),x81622)))+P1(f862(f862(f227(x81621),x81623),f862(f862(f281(x81621),x81624),x81622))) % 14.98/14.67 [8163]~P66(x81631)+~P1(f862(f862(f228(x81631),x81632),f2(x81631)))+P1(f862(f862(f228(x81631),f2(x81631)),x81632))+~P1(f862(f862(f227(x81631),x81634),f862(f862(f281(x81631),x81633),x81632)))+P1(f862(f862(f227(x81631),x81633),f862(f862(f74(x81631),x81634),x81632))) % 14.98/14.67 [8164]~P66(x81641)+~P1(f862(f862(f228(x81641),x81642),f2(x81641)))+P1(f862(f862(f228(x81641),f2(x81641)),x81642))+~P1(f862(f862(f228(x81641),x81644),f862(f862(f74(x81641),x81643),x81642)))+P1(f862(f862(f228(x81641),x81643),f862(f862(f281(x81641),x81644),x81642))) % 14.98/14.67 [8165]~P66(x81651)+~P1(f862(f862(f228(x81651),x81652),f2(x81651)))+P1(f862(f862(f228(x81651),f2(x81651)),x81652))+~P1(f862(f862(f228(x81651),x81654),f862(f862(f281(x81651),x81653),x81652)))+P1(f862(f862(f228(x81651),x81653),f862(f862(f74(x81651),x81654),x81652))) % 14.98/14.67 [8293]~P61(x82931)+~P1(f862(f862(f278(x82931),x82933),x82934))+~P1(f862(f862(f278(x82931),x82933),x82932))+~P1(f862(f862(f278(x82931),x82932),x82934))+P1(f862(f862(f278(x82931),f862(f862(f29(x82931),x82932),x82933)),f862(f862(f29(x82931),x82934),x82933))) % 14.98/14.67 [8309]~P109(x83091)+~P11(x83091,x83092)+~P1(f862(f862(f227(a924),x83093),x83094))+P1(f862(f862(f227(x83091),f862(f862(f157(x83091),x83092),x83093)),f862(f862(f157(x83091),x83092),x83094)))+~P1(f862(f862(f228(a924),x83094),f862(f182(f925(x83091)),x83092))) % 14.98/14.67 [8362]~P127(x83621)+~P1(f862(f862(f227(x83621),x83622),f71(x83621)))+~P1(f862(f862(f227(x83621),f2(x83621)),x83622))+~P1(f862(f862(f227(a924),x83624),x83623))+P1(f862(f862(f227(x83621),f862(f862(f236(x83621),x83622),x83623)),f862(f862(f236(x83621),x83622),x83624))) % 14.98/14.67 [8363]~P127(x83631)+~P1(f862(f862(f228(x83631),x83632),f71(x83631)))+~P1(f862(f862(f228(x83631),f2(x83631)),x83632))+~P1(f862(f862(f228(a924),x83634),x83633))+P1(f862(f862(f228(x83631),f862(f862(f236(x83631),x83632),x83633)),f862(f862(f236(x83631),x83632),x83634))) % 14.98/14.67 [8364]~P127(x83641)+~P1(f862(f862(f227(x83641),f2(x83641)),x83642))+~P1(f862(f862(f228(a924),f2(a924)),x83643))+~P1(f862(f862(f228(x83641),x83642),x83644))+P1(f862(f862(f228(x83641),f862(f862(f236(x83641),x83642),x83643)),f862(f862(f236(x83641),x83644),x83643))) % 14.98/14.67 [8383]~P109(x83831)+~P11(x83831,f862(f161(x83831),x83832))+~P1(f862(f862(f227(a924),x83834),x83833))+P1(f862(f862(f227(x83831),f862(f862(f157(x83831),x83832),x83833)),f862(f862(f157(x83831),x83832),x83834)))+~P1(f862(f862(f228(a924),x83833),f862(f182(f925(x83831)),x83832))) % 14.98/14.67 [8614]~P61(x86141)+P1(f862(f862(f278(x86141),x86142),x86143))+~P1(f862(f862(f278(x86141),x86144),x86143))+~P1(f862(f862(f278(x86141),x86144),x86142))+~P1(f862(f862(f278(x86141),f862(f862(f29(x86141),x86142),x86144)),f862(f862(f29(x86141),x86143),x86144))) % 14.98/14.67 [8629]~P66(x86291)+~P1(f862(f862(f227(x86291),x86292),f2(x86291)))+~P1(f862(f862(f227(x86291),x86293),x86294))+~P1(f862(f862(f228(x86291),f2(x86291)),f862(f862(f74(x86291),x86293),x86294)))+P1(f862(f862(f227(x86291),f862(f862(f281(x86291),x86292),x86293)),f862(f862(f281(x86291),x86292),x86294))) % 14.98/14.67 [8630]~P67(x86301)+~P1(f862(f862(f228(x86301),x86302),f2(x86301)))+~P1(f862(f862(f228(x86301),x86303),x86304))+~P1(f862(f862(f228(x86301),f2(x86301)),f862(f862(f74(x86301),x86303),x86304)))+P1(f862(f862(f228(x86301),f862(f862(f281(x86301),x86302),x86303)),f862(f862(f281(x86301),x86302),x86304))) % 14.98/14.67 [8639]~P67(x86391)+~P1(f862(f862(f227(x86391),x86394),x86393))+~P1(f862(f862(f227(x86391),f2(x86391)),x86392))+~P1(f862(f862(f228(x86391),f2(x86391)),f862(f862(f74(x86391),x86393),x86394)))+P1(f862(f862(f227(x86391),f862(f862(f281(x86391),x86392),x86393)),f862(f862(f281(x86391),x86392),x86394))) % 14.98/14.67 [8640]~P67(x86401)+~P1(f862(f862(f228(x86401),x86404),x86403))+~P1(f862(f862(f228(x86401),f2(x86401)),x86402))+~P1(f862(f862(f228(x86401),f2(x86401)),f862(f862(f74(x86401),x86403),x86404)))+P1(f862(f862(f228(x86401),f862(f862(f281(x86401),x86402),x86403)),f862(f862(f281(x86401),x86402),x86404))) % 14.98/14.67 [8742]P1(f862(x87421,x87422))+~P1(f862(f54(x87424),x87422))+P1(f862(x87421,f893(x87421,x87423,x87422,x87424)))+~P1(f862(x87421,f181(f932(x87424,a921))))+~P1(f862(f862(f227(f932(x87424,a921)),x87422),x87423)) % 14.98/14.67 [8751]P1(f862(x87511,x87512))+P1(f862(f54(x87513),f893(x87511,x87514,x87512,x87513)))+~P1(f862(f54(x87513),x87512))+~P1(f862(x87511,f181(f932(x87513,a921))))+~P1(f862(f862(f227(f932(x87513,a921)),x87512),x87514)) % 14.98/14.67 [9021]E(f862(f862(f73(a1),f398(x90211,x90212,x90213,x90214)),f399(x90211,x90212,x90213,x90214)),x90214)+~P1(f862(f862(f228(a1),f2(a1)),x90213))+~P1(f862(f862(f228(a1),x90212),x90214))+~P1(f862(f862(f321(a1),x90212),x90211))+P1(f862(f862(f228(a1),x90212),f862(f862(f3(a1),x90214),x90213))) % 14.98/14.67 [9236]~P1(f862(f862(f228(a1),f2(a1)),x92363))+~P1(f862(f862(f228(a1),x92362),x92364))+~P1(f862(f862(f321(a1),x92362),x92361))+P1(f862(f862(f321(a1),f398(x92361,x92362,x92363,x92364)),x92361))+P1(f862(f862(f228(a1),x92362),f862(f862(f3(a1),x92364),x92363))) % 14.98/14.67 [9247]P1(f862(x92471,x92472))+~P1(f862(f54(x92473),x92472))+P1(f862(f862(f321(x92473),f898(x92471,x92474,x92472,x92473)),x92474))+~P1(f862(x92471,f181(f932(x92473,a921))))+~P1(f862(f862(f227(f932(x92473,a921)),x92472),x92474)) % 14.98/14.67 [9264]E(f862(f862(f73(a1),f380(x92641,x92642,x92643,x92644)),f381(x92641,x92642,x92643,x92644)),x92644)+~P1(f862(f862(f228(a1),f2(a1)),x92643))+~P1(f862(f862(f227(a1),x92642),x92644))+P1(f862(f862(f227(a1),x92642),f862(f862(f3(a1),x92644),x92643)))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x92642),f71(a1))),x92641)) % 14.98/14.67 [9319]~P1(f862(f862(f228(a1),f2(a1)),x93193))+~P1(f862(f862(f228(a1),x93191),x93192))+~P1(f862(f862(f321(a1),x93191),x93194))+P1(f862(f862(f321(a1),f399(x93194,x93191,x93193,x93192)),f296(a1,f71(a1),x93193)))+P1(f862(f862(f228(a1),x93191),f862(f862(f3(a1),x93192),x93193))) % 14.98/14.67 [9346]~P72(x93462)+~E(f784(x93463,x93464,x93461,x93462),f785(x93463,x93464,x93461,x93462))+~P1(f862(f54(x93461),f786(x93463,x93464,x93461,x93462)))+E(f862(f862(f8(f932(x93461,a921),x93462),f862(f8(x93461,x93462),x93463)),x93464),f862(f862(f8(x93461,x93462),x93463),f30(f932(x93461,a921),x93464)))+~P1(f862(f54(f932(x93461,a921)),x93464)) % 14.98/14.67 [9350]~P72(x93502)+~E(f862(x93503,f787(x93503,x93504,x93501,x93502)),f2(x93502))+~P1(f862(f54(x93501),f786(x93503,x93504,x93501,x93502)))+E(f862(f862(f8(f932(x93501,a921),x93502),f862(f8(x93501,x93502),x93503)),x93504),f862(f862(f8(x93501,x93502),x93503),f30(f932(x93501,a921),x93504)))+~P1(f862(f54(f932(x93501,a921)),x93504)) % 14.98/14.67 [9414]~P1(f862(f862(f228(a1),f2(a1)),x94143))+~P1(f862(f862(f227(a1),x94142),x94144))+P1(f862(f862(f321(a1),f380(x94141,x94142,x94143,x94144)),x94141))+P1(f862(f862(f227(a1),x94142),f862(f862(f3(a1),x94144),x94143)))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x94142),f71(a1))),x94141)) % 14.98/14.67 [9459]~P1(f862(f862(f228(a1),f2(a1)),x94593))+~P1(f862(f862(f227(a1),x94591),x94592))+P1(f862(f862(f321(a1),f381(x94594,x94591,x94593,x94592)),f296(a1,f71(a1),x94593)))+P1(f862(f862(f227(a1),x94591),f862(f862(f3(a1),x94592),x94593)))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x94591),f71(a1))),x94594)) % 14.98/14.67 [9480]~P72(x94802)+~E(f784(x94803,x94804,x94801,x94802),f785(x94803,x94804,x94801,x94802))+E(f862(f862(f8(f932(x94801,a921),x94802),f862(f8(x94801,x94802),x94803)),x94804),f862(f862(f8(x94801,x94802),x94803),f30(f932(x94801,a921),x94804)))+P1(f862(f862(f321(f932(x94801,a921)),f786(x94803,x94804,x94801,x94802)),x94804))+~P1(f862(f54(f932(x94801,a921)),x94804)) % 14.98/14.67 [9485]~P72(x94852)+~E(f862(x94853,f787(x94853,x94854,x94851,x94852)),f2(x94852))+E(f862(f862(f8(f932(x94851,a921),x94852),f862(f8(x94851,x94852),x94853)),x94854),f862(f862(f8(x94851,x94852),x94853),f30(f932(x94851,a921),x94854)))+P1(f862(f862(f321(f932(x94851,a921)),f786(x94853,x94854,x94851,x94852)),x94854))+~P1(f862(f54(f932(x94851,a921)),x94854)) % 14.98/14.67 [9589]~P72(x95892)+~P1(f862(f54(x95891),f786(x95893,x95894,x95891,x95892)))+E(f862(f862(f8(f932(x95891,a921),x95892),f862(f8(x95891,x95892),x95893)),x95894),f862(f862(f8(x95891,x95892),x95893),f30(f932(x95891,a921),x95894)))+P1(f862(f862(f321(f932(x95891,a921)),f785(x95893,x95894,x95891,x95892)),x95894))+~P1(f862(f54(f932(x95891,a921)),x95894)) % 14.98/14.67 [9590]~P72(x95902)+~P1(f862(f54(x95901),f786(x95903,x95904,x95901,x95902)))+E(f862(f862(f8(f932(x95901,a921),x95902),f862(f8(x95901,x95902),x95903)),x95904),f862(f862(f8(x95901,x95902),x95903),f30(f932(x95901,a921),x95904)))+P1(f862(f862(f321(f932(x95901,a921)),f784(x95903,x95904,x95901,x95902)),x95904))+~P1(f862(f54(f932(x95901,a921)),x95904)) % 14.98/14.67 [9669]~P72(x96692)+E(f862(f862(f8(f932(x96691,a921),x96692),f862(f8(x96691,x96692),x96693)),x96694),f862(f862(f8(x96691,x96692),x96693),f30(f932(x96691,a921),x96694)))+P1(f862(f862(f321(f932(x96691,a921)),f786(x96693,x96694,x96691,x96692)),x96694))+P1(f862(f862(f321(f932(x96691,a921)),f785(x96693,x96694,x96691,x96692)),x96694))+~P1(f862(f54(f932(x96691,a921)),x96694)) % 14.98/14.67 [9670]~P72(x96702)+E(f862(f862(f8(f932(x96701,a921),x96702),f862(f8(x96701,x96702),x96703)),x96704),f862(f862(f8(x96701,x96702),x96703),f30(f932(x96701,a921),x96704)))+P1(f862(f862(f321(f932(x96701,a921)),f786(x96703,x96704,x96701,x96702)),x96704))+P1(f862(f862(f321(f932(x96701,a921)),f784(x96703,x96704,x96701,x96702)),x96704))+~P1(f862(f54(f932(x96701,a921)),x96704)) % 14.98/14.67 [9689]~P72(x96892)+P1(f862(f862(f321(x96891),f787(x96893,x96894,x96891,x96892)),f785(x96893,x96894,x96891,x96892)))+~P1(f862(f54(x96891),f786(x96893,x96894,x96891,x96892)))+E(f862(f862(f8(f932(x96891,a921),x96892),f862(f8(x96891,x96892),x96893)),x96894),f862(f862(f8(x96891,x96892),x96893),f30(f932(x96891,a921),x96894)))+~P1(f862(f54(f932(x96891,a921)),x96894)) % 14.98/14.67 [9690]~P72(x96902)+P1(f862(f862(f321(x96901),f787(x96903,x96904,x96901,x96902)),f784(x96903,x96904,x96901,x96902)))+~P1(f862(f54(x96901),f786(x96903,x96904,x96901,x96902)))+E(f862(f862(f8(f932(x96901,a921),x96902),f862(f8(x96901,x96902),x96903)),x96904),f862(f862(f8(x96901,x96902),x96903),f30(f932(x96901,a921),x96904)))+~P1(f862(f54(f932(x96901,a921)),x96904)) % 14.98/14.67 [9703]P1(f862(x97031,x97032))+~P1(f862(f862(f321(x97033),f898(x97031,x97034,x97032,x97033)),f893(x97031,x97034,x97032,x97033)))+~P1(f862(f54(x97033),x97032))+~P1(f862(x97031,f181(f932(x97033,a921))))+~P1(f862(f862(f227(f932(x97033,a921)),x97032),x97034)) % 14.98/14.67 [9740]~P72(x97402)+P1(f862(f862(f321(x97401),f787(x97403,x97404,x97401,x97402)),f785(x97403,x97404,x97401,x97402)))+E(f862(f862(f8(f932(x97401,a921),x97402),f862(f8(x97401,x97402),x97403)),x97404),f862(f862(f8(x97401,x97402),x97403),f30(f932(x97401,a921),x97404)))+P1(f862(f862(f321(f932(x97401,a921)),f786(x97403,x97404,x97401,x97402)),x97404))+~P1(f862(f54(f932(x97401,a921)),x97404)) % 14.98/14.67 [9741]~P72(x97412)+P1(f862(f862(f321(x97411),f787(x97413,x97414,x97411,x97412)),f784(x97413,x97414,x97411,x97412)))+E(f862(f862(f8(f932(x97411,a921),x97412),f862(f8(x97411,x97412),x97413)),x97414),f862(f862(f8(x97411,x97412),x97413),f30(f932(x97411,a921),x97414)))+P1(f862(f862(f321(f932(x97411,a921)),f786(x97413,x97414,x97411,x97412)),x97414))+~P1(f862(f54(f932(x97411,a921)),x97414)) % 14.98/14.67 [9917]P1(f862(x99171,x99172))+~P1(f862(f54(x99173),x99172))+~P1(f862(x99171,f862(f862(f301(x99173),f898(x99171,x99174,x99172,x99173)),f893(x99171,x99174,x99172,x99173))))+~P1(f862(x99171,f181(f932(x99173,a921))))+~P1(f862(f862(f227(f932(x99173,a921)),x99172),x99174)) % 14.98/14.67 [7928]~P66(x79281)+P1(f862(f862(f228(x79281),x79282),f2(x79281)))+~P1(f862(f862(f227(x79281),f2(x79281)),x79284))+P1(f862(f862(f228(x79281),f2(x79281)),x79282))+P1(f862(f862(f227(x79281),f862(f862(f281(x79281),x79283),x79282)),x79284)) % 14.98/14.67 [7929]~P66(x79291)+P1(f862(f862(f228(x79291),x79292),f2(x79291)))+P1(f862(f862(f228(x79291),f2(x79291)),x79292))+~P1(f862(f862(f228(x79291),f2(x79291)),x79294))+P1(f862(f862(f228(x79291),f862(f862(f281(x79291),x79293),x79292)),x79294)) % 14.98/14.67 [8213]~P1(f862(f862(f227(a1),x82134),f2(a1)))+~E(x82132,f862(f862(f73(a1),f862(f862(f74(a1),x82131),x82133)),x82134))+P1(f862(f862(f228(a1),f2(a1)),x82131))+~P1(f862(f862(f228(a1),x82131),x82134))+P1(f862(f42(x82132,x82131),f862(f862(f244(a1,a1),x82133),x82134))) % 14.98/14.67 [8247]~P1(f862(x82471,x82474))+P1(f862(x82471,f407(x82472,x82471,x82473)))+~P1(f862(f862(f227(a1),f2(a1)),x82472))+~P1(f862(f862(f228(a1),f2(a1)),x82473))+P1(f862(x82471,f862(f862(f3(a1),x82474),f862(f862(f74(a1),x82472),x82473)))) % 14.98/14.67 [8248]~P1(f862(x82481,x82484))+P1(f862(x82481,f408(x82482,x82481,x82483)))+~P1(f862(f862(f227(a1),f2(a1)),x82482))+~P1(f862(f862(f228(a1),f2(a1)),x82483))+P1(f862(x82481,f862(f862(f73(a1),x82484),f862(f862(f74(a1),x82482),x82483)))) % 14.98/14.67 [8249]~P66(x82491)+P1(f862(f862(f228(x82491),x82492),f2(x82491)))+P1(f862(f862(f228(x82491),f2(x82491)),x82492))+P1(f862(f862(f227(x82491),f2(x82491)),x82493))+~P1(f862(f862(f227(x82491),f862(f862(f281(x82491),x82494),x82492)),x82493)) % 14.98/14.67 [8250]~P66(x82501)+P1(f862(f862(f228(x82501),x82502),f2(x82501)))+P1(f862(f862(f228(x82501),f2(x82501)),x82502))+P1(f862(f862(f228(x82501),f2(x82501)),x82503))+~P1(f862(f862(f228(x82501),f862(f862(f281(x82501),x82504),x82502)),x82503)) % 14.98/14.67 [8304]~E(x83041,f862(f862(f73(a1),f862(f862(f74(a1),x83042),x83043)),x83044))+~P1(f862(f862(f227(a1),f2(a1)),x83044))+~P1(f862(f862(f228(a1),f2(a1)),x83042))+~P1(f862(f862(f228(a1),x83044),x83042))+P1(f862(f42(x83041,x83042),f862(f862(f244(a1,a1),x83043),x83044))) % 14.98/14.67 [8422]~P66(x84221)+P1(f862(f862(f228(x84221),x84222),f2(x84221)))+~P1(f862(f862(f227(x84221),f2(x84221)),x84224))+~P1(f862(f862(f227(x84221),x84223),f862(f862(f74(x84221),x84224),x84222)))+P1(f862(f862(f227(x84221),f862(f862(f281(x84221),x84223),x84222)),x84224)) % 14.98/14.67 [8423]~P66(x84231)+P1(f862(f862(f228(x84231),x84232),f2(x84231)))+~P1(f862(f862(f228(x84231),f2(x84231)),x84234))+~P1(f862(f862(f228(x84231),x84233),f862(f862(f74(x84231),x84234),x84232)))+P1(f862(f862(f228(x84231),f862(f862(f281(x84231),x84233),x84232)),x84234)) % 14.98/14.67 [8507]~P66(x85071)+P1(f862(f862(f228(x85071),x85072),f2(x85071)))+~P1(f862(f862(f227(x85071),x85073),f2(x85071)))+P1(f862(f862(f227(x85071),x85073),f862(f862(f281(x85071),x85074),x85072)))+~P1(f862(f862(f227(x85071),f862(f862(f74(x85071),x85073),x85072)),x85074)) % 14.98/14.67 [8508]~P66(x85081)+P1(f862(f862(f228(x85081),x85082),f2(x85081)))+~P1(f862(f862(f228(x85081),x85083),f2(x85081)))+P1(f862(f862(f228(x85081),x85083),f862(f862(f281(x85081),x85084),x85082)))+~P1(f862(f862(f228(x85081),f862(f862(f74(x85081),x85083),x85082)),x85084)) % 14.98/14.67 [8662]~P66(x86621)+~P1(f862(f862(f228(x86621),x86622),f2(x86621)))+P1(f862(f862(f228(x86621),f2(x86621)),x86622))+~P1(f862(f862(f227(x86621),f862(f862(f281(x86621),x86624),x86622)),x86623))+P1(f862(f862(f227(x86621),f862(f862(f74(x86621),x86623),x86622)),x86624)) % 14.98/14.67 [8663]~P66(x86631)+~P1(f862(f862(f228(x86631),x86632),f2(x86631)))+P1(f862(f862(f228(x86631),f2(x86631)),x86632))+~P1(f862(f862(f227(x86631),f862(f862(f74(x86631),x86634),x86632)),x86633))+P1(f862(f862(f227(x86631),f862(f862(f281(x86631),x86633),x86632)),x86634)) % 14.98/14.67 [8664]~P66(x86641)+~P1(f862(f862(f228(x86641),x86642),f2(x86641)))+P1(f862(f862(f228(x86641),f2(x86641)),x86642))+~P1(f862(f862(f228(x86641),f862(f862(f281(x86641),x86644),x86642)),x86643))+P1(f862(f862(f228(x86641),f862(f862(f74(x86641),x86643),x86642)),x86644)) % 14.98/14.67 [8665]~P66(x86651)+~P1(f862(f862(f228(x86651),x86652),f2(x86651)))+P1(f862(f862(f228(x86651),f2(x86651)),x86652))+~P1(f862(f862(f228(x86651),f862(f862(f74(x86651),x86654),x86652)),x86653))+P1(f862(f862(f228(x86651),f862(f862(f281(x86651),x86653),x86652)),x86654)) % 14.98/14.67 [8681]~P66(x86811)+~P1(f862(f862(f227(x86811),f2(x86811)),x86814))+P1(f862(f862(f228(x86811),f2(x86811)),x86812))+~P1(f862(f862(f227(x86811),f862(f862(f74(x86811),x86814),x86812)),x86813))+P1(f862(f862(f227(x86811),f862(f862(f281(x86811),x86813),x86812)),x86814)) % 14.98/14.67 [8682]~P66(x86821)+~P1(f862(f862(f228(x86821),f2(x86821)),x86824))+P1(f862(f862(f228(x86821),f2(x86821)),x86822))+~P1(f862(f862(f228(x86821),f862(f862(f74(x86821),x86824),x86822)),x86823))+P1(f862(f862(f228(x86821),f862(f862(f281(x86821),x86823),x86822)),x86824)) % 14.98/14.67 [8760]~P66(x87601)+~P1(f862(f862(f228(x87601),x87604),f2(x87601)))+~P1(f862(f862(f227(x87601),x87603),f862(f862(f74(x87601),x87602),x87604)))+P1(f862(f862(f227(x87601),x87602),f862(f862(f281(x87601),x87603),x87604)))+~P1(f862(f862(f227(x87601),f862(f862(f74(x87601),x87602),x87604)),x87603)) % 14.98/14.67 [8761]~P66(x87611)+~P1(f862(f862(f227(x87611),x87612),f2(x87611)))+~P1(f862(f862(f227(x87611),x87613),f862(f862(f74(x87611),x87612),x87614)))+P1(f862(f862(f227(x87611),x87612),f862(f862(f281(x87611),x87613),x87614)))+~P1(f862(f862(f227(x87611),f862(f862(f74(x87611),x87612),x87614)),x87613)) % 14.98/14.67 [8762]~P66(x87621)+~P1(f862(f862(f228(x87621),x87624),f2(x87621)))+~P1(f862(f862(f228(x87621),x87623),f862(f862(f74(x87621),x87622),x87624)))+P1(f862(f862(f228(x87621),x87622),f862(f862(f281(x87621),x87623),x87624)))+~P1(f862(f862(f228(x87621),f862(f862(f74(x87621),x87622),x87624)),x87623)) % 14.98/14.67 [8763]~P66(x87631)+~P1(f862(f862(f228(x87631),x87632),f2(x87631)))+~P1(f862(f862(f228(x87631),x87633),f862(f862(f74(x87631),x87632),x87634)))+P1(f862(f862(f228(x87631),x87632),f862(f862(f281(x87631),x87633),x87634)))+~P1(f862(f862(f228(x87631),f862(f862(f74(x87631),x87632),x87634)),x87633)) % 14.98/14.67 [8885]~P66(x88851)+~P1(f862(f862(f228(x88851),x88853),f2(x88851)))+~P1(f862(f862(f227(x88851),x88852),f862(f862(f74(x88851),x88854),x88853)))+~P1(f862(f862(f227(x88851),f862(f862(f74(x88851),x88854),x88853)),x88852))+P1(f862(f862(f227(x88851),f862(f862(f281(x88851),x88852),x88853)),x88854)) % 14.98/14.67 [8886]~P66(x88861)+~P1(f862(f862(f228(x88861),x88863),f2(x88861)))+~P1(f862(f862(f228(x88861),x88862),f862(f862(f74(x88861),x88864),x88863)))+~P1(f862(f862(f228(x88861),f862(f862(f74(x88861),x88864),x88863)),x88862))+P1(f862(f862(f228(x88861),f862(f862(f281(x88861),x88862),x88863)),x88864)) % 14.98/14.67 [8904]~P66(x89041)+~P1(f862(f862(f227(x89041),f2(x89041)),x89044))+~P1(f862(f862(f227(x89041),x89042),f862(f862(f74(x89041),x89044),x89043)))+~P1(f862(f862(f227(x89041),f862(f862(f74(x89041),x89044),x89043)),x89042))+P1(f862(f862(f227(x89041),f862(f862(f281(x89041),x89042),x89043)),x89044)) % 14.98/14.67 [8905]~P66(x89051)+~P1(f862(f862(f228(x89051),f2(x89051)),x89054))+~P1(f862(f862(f228(x89051),x89052),f862(f862(f74(x89051),x89054),x89053)))+~P1(f862(f862(f228(x89051),f862(f862(f74(x89051),x89054),x89053)),x89052))+P1(f862(f862(f228(x89051),f862(f862(f281(x89051),x89052),x89053)),x89054)) % 14.98/14.67 [9090]E(f862(f862(f3(a1),f400(x90901,x90902,x90903,x90904)),f401(x90901,x90902,x90903,x90904)),x90904)+~P1(f862(f862(f228(a1),f2(a1)),x90903))+~P1(f862(f862(f321(a1),x90902),x90901))+~P1(f862(f862(f228(a1),x90904),x90902))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x90904),x90903)),x90902)) % 14.98/14.67 [9161]~P1(f862(x91611,x91612))+~P1(f862(f862(f227(a1),f2(a1)),x91613))+~P1(f862(f862(f228(a1),f2(a1)),x91614))+~P1(f862(x91611,f862(f862(f3(a1),f407(x91613,x91611,x91614)),x91614)))+P1(f862(x91611,f862(f862(f3(a1),x91612),f862(f862(f74(a1),x91613),x91614)))) % 14.98/14.67 [9162]~P1(f862(x91621,x91622))+~P1(f862(f862(f227(a1),f2(a1)),x91623))+~P1(f862(f862(f228(a1),f2(a1)),x91624))+~P1(f862(x91621,f862(f862(f73(a1),f408(x91623,x91621,x91624)),x91624)))+P1(f862(x91621,f862(f862(f73(a1),x91622),f862(f862(f74(a1),x91623),x91624)))) % 14.98/14.67 [9313]~P1(f862(f862(f228(a1),f2(a1)),x93133))+~P1(f862(f862(f321(a1),x93132),x93131))+~P1(f862(f862(f228(a1),x93134),x93132))+P1(f862(f862(f321(a1),f400(x93131,x93132,x93133,x93134)),x93131))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x93134),x93133)),x93132)) % 14.98/14.67 [9333]E(f862(f862(f3(a1),f382(x93331,x93332,x93333,x93334)),f383(x93331,x93332,x93333,x93334)),x93334)+~P1(f862(f862(f228(a1),f2(a1)),x93333))+~P1(f862(f862(f227(a1),x93334),x93332))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x93332),f71(a1))),x93331))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x93334),x93333)),x93332)) % 14.98/14.67 [9361]~P1(f862(f862(f228(a1),f2(a1)),x93612))+~P1(f862(f862(f321(a1),x93613),x93614))+~P1(f862(f862(f228(a1),x93611),x93613))+P1(f862(f862(f321(a1),f401(x93614,x93613,x93612,x93611)),f296(a1,f71(a1),x93612)))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x93611),x93612)),x93613)) % 14.98/14.67 [9451]~P1(f862(f862(f228(a1),f2(a1)),x94513))+~P1(f862(f862(f227(a1),x94514),x94512))+P1(f862(f862(f321(a1),f382(x94511,x94512,x94513,x94514)),x94511))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x94512),f71(a1))),x94511))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x94514),x94513)),x94512)) % 14.98/14.67 [9496]~P1(f862(f862(f228(a1),f2(a1)),x94962))+~P1(f862(f862(f227(a1),x94961),x94963))+P1(f862(f862(f321(a1),f383(x94964,x94963,x94962,x94961)),f296(a1,f71(a1),x94962)))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x94963),f71(a1))),x94964))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x94961),x94962)),x94963)) % 14.98/14.67 [9794]~P35(x97941,x97943)+~P24(x97941,x97944)+P35(x97941,f862(f862(f103(f932(f931(x97941,x97941),a921)),x97942),x97943))+~P1(f862(f862(f227(f932(f931(x97941,x97941),a921)),x97942),f862(f243(f932(f931(x97941,x97941),a921),f932(f931(x97941,x97941),a921)),x97944)))+~P1(f862(f862(f227(f932(f931(x97941,x97941),a921)),x97943),f862(f248(f932(f931(x97941,x97941),a921),f932(f931(x97941,x97941),a921)),x97944))) % 14.98/14.67 [10176]~P16(x101762,x101764,x101763)+E(x101761,f181(f932(x101762,a921)))+~P1(f862(f54(x101762),x101761))+P1(f862(f862(f321(x101762),f862(x101763,x101761)),x101761))+~P1(f862(f862(f321(x101762),f862(f862(x101764,f881(x101761,x101763,x101764,x101762)),f882(x101761,x101763,x101764,x101762))),f862(f862(f301(x101762),f881(x101761,x101763,x101764,x101762)),f862(f862(f301(x101762),f882(x101761,x101763,x101764,x101762)),f181(f932(x101762,a921)))))) % 14.98/14.67 [10112]~P110(x101122)+~P63(x101121)+~P1(f862(f862(f227(f932(x101121,x101122)),x101123),x101124))+P1(f862(f862(f228(f932(x101121,x101122)),x101123),x101124))+~P1(f862(f49(x101121),f862(f862(f10(a921,a921,x101121),a314),f862(f862(f20(x101121,x101122,a921),f862(f862(f10(x101122,f932(x101122,a921),x101121),a317),x101123)),x101124)))) % 14.98/14.67 [9709]~P52(x97091,x97091,x97094)+P1(f862(f862(f321(f931(x97091,x97091)),f862(f862(f244(x97091,x97091),x97092),x97093)),f299(x97091,x97094)))+P1(f862(f862(f321(f931(x97091,x97091)),f862(f862(f244(x97091,x97091),x97093),x97092)),f299(x97091,x97094)))+~P1(f862(f862(f321(f931(x97091,x97091)),f862(f862(f244(x97091,x97091),x97095),x97092)),f299(x97091,x97094)))+~P1(f862(f862(f321(f931(x97091,x97091)),f862(f862(f244(x97091,x97091),x97095),x97093)),f299(x97091,x97094))) % 14.98/14.67 [5810]E(x58101,f2(a924))+~E(f862(f28(x58102),x58105),x58101)+E(f862(f28(x58102),x58103),f862(a105,x58101))+~E(x58103,f862(f862(f301(x58102),x58104),x58105))+P1(f862(f862(f321(x58102),x58104),x58105)) % 14.98/14.67 [5932]~P65(x59322)+E(x59321,f2(x59322))+E(x59323,f2(x59322))+~E(f862(f862(f281(x59322),x59324),x59323),f862(f862(f281(x59322),x59325),x59321))+E(f862(f862(f74(x59322),x59324),x59321),f862(f862(f74(x59322),x59325),x59323)) % 14.98/14.67 [5933]~P65(x59332)+E(x59331,f2(x59332))+E(x59333,f2(x59332))+~E(f862(f862(f74(x59332),x59334),x59333),f862(f862(f74(x59332),x59335),x59331))+E(f862(f862(f281(x59332),x59334),x59331),f862(f862(f281(x59332),x59335),x59333)) % 14.98/14.67 [6009]~E(f862(f28(x60091),x60095),x60093)+~E(x60095,f181(f932(x60091,a921)))+E(f862(f28(x60091),x60092),f862(a105,x60093))+~E(x60092,f862(f862(f301(x60091),x60094),x60095))+P1(f862(f862(f321(x60091),x60094),x60095)) % 14.98/14.67 [6246]~P119(x62462)+~E(f862(x62463,x62465),f2(x62462))+E(f862(f862(f11(x62461,x62462),x62463),x62464),f2(x62462))+~P1(f862(f54(x62461),x62464))+~P1(f862(f862(f321(x62461),x62465),x62464)) % 14.98/14.67 [6621]~P109(x66213)+E(x66211,x66212)+~E(f862(f295(x66213,x66214),x66211),f862(f295(x66213,x66215),x66212))+~P1(f862(f862(f228(x66213),x66215),x66212))+~P1(f862(f862(f228(x66213),x66214),x66211)) % 14.98/14.67 [6622]~P109(x66223)+E(x66221,x66222)+~E(f862(f295(x66223,x66221),x66224),f862(f295(x66223,x66222),x66225))+~P1(f862(f862(f228(x66223),x66222),x66225))+~P1(f862(f862(f228(x66223),x66221),x66224)) % 14.98/14.67 [7691]~P109(x76911)+~P11(x76911,f862(f862(f127(x76911),x76914),x76915))+~P1(f862(f862(f321(x76911),x76913),f862(f165(x76911),x76915)))+~P1(f862(f862(f321(x76911),x76912),f862(f165(x76911),x76914)))+P1(f862(f862(f227(x76911),x76912),x76913)) % 14.98/14.67 [8797]~P110(x87971)+~P1(f862(f862(f228(f932(x87971,a921)),f296(x87971,x87975,x87972)),f296(x87971,x87974,x87973)))+~P1(f862(f862(f227(x87971),x87975),x87972))+P1(f862(f862(f228(x87971),x87972),x87973))+P1(f862(f862(f228(x87971),x87974),x87975)) % 14.98/14.67 [10220]~P15(x102202,x102205,x102203)+E(x102201,f181(f932(x102202,a921)))+~E(f862(f862(x102205,f862(x102204,f899(x102201,x102204,x102203,x102205,x102202))),f862(x102204,f900(x102201,x102204,x102203,x102205,x102202))),f862(x102204,f862(f862(x102205,f899(x102201,x102204,x102203,x102205,x102202)),f900(x102201,x102204,x102203,x102205,x102202))))+E(f862(x102203,f862(f302(x102202,x102202,x102204),x102201)),f862(x102204,f862(x102203,x102201)))+~P1(f862(f54(x102202),x102201)) % 14.98/14.67 [6618]~P16(x66182,x66185,x66183)+E(x66181,f181(f932(x66182,a921)))+~P1(f862(f54(x66182),x66181))+E(f862(x66183,f862(f862(f301(x66182),x66184),x66181)),f862(f862(x66185,x66184),f862(x66183,x66181)))+P1(f862(f862(f321(x66182),x66184),x66181)) % 14.98/14.67 [7449]~P15(x74492,x74493,x74494)+E(f862(f862(x74493,f862(x74494,x74491)),f862(x74494,x74495)),f862(x74494,x74495))+E(x74491,f181(f932(x74492,a921)))+~P1(f862(f54(x74492),x74495))+~P1(f862(f862(f227(f932(x74492,a921)),x74491),x74495)) % 14.98/14.67 [7828]~P16(x78284,x78285,x78281)+E(f862(x78281,x78282),x78283)+~P1(f862(f54(x78284),x78282))+~E(f862(f862(f3(f932(x78284,a921)),x78282),f862(f862(f301(x78284),x78283),f181(f932(x78284,a921)))),f181(f932(x78284,a921)))+~P1(f862(f862(f321(x78284),x78283),x78282)) % 14.98/14.67 [8717]~P71(x87171)+~P120(x87171)+~P1(f862(f54(x87172),x87175))+P1(f862(f862(f278(x87171),f862(f862(f11(x87172,x87171),x87173),x87174)),f862(f862(f11(x87172,x87171),x87173),x87175)))+~P1(f862(f862(f227(f932(x87172,a921)),x87174),x87175)) % 14.98/14.67 [8767]E(x87671,x87672)+~P6(x87673,x87674,x87675)+E(f862(f862(f94(f932(x87673,a921)),x87671),x87672),f181(f932(x87673,a921)))+~P1(f862(f862(f321(f932(x87673,a921)),x87672),f862(f862(f53(x87673),x87674),x87675)))+~P1(f862(f862(f321(f932(x87673,a921)),x87671),f862(f862(f53(x87673),x87674),x87675))) % 14.98/14.67 [9582]~P72(x95822)+~E(f862(x95823,f365(x95823,x95824,x95825,x95821,x95822)),f2(x95822))+E(f862(f862(f8(x95821,x95822),x95823),x95824),f862(f862(f8(x95821,x95822),x95823),x95825))+~P1(f862(f54(x95821),x95825))+~P1(f862(f862(f227(f932(x95821,a921)),x95824),x95825)) % 14.98/14.67 [9583]~P72(x95832)+~E(f862(x95833,f366(x95833,x95834,x95835,x95831,x95832)),f2(x95832))+E(f862(f862(f8(x95831,x95832),x95833),x95834),f862(f862(f8(x95831,x95832),x95833),x95835))+~P1(f862(f54(x95831),x95835))+~P1(f862(f862(f227(f932(x95831,a921)),x95834),x95835)) % 14.98/14.67 [9584]~P71(x95842)+~E(f862(x95843,f916(x95843,x95844,x95845,x95841,x95842)),f71(x95842))+E(f862(f862(f11(x95841,x95842),x95843),x95844),f862(f862(f11(x95841,x95842),x95843),x95845))+~P1(f862(f54(x95841),x95845))+~P1(f862(f862(f227(f932(x95841,a921)),x95844),x95845)) % 14.98/14.67 [9585]~P71(x95852)+~E(f862(x95853,f330(x95853,x95854,x95855,x95851,x95852)),f71(x95852))+E(f862(f862(f11(x95851,x95852),x95853),x95854),f862(f862(f11(x95851,x95852),x95853),x95855))+~P1(f862(f54(x95851),x95855))+~P1(f862(f862(f227(f932(x95851,a921)),x95854),x95855)) % 14.98/14.67 [10062]~P87(x100621)+~P1(f862(f54(x100622),x100625))+~P1(f862(f862(f227(x100621),f2(x100621)),f862(x100623,f355(x100623,x100624,x100625,x100622,x100621))))+P1(f862(f862(f227(x100621),f862(f862(f8(x100622,x100621),x100623),x100624)),f862(f862(f8(x100622,x100621),x100623),x100625)))+~P1(f862(f862(f227(f932(x100622,a921)),x100624),x100625)) % 14.98/14.67 [7688]E(x76881,f2(a924))+P1(f862(x76882,x76883))+~E(x76884,f862(f862(f73(a924),f862(f862(f74(a924),x76881),x76883)),x76885))+~P1(f862(f862(f228(a924),x76885),x76881))+~P1(f862(x76882,f862(f862(f29(a924),x76884),x76881))) % 14.98/14.67 [7766]E(x77661,f2(a924))+P1(f862(x77662,x77663))+~P1(f862(x77662,f38(a924,x77664,x77661)))+~E(x77664,f862(f862(f73(a924),f862(f862(f74(a924),x77661),x77665)),x77663))+~P1(f862(f862(f228(a924),x77663),x77661)) % 14.98/14.67 [8059]~P65(x80593)+E(f862(x80591,x80592),f2(x80593))+~P1(f862(f54(x80594),x80595))+E(f862(f862(f11(x80594,x80593),x80591),f862(f862(f3(f932(x80594,a921)),x80595),f862(f862(f301(x80594),x80592),f181(f932(x80594,a921))))),f862(f862(f11(x80594,x80593),x80591),x80595))+P1(f862(f862(f321(x80594),x80592),x80595)) % 14.98/14.67 [8462]~P72(x84621)+~P1(f862(f54(x84622),x84625))+~P1(f862(f54(x84622),x84624))+~E(f862(f862(f94(f932(x84622,a921)),x84624),x84625),f181(f932(x84622,a921)))+E(f862(f862(f73(x84621),f862(f862(f8(x84622,x84621),x84623),x84624)),f862(f862(f8(x84622,x84621),x84623),x84625)),f862(f862(f8(x84622,x84621),x84623),f862(f862(f103(f932(x84622,a921)),x84624),x84625))) % 14.98/14.67 [8464]~P71(x84641)+~P1(f862(f54(x84642),x84645))+~P1(f862(f54(x84642),x84644))+~E(f862(f862(f94(f932(x84642,a921)),x84644),x84645),f181(f932(x84642,a921)))+E(f862(f862(f74(x84641),f862(f862(f11(x84642,x84641),x84643),x84644)),f862(f862(f11(x84642,x84641),x84643),x84645)),f862(f862(f11(x84642,x84641),x84643),f862(f862(f103(f932(x84642,a921)),x84644),x84645))) % 14.98/14.67 [8563]~P65(x85633)+E(f862(x85631,x85632),f2(x85633))+~P1(f862(f54(x85634),x85635))+E(f862(f862(f11(x85634,x85633),x85631),f862(f862(f3(f932(x85634,a921)),x85635),f862(f862(f301(x85634),x85632),f181(f932(x85634,a921))))),f862(f862(f281(x85633),f862(f862(f11(x85634,x85633),x85631),x85635)),f862(x85631,x85632)))+~P1(f862(f862(f321(x85634),x85632),x85635)) % 14.98/14.67 [9289]~P6(x92891,x92895,x92894)+~E(f862(f862(f53(x92891),f862(f862(f301(x92891),x92892),f181(f932(x92891,a921)))),x92894),f862(f862(f53(x92891),f862(f862(f301(x92891),x92893),f181(f932(x92891,a921)))),x92894))+~P1(f862(f862(f321(x92891),x92893),x92895))+~P1(f862(f862(f321(x92891),x92892),x92895))+P1(f862(f862(f321(f931(x92891,x92891)),f862(f862(f244(x92891,x92891),x92892),x92893)),x92894)) % 14.98/14.67 [9312]~P6(x93121,x93125,x93123)+E(f862(f862(f53(x93121),f862(f862(f301(x93121),x93122),f181(f932(x93121,a921)))),x93123),f862(f862(f53(x93121),f862(f862(f301(x93121),x93124),f181(f932(x93121,a921)))),x93123))+~P1(f862(f862(f321(x93121),x93124),x93125))+~P1(f862(f862(f321(x93121),x93122),x93125))+~P1(f862(f862(f321(f931(x93121,x93121)),f862(f862(f244(x93121,x93121),x93122),x93124)),x93123)) % 14.98/14.67 [9611]~P71(x96111)+~P1(f862(f54(x96112),x96115))+~P1(f862(f54(x96112),x96114))+~E(f862(f862(f94(f932(x96112,a921)),x96114),x96115),f181(f932(x96112,a921)))+E(f862(f862(f74(x96111),f862(f862(f862(f58(x96111,x96112,f74(x96111)),x96113),f71(x96111)),x96114)),f862(f862(f862(f58(x96111,x96112,f74(x96111)),x96113),f71(x96111)),x96115)),f862(f862(f862(f58(x96111,x96112,f74(x96111)),x96113),f71(x96111)),f862(f862(f103(f932(x96112,a921)),x96114),x96115))) % 14.98/14.67 [9622]~P72(x96221)+~E(f862(x96223,f353(x96223,x96225,x96224,x96222,x96221)),f2(x96221))+~P1(f862(f54(x96222),x96224))+~P1(f862(f54(x96222),x96225))+E(f862(f862(f73(x96221),f862(f862(f8(x96222,x96221),x96223),x96224)),f862(f862(f8(x96222,x96221),x96223),x96225)),f862(f862(f8(x96222,x96221),x96223),f862(f862(f103(f932(x96222,a921)),x96224),x96225))) % 14.98/14.67 [9623]~P72(x96231)+~E(f862(x96233,f356(x96233,x96235,x96234,x96232,x96231)),f2(x96231))+~P1(f862(f54(x96232),x96234))+~P1(f862(f54(x96232),x96235))+E(f862(f862(f73(x96231),f862(f862(f8(x96232,x96231),x96233),x96234)),f862(f862(f8(x96232,x96231),x96233),x96235)),f862(f862(f8(x96232,x96231),x96233),f862(f862(f103(f932(x96232,a921)),x96234),x96235))) % 14.98/14.67 [9624]~P71(x96241)+~E(f862(x96243,f917(x96243,x96245,x96244,x96242,x96241)),f71(x96241))+~P1(f862(f54(x96242),x96244))+~P1(f862(f54(x96242),x96245))+E(f862(f862(f74(x96241),f862(f862(f11(x96242,x96241),x96243),x96244)),f862(f862(f11(x96242,x96241),x96243),x96245)),f862(f862(f11(x96242,x96241),x96243),f862(f862(f103(f932(x96242,a921)),x96244),x96245))) % 14.98/14.67 [9625]~P71(x96251)+~E(f862(x96253,f918(x96253,x96255,x96254,x96252,x96251)),f71(x96251))+~P1(f862(f54(x96252),x96254))+~P1(f862(f54(x96252),x96255))+E(f862(f862(f74(x96251),f862(f862(f11(x96252,x96251),x96253),x96254)),f862(f862(f11(x96252,x96251),x96253),x96255)),f862(f862(f11(x96252,x96251),x96253),f862(f862(f103(f932(x96252,a921)),x96254),x96255))) % 14.98/14.67 [9837]~P71(x98371)+~E(f862(x98373,f354(x98373,x98375,x98374,x98372,x98371)),f71(x98371))+~P1(f862(f54(x98372),x98374))+~P1(f862(f54(x98372),x98375))+E(f862(f862(f74(x98371),f862(f862(f862(f58(x98371,x98372,f74(x98371)),x98373),f71(x98371)),x98374)),f862(f862(f862(f58(x98371,x98372,f74(x98371)),x98373),f71(x98371)),x98375)),f862(f862(f862(f58(x98371,x98372,f74(x98371)),x98373),f71(x98371)),f862(f862(f103(f932(x98372,a921)),x98374),x98375))) % 14.98/14.67 [9948]~P72(x99482)+E(f862(f862(f8(x99481,x99482),x99483),x99484),f862(f862(f8(x99481,x99482),x99483),x99485))+~P1(f862(f54(x99481),x99485))+~P1(f862(f862(f227(f932(x99481,a921)),x99484),x99485))+P1(f862(f862(f321(x99481),f365(x99483,x99484,x99485,x99481,x99482)),f862(f862(f3(f932(x99481,a921)),x99485),x99484))) % 14.98/14.67 [9949]~P72(x99492)+E(f862(f862(f8(x99491,x99492),x99493),x99494),f862(f862(f8(x99491,x99492),x99493),x99495))+~P1(f862(f54(x99491),x99495))+~P1(f862(f862(f227(f932(x99491,a921)),x99494),x99495))+P1(f862(f862(f321(x99491),f366(x99493,x99494,x99495,x99491,x99492)),f862(f862(f3(f932(x99491,a921)),x99495),x99494))) % 14.98/14.67 [9950]~P71(x99502)+E(f862(f862(f11(x99501,x99502),x99503),x99504),f862(f862(f11(x99501,x99502),x99503),x99505))+~P1(f862(f54(x99501),x99505))+~P1(f862(f862(f227(f932(x99501,a921)),x99504),x99505))+P1(f862(f862(f321(x99501),f916(x99503,x99504,x99505,x99501,x99502)),f862(f862(f3(f932(x99501,a921)),x99505),x99504))) % 14.98/14.67 [9951]~P71(x99512)+E(f862(f862(f11(x99511,x99512),x99513),x99514),f862(f862(f11(x99511,x99512),x99513),x99515))+~P1(f862(f54(x99511),x99515))+~P1(f862(f862(f227(f932(x99511,a921)),x99514),x99515))+P1(f862(f862(f321(x99511),f330(x99513,x99514,x99515,x99511,x99512)),f862(f862(f3(f932(x99511,a921)),x99515),x99514))) % 14.98/14.67 [9969]~P72(x99691)+~P1(f862(f54(x99692),x99694))+~P1(f862(f54(x99692),x99695))+E(f862(f862(f73(x99691),f862(f862(f8(x99692,x99691),x99693),x99694)),f862(f862(f8(x99692,x99691),x99693),x99695)),f862(f862(f8(x99692,x99691),x99693),f862(f862(f103(f932(x99692,a921)),x99694),x99695)))+P1(f862(f862(f321(x99692),f353(x99693,x99695,x99694,x99692,x99691)),f862(f862(f94(f932(x99692,a921)),x99694),x99695))) % 14.98/14.67 [9970]~P72(x99701)+~P1(f862(f54(x99702),x99704))+~P1(f862(f54(x99702),x99705))+E(f862(f862(f73(x99701),f862(f862(f8(x99702,x99701),x99703),x99704)),f862(f862(f8(x99702,x99701),x99703),x99705)),f862(f862(f8(x99702,x99701),x99703),f862(f862(f103(f932(x99702,a921)),x99704),x99705)))+P1(f862(f862(f321(x99702),f356(x99703,x99705,x99704,x99702,x99701)),f862(f862(f94(f932(x99702,a921)),x99704),x99705))) % 14.98/14.67 [9971]~P71(x99711)+~P1(f862(f54(x99712),x99714))+~P1(f862(f54(x99712),x99715))+E(f862(f862(f74(x99711),f862(f862(f11(x99712,x99711),x99713),x99714)),f862(f862(f11(x99712,x99711),x99713),x99715)),f862(f862(f11(x99712,x99711),x99713),f862(f862(f103(f932(x99712,a921)),x99714),x99715)))+P1(f862(f862(f321(x99712),f917(x99713,x99715,x99714,x99712,x99711)),f862(f862(f94(f932(x99712,a921)),x99714),x99715))) % 14.98/14.67 [9972]~P71(x99721)+~P1(f862(f54(x99722),x99724))+~P1(f862(f54(x99722),x99725))+E(f862(f862(f74(x99721),f862(f862(f11(x99722,x99721),x99723),x99724)),f862(f862(f11(x99722,x99721),x99723),x99725)),f862(f862(f11(x99722,x99721),x99723),f862(f862(f103(f932(x99722,a921)),x99724),x99725)))+P1(f862(f862(f321(x99722),f918(x99723,x99725,x99724,x99722,x99721)),f862(f862(f94(f932(x99722,a921)),x99724),x99725))) % 14.98/14.67 [9979]~P87(x99795)+~P1(f862(f54(x99791),x99794))+P1(f862(f862(f227(x99795),f862(f862(f8(x99791,x99795),x99792),x99793)),f862(f862(f8(x99791,x99795),x99792),x99794)))+~P1(f862(f862(f227(f932(x99791,a921)),x99793),x99794))+P1(f862(f862(f321(x99791),f355(x99792,x99793,x99794,x99791,x99795)),f862(f862(f3(f932(x99791,a921)),x99794),x99793))) % 14.98/14.67 [10024]~P71(x100241)+~P1(f862(f54(x100242),x100244))+~P1(f862(f54(x100242),x100245))+E(f862(f862(f74(x100241),f862(f862(f862(f58(x100241,x100242,f74(x100241)),x100243),f71(x100241)),x100244)),f862(f862(f862(f58(x100241,x100242,f74(x100241)),x100243),f71(x100241)),x100245)),f862(f862(f862(f58(x100241,x100242,f74(x100241)),x100243),f71(x100241)),f862(f862(f103(f932(x100242,a921)),x100244),x100245)))+P1(f862(f862(f321(x100242),f354(x100243,x100245,x100244,x100242,x100241)),f862(f862(f94(f932(x100242,a921)),x100244),x100245))) % 14.98/14.67 [8977]~P16(x89771,x89774,x89775)+~P1(f862(f54(x89771),x89772))+E(f862(f862(f3(f932(x89771,a921)),x89772),f862(f862(f301(x89771),x89773),f181(f932(x89771,a921)))),f181(f932(x89771,a921)))+~P1(f862(f862(f321(x89771),x89773),x89772))+E(f862(f862(x89774,x89773),f862(x89775,f862(f862(f3(f932(x89771,a921)),x89772),f862(f862(f301(x89771),x89773),f181(f932(x89771,a921)))))),f862(x89775,x89772)) % 14.98/14.67 [9057]~P16(x90571,x90574,x90575)+~P1(f862(f54(x90571),x90573))+~P1(f862(f54(x90571),x90572))+E(f862(f862(f94(f932(x90571,a921)),x90572),x90573),f181(f932(x90571,a921)))+E(f862(f862(x90574,f862(x90575,f862(f862(f103(f932(x90571,a921)),x90572),x90573))),f862(x90575,f862(f862(f94(f932(x90571,a921)),x90572),x90573))),f862(f862(x90574,f862(x90575,x90572)),f862(x90575,x90573))) % 14.98/14.67 [9627]~P1(f862(f862(f227(a1),x96274),f2(a1)))+~P1(f862(f862(f228(a1),x96273),x96275))+P1(f862(f862(f227(a1),x96271),x96272))+~P1(f862(f862(f228(a1),x96273),x96274))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),f862(f862(f74(a1),x96273),x96272)),x96275)),f862(f862(f73(a1),f862(f862(f74(a1),x96273),x96271)),x96274))) % 14.98/14.67 [9629]~P1(f862(f862(f227(a1),f2(a1)),x96295))+P1(f862(f862(f227(a1),x96291),x96292))+~P1(f862(f862(f228(a1),x96293),x96294))+~P1(f862(f862(f228(a1),x96295),x96294))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),f862(f862(f74(a1),x96294),x96291)),x96295)),f862(f862(f73(a1),f862(f862(f74(a1),x96294),x96292)),x96293))) % 14.98/14.67 [9746]~P65(x97465)+E(f862(x97461,f367(x97461,x97462,x97463,x97464,x97465)),f2(x97465))+~P1(f862(f54(x97464),x97463))+~P1(f862(f54(x97464),x97462))+E(f862(f862(f281(x97465),f862(f862(f74(x97465),f862(f862(f11(x97464,x97465),x97461),x97463)),f862(f862(f11(x97464,x97465),x97461),x97462))),f862(f862(f11(x97464,x97465),x97461),f862(f862(f94(f932(x97464,a921)),x97463),x97462))),f862(f862(f11(x97464,x97465),x97461),f862(f862(f103(f932(x97464,a921)),x97463),x97462))) % 14.98/14.67 [10016]~P65(x100161)+~P1(f862(f54(x100162),x100164))+~P1(f862(f54(x100162),x100165))+E(f862(f862(f281(x100161),f862(f862(f74(x100161),f862(f862(f11(x100162,x100161),x100163),x100164)),f862(f862(f11(x100162,x100161),x100163),x100165))),f862(f862(f11(x100162,x100161),x100163),f862(f862(f94(f932(x100162,a921)),x100164),x100165))),f862(f862(f11(x100162,x100161),x100163),f862(f862(f103(f932(x100162,a921)),x100164),x100165)))+P1(f862(f862(f321(x100162),f367(x100163,x100165,x100164,x100162,x100161)),f862(f862(f94(f932(x100162,a921)),x100164),x100165))) % 14.98/14.67 [9332]E(f862(f862(f127(x93321),x93322),x93323),f862(f862(f127(x93321),x93324),x93325))+~E(f862(f862(f168(x93321),f862(f182(f925(x93321)),x93324)),x93322),x93324)+~E(f862(f862(f168(x93321),f862(f182(f925(x93321)),x93322)),x93324),x93322)+~E(x93325,f862(f862(f127(x93321),f862(f862(f131(x93321),f862(f182(f925(x93321)),x93324)),x93322)),x93323))+~E(f862(f862(f127(x93321),f862(f862(f131(x93321),f862(f182(f925(x93321)),x93322)),x93324)),x93325),x93323) % 14.98/14.67 [9744]~P109(x97442)+E(f862(f862(f141(x97441,x97442,x97443),x97444),f163(x97441,x97444,x97445)),x97445)+~P11(x97442,f862(f862(f147(x97441,x97442),x97443),x97445))+~P1(f862(f862(f321(x97441),x97444),f862(f165(x97441),x97445)))+~E(f862(f134(x97441),f862(f129(x97441,f862(f862(f10(x97442,a921,x97441),f862(a317,f862(x97443,x97444))),x97443)),x97445)),x97444) % 14.98/14.67 [10080]~P69(x100801)+~P1(f862(f59(x100801,x100801,f74(x100801),x100802,x100803),x100805))+~P1(f862(f862(f321(x100801),x100804),x100803))+P1(f862(f862(f321(x100801),x100802),x100803))+P1(f862(f59(x100801,x100801,f74(x100801),x100804,f862(f862(f301(x100801),x100802),f862(f862(f3(f932(x100801,a921)),x100803),f862(f862(f301(x100801),x100804),f181(f932(x100801,a921)))))),x100805)) % 14.98/14.67 [7457]E(x74571,x74572)+~P22(x74574,x74575,x74573,x74576)+~E(f862(x74573,x74571),f862(x74573,x74572))+~P1(f862(f862(f321(x74574),x74572),x74576))+~P1(f862(f862(f321(x74574),x74571),x74576)) % 14.98/14.67 [6711]~P144(x67114)+E(x67111,x67112)+~E(x67115,x67116)+E(x67113,f2(x67114))+~E(f862(f862(f73(x67114),x67115),f862(f862(f74(x67114),x67113),x67111)),f862(f862(f73(x67114),x67116),f862(f862(f74(x67114),x67113),x67112))) % 14.98/14.67 [7745]~P3(x77451)+~P109(x77451)+~P1(f862(f862(f228(x77451),x77452),f862(x77455,x77456)))+~P1(f862(f862(f321(x77453),x77456),x77454))+P1(f862(f862(f228(x77451),x77452),f862(f862(f33(x77453,x77451),x77454),x77455))) % 14.98/14.67 [10076]~P22(x100762,x100761,x100763,x100764)+~P22(x100761,x100762,x100766,x100765)+P23(x100761,x100762,f830(x100763,x100764,x100765,x100766,x100762,x100761),x100765,x100764)+~P1(f862(f862(f227(f932(x100762,a921)),f862(f302(x100761,x100762,x100766),x100765)),x100764))+~P1(f862(f862(f227(f932(x100761,a921)),f862(f302(x100762,x100761,x100763),x100764)),x100765)) % 14.98/14.67 [8433]~P3(x84331)+~P109(x84331)+~P1(f862(f862(f228(x84331),f862(x84334,x84336)),x84335))+~P1(f862(f862(f321(x84332),x84336),x84333))+P1(f862(f862(f228(x84331),f862(f862(f32(x84332,x84331),x84333),x84334)),x84335)) % 14.98/14.67 [8688]~P17(x86882,x86885,x86886,x86881)+~P1(f862(f54(x86882),x86884))+~P1(f862(f54(x86882),x86883))+~E(f862(f862(f94(f932(x86882,a921)),x86883),x86884),f181(f932(x86882,a921)))+E(f862(x86881,f862(f862(f103(f932(x86882,a921)),x86883),x86884)),f862(f66(x86885,x86885,x86885,f862(x86881,x86883)),f862(x86881,x86884))) % 14.98/14.67 [10278]~P71(x102781)+~E(f820(x102784,x102785,x102783,x102786,x102782,x102781),f821(x102784,x102785,x102783,x102786,x102782,x102781))+~P1(f862(f54(x102782),x102786))+E(f862(f862(f862(f58(x102781,x102782,f74(x102781)),f862(f862(f10(f932(x102783,a921),x102781,x102782),f862(f862(f58(x102781,x102783,f74(x102781)),x102784),f71(x102781))),x102785)),f71(x102781)),x102786),f862(f862(f862(f58(x102781,x102783,f74(x102781)),x102784),f71(x102781)),f862(f862(f33(x102782,f932(x102783,a921)),x102786),x102785)))+P1(f862(f862(f321(x102782),f819(x102784,x102785,x102783,x102786,x102782,x102781)),x102786)) % 14.98/14.67 [10308]~P71(x103081)+~E(f820(x103084,x103085,x103083,x103086,x103082,x103081),f821(x103084,x103085,x103083,x103086,x103082,x103081))+~P1(f862(f54(x103082),x103086))+E(f862(f862(f862(f58(x103081,x103082,f74(x103081)),f862(f862(f10(f932(x103083,a921),x103081,x103082),f862(f862(f58(x103081,x103083,f74(x103081)),x103084),f71(x103081))),x103085)),f71(x103081)),x103086),f862(f862(f862(f58(x103081,x103083,f74(x103081)),x103084),f71(x103081)),f862(f862(f33(x103082,f932(x103083,a921)),x103086),x103085)))+~P1(f862(f54(x103083),f862(x103085,f819(x103084,x103085,x103083,x103086,x103082,x103081)))) % 14.98/14.67 [10311]~P71(x103111)+~P1(f862(f54(x103112),x103116))+E(f862(f862(f862(f58(x103111,x103112,f74(x103111)),f862(f862(f10(f932(x103113,a921),x103111,x103112),f862(f862(f58(x103111,x103113,f74(x103111)),x103114),f71(x103111))),x103115)),f71(x103111)),x103116),f862(f862(f862(f58(x103111,x103113,f74(x103111)),x103114),f71(x103111)),f862(f862(f33(x103112,f932(x103113,a921)),x103116),x103115)))+P1(f862(f862(f321(x103112),f819(x103114,x103115,x103113,x103116,x103112,x103111)),x103116))+P1(f862(f862(f321(x103112),f821(x103114,x103115,x103113,x103116,x103112,x103111)),x103116)) % 14.98/14.67 [10312]~P71(x103121)+~P1(f862(f54(x103122),x103126))+E(f862(f862(f862(f58(x103121,x103122,f74(x103121)),f862(f862(f10(f932(x103123,a921),x103121,x103122),f862(f862(f58(x103121,x103123,f74(x103121)),x103124),f71(x103121))),x103125)),f71(x103121)),x103126),f862(f862(f862(f58(x103121,x103123,f74(x103121)),x103124),f71(x103121)),f862(f862(f33(x103122,f932(x103123,a921)),x103126),x103125)))+P1(f862(f862(f321(x103122),f819(x103124,x103125,x103123,x103126,x103122,x103121)),x103126))+P1(f862(f862(f321(x103122),f820(x103124,x103125,x103123,x103126,x103122,x103121)),x103126)) % 14.98/14.67 [10331]~P71(x103311)+~P1(f862(f54(x103312),x103316))+E(f862(f862(f862(f58(x103311,x103312,f74(x103311)),f862(f862(f10(f932(x103313,a921),x103311,x103312),f862(f862(f58(x103311,x103313,f74(x103311)),x103314),f71(x103311))),x103315)),f71(x103311)),x103316),f862(f862(f862(f58(x103311,x103313,f74(x103311)),x103314),f71(x103311)),f862(f862(f33(x103312,f932(x103313,a921)),x103316),x103315)))+P1(f862(f862(f321(x103312),f821(x103314,x103315,x103313,x103316,x103312,x103311)),x103316))+~P1(f862(f54(x103313),f862(x103315,f819(x103314,x103315,x103313,x103316,x103312,x103311)))) % 14.98/14.67 [10332]~P71(x103321)+~P1(f862(f54(x103322),x103326))+E(f862(f862(f862(f58(x103321,x103322,f74(x103321)),f862(f862(f10(f932(x103323,a921),x103321,x103322),f862(f862(f58(x103321,x103323,f74(x103321)),x103324),f71(x103321))),x103325)),f71(x103321)),x103326),f862(f862(f862(f58(x103321,x103323,f74(x103321)),x103324),f71(x103321)),f862(f862(f33(x103322,f932(x103323,a921)),x103326),x103325)))+P1(f862(f862(f321(x103322),f820(x103324,x103325,x103323,x103326,x103322,x103321)),x103326))+~P1(f862(f54(x103323),f862(x103325,f819(x103324,x103325,x103323,x103326,x103322,x103321)))) % 14.98/14.67 [10343]~P71(x103431)+~E(f862(f862(f94(f932(x103433,a921)),f862(x103435,f821(x103434,x103435,x103433,x103436,x103432,x103431))),f862(x103435,f820(x103434,x103435,x103433,x103436,x103432,x103431))),f181(f932(x103433,a921)))+~P1(f862(f54(x103432),x103436))+E(f862(f862(f862(f58(x103431,x103432,f74(x103431)),f862(f862(f10(f932(x103433,a921),x103431,x103432),f862(f862(f58(x103431,x103433,f74(x103431)),x103434),f71(x103431))),x103435)),f71(x103431)),x103436),f862(f862(f862(f58(x103431,x103433,f74(x103431)),x103434),f71(x103431)),f862(f862(f33(x103432,f932(x103433,a921)),x103436),x103435)))+P1(f862(f862(f321(x103432),f819(x103434,x103435,x103433,x103436,x103432,x103431)),x103436)) % 14.98/14.67 [10354]~P71(x103541)+~E(f862(f862(f94(f932(x103543,a921)),f862(x103545,f821(x103544,x103545,x103543,x103546,x103542,x103541))),f862(x103545,f820(x103544,x103545,x103543,x103546,x103542,x103541))),f181(f932(x103543,a921)))+~P1(f862(f54(x103542),x103546))+E(f862(f862(f862(f58(x103541,x103542,f74(x103541)),f862(f862(f10(f932(x103543,a921),x103541,x103542),f862(f862(f58(x103541,x103543,f74(x103541)),x103544),f71(x103541))),x103545)),f71(x103541)),x103546),f862(f862(f862(f58(x103541,x103543,f74(x103541)),x103544),f71(x103541)),f862(f862(f33(x103542,f932(x103543,a921)),x103546),x103545)))+~P1(f862(f54(x103543),f862(x103545,f819(x103544,x103545,x103543,x103546,x103542,x103541)))) % 14.98/14.67 [9422]~P120(x94221)+~P118(x94221)+~P1(f862(f862(f278(x94221),x94222),x94225))+~P1(f862(f862(f278(x94221),x94222),f862(f862(f73(x94221),x94223),x94226)))+P1(f862(f862(f278(x94221),x94222),f862(f862(f73(x94221),f862(f862(f3(x94221),x94223),f862(f862(f74(x94221),x94224),x94225))),x94226))) % 14.98/14.67 [9616]~P120(x96161)+~P118(x96161)+~P1(f862(f862(f278(x96161),x96162),x96165))+P1(f862(f862(f278(x96161),x96162),f862(f862(f73(x96161),x96163),x96164)))+~P1(f862(f862(f278(x96161),x96162),f862(f862(f73(x96161),f862(f862(f3(x96161),x96163),f862(f862(f74(x96161),x96166),x96165))),x96164))) % 14.98/14.67 [9025]E(x90251,x90252)+~P54(x90254,x90255,x90256,x90253,x90257)+~E(f862(x90253,x90251),f862(x90253,x90252))+~P1(f862(f862(f321(x90255),x90252),x90257))+~P1(f862(f862(f321(x90255),x90251),x90257)) % 14.98/14.67 [10319]~P1(f862(x103192,x103194))+~E(x103195,f862(f129(x103191,x103192),x103197))+E(f862(f129(x103191,x103192),x103193),f862(f862(f144(x103191),x103194),x103195))+~E(x103193,f862(f862(f127(x103191),x103196),f862(f862(f144(x103191),x103194),x103197)))+P1(f862(x103192,f754(x103195,x103194,x103193,x103192,x103191,x103196,x103197))) % 14.98/14.67 [10320]~P1(f862(x103204,x103202))+~E(x103203,f862(f129(x103201,x103204),x103207))+E(f862(f862(f144(x103201),x103202),x103203),f862(f129(x103201,x103204),x103205))+~E(x103205,f862(f862(f127(x103201),x103206),f862(f862(f144(x103201),x103202),x103207)))+P1(f862(x103204,f755(x103205,x103204,x103203,x103202,x103201,x103206,x103207))) % 14.98/14.67 [10370]~P1(f862(x103702,x103704))+~E(x103705,f862(f129(x103701,x103702),x103707))+E(f862(f129(x103701,x103702),x103703),f862(f862(f144(x103701),x103704),x103705))+~E(x103703,f862(f862(f127(x103701),x103706),f862(f862(f144(x103701),x103704),x103707)))+P1(f862(f862(f321(x103701),f754(x103705,x103704,x103703,x103702,x103701,x103706,x103707)),f862(f165(x103701),x103706))) % 14.98/14.67 [10371]~P1(f862(x103714,x103712))+~E(x103713,f862(f129(x103711,x103714),x103717))+E(f862(f862(f144(x103711),x103712),x103713),f862(f129(x103711,x103714),x103715))+~E(x103715,f862(f862(f127(x103711),x103716),f862(f862(f144(x103711),x103712),x103717)))+P1(f862(f862(f321(x103711),f755(x103715,x103714,x103713,x103712,x103711,x103716,x103717)),f862(f165(x103711),x103716))) % 14.98/14.67 [10375]~P6(x103751,x103757,x103756)+~P9(x103751,f932(x103755,a921),x103756,x103754)+P1(f862(f862(f321(x103751),f532(x103752,x103753,x103754,x103755,x103756,x103757,x103751)),x103757))+~P1(f862(f862(f321(f932(x103751,a921)),x103753),f862(f862(f53(x103751),x103757),x103756)))+P1(f862(f862(f321(f932(x103755,a921)),f862(f862(f33(x103751,f932(x103755,a921)),x103753),x103754)),x103752)) % 14.98/14.67 [10430]~P6(x104302,x104306,x104307)+~P9(x104302,f932(x104301,a921),x104307,x104304)+~P1(f862(f862(f321(f932(x104302,a921)),x104303),f862(f862(f53(x104302),x104306),x104307)))+~P1(f862(f862(f321(f932(x104301,a921)),f862(x104304,f532(x104305,x104303,x104304,x104301,x104307,x104306,x104302))),x104305))+P1(f862(f862(f321(f932(x104301,a921)),f862(f862(f33(x104302,f932(x104301,a921)),x104303),x104304)),x104305)) % 14.98/14.67 [8606]~P71(x86062)+~P22(x86061,x86065,x86068,x86064)+~E(x86063,f862(f66(x86065,x86062,x86061,x86066),x86068))+~E(x86067,f862(f302(x86061,x86065,x86068),x86064))+E(f862(f862(f11(x86061,x86062),x86063),x86064),f862(f862(f11(x86065,x86062),x86066),x86067)) % 14.98/14.67 [10434]~P71(x104342)+~P22(x104345,x104341,x104348,x104347)+~E(f862(x104346,f605(x104343,x104346,x104344,x104347,x104348,x104341,x104345,x104342)),f862(f862(f66(x104341,x104342,x104345,x104343),x104348),f605(x104343,x104346,x104344,x104347,x104348,x104341,x104345,x104342)))+~E(x104344,f862(f302(x104345,x104341,x104348),x104347))+E(f862(f862(f11(x104341,x104342),x104343),x104344),f862(f862(f11(x104345,x104342),x104346),x104347)) % 14.98/14.67 [10437]~P72(x104372)+~P22(x104371,x104375,x104378,x104374)+~E(x104377,f862(f302(x104371,x104375,x104378),x104374))+E(f862(f862(f8(x104371,x104372),x104373),x104374),f862(f862(f8(x104375,x104372),x104376),x104377))+P1(f862(f862(f321(x104371),f619(x104376,x104373,x104377,x104374,x104378,x104375,x104371,x104372)),x104374)) % 14.98/14.67 [10438]~P71(x104382)+~P22(x104381,x104385,x104388,x104384)+~E(x104387,f862(f302(x104381,x104385,x104388),x104384))+E(f862(f862(f11(x104381,x104382),x104383),x104384),f862(f862(f11(x104385,x104382),x104386),x104387))+P1(f862(f862(f321(x104381),f605(x104386,x104383,x104387,x104384,x104388,x104385,x104381,x104382)),x104384)) % 14.98/14.67 [10443]~P72(x104432)+~P22(x104435,x104431,x104438,x104437)+~E(x104434,f862(f302(x104435,x104431,x104438),x104437))+~E(f862(x104436,f619(x104433,x104436,x104434,x104437,x104438,x104431,x104435,x104432)),f862(x104433,f862(x104438,f619(x104433,x104436,x104434,x104437,x104438,x104431,x104435,x104432))))+E(f862(f862(f8(x104431,x104432),x104433),x104434),f862(f862(f8(x104435,x104432),x104436),x104437)) % 14.98/14.67 [9911]~P21(x99116,x99112,x99115,x99117,x99118,x99111)+~P1(f862(f54(x99112),x99114))+~P1(f862(f54(x99112),x99113))+~E(f862(f862(f94(f932(x99112,a921)),x99113),x99114),f181(f932(x99112,a921)))+E(f862(x99111,f862(f862(f103(f932(x99112,a921)),x99113),x99114)),f862(f862(x99115,f862(x99111,x99113)),f862(x99111,x99114))) % 14.98/14.67 [10305]~P21(x103058,x103052,x103055,x103057,x103056,x103051)+~E(f862(x103056,f908(x103054,x103053,x103051,x103056,x103057,x103055,x103052)),x103057)+~P1(f862(f54(x103052),x103053))+~P1(f862(f54(x103052),x103054))+E(f862(x103051,f862(f862(f103(f932(x103052,a921)),x103053),x103054)),f862(f862(x103055,f862(x103051,x103053)),f862(x103051,x103054))) % 14.98/14.67 [10382]~P21(x103828,x103822,x103825,x103827,x103826,x103821)+~P1(f862(f54(x103822),x103823))+~P1(f862(f54(x103822),x103824))+E(f862(x103821,f862(f862(f103(f932(x103822,a921)),x103823),x103824)),f862(f862(x103825,f862(x103821,x103823)),f862(x103821,x103824)))+P1(f862(f862(f321(x103822),f908(x103824,x103823,x103821,x103826,x103827,x103825,x103822)),f862(f862(f94(f932(x103822,a921)),x103823),x103824))) % 14.98/14.67 [10067]~P6(x100674,x100678,x100675)+~P6(x100671,x100679,x100673)+~P10(x100671,x100674,f932(x100672,a921),x100673,x100675,x100677)+P9(x100671,f932(x100672,a921),x100673,f862(f862(f10(f932(x100674,f932(x100672,a921)),f932(x100672,a921),x100671),f862(f33(x100674,f932(x100672,a921)),f862(f276(x100674,x100674,x100675),f862(f862(f301(x100674),x100676),f181(f932(x100674,a921)))))),x100677))+~P1(f862(f862(f321(x100674),x100676),x100678)) % 14.98/14.67 [5604]~P109(x56043)+~P11(x56043,x56041)+E(x56041,f731(x56042,x56043))+~E(f862(f165(x56043),x56041),x56042)+~P1(f862(f54(x56043),x56042))+~P1(f862(f130(x56043),x56041)) % 14.98/14.67 [7448]P13(x74481,x74482)+~E(f862(x74482,f811(x74482)),f862(x74482,f813(x74482)))+~P1(f862(f862(x74482,f811(x74482)),f811(x74482)))+~P1(f862(f862(x74482,f811(x74482)),f813(x74482)))+~P1(f862(f862(x74482,f813(x74482)),f813(x74482)))+~P1(f862(f862(x74482,x74483),x74483)) % 14.98/14.67 [5227]~P133(x52272)+~P134(x52272)+~P145(x52272)+~P116(x52272)+E(x52271,f2(x52272))+~E(f862(f862(f236(x52272),x52271),x52273),f2(x52272)) % 14.98/14.67 [5228]~P133(x52282)+~P134(x52282)+~P145(x52282)+~P116(x52282)+~E(x52281,f2(a924))+~E(f862(f862(f236(x52282),x52283),x52281),f2(x52282)) % 14.98/14.67 [6693]~P87(x66931)+~E(x66933,f2(x66931))+~E(x66932,f2(x66931))+E(f862(f862(f73(x66931),x66932),x66933),f2(x66931))+~P1(f862(f862(f227(x66931),f2(x66931)),x66933))+~P1(f862(f862(f227(x66931),f2(x66931)),x66932)) % 14.98/14.67 [9095]~E(f862(f243(a924,a924),x90953),f2(a924))+~E(x90951,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x90953)),x90952)),f862(f248(a924,a924),x90953)))+P1(f862(f41(x90951,x90952),x90953))+~P1(f862(f862(f227(a924),f862(f248(a924,a924),x90953)),f2(a924)))+P1(f862(f862(f228(a924),f2(a924)),x90952))+~P1(f862(f862(f228(a924),x90952),f862(f248(a924,a924),x90953))) % 14.98/14.67 [9103]E(x91031,f2(a924))+~E(x91032,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x91033)),x91031)),f862(f248(a924,a924),x91033)))+P1(f862(f41(x91032,x91031),x91033))+~P1(f862(f862(f228(a924),f2(a924)),x91031))+~P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x91033)))+~P1(f862(f862(f228(a924),f862(f248(a924,a924),x91033)),x91031)) % 14.98/14.67 [9121]~E(f862(f243(a924,a924),x91213),f2(a924))+~E(x91211,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x91213)),x91212)),f862(f248(a924,a924),x91213)))+P1(f862(f41(x91211,x91212),x91213))+~P1(f862(f862(f228(a924),f2(a924)),x91212))+~P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x91213)))+~P1(f862(f862(f228(a924),f862(f248(a924,a924),x91213)),x91212)) % 14.98/14.67 [7073]~P93(x70732)+E(x70731,f181(f932(x70732,a921)))+E(x70733,f181(f932(x70732,a921)))+~P1(f862(f54(x70732),x70731))+~P1(f862(f54(x70732),x70733))+E(f12(x70732,f862(f862(f103(f932(x70732,a921)),x70733),x70731)),f862(f862(f94(x70732),f12(x70732,x70733)),f12(x70732,x70731))) % 14.98/14.67 [7074]~P93(x70742)+E(x70741,f181(f932(x70742,a921)))+E(x70743,f181(f932(x70742,a921)))+~P1(f862(f54(x70742),x70741))+~P1(f862(f54(x70742),x70743))+E(f15(x70742,f862(f862(f103(f932(x70742,a921)),x70743),x70741)),f862(f862(f103(x70742),f15(x70742,x70743)),f15(x70742,x70741))) % 14.98/14.67 [7075]~P109(x70752)+E(x70751,f181(f932(x70752,a921)))+E(x70753,f181(f932(x70752,a921)))+~P1(f862(f54(x70752),x70751))+~P1(f862(f54(x70752),x70753))+E(f16(x70752,f862(f862(f103(f932(x70752,a921)),x70753),x70751)),f862(f862(f225(x70752),f16(x70752,x70753)),f16(x70752,x70751))) % 14.98/14.67 [7076]~P109(x70762)+E(x70761,f181(f932(x70762,a921)))+E(x70763,f181(f932(x70762,a921)))+~P1(f862(f54(x70762),x70761))+~P1(f862(f54(x70762),x70763))+E(f17(x70762,f862(f862(f103(f932(x70762,a921)),x70763),x70761)),f862(f862(f226(x70762),f17(x70762,x70763)),f17(x70762,x70761))) % 14.98/14.67 [7719]~P100(x77192)+E(x77191,f181(f932(x77192,a921)))+E(x77193,f181(f932(x77192,a921)))+~P1(f862(f54(x77192),x77191))+~P1(f862(f54(x77192),x77193))+E(f862(f862(f74(x77192),f862(f56(x77192,f74(x77192)),x77193)),f862(f56(x77192,f74(x77192)),x77191)),f862(f56(x77192,f74(x77192)),f862(f862(f103(f932(x77192,a921)),x77193),x77191))) % 14.98/14.67 [7882]~P109(x78822)+E(x78821,f181(f932(x78822,a921)))+E(x78823,f181(f932(x78822,a921)))+~P1(f862(f54(x78822),x78821))+~P1(f862(f54(x78822),x78823))+E(f862(f862(f225(x78822),f13(x78822,f225(x78822),x78823)),f13(x78822,f225(x78822),x78821)),f13(x78822,f225(x78822),f862(f862(f103(f932(x78822,a921)),x78823),x78821))) % 14.98/14.67 [7883]~P109(x78832)+E(x78831,f181(f932(x78832,a921)))+E(x78833,f181(f932(x78832,a921)))+~P1(f862(f54(x78832),x78831))+~P1(f862(f54(x78832),x78833))+E(f862(f862(f226(x78832),f14(x78832,f226(x78832),x78833)),f14(x78832,f226(x78832),x78831)),f14(x78832,f226(x78832),f862(f862(f103(f932(x78832,a921)),x78833),x78831))) % 14.98/14.67 [8926]~P1(f862(x89261,x89263))+P1(f862(x89261,f392(x89261,x89262)))+P1(f862(x89261,f387(x89261,x89262)))+~P1(f862(f862(f228(a1),f2(a1)),x89262))+~P1(f862(f862(f321(a1),x89263),f296(a1,f71(a1),x89262)))+P1(f862(x89261,f862(f862(f3(a1),f387(x89261,x89262)),f862(f862(f74(a1),f389(x89261,x89262)),x89262)))) % 14.98/14.67 [9229]~P1(f862(x92291,x92293))+~P1(f862(x92291,f387(x92291,x92292)))+P1(f862(x92291,f392(x92291,x92292)))+~P1(f862(f862(f228(a1),f2(a1)),x92292))+~P1(f862(f862(f321(a1),x92293),f296(a1,f71(a1),x92292)))+~P1(f862(x92291,f862(f862(f3(a1),f387(x92291,x92292)),f862(f862(f74(a1),f389(x92291,x92292)),x92292)))) % 14.98/14.67 [10470]~P102(x104702)+E(x104701,f181(f932(x104702,a921)))+E(x104703,f181(f932(x104702,a921)))+~P1(f862(f54(x104702),x104701))+~P1(f862(f54(x104702),x104703))+E(f12(x104702,f862(f254(x104702),f862(f862(f10(f932(x104702,a921),a921,x104702),f80(x104702)),f862(f862(f10(f932(x104702,f932(x104702,a921)),f932(x104702,a921),x104702),f862(f10(f932(x104702,a921),a921,x104702),f80(x104702))),f862(f862(f9(x104702,f932(x104702,f932(x104702,a921)),f932(x104702,f932(x104702,a921))),f862(f862(f10(f932(x104702,f932(f932(x104702,a921),f932(x104702,a921))),f932(f932(x104702,f932(x104702,a921)),f932(x104702,f932(x104702,a921))),x104702),f20(x104702,f932(x104702,a921),f932(x104702,a921))),f862(f862(f10(f932(x104702,f932(x104702,f932(a921,a921))),f932(x104702,f932(f932(x104702,a921),f932(x104702,a921))),x104702),f862(f10(f932(x104702,f932(a921,a921)),f932(f932(x104702,a921),f932(x104702,a921)),x104702),f20(x104702,a921,a921))),f862(f862(f10(f932(x104702,f932(x104702,a921)),f932(x104702,f932(x104702,f932(a921,a921))),x104702),f862(f10(f932(x104702,a921),f932(x104702,f932(a921,a921)),x104702),f862(f10(a921,f932(a921,a921),x104702),a318))),f862(f862(f9(x104702,f932(x104702,f932(x104702,x104702)),f932(x104702,f932(x104702,a921))),f862(f862(f10(f932(f932(x104702,x104702),f932(x104702,a921)),f932(f932(x104702,f932(x104702,x104702)),f932(x104702,f932(x104702,a921))),x104702),f10(f932(x104702,x104702),f932(x104702,a921),x104702)),f862(f862(f10(f932(x104702,a921),f932(f932(x104702,x104702),f932(x104702,a921)),x104702),f10(x104702,a921,x104702)),a317))),f103(x104702)))))),f862(f862(f9(x104702,f932(x104702,a921),f932(x104702,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104702,a921),f932(x104702,a921)),x104702),f10(a921,a921,x104702)),f862(f862(f10(a921,f932(a921,a921),x104702),a318),f862(f862(f9(x104702,f932(x104702,a921),a921),f321(x104702)),x104703)))),f862(f862(f9(x104702,f932(x104702,a921),a921),f321(x104702)),x104701))))))),f862(f862(f103(x104702),f12(x104702,x104703)),f12(x104702,x104701))) % 14.98/14.67 [10471]~P102(x104712)+E(x104711,f181(f932(x104712,a921)))+E(x104713,f181(f932(x104712,a921)))+~P1(f862(f54(x104712),x104711))+~P1(f862(f54(x104712),x104713))+E(f15(x104712,f862(f254(x104712),f862(f862(f10(f932(x104712,a921),a921,x104712),f80(x104712)),f862(f862(f10(f932(x104712,f932(x104712,a921)),f932(x104712,a921),x104712),f862(f10(f932(x104712,a921),a921,x104712),f80(x104712))),f862(f862(f9(x104712,f932(x104712,f932(x104712,a921)),f932(x104712,f932(x104712,a921))),f862(f862(f10(f932(x104712,f932(f932(x104712,a921),f932(x104712,a921))),f932(f932(x104712,f932(x104712,a921)),f932(x104712,f932(x104712,a921))),x104712),f20(x104712,f932(x104712,a921),f932(x104712,a921))),f862(f862(f10(f932(x104712,f932(x104712,f932(a921,a921))),f932(x104712,f932(f932(x104712,a921),f932(x104712,a921))),x104712),f862(f10(f932(x104712,f932(a921,a921)),f932(f932(x104712,a921),f932(x104712,a921)),x104712),f20(x104712,a921,a921))),f862(f862(f10(f932(x104712,f932(x104712,a921)),f932(x104712,f932(x104712,f932(a921,a921))),x104712),f862(f10(f932(x104712,a921),f932(x104712,f932(a921,a921)),x104712),f862(f10(a921,f932(a921,a921),x104712),a318))),f862(f862(f9(x104712,f932(x104712,f932(x104712,x104712)),f932(x104712,f932(x104712,a921))),f862(f862(f10(f932(f932(x104712,x104712),f932(x104712,a921)),f932(f932(x104712,f932(x104712,x104712)),f932(x104712,f932(x104712,a921))),x104712),f10(f932(x104712,x104712),f932(x104712,a921),x104712)),f862(f862(f10(f932(x104712,a921),f932(f932(x104712,x104712),f932(x104712,a921)),x104712),f10(x104712,a921,x104712)),a317))),f94(x104712)))))),f862(f862(f9(x104712,f932(x104712,a921),f932(x104712,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104712,a921),f932(x104712,a921)),x104712),f10(a921,a921,x104712)),f862(f862(f10(a921,f932(a921,a921),x104712),a318),f862(f862(f9(x104712,f932(x104712,a921),a921),f321(x104712)),x104713)))),f862(f862(f9(x104712,f932(x104712,a921),a921),f321(x104712)),x104711))))))),f862(f862(f94(x104712),f15(x104712,x104713)),f15(x104712,x104711))) % 14.98/14.67 [10472]~P109(x104722)+E(x104721,f181(f932(x104722,a921)))+E(x104723,f181(f932(x104722,a921)))+~P1(f862(f54(x104722),x104721))+~P1(f862(f54(x104722),x104723))+E(f14(x104722,f226(x104722),f862(f254(x104722),f862(f862(f10(f932(x104722,a921),a921,x104722),f80(x104722)),f862(f862(f10(f932(x104722,f932(x104722,a921)),f932(x104722,a921),x104722),f862(f10(f932(x104722,a921),a921,x104722),f80(x104722))),f862(f862(f9(x104722,f932(x104722,f932(x104722,a921)),f932(x104722,f932(x104722,a921))),f862(f862(f10(f932(x104722,f932(f932(x104722,a921),f932(x104722,a921))),f932(f932(x104722,f932(x104722,a921)),f932(x104722,f932(x104722,a921))),x104722),f20(x104722,f932(x104722,a921),f932(x104722,a921))),f862(f862(f10(f932(x104722,f932(x104722,f932(a921,a921))),f932(x104722,f932(f932(x104722,a921),f932(x104722,a921))),x104722),f862(f10(f932(x104722,f932(a921,a921)),f932(f932(x104722,a921),f932(x104722,a921)),x104722),f20(x104722,a921,a921))),f862(f862(f10(f932(x104722,f932(x104722,a921)),f932(x104722,f932(x104722,f932(a921,a921))),x104722),f862(f10(f932(x104722,a921),f932(x104722,f932(a921,a921)),x104722),f862(f10(a921,f932(a921,a921),x104722),a318))),f862(f862(f9(x104722,f932(x104722,f932(x104722,x104722)),f932(x104722,f932(x104722,a921))),f862(f862(f10(f932(f932(x104722,x104722),f932(x104722,a921)),f932(f932(x104722,f932(x104722,x104722)),f932(x104722,f932(x104722,a921))),x104722),f10(f932(x104722,x104722),f932(x104722,a921),x104722)),f862(f862(f10(f932(x104722,a921),f932(f932(x104722,x104722),f932(x104722,a921)),x104722),f10(x104722,a921,x104722)),a317))),f225(x104722)))))),f862(f862(f9(x104722,f932(x104722,a921),f932(x104722,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104722,a921),f932(x104722,a921)),x104722),f10(a921,a921,x104722)),f862(f862(f10(a921,f932(a921,a921),x104722),a318),f862(f862(f9(x104722,f932(x104722,a921),a921),f321(x104722)),x104723)))),f862(f862(f9(x104722,f932(x104722,a921),a921),f321(x104722)),x104721))))))),f862(f862(f225(x104722),f14(x104722,f226(x104722),x104723)),f14(x104722,f226(x104722),x104721))) % 14.98/14.67 [10473]~P109(x104732)+E(x104731,f181(f932(x104732,a921)))+E(x104733,f181(f932(x104732,a921)))+~P1(f862(f54(x104732),x104731))+~P1(f862(f54(x104732),x104733))+E(f13(x104732,f225(x104732),f862(f254(x104732),f862(f862(f10(f932(x104732,a921),a921,x104732),f80(x104732)),f862(f862(f10(f932(x104732,f932(x104732,a921)),f932(x104732,a921),x104732),f862(f10(f932(x104732,a921),a921,x104732),f80(x104732))),f862(f862(f9(x104732,f932(x104732,f932(x104732,a921)),f932(x104732,f932(x104732,a921))),f862(f862(f10(f932(x104732,f932(f932(x104732,a921),f932(x104732,a921))),f932(f932(x104732,f932(x104732,a921)),f932(x104732,f932(x104732,a921))),x104732),f20(x104732,f932(x104732,a921),f932(x104732,a921))),f862(f862(f10(f932(x104732,f932(x104732,f932(a921,a921))),f932(x104732,f932(f932(x104732,a921),f932(x104732,a921))),x104732),f862(f10(f932(x104732,f932(a921,a921)),f932(f932(x104732,a921),f932(x104732,a921)),x104732),f20(x104732,a921,a921))),f862(f862(f10(f932(x104732,f932(x104732,a921)),f932(x104732,f932(x104732,f932(a921,a921))),x104732),f862(f10(f932(x104732,a921),f932(x104732,f932(a921,a921)),x104732),f862(f10(a921,f932(a921,a921),x104732),a318))),f862(f862(f9(x104732,f932(x104732,f932(x104732,x104732)),f932(x104732,f932(x104732,a921))),f862(f862(f10(f932(f932(x104732,x104732),f932(x104732,a921)),f932(f932(x104732,f932(x104732,x104732)),f932(x104732,f932(x104732,a921))),x104732),f10(f932(x104732,x104732),f932(x104732,a921),x104732)),f862(f862(f10(f932(x104732,a921),f932(f932(x104732,x104732),f932(x104732,a921)),x104732),f10(x104732,a921,x104732)),a317))),f226(x104732)))))),f862(f862(f9(x104732,f932(x104732,a921),f932(x104732,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104732,a921),f932(x104732,a921)),x104732),f10(a921,a921,x104732)),f862(f862(f10(a921,f932(a921,a921),x104732),a318),f862(f862(f9(x104732,f932(x104732,a921),a921),f321(x104732)),x104733)))),f862(f862(f9(x104732,f932(x104732,a921),a921),f321(x104732)),x104731))))))),f862(f862(f226(x104732),f13(x104732,f225(x104732),x104733)),f13(x104732,f225(x104732),x104731))) % 14.98/14.67 [7403]~P127(x74033)+E(x74031,x74032)+~E(f862(f862(f236(x74033),x74031),x74034),f862(f862(f236(x74033),x74032),x74034))+~P1(f862(f862(f227(x74033),f2(x74033)),x74032))+~P1(f862(f862(f227(x74033),f2(x74033)),x74031))+~P1(f862(f862(f228(a924),f2(a924)),x74034)) % 14.98/14.67 [7679]~P109(x76792)+E(x76791,f181(f932(x76792,a921)))+~P1(f862(f54(x76792),x76791))+~P1(f862(f862(f321(x76792),x76794),x76791))+P1(f862(f862(f227(x76792),x76793),x76794))+~P1(f862(f862(f227(x76792),x76793),f862(f56(x76792,f225(x76792)),x76791))) % 14.98/14.67 [7680]~P104(x76802)+E(x76801,f181(f932(x76802,a921)))+~P1(f862(f54(x76802),x76801))+~P1(f862(f862(f321(x76802),x76804),x76801))+P1(f862(f862(f227(x76802),x76803),x76804))+~P1(f862(f862(f227(x76802),x76803),f862(f56(x76802,f94(x76802)),x76801))) % 14.98/14.67 [7681]~P109(x76812)+E(x76811,f181(f932(x76812,a921)))+~P1(f862(f54(x76812),x76811))+~P1(f862(f862(f321(x76812),x76814),x76811))+P1(f862(f862(f228(x76812),x76813),x76814))+~P1(f862(f862(f228(x76812),x76813),f862(f56(x76812,f225(x76812)),x76811))) % 14.98/14.67 [7585]E(x75851,f2(a1))+E(f862(f862(f29(a1),x75852),x75851),x75853)+~P1(f862(f862(f227(a1),x75854),f2(a1)))+~E(x75852,f862(f862(f73(a1),f862(f862(f74(a1),x75851),x75853)),x75854))+P1(f862(f862(f228(a1),f2(a1)),x75851))+~P1(f862(f862(f228(a1),x75851),x75854)) % 14.98/14.67 [7603]E(f38(a1,x76032,x76031),x76033)+E(x76031,f2(a1))+~P1(f862(f862(f227(a1),x76033),f2(a1)))+~E(x76032,f862(f862(f73(a1),f862(f862(f74(a1),x76031),x76034)),x76033))+P1(f862(f862(f228(a1),f2(a1)),x76031))+~P1(f862(f862(f228(a1),x76031),x76033)) % 14.98/14.67 [7718]E(x77181,f2(a1))+E(f862(f862(f29(a1),x77182),x77181),x77183)+~E(x77182,f862(f862(f73(a1),f862(f862(f74(a1),x77181),x77183)),x77184))+~P1(f862(f862(f227(a1),f2(a1)),x77184))+~P1(f862(f862(f228(a1),f2(a1)),x77181))+~P1(f862(f862(f228(a1),x77184),x77181)) % 14.98/14.67 [7741]E(f38(a1,x77412,x77411),x77413)+E(x77411,f2(a1))+~E(x77412,f862(f862(f73(a1),f862(f862(f74(a1),x77411),x77414)),x77413))+~P1(f862(f862(f227(a1),f2(a1)),x77413))+~P1(f862(f862(f228(a1),f2(a1)),x77411))+~P1(f862(f862(f228(a1),x77413),x77411)) % 14.98/14.67 [7886]~P109(x78862)+E(x78861,f181(f932(x78862,a921)))+~P1(f862(f54(x78862),x78861))+~P1(f862(f862(f227(x78862),x78864),x78863))+~P1(f862(f862(f321(x78862),x78864),x78861))+P1(f862(f862(f227(x78862),f862(f56(x78862,f225(x78862)),x78861)),x78863)) % 14.98/14.67 [7887]~P109(x78872)+E(x78871,f181(f932(x78872,a921)))+~P1(f862(f54(x78872),x78871))+~P1(f862(f862(f228(x78872),x78874),x78873))+~P1(f862(f862(f321(x78872),x78874),x78871))+P1(f862(f862(f228(x78872),f862(f56(x78872,f225(x78872)),x78871)),x78873)) % 14.98/14.67 [8457]~P1(f862(f862(f227(a1),x84574),f2(a1)))+~E(x84571,f862(f862(f73(a1),f862(f862(f74(a1),x84572),x84573)),x84574))+~P1(f862(f862(f227(a1),f2(a1)),x84574))+~P1(f862(f862(f228(a1),x84574),x84572))+~P1(f862(f862(f228(a1),x84572),x84574))+P1(f862(f42(x84571,x84572),f862(f862(f244(a1,a1),x84573),x84574))) % 14.98/14.67 [8626]~P110(x86261)+P1(f862(f862(f228(f932(x86261,a921)),f296(x86261,x86262,x86263)),f296(x86261,x86264,x86265)))+~P1(f862(f862(f227(x86261),x86264),x86262))+~P1(f862(f862(f227(x86261),x86264),x86265))+~P1(f862(f862(f227(x86261),x86263),x86265))+~P1(f862(f862(f228(x86261),x86263),x86265)) % 14.98/14.67 [8627]~P110(x86271)+P1(f862(f862(f228(f932(x86271,a921)),f296(x86271,x86272,x86273)),f296(x86271,x86274,x86275)))+~P1(f862(f862(f227(x86271),x86273),x86275))+~P1(f862(f862(f227(x86271),x86274),x86275))+~P1(f862(f862(f227(x86271),x86274),x86272))+~P1(f862(f862(f228(x86271),x86274),x86272)) % 14.98/14.67 [9492]P56(x94922,x94923,x94924,x94921)+E(x94921,f181(f932(x94922,a921)))+~P1(f862(f54(x94922),x94924))+~P1(f862(f54(x94922),x94921))+~P1(f862(f862(x94923,f550(x94921,x94924,x94923,x94922)),x94925))+~P1(f862(f862(f321(x94922),x94925),x94921)) % 14.98/14.67 [9493]P56(x94932,x94933,x94934,x94931)+E(x94931,f181(f932(x94932,a921)))+~P1(f862(f54(x94932),x94934))+~P1(f862(f54(x94932),x94931))+~P1(f862(f862(x94933,f803(x94933,x94931,x94934,x94932)),x94935))+~P1(f862(f862(f321(x94932),x94935),x94931)) % 14.98/14.67 [9494]P56(x94942,x94943,x94944,x94941)+E(x94941,f181(f932(x94942,a921)))+~P1(f862(f54(x94942),x94944))+~P1(f862(f54(x94942),x94941))+~P1(f862(f862(x94943,f804(x94941,x94944,x94943,x94942)),x94945))+~P1(f862(f862(f321(x94942),x94945),x94941)) % 14.98/14.67 [9645]~E(x96453,x96455)+~P71(x96451)+~P72(x96451)+~P38(x96453)+E(f862(f862(f8(a1,x96451),x96452),x96453),f862(f862(f8(a1,x96451),x96454),x96455))+P1(f862(f862(f227(a1),f2(a1)),f549(x96452,x96454,x96453,x96455,x96451))) % 14.98/14.67 [9646]~E(x96463,x96465)+~P71(x96461)+~P72(x96461)+~P38(x96463)+E(f862(f862(f11(a1,x96461),x96462),x96463),f862(f862(f11(a1,x96461),x96464),x96465))+P1(f862(f862(f227(a1),f2(a1)),f514(x96462,x96464,x96463,x96465,x96461))) % 14.98/14.67 [9820]~E(x98205,x98203)+~P71(x98201)+~P72(x98201)+~P38(x98205)+~E(f862(x98202,f549(x98204,x98202,x98205,x98203,x98201)),f862(x98204,f549(x98204,x98202,x98205,x98203,x98201)))+E(f862(f862(f8(a1,x98201),x98202),x98203),f862(f862(f8(a1,x98201),x98204),x98205)) % 14.98/14.67 [9821]~E(x98215,x98213)+~P71(x98211)+~P72(x98211)+~P38(x98215)+~E(f862(x98212,f514(x98214,x98212,x98215,x98213,x98211)),f862(x98214,f514(x98214,x98212,x98215,x98213,x98211)))+E(f862(f862(f11(a1,x98211),x98212),x98213),f862(f862(f11(a1,x98211),x98214),x98215)) % 14.98/14.67 [9909]~P78(x99093)+E(f862(x99091,x99092),f2(x99093))+~E(f862(f862(f8(x99094,x99093),x99091),x99095),f2(x99093))+~P1(f862(f54(x99094),x99095))+P1(f862(f862(f321(x99094),f516(x99092,x99091,x99095,x99094,x99093)),x99095))+~P1(f862(f862(f321(x99094),x99092),x99095)) % 14.98/14.67 [10038]~P78(x100383)+E(f862(x100381,x100382),f2(x100383))+~E(f862(f862(f8(x100384,x100383),x100381),x100385),f2(x100383))+~P1(f862(f54(x100384),x100385))+~P1(f862(f862(f321(x100384),x100382),x100385))+~P1(f862(f862(f227(x100383),f2(x100383)),f862(x100381,f516(x100382,x100381,x100385,x100384,x100383)))) % 14.98/14.67 [8542]~P138(x85421)+~P1(f862(f862(f227(x85421),x85423),x85425))+~P1(f862(f862(f227(x85421),x85422),x85424))+~P1(f862(f862(f227(x85421),f2(x85421)),x85423))+~P1(f862(f862(f227(x85421),f2(x85421)),x85424))+P1(f862(f862(f227(x85421),f862(f862(f74(x85421),x85422),x85423)),f862(f862(f74(x85421),x85424),x85425))) % 14.98/14.67 [8543]~P138(x85431)+~P1(f862(f862(f227(x85431),x85433),x85435))+~P1(f862(f862(f227(x85431),x85432),x85434))+~P1(f862(f862(f227(x85431),f2(x85431)),x85433))+~P1(f862(f862(f227(x85431),f2(x85431)),x85432))+P1(f862(f862(f227(x85431),f862(f862(f74(x85431),x85432),x85433)),f862(f862(f74(x85431),x85434),x85435))) % 14.98/14.67 [8544]~P67(x85441)+~P1(f862(f862(f228(x85441),f2(x85441)),x85445))+~P1(f862(f862(f227(x85441),x85445),x85443))+~P1(f862(f862(f227(x85441),x85442),x85444))+~P1(f862(f862(f227(x85441),f2(x85441)),x85442))+P1(f862(f862(f227(x85441),f862(f862(f281(x85441),x85442),x85443)),f862(f862(f281(x85441),x85444),x85445))) % 14.98/14.67 [8545]~P135(x85451)+~P1(f862(f862(f227(x85451),x85453),x85455))+~P1(f862(f862(f227(x85451),f2(x85451)),x85452))+~P1(f862(f862(f228(x85451),x85452),x85454))+~P1(f862(f862(f228(x85451),f2(x85451)),x85453))+P1(f862(f862(f228(x85451),f862(f862(f74(x85451),x85452),x85453)),f862(f862(f74(x85451),x85454),x85455))) % 14.98/14.67 [8546]~P135(x85461)+~P1(f862(f862(f227(x85461),x85462),x85464))+~P1(f862(f862(f227(x85461),f2(x85461)),x85463))+~P1(f862(f862(f228(x85461),x85463),x85465))+~P1(f862(f862(f228(x85461),f2(x85461)),x85462))+P1(f862(f862(f228(x85461),f862(f862(f74(x85461),x85462),x85463)),f862(f862(f74(x85461),x85464),x85465))) % 14.98/14.67 [8547]~P135(x85471)+~P1(f862(f862(f227(x85471),f2(x85471)),x85473))+~P1(f862(f862(f227(x85471),f2(x85471)),x85472))+~P1(f862(f862(f228(x85471),x85473),x85475))+~P1(f862(f862(f228(x85471),x85472),x85474))+P1(f862(f862(f228(x85471),f862(f862(f74(x85471),x85472),x85473)),f862(f862(f74(x85471),x85474),x85475))) % 14.98/14.67 [8548]~P135(x85481)+~P1(f862(f862(f227(x85481),f2(x85481)),x85483))+~P1(f862(f862(f228(x85481),x85483),x85485))+~P1(f862(f862(f228(x85481),x85482),x85484))+~P1(f862(f862(f228(x85481),f2(x85481)),x85484))+P1(f862(f862(f228(x85481),f862(f862(f74(x85481),x85482),x85483)),f862(f862(f74(x85481),x85484),x85485))) % 14.98/14.67 [8549]~P67(x85491)+~P1(f862(f862(f227(x85491),x85495),x85493))+~P1(f862(f862(f227(x85491),f2(x85491)),x85492))+~P1(f862(f862(f228(x85491),x85492),x85494))+~P1(f862(f862(f228(x85491),f2(x85491)),x85495))+P1(f862(f862(f228(x85491),f862(f862(f281(x85491),x85492),x85493)),f862(f862(f281(x85491),x85494),x85495))) % 14.98/14.67 [8550]~P67(x85501)+~P1(f862(f862(f227(x85501),x85502),x85504))+~P1(f862(f862(f228(x85501),x85505),x85503))+~P1(f862(f862(f228(x85501),f2(x85501)),x85505))+~P1(f862(f862(f228(x85501),f2(x85501)),x85502))+P1(f862(f862(f228(x85501),f862(f862(f281(x85501),x85502),x85503)),f862(f862(f281(x85501),x85504),x85505))) % 14.98/14.67 [9952]~P72(x99525)+~P83(x99525)+E(x99521,f181(f932(x99522,a921)))+~P1(f862(f54(x99522),x99521))+P1(f862(f862(f321(x99522),f907(x99523,x99524,x99521,x99522,x99525)),x99521))+P1(f862(f862(f228(x99525),f862(f862(f8(x99522,x99525),x99524),x99521)),f862(f862(f8(x99522,x99525),x99523),x99521))) % 14.98/14.67 [10063]~P72(x100631)+~P85(x100631)+~P1(f862(f54(x100632),x100635))+~P1(f862(f862(f227(x100631),f2(x100631)),f862(x100633,f361(x100633,x100634,x100635,x100632,x100631))))+P1(f862(f862(f227(x100631),f862(f862(f8(x100632,x100631),x100633),x100634)),f862(f862(f8(x100632,x100631),x100633),x100635)))+~P1(f862(f862(f227(f932(x100632,a921)),x100634),x100635)) % 14.98/14.67 [10225]~P72(x102253)+~P83(x102253)+E(x102251,f181(f932(x102252,a921)))+~P1(f862(f54(x102252),x102251))+~P1(f862(f862(f228(x102253),f862(x102254,f907(x102255,x102254,x102251,x102252,x102253))),f862(x102255,f907(x102255,x102254,x102251,x102252,x102253))))+P1(f862(f862(f228(x102253),f862(f862(f8(x102252,x102253),x102254),x102251)),f862(f862(f8(x102252,x102253),x102255),x102251))) % 14.98/14.67 [7256]~P15(x72562,x72565,x72564)+E(x72561,f181(f932(x72562,a921)))+E(x72563,f181(f932(x72562,a921)))+~P1(f862(f54(x72562),x72561))+~P1(f862(f54(x72562),x72563))+E(f862(x72564,f862(f862(f103(f932(x72562,a921)),x72563),x72561)),f862(f862(x72565,f862(x72564,x72563)),f862(x72564,x72561))) % 14.98/14.67 [7852]~P149(x78521,x78524,x78523)+P1(f862(x78521,x78522))+~P1(f862(f862(f228(a1),x78524),f2(a1)))+~P1(f862(f862(f227(a1),x78525),f2(a1)))+~E(x78523,f862(f862(f73(a1),f862(f862(f74(a1),x78524),x78522)),x78525))+~P1(f862(f862(f228(a1),x78524),x78525)) % 14.98/14.67 [7853]~P148(x78531,x78534,x78533)+P1(f862(x78531,x78532))+~P1(f862(f862(f228(a1),x78534),f2(a1)))+~P1(f862(f862(f227(a1),x78532),f2(a1)))+~E(x78533,f862(f862(f73(a1),f862(f862(f74(a1),x78534),x78535)),x78532))+~P1(f862(f862(f228(a1),x78534),x78532)) % 14.98/14.67 [7895]~P149(x78951,x78954,x78953)+P1(f862(x78951,x78952))+~E(x78953,f862(f862(f73(a1),f862(f862(f74(a1),x78954),x78952)),x78955))+~P1(f862(f862(f227(a1),f2(a1)),x78955))+~P1(f862(f862(f228(a1),f2(a1)),x78954))+~P1(f862(f862(f228(a1),x78955),x78954)) % 14.98/14.67 [7896]~P148(x78961,x78964,x78963)+P1(f862(x78961,x78962))+~E(x78963,f862(f862(f73(a1),f862(f862(f74(a1),x78964),x78965)),x78962))+~P1(f862(f862(f227(a1),f2(a1)),x78962))+~P1(f862(f862(f228(a1),f2(a1)),x78964))+~P1(f862(f862(f228(a1),x78962),x78964)) % 14.98/14.67 [8838]P1(f862(f862(x88381,x88382),x88383))+~P1(f862(f862(x88381,f862(f862(f29(a1),x88384),x88385)),f38(a1,x88384,x88385)))+~P1(f862(f862(f228(a1),x88385),f2(a1)))+~P1(f862(f862(f227(a1),x88383),f2(a1)))+~E(x88384,f862(f862(f73(a1),f862(f862(f74(a1),x88385),x88382)),x88383))+~P1(f862(f862(f228(a1),x88385),x88383)) % 14.98/14.67 [8847]P1(f862(f862(x88471,x88472),x88473))+~P1(f862(f862(x88471,f862(f862(f29(a1),x88474),x88475)),f38(a1,x88474,x88475)))+~E(x88474,f862(f862(f73(a1),f862(f862(f74(a1),x88475),x88472)),x88473))+~P1(f862(f862(f227(a1),f2(a1)),x88473))+~P1(f862(f862(f228(a1),f2(a1)),x88475))+~P1(f862(f862(f228(a1),x88473),x88475)) % 14.98/14.67 [9111]E(x91111,x91112)+~P53(x91113,x91115,x91114)+~P1(f862(f862(f321(x91113),x91112),x91115))+~P1(f862(f862(f321(x91113),x91111),x91115))+P1(f862(f862(f321(f931(x91113,x91113)),f862(f862(f244(x91113,x91113),x91111),x91112)),x91114))+P1(f862(f862(f321(f931(x91113,x91113)),f862(f862(f244(x91113,x91113),x91112),x91111)),x91114)) % 14.98/14.67 [9980]~P72(x99805)+~P85(x99805)+~P1(f862(f54(x99801),x99804))+P1(f862(f862(f227(x99805),f862(f862(f8(x99801,x99805),x99802),x99803)),f862(f862(f8(x99801,x99805),x99802),x99804)))+~P1(f862(f862(f227(f932(x99801,a921)),x99803),x99804))+P1(f862(f862(f321(x99801),f361(x99802,x99803,x99804,x99801,x99805)),f862(f862(f3(f932(x99801,a921)),x99804),x99803))) % 14.98/14.67 [10071]E(x100711,f181(f932(x100712,a921)))+~P1(f862(f54(x100712),x100713))+~P1(f862(f54(x100712),x100711))+P1(f862(f862(f321(f931(f932(x100712,a921),f932(x100712,a921))),f862(f862(f244(f932(x100712,a921),f932(x100712,a921)),x100713),x100711)),f310(x100712,x100714)))+~P1(f862(f862(f321(x100712),x100715),x100711))+~P1(f862(f862(f321(f931(x100712,x100712)),f862(f862(f244(x100712,x100712),f559(x100714,x100711,x100713,x100712)),x100715)),x100714)) % 14.98/14.67 [10072]E(x100721,f181(f932(x100722,a921)))+~P1(f862(f54(x100722),x100723))+~P1(f862(f54(x100722),x100721))+P1(f862(f862(f321(f931(f932(x100722,a921),f932(x100722,a921))),f862(f862(f244(f932(x100722,a921),f932(x100722,a921)),x100723),x100721)),f310(x100722,x100724)))+~P1(f862(f862(f321(x100722),x100725),x100721))+~P1(f862(f862(f321(f931(x100722,x100722)),f862(f862(f244(x100722,x100722),f617(x100724,x100721,x100723,x100722)),x100725)),x100724)) % 14.98/14.67 [10229]~P78(x102291)+~E(f862(f862(f8(x102295,x102291),x102292),x102296),x102294)+~P1(f862(f54(x102295),x102296))+P1(f862(f862(f321(x102295),f520(x102293,x102294,x102292,x102296,x102295,x102291)),x102296))+P1(f862(f862(f227(x102291),f862(x102292,x102293)),x102294))+~P1(f862(f862(f321(x102295),x102293),x102296)) % 14.98/14.67 [10273]~P78(x102731)+~E(f862(f862(f8(x102735,x102731),x102732),x102736),x102734)+~P1(f862(f54(x102735),x102736))+~P1(f862(f862(f321(x102735),x102733),x102736))+~P1(f862(f862(f227(x102731),f2(x102731)),f862(x102732,f520(x102733,x102734,x102732,x102736,x102735,x102731))))+P1(f862(f862(f227(x102731),f862(x102732,x102733)),x102734)) % 14.98/14.67 [10417]~E(x104175,x104178)+~E(x104174,x104177)+~P108(x104171)+~P72(x104172)+E(f862(f862(f8(x104171,x104172),x104173),f862(f295(x104171,x104174),x104175)),f862(f862(f8(x104171,x104172),x104176),f862(f295(x104171,x104177),x104178)))+P1(f862(f862(f227(x104171),x104174),f911(x104173,x104176,x104175,x104178,x104174,x104177,x104171,x104172))) % 14.98/14.67 [10433]~E(x104337,x104334)+~E(x104338,x104335)+~P108(x104331)+~P72(x104332)+~E(f862(x104333,f911(x104336,x104333,x104338,x104335,x104337,x104334,x104331,x104332)),f862(x104336,f911(x104336,x104333,x104338,x104335,x104337,x104334,x104331,x104332)))+E(f862(f862(f8(x104331,x104332),x104333),f862(f295(x104331,x104334),x104335)),f862(f862(f8(x104331,x104332),x104336),f862(f295(x104331,x104337),x104338))) % 14.98/14.67 [10436]~E(x104364,x104367)+~E(x104365,x104368)+~P108(x104361)+~P72(x104362)+E(f862(f862(f8(x104361,x104362),x104363),f862(f295(x104361,x104364),x104365)),f862(f862(f8(x104361,x104362),x104366),f862(f295(x104361,x104367),x104368)))+P1(f862(f862(f228(x104361),f911(x104363,x104366,x104365,x104368,x104364,x104367,x104361,x104362)),x104365)) % 14.98/14.67 [10078]~P6(x100785,x100789,x100786)+~P6(x100781,x1007810,x100783)+~P10(x100781,x100785,f932(x100782,a921),x100783,x100786,x100788)+~P1(f862(f862(f321(x100785),x100787),x100789))+~P1(f862(f862(f321(x100781),x100784),x1007810))+E(f862(f862(f33(x100781,f932(x100782,a921)),f862(f276(x100781,x100781,x100783),f862(f862(f301(x100781),x100784),f181(f932(x100781,a921))))),f862(f862(f10(f932(x100785,f932(x100782,a921)),f932(x100782,a921),x100781),f862(f33(x100785,f932(x100782,a921)),f862(f276(x100785,x100785,x100786),f862(f862(f301(x100785),x100787),f181(f932(x100785,a921)))))),x100788)),f862(f862(x100788,x100784),x100787)) % 14.98/14.67 [5780]~P109(x57803)+~P11(x57803,x57802)+~P11(x57803,x57801)+E(x57801,x57802)+~E(f862(f165(x57803),x57801),f862(f165(x57803),x57802))+~P1(f862(f130(x57803),x57802))+~P1(f862(f130(x57803),x57801)) % 14.98/14.67 [5099]~P133(x50992)+~P134(x50992)+~P145(x50992)+~P116(x50992)+~E(x50993,f2(x50992))+E(x50991,f2(a924))+E(f862(f862(f236(x50992),x50993),x50991),f2(x50992)) % 14.98/14.67 [9368]E(x93681,f2(a924))+~E(x93682,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x93683)),x93681)),f862(f248(a924,a924),x93683)))+P1(f862(f41(x93682,x93681),x93683))+~P1(f862(f862(f227(a924),f862(f248(a924,a924),x93683)),f2(a924)))+~P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x93683)))+~P1(f862(f862(f228(a924),x93681),f862(f248(a924,a924),x93683)))+~P1(f862(f862(f228(a924),f862(f248(a924,a924),x93683)),x93681)) % 14.98/14.67 [9376]~E(f862(f243(a924,a924),x93763),f2(a924))+~E(x93761,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x93763)),x93762)),f862(f248(a924,a924),x93763)))+P1(f862(f41(x93761,x93762),x93763))+~P1(f862(f862(f227(a924),f862(f248(a924,a924),x93763)),f2(a924)))+~P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x93763)))+~P1(f862(f862(f228(a924),x93762),f862(f248(a924,a924),x93763)))+~P1(f862(f862(f228(a924),f862(f248(a924,a924),x93763)),x93762)) % 14.98/14.67 [8209]~P69(x82092)+E(x82091,f181(f932(x82092,a921)))+E(x82093,f181(f932(x82092,a921)))+~P1(f862(f54(x82092),x82091))+~P1(f862(f54(x82092),x82093))+~E(f862(f862(f94(f932(x82092,a921)),x82093),x82091),f181(f932(x82092,a921)))+E(f862(f862(f74(x82092),f862(f56(x82092,f74(x82092)),x82093)),f862(f56(x82092,f74(x82092)),x82091)),f862(f56(x82092,f74(x82092)),f862(f862(f103(f932(x82092,a921)),x82093),x82091))) % 14.98/14.67 [7989]E(x79891,f2(a1))+E(f862(f862(f29(a1),x79892),x79891),x79893)+~P1(f862(f862(f227(a1),x79894),f2(a1)))+~E(x79892,f862(f862(f73(a1),f862(f862(f74(a1),x79891),x79893)),x79894))+~P1(f862(f862(f227(a1),f2(a1)),x79894))+~P1(f862(f862(f228(a1),x79894),x79891))+~P1(f862(f862(f228(a1),x79891),x79894)) % 14.98/14.67 [7997]E(f38(a1,x79972,x79971),x79973)+E(x79971,f2(a1))+~P1(f862(f862(f227(a1),x79973),f2(a1)))+~E(x79972,f862(f862(f73(a1),f862(f862(f74(a1),x79971),x79974)),x79973))+~P1(f862(f862(f227(a1),f2(a1)),x79973))+~P1(f862(f862(f228(a1),x79973),x79971))+~P1(f862(f862(f228(a1),x79971),x79973)) % 14.98/14.67 [7040]~P61(x70402)+E(x70401,f2(x70402))+E(x70403,f2(x70402))+~E(f862(f862(f29(x70402),x70404),x70403),f862(f862(f29(x70402),x70405),x70401))+E(f862(f862(f74(x70402),x70404),x70401),f862(f862(f74(x70402),x70403),x70405))+~P1(f862(f862(f278(x70402),x70401),x70405))+~P1(f862(f862(f278(x70402),x70403),x70404)) % 14.98/14.67 [7041]~P61(x70412)+E(x70411,f2(x70412))+E(x70413,f2(x70412))+~E(f862(f862(f74(x70412),x70414),x70413),f862(f862(f74(x70412),x70411),x70415))+E(f862(f862(f29(x70412),x70414),x70411),f862(f862(f29(x70412),x70415),x70413))+~P1(f862(f862(f278(x70412),x70411),x70414))+~P1(f862(f862(f278(x70412),x70413),x70415)) % 14.98/14.67 [7904]~P16(x79042,x79045,x79044)+E(x79041,f181(f932(x79042,a921)))+E(x79043,f181(f932(x79042,a921)))+~P1(f862(f54(x79042),x79041))+~P1(f862(f54(x79042),x79043))+~E(f862(f862(f94(f932(x79042,a921)),x79043),x79041),f181(f932(x79042,a921)))+E(f862(x79044,f862(f862(f103(f932(x79042,a921)),x79043),x79041)),f862(f862(x79045,f862(x79044,x79043)),f862(x79044,x79041))) % 14.98/14.67 [9618]~P22(x96183,x96181,x96185,x96184)+~P22(x96181,x96183,x96186,x96182)+E(f862(f28(x96181),x96182),f862(f28(x96183),x96184))+~P1(f862(f54(x96183),x96184))+~P1(f862(f54(x96181),x96182))+~P1(f862(f862(f227(f932(x96183,a921)),f862(f302(x96181,x96183,x96186),x96182)),x96184))+~P1(f862(f862(f227(f932(x96181,a921)),f862(f302(x96183,x96181,x96185),x96184)),x96182)) % 14.98/14.67 [9558]~P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f74(a1),x95585),x95581)),x95586)),f2(a1)))+~E(f862(f862(f73(a1),f862(f862(f74(a1),x95583),x95582)),x95584),f862(f862(f73(a1),f862(f862(f74(a1),x95585),x95581)),x95586))+~P1(f862(f862(f227(a1),f2(a1)),x95586))+~P1(f862(f862(f228(a1),f2(a1)),x95585))+~P1(f862(f862(f227(a1),x95585),x95583))+~P1(f862(f862(f228(a1),x95584),x95583))+P1(f862(f862(f227(a1),x95581),x95582)) % 14.98/14.67 [9318]~E(f862(f862(f73(a1),f862(f862(f74(a1),x93183),x93181)),x93184),f862(f862(f73(a1),f862(f862(f74(a1),x93185),x93182)),x93186))+~P1(f862(f862(f227(a1),f2(a1)),x93184))+~P1(f862(f862(f228(a1),f2(a1)),x93185))+~P1(f862(f862(f227(a1),x93185),x93183))+~P1(f862(f862(f228(a1),x93186),x93185))+P1(f862(f862(f227(a1),x93181),x93182))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f862(f862(f74(a1),x93185),x93182)),x93186))) % 14.98/14.67 [9497]~P132(x94971)+~E(f862(f862(f73(x94971),x94972),x94974),f71(x94971))+~P1(f862(f862(f227(x94971),x94975),x94976))+~P1(f862(f862(f227(x94971),x94973),x94976))+~P1(f862(f862(f227(x94971),f2(x94971)),x94974))+~P1(f862(f862(f227(x94971),f2(x94971)),x94972))+P1(f862(f862(f227(x94971),f862(f862(f73(x94971),f862(f862(f74(x94971),x94972),x94973)),f862(f862(f74(x94971),x94974),x94975))),x94976)) % 14.98/14.67 [9498]~P130(x94981)+~E(f862(f862(f73(x94981),x94982),x94984),f71(x94981))+~P1(f862(f862(f227(x94981),f2(x94981)),x94984))+~P1(f862(f862(f227(x94981),f2(x94981)),x94982))+~P1(f862(f862(f228(x94981),x94985),x94986))+~P1(f862(f862(f228(x94981),x94983),x94986))+P1(f862(f862(f228(x94981),f862(f862(f73(x94981),f862(f862(f74(x94981),x94982),x94983)),f862(f862(f74(x94981),x94984),x94985))),x94986)) % 14.98/14.67 [10322]~P6(x103227,x103226,x103225)+E(x103221,x103222)+~P9(x103227,f932(x103224,a921),x103225,x103223)+E(f862(x103223,f530(x103221,x103222,x103223,x103224,x103225,x103226,x103227)),f862(x103223,f531(x103221,x103222,x103223,x103224,x103225,x103226,x103227)))+~E(f862(f862(f33(x103227,f932(x103224,a921)),x103221),x103223),f862(f862(f33(x103227,f932(x103224,a921)),x103222),x103223))+~P1(f862(f862(f321(f932(x103227,a921)),x103222),f862(f862(f53(x103227),x103226),x103225)))+~P1(f862(f862(f321(f932(x103227,a921)),x103221),f862(f862(f53(x103227),x103226),x103225))) % 14.98/14.67 [10373]~P6(x103733,x103737,x103736)+E(x103731,x103732)+~P9(x103733,f932(x103735,a921),x103736,x103734)+~E(f862(f862(f33(x103733,f932(x103735,a921)),x103731),x103734),f862(f862(f33(x103733,f932(x103735,a921)),x103732),x103734))+P1(f862(f862(f321(x103733),f531(x103731,x103732,x103734,x103735,x103736,x103737,x103733)),x103737))+~P1(f862(f862(f321(f932(x103733,a921)),x103732),f862(f862(f53(x103733),x103737),x103736)))+~P1(f862(f862(f321(f932(x103733,a921)),x103731),f862(f862(f53(x103733),x103737),x103736))) % 14.98/14.67 [10374]~P6(x103743,x103747,x103746)+E(x103741,x103742)+~P9(x103743,f932(x103745,a921),x103746,x103744)+~E(f862(f862(f33(x103743,f932(x103745,a921)),x103741),x103744),f862(f862(f33(x103743,f932(x103745,a921)),x103742),x103744))+P1(f862(f862(f321(x103743),f530(x103741,x103742,x103744,x103745,x103746,x103747,x103743)),x103747))+~P1(f862(f862(f321(f932(x103743,a921)),x103742),f862(f862(f53(x103743),x103747),x103746)))+~P1(f862(f862(f321(f932(x103743,a921)),x103741),f862(f862(f53(x103743),x103747),x103746))) % 14.98/14.67 [10452]E(x104521,x104522)+~P6(x104523,x104526,x104527)+~P9(x104523,f932(x104524,a921),x104527,x104525)+~E(f862(f862(f33(x104523,f932(x104524,a921)),x104521),x104525),f862(f862(f33(x104523,f932(x104524,a921)),x104522),x104525))+~P1(f862(f862(f321(f931(x104523,x104523)),f862(f862(f244(x104523,x104523),f531(x104521,x104522,x104525,x104524,x104527,x104526,x104523)),f530(x104521,x104522,x104525,x104524,x104527,x104526,x104523))),x104527))+~P1(f862(f862(f321(f932(x104523,a921)),x104522),f862(f862(f53(x104523),x104526),x104527)))+~P1(f862(f862(f321(f932(x104523,a921)),x104521),f862(f862(f53(x104523),x104526),x104527))) % 14.98/14.67 [9317]~P6(x93171,x93177,x93174)+~E(x93175,x93176)+~P1(f862(f862(f321(x93171),x93173),x93176))+~P1(f862(f862(f321(x93171),x93172),x93175))+~P1(f862(f862(f321(f932(x93171,a921)),x93176),f862(f862(f53(x93171),x93177),x93174)))+~P1(f862(f862(f321(f932(x93171,a921)),x93175),f862(f862(f53(x93171),x93177),x93174)))+P1(f862(f862(f321(f931(x93171,x93171)),f862(f862(f244(x93171,x93171),x93172),x93173)),x93174)) % 14.98/14.67 [9456]E(x94561,x94562)+~P6(x94563,x94564,x94565)+~P1(f862(f862(f321(x94563),x94566),x94562))+~P1(f862(f862(f321(x94563),x94567),x94561))+~P1(f862(f862(f321(f932(x94563,a921)),x94562),f862(f862(f53(x94563),x94564),x94565)))+~P1(f862(f862(f321(f932(x94563,a921)),x94561),f862(f862(f53(x94563),x94564),x94565)))+~P1(f862(f862(f321(f931(x94563,x94563)),f862(f862(f244(x94563,x94563),x94567),x94566)),x94565)) % 14.98/14.67 [10479]~P6(x104799,x104798,x104797)+~P6(x104791,x1047911,x1047910)+~P10(x104791,x104799,f932(x104796,a921),x1047910,x104797,x104795)+P1(f862(f862(f321(x104791),f533(x104792,x104793,x104794,x104795,x104796,x104797,x104798,x104799,x1047910,x1047911,x104791)),x1047911))+~P1(f862(f862(f321(f932(x104799,a921)),x104793),f862(f862(f53(x104799),x104798),x104797)))+~P1(f862(f862(f321(f932(x104791,a921)),x104794),f862(f862(f53(x104791),x1047911),x1047910)))+P1(f862(f862(f321(f932(x104796,a921)),f862(f862(f33(x104791,f932(x104796,a921)),x104794),f862(f862(f10(f932(x104799,f932(x104796,a921)),f932(x104796,a921),x104791),f862(f33(x104799,f932(x104796,a921)),x104793)),x104795))),x104792)) % 14.98/14.67 [10480]~P6(x1048011,x1048010,x104809)+~P6(x104801,x104808,x104807)+~P10(x1048011,x104801,f932(x104806,a921),x104809,x104807,x104805)+P1(f862(f862(f321(x104801),f534(x104802,x104803,x104804,x104805,x104806,x104807,x104808,x104801,x104809,x1048010,x1048011)),x104808))+~P1(f862(f862(f321(f932(x1048011,a921)),x104804),f862(f862(f53(x1048011),x1048010),x104809)))+~P1(f862(f862(f321(f932(x104801,a921)),x104803),f862(f862(f53(x104801),x104808),x104807)))+P1(f862(f862(f321(f932(x104806,a921)),f862(f862(f33(x1048011,f932(x104806,a921)),x104804),f862(f862(f10(f932(x104801,f932(x104806,a921)),f932(x104806,a921),x1048011),f862(f33(x104801,f932(x104806,a921)),x104803)),x104805))),x104802)) % 14.98/14.67 [10481]~P6(x104812,x104818,x104819)+~P6(x104814,x1048110,x1048111)+~P10(x104812,x104814,f932(x104811,a921),x104819,x1048111,x104816)+~P1(f862(f862(f321(f932(x104812,a921)),x104813),f862(f862(f53(x104812),x104818),x104819)))+~P1(f862(f862(f321(f932(x104814,a921)),x104815),f862(f862(f53(x104814),x1048110),x1048111)))+~P1(f862(f862(f321(f932(x104811,a921)),f862(f862(x104816,f533(x104817,x104815,x104813,x104816,x104811,x1048111,x1048110,x104814,x104819,x104818,x104812)),f534(x104817,x104815,x104813,x104816,x104811,x1048111,x1048110,x104814,x104819,x104818,x104812))),x104817))+P1(f862(f862(f321(f932(x104811,a921)),f862(f862(f33(x104812,f932(x104811,a921)),x104813),f862(f862(f10(f932(x104814,f932(x104811,a921)),f932(x104811,a921),x104812),f862(f33(x104814,f932(x104811,a921)),x104815)),x104816))),x104817)) % 14.98/14.67 [9354]E(x93541,x93542)+~P109(x93544)+~P22(x93543,x93544,x93545,f862(f862(f103(f932(x93543,a921)),f862(f165(x93543),x93541)),f862(f165(x93543),x93542)))+~E(f862(f165(x93543),x93541),f862(f165(x93543),x93542))+~P11(x93544,f862(f862(f147(x93543,x93544),x93545),x93542))+~P11(x93544,f862(f862(f147(x93543,x93544),x93545),x93541))+~P1(f862(f130(x93544),f862(f862(f147(x93543,x93544),x93545),x93542)))+~P1(f862(f130(x93544),f862(f862(f147(x93543,x93544),x93545),x93541))) % 14.98/14.67 %EqnAxiom % 14.98/14.67 [1]E(x11,x11) % 14.98/14.67 [2]E(x22,x21)+~E(x21,x22) % 14.98/14.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 14.98/14.67 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 14.98/14.67 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 14.98/14.67 [6]~E(x61,x62)+E(f93(x61),f93(x62)) % 14.98/14.67 [7]~E(x71,x72)+E(f181(x71),f181(x72)) % 14.98/14.67 [8]~E(x81,x82)+E(f862(x81,x83),f862(x82,x83)) % 14.98/14.67 [9]~E(x91,x92)+E(f862(x93,x91),f862(x93,x92)) % 14.98/14.67 [10]~E(x101,x102)+E(f94(x101),f94(x102)) % 14.98/14.67 [11]~E(x111,x112)+E(f225(x111),f225(x112)) % 14.98/14.67 [12]~E(x121,x122)+E(f103(x121),f103(x122)) % 14.98/14.67 [13]~E(x131,x132)+E(f226(x131),f226(x132)) % 14.98/14.67 [14]~E(x141,x142)+E(f95(x141),f95(x142)) % 14.98/14.67 [15]~E(x151,x152)+E(f25(x151),f25(x152)) % 14.98/14.67 [16]~E(x161,x162)+E(f77(x161),f77(x162)) % 14.98/14.67 [17]~E(x171,x172)+E(f165(x171),f165(x172)) % 14.98/14.67 [18]~E(x181,x182)+E(f56(x181,x183),f56(x182,x183)) % 14.98/14.67 [19]~E(x191,x192)+E(f56(x193,x191),f56(x193,x192)) % 14.98/14.67 [20]~E(x201,x202)+E(f227(x201),f227(x202)) % 14.98/14.67 [21]~E(x211,x212)+E(f71(x211),f71(x212)) % 14.98/14.67 [22]~E(x221,x222)+E(f534(x221,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f534(x222,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212)) % 14.98/14.67 [23]~E(x231,x232)+E(f534(x233,x231,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f534(x233,x232,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 14.98/14.67 [24]~E(x241,x242)+E(f534(x243,x244,x241,x245,x246,x247,x248,x249,x2410,x2411,x2412),f534(x243,x244,x242,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 14.98/14.67 [25]~E(x251,x252)+E(f534(x253,x254,x255,x251,x256,x257,x258,x259,x2510,x2511,x2512),f534(x253,x254,x255,x252,x256,x257,x258,x259,x2510,x2511,x2512)) % 14.98/14.67 [26]~E(x261,x262)+E(f534(x263,x264,x265,x266,x261,x267,x268,x269,x2610,x2611,x2612),f534(x263,x264,x265,x266,x262,x267,x268,x269,x2610,x2611,x2612)) % 14.98/14.67 [27]~E(x271,x272)+E(f534(x273,x274,x275,x276,x277,x271,x278,x279,x2710,x2711,x2712),f534(x273,x274,x275,x276,x277,x272,x278,x279,x2710,x2711,x2712)) % 14.98/14.67 [28]~E(x281,x282)+E(f534(x283,x284,x285,x286,x287,x288,x281,x289,x2810,x2811,x2812),f534(x283,x284,x285,x286,x287,x288,x282,x289,x2810,x2811,x2812)) % 14.98/14.67 [29]~E(x291,x292)+E(f534(x293,x294,x295,x296,x297,x298,x299,x291,x2910,x2911,x2912),f534(x293,x294,x295,x296,x297,x298,x299,x292,x2910,x2911,x2912)) % 14.98/14.67 [30]~E(x301,x302)+E(f534(x303,x304,x305,x306,x307,x308,x309,x3010,x301,x3011,x3012),f534(x303,x304,x305,x306,x307,x308,x309,x3010,x302,x3011,x3012)) % 14.98/14.67 [31]~E(x311,x312)+E(f534(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x311,x3112),f534(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x312,x3112)) % 14.98/14.67 [32]~E(x321,x322)+E(f534(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x321),f534(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x322)) % 14.98/14.67 [33]~E(x331,x332)+E(f932(x331,x333),f932(x332,x333)) % 14.98/14.67 [34]~E(x341,x342)+E(f932(x343,x341),f932(x343,x342)) % 14.98/14.67 [35]~E(x351,x352)+E(f6(x351),f6(x352)) % 14.98/14.67 [36]~E(x361,x362)+E(f533(x361,x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f533(x362,x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612)) % 14.98/14.67 [37]~E(x371,x372)+E(f533(x373,x371,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f533(x373,x372,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 14.98/14.67 [38]~E(x381,x382)+E(f533(x383,x384,x381,x385,x386,x387,x388,x389,x3810,x3811,x3812),f533(x383,x384,x382,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 14.98/14.67 [39]~E(x391,x392)+E(f533(x393,x394,x395,x391,x396,x397,x398,x399,x3910,x3911,x3912),f533(x393,x394,x395,x392,x396,x397,x398,x399,x3910,x3911,x3912)) % 14.98/14.67 [40]~E(x401,x402)+E(f533(x403,x404,x405,x406,x401,x407,x408,x409,x4010,x4011,x4012),f533(x403,x404,x405,x406,x402,x407,x408,x409,x4010,x4011,x4012)) % 14.98/14.67 [41]~E(x411,x412)+E(f533(x413,x414,x415,x416,x417,x411,x418,x419,x4110,x4111,x4112),f533(x413,x414,x415,x416,x417,x412,x418,x419,x4110,x4111,x4112)) % 14.98/14.67 [42]~E(x421,x422)+E(f533(x423,x424,x425,x426,x427,x428,x421,x429,x4210,x4211,x4212),f533(x423,x424,x425,x426,x427,x428,x422,x429,x4210,x4211,x4212)) % 14.98/14.67 [43]~E(x431,x432)+E(f533(x433,x434,x435,x436,x437,x438,x439,x431,x4310,x4311,x4312),f533(x433,x434,x435,x436,x437,x438,x439,x432,x4310,x4311,x4312)) % 14.98/14.67 [44]~E(x441,x442)+E(f533(x443,x444,x445,x446,x447,x448,x449,x4410,x441,x4411,x4412),f533(x443,x444,x445,x446,x447,x448,x449,x4410,x442,x4411,x4412)) % 14.98/14.67 [45]~E(x451,x452)+E(f533(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x451,x4512),f533(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x452,x4512)) % 14.98/14.67 [46]~E(x461,x462)+E(f533(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x4612,x461),f533(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x4612,x462)) % 14.98/14.67 [47]~E(x471,x472)+E(f321(x471),f321(x472)) % 14.98/14.67 [48]~E(x481,x482)+E(f104(x481),f104(x482)) % 14.98/14.67 [49]~E(x491,x492)+E(f122(x491),f122(x492)) % 14.98/14.67 [50]~E(x501,x502)+E(f923(x501),f923(x502)) % 14.98/14.67 [51]~E(x511,x512)+E(f928(x511),f928(x512)) % 14.98/14.67 [52]~E(x521,x522)+E(f925(x521),f925(x522)) % 14.98/14.67 [53]~E(x531,x532)+E(f926(x531),f926(x532)) % 14.98/14.67 [54]~E(x541,x542)+E(f443(x541,x543,x544,x545),f443(x542,x543,x544,x545)) % 14.98/14.67 [55]~E(x551,x552)+E(f443(x553,x551,x554,x555),f443(x553,x552,x554,x555)) % 14.98/14.67 [56]~E(x561,x562)+E(f443(x563,x564,x561,x565),f443(x563,x564,x562,x565)) % 14.98/14.67 [57]~E(x571,x572)+E(f443(x573,x574,x575,x571),f443(x573,x574,x575,x572)) % 14.98/14.67 [58]~E(x581,x582)+E(f74(x581),f74(x582)) % 14.98/14.67 [59]~E(x591,x592)+E(f54(x591),f54(x592)) % 14.98/14.67 [60]~E(x601,x602)+E(f182(x601),f182(x602)) % 14.98/14.67 [61]~E(x611,x612)+E(f72(x611),f72(x612)) % 14.98/14.67 [62]~E(x621,x622)+E(f10(x621,x623,x624),f10(x622,x623,x624)) % 14.98/14.67 [63]~E(x631,x632)+E(f10(x633,x631,x634),f10(x633,x632,x634)) % 14.98/14.67 [64]~E(x641,x642)+E(f10(x643,x644,x641),f10(x643,x644,x642)) % 14.98/14.67 [65]~E(x651,x652)+E(f96(x651),f96(x652)) % 14.98/14.67 [66]~E(x661,x662)+E(f157(x661),f157(x662)) % 14.98/14.67 [67]~E(x671,x672)+E(f164(x671),f164(x672)) % 14.98/14.67 [68]~E(x681,x682)+E(f147(x681,x683),f147(x682,x683)) % 14.98/14.67 [69]~E(x691,x692)+E(f147(x693,x691),f147(x693,x692)) % 14.98/14.67 [70]~E(x701,x702)+E(f73(x701),f73(x702)) % 14.98/14.67 [71]~E(x711,x712)+E(f31(x711,x713),f31(x712,x713)) % 14.98/14.67 [72]~E(x721,x722)+E(f31(x723,x721),f31(x723,x722)) % 14.98/14.67 [73]~E(x731,x732)+E(f144(x731),f144(x732)) % 14.98/14.67 [74]~E(x741,x742)+E(f228(x741),f228(x742)) % 14.98/14.67 [75]~E(x751,x752)+E(f9(x751,x753,x754),f9(x752,x753,x754)) % 14.98/14.67 [76]~E(x761,x762)+E(f9(x763,x761,x764),f9(x763,x762,x764)) % 14.98/14.67 [77]~E(x771,x772)+E(f9(x773,x774,x771),f9(x773,x774,x772)) % 14.98/14.67 [78]~E(x781,x782)+E(f813(x781),f813(x782)) % 14.98/14.67 [79]~E(x791,x792)+E(f416(x791,x793,x794),f416(x792,x793,x794)) % 14.98/14.67 [80]~E(x801,x802)+E(f416(x803,x801,x804),f416(x803,x802,x804)) % 14.98/14.67 [81]~E(x811,x812)+E(f416(x813,x814,x811),f416(x813,x814,x812)) % 14.98/14.67 [82]~E(x821,x822)+E(f299(x821,x823),f299(x822,x823)) % 14.98/14.67 [83]~E(x831,x832)+E(f299(x833,x831),f299(x833,x832)) % 14.98/14.67 [84]~E(x841,x842)+E(f29(x841),f29(x842)) % 14.98/14.67 [85]~E(x851,x852)+E(f106(x851),f106(x852)) % 14.98/14.67 [86]~E(x861,x862)+E(f243(x861,x863),f243(x862,x863)) % 14.98/14.67 [87]~E(x871,x872)+E(f243(x873,x871),f243(x873,x872)) % 14.98/14.67 [88]~E(x881,x882)+E(f301(x881),f301(x882)) % 14.98/14.67 [89]~E(x891,x892)+E(f53(x891),f53(x892)) % 14.98/14.67 [90]~E(x901,x902)+E(f121(x901,x903),f121(x902,x903)) % 14.98/14.67 [91]~E(x911,x912)+E(f121(x913,x911),f121(x913,x912)) % 14.98/14.67 [92]~E(x921,x922)+E(f20(x921,x923,x924),f20(x922,x923,x924)) % 14.98/14.67 [93]~E(x931,x932)+E(f20(x933,x931,x934),f20(x933,x932,x934)) % 14.98/14.67 [94]~E(x941,x942)+E(f20(x943,x944,x941),f20(x943,x944,x942)) % 14.98/14.67 [95]~E(x951,x952)+E(f931(x951,x953),f931(x952,x953)) % 14.98/14.67 [96]~E(x961,x962)+E(f931(x963,x961),f931(x963,x962)) % 14.98/14.67 [97]~E(x971,x972)+E(f254(x971),f254(x972)) % 14.98/14.67 [98]~E(x981,x982)+E(f131(x981),f131(x982)) % 14.98/14.67 [99]~E(x991,x992)+E(f266(x991,x993,x994),f266(x992,x993,x994)) % 14.98/14.67 [100]~E(x1001,x1002)+E(f266(x1003,x1001,x1004),f266(x1003,x1002,x1004)) % 14.98/14.67 [101]~E(x1011,x1012)+E(f266(x1013,x1014,x1011),f266(x1013,x1014,x1012)) % 14.98/14.67 [102]~E(x1021,x1022)+E(f302(x1021,x1023,x1024),f302(x1022,x1023,x1024)) % 14.98/14.67 [103]~E(x1031,x1032)+E(f302(x1033,x1031,x1034),f302(x1033,x1032,x1034)) % 14.98/14.67 [104]~E(x1041,x1042)+E(f302(x1043,x1044,x1041),f302(x1043,x1044,x1042)) % 14.98/14.67 [105]~E(x1051,x1052)+E(f109(x1051,x1053,x1054),f109(x1052,x1053,x1054)) % 14.98/14.67 [106]~E(x1061,x1062)+E(f109(x1063,x1061,x1064),f109(x1063,x1062,x1064)) % 14.98/14.67 [107]~E(x1071,x1072)+E(f109(x1073,x1074,x1071),f109(x1073,x1074,x1072)) % 14.98/14.67 [108]~E(x1081,x1082)+E(f158(x1081),f158(x1082)) % 14.98/14.67 [109]~E(x1091,x1092)+E(f437(x1091,x1093,x1094),f437(x1092,x1093,x1094)) % 14.98/14.67 [110]~E(x1101,x1102)+E(f437(x1103,x1101,x1104),f437(x1103,x1102,x1104)) % 14.98/14.67 [111]~E(x1111,x1112)+E(f437(x1113,x1114,x1111),f437(x1113,x1114,x1112)) % 14.98/14.67 [112]~E(x1121,x1122)+E(f81(x1121),f81(x1122)) % 14.98/14.67 [113]~E(x1131,x1132)+E(f187(x1131,x1133),f187(x1132,x1133)) % 14.98/14.67 [114]~E(x1141,x1142)+E(f187(x1143,x1141),f187(x1143,x1142)) % 14.98/14.67 [115]~E(x1151,x1152)+E(f278(x1151),f278(x1152)) % 14.98/14.67 [116]~E(x1161,x1162)+E(f80(x1161),f80(x1162)) % 14.98/14.67 [117]~E(x1171,x1172)+E(f244(x1171,x1173),f244(x1172,x1173)) % 14.98/14.67 [118]~E(x1181,x1182)+E(f244(x1183,x1181),f244(x1183,x1182)) % 14.98/14.67 [119]~E(x1191,x1192)+E(f33(x1191,x1193),f33(x1192,x1193)) % 14.98/14.67 [120]~E(x1201,x1202)+E(f33(x1203,x1201),f33(x1203,x1202)) % 14.98/14.67 [121]~E(x1211,x1212)+E(f8(x1211,x1213),f8(x1212,x1213)) % 14.98/14.67 [122]~E(x1221,x1222)+E(f8(x1223,x1221),f8(x1223,x1222)) % 14.98/14.67 [123]~E(x1231,x1232)+E(f127(x1231),f127(x1232)) % 14.98/14.67 [124]~E(x1241,x1242)+E(f66(x1241,x1243,x1244,x1245),f66(x1242,x1243,x1244,x1245)) % 14.98/14.67 [125]~E(x1251,x1252)+E(f66(x1253,x1251,x1254,x1255),f66(x1253,x1252,x1254,x1255)) % 14.98/14.67 [126]~E(x1261,x1262)+E(f66(x1263,x1264,x1261,x1265),f66(x1263,x1264,x1262,x1265)) % 14.98/14.67 [127]~E(x1271,x1272)+E(f66(x1273,x1274,x1275,x1271),f66(x1273,x1274,x1275,x1272)) % 14.98/14.67 [128]~E(x1281,x1282)+E(f30(x1281,x1283),f30(x1282,x1283)) % 14.98/14.67 [129]~E(x1291,x1292)+E(f30(x1293,x1291),f30(x1293,x1292)) % 14.98/14.67 [130]~E(x1301,x1302)+E(f32(x1301,x1303),f32(x1302,x1303)) % 14.98/14.67 [131]~E(x1311,x1312)+E(f32(x1313,x1311),f32(x1313,x1312)) % 14.98/14.67 [132]~E(x1321,x1322)+E(f611(x1321,x1323,x1324),f611(x1322,x1323,x1324)) % 14.98/14.67 [133]~E(x1331,x1332)+E(f611(x1333,x1331,x1334),f611(x1333,x1332,x1334)) % 14.98/14.67 [134]~E(x1341,x1342)+E(f611(x1343,x1344,x1341),f611(x1343,x1344,x1342)) % 14.98/14.67 [135]~E(x1351,x1352)+E(f150(x1351,x1353),f150(x1352,x1353)) % 14.98/14.67 [136]~E(x1361,x1362)+E(f150(x1363,x1361),f150(x1363,x1362)) % 14.98/14.67 [137]~E(x1371,x1372)+E(f98(x1371),f98(x1372)) % 14.98/14.67 [138]~E(x1381,x1382)+E(f99(x1381),f99(x1382)) % 14.98/14.67 [139]~E(x1391,x1392)+E(f320(x1391),f320(x1392)) % 14.98/14.67 [140]~E(x1401,x1402)+E(f292(x1401),f292(x1402)) % 14.98/14.67 [141]~E(x1411,x1412)+E(f587(x1411),f587(x1412)) % 14.98/14.67 [142]~E(x1421,x1422)+E(f790(x1421,x1423,x1424,x1425,x1426,x1427,x1428),f790(x1422,x1423,x1424,x1425,x1426,x1427,x1428)) % 14.98/14.67 [143]~E(x1431,x1432)+E(f790(x1433,x1431,x1434,x1435,x1436,x1437,x1438),f790(x1433,x1432,x1434,x1435,x1436,x1437,x1438)) % 14.98/14.67 [144]~E(x1441,x1442)+E(f790(x1443,x1444,x1441,x1445,x1446,x1447,x1448),f790(x1443,x1444,x1442,x1445,x1446,x1447,x1448)) % 14.98/14.67 [145]~E(x1451,x1452)+E(f790(x1453,x1454,x1455,x1451,x1456,x1457,x1458),f790(x1453,x1454,x1455,x1452,x1456,x1457,x1458)) % 14.98/14.67 [146]~E(x1461,x1462)+E(f790(x1463,x1464,x1465,x1466,x1461,x1467,x1468),f790(x1463,x1464,x1465,x1466,x1462,x1467,x1468)) % 14.98/14.67 [147]~E(x1471,x1472)+E(f790(x1473,x1474,x1475,x1476,x1477,x1471,x1478),f790(x1473,x1474,x1475,x1476,x1477,x1472,x1478)) % 14.98/14.67 [148]~E(x1481,x1482)+E(f790(x1483,x1484,x1485,x1486,x1487,x1488,x1481),f790(x1483,x1484,x1485,x1486,x1487,x1488,x1482)) % 14.98/14.67 [149]~E(x1491,x1492)+E(f249(x1491,x1493,x1494),f249(x1492,x1493,x1494)) % 14.98/14.67 [150]~E(x1501,x1502)+E(f249(x1503,x1501,x1504),f249(x1503,x1502,x1504)) % 14.98/14.67 [151]~E(x1511,x1512)+E(f249(x1513,x1514,x1511),f249(x1513,x1514,x1512)) % 14.98/14.67 [152]~E(x1521,x1522)+E(f233(x1521,x1523),f233(x1522,x1523)) % 14.98/14.67 [153]~E(x1531,x1532)+E(f233(x1533,x1531),f233(x1533,x1532)) % 14.98/14.67 [154]~E(x1541,x1542)+E(f169(x1541,x1543,x1544),f169(x1542,x1543,x1544)) % 14.98/14.67 [155]~E(x1551,x1552)+E(f169(x1553,x1551,x1554),f169(x1553,x1552,x1554)) % 14.98/14.67 [156]~E(x1561,x1562)+E(f169(x1563,x1564,x1561),f169(x1563,x1564,x1562)) % 14.98/14.67 [157]~E(x1571,x1572)+E(f296(x1571,x1573,x1574),f296(x1572,x1573,x1574)) % 14.98/14.67 [158]~E(x1581,x1582)+E(f296(x1583,x1581,x1584),f296(x1583,x1582,x1584)) % 14.98/14.67 [159]~E(x1591,x1592)+E(f296(x1593,x1594,x1591),f296(x1593,x1594,x1592)) % 14.98/14.67 [160]~E(x1601,x1602)+E(f38(x1601,x1603,x1604),f38(x1602,x1603,x1604)) % 14.98/14.67 [161]~E(x1611,x1612)+E(f38(x1613,x1611,x1614),f38(x1613,x1612,x1614)) % 14.98/14.67 [162]~E(x1621,x1622)+E(f38(x1623,x1624,x1621),f38(x1623,x1624,x1622)) % 14.98/14.67 [163]~E(x1631,x1632)+E(f930(x1631,x1633),f930(x1632,x1633)) % 14.98/14.67 [164]~E(x1641,x1642)+E(f930(x1643,x1641),f930(x1643,x1642)) % 14.98/14.67 [165]~E(x1651,x1652)+E(f170(x1651,x1653,x1654),f170(x1652,x1653,x1654)) % 14.98/14.67 [166]~E(x1661,x1662)+E(f170(x1663,x1661,x1664),f170(x1663,x1662,x1664)) % 14.98/14.67 [167]~E(x1671,x1672)+E(f170(x1673,x1674,x1671),f170(x1673,x1674,x1672)) % 14.98/14.67 [168]~E(x1681,x1682)+E(f499(x1681,x1683,x1684),f499(x1682,x1683,x1684)) % 14.98/14.67 [169]~E(x1691,x1692)+E(f499(x1693,x1691,x1694),f499(x1693,x1692,x1694)) % 14.98/14.67 [170]~E(x1701,x1702)+E(f499(x1703,x1704,x1701),f499(x1703,x1704,x1702)) % 14.98/14.67 [171]~E(x1711,x1712)+E(f7(x1711),f7(x1712)) % 14.98/14.67 [172]~E(x1721,x1722)+E(f135(x1721,x1723,x1724,x1725),f135(x1722,x1723,x1724,x1725)) % 14.98/14.67 [173]~E(x1731,x1732)+E(f135(x1733,x1731,x1734,x1735),f135(x1733,x1732,x1734,x1735)) % 14.98/14.67 [174]~E(x1741,x1742)+E(f135(x1743,x1744,x1741,x1745),f135(x1743,x1744,x1742,x1745)) % 14.98/14.67 [175]~E(x1751,x1752)+E(f135(x1753,x1754,x1755,x1751),f135(x1753,x1754,x1755,x1752)) % 14.98/14.67 [176]~E(x1761,x1762)+E(f313(x1761,x1763,x1764),f313(x1762,x1763,x1764)) % 14.98/14.67 [177]~E(x1771,x1772)+E(f313(x1773,x1771,x1774),f313(x1773,x1772,x1774)) % 14.98/14.67 [178]~E(x1781,x1782)+E(f313(x1783,x1784,x1781),f313(x1783,x1784,x1782)) % 14.98/14.67 [179]~E(x1791,x1792)+E(f88(x1791),f88(x1792)) % 14.98/14.67 [180]~E(x1801,x1802)+E(f13(x1801,x1803,x1804),f13(x1802,x1803,x1804)) % 14.98/14.67 [181]~E(x1811,x1812)+E(f13(x1813,x1811,x1814),f13(x1813,x1812,x1814)) % 14.98/14.67 [182]~E(x1821,x1822)+E(f13(x1823,x1824,x1821),f13(x1823,x1824,x1822)) % 14.98/14.67 [183]~E(x1831,x1832)+E(f749(x1831,x1833,x1834,x1835,x1836),f749(x1832,x1833,x1834,x1835,x1836)) % 14.98/14.67 [184]~E(x1841,x1842)+E(f749(x1843,x1841,x1844,x1845,x1846),f749(x1843,x1842,x1844,x1845,x1846)) % 14.98/14.67 [185]~E(x1851,x1852)+E(f749(x1853,x1854,x1851,x1855,x1856),f749(x1853,x1854,x1852,x1855,x1856)) % 14.98/14.67 [186]~E(x1861,x1862)+E(f749(x1863,x1864,x1865,x1861,x1866),f749(x1863,x1864,x1865,x1862,x1866)) % 14.98/14.67 [187]~E(x1871,x1872)+E(f749(x1873,x1874,x1875,x1876,x1871),f749(x1873,x1874,x1875,x1876,x1872)) % 14.98/14.67 [188]~E(x1881,x1882)+E(f735(x1881,x1883,x1884,x1885),f735(x1882,x1883,x1884,x1885)) % 14.98/14.67 [189]~E(x1891,x1892)+E(f735(x1893,x1891,x1894,x1895),f735(x1893,x1892,x1894,x1895)) % 14.98/14.67 [190]~E(x1901,x1902)+E(f735(x1903,x1904,x1901,x1905),f735(x1903,x1904,x1902,x1905)) % 14.98/14.67 [191]~E(x1911,x1912)+E(f735(x1913,x1914,x1915,x1911),f735(x1913,x1914,x1915,x1912)) % 14.98/14.67 [192]~E(x1921,x1922)+E(f632(x1921,x1923,x1924,x1925),f632(x1922,x1923,x1924,x1925)) % 14.98/14.67 [193]~E(x1931,x1932)+E(f632(x1933,x1931,x1934,x1935),f632(x1933,x1932,x1934,x1935)) % 14.98/14.67 [194]~E(x1941,x1942)+E(f632(x1943,x1944,x1941,x1945),f632(x1943,x1944,x1942,x1945)) % 14.98/14.67 [195]~E(x1951,x1952)+E(f632(x1953,x1954,x1955,x1951),f632(x1953,x1954,x1955,x1952)) % 14.98/14.67 [196]~E(x1961,x1962)+E(f130(x1961),f130(x1962)) % 14.98/14.67 [197]~E(x1971,x1972)+E(f524(x1971),f524(x1972)) % 14.98/14.67 [198]~E(x1981,x1982)+E(f68(x1981,x1983,x1984,x1985,x1986),f68(x1982,x1983,x1984,x1985,x1986)) % 14.98/14.67 [199]~E(x1991,x1992)+E(f68(x1993,x1991,x1994,x1995,x1996),f68(x1993,x1992,x1994,x1995,x1996)) % 14.98/14.67 [200]~E(x2001,x2002)+E(f68(x2003,x2004,x2001,x2005,x2006),f68(x2003,x2004,x2002,x2005,x2006)) % 14.98/14.67 [201]~E(x2011,x2012)+E(f68(x2013,x2014,x2015,x2011,x2016),f68(x2013,x2014,x2015,x2012,x2016)) % 14.98/14.67 [202]~E(x2021,x2022)+E(f68(x2023,x2024,x2025,x2026,x2021),f68(x2023,x2024,x2025,x2026,x2022)) % 14.98/14.67 [203]~E(x2031,x2032)+E(f295(x2031,x2033),f295(x2032,x2033)) % 14.98/14.67 [204]~E(x2041,x2042)+E(f295(x2043,x2041),f295(x2043,x2042)) % 14.98/14.67 [205]~E(x2051,x2052)+E(f307(x2051,x2053),f307(x2052,x2053)) % 14.98/14.67 [206]~E(x2061,x2062)+E(f307(x2063,x2061),f307(x2063,x2062)) % 14.98/14.67 [207]~E(x2071,x2072)+E(f738(x2071,x2073),f738(x2072,x2073)) % 14.98/14.67 [208]~E(x2081,x2082)+E(f738(x2083,x2081),f738(x2083,x2082)) % 14.98/14.67 [209]~E(x2091,x2092)+E(f287(x2091,x2093,x2094,x2095),f287(x2092,x2093,x2094,x2095)) % 14.98/14.67 [210]~E(x2101,x2102)+E(f287(x2103,x2101,x2104,x2105),f287(x2103,x2102,x2104,x2105)) % 14.98/14.67 [211]~E(x2111,x2112)+E(f287(x2113,x2114,x2111,x2115),f287(x2113,x2114,x2112,x2115)) % 14.98/14.67 [212]~E(x2121,x2122)+E(f287(x2123,x2124,x2125,x2121),f287(x2123,x2124,x2125,x2122)) % 14.98/14.67 [213]~E(x2131,x2132)+E(f346(x2131,x2133),f346(x2132,x2133)) % 14.98/14.67 [214]~E(x2141,x2142)+E(f346(x2143,x2141),f346(x2143,x2142)) % 14.98/14.67 [215]~E(x2151,x2152)+E(f422(x2151,x2153,x2154),f422(x2152,x2153,x2154)) % 14.98/14.67 [216]~E(x2161,x2162)+E(f422(x2163,x2161,x2164),f422(x2163,x2162,x2164)) % 14.98/14.67 [217]~E(x2171,x2172)+E(f422(x2173,x2174,x2171),f422(x2173,x2174,x2172)) % 14.98/14.67 [218]~E(x2181,x2182)+E(f773(x2181,x2183,x2184),f773(x2182,x2183,x2184)) % 14.98/14.67 [219]~E(x2191,x2192)+E(f773(x2193,x2191,x2194),f773(x2193,x2192,x2194)) % 14.98/14.67 [220]~E(x2201,x2202)+E(f773(x2203,x2204,x2201),f773(x2203,x2204,x2202)) % 14.98/14.67 [221]~E(x2211,x2212)+E(f176(x2211,x2213),f176(x2212,x2213)) % 14.98/14.67 [222]~E(x2221,x2222)+E(f176(x2223,x2221),f176(x2223,x2222)) % 14.98/14.67 [223]~E(x2231,x2232)+E(f161(x2231),f161(x2232)) % 14.98/14.67 [224]~E(x2241,x2242)+E(f129(x2241,x2243),f129(x2242,x2243)) % 14.98/14.67 [225]~E(x2251,x2252)+E(f129(x2253,x2251),f129(x2253,x2252)) % 14.98/14.67 [226]~E(x2261,x2262)+E(f289(x2261,x2263,x2264),f289(x2262,x2263,x2264)) % 14.98/14.67 [227]~E(x2271,x2272)+E(f289(x2273,x2271,x2274),f289(x2273,x2272,x2274)) % 14.98/14.67 [228]~E(x2281,x2282)+E(f289(x2283,x2284,x2281),f289(x2283,x2284,x2282)) % 14.98/14.67 [229]~E(x2291,x2292)+E(f236(x2291),f236(x2292)) % 14.98/14.67 [230]~E(x2301,x2302)+E(f69(x2301),f69(x2302)) % 14.98/14.67 [231]~E(x2311,x2312)+E(f42(x2311,x2313),f42(x2312,x2313)) % 14.98/14.67 [232]~E(x2321,x2322)+E(f42(x2323,x2321),f42(x2323,x2322)) % 14.98/14.67 [233]~E(x2331,x2332)+E(f280(x2331,x2333,x2334),f280(x2332,x2333,x2334)) % 14.98/14.67 [234]~E(x2341,x2342)+E(f280(x2343,x2341,x2344),f280(x2343,x2342,x2344)) % 14.98/14.67 [235]~E(x2351,x2352)+E(f280(x2353,x2354,x2351),f280(x2353,x2354,x2352)) % 14.98/14.67 [236]~E(x2361,x2362)+E(f120(x2361,x2363,x2364,x2365,x2366),f120(x2362,x2363,x2364,x2365,x2366)) % 14.98/14.67 [237]~E(x2371,x2372)+E(f120(x2373,x2371,x2374,x2375,x2376),f120(x2373,x2372,x2374,x2375,x2376)) % 14.98/14.67 [238]~E(x2381,x2382)+E(f120(x2383,x2384,x2381,x2385,x2386),f120(x2383,x2384,x2382,x2385,x2386)) % 14.98/14.67 [239]~E(x2391,x2392)+E(f120(x2393,x2394,x2395,x2391,x2396),f120(x2393,x2394,x2395,x2392,x2396)) % 14.98/14.67 [240]~E(x2401,x2402)+E(f120(x2403,x2404,x2405,x2406,x2401),f120(x2403,x2404,x2405,x2406,x2402)) % 14.98/14.67 [241]~E(x2411,x2412)+E(f11(x2411,x2413),f11(x2412,x2413)) % 14.98/14.67 [242]~E(x2421,x2422)+E(f11(x2423,x2421),f11(x2423,x2422)) % 14.98/14.67 [243]~E(x2431,x2432)+E(f530(x2431,x2433,x2434,x2435,x2436,x2437,x2438),f530(x2432,x2433,x2434,x2435,x2436,x2437,x2438)) % 14.98/14.67 [244]~E(x2441,x2442)+E(f530(x2443,x2441,x2444,x2445,x2446,x2447,x2448),f530(x2443,x2442,x2444,x2445,x2446,x2447,x2448)) % 14.98/14.67 [245]~E(x2451,x2452)+E(f530(x2453,x2454,x2451,x2455,x2456,x2457,x2458),f530(x2453,x2454,x2452,x2455,x2456,x2457,x2458)) % 14.98/14.67 [246]~E(x2461,x2462)+E(f530(x2463,x2464,x2465,x2461,x2466,x2467,x2468),f530(x2463,x2464,x2465,x2462,x2466,x2467,x2468)) % 14.98/14.67 [247]~E(x2471,x2472)+E(f530(x2473,x2474,x2475,x2476,x2471,x2477,x2478),f530(x2473,x2474,x2475,x2476,x2472,x2477,x2478)) % 14.98/14.67 [248]~E(x2481,x2482)+E(f530(x2483,x2484,x2485,x2486,x2487,x2481,x2488),f530(x2483,x2484,x2485,x2486,x2487,x2482,x2488)) % 14.98/14.67 [249]~E(x2491,x2492)+E(f530(x2493,x2494,x2495,x2496,x2497,x2498,x2491),f530(x2493,x2494,x2495,x2496,x2497,x2498,x2492)) % 14.98/14.67 [250]~E(x2501,x2502)+E(f75(x2501,x2503),f75(x2502,x2503)) % 14.98/14.67 [251]~E(x2511,x2512)+E(f75(x2513,x2511),f75(x2513,x2512)) % 14.98/14.67 [252]~E(x2521,x2522)+E(f132(x2521,x2523),f132(x2522,x2523)) % 14.98/14.67 [253]~E(x2531,x2532)+E(f132(x2533,x2531),f132(x2533,x2532)) % 14.98/14.67 [254]~E(x2541,x2542)+E(f248(x2541,x2543),f248(x2542,x2543)) % 14.98/14.67 [255]~E(x2551,x2552)+E(f248(x2553,x2551),f248(x2553,x2552)) % 14.98/14.67 [256]~E(x2561,x2562)+E(f281(x2561),f281(x2562)) % 14.98/14.67 [257]~E(x2571,x2572)+E(f40(x2571,x2573),f40(x2572,x2573)) % 14.98/14.67 [258]~E(x2581,x2582)+E(f40(x2583,x2581),f40(x2583,x2582)) % 14.98/14.67 [259]~E(x2591,x2592)+E(f153(x2591,x2593),f153(x2592,x2593)) % 14.98/14.67 [260]~E(x2601,x2602)+E(f153(x2603,x2601),f153(x2603,x2602)) % 14.98/14.67 [261]~E(x2611,x2612)+E(f107(x2611,x2613),f107(x2612,x2613)) % 14.98/14.67 [262]~E(x2621,x2622)+E(f107(x2623,x2621),f107(x2623,x2622)) % 14.98/14.67 [263]~E(x2631,x2632)+E(f140(x2631,x2633),f140(x2632,x2633)) % 14.98/14.67 [264]~E(x2641,x2642)+E(f140(x2643,x2641),f140(x2643,x2642)) % 14.98/14.67 [265]~E(x2651,x2652)+E(f536(x2651,x2653,x2654),f536(x2652,x2653,x2654)) % 14.98/14.67 [266]~E(x2661,x2662)+E(f536(x2663,x2661,x2664),f536(x2663,x2662,x2664)) % 14.98/14.67 [267]~E(x2671,x2672)+E(f536(x2673,x2674,x2671),f536(x2673,x2674,x2672)) % 14.98/14.67 [268]~E(x2681,x2682)+E(f145(x2681,x2683),f145(x2682,x2683)) % 14.98/14.67 [269]~E(x2691,x2692)+E(f145(x2693,x2691),f145(x2693,x2692)) % 14.98/14.67 [270]~E(x2701,x2702)+E(f160(x2701),f160(x2702)) % 14.98/14.67 [271]~E(x2711,x2712)+E(f184(x2711),f184(x2712)) % 14.98/14.67 [272]~E(x2721,x2722)+E(f654(x2721,x2723,x2724,x2725,x2726,x2727),f654(x2722,x2723,x2724,x2725,x2726,x2727)) % 14.98/14.67 [273]~E(x2731,x2732)+E(f654(x2733,x2731,x2734,x2735,x2736,x2737),f654(x2733,x2732,x2734,x2735,x2736,x2737)) % 14.98/14.67 [274]~E(x2741,x2742)+E(f654(x2743,x2744,x2741,x2745,x2746,x2747),f654(x2743,x2744,x2742,x2745,x2746,x2747)) % 14.98/14.67 [275]~E(x2751,x2752)+E(f654(x2753,x2754,x2755,x2751,x2756,x2757),f654(x2753,x2754,x2755,x2752,x2756,x2757)) % 14.98/14.67 [276]~E(x2761,x2762)+E(f654(x2763,x2764,x2765,x2766,x2761,x2767),f654(x2763,x2764,x2765,x2766,x2762,x2767)) % 14.98/14.67 [277]~E(x2771,x2772)+E(f654(x2773,x2774,x2775,x2776,x2777,x2771),f654(x2773,x2774,x2775,x2776,x2777,x2772)) % 14.98/14.67 [278]~E(x2781,x2782)+E(f108(x2781),f108(x2782)) % 14.98/14.67 [279]~E(x2791,x2792)+E(f276(x2791,x2793,x2794),f276(x2792,x2793,x2794)) % 14.98/14.67 [280]~E(x2801,x2802)+E(f276(x2803,x2801,x2804),f276(x2803,x2802,x2804)) % 14.98/14.67 [281]~E(x2811,x2812)+E(f276(x2813,x2814,x2811),f276(x2813,x2814,x2812)) % 14.98/14.67 [282]~E(x2821,x2822)+E(f79(x2821,x2823),f79(x2822,x2823)) % 14.98/14.67 [283]~E(x2831,x2832)+E(f79(x2833,x2831),f79(x2833,x2832)) % 14.98/14.67 [284]~E(x2841,x2842)+E(f929(x2841,x2843),f929(x2842,x2843)) % 14.98/14.67 [285]~E(x2851,x2852)+E(f929(x2853,x2851),f929(x2853,x2852)) % 14.98/14.67 [286]~E(x2861,x2862)+E(f151(x2861,x2863),f151(x2862,x2863)) % 14.98/14.67 [287]~E(x2871,x2872)+E(f151(x2873,x2871),f151(x2873,x2872)) % 14.98/14.67 [288]~E(x2881,x2882)+E(f872(x2881,x2883,x2884),f872(x2882,x2883,x2884)) % 14.98/14.67 [289]~E(x2891,x2892)+E(f872(x2893,x2891,x2894),f872(x2893,x2892,x2894)) % 14.98/14.67 [290]~E(x2901,x2902)+E(f872(x2903,x2904,x2901),f872(x2903,x2904,x2902)) % 14.98/14.67 [291]~E(x2911,x2912)+E(f246(x2911,x2913),f246(x2912,x2913)) % 14.98/14.67 [292]~E(x2921,x2922)+E(f246(x2923,x2921),f246(x2923,x2922)) % 14.98/14.67 [293]~E(x2931,x2932)+E(f48(x2931,x2933,x2934),f48(x2932,x2933,x2934)) % 14.98/14.67 [294]~E(x2941,x2942)+E(f48(x2943,x2941,x2944),f48(x2943,x2942,x2944)) % 14.98/14.67 [295]~E(x2951,x2952)+E(f48(x2953,x2954,x2951),f48(x2953,x2954,x2952)) % 14.98/14.67 [296]~E(x2961,x2962)+E(f308(x2961,x2963),f308(x2962,x2963)) % 14.98/14.67 [297]~E(x2971,x2972)+E(f308(x2973,x2971),f308(x2973,x2972)) % 14.98/14.67 [298]~E(x2981,x2982)+E(f702(x2981,x2983),f702(x2982,x2983)) % 14.98/14.67 [299]~E(x2991,x2992)+E(f702(x2993,x2991),f702(x2993,x2992)) % 14.98/14.67 [300]~E(x3001,x3002)+E(f873(x3001,x3003,x3004),f873(x3002,x3003,x3004)) % 14.98/14.67 [301]~E(x3011,x3012)+E(f873(x3013,x3011,x3014),f873(x3013,x3012,x3014)) % 14.98/14.67 [302]~E(x3021,x3022)+E(f873(x3023,x3024,x3021),f873(x3023,x3024,x3022)) % 14.98/14.67 [303]~E(x3031,x3032)+E(f174(x3031,x3033),f174(x3032,x3033)) % 14.98/14.67 [304]~E(x3041,x3042)+E(f174(x3043,x3041),f174(x3043,x3042)) % 14.98/14.67 [305]~E(x3051,x3052)+E(f753(x3051,x3053,x3054,x3055,x3056),f753(x3052,x3053,x3054,x3055,x3056)) % 14.98/14.67 [306]~E(x3061,x3062)+E(f753(x3063,x3061,x3064,x3065,x3066),f753(x3063,x3062,x3064,x3065,x3066)) % 14.98/14.67 [307]~E(x3071,x3072)+E(f753(x3073,x3074,x3071,x3075,x3076),f753(x3073,x3074,x3072,x3075,x3076)) % 14.98/14.67 [308]~E(x3081,x3082)+E(f753(x3083,x3084,x3085,x3081,x3086),f753(x3083,x3084,x3085,x3082,x3086)) % 14.98/14.67 [309]~E(x3091,x3092)+E(f753(x3093,x3094,x3095,x3096,x3091),f753(x3093,x3094,x3095,x3096,x3092)) % 14.98/14.67 [310]~E(x3101,x3102)+E(f234(x3101),f234(x3102)) % 14.98/14.67 [311]~E(x3111,x3112)+E(f152(x3111,x3113),f152(x3112,x3113)) % 14.98/14.67 [312]~E(x3121,x3122)+E(f152(x3123,x3121),f152(x3123,x3122)) % 14.98/14.67 [313]~E(x3131,x3132)+E(f335(x3131,x3133,x3134),f335(x3132,x3133,x3134)) % 14.98/14.67 [314]~E(x3141,x3142)+E(f335(x3143,x3141,x3144),f335(x3143,x3142,x3144)) % 14.98/14.67 [315]~E(x3151,x3152)+E(f335(x3153,x3154,x3151),f335(x3153,x3154,x3152)) % 14.98/14.67 [316]~E(x3161,x3162)+E(f729(x3161,x3163,x3164,x3165),f729(x3162,x3163,x3164,x3165)) % 14.98/14.67 [317]~E(x3171,x3172)+E(f729(x3173,x3171,x3174,x3175),f729(x3173,x3172,x3174,x3175)) % 14.98/14.67 [318]~E(x3181,x3182)+E(f729(x3183,x3184,x3181,x3185),f729(x3183,x3184,x3182,x3185)) % 14.98/14.67 [319]~E(x3191,x3192)+E(f729(x3193,x3194,x3195,x3191),f729(x3193,x3194,x3195,x3192)) % 14.98/14.67 [320]~E(x3201,x3202)+E(f43(x3201,x3203),f43(x3202,x3203)) % 14.98/14.67 [321]~E(x3211,x3212)+E(f43(x3213,x3211),f43(x3213,x3212)) % 14.98/14.67 [322]~E(x3221,x3222)+E(f41(x3221,x3223),f41(x3222,x3223)) % 14.98/14.67 [323]~E(x3231,x3232)+E(f41(x3233,x3231),f41(x3233,x3232)) % 14.98/14.67 [324]~E(x3241,x3242)+E(f84(x3241),f84(x3242)) % 14.98/14.67 [325]~E(x3251,x3252)+E(f28(x3251),f28(x3252)) % 14.98/14.67 [326]~E(x3261,x3262)+E(f342(x3261,x3263,x3264,x3265),f342(x3262,x3263,x3264,x3265)) % 14.98/14.67 [327]~E(x3271,x3272)+E(f342(x3273,x3271,x3274,x3275),f342(x3273,x3272,x3274,x3275)) % 14.98/14.67 [328]~E(x3281,x3282)+E(f342(x3283,x3284,x3281,x3285),f342(x3283,x3284,x3282,x3285)) % 14.98/14.67 [329]~E(x3291,x3292)+E(f342(x3293,x3294,x3295,x3291),f342(x3293,x3294,x3295,x3292)) % 14.98/14.67 [330]~E(x3301,x3302)+E(f49(x3301),f49(x3302)) % 14.98/14.67 [331]~E(x3311,x3312)+E(f142(x3311,x3313,x3314,x3315,x3316),f142(x3312,x3313,x3314,x3315,x3316)) % 14.98/14.67 [332]~E(x3321,x3322)+E(f142(x3323,x3321,x3324,x3325,x3326),f142(x3323,x3322,x3324,x3325,x3326)) % 14.98/14.67 [333]~E(x3331,x3332)+E(f142(x3333,x3334,x3331,x3335,x3336),f142(x3333,x3334,x3332,x3335,x3336)) % 14.98/14.67 [334]~E(x3341,x3342)+E(f142(x3343,x3344,x3345,x3341,x3346),f142(x3343,x3344,x3345,x3342,x3346)) % 14.98/14.67 [335]~E(x3351,x3352)+E(f142(x3353,x3354,x3355,x3356,x3351),f142(x3353,x3354,x3355,x3356,x3352)) % 14.98/14.67 [336]~E(x3361,x3362)+E(f310(x3361,x3363),f310(x3362,x3363)) % 14.98/14.67 [337]~E(x3371,x3372)+E(f310(x3373,x3371),f310(x3373,x3372)) % 14.98/14.67 [338]~E(x3381,x3382)+E(f15(x3381,x3383),f15(x3382,x3383)) % 14.98/14.67 [339]~E(x3391,x3392)+E(f15(x3393,x3391),f15(x3393,x3392)) % 14.98/14.67 [340]~E(x3401,x3402)+E(f312(x3401,x3403),f312(x3402,x3403)) % 14.98/14.67 [341]~E(x3411,x3412)+E(f312(x3413,x3411),f312(x3413,x3412)) % 14.98/14.67 [342]~E(x3421,x3422)+E(f168(x3421),f168(x3422)) % 14.98/14.67 [343]~E(x3431,x3432)+E(f293(x3431),f293(x3432)) % 14.98/14.67 [344]~E(x3441,x3442)+E(f60(x3441,x3443,x3444),f60(x3442,x3443,x3444)) % 14.98/14.67 [345]~E(x3451,x3452)+E(f60(x3453,x3451,x3454),f60(x3453,x3452,x3454)) % 14.98/14.67 [346]~E(x3461,x3462)+E(f60(x3463,x3464,x3461),f60(x3463,x3464,x3462)) % 14.98/14.67 [347]~E(x3471,x3472)+E(f16(x3471,x3473),f16(x3472,x3473)) % 14.98/14.67 [348]~E(x3481,x3482)+E(f16(x3483,x3481),f16(x3483,x3482)) % 14.98/14.67 [349]~E(x3491,x3492)+E(f102(x3491),f102(x3492)) % 14.98/14.67 [350]~E(x3501,x3502)+E(f14(x3501,x3503,x3504),f14(x3502,x3503,x3504)) % 14.98/14.67 [351]~E(x3511,x3512)+E(f14(x3513,x3511,x3514),f14(x3513,x3512,x3514)) % 14.98/14.67 [352]~E(x3521,x3522)+E(f14(x3523,x3524,x3521),f14(x3523,x3524,x3522)) % 14.98/14.67 [353]~E(x3531,x3532)+E(f431(x3531,x3533),f431(x3532,x3533)) % 14.98/14.67 [354]~E(x3541,x3542)+E(f431(x3543,x3541),f431(x3543,x3542)) % 14.98/14.67 [355]~E(x3551,x3552)+E(f666(x3551,x3553,x3554,x3555),f666(x3552,x3553,x3554,x3555)) % 14.98/14.67 [356]~E(x3561,x3562)+E(f666(x3563,x3561,x3564,x3565),f666(x3563,x3562,x3564,x3565)) % 14.98/14.67 [357]~E(x3571,x3572)+E(f666(x3573,x3574,x3571,x3575),f666(x3573,x3574,x3572,x3575)) % 14.98/14.67 [358]~E(x3581,x3582)+E(f666(x3583,x3584,x3585,x3581),f666(x3583,x3584,x3585,x3582)) % 14.98/14.67 [359]~E(x3591,x3592)+E(f171(x3591,x3593),f171(x3592,x3593)) % 14.98/14.67 [360]~E(x3601,x3602)+E(f171(x3603,x3601),f171(x3603,x3602)) % 14.98/14.67 [361]~E(x3611,x3612)+E(f482(x3611,x3613,x3614,x3615,x3616),f482(x3612,x3613,x3614,x3615,x3616)) % 14.98/14.67 [362]~E(x3621,x3622)+E(f482(x3623,x3621,x3624,x3625,x3626),f482(x3623,x3622,x3624,x3625,x3626)) % 14.98/14.67 [363]~E(x3631,x3632)+E(f482(x3633,x3634,x3631,x3635,x3636),f482(x3633,x3634,x3632,x3635,x3636)) % 14.98/14.67 [364]~E(x3641,x3642)+E(f482(x3643,x3644,x3645,x3641,x3646),f482(x3643,x3644,x3645,x3642,x3646)) % 14.98/14.67 [365]~E(x3651,x3652)+E(f482(x3653,x3654,x3655,x3656,x3651),f482(x3653,x3654,x3655,x3656,x3652)) % 14.98/14.67 [366]~E(x3661,x3662)+E(f78(x3661,x3663),f78(x3662,x3663)) % 14.98/14.67 [367]~E(x3671,x3672)+E(f78(x3673,x3671),f78(x3673,x3672)) % 14.98/14.67 [368]~E(x3681,x3682)+E(f297(x3681,x3683,x3684),f297(x3682,x3683,x3684)) % 14.98/14.67 [369]~E(x3691,x3692)+E(f297(x3693,x3691,x3694),f297(x3693,x3692,x3694)) % 14.98/14.67 [370]~E(x3701,x3702)+E(f297(x3703,x3704,x3701),f297(x3703,x3704,x3702)) % 14.98/14.67 [371]~E(x3711,x3712)+E(f398(x3711,x3713,x3714,x3715),f398(x3712,x3713,x3714,x3715)) % 14.98/14.67 [372]~E(x3721,x3722)+E(f398(x3723,x3721,x3724,x3725),f398(x3723,x3722,x3724,x3725)) % 14.98/14.67 [373]~E(x3731,x3732)+E(f398(x3733,x3734,x3731,x3735),f398(x3733,x3734,x3732,x3735)) % 14.98/14.67 [374]~E(x3741,x3742)+E(f398(x3743,x3744,x3745,x3741),f398(x3743,x3744,x3745,x3742)) % 14.98/14.67 [375]~E(x3751,x3752)+E(f137(x3751,x3753),f137(x3752,x3753)) % 14.98/14.67 [376]~E(x3761,x3762)+E(f137(x3763,x3761),f137(x3763,x3762)) % 14.98/14.67 [377]~E(x3771,x3772)+E(f112(x3771),f112(x3772)) % 14.98/14.67 [378]~E(x3781,x3782)+E(f113(x3781,x3783),f113(x3782,x3783)) % 14.98/14.67 [379]~E(x3791,x3792)+E(f113(x3793,x3791),f113(x3793,x3792)) % 14.98/14.67 [380]~E(x3801,x3802)+E(f695(x3801,x3803,x3804,x3805,x3806),f695(x3802,x3803,x3804,x3805,x3806)) % 14.98/14.67 [381]~E(x3811,x3812)+E(f695(x3813,x3811,x3814,x3815,x3816),f695(x3813,x3812,x3814,x3815,x3816)) % 14.98/14.67 [382]~E(x3821,x3822)+E(f695(x3823,x3824,x3821,x3825,x3826),f695(x3823,x3824,x3822,x3825,x3826)) % 14.98/14.67 [383]~E(x3831,x3832)+E(f695(x3833,x3834,x3835,x3831,x3836),f695(x3833,x3834,x3835,x3832,x3836)) % 14.98/14.67 [384]~E(x3841,x3842)+E(f695(x3843,x3844,x3845,x3846,x3841),f695(x3843,x3844,x3845,x3846,x3842)) % 14.98/14.67 [385]~E(x3851,x3852)+E(f118(x3851,x3853),f118(x3852,x3853)) % 14.98/14.67 [386]~E(x3861,x3862)+E(f118(x3863,x3861),f118(x3863,x3862)) % 14.98/14.67 [387]~E(x3871,x3872)+E(f535(x3871,x3873,x3874,x3875),f535(x3872,x3873,x3874,x3875)) % 14.98/14.67 [388]~E(x3881,x3882)+E(f535(x3883,x3881,x3884,x3885),f535(x3883,x3882,x3884,x3885)) % 14.98/14.67 [389]~E(x3891,x3892)+E(f535(x3893,x3894,x3891,x3895),f535(x3893,x3894,x3892,x3895)) % 14.98/14.67 [390]~E(x3901,x3902)+E(f535(x3903,x3904,x3905,x3901),f535(x3903,x3904,x3905,x3902)) % 14.98/14.67 [391]~E(x3911,x3912)+E(f737(x3911,x3913),f737(x3912,x3913)) % 14.98/14.67 [392]~E(x3921,x3922)+E(f737(x3923,x3921),f737(x3923,x3922)) % 14.98/14.67 [393]~E(x3931,x3932)+E(f36(x3931),f36(x3932)) % 14.98/14.67 [394]~E(x3941,x3942)+E(f242(x3941,x3943,x3944),f242(x3942,x3943,x3944)) % 14.98/14.67 [395]~E(x3951,x3952)+E(f242(x3953,x3951,x3954),f242(x3953,x3952,x3954)) % 14.98/14.67 [396]~E(x3961,x3962)+E(f242(x3963,x3964,x3961),f242(x3963,x3964,x3962)) % 14.98/14.67 [397]~E(x3971,x3972)+E(f83(x3971,x3973),f83(x3972,x3973)) % 14.98/14.67 [398]~E(x3981,x3982)+E(f83(x3983,x3981),f83(x3983,x3982)) % 14.98/14.67 [399]~E(x3991,x3992)+E(f867(x3991,x3993,x3994),f867(x3992,x3993,x3994)) % 14.98/14.67 [400]~E(x4001,x4002)+E(f867(x4003,x4001,x4004),f867(x4003,x4002,x4004)) % 14.98/14.67 [401]~E(x4011,x4012)+E(f867(x4013,x4014,x4011),f867(x4013,x4014,x4012)) % 14.98/14.67 [402]~E(x4021,x4022)+E(f146(x4021,x4023),f146(x4022,x4023)) % 14.98/14.67 [403]~E(x4031,x4032)+E(f146(x4033,x4031),f146(x4033,x4032)) % 14.98/14.67 [404]~E(x4041,x4042)+E(f255(x4041,x4043),f255(x4042,x4043)) % 14.98/14.67 [405]~E(x4051,x4052)+E(f255(x4053,x4051),f255(x4053,x4052)) % 14.98/14.67 [406]~E(x4061,x4062)+E(f718(x4061,x4063,x4064),f718(x4062,x4063,x4064)) % 14.98/14.67 [407]~E(x4071,x4072)+E(f718(x4073,x4071,x4074),f718(x4073,x4072,x4074)) % 14.98/14.67 [408]~E(x4081,x4082)+E(f718(x4083,x4084,x4081),f718(x4083,x4084,x4082)) % 14.98/14.67 [409]~E(x4091,x4092)+E(f250(x4091,x4093,x4094,x4095,x4096,x4097),f250(x4092,x4093,x4094,x4095,x4096,x4097)) % 14.98/14.67 [410]~E(x4101,x4102)+E(f250(x4103,x4101,x4104,x4105,x4106,x4107),f250(x4103,x4102,x4104,x4105,x4106,x4107)) % 14.98/14.67 [411]~E(x4111,x4112)+E(f250(x4113,x4114,x4111,x4115,x4116,x4117),f250(x4113,x4114,x4112,x4115,x4116,x4117)) % 14.98/14.67 [412]~E(x4121,x4122)+E(f250(x4123,x4124,x4125,x4121,x4126,x4127),f250(x4123,x4124,x4125,x4122,x4126,x4127)) % 14.98/14.67 [413]~E(x4131,x4132)+E(f250(x4133,x4134,x4135,x4136,x4131,x4137),f250(x4133,x4134,x4135,x4136,x4132,x4137)) % 14.98/14.67 [414]~E(x4141,x4142)+E(f250(x4143,x4144,x4145,x4146,x4147,x4141),f250(x4143,x4144,x4145,x4146,x4147,x4142)) % 14.98/14.67 [415]~E(x4151,x4152)+E(f784(x4151,x4153,x4154,x4155),f784(x4152,x4153,x4154,x4155)) % 14.98/14.67 [416]~E(x4161,x4162)+E(f784(x4163,x4161,x4164,x4165),f784(x4163,x4162,x4164,x4165)) % 14.98/14.67 [417]~E(x4171,x4172)+E(f784(x4173,x4174,x4171,x4175),f784(x4173,x4174,x4172,x4175)) % 14.98/14.67 [418]~E(x4181,x4182)+E(f784(x4183,x4184,x4185,x4181),f784(x4183,x4184,x4185,x4182)) % 14.98/14.67 [419]~E(x4191,x4192)+E(f12(x4191,x4193),f12(x4192,x4193)) % 14.98/14.67 [420]~E(x4201,x4202)+E(f12(x4203,x4201),f12(x4203,x4202)) % 14.98/14.67 [421]~E(x4211,x4212)+E(f787(x4211,x4213,x4214,x4215),f787(x4212,x4213,x4214,x4215)) % 14.98/14.67 [422]~E(x4221,x4222)+E(f787(x4223,x4221,x4224,x4225),f787(x4223,x4222,x4224,x4225)) % 14.98/14.67 [423]~E(x4231,x4232)+E(f787(x4233,x4234,x4231,x4235),f787(x4233,x4234,x4232,x4235)) % 14.98/14.67 [424]~E(x4241,x4242)+E(f787(x4243,x4244,x4245,x4241),f787(x4243,x4244,x4245,x4242)) % 14.98/14.67 [425]~E(x4251,x4252)+E(f440(x4251,x4253,x4254),f440(x4252,x4253,x4254)) % 14.98/14.67 [426]~E(x4261,x4262)+E(f440(x4263,x4261,x4264),f440(x4263,x4262,x4264)) % 14.98/14.67 [427]~E(x4271,x4272)+E(f440(x4273,x4274,x4271),f440(x4273,x4274,x4272)) % 14.98/14.67 [428]~E(x4281,x4282)+E(f163(x4281,x4283,x4284),f163(x4282,x4283,x4284)) % 14.98/14.67 [429]~E(x4291,x4292)+E(f163(x4293,x4291,x4294),f163(x4293,x4292,x4294)) % 14.98/14.67 [430]~E(x4301,x4302)+E(f163(x4303,x4304,x4301),f163(x4303,x4304,x4302)) % 14.98/14.67 [431]~E(x4311,x4312)+E(f376(x4311,x4313,x4314,x4315),f376(x4312,x4313,x4314,x4315)) % 14.98/14.67 [432]~E(x4321,x4322)+E(f376(x4323,x4321,x4324,x4325),f376(x4323,x4322,x4324,x4325)) % 14.98/14.67 [433]~E(x4331,x4332)+E(f376(x4333,x4334,x4331,x4335),f376(x4333,x4334,x4332,x4335)) % 14.98/14.67 [434]~E(x4341,x4342)+E(f376(x4343,x4344,x4345,x4341),f376(x4343,x4344,x4345,x4342)) % 14.98/14.67 [435]~E(x4351,x4352)+E(f762(x4351,x4353,x4354),f762(x4352,x4353,x4354)) % 14.98/14.67 [436]~E(x4361,x4362)+E(f762(x4363,x4361,x4364),f762(x4363,x4362,x4364)) % 14.98/14.67 [437]~E(x4371,x4372)+E(f762(x4373,x4374,x4371),f762(x4373,x4374,x4372)) % 14.98/14.67 [438]~E(x4381,x4382)+E(f521(x4381,x4383,x4384,x4385,x4386),f521(x4382,x4383,x4384,x4385,x4386)) % 14.98/14.67 [439]~E(x4391,x4392)+E(f521(x4393,x4391,x4394,x4395,x4396),f521(x4393,x4392,x4394,x4395,x4396)) % 14.98/14.67 [440]~E(x4401,x4402)+E(f521(x4403,x4404,x4401,x4405,x4406),f521(x4403,x4404,x4402,x4405,x4406)) % 14.98/14.67 [441]~E(x4411,x4412)+E(f521(x4413,x4414,x4415,x4411,x4416),f521(x4413,x4414,x4415,x4412,x4416)) % 14.98/14.67 [442]~E(x4421,x4422)+E(f521(x4423,x4424,x4425,x4426,x4421),f521(x4423,x4424,x4425,x4426,x4422)) % 14.98/14.67 [443]~E(x4431,x4432)+E(f235(x4431,x4433,x4434),f235(x4432,x4433,x4434)) % 14.98/14.67 [444]~E(x4441,x4442)+E(f235(x4443,x4441,x4444),f235(x4443,x4442,x4444)) % 14.98/14.67 [445]~E(x4451,x4452)+E(f235(x4453,x4454,x4451),f235(x4453,x4454,x4452)) % 14.98/14.67 [446]~E(x4461,x4462)+E(f504(x4461,x4463,x4464),f504(x4462,x4463,x4464)) % 14.98/14.67 [447]~E(x4471,x4472)+E(f504(x4473,x4471,x4474),f504(x4473,x4472,x4474)) % 14.98/14.67 [448]~E(x4481,x4482)+E(f504(x4483,x4484,x4481),f504(x4483,x4484,x4482)) % 14.98/14.67 [449]~E(x4491,x4492)+E(f908(x4491,x4493,x4494,x4495,x4496,x4497,x4498),f908(x4492,x4493,x4494,x4495,x4496,x4497,x4498)) % 14.98/14.67 [450]~E(x4501,x4502)+E(f908(x4503,x4501,x4504,x4505,x4506,x4507,x4508),f908(x4503,x4502,x4504,x4505,x4506,x4507,x4508)) % 14.98/14.67 [451]~E(x4511,x4512)+E(f908(x4513,x4514,x4511,x4515,x4516,x4517,x4518),f908(x4513,x4514,x4512,x4515,x4516,x4517,x4518)) % 14.98/14.67 [452]~E(x4521,x4522)+E(f908(x4523,x4524,x4525,x4521,x4526,x4527,x4528),f908(x4523,x4524,x4525,x4522,x4526,x4527,x4528)) % 14.98/14.67 [453]~E(x4531,x4532)+E(f908(x4533,x4534,x4535,x4536,x4531,x4537,x4538),f908(x4533,x4534,x4535,x4536,x4532,x4537,x4538)) % 14.98/14.67 [454]~E(x4541,x4542)+E(f908(x4543,x4544,x4545,x4546,x4547,x4541,x4548),f908(x4543,x4544,x4545,x4546,x4547,x4542,x4548)) % 14.98/14.67 [455]~E(x4551,x4552)+E(f908(x4553,x4554,x4555,x4556,x4557,x4558,x4551),f908(x4553,x4554,x4555,x4556,x4557,x4558,x4552)) % 14.98/14.67 [456]~E(x4561,x4562)+E(f802(x4561,x4563,x4564,x4565,x4566,x4567,x4568),f802(x4562,x4563,x4564,x4565,x4566,x4567,x4568)) % 14.98/14.67 [457]~E(x4571,x4572)+E(f802(x4573,x4571,x4574,x4575,x4576,x4577,x4578),f802(x4573,x4572,x4574,x4575,x4576,x4577,x4578)) % 14.98/14.67 [458]~E(x4581,x4582)+E(f802(x4583,x4584,x4581,x4585,x4586,x4587,x4588),f802(x4583,x4584,x4582,x4585,x4586,x4587,x4588)) % 14.98/14.67 [459]~E(x4591,x4592)+E(f802(x4593,x4594,x4595,x4591,x4596,x4597,x4598),f802(x4593,x4594,x4595,x4592,x4596,x4597,x4598)) % 14.98/14.67 [460]~E(x4601,x4602)+E(f802(x4603,x4604,x4605,x4606,x4601,x4607,x4608),f802(x4603,x4604,x4605,x4606,x4602,x4607,x4608)) % 14.98/14.67 [461]~E(x4611,x4612)+E(f802(x4613,x4614,x4615,x4616,x4617,x4611,x4618),f802(x4613,x4614,x4615,x4616,x4617,x4612,x4618)) % 14.98/14.67 [462]~E(x4621,x4622)+E(f802(x4623,x4624,x4625,x4626,x4627,x4628,x4621),f802(x4623,x4624,x4625,x4626,x4627,x4628,x4622)) % 14.98/14.67 [463]~E(x4631,x4632)+E(f344(x4631,x4633),f344(x4632,x4633)) % 14.98/14.67 [464]~E(x4641,x4642)+E(f344(x4643,x4641),f344(x4643,x4642)) % 14.98/14.67 [465]~E(x4651,x4652)+E(f57(x4651,x4653,x4654),f57(x4652,x4653,x4654)) % 14.98/14.67 [466]~E(x4661,x4662)+E(f57(x4663,x4661,x4664),f57(x4663,x4662,x4664)) % 14.98/14.67 [467]~E(x4671,x4672)+E(f57(x4673,x4674,x4671),f57(x4673,x4674,x4672)) % 14.98/14.67 [468]~E(x4681,x4682)+E(f664(x4681,x4683,x4684),f664(x4682,x4683,x4684)) % 14.98/14.67 [469]~E(x4691,x4692)+E(f664(x4693,x4691,x4694),f664(x4693,x4692,x4694)) % 14.98/14.67 [470]~E(x4701,x4702)+E(f664(x4703,x4704,x4701),f664(x4703,x4704,x4702)) % 14.98/14.67 [471]~E(x4711,x4712)+E(f851(x4711,x4713,x4714,x4715,x4716,x4717,x4718,x4719),f851(x4712,x4713,x4714,x4715,x4716,x4717,x4718,x4719)) % 14.98/14.67 [472]~E(x4721,x4722)+E(f851(x4723,x4721,x4724,x4725,x4726,x4727,x4728,x4729),f851(x4723,x4722,x4724,x4725,x4726,x4727,x4728,x4729)) % 14.98/14.67 [473]~E(x4731,x4732)+E(f851(x4733,x4734,x4731,x4735,x4736,x4737,x4738,x4739),f851(x4733,x4734,x4732,x4735,x4736,x4737,x4738,x4739)) % 14.98/14.67 [474]~E(x4741,x4742)+E(f851(x4743,x4744,x4745,x4741,x4746,x4747,x4748,x4749),f851(x4743,x4744,x4745,x4742,x4746,x4747,x4748,x4749)) % 14.98/14.67 [475]~E(x4751,x4752)+E(f851(x4753,x4754,x4755,x4756,x4751,x4757,x4758,x4759),f851(x4753,x4754,x4755,x4756,x4752,x4757,x4758,x4759)) % 14.98/14.67 [476]~E(x4761,x4762)+E(f851(x4763,x4764,x4765,x4766,x4767,x4761,x4768,x4769),f851(x4763,x4764,x4765,x4766,x4767,x4762,x4768,x4769)) % 14.98/14.67 [477]~E(x4771,x4772)+E(f851(x4773,x4774,x4775,x4776,x4777,x4778,x4771,x4779),f851(x4773,x4774,x4775,x4776,x4777,x4778,x4772,x4779)) % 14.98/14.67 [478]~E(x4781,x4782)+E(f851(x4783,x4784,x4785,x4786,x4787,x4788,x4789,x4781),f851(x4783,x4784,x4785,x4786,x4787,x4788,x4789,x4782)) % 14.98/14.67 [479]~E(x4791,x4792)+E(f751(x4791,x4793,x4794,x4795,x4796,x4797,x4798),f751(x4792,x4793,x4794,x4795,x4796,x4797,x4798)) % 14.98/14.67 [480]~E(x4801,x4802)+E(f751(x4803,x4801,x4804,x4805,x4806,x4807,x4808),f751(x4803,x4802,x4804,x4805,x4806,x4807,x4808)) % 14.98/14.67 [481]~E(x4811,x4812)+E(f751(x4813,x4814,x4811,x4815,x4816,x4817,x4818),f751(x4813,x4814,x4812,x4815,x4816,x4817,x4818)) % 14.98/14.67 [482]~E(x4821,x4822)+E(f751(x4823,x4824,x4825,x4821,x4826,x4827,x4828),f751(x4823,x4824,x4825,x4822,x4826,x4827,x4828)) % 14.98/14.67 [483]~E(x4831,x4832)+E(f751(x4833,x4834,x4835,x4836,x4831,x4837,x4838),f751(x4833,x4834,x4835,x4836,x4832,x4837,x4838)) % 14.98/14.67 [484]~E(x4841,x4842)+E(f751(x4843,x4844,x4845,x4846,x4847,x4841,x4848),f751(x4843,x4844,x4845,x4846,x4847,x4842,x4848)) % 14.98/14.67 [485]~E(x4851,x4852)+E(f751(x4853,x4854,x4855,x4856,x4857,x4858,x4851),f751(x4853,x4854,x4855,x4856,x4857,x4858,x4852)) % 14.98/14.67 [486]~E(x4861,x4862)+E(f506(x4861,x4863,x4864),f506(x4862,x4863,x4864)) % 14.98/14.67 [487]~E(x4871,x4872)+E(f506(x4873,x4871,x4874),f506(x4873,x4872,x4874)) % 14.98/14.67 [488]~E(x4881,x4882)+E(f506(x4883,x4884,x4881),f506(x4883,x4884,x4882)) % 14.98/14.67 [489]~E(x4891,x4892)+E(f172(x4891,x4893),f172(x4892,x4893)) % 14.98/14.67 [490]~E(x4901,x4902)+E(f172(x4903,x4901),f172(x4903,x4902)) % 14.98/14.67 [491]~E(x4911,x4912)+E(f58(x4911,x4913,x4914),f58(x4912,x4913,x4914)) % 14.98/14.67 [492]~E(x4921,x4922)+E(f58(x4923,x4921,x4924),f58(x4923,x4922,x4924)) % 14.98/14.67 [493]~E(x4931,x4932)+E(f58(x4933,x4934,x4931),f58(x4933,x4934,x4932)) % 14.98/14.67 [494]~E(x4941,x4942)+E(f59(x4941,x4943,x4944,x4945,x4946),f59(x4942,x4943,x4944,x4945,x4946)) % 14.98/14.67 [495]~E(x4951,x4952)+E(f59(x4953,x4951,x4954,x4955,x4956),f59(x4953,x4952,x4954,x4955,x4956)) % 14.98/14.67 [496]~E(x4961,x4962)+E(f59(x4963,x4964,x4961,x4965,x4966),f59(x4963,x4964,x4962,x4965,x4966)) % 14.98/14.67 [497]~E(x4971,x4972)+E(f59(x4973,x4974,x4975,x4971,x4976),f59(x4973,x4974,x4975,x4972,x4976)) % 14.98/14.67 [498]~E(x4981,x4982)+E(f59(x4983,x4984,x4985,x4986,x4981),f59(x4983,x4984,x4985,x4986,x4982)) % 14.98/14.67 [499]~E(x4991,x4992)+E(f327(x4991,x4993,x4994),f327(x4992,x4993,x4994)) % 14.98/14.67 [500]~E(x5001,x5002)+E(f327(x5003,x5001,x5004),f327(x5003,x5002,x5004)) % 14.98/14.67 [501]~E(x5011,x5012)+E(f327(x5013,x5014,x5011),f327(x5013,x5014,x5012)) % 14.98/14.67 [502]~E(x5021,x5022)+E(f794(x5021,x5023),f794(x5022,x5023)) % 14.98/14.67 [503]~E(x5031,x5032)+E(f794(x5033,x5031),f794(x5033,x5032)) % 14.98/14.67 [504]~E(x5041,x5042)+E(f741(x5041,x5043,x5044,x5045),f741(x5042,x5043,x5044,x5045)) % 14.98/14.67 [505]~E(x5051,x5052)+E(f741(x5053,x5051,x5054,x5055),f741(x5053,x5052,x5054,x5055)) % 14.98/14.67 [506]~E(x5061,x5062)+E(f741(x5063,x5064,x5061,x5065),f741(x5063,x5064,x5062,x5065)) % 14.98/14.67 [507]~E(x5071,x5072)+E(f741(x5073,x5074,x5075,x5071),f741(x5073,x5074,x5075,x5072)) % 14.98/14.67 [508]~E(x5081,x5082)+E(f274(x5081),f274(x5082)) % 14.98/14.67 [509]~E(x5091,x5092)+E(f740(x5091,x5093),f740(x5092,x5093)) % 14.98/14.67 [510]~E(x5101,x5102)+E(f740(x5103,x5101),f740(x5103,x5102)) % 14.98/14.67 [511]~E(x5111,x5112)+E(f306(x5111),f306(x5112)) % 14.98/14.67 [512]~E(x5121,x5122)+E(f134(x5121),f134(x5122)) % 14.98/14.67 [513]~E(x5131,x5132)+E(f922(x5131,x5133),f922(x5132,x5133)) % 14.98/14.67 [514]~E(x5141,x5142)+E(f922(x5143,x5141),f922(x5143,x5142)) % 14.98/14.67 [515]~E(x5151,x5152)+E(f303(x5151,x5153,x5154),f303(x5152,x5153,x5154)) % 14.98/14.67 [516]~E(x5161,x5162)+E(f303(x5163,x5161,x5164),f303(x5163,x5162,x5164)) % 14.98/14.67 [517]~E(x5171,x5172)+E(f303(x5173,x5174,x5171),f303(x5173,x5174,x5172)) % 14.98/14.67 [518]~E(x5181,x5182)+E(f356(x5181,x5183,x5184,x5185,x5186),f356(x5182,x5183,x5184,x5185,x5186)) % 14.98/14.67 [519]~E(x5191,x5192)+E(f356(x5193,x5191,x5194,x5195,x5196),f356(x5193,x5192,x5194,x5195,x5196)) % 14.98/14.67 [520]~E(x5201,x5202)+E(f356(x5203,x5204,x5201,x5205,x5206),f356(x5203,x5204,x5202,x5205,x5206)) % 14.98/14.67 [521]~E(x5211,x5212)+E(f356(x5213,x5214,x5215,x5211,x5216),f356(x5213,x5214,x5215,x5212,x5216)) % 14.98/14.67 [522]~E(x5221,x5222)+E(f356(x5223,x5224,x5225,x5226,x5221),f356(x5223,x5224,x5225,x5226,x5222)) % 14.98/14.67 [523]~E(x5231,x5232)+E(f884(x5231,x5233,x5234,x5235,x5236),f884(x5232,x5233,x5234,x5235,x5236)) % 14.98/14.67 [524]~E(x5241,x5242)+E(f884(x5243,x5241,x5244,x5245,x5246),f884(x5243,x5242,x5244,x5245,x5246)) % 14.98/14.67 [525]~E(x5251,x5252)+E(f884(x5253,x5254,x5251,x5255,x5256),f884(x5253,x5254,x5252,x5255,x5256)) % 14.98/14.67 [526]~E(x5261,x5262)+E(f884(x5263,x5264,x5265,x5261,x5266),f884(x5263,x5264,x5265,x5262,x5266)) % 14.98/14.67 [527]~E(x5271,x5272)+E(f884(x5273,x5274,x5275,x5276,x5271),f884(x5273,x5274,x5275,x5276,x5272)) % 14.98/14.67 [528]~E(x5281,x5282)+E(f138(x5281,x5283),f138(x5282,x5283)) % 14.98/14.67 [529]~E(x5291,x5292)+E(f138(x5293,x5291),f138(x5293,x5292)) % 14.98/14.67 [530]~E(x5301,x5302)+E(f141(x5301,x5303,x5304),f141(x5302,x5303,x5304)) % 14.98/14.67 [531]~E(x5311,x5312)+E(f141(x5313,x5311,x5314),f141(x5313,x5312,x5314)) % 14.98/14.67 [532]~E(x5321,x5322)+E(f141(x5323,x5324,x5321),f141(x5323,x5324,x5322)) % 14.98/14.67 [533]~E(x5331,x5332)+E(f18(x5331,x5333),f18(x5332,x5333)) % 14.98/14.67 [534]~E(x5341,x5342)+E(f18(x5343,x5341),f18(x5343,x5342)) % 14.98/14.67 [535]~E(x5351,x5352)+E(f364(x5351,x5353,x5354,x5355),f364(x5352,x5353,x5354,x5355)) % 14.98/14.67 [536]~E(x5361,x5362)+E(f364(x5363,x5361,x5364,x5365),f364(x5363,x5362,x5364,x5365)) % 14.98/14.67 [537]~E(x5371,x5372)+E(f364(x5373,x5374,x5371,x5375),f364(x5373,x5374,x5372,x5375)) % 14.98/14.67 [538]~E(x5381,x5382)+E(f364(x5383,x5384,x5385,x5381),f364(x5383,x5384,x5385,x5382)) % 14.98/14.67 [539]~E(x5391,x5392)+E(f560(x5391,x5393,x5394,x5395),f560(x5392,x5393,x5394,x5395)) % 14.98/14.67 [540]~E(x5401,x5402)+E(f560(x5403,x5401,x5404,x5405),f560(x5403,x5402,x5404,x5405)) % 14.98/14.67 [541]~E(x5411,x5412)+E(f560(x5413,x5414,x5411,x5415),f560(x5413,x5414,x5412,x5415)) % 14.98/14.67 [542]~E(x5421,x5422)+E(f560(x5423,x5424,x5425,x5421),f560(x5423,x5424,x5425,x5422)) % 14.98/14.67 [543]~E(x5431,x5432)+E(f727(x5431,x5433),f727(x5432,x5433)) % 14.98/14.67 [544]~E(x5441,x5442)+E(f727(x5443,x5441),f727(x5443,x5442)) % 14.98/14.67 [545]~E(x5451,x5452)+E(f484(x5451,x5453,x5454,x5455,x5456),f484(x5452,x5453,x5454,x5455,x5456)) % 14.98/14.67 [546]~E(x5461,x5462)+E(f484(x5463,x5461,x5464,x5465,x5466),f484(x5463,x5462,x5464,x5465,x5466)) % 14.98/14.67 [547]~E(x5471,x5472)+E(f484(x5473,x5474,x5471,x5475,x5476),f484(x5473,x5474,x5472,x5475,x5476)) % 14.98/14.67 [548]~E(x5481,x5482)+E(f484(x5483,x5484,x5485,x5481,x5486),f484(x5483,x5484,x5485,x5482,x5486)) % 14.98/14.67 [549]~E(x5491,x5492)+E(f484(x5493,x5494,x5495,x5496,x5491),f484(x5493,x5494,x5495,x5496,x5492)) % 14.98/14.67 [550]~E(x5501,x5502)+E(f148(x5501,x5503,x5504),f148(x5502,x5503,x5504)) % 14.98/14.67 [551]~E(x5511,x5512)+E(f148(x5513,x5511,x5514),f148(x5513,x5512,x5514)) % 14.98/14.67 [552]~E(x5521,x5522)+E(f148(x5523,x5524,x5521),f148(x5523,x5524,x5522)) % 14.98/14.67 [553]~E(x5531,x5532)+E(f901(x5531,x5533,x5534,x5535,x5536,x5537),f901(x5532,x5533,x5534,x5535,x5536,x5537)) % 14.98/14.67 [554]~E(x5541,x5542)+E(f901(x5543,x5541,x5544,x5545,x5546,x5547),f901(x5543,x5542,x5544,x5545,x5546,x5547)) % 14.98/14.67 [555]~E(x5551,x5552)+E(f901(x5553,x5554,x5551,x5555,x5556,x5557),f901(x5553,x5554,x5552,x5555,x5556,x5557)) % 14.98/14.67 [556]~E(x5561,x5562)+E(f901(x5563,x5564,x5565,x5561,x5566,x5567),f901(x5563,x5564,x5565,x5562,x5566,x5567)) % 14.98/14.67 [557]~E(x5571,x5572)+E(f901(x5573,x5574,x5575,x5576,x5571,x5577),f901(x5573,x5574,x5575,x5576,x5572,x5577)) % 14.98/14.67 [558]~E(x5581,x5582)+E(f901(x5583,x5584,x5585,x5586,x5587,x5581),f901(x5583,x5584,x5585,x5586,x5587,x5582)) % 14.98/14.67 [559]~E(x5591,x5592)+E(f626(x5591,x5593,x5594),f626(x5592,x5593,x5594)) % 14.98/14.67 [560]~E(x5601,x5602)+E(f626(x5603,x5601,x5604),f626(x5603,x5602,x5604)) % 14.98/14.67 [561]~E(x5611,x5612)+E(f626(x5613,x5614,x5611),f626(x5613,x5614,x5612)) % 14.98/14.67 [562]~E(x5621,x5622)+E(f791(x5621,x5623,x5624,x5625,x5626,x5627,x5628),f791(x5622,x5623,x5624,x5625,x5626,x5627,x5628)) % 14.98/14.67 [563]~E(x5631,x5632)+E(f791(x5633,x5631,x5634,x5635,x5636,x5637,x5638),f791(x5633,x5632,x5634,x5635,x5636,x5637,x5638)) % 14.98/14.67 [564]~E(x5641,x5642)+E(f791(x5643,x5644,x5641,x5645,x5646,x5647,x5648),f791(x5643,x5644,x5642,x5645,x5646,x5647,x5648)) % 14.98/14.67 [565]~E(x5651,x5652)+E(f791(x5653,x5654,x5655,x5651,x5656,x5657,x5658),f791(x5653,x5654,x5655,x5652,x5656,x5657,x5658)) % 14.98/14.67 [566]~E(x5661,x5662)+E(f791(x5663,x5664,x5665,x5666,x5661,x5667,x5668),f791(x5663,x5664,x5665,x5666,x5662,x5667,x5668)) % 14.98/14.67 [567]~E(x5671,x5672)+E(f791(x5673,x5674,x5675,x5676,x5677,x5671,x5678),f791(x5673,x5674,x5675,x5676,x5677,x5672,x5678)) % 14.98/14.67 [568]~E(x5681,x5682)+E(f791(x5683,x5684,x5685,x5686,x5687,x5688,x5681),f791(x5683,x5684,x5685,x5686,x5687,x5688,x5682)) % 14.98/14.67 [569]~E(x5691,x5692)+E(f913(x5691),f913(x5692)) % 14.98/14.67 [570]~E(x5701,x5702)+E(f465(x5701,x5703,x5704),f465(x5702,x5703,x5704)) % 14.98/14.67 [571]~E(x5711,x5712)+E(f465(x5713,x5711,x5714),f465(x5713,x5712,x5714)) % 14.98/14.67 [572]~E(x5721,x5722)+E(f465(x5723,x5724,x5721),f465(x5723,x5724,x5722)) % 14.98/14.67 [573]~E(x5731,x5732)+E(f277(x5731,x5733),f277(x5732,x5733)) % 14.98/14.67 [574]~E(x5741,x5742)+E(f277(x5743,x5741),f277(x5743,x5742)) % 14.98/14.67 [575]~E(x5751,x5752)+E(f736(x5751,x5753),f736(x5752,x5753)) % 14.98/14.67 [576]~E(x5761,x5762)+E(f736(x5763,x5761),f736(x5763,x5762)) % 14.98/14.67 [577]~E(x5771,x5772)+E(f780(x5771,x5773,x5774),f780(x5772,x5773,x5774)) % 14.98/14.67 [578]~E(x5781,x5782)+E(f780(x5783,x5781,x5784),f780(x5783,x5782,x5784)) % 14.98/14.67 [579]~E(x5791,x5792)+E(f780(x5793,x5794,x5791),f780(x5793,x5794,x5792)) % 14.98/14.67 [580]~E(x5801,x5802)+E(f650(x5801,x5803,x5804,x5805),f650(x5802,x5803,x5804,x5805)) % 14.98/14.67 [581]~E(x5811,x5812)+E(f650(x5813,x5811,x5814,x5815),f650(x5813,x5812,x5814,x5815)) % 14.98/14.67 [582]~E(x5821,x5822)+E(f650(x5823,x5824,x5821,x5825),f650(x5823,x5824,x5822,x5825)) % 14.98/14.67 [583]~E(x5831,x5832)+E(f650(x5833,x5834,x5835,x5831),f650(x5833,x5834,x5835,x5832)) % 14.98/14.67 [584]~E(x5841,x5842)+E(f143(x5841,x5843,x5844,x5845),f143(x5842,x5843,x5844,x5845)) % 14.98/14.67 [585]~E(x5851,x5852)+E(f143(x5853,x5851,x5854,x5855),f143(x5853,x5852,x5854,x5855)) % 14.98/14.67 [586]~E(x5861,x5862)+E(f143(x5863,x5864,x5861,x5865),f143(x5863,x5864,x5862,x5865)) % 14.98/14.67 [587]~E(x5871,x5872)+E(f143(x5873,x5874,x5875,x5871),f143(x5873,x5874,x5875,x5872)) % 14.98/14.67 [588]~E(x5881,x5882)+E(f494(x5881,x5883,x5884,x5885,x5886,x5887,x5888),f494(x5882,x5883,x5884,x5885,x5886,x5887,x5888)) % 14.98/14.67 [589]~E(x5891,x5892)+E(f494(x5893,x5891,x5894,x5895,x5896,x5897,x5898),f494(x5893,x5892,x5894,x5895,x5896,x5897,x5898)) % 14.98/14.67 [590]~E(x5901,x5902)+E(f494(x5903,x5904,x5901,x5905,x5906,x5907,x5908),f494(x5903,x5904,x5902,x5905,x5906,x5907,x5908)) % 14.98/14.67 [591]~E(x5911,x5912)+E(f494(x5913,x5914,x5915,x5911,x5916,x5917,x5918),f494(x5913,x5914,x5915,x5912,x5916,x5917,x5918)) % 14.98/14.67 [592]~E(x5921,x5922)+E(f494(x5923,x5924,x5925,x5926,x5921,x5927,x5928),f494(x5923,x5924,x5925,x5926,x5922,x5927,x5928)) % 14.98/14.67 [593]~E(x5931,x5932)+E(f494(x5933,x5934,x5935,x5936,x5937,x5931,x5938),f494(x5933,x5934,x5935,x5936,x5937,x5932,x5938)) % 14.98/14.67 [594]~E(x5941,x5942)+E(f494(x5943,x5944,x5945,x5946,x5947,x5948,x5941),f494(x5943,x5944,x5945,x5946,x5947,x5948,x5942)) % 14.98/14.67 [595]~E(x5951,x5952)+E(f545(x5951,x5953),f545(x5952,x5953)) % 14.98/14.67 [596]~E(x5961,x5962)+E(f545(x5963,x5961),f545(x5963,x5962)) % 14.98/14.67 [597]~E(x5971,x5972)+E(f464(x5971,x5973,x5974),f464(x5972,x5973,x5974)) % 14.98/14.67 [598]~E(x5981,x5982)+E(f464(x5983,x5981,x5984),f464(x5983,x5982,x5984)) % 14.98/14.67 [599]~E(x5991,x5992)+E(f464(x5993,x5994,x5991),f464(x5993,x5994,x5992)) % 14.98/14.67 [600]~E(x6001,x6002)+E(f497(x6001,x6003,x6004),f497(x6002,x6003,x6004)) % 14.98/14.67 [601]~E(x6011,x6012)+E(f497(x6013,x6011,x6014),f497(x6013,x6012,x6014)) % 14.98/14.67 [602]~E(x6021,x6022)+E(f497(x6023,x6024,x6021),f497(x6023,x6024,x6022)) % 14.98/14.67 [603]~E(x6031,x6032)+E(f85(x6031),f85(x6032)) % 14.98/14.67 [604]~E(x6041,x6042)+E(f588(x6041,x6043),f588(x6042,x6043)) % 14.98/14.67 [605]~E(x6051,x6052)+E(f588(x6053,x6051),f588(x6053,x6052)) % 14.98/14.67 [606]~E(x6061,x6062)+E(f89(x6061),f89(x6062)) % 14.98/14.67 [607]~E(x6071,x6072)+E(f273(x6071),f273(x6072)) % 14.98/14.67 [608]~E(x6081,x6082)+E(f183(x6081,x6083,x6084,x6085),f183(x6082,x6083,x6084,x6085)) % 14.98/14.67 [609]~E(x6091,x6092)+E(f183(x6093,x6091,x6094,x6095),f183(x6093,x6092,x6094,x6095)) % 14.98/14.67 [610]~E(x6101,x6102)+E(f183(x6103,x6104,x6101,x6105),f183(x6103,x6104,x6102,x6105)) % 14.98/14.67 [611]~E(x6111,x6112)+E(f183(x6113,x6114,x6115,x6111),f183(x6113,x6114,x6115,x6112)) % 14.98/14.67 [612]~E(x6121,x6122)+E(f573(x6121,x6123,x6124,x6125,x6126,x6127),f573(x6122,x6123,x6124,x6125,x6126,x6127)) % 14.98/14.67 [613]~E(x6131,x6132)+E(f573(x6133,x6131,x6134,x6135,x6136,x6137),f573(x6133,x6132,x6134,x6135,x6136,x6137)) % 14.98/14.67 [614]~E(x6141,x6142)+E(f573(x6143,x6144,x6141,x6145,x6146,x6147),f573(x6143,x6144,x6142,x6145,x6146,x6147)) % 14.98/14.67 [615]~E(x6151,x6152)+E(f573(x6153,x6154,x6155,x6151,x6156,x6157),f573(x6153,x6154,x6155,x6152,x6156,x6157)) % 14.98/14.67 [616]~E(x6161,x6162)+E(f573(x6163,x6164,x6165,x6166,x6161,x6167),f573(x6163,x6164,x6165,x6166,x6162,x6167)) % 14.98/14.67 [617]~E(x6171,x6172)+E(f573(x6173,x6174,x6175,x6176,x6177,x6171),f573(x6173,x6174,x6175,x6176,x6177,x6172)) % 14.98/14.67 [618]~E(x6181,x6182)+E(f383(x6181,x6183,x6184,x6185),f383(x6182,x6183,x6184,x6185)) % 14.98/14.67 [619]~E(x6191,x6192)+E(f383(x6193,x6191,x6194,x6195),f383(x6193,x6192,x6194,x6195)) % 14.98/14.67 [620]~E(x6201,x6202)+E(f383(x6203,x6204,x6201,x6205),f383(x6203,x6204,x6202,x6205)) % 14.98/14.67 [621]~E(x6211,x6212)+E(f383(x6213,x6214,x6215,x6211),f383(x6213,x6214,x6215,x6212)) % 14.98/14.67 [622]~E(x6221,x6222)+E(f446(x6221,x6223,x6224,x6225),f446(x6222,x6223,x6224,x6225)) % 14.98/14.67 [623]~E(x6231,x6232)+E(f446(x6233,x6231,x6234,x6235),f446(x6233,x6232,x6234,x6235)) % 14.98/14.67 [624]~E(x6241,x6242)+E(f446(x6243,x6244,x6241,x6245),f446(x6243,x6244,x6242,x6245)) % 14.98/14.67 [625]~E(x6251,x6252)+E(f446(x6253,x6254,x6255,x6251),f446(x6253,x6254,x6255,x6252)) % 14.98/14.67 [626]~E(x6261,x6262)+E(f635(x6261,x6263,x6264,x6265,x6266),f635(x6262,x6263,x6264,x6265,x6266)) % 14.98/14.67 [627]~E(x6271,x6272)+E(f635(x6273,x6271,x6274,x6275,x6276),f635(x6273,x6272,x6274,x6275,x6276)) % 14.98/14.67 [628]~E(x6281,x6282)+E(f635(x6283,x6284,x6281,x6285,x6286),f635(x6283,x6284,x6282,x6285,x6286)) % 14.98/14.67 [629]~E(x6291,x6292)+E(f635(x6293,x6294,x6295,x6291,x6296),f635(x6293,x6294,x6295,x6292,x6296)) % 14.98/14.67 [630]~E(x6301,x6302)+E(f635(x6303,x6304,x6305,x6306,x6301),f635(x6303,x6304,x6305,x6306,x6302)) % 14.98/14.67 [631]~E(x6311,x6312)+E(f732(x6311,x6313),f732(x6312,x6313)) % 14.98/14.67 [632]~E(x6321,x6322)+E(f732(x6323,x6321),f732(x6323,x6322)) % 14.98/14.67 [633]~E(x6331,x6332)+E(f449(x6331,x6333,x6334),f449(x6332,x6333,x6334)) % 14.98/14.67 [634]~E(x6341,x6342)+E(f449(x6343,x6341,x6344),f449(x6343,x6342,x6344)) % 14.98/14.67 [635]~E(x6351,x6352)+E(f449(x6353,x6354,x6351),f449(x6353,x6354,x6352)) % 14.98/14.67 [636]~E(x6361,x6362)+E(f649(x6361,x6363),f649(x6362,x6363)) % 14.98/14.67 [637]~E(x6371,x6372)+E(f649(x6373,x6371),f649(x6373,x6372)) % 14.98/14.67 [638]~E(x6381,x6382)+E(f215(x6381,x6383,x6384),f215(x6382,x6383,x6384)) % 14.98/14.67 [639]~E(x6391,x6392)+E(f215(x6393,x6391,x6394),f215(x6393,x6392,x6394)) % 14.98/14.67 [640]~E(x6401,x6402)+E(f215(x6403,x6404,x6401),f215(x6403,x6404,x6402)) % 14.98/14.67 [641]~E(x6411,x6412)+E(f538(x6411,x6413,x6414,x6415),f538(x6412,x6413,x6414,x6415)) % 14.98/14.67 [642]~E(x6421,x6422)+E(f538(x6423,x6421,x6424,x6425),f538(x6423,x6422,x6424,x6425)) % 14.98/14.67 [643]~E(x6431,x6432)+E(f538(x6433,x6434,x6431,x6435),f538(x6433,x6434,x6432,x6435)) % 14.98/14.67 [644]~E(x6441,x6442)+E(f538(x6443,x6444,x6445,x6441),f538(x6443,x6444,x6445,x6442)) % 14.98/14.67 [645]~E(x6451,x6452)+E(f86(x6451,x6453,x6454,x6455),f86(x6452,x6453,x6454,x6455)) % 14.98/14.67 [646]~E(x6461,x6462)+E(f86(x6463,x6461,x6464,x6465),f86(x6463,x6462,x6464,x6465)) % 14.98/14.67 [647]~E(x6471,x6472)+E(f86(x6473,x6474,x6471,x6475),f86(x6473,x6474,x6472,x6475)) % 14.98/14.67 [648]~E(x6481,x6482)+E(f86(x6483,x6484,x6485,x6481),f86(x6483,x6484,x6485,x6482)) % 14.98/14.67 [649]~E(x6491,x6492)+E(f689(x6491,x6493,x6494,x6495,x6496),f689(x6492,x6493,x6494,x6495,x6496)) % 14.98/14.67 [650]~E(x6501,x6502)+E(f689(x6503,x6501,x6504,x6505,x6506),f689(x6503,x6502,x6504,x6505,x6506)) % 14.98/14.67 [651]~E(x6511,x6512)+E(f689(x6513,x6514,x6511,x6515,x6516),f689(x6513,x6514,x6512,x6515,x6516)) % 14.98/14.67 [652]~E(x6521,x6522)+E(f689(x6523,x6524,x6525,x6521,x6526),f689(x6523,x6524,x6525,x6522,x6526)) % 14.98/14.67 [653]~E(x6531,x6532)+E(f689(x6533,x6534,x6535,x6536,x6531),f689(x6533,x6534,x6535,x6536,x6532)) % 14.98/14.67 [654]~E(x6541,x6542)+E(f887(x6541,x6543,x6544,x6545,x6546),f887(x6542,x6543,x6544,x6545,x6546)) % 14.98/14.67 [655]~E(x6551,x6552)+E(f887(x6553,x6551,x6554,x6555,x6556),f887(x6553,x6552,x6554,x6555,x6556)) % 14.98/14.67 [656]~E(x6561,x6562)+E(f887(x6563,x6564,x6561,x6565,x6566),f887(x6563,x6564,x6562,x6565,x6566)) % 14.98/14.67 [657]~E(x6571,x6572)+E(f887(x6573,x6574,x6575,x6571,x6576),f887(x6573,x6574,x6575,x6572,x6576)) % 14.98/14.67 [658]~E(x6581,x6582)+E(f887(x6583,x6584,x6585,x6586,x6581),f887(x6583,x6584,x6585,x6586,x6582)) % 14.98/14.67 [659]~E(x6591,x6592)+E(f811(x6591),f811(x6592)) % 14.98/14.67 [660]~E(x6601,x6602)+E(f492(x6601,x6603,x6604,x6605,x6606,x6607,x6608),f492(x6602,x6603,x6604,x6605,x6606,x6607,x6608)) % 14.98/14.67 [661]~E(x6611,x6612)+E(f492(x6613,x6611,x6614,x6615,x6616,x6617,x6618),f492(x6613,x6612,x6614,x6615,x6616,x6617,x6618)) % 14.98/14.67 [662]~E(x6621,x6622)+E(f492(x6623,x6624,x6621,x6625,x6626,x6627,x6628),f492(x6623,x6624,x6622,x6625,x6626,x6627,x6628)) % 14.98/14.67 [663]~E(x6631,x6632)+E(f492(x6633,x6634,x6635,x6631,x6636,x6637,x6638),f492(x6633,x6634,x6635,x6632,x6636,x6637,x6638)) % 14.98/14.67 [664]~E(x6641,x6642)+E(f492(x6643,x6644,x6645,x6646,x6641,x6647,x6648),f492(x6643,x6644,x6645,x6646,x6642,x6647,x6648)) % 14.98/14.67 [665]~E(x6651,x6652)+E(f492(x6653,x6654,x6655,x6656,x6657,x6651,x6658),f492(x6653,x6654,x6655,x6656,x6657,x6652,x6658)) % 14.98/14.67 [666]~E(x6661,x6662)+E(f492(x6663,x6664,x6665,x6666,x6667,x6668,x6661),f492(x6663,x6664,x6665,x6666,x6667,x6668,x6662)) % 14.98/14.67 [667]~E(x6671,x6672)+E(f339(x6671,x6673,x6674),f339(x6672,x6673,x6674)) % 14.98/14.67 [668]~E(x6681,x6682)+E(f339(x6683,x6681,x6684),f339(x6683,x6682,x6684)) % 14.98/14.67 [669]~E(x6691,x6692)+E(f339(x6693,x6694,x6691),f339(x6693,x6694,x6692)) % 14.98/14.67 [670]~E(x6701,x6702)+E(f869(x6701,x6703,x6704),f869(x6702,x6703,x6704)) % 14.98/14.67 [671]~E(x6711,x6712)+E(f869(x6713,x6711,x6714),f869(x6713,x6712,x6714)) % 14.98/14.67 [672]~E(x6721,x6722)+E(f869(x6723,x6724,x6721),f869(x6723,x6724,x6722)) % 14.98/14.67 [673]~E(x6731,x6732)+E(f262(x6731,x6733),f262(x6732,x6733)) % 14.98/14.67 [674]~E(x6741,x6742)+E(f262(x6743,x6741),f262(x6743,x6742)) % 14.98/14.67 [675]~E(x6751,x6752)+E(f880(x6751,x6753,x6754,x6755,x6756,x6757,x6758),f880(x6752,x6753,x6754,x6755,x6756,x6757,x6758)) % 14.98/14.67 [676]~E(x6761,x6762)+E(f880(x6763,x6761,x6764,x6765,x6766,x6767,x6768),f880(x6763,x6762,x6764,x6765,x6766,x6767,x6768)) % 14.98/14.67 [677]~E(x6771,x6772)+E(f880(x6773,x6774,x6771,x6775,x6776,x6777,x6778),f880(x6773,x6774,x6772,x6775,x6776,x6777,x6778)) % 14.98/14.67 [678]~E(x6781,x6782)+E(f880(x6783,x6784,x6785,x6781,x6786,x6787,x6788),f880(x6783,x6784,x6785,x6782,x6786,x6787,x6788)) % 14.98/14.67 [679]~E(x6791,x6792)+E(f880(x6793,x6794,x6795,x6796,x6791,x6797,x6798),f880(x6793,x6794,x6795,x6796,x6792,x6797,x6798)) % 14.98/14.67 [680]~E(x6801,x6802)+E(f880(x6803,x6804,x6805,x6806,x6807,x6801,x6808),f880(x6803,x6804,x6805,x6806,x6807,x6802,x6808)) % 14.98/14.67 [681]~E(x6811,x6812)+E(f880(x6813,x6814,x6815,x6816,x6817,x6818,x6811),f880(x6813,x6814,x6815,x6816,x6817,x6818,x6812)) % 14.98/14.67 [682]~E(x6821,x6822)+E(f875(x6821,x6823,x6824),f875(x6822,x6823,x6824)) % 14.98/14.67 [683]~E(x6831,x6832)+E(f875(x6833,x6831,x6834),f875(x6833,x6832,x6834)) % 14.98/14.67 [684]~E(x6841,x6842)+E(f875(x6843,x6844,x6841),f875(x6843,x6844,x6842)) % 14.98/14.67 [685]~E(x6851,x6852)+E(f819(x6851,x6853,x6854,x6855,x6856,x6857),f819(x6852,x6853,x6854,x6855,x6856,x6857)) % 14.98/14.67 [686]~E(x6861,x6862)+E(f819(x6863,x6861,x6864,x6865,x6866,x6867),f819(x6863,x6862,x6864,x6865,x6866,x6867)) % 14.98/14.67 [687]~E(x6871,x6872)+E(f819(x6873,x6874,x6871,x6875,x6876,x6877),f819(x6873,x6874,x6872,x6875,x6876,x6877)) % 14.98/14.67 [688]~E(x6881,x6882)+E(f819(x6883,x6884,x6885,x6881,x6886,x6887),f819(x6883,x6884,x6885,x6882,x6886,x6887)) % 14.98/14.67 [689]~E(x6891,x6892)+E(f819(x6893,x6894,x6895,x6896,x6891,x6897),f819(x6893,x6894,x6895,x6896,x6892,x6897)) % 14.98/14.67 [690]~E(x6901,x6902)+E(f819(x6903,x6904,x6905,x6906,x6907,x6901),f819(x6903,x6904,x6905,x6906,x6907,x6902)) % 14.98/14.67 [691]~E(x6911,x6912)+E(f516(x6911,x6913,x6914,x6915,x6916),f516(x6912,x6913,x6914,x6915,x6916)) % 14.98/14.67 [692]~E(x6921,x6922)+E(f516(x6923,x6921,x6924,x6925,x6926),f516(x6923,x6922,x6924,x6925,x6926)) % 14.98/14.67 [693]~E(x6931,x6932)+E(f516(x6933,x6934,x6931,x6935,x6936),f516(x6933,x6934,x6932,x6935,x6936)) % 14.98/14.67 [694]~E(x6941,x6942)+E(f516(x6943,x6944,x6945,x6941,x6946),f516(x6943,x6944,x6945,x6942,x6946)) % 14.98/14.67 [695]~E(x6951,x6952)+E(f516(x6953,x6954,x6955,x6956,x6951),f516(x6953,x6954,x6955,x6956,x6952)) % 14.98/14.67 [696]~E(x6961,x6962)+E(f387(x6961,x6963),f387(x6962,x6963)) % 14.98/14.67 [697]~E(x6971,x6972)+E(f387(x6973,x6971),f387(x6973,x6972)) % 14.98/14.67 [698]~E(x6981,x6982)+E(f436(x6981,x6983,x6984),f436(x6982,x6983,x6984)) % 14.98/14.67 [699]~E(x6991,x6992)+E(f436(x6993,x6991,x6994),f436(x6993,x6992,x6994)) % 14.98/14.67 [700]~E(x7001,x7002)+E(f436(x7003,x7004,x7001),f436(x7003,x7004,x7002)) % 14.98/14.67 [701]~E(x7011,x7012)+E(f701(x7011,x7013,x7014,x7015,x7016),f701(x7012,x7013,x7014,x7015,x7016)) % 14.98/14.67 [702]~E(x7021,x7022)+E(f701(x7023,x7021,x7024,x7025,x7026),f701(x7023,x7022,x7024,x7025,x7026)) % 14.98/14.67 [703]~E(x7031,x7032)+E(f701(x7033,x7034,x7031,x7035,x7036),f701(x7033,x7034,x7032,x7035,x7036)) % 14.98/14.67 [704]~E(x7041,x7042)+E(f701(x7043,x7044,x7045,x7041,x7046),f701(x7043,x7044,x7045,x7042,x7046)) % 14.98/14.67 [705]~E(x7051,x7052)+E(f701(x7053,x7054,x7055,x7056,x7051),f701(x7053,x7054,x7055,x7056,x7052)) % 14.98/14.67 [706]~E(x7061,x7062)+E(f481(x7061,x7063,x7064,x7065,x7066),f481(x7062,x7063,x7064,x7065,x7066)) % 14.98/14.67 [707]~E(x7071,x7072)+E(f481(x7073,x7071,x7074,x7075,x7076),f481(x7073,x7072,x7074,x7075,x7076)) % 14.98/14.67 [708]~E(x7081,x7082)+E(f481(x7083,x7084,x7081,x7085,x7086),f481(x7083,x7084,x7082,x7085,x7086)) % 14.98/14.67 [709]~E(x7091,x7092)+E(f481(x7093,x7094,x7095,x7091,x7096),f481(x7093,x7094,x7095,x7092,x7096)) % 14.98/14.67 [710]~E(x7101,x7102)+E(f481(x7103,x7104,x7105,x7106,x7101),f481(x7103,x7104,x7105,x7106,x7102)) % 14.98/14.67 [711]~E(x7111,x7112)+E(f546(x7111,x7113,x7114),f546(x7112,x7113,x7114)) % 14.98/14.67 [712]~E(x7121,x7122)+E(f546(x7123,x7121,x7124),f546(x7123,x7122,x7124)) % 14.98/14.67 [713]~E(x7131,x7132)+E(f546(x7133,x7134,x7131),f546(x7133,x7134,x7132)) % 14.98/14.67 [714]~E(x7141,x7142)+E(f17(x7141,x7143),f17(x7142,x7143)) % 14.98/14.67 [715]~E(x7151,x7152)+E(f17(x7153,x7151),f17(x7153,x7152)) % 14.98/14.67 [716]~E(x7161,x7162)+E(f809(x7161,x7163),f809(x7162,x7163)) % 14.98/14.67 [717]~E(x7171,x7172)+E(f809(x7173,x7171),f809(x7173,x7172)) % 14.98/14.67 [718]~E(x7181,x7182)+E(f569(x7181,x7183),f569(x7182,x7183)) % 14.98/14.67 [719]~E(x7191,x7192)+E(f569(x7193,x7191),f569(x7193,x7192)) % 14.98/14.67 [720]~E(x7201,x7202)+E(f586(x7201,x7203,x7204,x7205,x7206,x7207),f586(x7202,x7203,x7204,x7205,x7206,x7207)) % 14.98/14.67 [721]~E(x7211,x7212)+E(f586(x7213,x7211,x7214,x7215,x7216,x7217),f586(x7213,x7212,x7214,x7215,x7216,x7217)) % 14.98/14.67 [722]~E(x7221,x7222)+E(f586(x7223,x7224,x7221,x7225,x7226,x7227),f586(x7223,x7224,x7222,x7225,x7226,x7227)) % 14.98/14.67 [723]~E(x7231,x7232)+E(f586(x7233,x7234,x7235,x7231,x7236,x7237),f586(x7233,x7234,x7235,x7232,x7236,x7237)) % 14.98/14.67 [724]~E(x7241,x7242)+E(f586(x7243,x7244,x7245,x7246,x7241,x7247),f586(x7243,x7244,x7245,x7246,x7242,x7247)) % 14.98/14.67 [725]~E(x7251,x7252)+E(f586(x7253,x7254,x7255,x7256,x7257,x7251),f586(x7253,x7254,x7255,x7256,x7257,x7252)) % 14.98/14.67 [726]~E(x7261,x7262)+E(f87(x7261),f87(x7262)) % 14.98/14.67 [727]~E(x7271,x7272)+E(f189(x7271,x7273,x7274,x7275),f189(x7272,x7273,x7274,x7275)) % 14.98/14.67 [728]~E(x7281,x7282)+E(f189(x7283,x7281,x7284,x7285),f189(x7283,x7282,x7284,x7285)) % 14.98/14.67 [729]~E(x7291,x7292)+E(f189(x7293,x7294,x7291,x7295),f189(x7293,x7294,x7292,x7295)) % 14.98/14.67 [730]~E(x7301,x7302)+E(f189(x7303,x7304,x7305,x7301),f189(x7303,x7304,x7305,x7302)) % 14.98/14.67 [731]~E(x7311,x7312)+E(f284(x7311,x7313,x7314),f284(x7312,x7313,x7314)) % 14.98/14.67 [732]~E(x7321,x7322)+E(f284(x7323,x7321,x7324),f284(x7323,x7322,x7324)) % 14.98/14.67 [733]~E(x7331,x7332)+E(f284(x7333,x7334,x7331),f284(x7333,x7334,x7332)) % 14.98/14.67 [734]~E(x7341,x7342)+E(f798(x7341,x7343),f798(x7342,x7343)) % 14.98/14.67 [735]~E(x7351,x7352)+E(f798(x7353,x7351),f798(x7353,x7352)) % 14.98/14.67 [736]~E(x7361,x7362)+E(f532(x7361,x7363,x7364,x7365,x7366,x7367,x7368),f532(x7362,x7363,x7364,x7365,x7366,x7367,x7368)) % 14.98/14.67 [737]~E(x7371,x7372)+E(f532(x7373,x7371,x7374,x7375,x7376,x7377,x7378),f532(x7373,x7372,x7374,x7375,x7376,x7377,x7378)) % 14.98/14.67 [738]~E(x7381,x7382)+E(f532(x7383,x7384,x7381,x7385,x7386,x7387,x7388),f532(x7383,x7384,x7382,x7385,x7386,x7387,x7388)) % 14.98/14.67 [739]~E(x7391,x7392)+E(f532(x7393,x7394,x7395,x7391,x7396,x7397,x7398),f532(x7393,x7394,x7395,x7392,x7396,x7397,x7398)) % 14.98/14.67 [740]~E(x7401,x7402)+E(f532(x7403,x7404,x7405,x7406,x7401,x7407,x7408),f532(x7403,x7404,x7405,x7406,x7402,x7407,x7408)) % 14.98/14.67 [741]~E(x7411,x7412)+E(f532(x7413,x7414,x7415,x7416,x7417,x7411,x7418),f532(x7413,x7414,x7415,x7416,x7417,x7412,x7418)) % 14.98/14.67 [742]~E(x7421,x7422)+E(f532(x7423,x7424,x7425,x7426,x7427,x7428,x7421),f532(x7423,x7424,x7425,x7426,x7427,x7428,x7422)) % 14.98/14.67 [743]~E(x7431,x7432)+E(f270(x7431),f270(x7432)) % 14.98/14.67 [744]~E(x7441,x7442)+E(f39(x7441,x7443),f39(x7442,x7443)) % 14.98/14.67 [745]~E(x7451,x7452)+E(f39(x7453,x7451),f39(x7453,x7452)) % 14.98/14.67 [746]~E(x7461,x7462)+E(f915(x7461,x7463,x7464,x7465,x7466),f915(x7462,x7463,x7464,x7465,x7466)) % 14.98/14.67 [747]~E(x7471,x7472)+E(f915(x7473,x7471,x7474,x7475,x7476),f915(x7473,x7472,x7474,x7475,x7476)) % 14.98/14.67 [748]~E(x7481,x7482)+E(f915(x7483,x7484,x7481,x7485,x7486),f915(x7483,x7484,x7482,x7485,x7486)) % 14.98/14.67 [749]~E(x7491,x7492)+E(f915(x7493,x7494,x7495,x7491,x7496),f915(x7493,x7494,x7495,x7492,x7496)) % 14.98/14.67 [750]~E(x7501,x7502)+E(f915(x7503,x7504,x7505,x7506,x7501),f915(x7503,x7504,x7505,x7506,x7502)) % 14.98/14.67 [751]~E(x7511,x7512)+E(f154(x7511,x7513),f154(x7512,x7513)) % 14.98/14.67 [752]~E(x7521,x7522)+E(f154(x7523,x7521),f154(x7523,x7522)) % 14.98/14.67 [753]~E(x7531,x7532)+E(f514(x7531,x7533,x7534,x7535,x7536),f514(x7532,x7533,x7534,x7535,x7536)) % 14.98/14.67 [754]~E(x7541,x7542)+E(f514(x7543,x7541,x7544,x7545,x7546),f514(x7543,x7542,x7544,x7545,x7546)) % 14.98/14.67 [755]~E(x7551,x7552)+E(f514(x7553,x7554,x7551,x7555,x7556),f514(x7553,x7554,x7552,x7555,x7556)) % 14.98/14.67 [756]~E(x7561,x7562)+E(f514(x7563,x7564,x7565,x7561,x7566),f514(x7563,x7564,x7565,x7562,x7566)) % 14.98/14.67 [757]~E(x7571,x7572)+E(f514(x7573,x7574,x7575,x7576,x7571),f514(x7573,x7574,x7575,x7576,x7572)) % 14.98/14.67 [758]~E(x7581,x7582)+E(f604(x7581,x7583,x7584,x7585,x7586,x7587),f604(x7582,x7583,x7584,x7585,x7586,x7587)) % 14.98/14.67 [759]~E(x7591,x7592)+E(f604(x7593,x7591,x7594,x7595,x7596,x7597),f604(x7593,x7592,x7594,x7595,x7596,x7597)) % 14.98/14.67 [760]~E(x7601,x7602)+E(f604(x7603,x7604,x7601,x7605,x7606,x7607),f604(x7603,x7604,x7602,x7605,x7606,x7607)) % 14.98/14.67 [761]~E(x7611,x7612)+E(f604(x7613,x7614,x7615,x7611,x7616,x7617),f604(x7613,x7614,x7615,x7612,x7616,x7617)) % 14.98/14.67 [762]~E(x7621,x7622)+E(f604(x7623,x7624,x7625,x7626,x7621,x7627),f604(x7623,x7624,x7625,x7626,x7622,x7627)) % 14.98/14.67 [763]~E(x7631,x7632)+E(f604(x7633,x7634,x7635,x7636,x7637,x7631),f604(x7633,x7634,x7635,x7636,x7637,x7632)) % 14.98/14.67 [764]~E(x7641,x7642)+E(f655(x7641,x7643,x7644,x7645),f655(x7642,x7643,x7644,x7645)) % 14.98/14.67 [765]~E(x7651,x7652)+E(f655(x7653,x7651,x7654,x7655),f655(x7653,x7652,x7654,x7655)) % 14.98/14.67 [766]~E(x7661,x7662)+E(f655(x7663,x7664,x7661,x7665),f655(x7663,x7664,x7662,x7665)) % 14.98/14.67 [767]~E(x7671,x7672)+E(f655(x7673,x7674,x7675,x7671),f655(x7673,x7674,x7675,x7672)) % 14.98/14.67 [768]~E(x7681,x7682)+E(f679(x7681,x7683,x7684),f679(x7682,x7683,x7684)) % 14.98/14.67 [769]~E(x7691,x7692)+E(f679(x7693,x7691,x7694),f679(x7693,x7692,x7694)) % 14.98/14.67 [770]~E(x7701,x7702)+E(f679(x7703,x7704,x7701),f679(x7703,x7704,x7702)) % 14.98/14.67 [771]~E(x7711,x7712)+E(f70(x7711,x7713,x7714,x7715),f70(x7712,x7713,x7714,x7715)) % 14.98/14.67 [772]~E(x7721,x7722)+E(f70(x7723,x7721,x7724,x7725),f70(x7723,x7722,x7724,x7725)) % 14.98/14.67 [773]~E(x7731,x7732)+E(f70(x7733,x7734,x7731,x7735),f70(x7733,x7734,x7732,x7735)) % 14.98/14.67 [774]~E(x7741,x7742)+E(f70(x7743,x7744,x7745,x7741),f70(x7743,x7744,x7745,x7742)) % 14.98/14.67 [775]~E(x7751,x7752)+E(f750(x7751,x7753,x7754,x7755,x7756),f750(x7752,x7753,x7754,x7755,x7756)) % 14.98/14.67 [776]~E(x7761,x7762)+E(f750(x7763,x7761,x7764,x7765,x7766),f750(x7763,x7762,x7764,x7765,x7766)) % 14.98/14.67 [777]~E(x7771,x7772)+E(f750(x7773,x7774,x7771,x7775,x7776),f750(x7773,x7774,x7772,x7775,x7776)) % 14.98/14.67 [778]~E(x7781,x7782)+E(f750(x7783,x7784,x7785,x7781,x7786),f750(x7783,x7784,x7785,x7782,x7786)) % 14.98/14.67 [779]~E(x7791,x7792)+E(f750(x7793,x7794,x7795,x7796,x7791),f750(x7793,x7794,x7795,x7796,x7792)) % 14.98/14.67 [780]~E(x7801,x7802)+E(f550(x7801,x7803,x7804,x7805),f550(x7802,x7803,x7804,x7805)) % 14.98/14.67 [781]~E(x7811,x7812)+E(f550(x7813,x7811,x7814,x7815),f550(x7813,x7812,x7814,x7815)) % 14.98/14.67 [782]~E(x7821,x7822)+E(f550(x7823,x7824,x7821,x7825),f550(x7823,x7824,x7822,x7825)) % 14.98/14.67 [783]~E(x7831,x7832)+E(f550(x7833,x7834,x7835,x7831),f550(x7833,x7834,x7835,x7832)) % 14.98/14.67 [784]~E(x7841,x7842)+E(f162(x7841,x7843,x7844),f162(x7842,x7843,x7844)) % 14.98/14.67 [785]~E(x7851,x7852)+E(f162(x7853,x7851,x7854),f162(x7853,x7852,x7854)) % 14.98/14.67 [786]~E(x7861,x7862)+E(f162(x7863,x7864,x7861),f162(x7863,x7864,x7862)) % 14.98/14.67 [787]~E(x7871,x7872)+E(f467(x7871,x7873,x7874),f467(x7872,x7873,x7874)) % 14.98/14.67 [788]~E(x7881,x7882)+E(f467(x7883,x7881,x7884),f467(x7883,x7882,x7884)) % 14.98/14.67 [789]~E(x7891,x7892)+E(f467(x7893,x7894,x7891),f467(x7893,x7894,x7892)) % 14.98/14.67 [790]~E(x7901,x7902)+E(f119(x7901,x7903,x7904),f119(x7902,x7903,x7904)) % 14.98/14.67 [791]~E(x7911,x7912)+E(f119(x7913,x7911,x7914),f119(x7913,x7912,x7914)) % 14.98/14.67 [792]~E(x7921,x7922)+E(f119(x7923,x7924,x7921),f119(x7923,x7924,x7922)) % 14.98/14.67 [793]~E(x7931,x7932)+E(f247(x7931,x7933,x7934,x7935),f247(x7932,x7933,x7934,x7935)) % 14.98/14.67 [794]~E(x7941,x7942)+E(f247(x7943,x7941,x7944,x7945),f247(x7943,x7942,x7944,x7945)) % 14.98/14.67 [795]~E(x7951,x7952)+E(f247(x7953,x7954,x7951,x7955),f247(x7953,x7954,x7952,x7955)) % 14.98/14.67 [796]~E(x7961,x7962)+E(f247(x7963,x7964,x7965,x7961),f247(x7963,x7964,x7965,x7962)) % 14.98/14.67 [797]~E(x7971,x7972)+E(f874(x7971,x7973,x7974),f874(x7972,x7973,x7974)) % 14.98/14.67 [798]~E(x7981,x7982)+E(f874(x7983,x7981,x7984),f874(x7983,x7982,x7984)) % 14.98/14.67 [799]~E(x7991,x7992)+E(f874(x7993,x7994,x7991),f874(x7993,x7994,x7992)) % 14.98/14.67 [800]~E(x8001,x8002)+E(f712(x8001,x8003),f712(x8002,x8003)) % 14.98/14.67 [801]~E(x8011,x8012)+E(f712(x8013,x8011),f712(x8013,x8012)) % 14.98/14.67 [802]~E(x8021,x8022)+E(f558(x8021,x8023,x8024,x8025),f558(x8022,x8023,x8024,x8025)) % 14.98/14.67 [803]~E(x8031,x8032)+E(f558(x8033,x8031,x8034,x8035),f558(x8033,x8032,x8034,x8035)) % 14.98/14.67 [804]~E(x8041,x8042)+E(f558(x8043,x8044,x8041,x8045),f558(x8043,x8044,x8042,x8045)) % 14.98/14.67 [805]~E(x8051,x8052)+E(f558(x8053,x8054,x8055,x8051),f558(x8053,x8054,x8055,x8052)) % 14.98/14.67 [806]~E(x8061,x8062)+E(f707(x8061,x8063,x8064,x8065,x8066),f707(x8062,x8063,x8064,x8065,x8066)) % 14.98/14.67 [807]~E(x8071,x8072)+E(f707(x8073,x8071,x8074,x8075,x8076),f707(x8073,x8072,x8074,x8075,x8076)) % 14.98/14.67 [808]~E(x8081,x8082)+E(f707(x8083,x8084,x8081,x8085,x8086),f707(x8083,x8084,x8082,x8085,x8086)) % 14.98/14.67 [809]~E(x8091,x8092)+E(f707(x8093,x8094,x8095,x8091,x8096),f707(x8093,x8094,x8095,x8092,x8096)) % 14.98/14.67 [810]~E(x8101,x8102)+E(f707(x8103,x8104,x8105,x8106,x8101),f707(x8103,x8104,x8105,x8106,x8102)) % 14.98/14.67 [811]~E(x8111,x8112)+E(f404(x8111,x8113,x8114,x8115),f404(x8112,x8113,x8114,x8115)) % 14.98/14.67 [812]~E(x8121,x8122)+E(f404(x8123,x8121,x8124,x8125),f404(x8123,x8122,x8124,x8125)) % 14.98/14.68 [813]~E(x8131,x8132)+E(f404(x8133,x8134,x8131,x8135),f404(x8133,x8134,x8132,x8135)) % 14.98/14.68 [814]~E(x8141,x8142)+E(f404(x8143,x8144,x8145,x8141),f404(x8143,x8144,x8145,x8142)) % 14.98/14.68 [815]~E(x8151,x8152)+E(f264(x8151,x8153),f264(x8152,x8153)) % 14.98/14.68 [816]~E(x8161,x8162)+E(f264(x8163,x8161),f264(x8163,x8162)) % 14.98/14.68 [817]~E(x8171,x8172)+E(f418(x8171,x8173,x8174),f418(x8172,x8173,x8174)) % 14.98/14.68 [818]~E(x8181,x8182)+E(f418(x8183,x8181,x8184),f418(x8183,x8182,x8184)) % 14.98/14.68 [819]~E(x8191,x8192)+E(f418(x8193,x8194,x8191),f418(x8193,x8194,x8192)) % 14.98/14.68 [820]~E(x8201,x8202)+E(f245(x8201,x8203,x8204,x8205,x8206),f245(x8202,x8203,x8204,x8205,x8206)) % 14.98/14.68 [821]~E(x8211,x8212)+E(f245(x8213,x8211,x8214,x8215,x8216),f245(x8213,x8212,x8214,x8215,x8216)) % 14.98/14.68 [822]~E(x8221,x8222)+E(f245(x8223,x8224,x8221,x8225,x8226),f245(x8223,x8224,x8222,x8225,x8226)) % 14.98/14.68 [823]~E(x8231,x8232)+E(f245(x8233,x8234,x8235,x8231,x8236),f245(x8233,x8234,x8235,x8232,x8236)) % 14.98/14.68 [824]~E(x8241,x8242)+E(f245(x8243,x8244,x8245,x8246,x8241),f245(x8243,x8244,x8245,x8246,x8242)) % 14.98/14.68 [825]~E(x8251,x8252)+E(f205(x8251),f205(x8252)) % 14.98/14.68 [826]~E(x8261,x8262)+E(f133(x8261,x8263,x8264),f133(x8262,x8263,x8264)) % 14.98/14.68 [827]~E(x8271,x8272)+E(f133(x8273,x8271,x8274),f133(x8273,x8272,x8274)) % 14.98/14.68 [828]~E(x8281,x8282)+E(f133(x8283,x8284,x8281),f133(x8283,x8284,x8282)) % 14.98/14.68 [829]~E(x8291,x8292)+E(f821(x8291,x8293,x8294,x8295,x8296,x8297),f821(x8292,x8293,x8294,x8295,x8296,x8297)) % 14.98/14.68 [830]~E(x8301,x8302)+E(f821(x8303,x8301,x8304,x8305,x8306,x8307),f821(x8303,x8302,x8304,x8305,x8306,x8307)) % 14.98/14.68 [831]~E(x8311,x8312)+E(f821(x8313,x8314,x8311,x8315,x8316,x8317),f821(x8313,x8314,x8312,x8315,x8316,x8317)) % 14.98/14.68 [832]~E(x8321,x8322)+E(f821(x8323,x8324,x8325,x8321,x8326,x8327),f821(x8323,x8324,x8325,x8322,x8326,x8327)) % 14.98/14.68 [833]~E(x8331,x8332)+E(f821(x8333,x8334,x8335,x8336,x8331,x8337),f821(x8333,x8334,x8335,x8336,x8332,x8337)) % 14.98/14.68 [834]~E(x8341,x8342)+E(f821(x8343,x8344,x8345,x8346,x8347,x8341),f821(x8343,x8344,x8345,x8346,x8347,x8342)) % 14.98/14.68 [835]~E(x8351,x8352)+E(f746(x8351,x8353),f746(x8352,x8353)) % 14.98/14.68 [836]~E(x8361,x8362)+E(f746(x8363,x8361),f746(x8363,x8362)) % 14.98/14.68 [837]~E(x8371,x8372)+E(f256(x8371,x8373),f256(x8372,x8373)) % 14.98/14.68 [838]~E(x8381,x8382)+E(f256(x8383,x8381),f256(x8383,x8382)) % 14.98/14.68 [839]~E(x8391,x8392)+E(f298(x8391,x8393,x8394),f298(x8392,x8393,x8394)) % 14.98/14.68 [840]~E(x8401,x8402)+E(f298(x8403,x8401,x8404),f298(x8403,x8402,x8404)) % 14.98/14.68 [841]~E(x8411,x8412)+E(f298(x8413,x8414,x8411),f298(x8413,x8414,x8412)) % 14.98/14.68 [842]~E(x8421,x8422)+E(f300(x8421),f300(x8422)) % 14.98/14.68 [843]~E(x8431,x8432)+E(f461(x8431,x8433,x8434),f461(x8432,x8433,x8434)) % 14.98/14.68 [844]~E(x8441,x8442)+E(f461(x8443,x8441,x8444),f461(x8443,x8442,x8444)) % 14.98/14.68 [845]~E(x8451,x8452)+E(f461(x8453,x8454,x8451),f461(x8453,x8454,x8452)) % 14.98/14.68 [846]~E(x8461,x8462)+E(f871(x8461,x8463,x8464),f871(x8462,x8463,x8464)) % 14.98/14.68 [847]~E(x8471,x8472)+E(f871(x8473,x8471,x8474),f871(x8473,x8472,x8474)) % 14.98/14.68 [848]~E(x8481,x8482)+E(f871(x8483,x8484,x8481),f871(x8483,x8484,x8482)) % 14.98/14.68 [849]~E(x8491,x8492)+E(f556(x8491,x8493,x8494,x8495),f556(x8492,x8493,x8494,x8495)) % 14.98/14.68 [850]~E(x8501,x8502)+E(f556(x8503,x8501,x8504,x8505),f556(x8503,x8502,x8504,x8505)) % 14.98/14.68 [851]~E(x8511,x8512)+E(f556(x8513,x8514,x8511,x8515),f556(x8513,x8514,x8512,x8515)) % 14.98/14.68 [852]~E(x8521,x8522)+E(f556(x8523,x8524,x8525,x8521),f556(x8523,x8524,x8525,x8522)) % 14.98/14.68 [853]~E(x8531,x8532)+E(f305(x8531,x8533,x8534,x8535),f305(x8532,x8533,x8534,x8535)) % 14.98/14.68 [854]~E(x8541,x8542)+E(f305(x8543,x8541,x8544,x8545),f305(x8543,x8542,x8544,x8545)) % 14.98/14.68 [855]~E(x8551,x8552)+E(f305(x8553,x8554,x8551,x8555),f305(x8553,x8554,x8552,x8555)) % 14.98/14.68 [856]~E(x8561,x8562)+E(f305(x8563,x8564,x8565,x8561),f305(x8563,x8564,x8565,x8562)) % 14.98/14.68 [857]~E(x8571,x8572)+E(f585(x8571,x8573,x8574),f585(x8572,x8573,x8574)) % 14.98/14.68 [858]~E(x8581,x8582)+E(f585(x8583,x8581,x8584),f585(x8583,x8582,x8584)) % 14.98/14.68 [859]~E(x8591,x8592)+E(f585(x8593,x8594,x8591),f585(x8593,x8594,x8592)) % 14.98/14.68 [860]~E(x8601,x8602)+E(f190(x8601,x8603,x8604,x8605),f190(x8602,x8603,x8604,x8605)) % 14.98/14.68 [861]~E(x8611,x8612)+E(f190(x8613,x8611,x8614,x8615),f190(x8613,x8612,x8614,x8615)) % 14.98/14.68 [862]~E(x8621,x8622)+E(f190(x8623,x8624,x8621,x8625),f190(x8623,x8624,x8622,x8625)) % 14.98/14.68 [863]~E(x8631,x8632)+E(f190(x8633,x8634,x8635,x8631),f190(x8633,x8634,x8635,x8632)) % 14.98/14.68 [864]~E(x8641,x8642)+E(f251(x8641,x8643,x8644,x8645),f251(x8642,x8643,x8644,x8645)) % 14.98/14.68 [865]~E(x8651,x8652)+E(f251(x8653,x8651,x8654,x8655),f251(x8653,x8652,x8654,x8655)) % 14.98/14.68 [866]~E(x8661,x8662)+E(f251(x8663,x8664,x8661,x8665),f251(x8663,x8664,x8662,x8665)) % 14.98/14.68 [867]~E(x8671,x8672)+E(f251(x8673,x8674,x8675,x8671),f251(x8673,x8674,x8675,x8672)) % 14.98/14.68 [868]~E(x8681,x8682)+E(f55(x8681,x8683,x8684),f55(x8682,x8683,x8684)) % 14.98/14.68 [869]~E(x8691,x8692)+E(f55(x8693,x8691,x8694),f55(x8693,x8692,x8694)) % 14.98/14.68 [870]~E(x8701,x8702)+E(f55(x8703,x8704,x8701),f55(x8703,x8704,x8702)) % 14.98/14.68 [871]~E(x8711,x8712)+E(f279(x8711,x8713),f279(x8712,x8713)) % 14.98/14.68 [872]~E(x8721,x8722)+E(f279(x8723,x8721),f279(x8723,x8722)) % 14.98/14.68 [873]~E(x8731,x8732)+E(f294(x8731),f294(x8732)) % 14.98/14.68 [874]~E(x8741,x8742)+E(f641(x8741,x8743,x8744,x8745,x8746),f641(x8742,x8743,x8744,x8745,x8746)) % 14.98/14.68 [875]~E(x8751,x8752)+E(f641(x8753,x8751,x8754,x8755,x8756),f641(x8753,x8752,x8754,x8755,x8756)) % 14.98/14.68 [876]~E(x8761,x8762)+E(f641(x8763,x8764,x8761,x8765,x8766),f641(x8763,x8764,x8762,x8765,x8766)) % 14.98/14.68 [877]~E(x8771,x8772)+E(f641(x8773,x8774,x8775,x8771,x8776),f641(x8773,x8774,x8775,x8772,x8776)) % 14.98/14.68 [878]~E(x8781,x8782)+E(f641(x8783,x8784,x8785,x8786,x8781),f641(x8783,x8784,x8785,x8786,x8782)) % 14.98/14.68 [879]~E(x8791,x8792)+E(f833(x8791,x8793,x8794),f833(x8792,x8793,x8794)) % 14.98/14.68 [880]~E(x8801,x8802)+E(f833(x8803,x8801,x8804),f833(x8803,x8802,x8804)) % 14.98/14.68 [881]~E(x8811,x8812)+E(f833(x8813,x8814,x8811),f833(x8813,x8814,x8812)) % 14.98/14.68 [882]~E(x8821,x8822)+E(f694(x8821,x8823,x8824,x8825,x8826),f694(x8822,x8823,x8824,x8825,x8826)) % 14.98/14.68 [883]~E(x8831,x8832)+E(f694(x8833,x8831,x8834,x8835,x8836),f694(x8833,x8832,x8834,x8835,x8836)) % 14.98/14.68 [884]~E(x8841,x8842)+E(f694(x8843,x8844,x8841,x8845,x8846),f694(x8843,x8844,x8842,x8845,x8846)) % 14.98/14.68 [885]~E(x8851,x8852)+E(f694(x8853,x8854,x8855,x8851,x8856),f694(x8853,x8854,x8855,x8852,x8856)) % 14.98/14.68 [886]~E(x8861,x8862)+E(f694(x8863,x8864,x8865,x8866,x8861),f694(x8863,x8864,x8865,x8866,x8862)) % 14.98/14.68 [887]~E(x8871,x8872)+E(f542(x8871,x8873),f542(x8872,x8873)) % 14.98/14.68 [888]~E(x8881,x8882)+E(f542(x8883,x8881),f542(x8883,x8882)) % 14.98/14.68 [889]~E(x8891,x8892)+E(f531(x8891,x8893,x8894,x8895,x8896,x8897,x8898),f531(x8892,x8893,x8894,x8895,x8896,x8897,x8898)) % 14.98/14.68 [890]~E(x8901,x8902)+E(f531(x8903,x8901,x8904,x8905,x8906,x8907,x8908),f531(x8903,x8902,x8904,x8905,x8906,x8907,x8908)) % 14.98/14.68 [891]~E(x8911,x8912)+E(f531(x8913,x8914,x8911,x8915,x8916,x8917,x8918),f531(x8913,x8914,x8912,x8915,x8916,x8917,x8918)) % 14.98/14.68 [892]~E(x8921,x8922)+E(f531(x8923,x8924,x8925,x8921,x8926,x8927,x8928),f531(x8923,x8924,x8925,x8922,x8926,x8927,x8928)) % 14.98/14.68 [893]~E(x8931,x8932)+E(f531(x8933,x8934,x8935,x8936,x8931,x8937,x8938),f531(x8933,x8934,x8935,x8936,x8932,x8937,x8938)) % 14.98/14.68 [894]~E(x8941,x8942)+E(f531(x8943,x8944,x8945,x8946,x8947,x8941,x8948),f531(x8943,x8944,x8945,x8946,x8947,x8942,x8948)) % 14.98/14.68 [895]~E(x8951,x8952)+E(f531(x8953,x8954,x8955,x8956,x8957,x8958,x8951),f531(x8953,x8954,x8955,x8956,x8957,x8958,x8952)) % 14.98/14.68 [896]~E(x8961,x8962)+E(f710(x8961,x8963,x8964),f710(x8962,x8963,x8964)) % 14.98/14.68 [897]~E(x8971,x8972)+E(f710(x8973,x8971,x8974),f710(x8973,x8972,x8974)) % 14.98/14.68 [898]~E(x8981,x8982)+E(f710(x8983,x8984,x8981),f710(x8983,x8984,x8982)) % 14.98/14.68 [899]~E(x8991,x8992)+E(f275(x8991,x8993),f275(x8992,x8993)) % 14.98/14.68 [900]~E(x9001,x9002)+E(f275(x9003,x9001),f275(x9003,x9002)) % 14.98/14.68 [901]~E(x9011,x9012)+E(f486(x9011,x9013,x9014,x9015),f486(x9012,x9013,x9014,x9015)) % 14.98/14.68 [902]~E(x9021,x9022)+E(f486(x9023,x9021,x9024,x9025),f486(x9023,x9022,x9024,x9025)) % 14.98/14.68 [903]~E(x9031,x9032)+E(f486(x9033,x9034,x9031,x9035),f486(x9033,x9034,x9032,x9035)) % 14.98/14.68 [904]~E(x9041,x9042)+E(f486(x9043,x9044,x9045,x9041),f486(x9043,x9044,x9045,x9042)) % 14.98/14.68 [905]~E(x9051,x9052)+E(f744(x9051,x9053,x9054),f744(x9052,x9053,x9054)) % 14.98/14.68 [906]~E(x9061,x9062)+E(f744(x9063,x9061,x9064),f744(x9063,x9062,x9064)) % 14.98/14.68 [907]~E(x9071,x9072)+E(f744(x9073,x9074,x9071),f744(x9073,x9074,x9072)) % 14.98/14.68 [908]~E(x9081,x9082)+E(f859(x9081,x9083,x9084,x9085,x9086,x9087,x9088),f859(x9082,x9083,x9084,x9085,x9086,x9087,x9088)) % 14.98/14.68 [909]~E(x9091,x9092)+E(f859(x9093,x9091,x9094,x9095,x9096,x9097,x9098),f859(x9093,x9092,x9094,x9095,x9096,x9097,x9098)) % 14.98/14.68 [910]~E(x9101,x9102)+E(f859(x9103,x9104,x9101,x9105,x9106,x9107,x9108),f859(x9103,x9104,x9102,x9105,x9106,x9107,x9108)) % 14.98/14.68 [911]~E(x9111,x9112)+E(f859(x9113,x9114,x9115,x9111,x9116,x9117,x9118),f859(x9113,x9114,x9115,x9112,x9116,x9117,x9118)) % 14.98/14.68 [912]~E(x9121,x9122)+E(f859(x9123,x9124,x9125,x9126,x9121,x9127,x9128),f859(x9123,x9124,x9125,x9126,x9122,x9127,x9128)) % 14.98/14.68 [913]~E(x9131,x9132)+E(f859(x9133,x9134,x9135,x9136,x9137,x9131,x9138),f859(x9133,x9134,x9135,x9136,x9137,x9132,x9138)) % 14.98/14.68 [914]~E(x9141,x9142)+E(f859(x9143,x9144,x9145,x9146,x9147,x9148,x9141),f859(x9143,x9144,x9145,x9146,x9147,x9148,x9142)) % 14.98/14.68 [915]~E(x9151,x9152)+E(f688(x9151,x9153,x9154,x9155,x9156),f688(x9152,x9153,x9154,x9155,x9156)) % 14.98/14.68 [916]~E(x9161,x9162)+E(f688(x9163,x9161,x9164,x9165,x9166),f688(x9163,x9162,x9164,x9165,x9166)) % 14.98/14.68 [917]~E(x9171,x9172)+E(f688(x9173,x9174,x9171,x9175,x9176),f688(x9173,x9174,x9172,x9175,x9176)) % 14.98/14.68 [918]~E(x9181,x9182)+E(f688(x9183,x9184,x9185,x9181,x9186),f688(x9183,x9184,x9185,x9182,x9186)) % 14.98/14.68 [919]~E(x9191,x9192)+E(f688(x9193,x9194,x9195,x9196,x9191),f688(x9193,x9194,x9195,x9196,x9192)) % 14.98/14.68 [920]~E(x9201,x9202)+E(f620(x9201,x9203,x9204),f620(x9202,x9203,x9204)) % 14.98/14.68 [921]~E(x9211,x9212)+E(f620(x9213,x9211,x9214),f620(x9213,x9212,x9214)) % 14.98/14.68 [922]~E(x9221,x9222)+E(f620(x9223,x9224,x9221),f620(x9223,x9224,x9222)) % 14.98/14.68 [923]~E(x9231,x9232)+E(f508(x9231,x9233,x9234),f508(x9232,x9233,x9234)) % 14.98/14.68 [924]~E(x9241,x9242)+E(f508(x9243,x9241,x9244),f508(x9243,x9242,x9244)) % 14.98/14.68 [925]~E(x9251,x9252)+E(f508(x9253,x9254,x9251),f508(x9253,x9254,x9252)) % 14.98/14.68 [926]~E(x9261,x9262)+E(f572(x9261,x9263,x9264,x9265),f572(x9262,x9263,x9264,x9265)) % 14.98/14.68 [927]~E(x9271,x9272)+E(f572(x9273,x9271,x9274,x9275),f572(x9273,x9272,x9274,x9275)) % 14.98/14.68 [928]~E(x9281,x9282)+E(f572(x9283,x9284,x9281,x9285),f572(x9283,x9284,x9282,x9285)) % 14.98/14.68 [929]~E(x9291,x9292)+E(f572(x9293,x9294,x9295,x9291),f572(x9293,x9294,x9295,x9292)) % 14.98/14.68 [930]~E(x9301,x9302)+E(f203(x9301,x9303,x9304,x9305),f203(x9302,x9303,x9304,x9305)) % 14.98/14.68 [931]~E(x9311,x9312)+E(f203(x9313,x9311,x9314,x9315),f203(x9313,x9312,x9314,x9315)) % 14.98/14.68 [932]~E(x9321,x9322)+E(f203(x9323,x9324,x9321,x9325),f203(x9323,x9324,x9322,x9325)) % 14.98/14.68 [933]~E(x9331,x9332)+E(f203(x9333,x9334,x9335,x9331),f203(x9333,x9334,x9335,x9332)) % 14.98/14.68 [934]~E(x9341,x9342)+E(f149(x9341,x9343,x9344,x9345),f149(x9342,x9343,x9344,x9345)) % 14.98/14.68 [935]~E(x9351,x9352)+E(f149(x9353,x9351,x9354,x9355),f149(x9353,x9352,x9354,x9355)) % 14.98/14.68 [936]~E(x9361,x9362)+E(f149(x9363,x9364,x9361,x9365),f149(x9363,x9364,x9362,x9365)) % 14.98/14.68 [937]~E(x9371,x9372)+E(f149(x9373,x9374,x9375,x9371),f149(x9373,x9374,x9375,x9372)) % 14.98/14.68 [938]~E(x9381,x9382)+E(f565(x9381,x9383,x9384,x9385),f565(x9382,x9383,x9384,x9385)) % 14.98/14.68 [939]~E(x9391,x9392)+E(f565(x9393,x9391,x9394,x9395),f565(x9393,x9392,x9394,x9395)) % 14.98/14.68 [940]~E(x9401,x9402)+E(f565(x9403,x9404,x9401,x9405),f565(x9403,x9404,x9402,x9405)) % 14.98/14.68 [941]~E(x9411,x9412)+E(f565(x9413,x9414,x9415,x9411),f565(x9413,x9414,x9415,x9412)) % 14.98/14.68 [942]~E(x9421,x9422)+E(f723(x9421,x9423,x9424),f723(x9422,x9423,x9424)) % 14.98/14.68 [943]~E(x9431,x9432)+E(f723(x9433,x9431,x9434),f723(x9433,x9432,x9434)) % 14.98/14.68 [944]~E(x9441,x9442)+E(f723(x9443,x9444,x9441),f723(x9443,x9444,x9442)) % 14.98/14.68 [945]~E(x9451,x9452)+E(f331(x9451,x9453),f331(x9452,x9453)) % 14.98/14.68 [946]~E(x9461,x9462)+E(f331(x9463,x9461),f331(x9463,x9462)) % 14.98/14.68 [947]~E(x9471,x9472)+E(f367(x9471,x9473,x9474,x9475,x9476),f367(x9472,x9473,x9474,x9475,x9476)) % 14.98/14.68 [948]~E(x9481,x9482)+E(f367(x9483,x9481,x9484,x9485,x9486),f367(x9483,x9482,x9484,x9485,x9486)) % 14.98/14.68 [949]~E(x9491,x9492)+E(f367(x9493,x9494,x9491,x9495,x9496),f367(x9493,x9494,x9492,x9495,x9496)) % 14.98/14.68 [950]~E(x9501,x9502)+E(f367(x9503,x9504,x9505,x9501,x9506),f367(x9503,x9504,x9505,x9502,x9506)) % 14.98/14.68 [951]~E(x9511,x9512)+E(f367(x9513,x9514,x9515,x9516,x9511),f367(x9513,x9514,x9515,x9516,x9512)) % 14.98/14.68 [952]~E(x9521,x9522)+E(f555(x9521,x9523,x9524,x9525),f555(x9522,x9523,x9524,x9525)) % 14.98/14.68 [953]~E(x9531,x9532)+E(f555(x9533,x9531,x9534,x9535),f555(x9533,x9532,x9534,x9535)) % 14.98/14.68 [954]~E(x9541,x9542)+E(f555(x9543,x9544,x9541,x9545),f555(x9543,x9544,x9542,x9545)) % 14.98/14.68 [955]~E(x9551,x9552)+E(f555(x9553,x9554,x9555,x9551),f555(x9553,x9554,x9555,x9552)) % 14.98/14.68 [956]~E(x9561,x9562)+E(f185(x9561,x9563),f185(x9562,x9563)) % 14.98/14.68 [957]~E(x9571,x9572)+E(f185(x9573,x9571),f185(x9573,x9572)) % 14.98/14.68 [958]~E(x9581,x9582)+E(f139(x9581,x9583),f139(x9582,x9583)) % 14.98/14.68 [959]~E(x9591,x9592)+E(f139(x9593,x9591),f139(x9593,x9592)) % 14.98/14.68 [960]~E(x9601,x9602)+E(f114(x9601,x9603),f114(x9602,x9603)) % 14.98/14.68 [961]~E(x9611,x9612)+E(f114(x9613,x9611),f114(x9613,x9612)) % 14.98/14.68 [962]~E(x9621,x9622)+E(f779(x9621,x9623,x9624),f779(x9622,x9623,x9624)) % 14.98/14.68 [963]~E(x9631,x9632)+E(f779(x9633,x9631,x9634),f779(x9633,x9632,x9634)) % 14.98/14.68 [964]~E(x9641,x9642)+E(f779(x9643,x9644,x9641),f779(x9643,x9644,x9642)) % 14.98/14.68 [965]~E(x9651,x9652)+E(f669(x9651,x9653,x9654),f669(x9652,x9653,x9654)) % 14.98/14.68 [966]~E(x9661,x9662)+E(f669(x9663,x9661,x9664),f669(x9663,x9662,x9664)) % 14.98/14.68 [967]~E(x9671,x9672)+E(f669(x9673,x9674,x9671),f669(x9673,x9674,x9672)) % 14.98/14.68 [968]~E(x9681,x9682)+E(f372(x9681,x9683,x9684),f372(x9682,x9683,x9684)) % 14.98/14.68 [969]~E(x9691,x9692)+E(f372(x9693,x9691,x9694),f372(x9693,x9692,x9694)) % 14.98/14.68 [970]~E(x9701,x9702)+E(f372(x9703,x9704,x9701),f372(x9703,x9704,x9702)) % 14.98/14.68 [971]~E(x9711,x9712)+E(f50(x9711),f50(x9712)) % 14.98/14.68 [972]~E(x9721,x9722)+E(f355(x9721,x9723,x9724,x9725,x9726),f355(x9722,x9723,x9724,x9725,x9726)) % 14.98/14.68 [973]~E(x9731,x9732)+E(f355(x9733,x9731,x9734,x9735,x9736),f355(x9733,x9732,x9734,x9735,x9736)) % 14.98/14.68 [974]~E(x9741,x9742)+E(f355(x9743,x9744,x9741,x9745,x9746),f355(x9743,x9744,x9742,x9745,x9746)) % 14.98/14.68 [975]~E(x9751,x9752)+E(f355(x9753,x9754,x9755,x9751,x9756),f355(x9753,x9754,x9755,x9752,x9756)) % 14.98/14.68 [976]~E(x9761,x9762)+E(f355(x9763,x9764,x9765,x9766,x9761),f355(x9763,x9764,x9765,x9766,x9762)) % 14.98/14.68 [977]~E(x9771,x9772)+E(f778(x9771,x9773,x9774,x9775),f778(x9772,x9773,x9774,x9775)) % 14.98/14.68 [978]~E(x9781,x9782)+E(f778(x9783,x9781,x9784,x9785),f778(x9783,x9782,x9784,x9785)) % 14.98/14.68 [979]~E(x9791,x9792)+E(f778(x9793,x9794,x9791,x9795),f778(x9793,x9794,x9792,x9795)) % 14.98/14.68 [980]~E(x9801,x9802)+E(f778(x9803,x9804,x9805,x9801),f778(x9803,x9804,x9805,x9802)) % 14.98/14.68 [981]~E(x9811,x9812)+E(f208(x9811,x9813),f208(x9812,x9813)) % 14.98/14.68 [982]~E(x9821,x9822)+E(f208(x9823,x9821),f208(x9823,x9822)) % 14.98/14.68 [983]~E(x9831,x9832)+E(f755(x9831,x9833,x9834,x9835,x9836,x9837,x9838),f755(x9832,x9833,x9834,x9835,x9836,x9837,x9838)) % 14.98/14.68 [984]~E(x9841,x9842)+E(f755(x9843,x9841,x9844,x9845,x9846,x9847,x9848),f755(x9843,x9842,x9844,x9845,x9846,x9847,x9848)) % 14.98/14.68 [985]~E(x9851,x9852)+E(f755(x9853,x9854,x9851,x9855,x9856,x9857,x9858),f755(x9853,x9854,x9852,x9855,x9856,x9857,x9858)) % 14.98/14.68 [986]~E(x9861,x9862)+E(f755(x9863,x9864,x9865,x9861,x9866,x9867,x9868),f755(x9863,x9864,x9865,x9862,x9866,x9867,x9868)) % 14.98/14.68 [987]~E(x9871,x9872)+E(f755(x9873,x9874,x9875,x9876,x9871,x9877,x9878),f755(x9873,x9874,x9875,x9876,x9872,x9877,x9878)) % 14.98/14.68 [988]~E(x9881,x9882)+E(f755(x9883,x9884,x9885,x9886,x9887,x9881,x9888),f755(x9883,x9884,x9885,x9886,x9887,x9882,x9888)) % 14.98/14.68 [989]~E(x9891,x9892)+E(f755(x9893,x9894,x9895,x9896,x9897,x9898,x9891),f755(x9893,x9894,x9895,x9896,x9897,x9898,x9892)) % 14.98/14.68 [990]~E(x9901,x9902)+E(f633(x9901,x9903,x9904,x9905,x9906),f633(x9902,x9903,x9904,x9905,x9906)) % 14.98/14.68 [991]~E(x9911,x9912)+E(f633(x9913,x9911,x9914,x9915,x9916),f633(x9913,x9912,x9914,x9915,x9916)) % 14.98/14.68 [992]~E(x9921,x9922)+E(f633(x9923,x9924,x9921,x9925,x9926),f633(x9923,x9924,x9922,x9925,x9926)) % 14.98/14.68 [993]~E(x9931,x9932)+E(f633(x9933,x9934,x9935,x9931,x9936),f633(x9933,x9934,x9935,x9932,x9936)) % 14.98/14.68 [994]~E(x9941,x9942)+E(f633(x9943,x9944,x9945,x9946,x9941),f633(x9943,x9944,x9945,x9946,x9942)) % 14.98/14.68 [995]~E(x9951,x9952)+E(f489(x9951,x9953,x9954,x9955),f489(x9952,x9953,x9954,x9955)) % 14.98/14.68 [996]~E(x9961,x9962)+E(f489(x9963,x9961,x9964,x9965),f489(x9963,x9962,x9964,x9965)) % 14.98/14.68 [997]~E(x9971,x9972)+E(f489(x9973,x9974,x9971,x9975),f489(x9973,x9974,x9972,x9975)) % 14.98/14.68 [998]~E(x9981,x9982)+E(f489(x9983,x9984,x9985,x9981),f489(x9983,x9984,x9985,x9982)) % 14.98/14.68 [999]~E(x9991,x9992)+E(f840(x9991,x9993,x9994),f840(x9992,x9993,x9994)) % 14.98/14.68 [1000]~E(x10001,x10002)+E(f840(x10003,x10001,x10004),f840(x10003,x10002,x10004)) % 14.98/14.68 [1001]~E(x10011,x10012)+E(f840(x10013,x10014,x10011),f840(x10013,x10014,x10012)) % 14.98/14.68 [1002]~E(x10021,x10022)+E(f177(x10021,x10023,x10024),f177(x10022,x10023,x10024)) % 14.98/14.68 [1003]~E(x10031,x10032)+E(f177(x10033,x10031,x10034),f177(x10033,x10032,x10034)) % 14.98/14.68 [1004]~E(x10041,x10042)+E(f177(x10043,x10044,x10041),f177(x10043,x10044,x10042)) % 14.98/14.68 [1005]~E(x10051,x10052)+E(f432(x10051),f432(x10052)) % 14.98/14.68 [1006]~E(x10061,x10062)+E(f734(x10061,x10063,x10064),f734(x10062,x10063,x10064)) % 14.98/14.68 [1007]~E(x10071,x10072)+E(f734(x10073,x10071,x10074),f734(x10073,x10072,x10074)) % 14.98/14.68 [1008]~E(x10081,x10082)+E(f734(x10083,x10084,x10081),f734(x10083,x10084,x10082)) % 14.98/14.68 [1009]~E(x10091,x10092)+E(f594(x10091,x10093,x10094,x10095),f594(x10092,x10093,x10094,x10095)) % 14.98/14.68 [1010]~E(x10101,x10102)+E(f594(x10103,x10101,x10104,x10105),f594(x10103,x10102,x10104,x10105)) % 14.98/14.68 [1011]~E(x10111,x10112)+E(f594(x10113,x10114,x10111,x10115),f594(x10113,x10114,x10112,x10115)) % 14.98/14.68 [1012]~E(x10121,x10122)+E(f594(x10123,x10124,x10125,x10121),f594(x10123,x10124,x10125,x10122)) % 14.98/14.68 [1013]~E(x10131,x10132)+E(f52(x10131,x10133,x10134,x10135),f52(x10132,x10133,x10134,x10135)) % 14.98/14.68 [1014]~E(x10141,x10142)+E(f52(x10143,x10141,x10144,x10145),f52(x10143,x10142,x10144,x10145)) % 14.98/14.68 [1015]~E(x10151,x10152)+E(f52(x10153,x10154,x10151,x10155),f52(x10153,x10154,x10152,x10155)) % 14.98/14.68 [1016]~E(x10161,x10162)+E(f52(x10163,x10164,x10165,x10161),f52(x10163,x10164,x10165,x10162)) % 14.98/14.68 [1017]~E(x10171,x10172)+E(f282(x10171,x10173),f282(x10172,x10173)) % 14.98/14.68 [1018]~E(x10181,x10182)+E(f282(x10183,x10181),f282(x10183,x10182)) % 14.98/14.68 [1019]~E(x10191,x10192)+E(f754(x10191,x10193,x10194,x10195,x10196,x10197,x10198),f754(x10192,x10193,x10194,x10195,x10196,x10197,x10198)) % 14.98/14.68 [1020]~E(x10201,x10202)+E(f754(x10203,x10201,x10204,x10205,x10206,x10207,x10208),f754(x10203,x10202,x10204,x10205,x10206,x10207,x10208)) % 14.98/14.68 [1021]~E(x10211,x10212)+E(f754(x10213,x10214,x10211,x10215,x10216,x10217,x10218),f754(x10213,x10214,x10212,x10215,x10216,x10217,x10218)) % 14.98/14.68 [1022]~E(x10221,x10222)+E(f754(x10223,x10224,x10225,x10221,x10226,x10227,x10228),f754(x10223,x10224,x10225,x10222,x10226,x10227,x10228)) % 14.98/14.68 [1023]~E(x10231,x10232)+E(f754(x10233,x10234,x10235,x10236,x10231,x10237,x10238),f754(x10233,x10234,x10235,x10236,x10232,x10237,x10238)) % 14.98/14.68 [1024]~E(x10241,x10242)+E(f754(x10243,x10244,x10245,x10246,x10247,x10241,x10248),f754(x10243,x10244,x10245,x10246,x10247,x10242,x10248)) % 14.98/14.68 [1025]~E(x10251,x10252)+E(f754(x10253,x10254,x10255,x10256,x10257,x10258,x10251),f754(x10253,x10254,x10255,x10256,x10257,x10258,x10252)) % 14.98/14.68 [1026]~E(x10261,x10262)+E(f503(x10261,x10263,x10264),f503(x10262,x10263,x10264)) % 14.98/14.68 [1027]~E(x10271,x10272)+E(f503(x10273,x10271,x10274),f503(x10273,x10272,x10274)) % 14.98/14.68 [1028]~E(x10281,x10282)+E(f503(x10283,x10284,x10281),f503(x10283,x10284,x10282)) % 14.98/14.68 [1029]~E(x10291,x10292)+E(f258(x10291,x10293),f258(x10292,x10293)) % 14.98/14.68 [1030]~E(x10301,x10302)+E(f258(x10303,x10301),f258(x10303,x10302)) % 14.98/14.68 [1031]~E(x10311,x10312)+E(f677(x10311,x10313),f677(x10312,x10313)) % 14.98/14.68 [1032]~E(x10321,x10322)+E(f677(x10323,x10321),f677(x10323,x10322)) % 14.98/14.68 [1033]~E(x10331,x10332)+E(f218(x10331,x10333,x10334,x10335,x10336),f218(x10332,x10333,x10334,x10335,x10336)) % 14.98/14.68 [1034]~E(x10341,x10342)+E(f218(x10343,x10341,x10344,x10345,x10346),f218(x10343,x10342,x10344,x10345,x10346)) % 14.98/14.68 [1035]~E(x10351,x10352)+E(f218(x10353,x10354,x10351,x10355,x10356),f218(x10353,x10354,x10352,x10355,x10356)) % 14.98/14.68 [1036]~E(x10361,x10362)+E(f218(x10363,x10364,x10365,x10361,x10366),f218(x10363,x10364,x10365,x10362,x10366)) % 14.98/14.68 [1037]~E(x10371,x10372)+E(f218(x10373,x10374,x10375,x10376,x10371),f218(x10373,x10374,x10375,x10376,x10372)) % 14.98/14.68 [1038]~E(x10381,x10382)+E(f799(x10381,x10383,x10384),f799(x10382,x10383,x10384)) % 14.98/14.68 [1039]~E(x10391,x10392)+E(f799(x10393,x10391,x10394),f799(x10393,x10392,x10394)) % 14.98/14.68 [1040]~E(x10401,x10402)+E(f799(x10403,x10404,x10401),f799(x10403,x10404,x10402)) % 14.98/14.68 [1041]~E(x10411,x10412)+E(f290(x10411,x10413,x10414,x10415),f290(x10412,x10413,x10414,x10415)) % 14.98/14.68 [1042]~E(x10421,x10422)+E(f290(x10423,x10421,x10424,x10425),f290(x10423,x10422,x10424,x10425)) % 14.98/14.68 [1043]~E(x10431,x10432)+E(f290(x10433,x10434,x10431,x10435),f290(x10433,x10434,x10432,x10435)) % 14.98/14.68 [1044]~E(x10441,x10442)+E(f290(x10443,x10444,x10445,x10441),f290(x10443,x10444,x10445,x10442)) % 14.98/14.68 [1045]~E(x10451,x10452)+E(f179(x10451),f179(x10452)) % 14.98/14.68 [1046]~E(x10461,x10462)+E(f540(x10461,x10463,x10464,x10465,x10466),f540(x10462,x10463,x10464,x10465,x10466)) % 14.98/14.68 [1047]~E(x10471,x10472)+E(f540(x10473,x10471,x10474,x10475,x10476),f540(x10473,x10472,x10474,x10475,x10476)) % 14.98/14.68 [1048]~E(x10481,x10482)+E(f540(x10483,x10484,x10481,x10485,x10486),f540(x10483,x10484,x10482,x10485,x10486)) % 14.98/14.68 [1049]~E(x10491,x10492)+E(f540(x10493,x10494,x10495,x10491,x10496),f540(x10493,x10494,x10495,x10492,x10496)) % 14.98/14.68 [1050]~E(x10501,x10502)+E(f540(x10503,x10504,x10505,x10506,x10501),f540(x10503,x10504,x10505,x10506,x10502)) % 14.98/14.68 [1051]~E(x10511,x10512)+E(f216(x10511,x10513,x10514,x10515,x10516),f216(x10512,x10513,x10514,x10515,x10516)) % 14.98/14.68 [1052]~E(x10521,x10522)+E(f216(x10523,x10521,x10524,x10525,x10526),f216(x10523,x10522,x10524,x10525,x10526)) % 14.98/14.68 [1053]~E(x10531,x10532)+E(f216(x10533,x10534,x10531,x10535,x10536),f216(x10533,x10534,x10532,x10535,x10536)) % 14.98/14.68 [1054]~E(x10541,x10542)+E(f216(x10543,x10544,x10545,x10541,x10546),f216(x10543,x10544,x10545,x10542,x10546)) % 14.98/14.68 [1055]~E(x10551,x10552)+E(f216(x10553,x10554,x10555,x10556,x10551),f216(x10553,x10554,x10555,x10556,x10552)) % 14.98/14.68 [1056]~E(x10561,x10562)+E(f240(x10561,x10563),f240(x10562,x10563)) % 14.98/14.68 [1057]~E(x10571,x10572)+E(f240(x10573,x10571),f240(x10573,x10572)) % 14.98/14.68 [1058]~E(x10581,x10582)+E(f759(x10581,x10583,x10584,x10585),f759(x10582,x10583,x10584,x10585)) % 14.98/14.68 [1059]~E(x10591,x10592)+E(f759(x10593,x10591,x10594,x10595),f759(x10593,x10592,x10594,x10595)) % 14.98/14.68 [1060]~E(x10601,x10602)+E(f759(x10603,x10604,x10601,x10605),f759(x10603,x10604,x10602,x10605)) % 14.98/14.68 [1061]~E(x10611,x10612)+E(f759(x10613,x10614,x10615,x10611),f759(x10613,x10614,x10615,x10612)) % 14.98/14.68 [1062]~E(x10621,x10622)+E(f564(x10621,x10623,x10624,x10625),f564(x10622,x10623,x10624,x10625)) % 14.98/14.68 [1063]~E(x10631,x10632)+E(f564(x10633,x10631,x10634,x10635),f564(x10633,x10632,x10634,x10635)) % 14.98/14.68 [1064]~E(x10641,x10642)+E(f564(x10643,x10644,x10641,x10645),f564(x10643,x10644,x10642,x10645)) % 14.98/14.68 [1065]~E(x10651,x10652)+E(f564(x10653,x10654,x10655,x10651),f564(x10653,x10654,x10655,x10652)) % 14.98/14.68 [1066]~E(x10661,x10662)+E(f905(x10661,x10663,x10664),f905(x10662,x10663,x10664)) % 14.98/14.68 [1067]~E(x10671,x10672)+E(f905(x10673,x10671,x10674),f905(x10673,x10672,x10674)) % 14.98/14.68 [1068]~E(x10681,x10682)+E(f905(x10683,x10684,x10681),f905(x10683,x10684,x10682)) % 14.98/14.68 [1069]~E(x10691,x10692)+E(f475(x10691,x10693,x10694),f475(x10692,x10693,x10694)) % 14.98/14.68 [1070]~E(x10701,x10702)+E(f475(x10703,x10701,x10704),f475(x10703,x10702,x10704)) % 14.98/14.68 [1071]~E(x10711,x10712)+E(f475(x10713,x10714,x10711),f475(x10713,x10714,x10712)) % 14.98/14.68 [1072]~E(x10721,x10722)+E(f444(x10721,x10723,x10724,x10725),f444(x10722,x10723,x10724,x10725)) % 14.98/14.68 [1073]~E(x10731,x10732)+E(f444(x10733,x10731,x10734,x10735),f444(x10733,x10732,x10734,x10735)) % 14.98/14.68 [1074]~E(x10741,x10742)+E(f444(x10743,x10744,x10741,x10745),f444(x10743,x10744,x10742,x10745)) % 14.98/14.68 [1075]~E(x10751,x10752)+E(f444(x10753,x10754,x10755,x10751),f444(x10753,x10754,x10755,x10752)) % 14.98/14.68 [1076]~E(x10761,x10762)+E(f612(x10761,x10763,x10764),f612(x10762,x10763,x10764)) % 14.98/14.68 [1077]~E(x10771,x10772)+E(f612(x10773,x10771,x10774),f612(x10773,x10772,x10774)) % 14.98/14.68 [1078]~E(x10781,x10782)+E(f612(x10783,x10784,x10781),f612(x10783,x10784,x10782)) % 14.98/14.68 [1079]~E(x10791,x10792)+E(f220(x10791,x10793),f220(x10792,x10793)) % 14.98/14.68 [1080]~E(x10801,x10802)+E(f220(x10803,x10801),f220(x10803,x10802)) % 14.98/14.68 [1081]~E(x10811,x10812)+E(f125(x10811,x10813),f125(x10812,x10813)) % 14.98/14.68 [1082]~E(x10821,x10822)+E(f125(x10823,x10821),f125(x10823,x10822)) % 14.98/14.68 [1083]~E(x10831,x10832)+E(f178(x10831,x10833,x10834,x10835),f178(x10832,x10833,x10834,x10835)) % 14.98/14.68 [1084]~E(x10841,x10842)+E(f178(x10843,x10841,x10844,x10845),f178(x10843,x10842,x10844,x10845)) % 14.98/14.68 [1085]~E(x10851,x10852)+E(f178(x10853,x10854,x10851,x10855),f178(x10853,x10854,x10852,x10855)) % 14.98/14.68 [1086]~E(x10861,x10862)+E(f178(x10863,x10864,x10865,x10861),f178(x10863,x10864,x10865,x10862)) % 14.98/14.68 [1087]~E(x10871,x10872)+E(f304(x10871,x10873),f304(x10872,x10873)) % 14.98/14.68 [1088]~E(x10881,x10882)+E(f304(x10883,x10881),f304(x10883,x10882)) % 14.98/14.68 [1089]~E(x10891,x10892)+E(f361(x10891,x10893,x10894,x10895,x10896),f361(x10892,x10893,x10894,x10895,x10896)) % 14.98/14.68 [1090]~E(x10901,x10902)+E(f361(x10903,x10901,x10904,x10905,x10906),f361(x10903,x10902,x10904,x10905,x10906)) % 14.98/14.68 [1091]~E(x10911,x10912)+E(f361(x10913,x10914,x10911,x10915,x10916),f361(x10913,x10914,x10912,x10915,x10916)) % 14.98/14.68 [1092]~E(x10921,x10922)+E(f361(x10923,x10924,x10925,x10921,x10926),f361(x10923,x10924,x10925,x10922,x10926)) % 14.98/14.68 [1093]~E(x10931,x10932)+E(f361(x10933,x10934,x10935,x10936,x10931),f361(x10933,x10934,x10935,x10936,x10932)) % 14.98/14.68 [1094]~E(x10941,x10942)+E(f371(x10941,x10943,x10944),f371(x10942,x10943,x10944)) % 14.98/14.68 [1095]~E(x10951,x10952)+E(f371(x10953,x10951,x10954),f371(x10953,x10952,x10954)) % 14.98/14.68 [1096]~E(x10961,x10962)+E(f371(x10963,x10964,x10961),f371(x10963,x10964,x10962)) % 14.98/14.68 [1097]~E(x10971,x10972)+E(f493(x10971,x10973),f493(x10972,x10973)) % 14.98/14.68 [1098]~E(x10981,x10982)+E(f493(x10983,x10981),f493(x10983,x10982)) % 14.98/14.68 [1099]~E(x10991,x10992)+E(f115(x10991,x10993,x10994,x10995),f115(x10992,x10993,x10994,x10995)) % 14.98/14.68 [1100]~E(x11001,x11002)+E(f115(x11003,x11001,x11004,x11005),f115(x11003,x11002,x11004,x11005)) % 14.98/14.68 [1101]~E(x11011,x11012)+E(f115(x11013,x11014,x11011,x11015),f115(x11013,x11014,x11012,x11015)) % 14.98/14.68 [1102]~E(x11021,x11022)+E(f115(x11023,x11024,x11025,x11021),f115(x11023,x11024,x11025,x11022)) % 14.98/14.68 [1103]~E(x11031,x11032)+E(f776(x11031,x11033,x11034,x11035),f776(x11032,x11033,x11034,x11035)) % 14.98/14.68 [1104]~E(x11041,x11042)+E(f776(x11043,x11041,x11044,x11045),f776(x11043,x11042,x11044,x11045)) % 14.98/14.68 [1105]~E(x11051,x11052)+E(f776(x11053,x11054,x11051,x11055),f776(x11053,x11054,x11052,x11055)) % 14.98/14.68 [1106]~E(x11061,x11062)+E(f776(x11063,x11064,x11065,x11061),f776(x11063,x11064,x11065,x11062)) % 14.98/14.68 [1107]~E(x11071,x11072)+E(f365(x11071,x11073,x11074,x11075,x11076),f365(x11072,x11073,x11074,x11075,x11076)) % 14.98/14.68 [1108]~E(x11081,x11082)+E(f365(x11083,x11081,x11084,x11085,x11086),f365(x11083,x11082,x11084,x11085,x11086)) % 14.98/14.68 [1109]~E(x11091,x11092)+E(f365(x11093,x11094,x11091,x11095,x11096),f365(x11093,x11094,x11092,x11095,x11096)) % 14.98/14.68 [1110]~E(x11101,x11102)+E(f365(x11103,x11104,x11105,x11101,x11106),f365(x11103,x11104,x11105,x11102,x11106)) % 14.98/14.68 [1111]~E(x11111,x11112)+E(f365(x11113,x11114,x11115,x11116,x11111),f365(x11113,x11114,x11115,x11116,x11112)) % 14.98/14.68 [1112]~E(x11121,x11122)+E(f397(x11121,x11123,x11124,x11125),f397(x11122,x11123,x11124,x11125)) % 14.98/14.68 [1113]~E(x11131,x11132)+E(f397(x11133,x11131,x11134,x11135),f397(x11133,x11132,x11134,x11135)) % 14.98/14.68 [1114]~E(x11141,x11142)+E(f397(x11143,x11144,x11141,x11145),f397(x11143,x11144,x11142,x11145)) % 14.98/14.68 [1115]~E(x11151,x11152)+E(f397(x11153,x11154,x11155,x11151),f397(x11153,x11154,x11155,x11152)) % 14.98/14.68 [1116]~E(x11161,x11162)+E(f618(x11161,x11163,x11164),f618(x11162,x11163,x11164)) % 14.98/14.68 [1117]~E(x11171,x11172)+E(f618(x11173,x11171,x11174),f618(x11173,x11172,x11174)) % 14.98/14.68 [1118]~E(x11181,x11182)+E(f618(x11183,x11184,x11181),f618(x11183,x11184,x11182)) % 14.98/14.68 [1119]~E(x11191,x11192)+E(f645(x11191,x11193,x11194,x11195),f645(x11192,x11193,x11194,x11195)) % 14.98/14.68 [1120]~E(x11201,x11202)+E(f645(x11203,x11201,x11204,x11205),f645(x11203,x11202,x11204,x11205)) % 14.98/14.68 [1121]~E(x11211,x11212)+E(f645(x11213,x11214,x11211,x11215),f645(x11213,x11214,x11212,x11215)) % 14.98/14.68 [1122]~E(x11221,x11222)+E(f645(x11223,x11224,x11225,x11221),f645(x11223,x11224,x11225,x11222)) % 14.98/14.68 [1123]~E(x11231,x11232)+E(f716(x11231,x11233),f716(x11232,x11233)) % 14.98/14.68 [1124]~E(x11241,x11242)+E(f716(x11243,x11241),f716(x11243,x11242)) % 14.98/14.68 [1125]~E(x11251,x11252)+E(f510(x11251,x11253,x11254),f510(x11252,x11253,x11254)) % 14.98/14.68 [1126]~E(x11261,x11262)+E(f510(x11263,x11261,x11264),f510(x11263,x11262,x11264)) % 14.98/14.68 [1127]~E(x11271,x11272)+E(f510(x11273,x11274,x11271),f510(x11273,x11274,x11272)) % 14.98/14.68 [1128]~E(x11281,x11282)+E(f260(x11281,x11283),f260(x11282,x11283)) % 14.98/14.68 [1129]~E(x11291,x11292)+E(f260(x11293,x11291),f260(x11293,x11292)) % 14.98/14.68 [1130]~E(x11301,x11302)+E(f705(x11301,x11303,x11304,x11305,x11306),f705(x11302,x11303,x11304,x11305,x11306)) % 14.98/14.68 [1131]~E(x11311,x11312)+E(f705(x11313,x11311,x11314,x11315,x11316),f705(x11313,x11312,x11314,x11315,x11316)) % 14.98/14.68 [1132]~E(x11321,x11322)+E(f705(x11323,x11324,x11321,x11325,x11326),f705(x11323,x11324,x11322,x11325,x11326)) % 14.98/14.68 [1133]~E(x11331,x11332)+E(f705(x11333,x11334,x11335,x11331,x11336),f705(x11333,x11334,x11335,x11332,x11336)) % 14.98/14.68 [1134]~E(x11341,x11342)+E(f705(x11343,x11344,x11345,x11346,x11341),f705(x11343,x11344,x11345,x11346,x11342)) % 14.98/14.68 [1135]~E(x11351,x11352)+E(f601(x11351,x11353,x11354,x11355,x11356,x11357),f601(x11352,x11353,x11354,x11355,x11356,x11357)) % 14.98/14.68 [1136]~E(x11361,x11362)+E(f601(x11363,x11361,x11364,x11365,x11366,x11367),f601(x11363,x11362,x11364,x11365,x11366,x11367)) % 14.98/14.68 [1137]~E(x11371,x11372)+E(f601(x11373,x11374,x11371,x11375,x11376,x11377),f601(x11373,x11374,x11372,x11375,x11376,x11377)) % 14.98/14.68 [1138]~E(x11381,x11382)+E(f601(x11383,x11384,x11385,x11381,x11386,x11387),f601(x11383,x11384,x11385,x11382,x11386,x11387)) % 14.98/14.68 [1139]~E(x11391,x11392)+E(f601(x11393,x11394,x11395,x11396,x11391,x11397),f601(x11393,x11394,x11395,x11396,x11392,x11397)) % 14.98/14.68 [1140]~E(x11401,x11402)+E(f601(x11403,x11404,x11405,x11406,x11407,x11401),f601(x11403,x11404,x11405,x11406,x11407,x11402)) % 14.98/14.68 [1141]~E(x11411,x11412)+E(f619(x11411,x11413,x11414,x11415,x11416,x11417,x11418,x11419),f619(x11412,x11413,x11414,x11415,x11416,x11417,x11418,x11419)) % 14.98/14.68 [1142]~E(x11421,x11422)+E(f619(x11423,x11421,x11424,x11425,x11426,x11427,x11428,x11429),f619(x11423,x11422,x11424,x11425,x11426,x11427,x11428,x11429)) % 14.98/14.68 [1143]~E(x11431,x11432)+E(f619(x11433,x11434,x11431,x11435,x11436,x11437,x11438,x11439),f619(x11433,x11434,x11432,x11435,x11436,x11437,x11438,x11439)) % 14.98/14.68 [1144]~E(x11441,x11442)+E(f619(x11443,x11444,x11445,x11441,x11446,x11447,x11448,x11449),f619(x11443,x11444,x11445,x11442,x11446,x11447,x11448,x11449)) % 14.98/14.68 [1145]~E(x11451,x11452)+E(f619(x11453,x11454,x11455,x11456,x11451,x11457,x11458,x11459),f619(x11453,x11454,x11455,x11456,x11452,x11457,x11458,x11459)) % 14.98/14.68 [1146]~E(x11461,x11462)+E(f619(x11463,x11464,x11465,x11466,x11467,x11461,x11468,x11469),f619(x11463,x11464,x11465,x11466,x11467,x11462,x11468,x11469)) % 14.98/14.68 [1147]~E(x11471,x11472)+E(f619(x11473,x11474,x11475,x11476,x11477,x11478,x11471,x11479),f619(x11473,x11474,x11475,x11476,x11477,x11478,x11472,x11479)) % 14.98/14.68 [1148]~E(x11481,x11482)+E(f619(x11483,x11484,x11485,x11486,x11487,x11488,x11489,x11481),f619(x11483,x11484,x11485,x11486,x11487,x11488,x11489,x11482)) % 14.98/14.68 [1149]~E(x11491,x11492)+E(f201(x11491),f201(x11492)) % 14.98/14.68 [1150]~E(x11501,x11502)+E(f362(x11501,x11503),f362(x11502,x11503)) % 14.98/14.68 [1151]~E(x11511,x11512)+E(f362(x11513,x11511),f362(x11513,x11512)) % 14.98/14.68 [1152]~E(x11521,x11522)+E(f198(x11521,x11523,x11524,x11525),f198(x11522,x11523,x11524,x11525)) % 14.98/14.68 [1153]~E(x11531,x11532)+E(f198(x11533,x11531,x11534,x11535),f198(x11533,x11532,x11534,x11535)) % 14.98/14.68 [1154]~E(x11541,x11542)+E(f198(x11543,x11544,x11541,x11545),f198(x11543,x11544,x11542,x11545)) % 14.98/14.68 [1155]~E(x11551,x11552)+E(f198(x11553,x11554,x11555,x11551),f198(x11553,x11554,x11555,x11552)) % 14.98/14.68 [1156]~E(x11561,x11562)+E(f868(x11561,x11563,x11564),f868(x11562,x11563,x11564)) % 14.98/14.68 [1157]~E(x11571,x11572)+E(f868(x11573,x11571,x11574),f868(x11573,x11572,x11574)) % 14.98/14.68 [1158]~E(x11581,x11582)+E(f868(x11583,x11584,x11581),f868(x11583,x11584,x11582)) % 14.98/14.68 [1159]~E(x11591,x11592)+E(f239(x11591,x11593,x11594),f239(x11592,x11593,x11594)) % 14.98/14.68 [1160]~E(x11601,x11602)+E(f239(x11603,x11601,x11604),f239(x11603,x11602,x11604)) % 14.98/14.68 [1161]~E(x11611,x11612)+E(f239(x11613,x11614,x11611),f239(x11613,x11614,x11612)) % 14.98/14.68 [1162]~E(x11621,x11622)+E(f603(x11621,x11623,x11624,x11625,x11626,x11627),f603(x11622,x11623,x11624,x11625,x11626,x11627)) % 14.98/14.68 [1163]~E(x11631,x11632)+E(f603(x11633,x11631,x11634,x11635,x11636,x11637),f603(x11633,x11632,x11634,x11635,x11636,x11637)) % 14.98/14.68 [1164]~E(x11641,x11642)+E(f603(x11643,x11644,x11641,x11645,x11646,x11647),f603(x11643,x11644,x11642,x11645,x11646,x11647)) % 14.98/14.68 [1165]~E(x11651,x11652)+E(f603(x11653,x11654,x11655,x11651,x11656,x11657),f603(x11653,x11654,x11655,x11652,x11656,x11657)) % 14.98/14.68 [1166]~E(x11661,x11662)+E(f603(x11663,x11664,x11665,x11666,x11661,x11667),f603(x11663,x11664,x11665,x11666,x11662,x11667)) % 14.98/14.68 [1167]~E(x11671,x11672)+E(f603(x11673,x11674,x11675,x11676,x11677,x11671),f603(x11673,x11674,x11675,x11676,x11677,x11672)) % 14.98/14.68 [1168]~E(x11681,x11682)+E(f213(x11681,x11683,x11684,x11685),f213(x11682,x11683,x11684,x11685)) % 14.98/14.68 [1169]~E(x11691,x11692)+E(f213(x11693,x11691,x11694,x11695),f213(x11693,x11692,x11694,x11695)) % 14.98/14.68 [1170]~E(x11701,x11702)+E(f213(x11703,x11704,x11701,x11705),f213(x11703,x11704,x11702,x11705)) % 14.98/14.68 [1171]~E(x11711,x11712)+E(f213(x11713,x11714,x11715,x11711),f213(x11713,x11714,x11715,x11712)) % 14.98/14.68 [1172]~E(x11721,x11722)+E(f696(x11721,x11723,x11724),f696(x11722,x11723,x11724)) % 14.98/14.68 [1173]~E(x11731,x11732)+E(f696(x11733,x11731,x11734),f696(x11733,x11732,x11734)) % 14.98/14.68 [1174]~E(x11741,x11742)+E(f696(x11743,x11744,x11741),f696(x11743,x11744,x11742)) % 14.98/14.68 [1175]~E(x11751,x11752)+E(f820(x11751,x11753,x11754,x11755,x11756,x11757),f820(x11752,x11753,x11754,x11755,x11756,x11757)) % 14.98/14.68 [1176]~E(x11761,x11762)+E(f820(x11763,x11761,x11764,x11765,x11766,x11767),f820(x11763,x11762,x11764,x11765,x11766,x11767)) % 14.98/14.68 [1177]~E(x11771,x11772)+E(f820(x11773,x11774,x11771,x11775,x11776,x11777),f820(x11773,x11774,x11772,x11775,x11776,x11777)) % 14.98/14.68 [1178]~E(x11781,x11782)+E(f820(x11783,x11784,x11785,x11781,x11786,x11787),f820(x11783,x11784,x11785,x11782,x11786,x11787)) % 14.98/14.68 [1179]~E(x11791,x11792)+E(f820(x11793,x11794,x11795,x11796,x11791,x11797),f820(x11793,x11794,x11795,x11796,x11792,x11797)) % 14.98/14.68 [1180]~E(x11801,x11802)+E(f820(x11803,x11804,x11805,x11806,x11807,x11801),f820(x11803,x11804,x11805,x11806,x11807,x11802)) % 14.98/14.68 [1181]~E(x11811,x11812)+E(f823(x11811,x11813),f823(x11812,x11813)) % 14.98/14.68 [1182]~E(x11821,x11822)+E(f823(x11823,x11821),f823(x11823,x11822)) % 14.98/14.68 [1183]~E(x11831,x11832)+E(f439(x11831,x11833,x11834),f439(x11832,x11833,x11834)) % 14.98/14.68 [1184]~E(x11841,x11842)+E(f439(x11843,x11841,x11844),f439(x11843,x11842,x11844)) % 14.98/14.68 [1185]~E(x11851,x11852)+E(f439(x11853,x11854,x11851),f439(x11853,x11854,x11852)) % 14.98/14.68 [1186]~E(x11861,x11862)+E(f660(x11861,x11863,x11864,x11865,x11866),f660(x11862,x11863,x11864,x11865,x11866)) % 14.98/14.68 [1187]~E(x11871,x11872)+E(f660(x11873,x11871,x11874,x11875,x11876),f660(x11873,x11872,x11874,x11875,x11876)) % 14.98/14.68 [1188]~E(x11881,x11882)+E(f660(x11883,x11884,x11881,x11885,x11886),f660(x11883,x11884,x11882,x11885,x11886)) % 14.98/14.68 [1189]~E(x11891,x11892)+E(f660(x11893,x11894,x11895,x11891,x11896),f660(x11893,x11894,x11895,x11892,x11896)) % 14.98/14.68 [1190]~E(x11901,x11902)+E(f660(x11903,x11904,x11905,x11906,x11901),f660(x11903,x11904,x11905,x11906,x11902)) % 14.98/14.68 [1191]~E(x11911,x11912)+E(f864(x11911,x11913),f864(x11912,x11913)) % 14.98/14.68 [1192]~E(x11921,x11922)+E(f864(x11923,x11921),f864(x11923,x11922)) % 14.98/14.68 [1193]~E(x11931,x11932)+E(f46(x11931,x11933),f46(x11932,x11933)) % 14.98/14.68 [1194]~E(x11941,x11942)+E(f46(x11943,x11941),f46(x11943,x11942)) % 14.98/14.68 [1195]~E(x11951,x11952)+E(f574(x11951,x11953,x11954,x11955,x11956,x11957),f574(x11952,x11953,x11954,x11955,x11956,x11957)) % 14.98/14.68 [1196]~E(x11961,x11962)+E(f574(x11963,x11961,x11964,x11965,x11966,x11967),f574(x11963,x11962,x11964,x11965,x11966,x11967)) % 14.98/14.68 [1197]~E(x11971,x11972)+E(f574(x11973,x11974,x11971,x11975,x11976,x11977),f574(x11973,x11974,x11972,x11975,x11976,x11977)) % 14.98/14.68 [1198]~E(x11981,x11982)+E(f574(x11983,x11984,x11985,x11981,x11986,x11987),f574(x11983,x11984,x11985,x11982,x11986,x11987)) % 14.98/14.68 [1199]~E(x11991,x11992)+E(f574(x11993,x11994,x11995,x11996,x11991,x11997),f574(x11993,x11994,x11995,x11996,x11992,x11997)) % 14.98/14.68 [1200]~E(x12001,x12002)+E(f574(x12003,x12004,x12005,x12006,x12007,x12001),f574(x12003,x12004,x12005,x12006,x12007,x12002)) % 14.98/14.68 [1201]~E(x12011,x12012)+E(f602(x12011,x12013,x12014,x12015,x12016,x12017),f602(x12012,x12013,x12014,x12015,x12016,x12017)) % 14.98/14.68 [1202]~E(x12021,x12022)+E(f602(x12023,x12021,x12024,x12025,x12026,x12027),f602(x12023,x12022,x12024,x12025,x12026,x12027)) % 14.98/14.68 [1203]~E(x12031,x12032)+E(f602(x12033,x12034,x12031,x12035,x12036,x12037),f602(x12033,x12034,x12032,x12035,x12036,x12037)) % 14.98/14.68 [1204]~E(x12041,x12042)+E(f602(x12043,x12044,x12045,x12041,x12046,x12047),f602(x12043,x12044,x12045,x12042,x12046,x12047)) % 14.98/14.68 [1205]~E(x12051,x12052)+E(f602(x12053,x12054,x12055,x12056,x12051,x12057),f602(x12053,x12054,x12055,x12056,x12052,x12057)) % 14.98/14.68 [1206]~E(x12061,x12062)+E(f602(x12063,x12064,x12065,x12066,x12067,x12061),f602(x12063,x12064,x12065,x12066,x12067,x12062)) % 14.98/14.68 [1207]~E(x12071,x12072)+E(f747(x12071,x12073,x12074,x12075),f747(x12072,x12073,x12074,x12075)) % 14.98/14.68 [1208]~E(x12081,x12082)+E(f747(x12083,x12081,x12084,x12085),f747(x12083,x12082,x12084,x12085)) % 14.98/14.68 [1209]~E(x12091,x12092)+E(f747(x12093,x12094,x12091,x12095),f747(x12093,x12094,x12092,x12095)) % 14.98/14.68 [1210]~E(x12101,x12102)+E(f747(x12103,x12104,x12105,x12101),f747(x12103,x12104,x12105,x12102)) % 14.98/14.68 [1211]~E(x12111,x12112)+E(f686(x12111,x12113,x12114,x12115,x12116),f686(x12112,x12113,x12114,x12115,x12116)) % 14.98/14.68 [1212]~E(x12121,x12122)+E(f686(x12123,x12121,x12124,x12125,x12126),f686(x12123,x12122,x12124,x12125,x12126)) % 14.98/14.68 [1213]~E(x12131,x12132)+E(f686(x12133,x12134,x12131,x12135,x12136),f686(x12133,x12134,x12132,x12135,x12136)) % 14.98/14.68 [1214]~E(x12141,x12142)+E(f686(x12143,x12144,x12145,x12141,x12146),f686(x12143,x12144,x12145,x12142,x12146)) % 14.98/14.68 [1215]~E(x12151,x12152)+E(f686(x12153,x12154,x12155,x12156,x12151),f686(x12153,x12154,x12155,x12156,x12152)) % 14.98/14.68 [1216]~E(x12161,x12162)+E(f739(x12161,x12163,x12164,x12165,x12166,x12167,x12168,x12169),f739(x12162,x12163,x12164,x12165,x12166,x12167,x12168,x12169)) % 14.98/14.68 [1217]~E(x12171,x12172)+E(f739(x12173,x12171,x12174,x12175,x12176,x12177,x12178,x12179),f739(x12173,x12172,x12174,x12175,x12176,x12177,x12178,x12179)) % 14.98/14.68 [1218]~E(x12181,x12182)+E(f739(x12183,x12184,x12181,x12185,x12186,x12187,x12188,x12189),f739(x12183,x12184,x12182,x12185,x12186,x12187,x12188,x12189)) % 14.98/14.68 [1219]~E(x12191,x12192)+E(f739(x12193,x12194,x12195,x12191,x12196,x12197,x12198,x12199),f739(x12193,x12194,x12195,x12192,x12196,x12197,x12198,x12199)) % 14.98/14.68 [1220]~E(x12201,x12202)+E(f739(x12203,x12204,x12205,x12206,x12201,x12207,x12208,x12209),f739(x12203,x12204,x12205,x12206,x12202,x12207,x12208,x12209)) % 14.98/14.68 [1221]~E(x12211,x12212)+E(f739(x12213,x12214,x12215,x12216,x12217,x12211,x12218,x12219),f739(x12213,x12214,x12215,x12216,x12217,x12212,x12218,x12219)) % 14.98/14.68 [1222]~E(x12221,x12222)+E(f739(x12223,x12224,x12225,x12226,x12227,x12228,x12221,x12229),f739(x12223,x12224,x12225,x12226,x12227,x12228,x12222,x12229)) % 14.98/14.68 [1223]~E(x12231,x12232)+E(f739(x12233,x12234,x12235,x12236,x12237,x12238,x12239,x12231),f739(x12233,x12234,x12235,x12236,x12237,x12238,x12239,x12232)) % 14.98/14.68 [1224]~E(x12241,x12242)+E(f888(x12241,x12243,x12244,x12245,x12246),f888(x12242,x12243,x12244,x12245,x12246)) % 14.98/14.68 [1225]~E(x12251,x12252)+E(f888(x12253,x12251,x12254,x12255,x12256),f888(x12253,x12252,x12254,x12255,x12256)) % 14.98/14.68 [1226]~E(x12261,x12262)+E(f888(x12263,x12264,x12261,x12265,x12266),f888(x12263,x12264,x12262,x12265,x12266)) % 14.98/14.68 [1227]~E(x12271,x12272)+E(f888(x12273,x12274,x12275,x12271,x12276),f888(x12273,x12274,x12275,x12272,x12276)) % 14.98/14.68 [1228]~E(x12281,x12282)+E(f888(x12283,x12284,x12285,x12286,x12281),f888(x12283,x12284,x12285,x12286,x12282)) % 14.98/14.68 [1229]~E(x12291,x12292)+E(f265(x12291,x12293,x12294,x12295),f265(x12292,x12293,x12294,x12295)) % 14.98/14.68 [1230]~E(x12301,x12302)+E(f265(x12303,x12301,x12304,x12305),f265(x12303,x12302,x12304,x12305)) % 14.98/14.68 [1231]~E(x12311,x12312)+E(f265(x12313,x12314,x12311,x12315),f265(x12313,x12314,x12312,x12315)) % 14.98/14.68 [1232]~E(x12321,x12322)+E(f265(x12323,x12324,x12325,x12321),f265(x12323,x12324,x12325,x12322)) % 14.98/14.68 [1233]~E(x12331,x12332)+E(f217(x12331,x12333,x12334,x12335,x12336),f217(x12332,x12333,x12334,x12335,x12336)) % 14.98/14.68 [1234]~E(x12341,x12342)+E(f217(x12343,x12341,x12344,x12345,x12346),f217(x12343,x12342,x12344,x12345,x12346)) % 14.98/14.68 [1235]~E(x12351,x12352)+E(f217(x12353,x12354,x12351,x12355,x12356),f217(x12353,x12354,x12352,x12355,x12356)) % 14.98/14.68 [1236]~E(x12361,x12362)+E(f217(x12363,x12364,x12365,x12361,x12366),f217(x12363,x12364,x12365,x12362,x12366)) % 14.98/14.68 [1237]~E(x12371,x12372)+E(f217(x12373,x12374,x12375,x12376,x12371),f217(x12373,x12374,x12375,x12376,x12372)) % 14.98/14.68 [1238]~E(x12381,x12382)+E(f837(x12381,x12383,x12384,x12385),f837(x12382,x12383,x12384,x12385)) % 14.98/14.68 [1239]~E(x12391,x12392)+E(f837(x12393,x12391,x12394,x12395),f837(x12393,x12392,x12394,x12395)) % 14.98/14.68 [1240]~E(x12401,x12402)+E(f837(x12403,x12404,x12401,x12405),f837(x12403,x12404,x12402,x12405)) % 14.98/14.68 [1241]~E(x12411,x12412)+E(f837(x12413,x12414,x12415,x12411),f837(x12413,x12414,x12415,x12412)) % 14.98/14.68 [1242]~E(x12421,x12422)+E(f237(x12421,x12423,x12424),f237(x12422,x12423,x12424)) % 14.98/14.68 [1243]~E(x12431,x12432)+E(f237(x12433,x12431,x12434),f237(x12433,x12432,x12434)) % 14.98/14.68 [1244]~E(x12441,x12442)+E(f237(x12443,x12444,x12441),f237(x12443,x12444,x12442)) % 14.98/14.68 [1245]~E(x12451,x12452)+E(f462(x12451,x12453,x12454),f462(x12452,x12453,x12454)) % 14.98/14.68 [1246]~E(x12461,x12462)+E(f462(x12463,x12461,x12464),f462(x12463,x12462,x12464)) % 14.98/14.68 [1247]~E(x12471,x12472)+E(f462(x12473,x12474,x12471),f462(x12473,x12474,x12472)) % 14.98/14.68 [1248]~E(x12481,x12482)+E(f693(x12481,x12483,x12484,x12485),f693(x12482,x12483,x12484,x12485)) % 14.98/14.68 [1249]~E(x12491,x12492)+E(f693(x12493,x12491,x12494,x12495),f693(x12493,x12492,x12494,x12495)) % 14.98/14.68 [1250]~E(x12501,x12502)+E(f693(x12503,x12504,x12501,x12505),f693(x12503,x12504,x12502,x12505)) % 14.98/14.68 [1251]~E(x12511,x12512)+E(f693(x12513,x12514,x12515,x12511),f693(x12513,x12514,x12515,x12512)) % 14.98/14.68 [1252]~E(x12521,x12522)+E(f810(x12521,x12523),f810(x12522,x12523)) % 14.98/14.68 [1253]~E(x12531,x12532)+E(f810(x12533,x12531),f810(x12533,x12532)) % 14.98/14.68 [1254]~E(x12541,x12542)+E(f675(x12541,x12543,x12544,x12545),f675(x12542,x12543,x12544,x12545)) % 14.98/14.68 [1255]~E(x12551,x12552)+E(f675(x12553,x12551,x12554,x12555),f675(x12553,x12552,x12554,x12555)) % 14.98/14.68 [1256]~E(x12561,x12562)+E(f675(x12563,x12564,x12561,x12565),f675(x12563,x12564,x12562,x12565)) % 14.98/14.68 [1257]~E(x12571,x12572)+E(f675(x12573,x12574,x12575,x12571),f675(x12573,x12574,x12575,x12572)) % 14.98/14.68 [1258]~E(x12581,x12582)+E(f192(x12581,x12583),f192(x12582,x12583)) % 14.98/14.68 [1259]~E(x12591,x12592)+E(f192(x12593,x12591),f192(x12593,x12592)) % 14.98/14.68 [1260]~E(x12601,x12602)+E(f478(x12601,x12603,x12604,x12605,x12606),f478(x12602,x12603,x12604,x12605,x12606)) % 14.98/14.68 [1261]~E(x12611,x12612)+E(f478(x12613,x12611,x12614,x12615,x12616),f478(x12613,x12612,x12614,x12615,x12616)) % 14.98/14.68 [1262]~E(x12621,x12622)+E(f478(x12623,x12624,x12621,x12625,x12626),f478(x12623,x12624,x12622,x12625,x12626)) % 14.98/14.68 [1263]~E(x12631,x12632)+E(f478(x12633,x12634,x12635,x12631,x12636),f478(x12633,x12634,x12635,x12632,x12636)) % 14.98/14.68 [1264]~E(x12641,x12642)+E(f478(x12643,x12644,x12645,x12646,x12641),f478(x12643,x12644,x12645,x12646,x12642)) % 14.98/14.68 [1265]~E(x12651,x12652)+E(f598(x12651,x12653,x12654,x12655),f598(x12652,x12653,x12654,x12655)) % 14.98/14.68 [1266]~E(x12661,x12662)+E(f598(x12663,x12661,x12664,x12665),f598(x12663,x12662,x12664,x12665)) % 14.98/14.68 [1267]~E(x12671,x12672)+E(f598(x12673,x12674,x12671,x12675),f598(x12673,x12674,x12672,x12675)) % 14.98/14.68 [1268]~E(x12681,x12682)+E(f598(x12683,x12684,x12685,x12681),f598(x12683,x12684,x12685,x12682)) % 14.98/14.68 [1269]~E(x12691,x12692)+E(f591(x12691,x12693,x12694,x12695),f591(x12692,x12693,x12694,x12695)) % 14.98/14.68 [1270]~E(x12701,x12702)+E(f591(x12703,x12701,x12704,x12705),f591(x12703,x12702,x12704,x12705)) % 14.98/14.68 [1271]~E(x12711,x12712)+E(f591(x12713,x12714,x12711,x12715),f591(x12713,x12714,x12712,x12715)) % 14.98/14.68 [1272]~E(x12721,x12722)+E(f591(x12723,x12724,x12725,x12721),f591(x12723,x12724,x12725,x12722)) % 14.98/14.68 [1273]~E(x12731,x12732)+E(f392(x12731,x12733),f392(x12732,x12733)) % 14.98/14.68 [1274]~E(x12741,x12742)+E(f392(x12743,x12741),f392(x12743,x12742)) % 14.98/14.68 [1275]~E(x12751,x12752)+E(f340(x12751,x12753,x12754),f340(x12752,x12753,x12754)) % 14.98/14.68 [1276]~E(x12761,x12762)+E(f340(x12763,x12761,x12764),f340(x12763,x12762,x12764)) % 14.98/14.68 [1277]~E(x12771,x12772)+E(f340(x12773,x12774,x12771),f340(x12773,x12774,x12772)) % 14.98/14.68 [1278]~E(x12781,x12782)+E(f452(x12781,x12783,x12784),f452(x12782,x12783,x12784)) % 14.98/14.68 [1279]~E(x12791,x12792)+E(f452(x12793,x12791,x12794),f452(x12793,x12792,x12794)) % 14.98/14.68 [1280]~E(x12801,x12802)+E(f452(x12803,x12804,x12801),f452(x12803,x12804,x12802)) % 14.98/14.68 [1281]~E(x12811,x12812)+E(f551(x12811,x12813,x12814,x12815,x12816),f551(x12812,x12813,x12814,x12815,x12816)) % 14.98/14.68 [1282]~E(x12821,x12822)+E(f551(x12823,x12821,x12824,x12825,x12826),f551(x12823,x12822,x12824,x12825,x12826)) % 14.98/14.68 [1283]~E(x12831,x12832)+E(f551(x12833,x12834,x12831,x12835,x12836),f551(x12833,x12834,x12832,x12835,x12836)) % 14.98/14.68 [1284]~E(x12841,x12842)+E(f551(x12843,x12844,x12845,x12841,x12846),f551(x12843,x12844,x12845,x12842,x12846)) % 14.98/14.68 [1285]~E(x12851,x12852)+E(f551(x12853,x12854,x12855,x12856,x12851),f551(x12853,x12854,x12855,x12856,x12852)) % 14.98/14.68 [1286]~E(x12861,x12862)+E(f336(x12861,x12863,x12864),f336(x12862,x12863,x12864)) % 14.98/14.68 [1287]~E(x12871,x12872)+E(f336(x12873,x12871,x12874),f336(x12873,x12872,x12874)) % 14.98/14.68 [1288]~E(x12881,x12882)+E(f336(x12883,x12884,x12881),f336(x12883,x12884,x12882)) % 14.98/14.68 [1289]~E(x12891,x12892)+E(f812(x12891,x12893,x12894,x12895),f812(x12892,x12893,x12894,x12895)) % 14.98/14.68 [1290]~E(x12901,x12902)+E(f812(x12903,x12901,x12904,x12905),f812(x12903,x12902,x12904,x12905)) % 14.98/14.68 [1291]~E(x12911,x12912)+E(f812(x12913,x12914,x12911,x12915),f812(x12913,x12914,x12912,x12915)) % 14.98/14.68 [1292]~E(x12921,x12922)+E(f812(x12923,x12924,x12925,x12921),f812(x12923,x12924,x12925,x12922)) % 14.98/14.68 [1293]~E(x12931,x12932)+E(f786(x12931,x12933,x12934,x12935),f786(x12932,x12933,x12934,x12935)) % 14.98/14.68 [1294]~E(x12941,x12942)+E(f786(x12943,x12941,x12944,x12945),f786(x12943,x12942,x12944,x12945)) % 14.98/14.68 [1295]~E(x12951,x12952)+E(f786(x12953,x12954,x12951,x12955),f786(x12953,x12954,x12952,x12955)) % 14.98/14.68 [1296]~E(x12961,x12962)+E(f786(x12963,x12964,x12965,x12961),f786(x12963,x12964,x12965,x12962)) % 14.98/14.68 [1297]~E(x12971,x12972)+E(f662(x12971,x12973,x12974,x12975,x12976),f662(x12972,x12973,x12974,x12975,x12976)) % 14.98/14.68 [1298]~E(x12981,x12982)+E(f662(x12983,x12981,x12984,x12985,x12986),f662(x12983,x12982,x12984,x12985,x12986)) % 14.98/14.68 [1299]~E(x12991,x12992)+E(f662(x12993,x12994,x12991,x12995,x12996),f662(x12993,x12994,x12992,x12995,x12996)) % 14.98/14.68 [1300]~E(x13001,x13002)+E(f662(x13003,x13004,x13005,x13001,x13006),f662(x13003,x13004,x13005,x13002,x13006)) % 14.98/14.68 [1301]~E(x13011,x13012)+E(f662(x13013,x13014,x13015,x13016,x13011),f662(x13013,x13014,x13015,x13016,x13012)) % 14.98/14.68 [1302]~E(x13021,x13022)+E(f629(x13021,x13023,x13024),f629(x13022,x13023,x13024)) % 14.98/14.68 [1303]~E(x13031,x13032)+E(f629(x13033,x13031,x13034),f629(x13033,x13032,x13034)) % 14.98/14.68 [1304]~E(x13041,x13042)+E(f629(x13043,x13044,x13041),f629(x13043,x13044,x13042)) % 14.98/14.68 [1305]~E(x13051,x13052)+E(f854(x13051,x13053,x13054,x13055,x13056,x13057),f854(x13052,x13053,x13054,x13055,x13056,x13057)) % 14.98/14.68 [1306]~E(x13061,x13062)+E(f854(x13063,x13061,x13064,x13065,x13066,x13067),f854(x13063,x13062,x13064,x13065,x13066,x13067)) % 14.98/14.68 [1307]~E(x13071,x13072)+E(f854(x13073,x13074,x13071,x13075,x13076,x13077),f854(x13073,x13074,x13072,x13075,x13076,x13077)) % 14.98/14.68 [1308]~E(x13081,x13082)+E(f854(x13083,x13084,x13085,x13081,x13086,x13087),f854(x13083,x13084,x13085,x13082,x13086,x13087)) % 14.98/14.68 [1309]~E(x13091,x13092)+E(f854(x13093,x13094,x13095,x13096,x13091,x13097),f854(x13093,x13094,x13095,x13096,x13092,x13097)) % 14.98/14.68 [1310]~E(x13101,x13102)+E(f854(x13103,x13104,x13105,x13106,x13107,x13101),f854(x13103,x13104,x13105,x13106,x13107,x13102)) % 14.98/14.68 [1311]~E(x13111,x13112)+E(f674(x13111,x13113,x13114,x13115),f674(x13112,x13113,x13114,x13115)) % 14.98/14.68 [1312]~E(x13121,x13122)+E(f674(x13123,x13121,x13124,x13125),f674(x13123,x13122,x13124,x13125)) % 14.98/14.68 [1313]~E(x13131,x13132)+E(f674(x13133,x13134,x13131,x13135),f674(x13133,x13134,x13132,x13135)) % 14.98/14.68 [1314]~E(x13141,x13142)+E(f674(x13143,x13144,x13145,x13141),f674(x13143,x13144,x13145,x13142)) % 14.98/14.68 [1315]~E(x13151,x13152)+E(f615(x13151,x13153,x13154,x13155),f615(x13152,x13153,x13154,x13155)) % 14.98/14.68 [1316]~E(x13161,x13162)+E(f615(x13163,x13161,x13164,x13165),f615(x13163,x13162,x13164,x13165)) % 14.98/14.68 [1317]~E(x13171,x13172)+E(f615(x13173,x13174,x13171,x13175),f615(x13173,x13174,x13172,x13175)) % 14.98/14.68 [1318]~E(x13181,x13182)+E(f615(x13183,x13184,x13185,x13181),f615(x13183,x13184,x13185,x13182)) % 14.98/14.68 [1319]~E(x13191,x13192)+E(f166(x13191,x13193,x13194),f166(x13192,x13193,x13194)) % 14.98/14.68 [1320]~E(x13201,x13202)+E(f166(x13203,x13201,x13204),f166(x13203,x13202,x13204)) % 14.98/14.68 [1321]~E(x13211,x13212)+E(f166(x13213,x13214,x13211),f166(x13213,x13214,x13212)) % 14.98/14.68 [1322]~E(x13221,x13222)+E(f34(x13221),f34(x13222)) % 14.98/14.68 [1323]~E(x13231,x13232)+E(f579(x13231,x13233,x13234),f579(x13232,x13233,x13234)) % 14.98/14.68 [1324]~E(x13241,x13242)+E(f579(x13243,x13241,x13244),f579(x13243,x13242,x13244)) % 14.98/14.68 [1325]~E(x13251,x13252)+E(f579(x13253,x13254,x13251),f579(x13253,x13254,x13252)) % 14.98/14.68 [1326]~E(x13261,x13262)+E(f136(x13261,x13263),f136(x13262,x13263)) % 14.98/14.68 [1327]~E(x13271,x13272)+E(f136(x13273,x13271),f136(x13273,x13272)) % 14.98/14.68 [1328]~E(x13281,x13282)+E(f628(x13281,x13283,x13284,x13285),f628(x13282,x13283,x13284,x13285)) % 14.98/14.68 [1329]~E(x13291,x13292)+E(f628(x13293,x13291,x13294,x13295),f628(x13293,x13292,x13294,x13295)) % 14.98/14.68 [1330]~E(x13301,x13302)+E(f628(x13303,x13304,x13301,x13305),f628(x13303,x13304,x13302,x13305)) % 14.98/14.68 [1331]~E(x13311,x13312)+E(f628(x13313,x13314,x13315,x13311),f628(x13313,x13314,x13315,x13312)) % 14.98/14.68 [1332]~E(x13321,x13322)+E(f544(x13321,x13323,x13324,x13325,x13326,x13327,x13328,x13329),f544(x13322,x13323,x13324,x13325,x13326,x13327,x13328,x13329)) % 14.98/14.68 [1333]~E(x13331,x13332)+E(f544(x13333,x13331,x13334,x13335,x13336,x13337,x13338,x13339),f544(x13333,x13332,x13334,x13335,x13336,x13337,x13338,x13339)) % 14.98/14.68 [1334]~E(x13341,x13342)+E(f544(x13343,x13344,x13341,x13345,x13346,x13347,x13348,x13349),f544(x13343,x13344,x13342,x13345,x13346,x13347,x13348,x13349)) % 14.98/14.68 [1335]~E(x13351,x13352)+E(f544(x13353,x13354,x13355,x13351,x13356,x13357,x13358,x13359),f544(x13353,x13354,x13355,x13352,x13356,x13357,x13358,x13359)) % 14.98/14.68 [1336]~E(x13361,x13362)+E(f544(x13363,x13364,x13365,x13366,x13361,x13367,x13368,x13369),f544(x13363,x13364,x13365,x13366,x13362,x13367,x13368,x13369)) % 14.98/14.68 [1337]~E(x13371,x13372)+E(f544(x13373,x13374,x13375,x13376,x13377,x13371,x13378,x13379),f544(x13373,x13374,x13375,x13376,x13377,x13372,x13378,x13379)) % 14.98/14.68 [1338]~E(x13381,x13382)+E(f544(x13383,x13384,x13385,x13386,x13387,x13388,x13381,x13389),f544(x13383,x13384,x13385,x13386,x13387,x13388,x13382,x13389)) % 14.98/14.68 [1339]~E(x13391,x13392)+E(f544(x13393,x13394,x13395,x13396,x13397,x13398,x13399,x13391),f544(x13393,x13394,x13395,x13396,x13397,x13398,x13399,x13392)) % 14.98/14.68 [1340]~E(x13401,x13402)+E(f557(x13401,x13403),f557(x13402,x13403)) % 14.98/14.68 [1341]~E(x13411,x13412)+E(f557(x13413,x13411),f557(x13413,x13412)) % 14.98/14.68 [1342]~E(x13421,x13422)+E(f673(x13421,x13423),f673(x13422,x13423)) % 14.98/14.68 [1343]~E(x13431,x13432)+E(f673(x13433,x13431),f673(x13433,x13432)) % 14.98/14.68 [1344]~E(x13441,x13442)+E(f605(x13441,x13443,x13444,x13445,x13446,x13447,x13448,x13449),f605(x13442,x13443,x13444,x13445,x13446,x13447,x13448,x13449)) % 14.98/14.68 [1345]~E(x13451,x13452)+E(f605(x13453,x13451,x13454,x13455,x13456,x13457,x13458,x13459),f605(x13453,x13452,x13454,x13455,x13456,x13457,x13458,x13459)) % 14.98/14.68 [1346]~E(x13461,x13462)+E(f605(x13463,x13464,x13461,x13465,x13466,x13467,x13468,x13469),f605(x13463,x13464,x13462,x13465,x13466,x13467,x13468,x13469)) % 14.98/14.68 [1347]~E(x13471,x13472)+E(f605(x13473,x13474,x13475,x13471,x13476,x13477,x13478,x13479),f605(x13473,x13474,x13475,x13472,x13476,x13477,x13478,x13479)) % 14.98/14.68 [1348]~E(x13481,x13482)+E(f605(x13483,x13484,x13485,x13486,x13481,x13487,x13488,x13489),f605(x13483,x13484,x13485,x13486,x13482,x13487,x13488,x13489)) % 14.98/14.68 [1349]~E(x13491,x13492)+E(f605(x13493,x13494,x13495,x13496,x13497,x13491,x13498,x13499),f605(x13493,x13494,x13495,x13496,x13497,x13492,x13498,x13499)) % 14.98/14.68 [1350]~E(x13501,x13502)+E(f605(x13503,x13504,x13505,x13506,x13507,x13508,x13501,x13509),f605(x13503,x13504,x13505,x13506,x13507,x13508,x13502,x13509)) % 14.98/14.68 [1351]~E(x13511,x13512)+E(f605(x13513,x13514,x13515,x13516,x13517,x13518,x13519,x13511),f605(x13513,x13514,x13515,x13516,x13517,x13518,x13519,x13512)) % 14.98/14.68 [1352]~E(x13521,x13522)+E(f634(x13521,x13523,x13524,x13525,x13526),f634(x13522,x13523,x13524,x13525,x13526)) % 14.98/14.68 [1353]~E(x13531,x13532)+E(f634(x13533,x13531,x13534,x13535,x13536),f634(x13533,x13532,x13534,x13535,x13536)) % 14.98/14.68 [1354]~E(x13541,x13542)+E(f634(x13543,x13544,x13541,x13545,x13546),f634(x13543,x13544,x13542,x13545,x13546)) % 14.98/14.68 [1355]~E(x13551,x13552)+E(f634(x13553,x13554,x13555,x13551,x13556),f634(x13553,x13554,x13555,x13552,x13556)) % 14.98/14.68 [1356]~E(x13561,x13562)+E(f634(x13563,x13564,x13565,x13566,x13561),f634(x13563,x13564,x13565,x13566,x13562)) % 14.98/14.68 [1357]~E(x13571,x13572)+E(f782(x13571,x13573,x13574,x13575),f782(x13572,x13573,x13574,x13575)) % 14.98/14.68 [1358]~E(x13581,x13582)+E(f782(x13583,x13581,x13584,x13585),f782(x13583,x13582,x13584,x13585)) % 14.98/14.68 [1359]~E(x13591,x13592)+E(f782(x13593,x13594,x13591,x13595),f782(x13593,x13594,x13592,x13595)) % 14.98/14.68 [1360]~E(x13601,x13602)+E(f782(x13603,x13604,x13605,x13601),f782(x13603,x13604,x13605,x13602)) % 14.98/14.68 [1361]~E(x13611,x13612)+E(f914(x13611,x13613,x13614),f914(x13612,x13613,x13614)) % 14.98/14.68 [1362]~E(x13621,x13622)+E(f914(x13623,x13621,x13624),f914(x13623,x13622,x13624)) % 14.98/14.68 [1363]~E(x13631,x13632)+E(f914(x13633,x13634,x13631),f914(x13633,x13634,x13632)) % 14.98/14.68 [1364]~E(x13641,x13642)+E(f191(x13641,x13643,x13644,x13645),f191(x13642,x13643,x13644,x13645)) % 14.98/14.68 [1365]~E(x13651,x13652)+E(f191(x13653,x13651,x13654,x13655),f191(x13653,x13652,x13654,x13655)) % 14.98/14.68 [1366]~E(x13661,x13662)+E(f191(x13663,x13664,x13661,x13665),f191(x13663,x13664,x13662,x13665)) % 14.98/14.68 [1367]~E(x13671,x13672)+E(f191(x13673,x13674,x13675,x13671),f191(x13673,x13674,x13675,x13672)) % 14.98/14.68 [1368]~E(x13681,x13682)+E(f853(x13681,x13683,x13684,x13685,x13686),f853(x13682,x13683,x13684,x13685,x13686)) % 14.98/14.68 [1369]~E(x13691,x13692)+E(f853(x13693,x13691,x13694,x13695,x13696),f853(x13693,x13692,x13694,x13695,x13696)) % 14.98/14.68 [1370]~E(x13701,x13702)+E(f853(x13703,x13704,x13701,x13705,x13706),f853(x13703,x13704,x13702,x13705,x13706)) % 14.98/14.68 [1371]~E(x13711,x13712)+E(f853(x13713,x13714,x13715,x13711,x13716),f853(x13713,x13714,x13715,x13712,x13716)) % 14.98/14.68 [1372]~E(x13721,x13722)+E(f853(x13723,x13724,x13725,x13726,x13721),f853(x13723,x13724,x13725,x13726,x13722)) % 14.98/14.68 [1373]~E(x13731,x13732)+E(f899(x13731,x13733,x13734,x13735,x13736),f899(x13732,x13733,x13734,x13735,x13736)) % 14.98/14.68 [1374]~E(x13741,x13742)+E(f899(x13743,x13741,x13744,x13745,x13746),f899(x13743,x13742,x13744,x13745,x13746)) % 14.98/14.68 [1375]~E(x13751,x13752)+E(f899(x13753,x13754,x13751,x13755,x13756),f899(x13753,x13754,x13752,x13755,x13756)) % 14.98/14.68 [1376]~E(x13761,x13762)+E(f899(x13763,x13764,x13765,x13761,x13766),f899(x13763,x13764,x13765,x13762,x13766)) % 14.98/14.68 [1377]~E(x13771,x13772)+E(f899(x13773,x13774,x13775,x13776,x13771),f899(x13773,x13774,x13775,x13776,x13772)) % 14.98/14.68 [1378]~E(x13781,x13782)+E(f425(x13781),f425(x13782)) % 14.98/14.68 [1379]~E(x13791,x13792)+E(f789(x13791,x13793),f789(x13792,x13793)) % 14.98/14.68 [1380]~E(x13801,x13802)+E(f789(x13803,x13801),f789(x13803,x13802)) % 14.98/14.68 [1381]~E(x13811,x13812)+E(f670(x13811,x13813,x13814),f670(x13812,x13813,x13814)) % 14.98/14.68 [1382]~E(x13821,x13822)+E(f670(x13823,x13821,x13824),f670(x13823,x13822,x13824)) % 14.98/14.68 [1383]~E(x13831,x13832)+E(f670(x13833,x13834,x13831),f670(x13833,x13834,x13832)) % 14.98/14.68 [1384]~E(x13841,x13842)+E(f578(x13841,x13843),f578(x13842,x13843)) % 14.98/14.68 [1385]~E(x13851,x13852)+E(f578(x13853,x13851),f578(x13853,x13852)) % 14.98/14.68 [1386]~E(x13861,x13862)+E(f842(x13861,x13863,x13864,x13865,x13866,x13867),f842(x13862,x13863,x13864,x13865,x13866,x13867)) % 14.98/14.68 [1387]~E(x13871,x13872)+E(f842(x13873,x13871,x13874,x13875,x13876,x13877),f842(x13873,x13872,x13874,x13875,x13876,x13877)) % 14.98/14.68 [1388]~E(x13881,x13882)+E(f842(x13883,x13884,x13881,x13885,x13886,x13887),f842(x13883,x13884,x13882,x13885,x13886,x13887)) % 14.98/14.68 [1389]~E(x13891,x13892)+E(f842(x13893,x13894,x13895,x13891,x13896,x13897),f842(x13893,x13894,x13895,x13892,x13896,x13897)) % 14.98/14.68 [1390]~E(x13901,x13902)+E(f842(x13903,x13904,x13905,x13906,x13901,x13907),f842(x13903,x13904,x13905,x13906,x13902,x13907)) % 14.98/14.68 [1391]~E(x13911,x13912)+E(f842(x13913,x13914,x13915,x13916,x13917,x13911),f842(x13913,x13914,x13915,x13916,x13917,x13912)) % 14.98/14.68 [1392]~E(x13921,x13922)+E(f199(x13921,x13923,x13924,x13925),f199(x13922,x13923,x13924,x13925)) % 14.98/14.68 [1393]~E(x13931,x13932)+E(f199(x13933,x13931,x13934,x13935),f199(x13933,x13932,x13934,x13935)) % 14.98/14.68 [1394]~E(x13941,x13942)+E(f199(x13943,x13944,x13941,x13945),f199(x13943,x13944,x13942,x13945)) % 14.98/14.68 [1395]~E(x13951,x13952)+E(f199(x13953,x13954,x13955,x13951),f199(x13953,x13954,x13955,x13952)) % 14.98/14.68 [1396]~E(x13961,x13962)+E(f502(x13961,x13963,x13964),f502(x13962,x13963,x13964)) % 14.98/14.68 [1397]~E(x13971,x13972)+E(f502(x13973,x13971,x13974),f502(x13973,x13972,x13974)) % 14.98/14.68 [1398]~E(x13981,x13982)+E(f502(x13983,x13984,x13981),f502(x13983,x13984,x13982)) % 14.98/14.68 [1399]~E(x13991,x13992)+E(f351(x13991,x13993,x13994),f351(x13992,x13993,x13994)) % 14.98/14.68 [1400]~E(x14001,x14002)+E(f351(x14003,x14001,x14004),f351(x14003,x14002,x14004)) % 14.98/14.68 [1401]~E(x14011,x14012)+E(f351(x14013,x14014,x14011),f351(x14013,x14014,x14012)) % 14.98/14.68 [1402]~E(x14021,x14022)+E(f333(x14021,x14023,x14024),f333(x14022,x14023,x14024)) % 14.98/14.68 [1403]~E(x14031,x14032)+E(f333(x14033,x14031,x14034),f333(x14033,x14032,x14034)) % 14.98/14.68 [1404]~E(x14041,x14042)+E(f333(x14043,x14044,x14041),f333(x14043,x14044,x14042)) % 14.98/14.68 [1405]~E(x14051,x14052)+E(f241(x14051,x14053,x14054),f241(x14052,x14053,x14054)) % 14.98/14.68 [1406]~E(x14061,x14062)+E(f241(x14063,x14061,x14064),f241(x14063,x14062,x14064)) % 14.98/14.68 [1407]~E(x14071,x14072)+E(f241(x14073,x14074,x14071),f241(x14073,x14074,x14072)) % 14.98/14.68 [1408]~E(x14081,x14082)+E(f420(x14081,x14083,x14084),f420(x14082,x14083,x14084)) % 14.98/14.68 [1409]~E(x14091,x14092)+E(f420(x14093,x14091,x14094),f420(x14093,x14092,x14094)) % 14.98/14.68 [1410]~E(x14101,x14102)+E(f420(x14103,x14104,x14101),f420(x14103,x14104,x14102)) % 14.98/14.68 [1411]~E(x14111,x14112)+E(f286(x14111,x14113,x14114),f286(x14112,x14113,x14114)) % 14.98/14.68 [1412]~E(x14121,x14122)+E(f286(x14123,x14121,x14124),f286(x14123,x14122,x14124)) % 14.98/14.68 [1413]~E(x14131,x14132)+E(f286(x14133,x14134,x14131),f286(x14133,x14134,x14132)) % 14.98/14.68 [1414]~E(x14141,x14142)+E(f490(x14141,x14143,x14144),f490(x14142,x14143,x14144)) % 14.98/14.68 [1415]~E(x14151,x14152)+E(f490(x14153,x14151,x14154),f490(x14153,x14152,x14154)) % 14.98/14.68 [1416]~E(x14161,x14162)+E(f490(x14163,x14164,x14161),f490(x14163,x14164,x14162)) % 14.98/14.68 [1417]~E(x14171,x14172)+E(f625(x14171,x14173,x14174),f625(x14172,x14173,x14174)) % 14.98/14.68 [1418]~E(x14181,x14182)+E(f625(x14183,x14181,x14184),f625(x14183,x14182,x14184)) % 14.98/14.68 [1419]~E(x14191,x14192)+E(f625(x14193,x14194,x14191),f625(x14193,x14194,x14192)) % 14.98/14.68 [1420]~E(x14201,x14202)+E(f552(x14201,x14203,x14204,x14205),f552(x14202,x14203,x14204,x14205)) % 14.98/14.68 [1421]~E(x14211,x14212)+E(f552(x14213,x14211,x14214,x14215),f552(x14213,x14212,x14214,x14215)) % 14.98/14.68 [1422]~E(x14221,x14222)+E(f552(x14223,x14224,x14221,x14225),f552(x14223,x14224,x14222,x14225)) % 14.98/14.68 [1423]~E(x14231,x14232)+E(f552(x14233,x14234,x14235,x14231),f552(x14233,x14234,x14235,x14232)) % 14.98/14.68 [1424]~E(x14241,x14242)+E(f918(x14241,x14243,x14244,x14245,x14246),f918(x14242,x14243,x14244,x14245,x14246)) % 14.98/14.68 [1425]~E(x14251,x14252)+E(f918(x14253,x14251,x14254,x14255,x14256),f918(x14253,x14252,x14254,x14255,x14256)) % 14.98/14.68 [1426]~E(x14261,x14262)+E(f918(x14263,x14264,x14261,x14265,x14266),f918(x14263,x14264,x14262,x14265,x14266)) % 14.98/14.68 [1427]~E(x14271,x14272)+E(f918(x14273,x14274,x14275,x14271,x14276),f918(x14273,x14274,x14275,x14272,x14276)) % 14.98/14.68 [1428]~E(x14281,x14282)+E(f918(x14283,x14284,x14285,x14286,x14281),f918(x14283,x14284,x14285,x14286,x14282)) % 14.98/14.68 [1429]~E(x14291,x14292)+E(f454(x14291,x14293,x14294),f454(x14292,x14293,x14294)) % 14.98/14.68 [1430]~E(x14301,x14302)+E(f454(x14303,x14301,x14304),f454(x14303,x14302,x14304)) % 14.98/14.68 [1431]~E(x14311,x14312)+E(f454(x14313,x14314,x14311),f454(x14313,x14314,x14312)) % 14.98/14.68 [1432]~E(x14321,x14322)+E(f399(x14321,x14323,x14324,x14325),f399(x14322,x14323,x14324,x14325)) % 14.98/14.68 [1433]~E(x14331,x14332)+E(f399(x14333,x14331,x14334,x14335),f399(x14333,x14332,x14334,x14335)) % 14.98/14.68 [1434]~E(x14341,x14342)+E(f399(x14343,x14344,x14341,x14345),f399(x14343,x14344,x14342,x14345)) % 14.98/14.68 [1435]~E(x14351,x14352)+E(f399(x14353,x14354,x14355,x14351),f399(x14353,x14354,x14355,x14352)) % 14.98/14.68 [1436]~E(x14361,x14362)+E(f893(x14361,x14363,x14364,x14365),f893(x14362,x14363,x14364,x14365)) % 14.98/14.68 [1437]~E(x14371,x14372)+E(f893(x14373,x14371,x14374,x14375),f893(x14373,x14372,x14374,x14375)) % 14.98/14.68 [1438]~E(x14381,x14382)+E(f893(x14383,x14384,x14381,x14385),f893(x14383,x14384,x14382,x14385)) % 14.98/14.68 [1439]~E(x14391,x14392)+E(f893(x14393,x14394,x14395,x14391),f893(x14393,x14394,x14395,x14392)) % 14.98/14.68 [1440]~E(x14401,x14402)+E(f800(x14401,x14403,x14404,x14405),f800(x14402,x14403,x14404,x14405)) % 14.98/14.68 [1441]~E(x14411,x14412)+E(f800(x14413,x14411,x14414,x14415),f800(x14413,x14412,x14414,x14415)) % 14.98/14.68 [1442]~E(x14421,x14422)+E(f800(x14423,x14424,x14421,x14425),f800(x14423,x14424,x14422,x14425)) % 14.98/14.68 [1443]~E(x14431,x14432)+E(f800(x14433,x14434,x14435,x14431),f800(x14433,x14434,x14435,x14432)) % 14.98/14.68 [1444]~E(x14441,x14442)+E(f708(x14441,x14443),f708(x14442,x14443)) % 14.98/14.68 [1445]~E(x14451,x14452)+E(f708(x14453,x14451),f708(x14453,x14452)) % 14.98/14.68 [1446]~E(x14461,x14462)+E(f349(x14461,x14463),f349(x14462,x14463)) % 14.98/14.68 [1447]~E(x14471,x14472)+E(f349(x14473,x14471),f349(x14473,x14472)) % 14.98/14.68 [1448]~E(x14481,x14482)+E(f385(x14481,x14483,x14484),f385(x14482,x14483,x14484)) % 14.98/14.68 [1449]~E(x14491,x14492)+E(f385(x14493,x14491,x14494),f385(x14493,x14492,x14494)) % 14.98/14.68 [1450]~E(x14501,x14502)+E(f385(x14503,x14504,x14501),f385(x14503,x14504,x14502)) % 14.98/14.68 [1451]~E(x14511,x14512)+E(f900(x14511,x14513,x14514,x14515,x14516),f900(x14512,x14513,x14514,x14515,x14516)) % 14.98/14.68 [1452]~E(x14521,x14522)+E(f900(x14523,x14521,x14524,x14525,x14526),f900(x14523,x14522,x14524,x14525,x14526)) % 14.98/14.68 [1453]~E(x14531,x14532)+E(f900(x14533,x14534,x14531,x14535,x14536),f900(x14533,x14534,x14532,x14535,x14536)) % 14.98/14.68 [1454]~E(x14541,x14542)+E(f900(x14543,x14544,x14545,x14541,x14546),f900(x14543,x14544,x14545,x14542,x14546)) % 14.98/14.68 [1455]~E(x14551,x14552)+E(f900(x14553,x14554,x14555,x14556,x14551),f900(x14553,x14554,x14555,x14556,x14552)) % 14.98/14.68 [1456]~E(x14561,x14562)+E(f124(x14561,x14563,x14564,x14565),f124(x14562,x14563,x14564,x14565)) % 14.98/14.68 [1457]~E(x14571,x14572)+E(f124(x14573,x14571,x14574,x14575),f124(x14573,x14572,x14574,x14575)) % 14.98/14.68 [1458]~E(x14581,x14582)+E(f124(x14583,x14584,x14581,x14585),f124(x14583,x14584,x14582,x14585)) % 14.98/14.68 [1459]~E(x14591,x14592)+E(f124(x14593,x14594,x14595,x14591),f124(x14593,x14594,x14595,x14592)) % 14.98/14.68 [1460]~E(x14601,x14602)+E(f453(x14601,x14603,x14604),f453(x14602,x14603,x14604)) % 14.98/14.68 [1461]~E(x14611,x14612)+E(f453(x14613,x14611,x14614),f453(x14613,x14612,x14614)) % 14.98/14.68 [1462]~E(x14621,x14622)+E(f453(x14623,x14624,x14621),f453(x14623,x14624,x14622)) % 14.98/14.68 [1463]~E(x14631,x14632)+E(f678(x14631,x14633,x14634),f678(x14632,x14633,x14634)) % 14.98/14.68 [1464]~E(x14641,x14642)+E(f678(x14643,x14641,x14644),f678(x14643,x14642,x14644)) % 14.98/14.68 [1465]~E(x14651,x14652)+E(f678(x14653,x14654,x14651),f678(x14653,x14654,x14652)) % 14.98/14.68 [1466]~E(x14661,x14662)+E(f370(x14661,x14663,x14664),f370(x14662,x14663,x14664)) % 14.98/14.68 [1467]~E(x14671,x14672)+E(f370(x14673,x14671,x14674),f370(x14673,x14672,x14674)) % 14.98/14.68 [1468]~E(x14681,x14682)+E(f370(x14683,x14684,x14681),f370(x14683,x14684,x14682)) % 14.98/14.68 [1469]~E(x14691,x14692)+E(f123(x14691,x14693,x14694,x14695),f123(x14692,x14693,x14694,x14695)) % 14.98/14.68 [1470]~E(x14701,x14702)+E(f123(x14703,x14701,x14704,x14705),f123(x14703,x14702,x14704,x14705)) % 14.98/14.68 [1471]~E(x14711,x14712)+E(f123(x14713,x14714,x14711,x14715),f123(x14713,x14714,x14712,x14715)) % 14.98/14.68 [1472]~E(x14721,x14722)+E(f123(x14723,x14724,x14725,x14721),f123(x14723,x14724,x14725,x14722)) % 14.98/14.68 [1473]~E(x14731,x14732)+E(f846(x14731,x14733,x14734,x14735,x14736,x14737,x14738,x14739),f846(x14732,x14733,x14734,x14735,x14736,x14737,x14738,x14739)) % 14.98/14.68 [1474]~E(x14741,x14742)+E(f846(x14743,x14741,x14744,x14745,x14746,x14747,x14748,x14749),f846(x14743,x14742,x14744,x14745,x14746,x14747,x14748,x14749)) % 14.98/14.68 [1475]~E(x14751,x14752)+E(f846(x14753,x14754,x14751,x14755,x14756,x14757,x14758,x14759),f846(x14753,x14754,x14752,x14755,x14756,x14757,x14758,x14759)) % 14.98/14.68 [1476]~E(x14761,x14762)+E(f846(x14763,x14764,x14765,x14761,x14766,x14767,x14768,x14769),f846(x14763,x14764,x14765,x14762,x14766,x14767,x14768,x14769)) % 14.98/14.68 [1477]~E(x14771,x14772)+E(f846(x14773,x14774,x14775,x14776,x14771,x14777,x14778,x14779),f846(x14773,x14774,x14775,x14776,x14772,x14777,x14778,x14779)) % 14.98/14.68 [1478]~E(x14781,x14782)+E(f846(x14783,x14784,x14785,x14786,x14787,x14781,x14788,x14789),f846(x14783,x14784,x14785,x14786,x14787,x14782,x14788,x14789)) % 14.98/14.68 [1479]~E(x14791,x14792)+E(f846(x14793,x14794,x14795,x14796,x14797,x14798,x14791,x14799),f846(x14793,x14794,x14795,x14796,x14797,x14798,x14792,x14799)) % 14.98/14.68 [1480]~E(x14801,x14802)+E(f846(x14803,x14804,x14805,x14806,x14807,x14808,x14809,x14801),f846(x14803,x14804,x14805,x14806,x14807,x14808,x14809,x14802)) % 14.98/14.68 [1481]~E(x14811,x14812)+E(f624(x14811,x14813,x14814,x14815,x14816),f624(x14812,x14813,x14814,x14815,x14816)) % 14.98/14.68 [1482]~E(x14821,x14822)+E(f624(x14823,x14821,x14824,x14825,x14826),f624(x14823,x14822,x14824,x14825,x14826)) % 14.98/14.68 [1483]~E(x14831,x14832)+E(f624(x14833,x14834,x14831,x14835,x14836),f624(x14833,x14834,x14832,x14835,x14836)) % 14.98/14.68 [1484]~E(x14841,x14842)+E(f624(x14843,x14844,x14845,x14841,x14846),f624(x14843,x14844,x14845,x14842,x14846)) % 14.98/14.68 [1485]~E(x14851,x14852)+E(f624(x14853,x14854,x14855,x14856,x14851),f624(x14853,x14854,x14855,x14856,x14852)) % 14.98/14.68 [1486]~E(x14861,x14862)+E(f61(x14861,x14863,x14864),f61(x14862,x14863,x14864)) % 14.98/14.68 [1487]~E(x14871,x14872)+E(f61(x14873,x14871,x14874),f61(x14873,x14872,x14874)) % 14.98/14.68 [1488]~E(x14881,x14882)+E(f61(x14883,x14884,x14881),f61(x14883,x14884,x14882)) % 14.98/14.68 [1489]~E(x14891,x14892)+E(f360(x14891,x14893),f360(x14892,x14893)) % 14.98/14.68 [1490]~E(x14901,x14902)+E(f360(x14903,x14901),f360(x14903,x14902)) % 14.98/14.68 [1491]~E(x14911,x14912)+E(f785(x14911,x14913,x14914,x14915),f785(x14912,x14913,x14914,x14915)) % 14.98/14.68 [1492]~E(x14921,x14922)+E(f785(x14923,x14921,x14924,x14925),f785(x14923,x14922,x14924,x14925)) % 14.98/14.68 [1493]~E(x14931,x14932)+E(f785(x14933,x14934,x14931,x14935),f785(x14933,x14934,x14932,x14935)) % 14.98/14.68 [1494]~E(x14941,x14942)+E(f785(x14943,x14944,x14945,x14941),f785(x14943,x14944,x14945,x14942)) % 14.98/14.68 [1495]~E(x14951,x14952)+E(f209(x14951,x14953),f209(x14952,x14953)) % 14.98/14.68 [1496]~E(x14961,x14962)+E(f209(x14963,x14961),f209(x14963,x14962)) % 14.98/14.68 [1497]~E(x14971,x14972)+E(f826(x14971,x14973),f826(x14972,x14973)) % 14.98/14.68 [1498]~E(x14981,x14982)+E(f826(x14983,x14981),f826(x14983,x14982)) % 14.98/14.68 [1499]~E(x14991,x14992)+E(f714(x14991,x14993),f714(x14992,x14993)) % 14.98/14.68 [1500]~E(x15001,x15002)+E(f714(x15003,x15001),f714(x15003,x15002)) % 14.98/14.68 [1501]~E(x15011,x15012)+E(f463(x15011,x15013,x15014,x15015),f463(x15012,x15013,x15014,x15015)) % 14.98/14.68 [1502]~E(x15021,x15022)+E(f463(x15023,x15021,x15024,x15025),f463(x15023,x15022,x15024,x15025)) % 14.98/14.68 [1503]~E(x15031,x15032)+E(f463(x15033,x15034,x15031,x15035),f463(x15033,x15034,x15032,x15035)) % 14.98/14.68 [1504]~E(x15041,x15042)+E(f463(x15043,x15044,x15045,x15041),f463(x15043,x15044,x15045,x15042)) % 14.98/14.68 [1505]~E(x15051,x15052)+E(f547(x15051,x15053,x15054),f547(x15052,x15053,x15054)) % 14.98/14.68 [1506]~E(x15061,x15062)+E(f547(x15063,x15061,x15064),f547(x15063,x15062,x15064)) % 14.98/14.68 [1507]~E(x15071,x15072)+E(f547(x15073,x15074,x15071),f547(x15073,x15074,x15072)) % 14.98/14.68 [1508]~E(x15081,x15082)+E(f808(x15081,x15083),f808(x15082,x15083)) % 14.98/14.68 [1509]~E(x15091,x15092)+E(f808(x15093,x15091),f808(x15093,x15092)) % 14.98/14.68 [1510]~E(x15101,x15102)+E(f263(x15101,x15103,x15104,x15105),f263(x15102,x15103,x15104,x15105)) % 14.98/14.68 [1511]~E(x15111,x15112)+E(f263(x15113,x15111,x15114,x15115),f263(x15113,x15112,x15114,x15115)) % 14.98/14.68 [1512]~E(x15121,x15122)+E(f263(x15123,x15124,x15121,x15125),f263(x15123,x15124,x15122,x15125)) % 14.98/14.68 [1513]~E(x15131,x15132)+E(f263(x15133,x15134,x15135,x15131),f263(x15133,x15134,x15135,x15132)) % 14.98/14.68 [1514]~E(x15141,x15142)+E(f797(x15141,x15143),f797(x15142,x15143)) % 14.98/14.68 [1515]~E(x15151,x15152)+E(f797(x15153,x15151),f797(x15153,x15152)) % 14.98/14.68 [1516]~E(x15161,x15162)+E(f806(x15161),f806(x15162)) % 14.98/14.68 [1517]~E(x15171,x15172)+E(f886(x15171,x15173,x15174,x15175,x15176),f886(x15172,x15173,x15174,x15175,x15176)) % 14.98/14.68 [1518]~E(x15181,x15182)+E(f886(x15183,x15181,x15184,x15185,x15186),f886(x15183,x15182,x15184,x15185,x15186)) % 14.98/14.68 [1519]~E(x15191,x15192)+E(f886(x15193,x15194,x15191,x15195,x15196),f886(x15193,x15194,x15192,x15195,x15196)) % 14.98/14.68 [1520]~E(x15201,x15202)+E(f886(x15203,x15204,x15205,x15201,x15206),f886(x15203,x15204,x15205,x15202,x15206)) % 14.98/14.68 [1521]~E(x15211,x15212)+E(f886(x15213,x15214,x15215,x15216,x15211),f886(x15213,x15214,x15215,x15216,x15212)) % 14.98/14.68 [1522]~E(x15221,x15222)+E(f582(x15221,x15223,x15224),f582(x15222,x15223,x15224)) % 14.98/14.68 [1523]~E(x15231,x15232)+E(f582(x15233,x15231,x15234),f582(x15233,x15232,x15234)) % 14.98/14.68 [1524]~E(x15241,x15242)+E(f582(x15243,x15244,x15241),f582(x15243,x15244,x15242)) % 14.98/14.68 [1525]~E(x15251,x15252)+E(f699(x15251,x15253,x15254),f699(x15252,x15253,x15254)) % 14.98/14.68 [1526]~E(x15261,x15262)+E(f699(x15263,x15261,x15264),f699(x15263,x15262,x15264)) % 14.98/14.68 [1527]~E(x15271,x15272)+E(f699(x15273,x15274,x15271),f699(x15273,x15274,x15272)) % 14.98/14.68 [1528]~E(x15281,x15282)+E(f526(x15281,x15283,x15284,x15285,x15286),f526(x15282,x15283,x15284,x15285,x15286)) % 14.98/14.68 [1529]~E(x15291,x15292)+E(f526(x15293,x15291,x15294,x15295,x15296),f526(x15293,x15292,x15294,x15295,x15296)) % 14.98/14.68 [1530]~E(x15301,x15302)+E(f526(x15303,x15304,x15301,x15305,x15306),f526(x15303,x15304,x15302,x15305,x15306)) % 14.98/14.68 [1531]~E(x15311,x15312)+E(f526(x15313,x15314,x15315,x15311,x15316),f526(x15313,x15314,x15315,x15312,x15316)) % 14.98/14.68 [1532]~E(x15321,x15322)+E(f526(x15323,x15324,x15325,x15326,x15321),f526(x15323,x15324,x15325,x15326,x15322)) % 14.98/14.68 [1533]~E(x15331,x15332)+E(f445(x15331,x15333,x15334,x15335),f445(x15332,x15333,x15334,x15335)) % 14.98/14.68 [1534]~E(x15341,x15342)+E(f445(x15343,x15341,x15344,x15345),f445(x15343,x15342,x15344,x15345)) % 14.98/14.68 [1535]~E(x15351,x15352)+E(f445(x15353,x15354,x15351,x15355),f445(x15353,x15354,x15352,x15355)) % 14.98/14.68 [1536]~E(x15361,x15362)+E(f445(x15363,x15364,x15365,x15361),f445(x15363,x15364,x15365,x15362)) % 14.98/14.68 [1537]~E(x15371,x15372)+E(f742(x15371,x15373,x15374,x15375,x15376),f742(x15372,x15373,x15374,x15375,x15376)) % 14.98/14.68 [1538]~E(x15381,x15382)+E(f742(x15383,x15381,x15384,x15385,x15386),f742(x15383,x15382,x15384,x15385,x15386)) % 14.98/14.68 [1539]~E(x15391,x15392)+E(f742(x15393,x15394,x15391,x15395,x15396),f742(x15393,x15394,x15392,x15395,x15396)) % 14.98/14.68 [1540]~E(x15401,x15402)+E(f742(x15403,x15404,x15405,x15401,x15406),f742(x15403,x15404,x15405,x15402,x15406)) % 14.98/14.68 [1541]~E(x15411,x15412)+E(f742(x15413,x15414,x15415,x15416,x15411),f742(x15413,x15414,x15415,x15416,x15412)) % 14.98/14.68 [1542]~E(x15421,x15422)+E(f111(x15421,x15423,x15424),f111(x15422,x15423,x15424)) % 14.98/14.68 [1543]~E(x15431,x15432)+E(f111(x15433,x15431,x15434),f111(x15433,x15432,x15434)) % 14.98/14.68 [1544]~E(x15441,x15442)+E(f111(x15443,x15444,x15441),f111(x15443,x15444,x15442)) % 14.98/14.68 [1545]~E(x15451,x15452)+E(f728(x15451,x15453,x15454),f728(x15452,x15453,x15454)) % 14.98/14.68 [1546]~E(x15461,x15462)+E(f728(x15463,x15461,x15464),f728(x15463,x15462,x15464)) % 14.98/14.68 [1547]~E(x15471,x15472)+E(f728(x15473,x15474,x15471),f728(x15473,x15474,x15472)) % 14.98/14.68 [1548]~E(x15481,x15482)+E(f731(x15481,x15483),f731(x15482,x15483)) % 14.98/14.68 [1549]~E(x15491,x15492)+E(f731(x15493,x15491),f731(x15493,x15492)) % 14.98/14.68 [1550]~E(x15501,x15502)+E(f384(x15501,x15503,x15504,x15505,x15506,x15507),f384(x15502,x15503,x15504,x15505,x15506,x15507)) % 14.98/14.68 [1551]~E(x15511,x15512)+E(f384(x15513,x15511,x15514,x15515,x15516,x15517),f384(x15513,x15512,x15514,x15515,x15516,x15517)) % 14.98/14.68 [1552]~E(x15521,x15522)+E(f384(x15523,x15524,x15521,x15525,x15526,x15527),f384(x15523,x15524,x15522,x15525,x15526,x15527)) % 14.98/14.68 [1553]~E(x15531,x15532)+E(f384(x15533,x15534,x15535,x15531,x15536,x15537),f384(x15533,x15534,x15535,x15532,x15536,x15537)) % 14.98/14.68 [1554]~E(x15541,x15542)+E(f384(x15543,x15544,x15545,x15546,x15541,x15547),f384(x15543,x15544,x15545,x15546,x15542,x15547)) % 14.98/14.68 [1555]~E(x15551,x15552)+E(f384(x15553,x15554,x15555,x15556,x15557,x15551),f384(x15553,x15554,x15555,x15556,x15557,x15552)) % 14.98/14.68 [1556]~E(x15561,x15562)+E(f911(x15561,x15563,x15564,x15565,x15566,x15567,x15568,x15569),f911(x15562,x15563,x15564,x15565,x15566,x15567,x15568,x15569)) % 14.98/14.68 [1557]~E(x15571,x15572)+E(f911(x15573,x15571,x15574,x15575,x15576,x15577,x15578,x15579),f911(x15573,x15572,x15574,x15575,x15576,x15577,x15578,x15579)) % 14.98/14.68 [1558]~E(x15581,x15582)+E(f911(x15583,x15584,x15581,x15585,x15586,x15587,x15588,x15589),f911(x15583,x15584,x15582,x15585,x15586,x15587,x15588,x15589)) % 14.98/14.68 [1559]~E(x15591,x15592)+E(f911(x15593,x15594,x15595,x15591,x15596,x15597,x15598,x15599),f911(x15593,x15594,x15595,x15592,x15596,x15597,x15598,x15599)) % 14.98/14.68 [1560]~E(x15601,x15602)+E(f911(x15603,x15604,x15605,x15606,x15601,x15607,x15608,x15609),f911(x15603,x15604,x15605,x15606,x15602,x15607,x15608,x15609)) % 14.98/14.68 [1561]~E(x15611,x15612)+E(f911(x15613,x15614,x15615,x15616,x15617,x15611,x15618,x15619),f911(x15613,x15614,x15615,x15616,x15617,x15612,x15618,x15619)) % 14.98/14.68 [1562]~E(x15621,x15622)+E(f911(x15623,x15624,x15625,x15626,x15627,x15628,x15621,x15629),f911(x15623,x15624,x15625,x15626,x15627,x15628,x15622,x15629)) % 14.98/14.68 [1563]~E(x15631,x15632)+E(f911(x15633,x15634,x15635,x15636,x15637,x15638,x15639,x15631),f911(x15633,x15634,x15635,x15636,x15637,x15638,x15639,x15632)) % 14.98/14.68 [1564]~E(x15641,x15642)+E(f219(x15641,x15643,x15644,x15645,x15646),f219(x15642,x15643,x15644,x15645,x15646)) % 14.98/14.68 [1565]~E(x15651,x15652)+E(f219(x15653,x15651,x15654,x15655,x15656),f219(x15653,x15652,x15654,x15655,x15656)) % 14.98/14.68 [1566]~E(x15661,x15662)+E(f219(x15663,x15664,x15661,x15665,x15666),f219(x15663,x15664,x15662,x15665,x15666)) % 14.98/14.68 [1567]~E(x15671,x15672)+E(f219(x15673,x15674,x15675,x15671,x15676),f219(x15673,x15674,x15675,x15672,x15676)) % 14.98/14.68 [1568]~E(x15681,x15682)+E(f219(x15683,x15684,x15685,x15686,x15681),f219(x15683,x15684,x15685,x15686,x15682)) % 14.98/14.68 [1569]~E(x15691,x15692)+E(f636(x15691,x15693,x15694,x15695,x15696),f636(x15692,x15693,x15694,x15695,x15696)) % 14.98/14.68 [1570]~E(x15701,x15702)+E(f636(x15703,x15701,x15704,x15705,x15706),f636(x15703,x15702,x15704,x15705,x15706)) % 14.98/14.68 [1571]~E(x15711,x15712)+E(f636(x15713,x15714,x15711,x15715,x15716),f636(x15713,x15714,x15712,x15715,x15716)) % 14.98/14.68 [1572]~E(x15721,x15722)+E(f636(x15723,x15724,x15725,x15721,x15726),f636(x15723,x15724,x15725,x15722,x15726)) % 14.98/14.68 [1573]~E(x15731,x15732)+E(f636(x15733,x15734,x15735,x15736,x15731),f636(x15733,x15734,x15735,x15736,x15732)) % 14.98/14.68 [1574]~E(x15741,x15742)+E(f761(x15741,x15743,x15744,x15745,x15746,x15747,x15748),f761(x15742,x15743,x15744,x15745,x15746,x15747,x15748)) % 14.98/14.68 [1575]~E(x15751,x15752)+E(f761(x15753,x15751,x15754,x15755,x15756,x15757,x15758),f761(x15753,x15752,x15754,x15755,x15756,x15757,x15758)) % 14.98/14.68 [1576]~E(x15761,x15762)+E(f761(x15763,x15764,x15761,x15765,x15766,x15767,x15768),f761(x15763,x15764,x15762,x15765,x15766,x15767,x15768)) % 14.98/14.68 [1577]~E(x15771,x15772)+E(f761(x15773,x15774,x15775,x15771,x15776,x15777,x15778),f761(x15773,x15774,x15775,x15772,x15776,x15777,x15778)) % 14.98/14.68 [1578]~E(x15781,x15782)+E(f761(x15783,x15784,x15785,x15786,x15781,x15787,x15788),f761(x15783,x15784,x15785,x15786,x15782,x15787,x15788)) % 14.98/14.68 [1579]~E(x15791,x15792)+E(f761(x15793,x15794,x15795,x15796,x15797,x15791,x15798),f761(x15793,x15794,x15795,x15796,x15797,x15792,x15798)) % 14.98/14.68 [1580]~E(x15801,x15802)+E(f761(x15803,x15804,x15805,x15806,x15807,x15808,x15801),f761(x15803,x15804,x15805,x15806,x15807,x15808,x15802)) % 14.98/14.68 [1581]~E(x15811,x15812)+E(f403(x15811,x15813,x15814,x15815),f403(x15812,x15813,x15814,x15815)) % 14.98/14.68 [1582]~E(x15821,x15822)+E(f403(x15823,x15821,x15824,x15825),f403(x15823,x15822,x15824,x15825)) % 14.98/14.68 [1583]~E(x15831,x15832)+E(f403(x15833,x15834,x15831,x15835),f403(x15833,x15834,x15832,x15835)) % 14.98/14.68 [1584]~E(x15841,x15842)+E(f403(x15843,x15844,x15845,x15841),f403(x15843,x15844,x15845,x15842)) % 14.98/14.68 [1585]~E(x15851,x15852)+E(f575(x15851,x15853,x15854,x15855,x15856,x15857),f575(x15852,x15853,x15854,x15855,x15856,x15857)) % 14.98/14.68 [1586]~E(x15861,x15862)+E(f575(x15863,x15861,x15864,x15865,x15866,x15867),f575(x15863,x15862,x15864,x15865,x15866,x15867)) % 14.98/14.68 [1587]~E(x15871,x15872)+E(f575(x15873,x15874,x15871,x15875,x15876,x15877),f575(x15873,x15874,x15872,x15875,x15876,x15877)) % 14.98/14.68 [1588]~E(x15881,x15882)+E(f575(x15883,x15884,x15885,x15881,x15886,x15887),f575(x15883,x15884,x15885,x15882,x15886,x15887)) % 14.98/14.68 [1589]~E(x15891,x15892)+E(f575(x15893,x15894,x15895,x15896,x15891,x15897),f575(x15893,x15894,x15895,x15896,x15892,x15897)) % 14.98/14.68 [1590]~E(x15901,x15902)+E(f575(x15903,x15904,x15905,x15906,x15907,x15901),f575(x15903,x15904,x15905,x15906,x15907,x15902)) % 14.98/14.68 [1591]~E(x15911,x15912)+E(f665(x15911,x15913,x15914),f665(x15912,x15913,x15914)) % 14.98/14.68 [1592]~E(x15921,x15922)+E(f665(x15923,x15921,x15924),f665(x15923,x15922,x15924)) % 14.98/14.68 [1593]~E(x15931,x15932)+E(f665(x15933,x15934,x15931),f665(x15933,x15934,x15932)) % 14.98/14.68 [1594]~E(x15941,x15942)+E(f110(x15941,x15943,x15944),f110(x15942,x15943,x15944)) % 14.98/14.68 [1595]~E(x15951,x15952)+E(f110(x15953,x15951,x15954),f110(x15953,x15952,x15954)) % 14.98/14.68 [1596]~E(x15961,x15962)+E(f110(x15963,x15964,x15961),f110(x15963,x15964,x15962)) % 14.98/14.68 [1597]~E(x15971,x15972)+E(f668(x15971,x15973,x15974),f668(x15972,x15973,x15974)) % 14.98/14.68 [1598]~E(x15981,x15982)+E(f668(x15983,x15981,x15984),f668(x15983,x15982,x15984)) % 14.98/14.68 [1599]~E(x15991,x15992)+E(f668(x15993,x15994,x15991),f668(x15993,x15994,x15992)) % 14.98/14.68 [1600]~E(x16001,x16002)+E(f897(x16001,x16003,x16004),f897(x16002,x16003,x16004)) % 14.98/14.68 [1601]~E(x16011,x16012)+E(f897(x16013,x16011,x16014),f897(x16013,x16012,x16014)) % 14.98/14.68 [1602]~E(x16021,x16022)+E(f897(x16023,x16024,x16021),f897(x16023,x16024,x16022)) % 14.98/14.68 [1603]~E(x16031,x16032)+E(f878(x16031,x16033,x16034,x16035),f878(x16032,x16033,x16034,x16035)) % 14.98/14.68 [1604]~E(x16041,x16042)+E(f878(x16043,x16041,x16044,x16045),f878(x16043,x16042,x16044,x16045)) % 14.98/14.68 [1605]~E(x16051,x16052)+E(f878(x16053,x16054,x16051,x16055),f878(x16053,x16054,x16052,x16055)) % 14.98/14.68 [1606]~E(x16061,x16062)+E(f878(x16063,x16064,x16065,x16061),f878(x16063,x16064,x16065,x16062)) % 14.98/14.68 [1607]~E(x16071,x16072)+E(f581(x16071,x16073,x16074,x16075),f581(x16072,x16073,x16074,x16075)) % 14.98/14.68 [1608]~E(x16081,x16082)+E(f581(x16083,x16081,x16084,x16085),f581(x16083,x16082,x16084,x16085)) % 14.98/14.68 [1609]~E(x16091,x16092)+E(f581(x16093,x16094,x16091,x16095),f581(x16093,x16094,x16092,x16095)) % 14.98/14.68 [1610]~E(x16101,x16102)+E(f581(x16103,x16104,x16105,x16101),f581(x16103,x16104,x16105,x16102)) % 14.98/14.68 [1611]~E(x16111,x16112)+E(f456(x16111,x16113),f456(x16112,x16113)) % 14.98/14.68 [1612]~E(x16121,x16122)+E(f456(x16123,x16121),f456(x16123,x16122)) % 14.98/14.68 [1613]~E(x16131,x16132)+E(f285(x16131,x16133,x16134),f285(x16132,x16133,x16134)) % 14.98/14.68 [1614]~E(x16141,x16142)+E(f285(x16143,x16141,x16144),f285(x16143,x16142,x16144)) % 14.98/14.68 [1615]~E(x16151,x16152)+E(f285(x16153,x16154,x16151),f285(x16153,x16154,x16152)) % 14.98/14.68 [1616]~E(x16161,x16162)+E(f865(x16161,x16163),f865(x16162,x16163)) % 14.98/14.68 [1617]~E(x16171,x16172)+E(f865(x16173,x16171),f865(x16173,x16172)) % 14.98/14.68 [1618]~E(x16181,x16182)+E(f194(x16181),f194(x16182)) % 14.98/14.68 [1619]~E(x16191,x16192)+E(f389(x16191,x16193),f389(x16192,x16193)) % 14.98/14.68 [1620]~E(x16201,x16202)+E(f389(x16203,x16201),f389(x16203,x16202)) % 14.98/14.68 [1621]~E(x16211,x16212)+E(f589(x16211,x16213),f589(x16212,x16213)) % 14.98/14.68 [1622]~E(x16221,x16222)+E(f589(x16223,x16221),f589(x16223,x16222)) % 14.98/14.68 [1623]~E(x16231,x16232)+E(f610(x16231,x16233),f610(x16232,x16233)) % 14.98/14.68 [1624]~E(x16241,x16242)+E(f610(x16243,x16241),f610(x16243,x16242)) % 14.98/14.68 [1625]~E(x16251,x16252)+E(f23(x16251,x16253),f23(x16252,x16253)) % 14.98/14.68 [1626]~E(x16261,x16262)+E(f23(x16263,x16261),f23(x16263,x16262)) % 14.98/14.68 [1627]~E(x16271,x16272)+E(f590(x16271,x16273,x16274),f590(x16272,x16273,x16274)) % 14.98/14.68 [1628]~E(x16281,x16282)+E(f590(x16283,x16281,x16284),f590(x16283,x16282,x16284)) % 14.98/14.68 [1629]~E(x16291,x16292)+E(f590(x16293,x16294,x16291),f590(x16293,x16294,x16292)) % 14.98/14.68 [1630]~E(x16301,x16302)+E(f912(x16301,x16303),f912(x16302,x16303)) % 14.98/14.68 [1631]~E(x16311,x16312)+E(f912(x16313,x16311),f912(x16313,x16312)) % 14.98/14.68 [1632]~E(x16321,x16322)+E(f441(x16321,x16323,x16324),f441(x16322,x16323,x16324)) % 14.98/14.68 [1633]~E(x16331,x16332)+E(f441(x16333,x16331,x16334),f441(x16333,x16332,x16334)) % 14.98/14.68 [1634]~E(x16341,x16342)+E(f441(x16343,x16344,x16341),f441(x16343,x16344,x16342)) % 14.98/14.68 [1635]~E(x16351,x16352)+E(f592(x16351,x16353),f592(x16352,x16353)) % 14.98/14.68 [1636]~E(x16361,x16362)+E(f592(x16363,x16361),f592(x16363,x16362)) % 14.98/14.68 [1637]~E(x16371,x16372)+E(f661(x16371,x16373,x16374,x16375,x16376),f661(x16372,x16373,x16374,x16375,x16376)) % 14.98/14.68 [1638]~E(x16381,x16382)+E(f661(x16383,x16381,x16384,x16385,x16386),f661(x16383,x16382,x16384,x16385,x16386)) % 14.98/14.68 [1639]~E(x16391,x16392)+E(f661(x16393,x16394,x16391,x16395,x16396),f661(x16393,x16394,x16392,x16395,x16396)) % 14.98/14.68 [1640]~E(x16401,x16402)+E(f661(x16403,x16404,x16405,x16401,x16406),f661(x16403,x16404,x16405,x16402,x16406)) % 14.98/14.68 [1641]~E(x16411,x16412)+E(f661(x16413,x16414,x16415,x16416,x16411),f661(x16413,x16414,x16415,x16416,x16412)) % 14.98/14.68 [1642]~E(x16421,x16422)+E(f288(x16421,x16423,x16424,x16425,x16426),f288(x16422,x16423,x16424,x16425,x16426)) % 14.98/14.68 [1643]~E(x16431,x16432)+E(f288(x16433,x16431,x16434,x16435,x16436),f288(x16433,x16432,x16434,x16435,x16436)) % 14.98/14.68 [1644]~E(x16441,x16442)+E(f288(x16443,x16444,x16441,x16445,x16446),f288(x16443,x16444,x16442,x16445,x16446)) % 14.98/14.68 [1645]~E(x16451,x16452)+E(f288(x16453,x16454,x16455,x16451,x16456),f288(x16453,x16454,x16455,x16452,x16456)) % 14.98/14.68 [1646]~E(x16461,x16462)+E(f288(x16463,x16464,x16465,x16466,x16461),f288(x16463,x16464,x16465,x16466,x16462)) % 14.98/14.68 [1647]~E(x16471,x16472)+E(f622(x16471,x16473,x16474,x16475),f622(x16472,x16473,x16474,x16475)) % 14.98/14.68 [1648]~E(x16481,x16482)+E(f622(x16483,x16481,x16484,x16485),f622(x16483,x16482,x16484,x16485)) % 14.98/14.68 [1649]~E(x16491,x16492)+E(f622(x16493,x16494,x16491,x16495),f622(x16493,x16494,x16492,x16495)) % 14.98/14.68 [1650]~E(x16501,x16502)+E(f622(x16503,x16504,x16505,x16501),f622(x16503,x16504,x16505,x16502)) % 14.98/14.68 [1651]~E(x16511,x16512)+E(f401(x16511,x16513,x16514,x16515),f401(x16512,x16513,x16514,x16515)) % 14.98/14.68 [1652]~E(x16521,x16522)+E(f401(x16523,x16521,x16524,x16525),f401(x16523,x16522,x16524,x16525)) % 14.98/14.68 [1653]~E(x16531,x16532)+E(f401(x16533,x16534,x16531,x16535),f401(x16533,x16534,x16532,x16535)) % 14.98/14.68 [1654]~E(x16541,x16542)+E(f401(x16543,x16544,x16545,x16541),f401(x16543,x16544,x16545,x16542)) % 14.98/14.68 [1655]~E(x16551,x16552)+E(f197(x16551),f197(x16552)) % 14.98/14.68 [1656]~E(x16561,x16562)+E(f600(x16561,x16563,x16564,x16565,x16566,x16567),f600(x16562,x16563,x16564,x16565,x16566,x16567)) % 14.98/14.68 [1657]~E(x16571,x16572)+E(f600(x16573,x16571,x16574,x16575,x16576,x16577),f600(x16573,x16572,x16574,x16575,x16576,x16577)) % 14.98/14.68 [1658]~E(x16581,x16582)+E(f600(x16583,x16584,x16581,x16585,x16586,x16587),f600(x16583,x16584,x16582,x16585,x16586,x16587)) % 14.98/14.68 [1659]~E(x16591,x16592)+E(f600(x16593,x16594,x16595,x16591,x16596,x16597),f600(x16593,x16594,x16595,x16592,x16596,x16597)) % 14.98/14.68 [1660]~E(x16601,x16602)+E(f600(x16603,x16604,x16605,x16606,x16601,x16607),f600(x16603,x16604,x16605,x16606,x16602,x16607)) % 14.98/14.68 [1661]~E(x16611,x16612)+E(f600(x16613,x16614,x16615,x16616,x16617,x16611),f600(x16613,x16614,x16615,x16616,x16617,x16612)) % 14.98/14.68 [1662]~E(x16621,x16622)+E(f323(x16621),f323(x16622)) % 14.98/14.68 [1663]~E(x16631,x16632)+E(f652(x16631,x16633,x16634,x16635,x16636,x16637),f652(x16632,x16633,x16634,x16635,x16636,x16637)) % 14.98/14.68 [1664]~E(x16641,x16642)+E(f652(x16643,x16641,x16644,x16645,x16646,x16647),f652(x16643,x16642,x16644,x16645,x16646,x16647)) % 14.98/14.68 [1665]~E(x16651,x16652)+E(f652(x16653,x16654,x16651,x16655,x16656,x16657),f652(x16653,x16654,x16652,x16655,x16656,x16657)) % 14.98/14.68 [1666]~E(x16661,x16662)+E(f652(x16663,x16664,x16665,x16661,x16666,x16667),f652(x16663,x16664,x16665,x16662,x16666,x16667)) % 14.98/14.68 [1667]~E(x16671,x16672)+E(f652(x16673,x16674,x16675,x16676,x16671,x16677),f652(x16673,x16674,x16675,x16676,x16672,x16677)) % 14.98/14.68 [1668]~E(x16681,x16682)+E(f652(x16683,x16684,x16685,x16686,x16687,x16681),f652(x16683,x16684,x16685,x16686,x16687,x16682)) % 14.98/14.68 [1669]~E(x16691,x16692)+E(f500(x16691,x16693,x16694),f500(x16692,x16693,x16694)) % 14.98/14.68 [1670]~E(x16701,x16702)+E(f500(x16703,x16701,x16704),f500(x16703,x16702,x16704)) % 14.98/14.68 [1671]~E(x16711,x16712)+E(f500(x16713,x16714,x16711),f500(x16713,x16714,x16712)) % 14.98/14.68 [1672]~E(x16721,x16722)+E(f507(x16721,x16723,x16724),f507(x16722,x16723,x16724)) % 14.98/14.68 [1673]~E(x16731,x16732)+E(f507(x16733,x16731,x16734),f507(x16733,x16732,x16734)) % 14.98/14.68 [1674]~E(x16741,x16742)+E(f507(x16743,x16744,x16741),f507(x16743,x16744,x16742)) % 14.98/14.68 [1675]~E(x16751,x16752)+E(f434(x16751,x16753,x16754),f434(x16752,x16753,x16754)) % 14.98/14.68 [1676]~E(x16761,x16762)+E(f434(x16763,x16761,x16764),f434(x16763,x16762,x16764)) % 14.98/14.68 [1677]~E(x16771,x16772)+E(f434(x16773,x16774,x16771),f434(x16773,x16774,x16772)) % 14.98/14.68 [1678]~E(x16781,x16782)+E(f238(x16781,x16783,x16784,x16785,x16786,x16787),f238(x16782,x16783,x16784,x16785,x16786,x16787)) % 14.98/14.68 [1679]~E(x16791,x16792)+E(f238(x16793,x16791,x16794,x16795,x16796,x16797),f238(x16793,x16792,x16794,x16795,x16796,x16797)) % 14.98/14.68 [1680]~E(x16801,x16802)+E(f238(x16803,x16804,x16801,x16805,x16806,x16807),f238(x16803,x16804,x16802,x16805,x16806,x16807)) % 14.98/14.68 [1681]~E(x16811,x16812)+E(f238(x16813,x16814,x16815,x16811,x16816,x16817),f238(x16813,x16814,x16815,x16812,x16816,x16817)) % 14.98/14.68 [1682]~E(x16821,x16822)+E(f238(x16823,x16824,x16825,x16826,x16821,x16827),f238(x16823,x16824,x16825,x16826,x16822,x16827)) % 14.98/14.68 [1683]~E(x16831,x16832)+E(f238(x16833,x16834,x16835,x16836,x16837,x16831),f238(x16833,x16834,x16835,x16836,x16837,x16832)) % 14.98/14.68 [1684]~E(x16841,x16842)+E(f259(x16841),f259(x16842)) % 14.98/14.68 [1685]~E(x16851,x16852)+E(f519(x16851,x16853,x16854,x16855,x16856,x16857),f519(x16852,x16853,x16854,x16855,x16856,x16857)) % 14.98/14.68 [1686]~E(x16861,x16862)+E(f519(x16863,x16861,x16864,x16865,x16866,x16867),f519(x16863,x16862,x16864,x16865,x16866,x16867)) % 14.98/14.68 [1687]~E(x16871,x16872)+E(f519(x16873,x16874,x16871,x16875,x16876,x16877),f519(x16873,x16874,x16872,x16875,x16876,x16877)) % 14.98/14.68 [1688]~E(x16881,x16882)+E(f519(x16883,x16884,x16885,x16881,x16886,x16887),f519(x16883,x16884,x16885,x16882,x16886,x16887)) % 14.98/14.68 [1689]~E(x16891,x16892)+E(f519(x16893,x16894,x16895,x16896,x16891,x16897),f519(x16893,x16894,x16895,x16896,x16892,x16897)) % 14.98/14.68 [1690]~E(x16901,x16902)+E(f519(x16903,x16904,x16905,x16906,x16907,x16901),f519(x16903,x16904,x16905,x16906,x16907,x16902)) % 14.98/14.68 [1691]~E(x16911,x16912)+E(f838(x16911,x16913,x16914,x16915,x16916),f838(x16912,x16913,x16914,x16915,x16916)) % 14.98/14.68 [1692]~E(x16921,x16922)+E(f838(x16923,x16921,x16924,x16925,x16926),f838(x16923,x16922,x16924,x16925,x16926)) % 14.98/14.68 [1693]~E(x16931,x16932)+E(f838(x16933,x16934,x16931,x16935,x16936),f838(x16933,x16934,x16932,x16935,x16936)) % 14.98/14.68 [1694]~E(x16941,x16942)+E(f838(x16943,x16944,x16945,x16941,x16946),f838(x16943,x16944,x16945,x16942,x16946)) % 14.98/14.68 [1695]~E(x16951,x16952)+E(f838(x16953,x16954,x16955,x16956,x16951),f838(x16953,x16954,x16955,x16956,x16952)) % 14.98/14.68 [1696]~E(x16961,x16962)+E(f617(x16961,x16963,x16964,x16965),f617(x16962,x16963,x16964,x16965)) % 14.98/14.68 [1697]~E(x16971,x16972)+E(f617(x16973,x16971,x16974,x16975),f617(x16973,x16972,x16974,x16975)) % 14.98/14.68 [1698]~E(x16981,x16982)+E(f617(x16983,x16984,x16981,x16985),f617(x16983,x16984,x16982,x16985)) % 14.98/14.68 [1699]~E(x16991,x16992)+E(f617(x16993,x16994,x16995,x16991),f617(x16993,x16994,x16995,x16992)) % 14.98/14.68 [1700]~E(x17001,x17002)+E(f713(x17001,x17003),f713(x17002,x17003)) % 14.98/14.68 [1701]~E(x17011,x17012)+E(f713(x17013,x17011),f713(x17013,x17012)) % 14.98/14.68 [1702]~E(x17021,x17022)+E(f870(x17021,x17023,x17024,x17025,x17026),f870(x17022,x17023,x17024,x17025,x17026)) % 14.98/14.68 [1703]~E(x17031,x17032)+E(f870(x17033,x17031,x17034,x17035,x17036),f870(x17033,x17032,x17034,x17035,x17036)) % 14.98/14.68 [1704]~E(x17041,x17042)+E(f870(x17043,x17044,x17041,x17045,x17046),f870(x17043,x17044,x17042,x17045,x17046)) % 14.98/14.68 [1705]~E(x17051,x17052)+E(f870(x17053,x17054,x17055,x17051,x17056),f870(x17053,x17054,x17055,x17052,x17056)) % 14.98/14.68 [1706]~E(x17061,x17062)+E(f870(x17063,x17064,x17065,x17066,x17061),f870(x17063,x17064,x17065,x17066,x17062)) % 14.98/14.68 [1707]~E(x17071,x17072)+E(f683(x17071,x17073,x17074),f683(x17072,x17073,x17074)) % 14.98/14.68 [1708]~E(x17081,x17082)+E(f683(x17083,x17081,x17084),f683(x17083,x17082,x17084)) % 14.98/14.68 [1709]~E(x17091,x17092)+E(f683(x17093,x17094,x17091),f683(x17093,x17094,x17092)) % 14.98/14.68 [1710]~E(x17101,x17102)+E(f904(x17101,x17103),f904(x17102,x17103)) % 14.98/14.68 [1711]~E(x17111,x17112)+E(f904(x17113,x17111),f904(x17113,x17112)) % 14.98/14.68 [1712]~E(x17121,x17122)+E(f488(x17121,x17123,x17124,x17125,x17126),f488(x17122,x17123,x17124,x17125,x17126)) % 14.98/14.68 [1713]~E(x17131,x17132)+E(f488(x17133,x17131,x17134,x17135,x17136),f488(x17133,x17132,x17134,x17135,x17136)) % 14.98/14.68 [1714]~E(x17141,x17142)+E(f488(x17143,x17144,x17141,x17145,x17146),f488(x17143,x17144,x17142,x17145,x17146)) % 14.98/14.68 [1715]~E(x17151,x17152)+E(f488(x17153,x17154,x17155,x17151,x17156),f488(x17153,x17154,x17155,x17152,x17156)) % 14.98/14.68 [1716]~E(x17161,x17162)+E(f488(x17163,x17164,x17165,x17166,x17161),f488(x17163,x17164,x17165,x17166,x17162)) % 14.98/14.68 [1717]~E(x17171,x17172)+E(f844(x17171,x17173,x17174,x17175,x17176,x17177,x17178,x17179),f844(x17172,x17173,x17174,x17175,x17176,x17177,x17178,x17179)) % 14.98/14.68 [1718]~E(x17181,x17182)+E(f844(x17183,x17181,x17184,x17185,x17186,x17187,x17188,x17189),f844(x17183,x17182,x17184,x17185,x17186,x17187,x17188,x17189)) % 14.98/14.68 [1719]~E(x17191,x17192)+E(f844(x17193,x17194,x17191,x17195,x17196,x17197,x17198,x17199),f844(x17193,x17194,x17192,x17195,x17196,x17197,x17198,x17199)) % 14.98/14.68 [1720]~E(x17201,x17202)+E(f844(x17203,x17204,x17205,x17201,x17206,x17207,x17208,x17209),f844(x17203,x17204,x17205,x17202,x17206,x17207,x17208,x17209)) % 14.98/14.68 [1721]~E(x17211,x17212)+E(f844(x17213,x17214,x17215,x17216,x17211,x17217,x17218,x17219),f844(x17213,x17214,x17215,x17216,x17212,x17217,x17218,x17219)) % 14.98/14.68 [1722]~E(x17221,x17222)+E(f844(x17223,x17224,x17225,x17226,x17227,x17221,x17228,x17229),f844(x17223,x17224,x17225,x17226,x17227,x17222,x17228,x17229)) % 14.98/14.68 [1723]~E(x17231,x17232)+E(f844(x17233,x17234,x17235,x17236,x17237,x17238,x17231,x17239),f844(x17233,x17234,x17235,x17236,x17237,x17238,x17232,x17239)) % 14.98/14.68 [1724]~E(x17241,x17242)+E(f844(x17243,x17244,x17245,x17246,x17247,x17248,x17249,x17241),f844(x17243,x17244,x17245,x17246,x17247,x17248,x17249,x17242)) % 14.98/14.68 [1725]~E(x17251,x17252)+E(f763(x17251,x17253,x17254),f763(x17252,x17253,x17254)) % 14.98/14.68 [1726]~E(x17261,x17262)+E(f763(x17263,x17261,x17264),f763(x17263,x17262,x17264)) % 14.98/14.68 [1727]~E(x17271,x17272)+E(f763(x17273,x17274,x17271),f763(x17273,x17274,x17272)) % 14.98/14.68 [1728]~E(x17281,x17282)+E(f173(x17281),f173(x17282)) % 14.98/14.68 [1729]~E(x17291,x17292)+E(f898(x17291,x17293,x17294,x17295),f898(x17292,x17293,x17294,x17295)) % 14.98/14.68 [1730]~E(x17301,x17302)+E(f898(x17303,x17301,x17304,x17305),f898(x17303,x17302,x17304,x17305)) % 14.98/14.68 [1731]~E(x17311,x17312)+E(f898(x17313,x17314,x17311,x17315),f898(x17313,x17314,x17312,x17315)) % 14.98/14.68 [1732]~E(x17321,x17322)+E(f898(x17323,x17324,x17325,x17321),f898(x17323,x17324,x17325,x17322)) % 14.98/14.68 [1733]~E(x17331,x17332)+E(f847(x17331,x17333,x17334,x17335,x17336,x17337,x17338,x17339),f847(x17332,x17333,x17334,x17335,x17336,x17337,x17338,x17339)) % 14.98/14.68 [1734]~E(x17341,x17342)+E(f847(x17343,x17341,x17344,x17345,x17346,x17347,x17348,x17349),f847(x17343,x17342,x17344,x17345,x17346,x17347,x17348,x17349)) % 14.98/14.68 [1735]~E(x17351,x17352)+E(f847(x17353,x17354,x17351,x17355,x17356,x17357,x17358,x17359),f847(x17353,x17354,x17352,x17355,x17356,x17357,x17358,x17359)) % 14.98/14.68 [1736]~E(x17361,x17362)+E(f847(x17363,x17364,x17365,x17361,x17366,x17367,x17368,x17369),f847(x17363,x17364,x17365,x17362,x17366,x17367,x17368,x17369)) % 14.98/14.68 [1737]~E(x17371,x17372)+E(f847(x17373,x17374,x17375,x17376,x17371,x17377,x17378,x17379),f847(x17373,x17374,x17375,x17376,x17372,x17377,x17378,x17379)) % 14.98/14.68 [1738]~E(x17381,x17382)+E(f847(x17383,x17384,x17385,x17386,x17387,x17381,x17388,x17389),f847(x17383,x17384,x17385,x17386,x17387,x17382,x17388,x17389)) % 14.98/14.68 [1739]~E(x17391,x17392)+E(f847(x17393,x17394,x17395,x17396,x17397,x17398,x17391,x17399),f847(x17393,x17394,x17395,x17396,x17397,x17398,x17392,x17399)) % 14.98/14.68 [1740]~E(x17401,x17402)+E(f847(x17403,x17404,x17405,x17406,x17407,x17408,x17409,x17401),f847(x17403,x17404,x17405,x17406,x17407,x17408,x17409,x17402)) % 14.98/14.68 [1741]~E(x17411,x17412)+E(f593(x17411,x17413,x17414,x17415),f593(x17412,x17413,x17414,x17415)) % 14.98/14.68 [1742]~E(x17421,x17422)+E(f593(x17423,x17421,x17424,x17425),f593(x17423,x17422,x17424,x17425)) % 14.98/14.68 [1743]~E(x17431,x17432)+E(f593(x17433,x17434,x17431,x17435),f593(x17433,x17434,x17432,x17435)) % 14.98/14.68 [1744]~E(x17441,x17442)+E(f593(x17443,x17444,x17445,x17441),f593(x17443,x17444,x17445,x17442)) % 14.98/14.68 [1745]~E(x17451,x17452)+E(f374(x17451,x17453,x17454,x17455),f374(x17452,x17453,x17454,x17455)) % 14.98/14.68 [1746]~E(x17461,x17462)+E(f374(x17463,x17461,x17464,x17465),f374(x17463,x17462,x17464,x17465)) % 14.98/14.68 [1747]~E(x17471,x17472)+E(f374(x17473,x17474,x17471,x17475),f374(x17473,x17474,x17472,x17475)) % 14.98/14.68 [1748]~E(x17481,x17482)+E(f374(x17483,x17484,x17485,x17481),f374(x17483,x17484,x17485,x17482)) % 14.98/14.68 [1749]~E(x17491,x17492)+E(f421(x17491,x17493,x17494),f421(x17492,x17493,x17494)) % 14.98/14.68 [1750]~E(x17501,x17502)+E(f421(x17503,x17501,x17504),f421(x17503,x17502,x17504)) % 14.98/14.68 [1751]~E(x17511,x17512)+E(f421(x17513,x17514,x17511),f421(x17513,x17514,x17512)) % 14.98/14.68 [1752]~E(x17521,x17522)+E(f395(x17521,x17523),f395(x17522,x17523)) % 14.98/14.68 [1753]~E(x17531,x17532)+E(f395(x17533,x17531),f395(x17533,x17532)) % 14.98/14.68 [1754]~E(x17541,x17542)+E(f850(x17541,x17543,x17544,x17545,x17546,x17547,x17548),f850(x17542,x17543,x17544,x17545,x17546,x17547,x17548)) % 14.98/14.68 [1755]~E(x17551,x17552)+E(f850(x17553,x17551,x17554,x17555,x17556,x17557,x17558),f850(x17553,x17552,x17554,x17555,x17556,x17557,x17558)) % 14.98/14.68 [1756]~E(x17561,x17562)+E(f850(x17563,x17564,x17561,x17565,x17566,x17567,x17568),f850(x17563,x17564,x17562,x17565,x17566,x17567,x17568)) % 14.98/14.68 [1757]~E(x17571,x17572)+E(f850(x17573,x17574,x17575,x17571,x17576,x17577,x17578),f850(x17573,x17574,x17575,x17572,x17576,x17577,x17578)) % 14.98/14.68 [1758]~E(x17581,x17582)+E(f850(x17583,x17584,x17585,x17586,x17581,x17587,x17588),f850(x17583,x17584,x17585,x17586,x17582,x17587,x17588)) % 14.98/14.68 [1759]~E(x17591,x17592)+E(f850(x17593,x17594,x17595,x17596,x17597,x17591,x17598),f850(x17593,x17594,x17595,x17596,x17597,x17592,x17598)) % 14.98/14.68 [1760]~E(x17601,x17602)+E(f850(x17603,x17604,x17605,x17606,x17607,x17608,x17601),f850(x17603,x17604,x17605,x17606,x17607,x17608,x17602)) % 14.98/14.68 [1761]~E(x17611,x17612)+E(f831(x17611,x17613,x17614,x17615,x17616),f831(x17612,x17613,x17614,x17615,x17616)) % 14.98/14.68 [1762]~E(x17621,x17622)+E(f831(x17623,x17621,x17624,x17625,x17626),f831(x17623,x17622,x17624,x17625,x17626)) % 14.98/14.68 [1763]~E(x17631,x17632)+E(f831(x17633,x17634,x17631,x17635,x17636),f831(x17633,x17634,x17632,x17635,x17636)) % 14.98/14.68 [1764]~E(x17641,x17642)+E(f831(x17643,x17644,x17645,x17641,x17646),f831(x17643,x17644,x17645,x17642,x17646)) % 14.98/14.68 [1765]~E(x17651,x17652)+E(f831(x17653,x17654,x17655,x17656,x17651),f831(x17653,x17654,x17655,x17656,x17652)) % 14.98/14.68 [1766]~E(x17661,x17662)+E(f513(x17661,x17663),f513(x17662,x17663)) % 14.98/14.68 [1767]~E(x17671,x17672)+E(f513(x17673,x17671),f513(x17673,x17672)) % 14.98/14.68 [1768]~E(x17681,x17682)+E(f896(x17681,x17683,x17684),f896(x17682,x17683,x17684)) % 14.98/14.68 [1769]~E(x17691,x17692)+E(f896(x17693,x17691,x17694),f896(x17693,x17692,x17694)) % 14.98/14.68 [1770]~E(x17701,x17702)+E(f896(x17703,x17704,x17701),f896(x17703,x17704,x17702)) % 14.98/14.68 [1771]~E(x17711,x17712)+E(f291(x17711,x17713,x17714,x17715,x17716),f291(x17712,x17713,x17714,x17715,x17716)) % 14.98/14.68 [1772]~E(x17721,x17722)+E(f291(x17723,x17721,x17724,x17725,x17726),f291(x17723,x17722,x17724,x17725,x17726)) % 14.98/14.68 [1773]~E(x17731,x17732)+E(f291(x17733,x17734,x17731,x17735,x17736),f291(x17733,x17734,x17732,x17735,x17736)) % 14.98/14.68 [1774]~E(x17741,x17742)+E(f291(x17743,x17744,x17745,x17741,x17746),f291(x17743,x17744,x17745,x17742,x17746)) % 14.98/14.68 [1775]~E(x17751,x17752)+E(f291(x17753,x17754,x17755,x17756,x17751),f291(x17753,x17754,x17755,x17756,x17752)) % 14.98/14.68 [1776]~E(x17761,x17762)+E(f824(x17761,x17763,x17764),f824(x17762,x17763,x17764)) % 14.98/14.68 [1777]~E(x17771,x17772)+E(f824(x17773,x17771,x17774),f824(x17773,x17772,x17774)) % 14.98/14.68 [1778]~E(x17781,x17782)+E(f824(x17783,x17784,x17781),f824(x17783,x17784,x17782)) % 14.98/14.68 [1779]~E(x17791,x17792)+E(f549(x17791,x17793,x17794,x17795,x17796),f549(x17792,x17793,x17794,x17795,x17796)) % 14.98/14.68 [1780]~E(x17801,x17802)+E(f549(x17803,x17801,x17804,x17805,x17806),f549(x17803,x17802,x17804,x17805,x17806)) % 14.98/14.68 [1781]~E(x17811,x17812)+E(f549(x17813,x17814,x17811,x17815,x17816),f549(x17813,x17814,x17812,x17815,x17816)) % 14.98/14.68 [1782]~E(x17821,x17822)+E(f549(x17823,x17824,x17825,x17821,x17826),f549(x17823,x17824,x17825,x17822,x17826)) % 14.98/14.68 [1783]~E(x17831,x17832)+E(f549(x17833,x17834,x17835,x17836,x17831),f549(x17833,x17834,x17835,x17836,x17832)) % 14.98/14.68 [1784]~E(x17841,x17842)+E(f724(x17841,x17843,x17844),f724(x17842,x17843,x17844)) % 14.98/14.68 [1785]~E(x17851,x17852)+E(f724(x17853,x17851,x17854),f724(x17853,x17852,x17854)) % 14.98/14.68 [1786]~E(x17861,x17862)+E(f724(x17863,x17864,x17861),f724(x17863,x17864,x17862)) % 14.98/14.68 [1787]~E(x17871,x17872)+E(f457(x17871,x17873),f457(x17872,x17873)) % 14.98/14.68 [1788]~E(x17881,x17882)+E(f457(x17883,x17881),f457(x17883,x17882)) % 14.98/14.68 [1789]~E(x17891,x17892)+E(f722(x17891,x17893),f722(x17892,x17893)) % 14.98/14.68 [1790]~E(x17901,x17902)+E(f722(x17903,x17901),f722(x17903,x17902)) % 14.98/14.68 [1791]~E(x17911,x17912)+E(f836(x17911,x17913,x17914,x17915),f836(x17912,x17913,x17914,x17915)) % 14.98/14.68 [1792]~E(x17921,x17922)+E(f836(x17923,x17921,x17924,x17925),f836(x17923,x17922,x17924,x17925)) % 14.98/14.68 [1793]~E(x17931,x17932)+E(f836(x17933,x17934,x17931,x17935),f836(x17933,x17934,x17932,x17935)) % 14.98/14.68 [1794]~E(x17941,x17942)+E(f836(x17943,x17944,x17945,x17941),f836(x17943,x17944,x17945,x17942)) % 14.98/14.68 [1795]~E(x17951,x17952)+E(f583(x17951,x17953,x17954,x17955,x17956,x17957,x17958,x17959),f583(x17952,x17953,x17954,x17955,x17956,x17957,x17958,x17959)) % 14.98/14.68 [1796]~E(x17961,x17962)+E(f583(x17963,x17961,x17964,x17965,x17966,x17967,x17968,x17969),f583(x17963,x17962,x17964,x17965,x17966,x17967,x17968,x17969)) % 14.98/14.68 [1797]~E(x17971,x17972)+E(f583(x17973,x17974,x17971,x17975,x17976,x17977,x17978,x17979),f583(x17973,x17974,x17972,x17975,x17976,x17977,x17978,x17979)) % 14.98/14.68 [1798]~E(x17981,x17982)+E(f583(x17983,x17984,x17985,x17981,x17986,x17987,x17988,x17989),f583(x17983,x17984,x17985,x17982,x17986,x17987,x17988,x17989)) % 14.98/14.68 [1799]~E(x17991,x17992)+E(f583(x17993,x17994,x17995,x17996,x17991,x17997,x17998,x17999),f583(x17993,x17994,x17995,x17996,x17992,x17997,x17998,x17999)) % 14.98/14.68 [1800]~E(x18001,x18002)+E(f583(x18003,x18004,x18005,x18006,x18007,x18001,x18008,x18009),f583(x18003,x18004,x18005,x18006,x18007,x18002,x18008,x18009)) % 14.98/14.68 [1801]~E(x18011,x18012)+E(f583(x18013,x18014,x18015,x18016,x18017,x18018,x18011,x18019),f583(x18013,x18014,x18015,x18016,x18017,x18018,x18012,x18019)) % 14.98/14.68 [1802]~E(x18021,x18022)+E(f583(x18023,x18024,x18025,x18026,x18027,x18028,x18029,x18021),f583(x18023,x18024,x18025,x18026,x18027,x18028,x18029,x18022)) % 14.98/14.68 [1803]~E(x18031,x18032)+E(f684(x18031,x18033,x18034,x18035),f684(x18032,x18033,x18034,x18035)) % 14.98/14.68 [1804]~E(x18041,x18042)+E(f684(x18043,x18041,x18044,x18045),f684(x18043,x18042,x18044,x18045)) % 14.98/14.68 [1805]~E(x18051,x18052)+E(f684(x18053,x18054,x18051,x18055),f684(x18053,x18054,x18052,x18055)) % 14.98/14.68 [1806]~E(x18061,x18062)+E(f684(x18063,x18064,x18065,x18061),f684(x18063,x18064,x18065,x18062)) % 14.98/14.68 [1807]~E(x18071,x18072)+E(f804(x18071,x18073,x18074,x18075),f804(x18072,x18073,x18074,x18075)) % 14.98/14.68 [1808]~E(x18081,x18082)+E(f804(x18083,x18081,x18084,x18085),f804(x18083,x18082,x18084,x18085)) % 14.98/14.68 [1809]~E(x18091,x18092)+E(f804(x18093,x18094,x18091,x18095),f804(x18093,x18094,x18092,x18095)) % 14.98/14.68 [1810]~E(x18101,x18102)+E(f804(x18103,x18104,x18105,x18101),f804(x18103,x18104,x18105,x18102)) % 14.98/14.68 [1811]~E(x18111,x18112)+E(f21(x18111,x18113,x18114,x18115),f21(x18112,x18113,x18114,x18115)) % 14.98/14.68 [1812]~E(x18121,x18122)+E(f21(x18123,x18121,x18124,x18125),f21(x18123,x18122,x18124,x18125)) % 14.98/14.68 [1813]~E(x18131,x18132)+E(f21(x18133,x18134,x18131,x18135),f21(x18133,x18134,x18132,x18135)) % 14.98/14.68 [1814]~E(x18141,x18142)+E(f21(x18143,x18144,x18145,x18141),f21(x18143,x18144,x18145,x18142)) % 14.98/14.68 [1815]~E(x18151,x18152)+E(f167(x18151,x18153,x18154),f167(x18152,x18153,x18154)) % 14.98/14.68 [1816]~E(x18161,x18162)+E(f167(x18163,x18161,x18164),f167(x18163,x18162,x18164)) % 14.98/14.68 [1817]~E(x18171,x18172)+E(f167(x18173,x18174,x18171),f167(x18173,x18174,x18172)) % 14.98/14.68 [1818]~E(x18181,x18182)+E(f448(x18181,x18183,x18184),f448(x18182,x18183,x18184)) % 14.98/14.68 [1819]~E(x18191,x18192)+E(f448(x18193,x18191,x18194),f448(x18193,x18192,x18194)) % 14.98/14.68 [1820]~E(x18201,x18202)+E(f448(x18203,x18204,x18201),f448(x18203,x18204,x18202)) % 14.98/14.68 [1821]~E(x18211,x18212)+E(f562(x18211,x18213),f562(x18212,x18213)) % 14.98/14.68 [1822]~E(x18221,x18222)+E(f562(x18223,x18221),f562(x18223,x18222)) % 14.98/14.68 [1823]~E(x18231,x18232)+E(f700(x18231,x18233,x18234,x18235,x18236),f700(x18232,x18233,x18234,x18235,x18236)) % 14.98/14.68 [1824]~E(x18241,x18242)+E(f700(x18243,x18241,x18244,x18245,x18246),f700(x18243,x18242,x18244,x18245,x18246)) % 14.98/14.68 [1825]~E(x18251,x18252)+E(f700(x18253,x18254,x18251,x18255,x18256),f700(x18253,x18254,x18252,x18255,x18256)) % 14.98/14.68 [1826]~E(x18261,x18262)+E(f700(x18263,x18264,x18265,x18261,x18266),f700(x18263,x18264,x18265,x18262,x18266)) % 14.98/14.68 [1827]~E(x18271,x18272)+E(f700(x18273,x18274,x18275,x18276,x18271),f700(x18273,x18274,x18275,x18276,x18272)) % 14.98/14.68 [1828]~E(x18281,x18282)+E(f807(x18281,x18283),f807(x18282,x18283)) % 14.98/14.68 [1829]~E(x18291,x18292)+E(f807(x18293,x18291),f807(x18293,x18292)) % 14.98/14.68 [1830]~E(x18301,x18302)+E(f460(x18301,x18303,x18304),f460(x18302,x18303,x18304)) % 14.98/14.68 [1831]~E(x18311,x18312)+E(f460(x18313,x18311,x18314),f460(x18313,x18312,x18314)) % 14.98/14.68 [1832]~E(x18321,x18322)+E(f460(x18323,x18324,x18321),f460(x18323,x18324,x18322)) % 14.98/14.68 [1833]~E(x18331,x18332)+E(f156(x18331,x18333,x18334,x18335),f156(x18332,x18333,x18334,x18335)) % 14.98/14.68 [1834]~E(x18341,x18342)+E(f156(x18343,x18341,x18344,x18345),f156(x18343,x18342,x18344,x18345)) % 14.98/14.68 [1835]~E(x18351,x18352)+E(f156(x18353,x18354,x18351,x18355),f156(x18353,x18354,x18352,x18355)) % 14.98/14.68 [1836]~E(x18361,x18362)+E(f156(x18363,x18364,x18365,x18361),f156(x18363,x18364,x18365,x18362)) % 14.98/14.68 [1837]~E(x18371,x18372)+E(f630(x18371,x18373),f630(x18372,x18373)) % 14.98/14.68 [1838]~E(x18381,x18382)+E(f630(x18383,x18381),f630(x18383,x18382)) % 14.98/14.68 [1839]~E(x18391,x18392)+E(f543(x18391,x18393,x18394,x18395),f543(x18392,x18393,x18394,x18395)) % 14.98/14.68 [1840]~E(x18401,x18402)+E(f543(x18403,x18401,x18404,x18405),f543(x18403,x18402,x18404,x18405)) % 14.98/14.68 [1841]~E(x18411,x18412)+E(f543(x18413,x18414,x18411,x18415),f543(x18413,x18414,x18412,x18415)) % 14.98/14.68 [1842]~E(x18421,x18422)+E(f543(x18423,x18424,x18425,x18421),f543(x18423,x18424,x18425,x18422)) % 14.98/14.68 [1843]~E(x18431,x18432)+E(f311(x18431,x18433,x18434,x18435),f311(x18432,x18433,x18434,x18435)) % 14.98/14.68 [1844]~E(x18441,x18442)+E(f311(x18443,x18441,x18444,x18445),f311(x18443,x18442,x18444,x18445)) % 14.98/14.68 [1845]~E(x18451,x18452)+E(f311(x18453,x18454,x18451,x18455),f311(x18453,x18454,x18452,x18455)) % 14.98/14.68 [1846]~E(x18461,x18462)+E(f311(x18463,x18464,x18465,x18461),f311(x18463,x18464,x18465,x18462)) % 14.98/14.68 [1847]~E(x18471,x18472)+E(f430(x18471,x18473,x18474),f430(x18472,x18473,x18474)) % 14.98/14.68 [1848]~E(x18481,x18482)+E(f430(x18483,x18481,x18484),f430(x18483,x18482,x18484)) % 14.98/14.68 [1849]~E(x18491,x18492)+E(f430(x18493,x18494,x18491),f430(x18493,x18494,x18492)) % 14.98/14.68 [1850]~E(x18501,x18502)+E(f830(x18501,x18503,x18504,x18505,x18506,x18507),f830(x18502,x18503,x18504,x18505,x18506,x18507)) % 14.98/14.68 [1851]~E(x18511,x18512)+E(f830(x18513,x18511,x18514,x18515,x18516,x18517),f830(x18513,x18512,x18514,x18515,x18516,x18517)) % 14.98/14.68 [1852]~E(x18521,x18522)+E(f830(x18523,x18524,x18521,x18525,x18526,x18527),f830(x18523,x18524,x18522,x18525,x18526,x18527)) % 14.98/14.68 [1853]~E(x18531,x18532)+E(f830(x18533,x18534,x18535,x18531,x18536,x18537),f830(x18533,x18534,x18535,x18532,x18536,x18537)) % 14.98/14.68 [1854]~E(x18541,x18542)+E(f830(x18543,x18544,x18545,x18546,x18541,x18547),f830(x18543,x18544,x18545,x18546,x18542,x18547)) % 14.98/14.68 [1855]~E(x18551,x18552)+E(f830(x18553,x18554,x18555,x18556,x18557,x18551),f830(x18553,x18554,x18555,x18556,x18557,x18552)) % 14.98/14.68 [1856]~E(x18561,x18562)+E(f563(x18561,x18563,x18564,x18565),f563(x18562,x18563,x18564,x18565)) % 14.98/14.68 [1857]~E(x18571,x18572)+E(f563(x18573,x18571,x18574,x18575),f563(x18573,x18572,x18574,x18575)) % 14.98/14.68 [1858]~E(x18581,x18582)+E(f563(x18583,x18584,x18581,x18585),f563(x18583,x18584,x18582,x18585)) % 14.98/14.68 [1859]~E(x18591,x18592)+E(f563(x18593,x18594,x18595,x18591),f563(x18593,x18594,x18595,x18592)) % 14.98/14.68 [1860]~E(x18601,x18602)+E(f613(x18601,x18603,x18604,x18605,x18606,x18607),f613(x18602,x18603,x18604,x18605,x18606,x18607)) % 14.98/14.68 [1861]~E(x18611,x18612)+E(f613(x18613,x18611,x18614,x18615,x18616,x18617),f613(x18613,x18612,x18614,x18615,x18616,x18617)) % 14.98/14.68 [1862]~E(x18621,x18622)+E(f613(x18623,x18624,x18621,x18625,x18626,x18627),f613(x18623,x18624,x18622,x18625,x18626,x18627)) % 14.98/14.68 [1863]~E(x18631,x18632)+E(f613(x18633,x18634,x18635,x18631,x18636,x18637),f613(x18633,x18634,x18635,x18632,x18636,x18637)) % 14.98/14.68 [1864]~E(x18641,x18642)+E(f613(x18643,x18644,x18645,x18646,x18641,x18647),f613(x18643,x18644,x18645,x18646,x18642,x18647)) % 14.98/14.68 [1865]~E(x18651,x18652)+E(f613(x18653,x18654,x18655,x18656,x18657,x18651),f613(x18653,x18654,x18655,x18656,x18657,x18652)) % 14.98/14.68 [1866]~E(x18661,x18662)+E(f793(x18661,x18663,x18664),f793(x18662,x18663,x18664)) % 14.98/14.68 [1867]~E(x18671,x18672)+E(f793(x18673,x18671,x18674),f793(x18673,x18672,x18674)) % 14.98/14.68 [1868]~E(x18681,x18682)+E(f793(x18683,x18684,x18681),f793(x18683,x18684,x18682)) % 14.98/14.68 [1869]~E(x18691,x18692)+E(f841(x18691,x18693,x18694),f841(x18692,x18693,x18694)) % 14.98/14.68 [1870]~E(x18701,x18702)+E(f841(x18703,x18701,x18704),f841(x18703,x18702,x18704)) % 14.98/14.68 [1871]~E(x18711,x18712)+E(f841(x18713,x18714,x18711),f841(x18713,x18714,x18712)) % 14.98/14.68 [1872]~E(x18721,x18722)+E(f388(x18721,x18723),f388(x18722,x18723)) % 14.98/14.68 [1873]~E(x18731,x18732)+E(f388(x18733,x18731),f388(x18733,x18732)) % 14.98/14.68 [1874]~E(x18741,x18742)+E(f682(x18741,x18743,x18744),f682(x18742,x18743,x18744)) % 14.98/14.68 [1875]~E(x18751,x18752)+E(f682(x18753,x18751,x18754),f682(x18753,x18752,x18754)) % 14.98/14.68 [1876]~E(x18761,x18762)+E(f682(x18763,x18764,x18761),f682(x18763,x18764,x18762)) % 14.98/14.68 [1877]~E(x18771,x18772)+E(f848(x18771,x18773,x18774,x18775,x18776,x18777,x18778,x18779),f848(x18772,x18773,x18774,x18775,x18776,x18777,x18778,x18779)) % 14.98/14.68 [1878]~E(x18781,x18782)+E(f848(x18783,x18781,x18784,x18785,x18786,x18787,x18788,x18789),f848(x18783,x18782,x18784,x18785,x18786,x18787,x18788,x18789)) % 14.98/14.68 [1879]~E(x18791,x18792)+E(f848(x18793,x18794,x18791,x18795,x18796,x18797,x18798,x18799),f848(x18793,x18794,x18792,x18795,x18796,x18797,x18798,x18799)) % 14.98/14.68 [1880]~E(x18801,x18802)+E(f848(x18803,x18804,x18805,x18801,x18806,x18807,x18808,x18809),f848(x18803,x18804,x18805,x18802,x18806,x18807,x18808,x18809)) % 14.98/14.68 [1881]~E(x18811,x18812)+E(f848(x18813,x18814,x18815,x18816,x18811,x18817,x18818,x18819),f848(x18813,x18814,x18815,x18816,x18812,x18817,x18818,x18819)) % 14.98/14.68 [1882]~E(x18821,x18822)+E(f848(x18823,x18824,x18825,x18826,x18827,x18821,x18828,x18829),f848(x18823,x18824,x18825,x18826,x18827,x18822,x18828,x18829)) % 14.98/14.68 [1883]~E(x18831,x18832)+E(f848(x18833,x18834,x18835,x18836,x18837,x18838,x18831,x18839),f848(x18833,x18834,x18835,x18836,x18837,x18838,x18832,x18839)) % 14.98/14.68 [1884]~E(x18841,x18842)+E(f848(x18843,x18844,x18845,x18846,x18847,x18848,x18849,x18841),f848(x18843,x18844,x18845,x18846,x18847,x18848,x18849,x18842)) % 14.98/14.68 [1885]~E(x18851,x18852)+E(f685(x18851,x18853,x18854),f685(x18852,x18853,x18854)) % 14.98/14.68 [1886]~E(x18861,x18862)+E(f685(x18863,x18861,x18864),f685(x18863,x18862,x18864)) % 14.98/14.68 [1887]~E(x18871,x18872)+E(f685(x18873,x18874,x18871),f685(x18873,x18874,x18872)) % 14.98/14.68 [1888]~E(x18881,x18882)+E(f414(x18881),f414(x18882)) % 14.98/14.68 [1889]~E(x18891,x18892)+E(f642(x18891,x18893,x18894,x18895,x18896),f642(x18892,x18893,x18894,x18895,x18896)) % 14.98/14.68 [1890]~E(x18901,x18902)+E(f642(x18903,x18901,x18904,x18905,x18906),f642(x18903,x18902,x18904,x18905,x18906)) % 14.98/14.68 [1891]~E(x18911,x18912)+E(f642(x18913,x18914,x18911,x18915,x18916),f642(x18913,x18914,x18912,x18915,x18916)) % 14.98/14.68 [1892]~E(x18921,x18922)+E(f642(x18923,x18924,x18925,x18921,x18926),f642(x18923,x18924,x18925,x18922,x18926)) % 14.98/14.68 [1893]~E(x18931,x18932)+E(f642(x18933,x18934,x18935,x18936,x18931),f642(x18933,x18934,x18935,x18936,x18932)) % 14.98/14.68 [1894]~E(x18941,x18942)+E(f720(x18941,x18943,x18944),f720(x18942,x18943,x18944)) % 14.98/14.68 [1895]~E(x18951,x18952)+E(f720(x18953,x18951,x18954),f720(x18953,x18952,x18954)) % 14.98/14.68 [1896]~E(x18961,x18962)+E(f720(x18963,x18964,x18961),f720(x18963,x18964,x18962)) % 14.98/14.68 [1897]~E(x18971,x18972)+E(f539(x18971,x18973,x18974,x18975),f539(x18972,x18973,x18974,x18975)) % 14.98/14.68 [1898]~E(x18981,x18982)+E(f539(x18983,x18981,x18984,x18985),f539(x18983,x18982,x18984,x18985)) % 14.98/14.68 [1899]~E(x18991,x18992)+E(f539(x18993,x18994,x18991,x18995),f539(x18993,x18994,x18992,x18995)) % 14.98/14.68 [1900]~E(x19001,x19002)+E(f539(x19003,x19004,x19005,x19001),f539(x19003,x19004,x19005,x19002)) % 14.98/14.68 [1901]~E(x19011,x19012)+E(f159(x19011,x19013,x19014),f159(x19012,x19013,x19014)) % 14.98/14.68 [1902]~E(x19021,x19022)+E(f159(x19023,x19021,x19024),f159(x19023,x19022,x19024)) % 14.98/14.68 [1903]~E(x19031,x19032)+E(f159(x19033,x19034,x19031),f159(x19033,x19034,x19032)) % 14.98/14.68 [1904]~E(x19041,x19042)+E(f455(x19041,x19043),f455(x19042,x19043)) % 14.98/14.68 [1905]~E(x19051,x19052)+E(f455(x19053,x19051),f455(x19053,x19052)) % 14.98/14.68 [1906]~E(x19061,x19062)+E(f412(x19061,x19063,x19064),f412(x19062,x19063,x19064)) % 14.98/14.68 [1907]~E(x19071,x19072)+E(f412(x19073,x19071,x19074),f412(x19073,x19072,x19074)) % 14.98/14.68 [1908]~E(x19081,x19082)+E(f412(x19083,x19084,x19081),f412(x19083,x19084,x19082)) % 14.98/14.68 [1909]~E(x19091,x19092)+E(f324(x19091),f324(x19092)) % 14.98/14.68 [1910]~E(x19101,x19102)+E(f909(x19101,x19103,x19104,x19105),f909(x19102,x19103,x19104,x19105)) % 14.98/14.68 [1911]~E(x19111,x19112)+E(f909(x19113,x19111,x19114,x19115),f909(x19113,x19112,x19114,x19115)) % 14.98/14.68 [1912]~E(x19121,x19122)+E(f909(x19123,x19124,x19121,x19125),f909(x19123,x19124,x19122,x19125)) % 14.98/14.68 [1913]~E(x19131,x19132)+E(f909(x19133,x19134,x19135,x19131),f909(x19133,x19134,x19135,x19132)) % 14.98/14.68 [1914]~E(x19141,x19142)+E(f663(x19141,x19143,x19144,x19145,x19146),f663(x19142,x19143,x19144,x19145,x19146)) % 14.98/14.68 [1915]~E(x19151,x19152)+E(f663(x19153,x19151,x19154,x19155,x19156),f663(x19153,x19152,x19154,x19155,x19156)) % 14.98/14.68 [1916]~E(x19161,x19162)+E(f663(x19163,x19164,x19161,x19165,x19166),f663(x19163,x19164,x19162,x19165,x19166)) % 14.98/14.68 [1917]~E(x19171,x19172)+E(f663(x19173,x19174,x19175,x19171,x19176),f663(x19173,x19174,x19175,x19172,x19176)) % 14.98/14.68 [1918]~E(x19181,x19182)+E(f663(x19183,x19184,x19185,x19186,x19181),f663(x19183,x19184,x19185,x19186,x19182)) % 14.98/14.68 [1919]~E(x19191,x19192)+E(f907(x19191,x19193,x19194,x19195,x19196),f907(x19192,x19193,x19194,x19195,x19196)) % 14.98/14.68 [1920]~E(x19201,x19202)+E(f907(x19203,x19201,x19204,x19205,x19206),f907(x19203,x19202,x19204,x19205,x19206)) % 14.98/14.68 [1921]~E(x19211,x19212)+E(f907(x19213,x19214,x19211,x19215,x19216),f907(x19213,x19214,x19212,x19215,x19216)) % 14.98/14.68 [1922]~E(x19221,x19222)+E(f907(x19223,x19224,x19225,x19221,x19226),f907(x19223,x19224,x19225,x19222,x19226)) % 14.98/14.68 [1923]~E(x19231,x19232)+E(f907(x19233,x19234,x19235,x19236,x19231),f907(x19233,x19234,x19235,x19236,x19232)) % 14.98/14.68 [1924]~E(x19241,x19242)+E(f366(x19241,x19243,x19244,x19245,x19246),f366(x19242,x19243,x19244,x19245,x19246)) % 14.98/14.68 [1925]~E(x19251,x19252)+E(f366(x19253,x19251,x19254,x19255,x19256),f366(x19253,x19252,x19254,x19255,x19256)) % 14.98/14.68 [1926]~E(x19261,x19262)+E(f366(x19263,x19264,x19261,x19265,x19266),f366(x19263,x19264,x19262,x19265,x19266)) % 14.98/14.68 [1927]~E(x19271,x19272)+E(f366(x19273,x19274,x19275,x19271,x19276),f366(x19273,x19274,x19275,x19272,x19276)) % 14.98/14.68 [1928]~E(x19281,x19282)+E(f366(x19283,x19284,x19285,x19286,x19281),f366(x19283,x19284,x19285,x19286,x19282)) % 14.98/14.68 [1929]~E(x19291,x19292)+E(f207(x19291,x19293),f207(x19292,x19293)) % 14.98/14.68 [1930]~E(x19301,x19302)+E(f207(x19303,x19301),f207(x19303,x19302)) % 14.98/14.68 [1931]~E(x19311,x19312)+E(f857(x19311,x19313,x19314,x19315,x19316,x19317),f857(x19312,x19313,x19314,x19315,x19316,x19317)) % 14.98/14.68 [1932]~E(x19321,x19322)+E(f857(x19323,x19321,x19324,x19325,x19326,x19327),f857(x19323,x19322,x19324,x19325,x19326,x19327)) % 14.98/14.68 [1933]~E(x19331,x19332)+E(f857(x19333,x19334,x19331,x19335,x19336,x19337),f857(x19333,x19334,x19332,x19335,x19336,x19337)) % 14.98/14.68 [1934]~E(x19341,x19342)+E(f857(x19343,x19344,x19345,x19341,x19346,x19347),f857(x19343,x19344,x19345,x19342,x19346,x19347)) % 14.98/14.68 [1935]~E(x19351,x19352)+E(f857(x19353,x19354,x19355,x19356,x19351,x19357),f857(x19353,x19354,x19355,x19356,x19352,x19357)) % 14.98/14.68 [1936]~E(x19361,x19362)+E(f857(x19363,x19364,x19365,x19366,x19367,x19361),f857(x19363,x19364,x19365,x19366,x19367,x19362)) % 14.98/14.68 [1937]~E(x19371,x19372)+E(f599(x19371,x19373,x19374,x19375,x19376,x19377),f599(x19372,x19373,x19374,x19375,x19376,x19377)) % 14.98/14.68 [1938]~E(x19381,x19382)+E(f599(x19383,x19381,x19384,x19385,x19386,x19387),f599(x19383,x19382,x19384,x19385,x19386,x19387)) % 14.98/14.68 [1939]~E(x19391,x19392)+E(f599(x19393,x19394,x19391,x19395,x19396,x19397),f599(x19393,x19394,x19392,x19395,x19396,x19397)) % 14.98/14.68 [1940]~E(x19401,x19402)+E(f599(x19403,x19404,x19405,x19401,x19406,x19407),f599(x19403,x19404,x19405,x19402,x19406,x19407)) % 14.98/14.68 [1941]~E(x19411,x19412)+E(f599(x19413,x19414,x19415,x19416,x19411,x19417),f599(x19413,x19414,x19415,x19416,x19412,x19417)) % 14.98/14.68 [1942]~E(x19421,x19422)+E(f599(x19423,x19424,x19425,x19426,x19427,x19421),f599(x19423,x19424,x19425,x19426,x19427,x19422)) % 14.98/14.68 [1943]~E(x19431,x19432)+E(f402(x19431,x19433,x19434,x19435),f402(x19432,x19433,x19434,x19435)) % 14.98/14.68 [1944]~E(x19441,x19442)+E(f402(x19443,x19441,x19444,x19445),f402(x19443,x19442,x19444,x19445)) % 14.98/14.68 [1945]~E(x19451,x19452)+E(f402(x19453,x19454,x19451,x19455),f402(x19453,x19454,x19452,x19455)) % 14.98/14.68 [1946]~E(x19461,x19462)+E(f402(x19463,x19464,x19465,x19461),f402(x19463,x19464,x19465,x19462)) % 14.98/14.68 [1947]~E(x19471,x19472)+E(f839(x19471,x19473,x19474,x19475,x19476),f839(x19472,x19473,x19474,x19475,x19476)) % 14.98/14.68 [1948]~E(x19481,x19482)+E(f839(x19483,x19481,x19484,x19485,x19486),f839(x19483,x19482,x19484,x19485,x19486)) % 14.98/14.68 [1949]~E(x19491,x19492)+E(f839(x19493,x19494,x19491,x19495,x19496),f839(x19493,x19494,x19492,x19495,x19496)) % 14.98/14.68 [1950]~E(x19501,x19502)+E(f839(x19503,x19504,x19505,x19501,x19506),f839(x19503,x19504,x19505,x19502,x19506)) % 14.98/14.68 [1951]~E(x19511,x19512)+E(f839(x19513,x19514,x19515,x19516,x19511),f839(x19513,x19514,x19515,x19516,x19512)) % 14.98/14.68 [1952]~E(x19521,x19522)+E(f711(x19521,x19523,x19524),f711(x19522,x19523,x19524)) % 14.98/14.68 [1953]~E(x19531,x19532)+E(f711(x19533,x19531,x19534),f711(x19533,x19532,x19534)) % 14.98/14.68 [1954]~E(x19541,x19542)+E(f711(x19543,x19544,x19541),f711(x19543,x19544,x19542)) % 14.98/14.68 [1955]~E(x19551,x19552)+E(f527(x19551),f527(x19552)) % 14.98/14.68 [1956]~E(x19561,x19562)+E(f783(x19561,x19563,x19564,x19565),f783(x19562,x19563,x19564,x19565)) % 14.98/14.68 [1957]~E(x19571,x19572)+E(f783(x19573,x19571,x19574,x19575),f783(x19573,x19572,x19574,x19575)) % 14.98/14.68 [1958]~E(x19581,x19582)+E(f783(x19583,x19584,x19581,x19585),f783(x19583,x19584,x19582,x19585)) % 14.98/14.68 [1959]~E(x19591,x19592)+E(f783(x19593,x19594,x19595,x19591),f783(x19593,x19594,x19595,x19592)) % 14.98/14.68 [1960]~E(x19601,x19602)+E(f881(x19601,x19603,x19604,x19605),f881(x19602,x19603,x19604,x19605)) % 14.98/14.68 [1961]~E(x19611,x19612)+E(f881(x19613,x19611,x19614,x19615),f881(x19613,x19612,x19614,x19615)) % 14.98/14.68 [1962]~E(x19621,x19622)+E(f881(x19623,x19624,x19621,x19625),f881(x19623,x19624,x19622,x19625)) % 14.98/14.68 [1963]~E(x19631,x19632)+E(f881(x19633,x19634,x19635,x19631),f881(x19633,x19634,x19635,x19632)) % 14.98/14.68 [1964]~E(x19641,x19642)+E(f760(x19641,x19643,x19644),f760(x19642,x19643,x19644)) % 14.98/14.68 [1965]~E(x19651,x19652)+E(f760(x19653,x19651,x19654),f760(x19653,x19652,x19654)) % 14.98/14.68 [1966]~E(x19661,x19662)+E(f760(x19663,x19664,x19661),f760(x19663,x19664,x19662)) % 14.98/14.68 [1967]~E(x19671,x19672)+E(f343(x19671,x19673),f343(x19672,x19673)) % 14.98/14.68 [1968]~E(x19681,x19682)+E(f343(x19683,x19681),f343(x19683,x19682)) % 14.98/14.68 [1969]~E(x19691,x19692)+E(f377(x19691,x19693,x19694,x19695),f377(x19692,x19693,x19694,x19695)) % 14.98/14.68 [1970]~E(x19701,x19702)+E(f377(x19703,x19701,x19704,x19705),f377(x19703,x19702,x19704,x19705)) % 14.98/14.68 [1971]~E(x19711,x19712)+E(f377(x19713,x19714,x19711,x19715),f377(x19713,x19714,x19712,x19715)) % 14.98/14.68 [1972]~E(x19721,x19722)+E(f377(x19723,x19724,x19725,x19721),f377(x19723,x19724,x19725,x19722)) % 14.98/14.68 [1973]~E(x19731,x19732)+E(f709(x19731,x19733,x19734),f709(x19732,x19733,x19734)) % 14.98/14.68 [1974]~E(x19741,x19742)+E(f709(x19743,x19741,x19744),f709(x19743,x19742,x19744)) % 14.98/14.68 [1975]~E(x19751,x19752)+E(f709(x19753,x19754,x19751),f709(x19753,x19754,x19752)) % 14.98/14.68 [1976]~E(x19761,x19762)+E(f548(x19761,x19763),f548(x19762,x19763)) % 14.98/14.68 [1977]~E(x19771,x19772)+E(f548(x19773,x19771),f548(x19773,x19772)) % 14.98/14.68 [1978]~E(x19781,x19782)+E(f451(x19781,x19783,x19784),f451(x19782,x19783,x19784)) % 14.98/14.68 [1979]~E(x19791,x19792)+E(f451(x19793,x19791,x19794),f451(x19793,x19792,x19794)) % 14.98/14.68 [1980]~E(x19801,x19802)+E(f451(x19803,x19804,x19801),f451(x19803,x19804,x19802)) % 14.98/14.68 [1981]~E(x19811,x19812)+E(f479(x19811,x19813,x19814,x19815,x19816),f479(x19812,x19813,x19814,x19815,x19816)) % 14.98/14.68 [1982]~E(x19821,x19822)+E(f479(x19823,x19821,x19824,x19825,x19826),f479(x19823,x19822,x19824,x19825,x19826)) % 14.98/14.68 [1983]~E(x19831,x19832)+E(f479(x19833,x19834,x19831,x19835,x19836),f479(x19833,x19834,x19832,x19835,x19836)) % 14.98/14.68 [1984]~E(x19841,x19842)+E(f479(x19843,x19844,x19845,x19841,x19846),f479(x19843,x19844,x19845,x19842,x19846)) % 14.98/14.68 [1985]~E(x19851,x19852)+E(f479(x19853,x19854,x19855,x19856,x19851),f479(x19853,x19854,x19855,x19856,x19852)) % 14.98/14.68 [1986]~E(x19861,x19862)+E(f338(x19861,x19863,x19864),f338(x19862,x19863,x19864)) % 14.98/14.68 [1987]~E(x19871,x19872)+E(f338(x19873,x19871,x19874),f338(x19873,x19872,x19874)) % 14.98/14.68 [1988]~E(x19881,x19882)+E(f338(x19883,x19884,x19881),f338(x19883,x19884,x19882)) % 14.98/14.68 [1989]~E(x19891,x19892)+E(f795(x19891,x19893,x19894,x19895,x19896,x19897,x19898),f795(x19892,x19893,x19894,x19895,x19896,x19897,x19898)) % 14.98/14.68 [1990]~E(x19901,x19902)+E(f795(x19903,x19901,x19904,x19905,x19906,x19907,x19908),f795(x19903,x19902,x19904,x19905,x19906,x19907,x19908)) % 14.98/14.68 [1991]~E(x19911,x19912)+E(f795(x19913,x19914,x19911,x19915,x19916,x19917,x19918),f795(x19913,x19914,x19912,x19915,x19916,x19917,x19918)) % 14.98/14.68 [1992]~E(x19921,x19922)+E(f795(x19923,x19924,x19925,x19921,x19926,x19927,x19928),f795(x19923,x19924,x19925,x19922,x19926,x19927,x19928)) % 14.98/14.68 [1993]~E(x19931,x19932)+E(f795(x19933,x19934,x19935,x19936,x19931,x19937,x19938),f795(x19933,x19934,x19935,x19936,x19932,x19937,x19938)) % 14.98/14.68 [1994]~E(x19941,x19942)+E(f795(x19943,x19944,x19945,x19946,x19947,x19941,x19948),f795(x19943,x19944,x19945,x19946,x19947,x19942,x19948)) % 14.98/14.68 [1995]~E(x19951,x19952)+E(f795(x19953,x19954,x19955,x19956,x19957,x19958,x19951),f795(x19953,x19954,x19955,x19956,x19957,x19958,x19952)) % 14.98/14.68 [1996]~E(x19961,x19962)+E(f221(x19961,x19963,x19964),f221(x19962,x19963,x19964)) % 14.98/14.68 [1997]~E(x19971,x19972)+E(f221(x19973,x19971,x19974),f221(x19973,x19972,x19974)) % 14.98/14.68 [1998]~E(x19981,x19982)+E(f221(x19983,x19984,x19981),f221(x19983,x19984,x19982)) % 14.98/14.68 [1999]~E(x19991,x19992)+E(f471(x19991,x19993),f471(x19992,x19993)) % 14.98/14.68 [2000]~E(x20001,x20002)+E(f471(x20003,x20001),f471(x20003,x20002)) % 14.98/14.68 [2001]~E(x20011,x20012)+E(f852(x20011,x20013,x20014,x20015,x20016,x20017,x20018,x20019),f852(x20012,x20013,x20014,x20015,x20016,x20017,x20018,x20019)) % 14.98/14.68 [2002]~E(x20021,x20022)+E(f852(x20023,x20021,x20024,x20025,x20026,x20027,x20028,x20029),f852(x20023,x20022,x20024,x20025,x20026,x20027,x20028,x20029)) % 14.98/14.68 [2003]~E(x20031,x20032)+E(f852(x20033,x20034,x20031,x20035,x20036,x20037,x20038,x20039),f852(x20033,x20034,x20032,x20035,x20036,x20037,x20038,x20039)) % 14.98/14.68 [2004]~E(x20041,x20042)+E(f852(x20043,x20044,x20045,x20041,x20046,x20047,x20048,x20049),f852(x20043,x20044,x20045,x20042,x20046,x20047,x20048,x20049)) % 14.98/14.68 [2005]~E(x20051,x20052)+E(f852(x20053,x20054,x20055,x20056,x20051,x20057,x20058,x20059),f852(x20053,x20054,x20055,x20056,x20052,x20057,x20058,x20059)) % 14.98/14.68 [2006]~E(x20061,x20062)+E(f852(x20063,x20064,x20065,x20066,x20067,x20061,x20068,x20069),f852(x20063,x20064,x20065,x20066,x20067,x20062,x20068,x20069)) % 14.98/14.68 [2007]~E(x20071,x20072)+E(f852(x20073,x20074,x20075,x20076,x20077,x20078,x20071,x20079),f852(x20073,x20074,x20075,x20076,x20077,x20078,x20072,x20079)) % 14.98/14.68 [2008]~E(x20081,x20082)+E(f852(x20083,x20084,x20085,x20086,x20087,x20088,x20089,x20081),f852(x20083,x20084,x20085,x20086,x20087,x20088,x20089,x20082)) % 14.98/14.68 [2009]~E(x20091,x20092)+E(f667(x20091,x20093,x20094),f667(x20092,x20093,x20094)) % 14.98/14.68 [2010]~E(x20101,x20102)+E(f667(x20103,x20101,x20104),f667(x20103,x20102,x20104)) % 14.98/14.68 [2011]~E(x20111,x20112)+E(f667(x20113,x20114,x20111),f667(x20113,x20114,x20112)) % 14.98/14.68 [2012]~E(x20121,x20122)+E(f19(x20121,x20123,x20124,x20125),f19(x20122,x20123,x20124,x20125)) % 14.98/14.68 [2013]~E(x20131,x20132)+E(f19(x20133,x20131,x20134,x20135),f19(x20133,x20132,x20134,x20135)) % 14.98/14.68 [2014]~E(x20141,x20142)+E(f19(x20143,x20144,x20141,x20145),f19(x20143,x20144,x20142,x20145)) % 14.98/14.68 [2015]~E(x20151,x20152)+E(f19(x20153,x20154,x20155,x20151),f19(x20153,x20154,x20155,x20152)) % 14.98/14.68 [2016]~E(x20161,x20162)+E(f623(x20161,x20163,x20164),f623(x20162,x20163,x20164)) % 14.98/14.68 [2017]~E(x20171,x20172)+E(f623(x20173,x20171,x20174),f623(x20173,x20172,x20174)) % 14.98/14.68 [2018]~E(x20181,x20182)+E(f623(x20183,x20184,x20181),f623(x20183,x20184,x20182)) % 14.98/14.68 [2019]~E(x20191,x20192)+E(f733(x20191,x20193),f733(x20192,x20193)) % 14.98/14.68 [2020]~E(x20201,x20202)+E(f733(x20203,x20201),f733(x20203,x20202)) % 14.98/14.68 [2021]~E(x20211,x20212)+E(f659(x20211,x20213,x20214,x20215),f659(x20212,x20213,x20214,x20215)) % 14.98/14.68 [2022]~E(x20221,x20222)+E(f659(x20223,x20221,x20224,x20225),f659(x20223,x20222,x20224,x20225)) % 14.98/14.68 [2023]~E(x20231,x20232)+E(f659(x20233,x20234,x20231,x20235),f659(x20233,x20234,x20232,x20235)) % 14.98/14.68 [2024]~E(x20241,x20242)+E(f659(x20243,x20244,x20245,x20241),f659(x20243,x20244,x20245,x20242)) % 14.98/14.68 [2025]~E(x20251,x20252)+E(f47(x20251,x20253),f47(x20252,x20253)) % 14.98/14.68 [2026]~E(x20261,x20262)+E(f47(x20263,x20261),f47(x20263,x20262)) % 14.98/14.68 [2027]~E(x20271,x20272)+E(f325(x20271),f325(x20272)) % 14.98/14.68 [2028]~E(x20281,x20282)+E(f195(x20281,x20283),f195(x20282,x20283)) % 14.98/14.68 [2029]~E(x20291,x20292)+E(f195(x20293,x20291),f195(x20293,x20292)) % 14.98/14.68 [2030]~E(x20301,x20302)+E(f607(x20301,x20303,x20304),f607(x20302,x20303,x20304)) % 14.98/14.68 [2031]~E(x20311,x20312)+E(f607(x20313,x20311,x20314),f607(x20313,x20312,x20314)) % 14.98/14.68 [2032]~E(x20321,x20322)+E(f607(x20323,x20324,x20321),f607(x20323,x20324,x20322)) % 14.98/14.68 [2033]~E(x20331,x20332)+E(f576(x20331,x20333,x20334,x20335,x20336),f576(x20332,x20333,x20334,x20335,x20336)) % 14.98/14.68 [2034]~E(x20341,x20342)+E(f576(x20343,x20341,x20344,x20345,x20346),f576(x20343,x20342,x20344,x20345,x20346)) % 14.98/14.68 [2035]~E(x20351,x20352)+E(f576(x20353,x20354,x20351,x20355,x20356),f576(x20353,x20354,x20352,x20355,x20356)) % 14.98/14.68 [2036]~E(x20361,x20362)+E(f576(x20363,x20364,x20365,x20361,x20366),f576(x20363,x20364,x20365,x20362,x20366)) % 14.98/14.68 [2037]~E(x20371,x20372)+E(f576(x20373,x20374,x20375,x20376,x20371),f576(x20373,x20374,x20375,x20376,x20372)) % 14.98/14.68 [2038]~E(x20381,x20382)+E(f128(x20381),f128(x20382)) % 14.98/14.68 [2039]~E(x20391,x20392)+E(f474(x20391,x20393,x20394),f474(x20392,x20393,x20394)) % 14.98/14.68 [2040]~E(x20401,x20402)+E(f474(x20403,x20401,x20404),f474(x20403,x20402,x20404)) % 14.98/14.68 [2041]~E(x20411,x20412)+E(f474(x20413,x20414,x20411),f474(x20413,x20414,x20412)) % 14.98/14.68 [2042]~E(x20421,x20422)+E(f777(x20421,x20423,x20424,x20425),f777(x20422,x20423,x20424,x20425)) % 14.98/14.68 [2043]~E(x20431,x20432)+E(f777(x20433,x20431,x20434,x20435),f777(x20433,x20432,x20434,x20435)) % 14.98/14.68 [2044]~E(x20441,x20442)+E(f777(x20443,x20444,x20441,x20445),f777(x20443,x20444,x20442,x20445)) % 14.98/14.68 [2045]~E(x20451,x20452)+E(f777(x20453,x20454,x20455,x20451),f777(x20453,x20454,x20455,x20452)) % 14.98/14.68 [2046]~E(x20461,x20462)+E(f553(x20461,x20463),f553(x20462,x20463)) % 14.98/14.68 [2047]~E(x20471,x20472)+E(f553(x20473,x20471),f553(x20473,x20472)) % 14.98/14.68 [2048]~E(x20481,x20482)+E(f350(x20481,x20483),f350(x20482,x20483)) % 14.98/14.68 [2049]~E(x20491,x20492)+E(f350(x20493,x20491),f350(x20493,x20492)) % 14.98/14.68 [2050]~E(x20501,x20502)+E(f580(x20501,x20503,x20504),f580(x20502,x20503,x20504)) % 14.98/14.68 [2051]~E(x20511,x20512)+E(f580(x20513,x20511,x20514),f580(x20513,x20512,x20514)) % 14.98/14.68 [2052]~E(x20521,x20522)+E(f580(x20523,x20524,x20521),f580(x20523,x20524,x20522)) % 14.98/14.68 [2053]~E(x20531,x20532)+E(f892(x20531,x20533,x20534),f892(x20532,x20533,x20534)) % 14.98/14.68 [2054]~E(x20541,x20542)+E(f892(x20543,x20541,x20544),f892(x20543,x20542,x20544)) % 14.98/14.68 [2055]~E(x20551,x20552)+E(f892(x20553,x20554,x20551),f892(x20553,x20554,x20552)) % 14.98/14.68 [2056]~E(x20561,x20562)+E(f473(x20561,x20563,x20564),f473(x20562,x20563,x20564)) % 14.98/14.68 [2057]~E(x20571,x20572)+E(f473(x20573,x20571,x20574),f473(x20573,x20572,x20574)) % 14.98/14.68 [2058]~E(x20581,x20582)+E(f473(x20583,x20584,x20581),f473(x20583,x20584,x20582)) % 14.98/14.68 [2059]~E(x20591,x20592)+E(f501(x20591,x20593,x20594),f501(x20592,x20593,x20594)) % 14.98/14.68 [2060]~E(x20601,x20602)+E(f501(x20603,x20601,x20604),f501(x20603,x20602,x20604)) % 14.98/14.68 [2061]~E(x20611,x20612)+E(f501(x20613,x20614,x20611),f501(x20613,x20614,x20612)) % 14.98/14.68 [2062]~E(x20621,x20622)+E(f781(x20621,x20623,x20624,x20625,x20626),f781(x20622,x20623,x20624,x20625,x20626)) % 14.98/14.68 [2063]~E(x20631,x20632)+E(f781(x20633,x20631,x20634,x20635,x20636),f781(x20633,x20632,x20634,x20635,x20636)) % 14.98/14.68 [2064]~E(x20641,x20642)+E(f781(x20643,x20644,x20641,x20645,x20646),f781(x20643,x20644,x20642,x20645,x20646)) % 14.98/14.68 [2065]~E(x20651,x20652)+E(f781(x20653,x20654,x20655,x20651,x20656),f781(x20653,x20654,x20655,x20652,x20656)) % 14.98/14.68 [2066]~E(x20661,x20662)+E(f781(x20663,x20664,x20665,x20666,x20661),f781(x20663,x20664,x20665,x20666,x20662)) % 14.98/14.68 [2067]~E(x20671,x20672)+E(f627(x20671,x20673,x20674),f627(x20672,x20673,x20674)) % 14.98/14.68 [2068]~E(x20681,x20682)+E(f627(x20683,x20681,x20684),f627(x20683,x20682,x20684)) % 14.98/14.68 [2069]~E(x20691,x20692)+E(f627(x20693,x20694,x20691),f627(x20693,x20694,x20692)) % 14.98/14.68 [2070]~E(x20701,x20702)+E(f382(x20701,x20703,x20704,x20705),f382(x20702,x20703,x20704,x20705)) % 14.98/14.68 [2071]~E(x20711,x20712)+E(f382(x20713,x20711,x20714,x20715),f382(x20713,x20712,x20714,x20715)) % 14.98/14.68 [2072]~E(x20721,x20722)+E(f382(x20723,x20724,x20721,x20725),f382(x20723,x20724,x20722,x20725)) % 14.98/14.68 [2073]~E(x20731,x20732)+E(f382(x20733,x20734,x20735,x20731),f382(x20733,x20734,x20735,x20732)) % 14.98/14.68 [2074]~E(x20741,x20742)+E(f261(x20741,x20743),f261(x20742,x20743)) % 14.98/14.68 [2075]~E(x20751,x20752)+E(f261(x20753,x20751),f261(x20753,x20752)) % 14.98/14.68 [2076]~E(x20761,x20762)+E(f477(x20761,x20763,x20764,x20765),f477(x20762,x20763,x20764,x20765)) % 14.98/14.68 [2077]~E(x20771,x20772)+E(f477(x20773,x20771,x20774,x20775),f477(x20773,x20772,x20774,x20775)) % 14.98/14.68 [2078]~E(x20781,x20782)+E(f477(x20783,x20784,x20781,x20785),f477(x20783,x20784,x20782,x20785)) % 14.98/14.68 [2079]~E(x20791,x20792)+E(f477(x20793,x20794,x20795,x20791),f477(x20793,x20794,x20795,x20792)) % 14.98/14.68 [2080]~E(x20801,x20802)+E(f345(x20801,x20803),f345(x20802,x20803)) % 14.98/14.68 [2081]~E(x20811,x20812)+E(f345(x20813,x20811),f345(x20813,x20812)) % 14.98/14.68 [2082]~E(x20821,x20822)+E(f515(x20821,x20823,x20824),f515(x20822,x20823,x20824)) % 14.98/14.68 [2083]~E(x20831,x20832)+E(f515(x20833,x20831,x20834),f515(x20833,x20832,x20834)) % 14.98/14.68 [2084]~E(x20841,x20842)+E(f515(x20843,x20844,x20841),f515(x20843,x20844,x20842)) % 14.98/14.68 [2085]~E(x20851,x20852)+E(f537(x20851,x20853,x20854,x20855),f537(x20852,x20853,x20854,x20855)) % 14.98/14.68 [2086]~E(x20861,x20862)+E(f537(x20863,x20861,x20864,x20865),f537(x20863,x20862,x20864,x20865)) % 14.98/14.68 [2087]~E(x20871,x20872)+E(f537(x20873,x20874,x20871,x20875),f537(x20873,x20874,x20872,x20875)) % 14.98/14.68 [2088]~E(x20881,x20882)+E(f537(x20883,x20884,x20885,x20881),f537(x20883,x20884,x20885,x20882)) % 14.98/14.68 [2089]~E(x20891,x20892)+E(f656(x20891),f656(x20892)) % 14.98/14.68 [2090]~E(x20901,x20902)+E(f357(x20901),f357(x20902)) % 14.98/14.68 [2091]~E(x20911,x20912)+E(f528(x20911,x20913),f528(x20912,x20913)) % 14.98/14.68 [2092]~E(x20921,x20922)+E(f528(x20923,x20921),f528(x20923,x20922)) % 14.98/14.68 [2093]~E(x20931,x20932)+E(f774(x20931,x20933,x20934),f774(x20932,x20933,x20934)) % 14.98/14.68 [2094]~E(x20941,x20942)+E(f774(x20943,x20941,x20944),f774(x20943,x20942,x20944)) % 14.98/14.68 [2095]~E(x20951,x20952)+E(f774(x20953,x20954,x20951),f774(x20953,x20954,x20952)) % 14.98/14.68 [2096]~E(x20961,x20962)+E(f715(x20961,x20963),f715(x20962,x20963)) % 14.98/14.68 [2097]~E(x20971,x20972)+E(f715(x20973,x20971),f715(x20973,x20972)) % 14.98/14.68 [2098]~E(x20981,x20982)+E(f910(x20981,x20983,x20984,x20985,x20986,x20987),f910(x20982,x20983,x20984,x20985,x20986,x20987)) % 14.98/14.68 [2099]~E(x20991,x20992)+E(f910(x20993,x20991,x20994,x20995,x20996,x20997),f910(x20993,x20992,x20994,x20995,x20996,x20997)) % 14.98/14.68 [2100]~E(x21001,x21002)+E(f910(x21003,x21004,x21001,x21005,x21006,x21007),f910(x21003,x21004,x21002,x21005,x21006,x21007)) % 14.98/14.68 [2101]~E(x21011,x21012)+E(f910(x21013,x21014,x21015,x21011,x21016,x21017),f910(x21013,x21014,x21015,x21012,x21016,x21017)) % 14.98/14.68 [2102]~E(x21021,x21022)+E(f910(x21023,x21024,x21025,x21026,x21021,x21027),f910(x21023,x21024,x21025,x21026,x21022,x21027)) % 14.98/14.68 [2103]~E(x21031,x21032)+E(f910(x21033,x21034,x21035,x21036,x21037,x21031),f910(x21033,x21034,x21035,x21036,x21037,x21032)) % 14.98/14.68 [2104]~E(x21041,x21042)+E(f480(x21041,x21043,x21044,x21045,x21046),f480(x21042,x21043,x21044,x21045,x21046)) % 14.98/14.68 [2105]~E(x21051,x21052)+E(f480(x21053,x21051,x21054,x21055,x21056),f480(x21053,x21052,x21054,x21055,x21056)) % 14.98/14.68 [2106]~E(x21061,x21062)+E(f480(x21063,x21064,x21061,x21065,x21066),f480(x21063,x21064,x21062,x21065,x21066)) % 14.98/14.68 [2107]~E(x21071,x21072)+E(f480(x21073,x21074,x21075,x21071,x21076),f480(x21073,x21074,x21075,x21072,x21076)) % 14.98/14.68 [2108]~E(x21081,x21082)+E(f480(x21083,x21084,x21085,x21086,x21081),f480(x21083,x21084,x21085,x21086,x21082)) % 14.98/14.68 [2109]~E(x21091,x21092)+E(f211(x21091,x21093),f211(x21092,x21093)) % 14.98/14.68 [2110]~E(x21101,x21102)+E(f211(x21103,x21101),f211(x21103,x21102)) % 14.98/14.68 [2111]~E(x21111,x21112)+E(f866(x21111),f866(x21112)) % 14.98/14.68 [2112]~E(x21121,x21122)+E(f272(x21121,x21123,x21124,x21125),f272(x21122,x21123,x21124,x21125)) % 14.98/14.68 [2113]~E(x21131,x21132)+E(f272(x21133,x21131,x21134,x21135),f272(x21133,x21132,x21134,x21135)) % 14.98/14.68 [2114]~E(x21141,x21142)+E(f272(x21143,x21144,x21141,x21145),f272(x21143,x21144,x21142,x21145)) % 14.98/14.68 [2115]~E(x21151,x21152)+E(f272(x21153,x21154,x21155,x21151),f272(x21153,x21154,x21155,x21152)) % 14.98/14.68 [2116]~E(x21161,x21162)+E(f687(x21161,x21163,x21164,x21165,x21166),f687(x21162,x21163,x21164,x21165,x21166)) % 14.98/14.68 [2117]~E(x21171,x21172)+E(f687(x21173,x21171,x21174,x21175,x21176),f687(x21173,x21172,x21174,x21175,x21176)) % 14.98/14.68 [2118]~E(x21181,x21182)+E(f687(x21183,x21184,x21181,x21185,x21186),f687(x21183,x21184,x21182,x21185,x21186)) % 14.98/14.68 [2119]~E(x21191,x21192)+E(f687(x21193,x21194,x21195,x21191,x21196),f687(x21193,x21194,x21195,x21192,x21196)) % 14.98/14.68 [2120]~E(x21201,x21202)+E(f687(x21203,x21204,x21205,x21206,x21201),f687(x21203,x21204,x21205,x21206,x21202)) % 14.98/14.68 [2121]~E(x21211,x21212)+E(f229(x21211,x21213),f229(x21212,x21213)) % 14.98/14.68 [2122]~E(x21221,x21222)+E(f229(x21223,x21221),f229(x21223,x21222)) % 14.98/14.68 [2123]~E(x21231,x21232)+E(f332(x21231,x21233),f332(x21232,x21233)) % 14.98/14.68 [2124]~E(x21241,x21242)+E(f332(x21243,x21241),f332(x21243,x21242)) % 14.98/14.68 [2125]~E(x21251,x21252)+E(f459(x21251,x21253,x21254),f459(x21252,x21253,x21254)) % 14.98/14.68 [2126]~E(x21261,x21262)+E(f459(x21263,x21261,x21264),f459(x21263,x21262,x21264)) % 14.98/14.68 [2127]~E(x21271,x21272)+E(f459(x21273,x21274,x21271),f459(x21273,x21274,x21272)) % 14.98/14.68 [2128]~E(x21281,x21282)+E(f267(x21281,x21283),f267(x21282,x21283)) % 14.98/14.68 [2129]~E(x21291,x21292)+E(f267(x21293,x21291),f267(x21293,x21292)) % 14.98/14.68 [2130]~E(x21301,x21302)+E(f752(x21301,x21303,x21304,x21305,x21306),f752(x21302,x21303,x21304,x21305,x21306)) % 14.98/14.68 [2131]~E(x21311,x21312)+E(f752(x21313,x21311,x21314,x21315,x21316),f752(x21313,x21312,x21314,x21315,x21316)) % 14.98/14.68 [2132]~E(x21321,x21322)+E(f752(x21323,x21324,x21321,x21325,x21326),f752(x21323,x21324,x21322,x21325,x21326)) % 14.98/14.68 [2133]~E(x21331,x21332)+E(f752(x21333,x21334,x21335,x21331,x21336),f752(x21333,x21334,x21335,x21332,x21336)) % 14.98/14.68 [2134]~E(x21341,x21342)+E(f752(x21343,x21344,x21345,x21346,x21341),f752(x21343,x21344,x21345,x21346,x21342)) % 14.98/14.68 [2135]~E(x21351,x21352)+E(f517(x21351,x21353,x21354),f517(x21352,x21353,x21354)) % 14.98/14.68 [2136]~E(x21361,x21362)+E(f517(x21363,x21361,x21364),f517(x21363,x21362,x21364)) % 14.98/14.68 [2137]~E(x21371,x21372)+E(f517(x21373,x21374,x21371),f517(x21373,x21374,x21372)) % 14.98/14.68 [2138]~E(x21381,x21382)+E(f193(x21381),f193(x21382)) % 14.98/14.68 [2139]~E(x21391,x21392)+E(f485(x21391,x21393,x21394,x21395,x21396),f485(x21392,x21393,x21394,x21395,x21396)) % 14.98/14.68 [2140]~E(x21401,x21402)+E(f485(x21403,x21401,x21404,x21405,x21406),f485(x21403,x21402,x21404,x21405,x21406)) % 14.98/14.68 [2141]~E(x21411,x21412)+E(f485(x21413,x21414,x21411,x21415,x21416),f485(x21413,x21414,x21412,x21415,x21416)) % 14.98/14.68 [2142]~E(x21421,x21422)+E(f485(x21423,x21424,x21425,x21421,x21426),f485(x21423,x21424,x21425,x21422,x21426)) % 14.98/14.68 [2143]~E(x21431,x21432)+E(f485(x21433,x21434,x21435,x21436,x21431),f485(x21433,x21434,x21435,x21436,x21432)) % 14.98/14.68 [2144]~E(x21441,x21442)+E(f803(x21441,x21443,x21444,x21445),f803(x21442,x21443,x21444,x21445)) % 14.98/14.68 [2145]~E(x21451,x21452)+E(f803(x21453,x21451,x21454,x21455),f803(x21453,x21452,x21454,x21455)) % 14.98/14.68 [2146]~E(x21461,x21462)+E(f803(x21463,x21464,x21461,x21465),f803(x21463,x21464,x21462,x21465)) % 14.98/14.68 [2147]~E(x21471,x21472)+E(f803(x21473,x21474,x21475,x21471),f803(x21473,x21474,x21475,x21472)) % 14.98/14.68 [2148]~E(x21481,x21482)+E(f330(x21481,x21483,x21484,x21485,x21486),f330(x21482,x21483,x21484,x21485,x21486)) % 14.98/14.68 [2149]~E(x21491,x21492)+E(f330(x21493,x21491,x21494,x21495,x21496),f330(x21493,x21492,x21494,x21495,x21496)) % 14.98/14.68 [2150]~E(x21501,x21502)+E(f330(x21503,x21504,x21501,x21505,x21506),f330(x21503,x21504,x21502,x21505,x21506)) % 14.98/14.68 [2151]~E(x21511,x21512)+E(f330(x21513,x21514,x21515,x21511,x21516),f330(x21513,x21514,x21515,x21512,x21516)) % 14.98/14.68 [2152]~E(x21521,x21522)+E(f330(x21523,x21524,x21525,x21526,x21521),f330(x21523,x21524,x21525,x21526,x21522)) % 14.98/14.68 [2153]~E(x21531,x21532)+E(f757(x21531,x21533,x21534),f757(x21532,x21533,x21534)) % 14.98/14.68 [2154]~E(x21541,x21542)+E(f757(x21543,x21541,x21544),f757(x21543,x21542,x21544)) % 14.98/14.68 [2155]~E(x21551,x21552)+E(f757(x21553,x21554,x21551),f757(x21553,x21554,x21552)) % 14.98/14.68 [2156]~E(x21561,x21562)+E(f505(x21561,x21563,x21564),f505(x21562,x21563,x21564)) % 14.98/14.68 [2157]~E(x21571,x21572)+E(f505(x21573,x21571,x21574),f505(x21573,x21572,x21574)) % 14.98/14.68 [2158]~E(x21581,x21582)+E(f505(x21583,x21584,x21581),f505(x21583,x21584,x21582)) % 14.98/14.68 [2159]~E(x21591,x21592)+E(f509(x21591,x21593,x21594,x21595),f509(x21592,x21593,x21594,x21595)) % 14.98/14.68 [2160]~E(x21601,x21602)+E(f509(x21603,x21601,x21604,x21605),f509(x21603,x21602,x21604,x21605)) % 14.98/14.68 [2161]~E(x21611,x21612)+E(f509(x21613,x21614,x21611,x21615),f509(x21613,x21614,x21612,x21615)) % 14.98/14.68 [2162]~E(x21621,x21622)+E(f509(x21623,x21624,x21625,x21621),f509(x21623,x21624,x21625,x21622)) % 14.98/14.68 [2163]~E(x21631,x21632)+E(f269(x21631,x21633,x21634,x21635),f269(x21632,x21633,x21634,x21635)) % 14.98/14.68 [2164]~E(x21641,x21642)+E(f269(x21643,x21641,x21644,x21645),f269(x21643,x21642,x21644,x21645)) % 14.98/14.68 [2165]~E(x21651,x21652)+E(f269(x21653,x21654,x21651,x21655),f269(x21653,x21654,x21652,x21655)) % 14.98/14.68 [2166]~E(x21661,x21662)+E(f269(x21663,x21664,x21665,x21661),f269(x21663,x21664,x21665,x21662)) % 14.98/14.68 [2167]~E(x21671,x21672)+E(f597(x21671,x21673,x21674),f597(x21672,x21673,x21674)) % 14.98/14.68 [2168]~E(x21681,x21682)+E(f597(x21683,x21681,x21684),f597(x21683,x21682,x21684)) % 14.98/14.68 [2169]~E(x21691,x21692)+E(f597(x21693,x21694,x21691),f597(x21693,x21694,x21692)) % 14.98/14.68 [2170]~E(x21701,x21702)+E(f435(x21701,x21703,x21704,x21705),f435(x21702,x21703,x21704,x21705)) % 14.98/14.68 [2171]~E(x21711,x21712)+E(f435(x21713,x21711,x21714,x21715),f435(x21713,x21712,x21714,x21715)) % 14.98/14.68 [2172]~E(x21721,x21722)+E(f435(x21723,x21724,x21721,x21725),f435(x21723,x21724,x21722,x21725)) % 14.98/14.68 [2173]~E(x21731,x21732)+E(f435(x21733,x21734,x21735,x21731),f435(x21733,x21734,x21735,x21732)) % 14.98/14.68 [2174]~E(x21741,x21742)+E(f902(x21741,x21743,x21744),f902(x21742,x21743,x21744)) % 14.98/14.68 [2175]~E(x21751,x21752)+E(f902(x21753,x21751,x21754),f902(x21753,x21752,x21754)) % 14.98/14.68 [2176]~E(x21761,x21762)+E(f902(x21763,x21764,x21761),f902(x21763,x21764,x21762)) % 14.98/14.68 [2177]~E(x21771,x21772)+E(f429(x21771,x21773,x21774),f429(x21772,x21773,x21774)) % 14.98/14.68 [2178]~E(x21781,x21782)+E(f429(x21783,x21781,x21784),f429(x21783,x21782,x21784)) % 14.98/14.68 [2179]~E(x21791,x21792)+E(f429(x21793,x21794,x21791),f429(x21793,x21794,x21792)) % 14.98/14.68 [2180]~E(x21801,x21802)+E(f895(x21801,x21803,x21804),f895(x21802,x21803,x21804)) % 14.98/14.68 [2181]~E(x21811,x21812)+E(f895(x21813,x21811,x21814),f895(x21813,x21812,x21814)) % 14.98/14.68 [2182]~E(x21821,x21822)+E(f895(x21823,x21824,x21821),f895(x21823,x21824,x21822)) % 14.98/14.68 [2183]~E(x21831,x21832)+E(f427(x21831,x21833),f427(x21832,x21833)) % 14.98/14.68 [2184]~E(x21841,x21842)+E(f427(x21843,x21841),f427(x21843,x21842)) % 14.98/14.68 [2185]~E(x21851,x21852)+E(f466(x21851,x21853,x21854,x21855),f466(x21852,x21853,x21854,x21855)) % 14.98/14.68 [2186]~E(x21861,x21862)+E(f466(x21863,x21861,x21864,x21865),f466(x21863,x21862,x21864,x21865)) % 14.98/14.68 [2187]~E(x21871,x21872)+E(f466(x21873,x21874,x21871,x21875),f466(x21873,x21874,x21872,x21875)) % 14.98/14.68 [2188]~E(x21881,x21882)+E(f466(x21883,x21884,x21885,x21881),f466(x21883,x21884,x21885,x21882)) % 14.98/14.68 [2189]~E(x21891,x21892)+E(f860(x21891,x21893,x21894),f860(x21892,x21893,x21894)) % 14.98/14.68 [2190]~E(x21901,x21902)+E(f860(x21903,x21901,x21904),f860(x21903,x21902,x21904)) % 14.98/14.68 [2191]~E(x21911,x21912)+E(f860(x21913,x21914,x21911),f860(x21913,x21914,x21912)) % 14.98/14.68 [2192]~E(x21921,x21922)+E(f584(x21921,x21923,x21924,x21925,x21926,x21927,x21928,x21929),f584(x21922,x21923,x21924,x21925,x21926,x21927,x21928,x21929)) % 14.98/14.68 [2193]~E(x21931,x21932)+E(f584(x21933,x21931,x21934,x21935,x21936,x21937,x21938,x21939),f584(x21933,x21932,x21934,x21935,x21936,x21937,x21938,x21939)) % 14.98/14.68 [2194]~E(x21941,x21942)+E(f584(x21943,x21944,x21941,x21945,x21946,x21947,x21948,x21949),f584(x21943,x21944,x21942,x21945,x21946,x21947,x21948,x21949)) % 14.98/14.68 [2195]~E(x21951,x21952)+E(f584(x21953,x21954,x21955,x21951,x21956,x21957,x21958,x21959),f584(x21953,x21954,x21955,x21952,x21956,x21957,x21958,x21959)) % 14.98/14.68 [2196]~E(x21961,x21962)+E(f584(x21963,x21964,x21965,x21966,x21961,x21967,x21968,x21969),f584(x21963,x21964,x21965,x21966,x21962,x21967,x21968,x21969)) % 14.98/14.68 [2197]~E(x21971,x21972)+E(f584(x21973,x21974,x21975,x21976,x21977,x21971,x21978,x21979),f584(x21973,x21974,x21975,x21976,x21977,x21972,x21978,x21979)) % 14.98/14.68 [2198]~E(x21981,x21982)+E(f584(x21983,x21984,x21985,x21986,x21987,x21988,x21981,x21989),f584(x21983,x21984,x21985,x21986,x21987,x21988,x21982,x21989)) % 14.98/14.68 [2199]~E(x21991,x21992)+E(f584(x21993,x21994,x21995,x21996,x21997,x21998,x21999,x21991),f584(x21993,x21994,x21995,x21996,x21997,x21998,x21999,x21992)) % 14.98/14.68 [2200]~E(x22001,x22002)+E(f512(x22001,x22003,x22004,x22005,x22006,x22007),f512(x22002,x22003,x22004,x22005,x22006,x22007)) % 14.98/14.68 [2201]~E(x22011,x22012)+E(f512(x22013,x22011,x22014,x22015,x22016,x22017),f512(x22013,x22012,x22014,x22015,x22016,x22017)) % 14.98/14.68 [2202]~E(x22021,x22022)+E(f512(x22023,x22024,x22021,x22025,x22026,x22027),f512(x22023,x22024,x22022,x22025,x22026,x22027)) % 14.98/14.68 [2203]~E(x22031,x22032)+E(f512(x22033,x22034,x22035,x22031,x22036,x22037),f512(x22033,x22034,x22035,x22032,x22036,x22037)) % 14.98/14.68 [2204]~E(x22041,x22042)+E(f512(x22043,x22044,x22045,x22046,x22041,x22047),f512(x22043,x22044,x22045,x22046,x22042,x22047)) % 14.98/14.68 [2205]~E(x22051,x22052)+E(f512(x22053,x22054,x22055,x22056,x22057,x22051),f512(x22053,x22054,x22055,x22056,x22057,x22052)) % 14.98/14.68 [2206]~E(x22061,x22062)+E(f498(x22061,x22063,x22064),f498(x22062,x22063,x22064)) % 14.98/14.68 [2207]~E(x22071,x22072)+E(f498(x22073,x22071,x22074),f498(x22073,x22072,x22074)) % 14.98/14.68 [2208]~E(x22081,x22082)+E(f498(x22083,x22084,x22081),f498(x22083,x22084,x22082)) % 14.98/14.68 [2209]~E(x22091,x22092)+E(f496(x22091,x22093,x22094),f496(x22092,x22093,x22094)) % 14.98/14.68 [2210]~E(x22101,x22102)+E(f496(x22103,x22101,x22104),f496(x22103,x22102,x22104)) % 14.98/14.68 [2211]~E(x22111,x22112)+E(f496(x22113,x22114,x22111),f496(x22113,x22114,x22112)) % 14.98/14.68 [2212]~E(x22121,x22122)+E(f792(x22121),f792(x22122)) % 14.98/14.68 [2213]~E(x22131,x22132)+E(f894(x22131,x22133,x22134),f894(x22132,x22133,x22134)) % 14.98/14.68 [2214]~E(x22141,x22142)+E(f894(x22143,x22141,x22144),f894(x22143,x22142,x22144)) % 14.98/14.68 [2215]~E(x22151,x22152)+E(f894(x22153,x22154,x22151),f894(x22153,x22154,x22152)) % 14.98/14.68 [2216]~E(x22161,x22162)+E(f487(x22161,x22163,x22164,x22165),f487(x22162,x22163,x22164,x22165)) % 14.98/14.68 [2217]~E(x22171,x22172)+E(f487(x22173,x22171,x22174,x22175),f487(x22173,x22172,x22174,x22175)) % 14.98/14.68 [2218]~E(x22181,x22182)+E(f487(x22183,x22184,x22181,x22185),f487(x22183,x22184,x22182,x22185)) % 14.98/14.68 [2219]~E(x22191,x22192)+E(f487(x22193,x22194,x22195,x22191),f487(x22193,x22194,x22195,x22192)) % 14.98/14.68 [2220]~E(x22201,x22202)+E(f801(x22201,x22203,x22204),f801(x22202,x22203,x22204)) % 14.98/14.68 [2221]~E(x22211,x22212)+E(f801(x22213,x22211,x22214),f801(x22213,x22212,x22214)) % 14.98/14.68 [2222]~E(x22221,x22222)+E(f801(x22223,x22224,x22221),f801(x22223,x22224,x22222)) % 14.98/14.68 [2223]~E(x22231,x22232)+E(f614(x22231,x22233,x22234),f614(x22232,x22233,x22234)) % 14.98/14.68 [2224]~E(x22241,x22242)+E(f614(x22243,x22241,x22244),f614(x22243,x22242,x22244)) % 14.98/14.68 [2225]~E(x22251,x22252)+E(f614(x22253,x22254,x22251),f614(x22253,x22254,x22252)) % 14.98/14.68 [2226]~E(x22261,x22262)+E(f796(x22261,x22263,x22264,x22265,x22266,x22267,x22268),f796(x22262,x22263,x22264,x22265,x22266,x22267,x22268)) % 14.98/14.68 [2227]~E(x22271,x22272)+E(f796(x22273,x22271,x22274,x22275,x22276,x22277,x22278),f796(x22273,x22272,x22274,x22275,x22276,x22277,x22278)) % 14.98/14.68 [2228]~E(x22281,x22282)+E(f796(x22283,x22284,x22281,x22285,x22286,x22287,x22288),f796(x22283,x22284,x22282,x22285,x22286,x22287,x22288)) % 14.98/14.68 [2229]~E(x22291,x22292)+E(f796(x22293,x22294,x22295,x22291,x22296,x22297,x22298),f796(x22293,x22294,x22295,x22292,x22296,x22297,x22298)) % 14.98/14.68 [2230]~E(x22301,x22302)+E(f796(x22303,x22304,x22305,x22306,x22301,x22307,x22308),f796(x22303,x22304,x22305,x22306,x22302,x22307,x22308)) % 14.98/14.68 [2231]~E(x22311,x22312)+E(f796(x22313,x22314,x22315,x22316,x22317,x22311,x22318),f796(x22313,x22314,x22315,x22316,x22317,x22312,x22318)) % 14.98/14.68 [2232]~E(x22321,x22322)+E(f796(x22323,x22324,x22325,x22326,x22327,x22328,x22321),f796(x22323,x22324,x22325,x22326,x22327,x22328,x22322)) % 14.98/14.68 [2233]~E(x22331,x22332)+E(f417(x22331,x22333,x22334),f417(x22332,x22333,x22334)) % 14.98/14.68 [2234]~E(x22341,x22342)+E(f417(x22343,x22341,x22344),f417(x22343,x22342,x22344)) % 14.98/14.68 [2235]~E(x22351,x22352)+E(f417(x22353,x22354,x22351),f417(x22353,x22354,x22352)) % 14.98/14.68 [2236]~E(x22361,x22362)+E(f917(x22361,x22363,x22364,x22365,x22366),f917(x22362,x22363,x22364,x22365,x22366)) % 14.98/14.68 [2237]~E(x22371,x22372)+E(f917(x22373,x22371,x22374,x22375,x22376),f917(x22373,x22372,x22374,x22375,x22376)) % 14.98/14.68 [2238]~E(x22381,x22382)+E(f917(x22383,x22384,x22381,x22385,x22386),f917(x22383,x22384,x22382,x22385,x22386)) % 14.98/14.68 [2239]~E(x22391,x22392)+E(f917(x22393,x22394,x22395,x22391,x22396),f917(x22393,x22394,x22395,x22392,x22396)) % 14.98/14.68 [2240]~E(x22401,x22402)+E(f917(x22403,x22404,x22405,x22406,x22401),f917(x22403,x22404,x22405,x22406,x22402)) % 14.98/14.68 [2241]~E(x22411,x22412)+E(f805(x22411,x22413,x22414,x22415,x22416),f805(x22412,x22413,x22414,x22415,x22416)) % 14.98/14.68 [2242]~E(x22421,x22422)+E(f805(x22423,x22421,x22424,x22425,x22426),f805(x22423,x22422,x22424,x22425,x22426)) % 14.98/14.68 [2243]~E(x22431,x22432)+E(f805(x22433,x22434,x22431,x22435,x22436),f805(x22433,x22434,x22432,x22435,x22436)) % 14.98/14.68 [2244]~E(x22441,x22442)+E(f805(x22443,x22444,x22445,x22441,x22446),f805(x22443,x22444,x22445,x22442,x22446)) % 14.98/14.68 [2245]~E(x22451,x22452)+E(f805(x22453,x22454,x22455,x22456,x22451),f805(x22453,x22454,x22455,x22456,x22452)) % 14.98/14.68 [2246]~E(x22461,x22462)+E(f419(x22461),f419(x22462)) % 14.98/14.68 [2247]~E(x22471,x22472)+E(f329(x22471,x22473),f329(x22472,x22473)) % 14.98/14.68 [2248]~E(x22481,x22482)+E(f329(x22483,x22481),f329(x22483,x22482)) % 14.98/14.68 [2249]~E(x22491,x22492)+E(f643(x22491,x22493,x22494,x22495,x22496),f643(x22492,x22493,x22494,x22495,x22496)) % 14.98/14.68 [2250]~E(x22501,x22502)+E(f643(x22503,x22501,x22504,x22505,x22506),f643(x22503,x22502,x22504,x22505,x22506)) % 14.98/14.68 [2251]~E(x22511,x22512)+E(f643(x22513,x22514,x22511,x22515,x22516),f643(x22513,x22514,x22512,x22515,x22516)) % 14.98/14.68 [2252]~E(x22521,x22522)+E(f643(x22523,x22524,x22525,x22521,x22526),f643(x22523,x22524,x22525,x22522,x22526)) % 14.98/14.68 [2253]~E(x22531,x22532)+E(f643(x22533,x22534,x22535,x22536,x22531),f643(x22533,x22534,x22535,x22536,x22532)) % 14.98/14.68 [2254]~E(x22541,x22542)+E(f348(x22541,x22543,x22544),f348(x22542,x22543,x22544)) % 14.98/14.68 [2255]~E(x22551,x22552)+E(f348(x22553,x22551,x22554),f348(x22553,x22552,x22554)) % 14.98/14.68 [2256]~E(x22561,x22562)+E(f348(x22563,x22564,x22561),f348(x22563,x22564,x22562)) % 14.98/14.68 [2257]~E(x22571,x22572)+E(f651(x22571,x22573),f651(x22572,x22573)) % 14.98/14.68 [2258]~E(x22581,x22582)+E(f651(x22583,x22581),f651(x22583,x22582)) % 14.98/14.68 [2259]~E(x22591,x22592)+E(f433(x22591,x22593,x22594),f433(x22592,x22593,x22594)) % 14.98/14.68 [2260]~E(x22601,x22602)+E(f433(x22603,x22601,x22604),f433(x22603,x22602,x22604)) % 14.98/14.68 [2261]~E(x22611,x22612)+E(f433(x22613,x22614,x22611),f433(x22613,x22614,x22612)) % 14.98/14.68 [2262]~E(x22621,x22622)+E(f657(x22621,x22623,x22624),f657(x22622,x22623,x22624)) % 14.98/14.68 [2263]~E(x22631,x22632)+E(f657(x22633,x22631,x22634),f657(x22633,x22632,x22634)) % 14.98/14.68 [2264]~E(x22641,x22642)+E(f657(x22643,x22644,x22641),f657(x22643,x22644,x22642)) % 14.98/14.68 [2265]~E(x22651,x22652)+E(f706(x22651,x22653,x22654,x22655,x22656),f706(x22652,x22653,x22654,x22655,x22656)) % 14.98/14.68 [2266]~E(x22661,x22662)+E(f706(x22663,x22661,x22664,x22665,x22666),f706(x22663,x22662,x22664,x22665,x22666)) % 14.98/14.68 [2267]~E(x22671,x22672)+E(f706(x22673,x22674,x22671,x22675,x22676),f706(x22673,x22674,x22672,x22675,x22676)) % 14.98/14.68 [2268]~E(x22681,x22682)+E(f706(x22683,x22684,x22685,x22681,x22686),f706(x22683,x22684,x22685,x22682,x22686)) % 14.98/14.68 [2269]~E(x22691,x22692)+E(f706(x22693,x22694,x22695,x22696,x22691),f706(x22693,x22694,x22695,x22696,x22692)) % 14.98/14.68 [2270]~E(x22701,x22702)+E(f373(x22701,x22703,x22704,x22705),f373(x22702,x22703,x22704,x22705)) % 14.98/14.68 [2271]~E(x22711,x22712)+E(f373(x22713,x22711,x22714,x22715),f373(x22713,x22712,x22714,x22715)) % 14.98/14.68 [2272]~E(x22721,x22722)+E(f373(x22723,x22724,x22721,x22725),f373(x22723,x22724,x22722,x22725)) % 14.98/14.68 [2273]~E(x22731,x22732)+E(f373(x22733,x22734,x22735,x22731),f373(x22733,x22734,x22735,x22732)) % 14.98/14.68 [2274]~E(x22741,x22742)+E(f423(x22741),f423(x22742)) % 14.98/14.68 [2275]~E(x22751,x22752)+E(f638(x22751,x22753,x22754,x22755,x22756),f638(x22752,x22753,x22754,x22755,x22756)) % 14.98/14.68 [2276]~E(x22761,x22762)+E(f638(x22763,x22761,x22764,x22765,x22766),f638(x22763,x22762,x22764,x22765,x22766)) % 14.98/14.68 [2277]~E(x22771,x22772)+E(f638(x22773,x22774,x22771,x22775,x22776),f638(x22773,x22774,x22772,x22775,x22776)) % 14.98/14.68 [2278]~E(x22781,x22782)+E(f638(x22783,x22784,x22785,x22781,x22786),f638(x22783,x22784,x22785,x22782,x22786)) % 14.98/14.68 [2279]~E(x22791,x22792)+E(f638(x22793,x22794,x22795,x22796,x22791),f638(x22793,x22794,x22795,x22796,x22792)) % 14.98/14.68 [2280]~E(x22801,x22802)+E(f257(x22801,x22803,x22804),f257(x22802,x22803,x22804)) % 14.98/14.68 [2281]~E(x22811,x22812)+E(f257(x22813,x22811,x22814),f257(x22813,x22812,x22814)) % 14.98/14.68 [2282]~E(x22821,x22822)+E(f257(x22823,x22824,x22821),f257(x22823,x22824,x22822)) % 14.98/14.68 [2283]~E(x22831,x22832)+E(f411(x22831,x22833),f411(x22832,x22833)) % 14.98/14.68 [2284]~E(x22841,x22842)+E(f411(x22843,x22841),f411(x22843,x22842)) % 14.98/14.68 [2285]~E(x22851,x22852)+E(f676(x22851,x22853,x22854,x22855),f676(x22852,x22853,x22854,x22855)) % 14.98/14.68 [2286]~E(x22861,x22862)+E(f676(x22863,x22861,x22864,x22865),f676(x22863,x22862,x22864,x22865)) % 14.98/14.68 [2287]~E(x22871,x22872)+E(f676(x22873,x22874,x22871,x22875),f676(x22873,x22874,x22872,x22875)) % 14.98/14.68 [2288]~E(x22881,x22882)+E(f676(x22883,x22884,x22885,x22881),f676(x22883,x22884,x22885,x22882)) % 14.98/14.68 [2289]~E(x22891,x22892)+E(f568(x22891,x22893,x22894,x22895),f568(x22892,x22893,x22894,x22895)) % 14.98/14.68 [2290]~E(x22901,x22902)+E(f568(x22903,x22901,x22904,x22905),f568(x22903,x22902,x22904,x22905)) % 14.98/14.68 [2291]~E(x22911,x22912)+E(f568(x22913,x22914,x22911,x22915),f568(x22913,x22914,x22912,x22915)) % 14.98/14.68 [2292]~E(x22921,x22922)+E(f568(x22923,x22924,x22925,x22921),f568(x22923,x22924,x22925,x22922)) % 14.98/14.68 [2293]~E(x22931,x22932)+E(f458(x22931,x22933),f458(x22932,x22933)) % 14.98/14.68 [2294]~E(x22941,x22942)+E(f458(x22943,x22941),f458(x22943,x22942)) % 14.98/14.68 [2295]~E(x22951,x22952)+E(f748(x22951,x22953,x22954,x22955,x22956),f748(x22952,x22953,x22954,x22955,x22956)) % 14.98/14.68 [2296]~E(x22961,x22962)+E(f748(x22963,x22961,x22964,x22965,x22966),f748(x22963,x22962,x22964,x22965,x22966)) % 14.98/14.68 [2297]~E(x22971,x22972)+E(f748(x22973,x22974,x22971,x22975,x22976),f748(x22973,x22974,x22972,x22975,x22976)) % 14.98/14.68 [2298]~E(x22981,x22982)+E(f748(x22983,x22984,x22985,x22981,x22986),f748(x22983,x22984,x22985,x22982,x22986)) % 14.98/14.68 [2299]~E(x22991,x22992)+E(f748(x22993,x22994,x22995,x22996,x22991),f748(x22993,x22994,x22995,x22996,x22992)) % 14.98/14.68 [2300]~E(x23001,x23002)+E(f719(x23001,x23003,x23004),f719(x23002,x23003,x23004)) % 14.98/14.68 [2301]~E(x23011,x23012)+E(f719(x23013,x23011,x23014),f719(x23013,x23012,x23014)) % 14.98/14.68 [2302]~E(x23021,x23022)+E(f719(x23023,x23024,x23021),f719(x23023,x23024,x23022)) % 14.98/14.68 [2303]~E(x23031,x23032)+E(f472(x23031,x23033,x23034),f472(x23032,x23033,x23034)) % 14.98/14.68 [2304]~E(x23041,x23042)+E(f472(x23043,x23041,x23044),f472(x23043,x23042,x23044)) % 14.98/14.68 [2305]~E(x23051,x23052)+E(f472(x23053,x23054,x23051),f472(x23053,x23054,x23052)) % 14.98/14.68 [2306]~E(x23061,x23062)+E(f765(x23061,x23063,x23064),f765(x23062,x23063,x23064)) % 14.98/14.68 [2307]~E(x23071,x23072)+E(f765(x23073,x23071,x23074),f765(x23073,x23072,x23074)) % 14.98/14.68 [2308]~E(x23081,x23082)+E(f765(x23083,x23084,x23081),f765(x23083,x23084,x23082)) % 14.98/14.68 [2309]~E(x23091,x23092)+E(f188(x23091,x23093,x23094,x23095),f188(x23092,x23093,x23094,x23095)) % 14.98/14.68 [2310]~E(x23101,x23102)+E(f188(x23103,x23101,x23104,x23105),f188(x23103,x23102,x23104,x23105)) % 14.98/14.68 [2311]~E(x23111,x23112)+E(f188(x23113,x23114,x23111,x23115),f188(x23113,x23114,x23112,x23115)) % 14.98/14.68 [2312]~E(x23121,x23122)+E(f188(x23123,x23124,x23125,x23121),f188(x23123,x23124,x23125,x23122)) % 14.98/14.68 [2313]~E(x23131,x23132)+E(f358(x23131),f358(x23132)) % 14.98/14.68 [2314]~E(x23141,x23142)+E(f672(x23141,x23143),f672(x23142,x23143)) % 14.98/14.68 [2315]~E(x23151,x23152)+E(f672(x23153,x23151),f672(x23153,x23152)) % 14.98/14.68 [2316]~E(x23161,x23162)+E(f67(x23161,x23163),f67(x23162,x23163)) % 14.98/14.68 [2317]~E(x23171,x23172)+E(f67(x23173,x23171),f67(x23173,x23172)) % 14.98/14.68 [2318]~E(x23181,x23182)+E(f889(x23181,x23183),f889(x23182,x23183)) % 14.98/14.68 [2319]~E(x23191,x23192)+E(f889(x23193,x23191),f889(x23193,x23192)) % 14.98/14.68 [2320]~E(x23201,x23202)+E(f447(x23201,x23203,x23204),f447(x23202,x23203,x23204)) % 14.98/14.68 [2321]~E(x23211,x23212)+E(f447(x23213,x23211,x23214),f447(x23213,x23212,x23214)) % 14.98/14.68 [2322]~E(x23221,x23222)+E(f447(x23223,x23224,x23221),f447(x23223,x23224,x23222)) % 14.98/14.68 [2323]~E(x23231,x23232)+E(f518(x23231,x23233,x23234,x23235),f518(x23232,x23233,x23234,x23235)) % 14.98/14.68 [2324]~E(x23241,x23242)+E(f518(x23243,x23241,x23244,x23245),f518(x23243,x23242,x23244,x23245)) % 14.98/14.68 [2325]~E(x23251,x23252)+E(f518(x23253,x23254,x23251,x23255),f518(x23253,x23254,x23252,x23255)) % 14.98/14.68 [2326]~E(x23261,x23262)+E(f518(x23263,x23264,x23265,x23261),f518(x23263,x23264,x23265,x23262)) % 14.98/14.68 [2327]~E(x23271,x23272)+E(f577(x23271,x23273,x23274,x23275,x23276),f577(x23272,x23273,x23274,x23275,x23276)) % 14.98/14.68 [2328]~E(x23281,x23282)+E(f577(x23283,x23281,x23284,x23285,x23286),f577(x23283,x23282,x23284,x23285,x23286)) % 14.98/14.68 [2329]~E(x23291,x23292)+E(f577(x23293,x23294,x23291,x23295,x23296),f577(x23293,x23294,x23292,x23295,x23296)) % 14.98/14.68 [2330]~E(x23301,x23302)+E(f577(x23303,x23304,x23305,x23301,x23306),f577(x23303,x23304,x23305,x23302,x23306)) % 14.98/14.68 [2331]~E(x23311,x23312)+E(f577(x23313,x23314,x23315,x23316,x23311),f577(x23313,x23314,x23315,x23316,x23312)) % 14.98/14.68 [2332]~E(x23321,x23322)+E(f834(x23321,x23323,x23324,x23325),f834(x23322,x23323,x23324,x23325)) % 14.98/14.68 [2333]~E(x23331,x23332)+E(f834(x23333,x23331,x23334,x23335),f834(x23333,x23332,x23334,x23335)) % 14.98/14.68 [2334]~E(x23341,x23342)+E(f834(x23343,x23344,x23341,x23345),f834(x23343,x23344,x23342,x23345)) % 14.98/14.68 [2335]~E(x23351,x23352)+E(f834(x23353,x23354,x23355,x23351),f834(x23353,x23354,x23355,x23352)) % 14.98/14.68 [2336]~E(x23361,x23362)+E(f725(x23361,x23363,x23364),f725(x23362,x23363,x23364)) % 14.98/14.68 [2337]~E(x23371,x23372)+E(f725(x23373,x23371,x23374),f725(x23373,x23372,x23374)) % 14.98/14.68 [2338]~E(x23381,x23382)+E(f725(x23383,x23384,x23381),f725(x23383,x23384,x23382)) % 14.98/14.68 [2339]~E(x23391,x23392)+E(f442(x23391,x23393,x23394),f442(x23392,x23393,x23394)) % 14.98/14.68 [2340]~E(x23401,x23402)+E(f442(x23403,x23401,x23404),f442(x23403,x23402,x23404)) % 14.98/14.68 [2341]~E(x23411,x23412)+E(f442(x23413,x23414,x23411),f442(x23413,x23414,x23412)) % 14.98/14.68 [2342]~E(x23421,x23422)+E(f394(x23421,x23423,x23424),f394(x23422,x23423,x23424)) % 14.98/14.68 [2343]~E(x23431,x23432)+E(f394(x23433,x23431,x23434),f394(x23433,x23432,x23434)) % 14.98/14.68 [2344]~E(x23441,x23442)+E(f394(x23443,x23444,x23441),f394(x23443,x23444,x23442)) % 14.98/14.68 [2345]~E(x23451,x23452)+E(f845(x23451,x23453,x23454,x23455,x23456,x23457,x23458,x23459),f845(x23452,x23453,x23454,x23455,x23456,x23457,x23458,x23459)) % 14.98/14.68 [2346]~E(x23461,x23462)+E(f845(x23463,x23461,x23464,x23465,x23466,x23467,x23468,x23469),f845(x23463,x23462,x23464,x23465,x23466,x23467,x23468,x23469)) % 14.98/14.68 [2347]~E(x23471,x23472)+E(f845(x23473,x23474,x23471,x23475,x23476,x23477,x23478,x23479),f845(x23473,x23474,x23472,x23475,x23476,x23477,x23478,x23479)) % 14.98/14.68 [2348]~E(x23481,x23482)+E(f845(x23483,x23484,x23485,x23481,x23486,x23487,x23488,x23489),f845(x23483,x23484,x23485,x23482,x23486,x23487,x23488,x23489)) % 14.98/14.68 [2349]~E(x23491,x23492)+E(f845(x23493,x23494,x23495,x23496,x23491,x23497,x23498,x23499),f845(x23493,x23494,x23495,x23496,x23492,x23497,x23498,x23499)) % 14.98/14.68 [2350]~E(x23501,x23502)+E(f845(x23503,x23504,x23505,x23506,x23507,x23501,x23508,x23509),f845(x23503,x23504,x23505,x23506,x23507,x23502,x23508,x23509)) % 14.98/14.68 [2351]~E(x23511,x23512)+E(f845(x23513,x23514,x23515,x23516,x23517,x23518,x23511,x23519),f845(x23513,x23514,x23515,x23516,x23517,x23518,x23512,x23519)) % 14.98/14.68 [2352]~E(x23521,x23522)+E(f845(x23523,x23524,x23525,x23526,x23527,x23528,x23529,x23521),f845(x23523,x23524,x23525,x23526,x23527,x23528,x23529,x23522)) % 14.98/14.68 [2353]~E(x23531,x23532)+E(f283(x23531,x23533),f283(x23532,x23533)) % 14.98/14.68 [2354]~E(x23541,x23542)+E(f283(x23543,x23541),f283(x23543,x23542)) % 14.98/14.68 [2355]~E(x23551,x23552)+E(f681(x23551,x23553),f681(x23552,x23553)) % 14.98/14.68 [2356]~E(x23561,x23562)+E(f681(x23563,x23561),f681(x23563,x23562)) % 14.98/14.68 [2357]~E(x23571,x23572)+E(f690(x23571,x23573,x23574,x23575),f690(x23572,x23573,x23574,x23575)) % 14.98/14.68 [2358]~E(x23581,x23582)+E(f690(x23583,x23581,x23584,x23585),f690(x23583,x23582,x23584,x23585)) % 14.98/14.68 [2359]~E(x23591,x23592)+E(f690(x23593,x23594,x23591,x23595),f690(x23593,x23594,x23592,x23595)) % 14.98/14.68 [2360]~E(x23601,x23602)+E(f690(x23603,x23604,x23605,x23601),f690(x23603,x23604,x23605,x23602)) % 14.98/14.68 [2361]~E(x23611,x23612)+E(f341(x23611,x23613,x23614,x23615),f341(x23612,x23613,x23614,x23615)) % 14.98/14.68 [2362]~E(x23621,x23622)+E(f341(x23623,x23621,x23624,x23625),f341(x23623,x23622,x23624,x23625)) % 14.98/14.68 [2363]~E(x23631,x23632)+E(f341(x23633,x23634,x23631,x23635),f341(x23633,x23634,x23632,x23635)) % 14.98/14.68 [2364]~E(x23641,x23642)+E(f341(x23643,x23644,x23645,x23641),f341(x23643,x23644,x23645,x23642)) % 14.98/14.68 [2365]~E(x23651,x23652)+E(f529(x23651,x23653,x23654),f529(x23652,x23653,x23654)) % 14.98/14.68 [2366]~E(x23661,x23662)+E(f529(x23663,x23661,x23664),f529(x23663,x23662,x23664)) % 14.98/14.68 [2367]~E(x23671,x23672)+E(f529(x23673,x23674,x23671),f529(x23673,x23674,x23672)) % 14.98/14.68 [2368]~E(x23681,x23682)+E(f771(x23681,x23683,x23684),f771(x23682,x23683,x23684)) % 14.98/14.68 [2369]~E(x23691,x23692)+E(f771(x23693,x23691,x23694),f771(x23693,x23692,x23694)) % 14.98/14.68 [2370]~E(x23701,x23702)+E(f771(x23703,x23704,x23701),f771(x23703,x23704,x23702)) % 14.98/14.68 [2371]~E(x23711,x23712)+E(f352(x23711,x23713,x23714),f352(x23712,x23713,x23714)) % 14.98/14.68 [2372]~E(x23721,x23722)+E(f352(x23723,x23721,x23724),f352(x23723,x23722,x23724)) % 14.98/14.68 [2373]~E(x23731,x23732)+E(f352(x23733,x23734,x23731),f352(x23733,x23734,x23732)) % 14.98/14.68 [2374]~E(x23741,x23742)+E(f883(x23741,x23743),f883(x23742,x23743)) % 14.98/14.68 [2375]~E(x23751,x23752)+E(f883(x23753,x23751),f883(x23753,x23752)) % 14.98/14.68 [2376]~E(x23761,x23762)+E(f369(x23761,x23763,x23764),f369(x23762,x23763,x23764)) % 14.98/14.68 [2377]~E(x23771,x23772)+E(f369(x23773,x23771,x23774),f369(x23773,x23772,x23774)) % 14.98/14.68 [2378]~E(x23781,x23782)+E(f369(x23783,x23784,x23781),f369(x23783,x23784,x23782)) % 14.98/14.68 [2379]~E(x23791,x23792)+E(f639(x23791,x23793,x23794,x23795,x23796),f639(x23792,x23793,x23794,x23795,x23796)) % 14.98/14.68 [2380]~E(x23801,x23802)+E(f639(x23803,x23801,x23804,x23805,x23806),f639(x23803,x23802,x23804,x23805,x23806)) % 14.98/14.68 [2381]~E(x23811,x23812)+E(f639(x23813,x23814,x23811,x23815,x23816),f639(x23813,x23814,x23812,x23815,x23816)) % 14.98/14.68 [2382]~E(x23821,x23822)+E(f639(x23823,x23824,x23825,x23821,x23826),f639(x23823,x23824,x23825,x23822,x23826)) % 14.98/14.68 [2383]~E(x23831,x23832)+E(f639(x23833,x23834,x23835,x23836,x23831),f639(x23833,x23834,x23835,x23836,x23832)) % 14.98/14.68 [2384]~E(x23841,x23842)+E(f155(x23841,x23843),f155(x23842,x23843)) % 14.98/14.68 [2385]~E(x23851,x23852)+E(f155(x23853,x23851),f155(x23853,x23852)) % 14.98/14.68 [2386]~E(x23861,x23862)+E(f375(x23861,x23863,x23864),f375(x23862,x23863,x23864)) % 14.98/14.68 [2387]~E(x23871,x23872)+E(f375(x23873,x23871,x23874),f375(x23873,x23872,x23874)) % 14.98/14.68 [2388]~E(x23881,x23882)+E(f375(x23883,x23884,x23881),f375(x23883,x23884,x23882)) % 14.98/14.68 [2389]~E(x23891,x23892)+E(f561(x23891,x23893),f561(x23892,x23893)) % 14.98/14.68 [2390]~E(x23901,x23902)+E(f561(x23903,x23901),f561(x23903,x23902)) % 14.98/14.68 [2391]~E(x23911,x23912)+E(f775(x23911,x23913,x23914),f775(x23912,x23913,x23914)) % 14.98/14.68 [2392]~E(x23921,x23922)+E(f775(x23923,x23921,x23924),f775(x23923,x23922,x23924)) % 14.98/14.68 [2393]~E(x23931,x23932)+E(f775(x23933,x23934,x23931),f775(x23933,x23934,x23932)) % 14.98/14.68 [2394]~E(x23941,x23942)+E(f766(x23941,x23943,x23944),f766(x23942,x23943,x23944)) % 14.98/14.68 [2395]~E(x23951,x23952)+E(f766(x23953,x23951,x23954),f766(x23953,x23952,x23954)) % 14.98/14.68 [2396]~E(x23961,x23962)+E(f766(x23963,x23964,x23961),f766(x23963,x23964,x23962)) % 14.98/14.68 [2397]~E(x23971,x23972)+E(f743(x23971,x23973),f743(x23972,x23973)) % 14.98/14.68 [2398]~E(x23981,x23982)+E(f743(x23983,x23981),f743(x23983,x23982)) % 14.98/14.68 [2399]~E(x23991,x23992)+E(f522(x23991),f522(x23992)) % 14.98/14.68 [2400]~E(x24001,x24002)+E(f692(x24001,x24003,x24004,x24005),f692(x24002,x24003,x24004,x24005)) % 14.98/14.68 [2401]~E(x24011,x24012)+E(f692(x24013,x24011,x24014,x24015),f692(x24013,x24012,x24014,x24015)) % 14.98/14.68 [2402]~E(x24021,x24022)+E(f692(x24023,x24024,x24021,x24025),f692(x24023,x24024,x24022,x24025)) % 14.98/14.68 [2403]~E(x24031,x24032)+E(f692(x24033,x24034,x24035,x24031),f692(x24033,x24034,x24035,x24032)) % 14.98/14.68 [2404]~E(x24041,x24042)+E(f703(x24041,x24043,x24044),f703(x24042,x24043,x24044)) % 14.98/14.68 [2405]~E(x24051,x24052)+E(f703(x24053,x24051,x24054),f703(x24053,x24052,x24054)) % 14.98/14.68 [2406]~E(x24061,x24062)+E(f703(x24063,x24064,x24061),f703(x24063,x24064,x24062)) % 14.98/14.68 [2407]~E(x24071,x24072)+E(f378(x24071,x24073,x24074,x24075),f378(x24072,x24073,x24074,x24075)) % 14.98/14.68 [2408]~E(x24081,x24082)+E(f378(x24083,x24081,x24084,x24085),f378(x24083,x24082,x24084,x24085)) % 14.98/14.68 [2409]~E(x24091,x24092)+E(f378(x24093,x24094,x24091,x24095),f378(x24093,x24094,x24092,x24095)) % 14.98/14.68 [2410]~E(x24101,x24102)+E(f378(x24103,x24104,x24105,x24101),f378(x24103,x24104,x24105,x24102)) % 14.98/14.68 [2411]~E(x24111,x24112)+E(f413(x24111,x24113,x24114,x24115,x24116),f413(x24112,x24113,x24114,x24115,x24116)) % 14.98/14.68 [2412]~E(x24121,x24122)+E(f413(x24123,x24121,x24124,x24125,x24126),f413(x24123,x24122,x24124,x24125,x24126)) % 14.98/14.68 [2413]~E(x24131,x24132)+E(f413(x24133,x24134,x24131,x24135,x24136),f413(x24133,x24134,x24132,x24135,x24136)) % 14.98/14.68 [2414]~E(x24141,x24142)+E(f413(x24143,x24144,x24145,x24141,x24146),f413(x24143,x24144,x24145,x24142,x24146)) % 14.98/14.68 [2415]~E(x24151,x24152)+E(f413(x24153,x24154,x24155,x24156,x24151),f413(x24153,x24154,x24155,x24156,x24152)) % 14.98/14.68 [2416]~E(x24161,x24162)+E(f525(x24161,x24163,x24164,x24165),f525(x24162,x24163,x24164,x24165)) % 14.98/14.68 [2417]~E(x24171,x24172)+E(f525(x24173,x24171,x24174,x24175),f525(x24173,x24172,x24174,x24175)) % 14.98/14.68 [2418]~E(x24181,x24182)+E(f525(x24183,x24184,x24181,x24185),f525(x24183,x24184,x24182,x24185)) % 14.98/14.68 [2419]~E(x24191,x24192)+E(f525(x24193,x24194,x24195,x24191),f525(x24193,x24194,x24195,x24192)) % 14.98/14.68 [2420]~E(x24201,x24202)+E(f230(x24201,x24203),f230(x24202,x24203)) % 14.98/14.68 [2421]~E(x24211,x24212)+E(f230(x24213,x24211),f230(x24213,x24212)) % 14.98/14.68 [2422]~E(x24221,x24222)+E(f769(x24221,x24223,x24224),f769(x24222,x24223,x24224)) % 14.98/14.68 [2423]~E(x24231,x24232)+E(f769(x24233,x24231,x24234),f769(x24233,x24232,x24234)) % 14.98/14.68 [2424]~E(x24241,x24242)+E(f769(x24243,x24244,x24241),f769(x24243,x24244,x24242)) % 14.98/14.68 [2425]~E(x24251,x24252)+E(f353(x24251,x24253,x24254,x24255,x24256),f353(x24252,x24253,x24254,x24255,x24256)) % 14.98/14.68 [2426]~E(x24261,x24262)+E(f353(x24263,x24261,x24264,x24265,x24266),f353(x24263,x24262,x24264,x24265,x24266)) % 14.98/14.68 [2427]~E(x24271,x24272)+E(f353(x24273,x24274,x24271,x24275,x24276),f353(x24273,x24274,x24272,x24275,x24276)) % 14.98/14.68 [2428]~E(x24281,x24282)+E(f353(x24283,x24284,x24285,x24281,x24286),f353(x24283,x24284,x24285,x24282,x24286)) % 14.98/14.68 [2429]~E(x24291,x24292)+E(f353(x24293,x24294,x24295,x24296,x24291),f353(x24293,x24294,x24295,x24296,x24292)) % 14.98/14.68 [2430]~E(x24301,x24302)+E(f337(x24301,x24303,x24304,x24305),f337(x24302,x24303,x24304,x24305)) % 14.98/14.68 [2431]~E(x24311,x24312)+E(f337(x24313,x24311,x24314,x24315),f337(x24313,x24312,x24314,x24315)) % 14.98/14.68 [2432]~E(x24321,x24322)+E(f337(x24323,x24324,x24321,x24325),f337(x24323,x24324,x24322,x24325)) % 14.98/14.68 [2433]~E(x24331,x24332)+E(f337(x24333,x24334,x24335,x24331),f337(x24333,x24334,x24335,x24332)) % 14.98/14.68 [2434]~E(x24341,x24342)+E(f359(x24341,x24343),f359(x24342,x24343)) % 14.98/14.68 [2435]~E(x24351,x24352)+E(f359(x24353,x24351),f359(x24353,x24352)) % 14.98/14.68 [2436]~E(x24361,x24362)+E(f428(x24361,x24363),f428(x24362,x24363)) % 14.98/14.68 [2437]~E(x24371,x24372)+E(f428(x24373,x24371),f428(x24373,x24372)) % 14.98/14.68 [2438]~E(x24381,x24382)+E(f648(x24381,x24383,x24384,x24385),f648(x24382,x24383,x24384,x24385)) % 14.98/14.68 [2439]~E(x24391,x24392)+E(f648(x24393,x24391,x24394,x24395),f648(x24393,x24392,x24394,x24395)) % 14.98/14.68 [2440]~E(x24401,x24402)+E(f648(x24403,x24404,x24401,x24405),f648(x24403,x24404,x24402,x24405)) % 14.98/14.68 [2441]~E(x24411,x24412)+E(f648(x24413,x24414,x24415,x24411),f648(x24413,x24414,x24415,x24412)) % 14.98/14.68 [2442]~E(x24421,x24422)+E(f717(x24421,x24423,x24424),f717(x24422,x24423,x24424)) % 14.98/14.68 [2443]~E(x24431,x24432)+E(f717(x24433,x24431,x24434),f717(x24433,x24432,x24434)) % 14.98/14.68 [2444]~E(x24441,x24442)+E(f717(x24443,x24444,x24441),f717(x24443,x24444,x24442)) % 14.98/14.68 [2445]~E(x24451,x24452)+E(f204(x24451,x24453,x24454,x24455,x24456,x24457,x24458),f204(x24452,x24453,x24454,x24455,x24456,x24457,x24458)) % 14.98/14.68 [2446]~E(x24461,x24462)+E(f204(x24463,x24461,x24464,x24465,x24466,x24467,x24468),f204(x24463,x24462,x24464,x24465,x24466,x24467,x24468)) % 14.98/14.68 [2447]~E(x24471,x24472)+E(f204(x24473,x24474,x24471,x24475,x24476,x24477,x24478),f204(x24473,x24474,x24472,x24475,x24476,x24477,x24478)) % 14.98/14.68 [2448]~E(x24481,x24482)+E(f204(x24483,x24484,x24485,x24481,x24486,x24487,x24488),f204(x24483,x24484,x24485,x24482,x24486,x24487,x24488)) % 14.98/14.68 [2449]~E(x24491,x24492)+E(f204(x24493,x24494,x24495,x24496,x24491,x24497,x24498),f204(x24493,x24494,x24495,x24496,x24492,x24497,x24498)) % 14.98/14.68 [2450]~E(x24501,x24502)+E(f204(x24503,x24504,x24505,x24506,x24507,x24501,x24508),f204(x24503,x24504,x24505,x24506,x24507,x24502,x24508)) % 14.98/14.68 [2451]~E(x24511,x24512)+E(f204(x24513,x24514,x24515,x24516,x24517,x24518,x24511),f204(x24513,x24514,x24515,x24516,x24517,x24518,x24512)) % 14.98/14.68 [2452]~E(x24521,x24522)+E(f704(x24521,x24523,x24524,x24525),f704(x24522,x24523,x24524,x24525)) % 14.98/14.68 [2453]~E(x24531,x24532)+E(f704(x24533,x24531,x24534,x24535),f704(x24533,x24532,x24534,x24535)) % 14.98/14.68 [2454]~E(x24541,x24542)+E(f704(x24543,x24544,x24541,x24545),f704(x24543,x24544,x24542,x24545)) % 14.98/14.68 [2455]~E(x24551,x24552)+E(f704(x24553,x24554,x24555,x24551),f704(x24553,x24554,x24555,x24552)) % 14.98/14.68 [2456]~E(x24561,x24562)+E(f35(x24561),f35(x24562)) % 14.98/14.68 [2457]~E(x24571,x24572)+E(f758(x24571,x24573,x24574),f758(x24572,x24573,x24574)) % 14.98/14.68 [2458]~E(x24581,x24582)+E(f758(x24583,x24581,x24584),f758(x24583,x24582,x24584)) % 14.98/14.68 [2459]~E(x24591,x24592)+E(f758(x24593,x24594,x24591),f758(x24593,x24594,x24592)) % 14.98/14.68 [2460]~E(x24601,x24602)+E(f916(x24601,x24603,x24604,x24605,x24606),f916(x24602,x24603,x24604,x24605,x24606)) % 14.98/14.68 [2461]~E(x24611,x24612)+E(f916(x24613,x24611,x24614,x24615,x24616),f916(x24613,x24612,x24614,x24615,x24616)) % 14.98/14.68 [2462]~E(x24621,x24622)+E(f916(x24623,x24624,x24621,x24625,x24626),f916(x24623,x24624,x24622,x24625,x24626)) % 14.98/14.68 [2463]~E(x24631,x24632)+E(f916(x24633,x24634,x24635,x24631,x24636),f916(x24633,x24634,x24635,x24632,x24636)) % 14.98/14.68 [2464]~E(x24641,x24642)+E(f916(x24643,x24644,x24645,x24646,x24641),f916(x24643,x24644,x24645,x24646,x24642)) % 14.98/14.68 [2465]~E(x24651,x24652)+E(f202(x24651,x24653,x24654,x24655),f202(x24652,x24653,x24654,x24655)) % 14.98/14.68 [2466]~E(x24661,x24662)+E(f202(x24663,x24661,x24664,x24665),f202(x24663,x24662,x24664,x24665)) % 14.98/14.68 [2467]~E(x24671,x24672)+E(f202(x24673,x24674,x24671,x24675),f202(x24673,x24674,x24672,x24675)) % 14.98/14.68 [2468]~E(x24681,x24682)+E(f202(x24683,x24684,x24685,x24681),f202(x24683,x24684,x24685,x24682)) % 14.98/14.68 [2469]~E(x24691,x24692)+E(f566(x24691,x24693,x24694,x24695),f566(x24692,x24693,x24694,x24695)) % 14.98/14.68 [2470]~E(x24701,x24702)+E(f566(x24703,x24701,x24704,x24705),f566(x24703,x24702,x24704,x24705)) % 14.98/14.68 [2471]~E(x24711,x24712)+E(f566(x24713,x24714,x24711,x24715),f566(x24713,x24714,x24712,x24715)) % 14.98/14.68 [2472]~E(x24721,x24722)+E(f566(x24723,x24724,x24725,x24721),f566(x24723,x24724,x24725,x24722)) % 14.98/14.68 [2473]~E(x24731,x24732)+E(f835(x24731,x24733,x24734,x24735),f835(x24732,x24733,x24734,x24735)) % 14.98/14.68 [2474]~E(x24741,x24742)+E(f835(x24743,x24741,x24744,x24745),f835(x24743,x24742,x24744,x24745)) % 14.98/14.68 [2475]~E(x24751,x24752)+E(f835(x24753,x24754,x24751,x24755),f835(x24753,x24754,x24752,x24755)) % 14.98/14.68 [2476]~E(x24761,x24762)+E(f835(x24763,x24764,x24765,x24761),f835(x24763,x24764,x24765,x24762)) % 14.98/14.68 [2477]~E(x24771,x24772)+E(f815(x24771,x24773),f815(x24772,x24773)) % 14.98/14.68 [2478]~E(x24781,x24782)+E(f815(x24783,x24781),f815(x24783,x24782)) % 14.98/14.68 [2479]~E(x24791,x24792)+E(f906(x24791,x24793,x24794,x24795),f906(x24792,x24793,x24794,x24795)) % 14.98/14.68 [2480]~E(x24801,x24802)+E(f906(x24803,x24801,x24804,x24805),f906(x24803,x24802,x24804,x24805)) % 14.98/14.68 [2481]~E(x24811,x24812)+E(f906(x24813,x24814,x24811,x24815),f906(x24813,x24814,x24812,x24815)) % 14.98/14.68 [2482]~E(x24821,x24822)+E(f906(x24823,x24824,x24825,x24821),f906(x24823,x24824,x24825,x24822)) % 14.98/14.68 [2483]~E(x24831,x24832)+E(f379(x24831,x24833,x24834,x24835),f379(x24832,x24833,x24834,x24835)) % 14.98/14.68 [2484]~E(x24841,x24842)+E(f379(x24843,x24841,x24844,x24845),f379(x24843,x24842,x24844,x24845)) % 14.98/14.68 [2485]~E(x24851,x24852)+E(f379(x24853,x24854,x24851,x24855),f379(x24853,x24854,x24852,x24855)) % 14.98/14.68 [2486]~E(x24861,x24862)+E(f379(x24863,x24864,x24865,x24861),f379(x24863,x24864,x24865,x24862)) % 14.98/14.68 [2487]~E(x24871,x24872)+E(f788(x24871,x24873),f788(x24872,x24873)) % 14.98/14.68 [2488]~E(x24881,x24882)+E(f788(x24883,x24881),f788(x24883,x24882)) % 14.98/14.68 [2489]~E(x24891,x24892)+E(f843(x24891,x24893,x24894,x24895,x24896,x24897,x24898,x24899),f843(x24892,x24893,x24894,x24895,x24896,x24897,x24898,x24899)) % 14.98/14.68 [2490]~E(x24901,x24902)+E(f843(x24903,x24901,x24904,x24905,x24906,x24907,x24908,x24909),f843(x24903,x24902,x24904,x24905,x24906,x24907,x24908,x24909)) % 14.98/14.68 [2491]~E(x24911,x24912)+E(f843(x24913,x24914,x24911,x24915,x24916,x24917,x24918,x24919),f843(x24913,x24914,x24912,x24915,x24916,x24917,x24918,x24919)) % 14.98/14.68 [2492]~E(x24921,x24922)+E(f843(x24923,x24924,x24925,x24921,x24926,x24927,x24928,x24929),f843(x24923,x24924,x24925,x24922,x24926,x24927,x24928,x24929)) % 14.98/14.68 [2493]~E(x24931,x24932)+E(f843(x24933,x24934,x24935,x24936,x24931,x24937,x24938,x24939),f843(x24933,x24934,x24935,x24936,x24932,x24937,x24938,x24939)) % 14.98/14.68 [2494]~E(x24941,x24942)+E(f843(x24943,x24944,x24945,x24946,x24947,x24941,x24948,x24949),f843(x24943,x24944,x24945,x24946,x24947,x24942,x24948,x24949)) % 14.98/14.68 [2495]~E(x24951,x24952)+E(f843(x24953,x24954,x24955,x24956,x24957,x24958,x24951,x24959),f843(x24953,x24954,x24955,x24956,x24957,x24958,x24952,x24959)) % 14.98/14.68 [2496]~E(x24961,x24962)+E(f843(x24963,x24964,x24965,x24966,x24967,x24968,x24969,x24961),f843(x24963,x24964,x24965,x24966,x24967,x24968,x24969,x24962)) % 14.98/14.68 [2497]~E(x24971,x24972)+E(f223(x24971,x24973,x24974),f223(x24972,x24973,x24974)) % 14.98/14.68 [2498]~E(x24981,x24982)+E(f223(x24983,x24981,x24984),f223(x24983,x24982,x24984)) % 14.98/14.68 [2499]~E(x24991,x24992)+E(f223(x24993,x24994,x24991),f223(x24993,x24994,x24992)) % 14.98/14.68 [2500]~E(x25001,x25002)+E(f405(x25001,x25003,x25004,x25005),f405(x25002,x25003,x25004,x25005)) % 14.98/14.68 [2501]~E(x25011,x25012)+E(f405(x25013,x25011,x25014,x25015),f405(x25013,x25012,x25014,x25015)) % 14.98/14.68 [2502]~E(x25021,x25022)+E(f405(x25023,x25024,x25021,x25025),f405(x25023,x25024,x25022,x25025)) % 14.98/14.68 [2503]~E(x25031,x25032)+E(f405(x25033,x25034,x25035,x25031),f405(x25033,x25034,x25035,x25032)) % 14.98/14.68 [2504]~E(x25041,x25042)+E(f726(x25041,x25043,x25044,x25045,x25046),f726(x25042,x25043,x25044,x25045,x25046)) % 14.98/14.68 [2505]~E(x25051,x25052)+E(f726(x25053,x25051,x25054,x25055,x25056),f726(x25053,x25052,x25054,x25055,x25056)) % 14.98/14.68 [2506]~E(x25061,x25062)+E(f726(x25063,x25064,x25061,x25065,x25066),f726(x25063,x25064,x25062,x25065,x25066)) % 14.98/14.68 [2507]~E(x25071,x25072)+E(f726(x25073,x25074,x25075,x25071,x25076),f726(x25073,x25074,x25075,x25072,x25076)) % 14.98/14.68 [2508]~E(x25081,x25082)+E(f726(x25083,x25084,x25085,x25086,x25081),f726(x25083,x25084,x25085,x25086,x25082)) % 14.98/14.68 [2509]~E(x25091,x25092)+E(f567(x25091),f567(x25092)) % 14.98/14.68 [2510]~E(x25101,x25102)+E(f409(x25101,x25103),f409(x25102,x25103)) % 14.98/14.68 [2511]~E(x25111,x25112)+E(f409(x25113,x25111),f409(x25113,x25112)) % 14.98/14.68 [2512]~E(x25121,x25122)+E(f671(x25121,x25123,x25124,x25125),f671(x25122,x25123,x25124,x25125)) % 14.98/14.68 [2513]~E(x25131,x25132)+E(f671(x25133,x25131,x25134,x25135),f671(x25133,x25132,x25134,x25135)) % 14.98/14.68 [2514]~E(x25141,x25142)+E(f671(x25143,x25144,x25141,x25145),f671(x25143,x25144,x25142,x25145)) % 14.98/14.68 [2515]~E(x25151,x25152)+E(f671(x25153,x25154,x25155,x25151),f671(x25153,x25154,x25155,x25152)) % 14.98/14.68 [2516]~E(x25161,x25162)+E(f380(x25161,x25163,x25164,x25165),f380(x25162,x25163,x25164,x25165)) % 14.98/14.68 [2517]~E(x25171,x25172)+E(f380(x25173,x25171,x25174,x25175),f380(x25173,x25172,x25174,x25175)) % 14.98/14.68 [2518]~E(x25181,x25182)+E(f380(x25183,x25184,x25181,x25185),f380(x25183,x25184,x25182,x25185)) % 14.98/14.68 [2519]~E(x25191,x25192)+E(f380(x25193,x25194,x25195,x25191),f380(x25193,x25194,x25195,x25192)) % 14.98/14.68 [2520]~E(x25201,x25202)+E(f772(x25201,x25203,x25204),f772(x25202,x25203,x25204)) % 14.98/14.68 [2521]~E(x25211,x25212)+E(f772(x25213,x25211,x25214),f772(x25213,x25212,x25214)) % 14.98/14.68 [2522]~E(x25221,x25222)+E(f772(x25223,x25224,x25221),f772(x25223,x25224,x25222)) % 14.98/14.68 [2523]~E(x25231,x25232)+E(f621(x25231,x25233),f621(x25232,x25233)) % 14.98/14.68 [2524]~E(x25241,x25242)+E(f621(x25243,x25241),f621(x25243,x25242)) % 14.98/14.68 [2525]~E(x25251,x25252)+E(f470(x25251,x25253),f470(x25252,x25253)) % 14.98/14.68 [2526]~E(x25261,x25262)+E(f470(x25263,x25261),f470(x25263,x25262)) % 14.98/14.68 [2527]~E(x25271,x25272)+E(f386(x25271,x25273,x25274),f386(x25272,x25273,x25274)) % 14.98/14.68 [2528]~E(x25281,x25282)+E(f386(x25283,x25281,x25284),f386(x25283,x25282,x25284)) % 14.98/14.68 [2529]~E(x25291,x25292)+E(f386(x25293,x25294,x25291),f386(x25293,x25294,x25292)) % 14.98/14.68 [2530]~E(x25301,x25302)+E(f117(x25301),f117(x25302)) % 14.98/14.68 [2531]~E(x25311,x25312)+E(f658(x25311,x25313,x25314),f658(x25312,x25313,x25314)) % 14.98/14.68 [2532]~E(x25321,x25322)+E(f658(x25323,x25321,x25324),f658(x25323,x25322,x25324)) % 14.98/14.68 [2533]~E(x25331,x25332)+E(f658(x25333,x25334,x25331),f658(x25333,x25334,x25332)) % 14.98/14.68 [2534]~E(x25341,x25342)+E(f469(x25341,x25343),f469(x25342,x25343)) % 14.98/14.68 [2535]~E(x25351,x25352)+E(f469(x25353,x25351),f469(x25353,x25352)) % 14.98/14.68 [2536]~E(x25361,x25362)+E(f511(x25361,x25363,x25364,x25365),f511(x25362,x25363,x25364,x25365)) % 14.98/14.68 [2537]~E(x25371,x25372)+E(f511(x25373,x25371,x25374,x25375),f511(x25373,x25372,x25374,x25375)) % 14.98/14.68 [2538]~E(x25381,x25382)+E(f511(x25383,x25384,x25381,x25385),f511(x25383,x25384,x25382,x25385)) % 14.98/14.68 [2539]~E(x25391,x25392)+E(f511(x25393,x25394,x25395,x25391),f511(x25393,x25394,x25395,x25392)) % 14.98/14.68 [2540]~E(x25401,x25402)+E(f407(x25401,x25403,x25404),f407(x25402,x25403,x25404)) % 14.98/14.68 [2541]~E(x25411,x25412)+E(f407(x25413,x25411,x25414),f407(x25413,x25412,x25414)) % 14.98/14.68 [2542]~E(x25421,x25422)+E(f407(x25423,x25424,x25421),f407(x25423,x25424,x25422)) % 14.98/14.68 [2543]~E(x25431,x25432)+E(f616(x25431,x25433,x25434,x25435,x25436),f616(x25432,x25433,x25434,x25435,x25436)) % 14.98/14.68 [2544]~E(x25441,x25442)+E(f616(x25443,x25441,x25444,x25445,x25446),f616(x25443,x25442,x25444,x25445,x25446)) % 14.98/14.68 [2545]~E(x25451,x25452)+E(f616(x25453,x25454,x25451,x25455,x25456),f616(x25453,x25454,x25452,x25455,x25456)) % 14.98/14.68 [2546]~E(x25461,x25462)+E(f616(x25463,x25464,x25465,x25461,x25466),f616(x25463,x25464,x25465,x25462,x25466)) % 14.98/14.68 [2547]~E(x25471,x25472)+E(f616(x25473,x25474,x25475,x25476,x25471),f616(x25473,x25474,x25475,x25476,x25472)) % 14.98/14.68 [2548]~E(x25481,x25482)+E(f37(x25481),f37(x25482)) % 14.98/14.68 [2549]~E(x25491,x25492)+E(f541(x25491,x25493,x25494,x25495),f541(x25492,x25493,x25494,x25495)) % 14.98/14.68 [2550]~E(x25501,x25502)+E(f541(x25503,x25501,x25504,x25505),f541(x25503,x25502,x25504,x25505)) % 14.98/14.68 [2551]~E(x25511,x25512)+E(f541(x25513,x25514,x25511,x25515),f541(x25513,x25514,x25512,x25515)) % 14.98/14.68 [2552]~E(x25521,x25522)+E(f541(x25523,x25524,x25525,x25521),f541(x25523,x25524,x25525,x25522)) % 14.98/14.68 [2553]~E(x25531,x25532)+E(f368(x25531,x25533,x25534),f368(x25532,x25533,x25534)) % 14.98/14.68 [2554]~E(x25541,x25542)+E(f368(x25543,x25541,x25544),f368(x25543,x25542,x25544)) % 14.98/14.68 [2555]~E(x25551,x25552)+E(f368(x25553,x25554,x25551),f368(x25553,x25554,x25552)) % 14.98/14.68 [2556]~E(x25561,x25562)+E(f609(x25561,x25563),f609(x25562,x25563)) % 14.98/14.68 [2557]~E(x25571,x25572)+E(f609(x25573,x25571),f609(x25573,x25572)) % 14.98/14.68 [2558]~E(x25581,x25582)+E(f756(x25581,x25583),f756(x25582,x25583)) % 14.98/14.68 [2559]~E(x25591,x25592)+E(f756(x25593,x25591),f756(x25593,x25592)) % 14.98/14.68 [2560]~E(x25601,x25602)+E(f271(x25601,x25603,x25604,x25605),f271(x25602,x25603,x25604,x25605)) % 14.98/14.68 [2561]~E(x25611,x25612)+E(f271(x25613,x25611,x25614,x25615),f271(x25613,x25612,x25614,x25615)) % 14.98/14.68 [2562]~E(x25621,x25622)+E(f271(x25623,x25624,x25621,x25625),f271(x25623,x25624,x25622,x25625)) % 14.98/14.68 [2563]~E(x25631,x25632)+E(f271(x25633,x25634,x25635,x25631),f271(x25633,x25634,x25635,x25632)) % 14.98/14.68 [2564]~E(x25641,x25642)+E(f877(x25641,x25643,x25644),f877(x25642,x25643,x25644)) % 14.98/14.68 [2565]~E(x25651,x25652)+E(f877(x25653,x25651,x25654),f877(x25653,x25652,x25654)) % 14.98/14.68 [2566]~E(x25661,x25662)+E(f877(x25663,x25664,x25661),f877(x25663,x25664,x25662)) % 14.98/14.68 [2567]~E(x25671,x25672)+E(f697(x25671,x25673,x25674),f697(x25672,x25673,x25674)) % 14.98/14.68 [2568]~E(x25681,x25682)+E(f697(x25683,x25681,x25684),f697(x25683,x25682,x25684)) % 14.98/14.68 [2569]~E(x25691,x25692)+E(f697(x25693,x25694,x25691),f697(x25693,x25694,x25692)) % 14.98/14.68 [2570]~E(x25701,x25702)+E(f450(x25701,x25703,x25704),f450(x25702,x25703,x25704)) % 14.98/14.68 [2571]~E(x25711,x25712)+E(f450(x25713,x25711,x25714),f450(x25713,x25712,x25714)) % 14.98/14.68 [2572]~E(x25721,x25722)+E(f450(x25723,x25724,x25721),f450(x25723,x25724,x25722)) % 14.98/14.68 [2573]~E(x25731,x25732)+E(f334(x25731,x25733,x25734,x25735),f334(x25732,x25733,x25734,x25735)) % 14.98/14.68 [2574]~E(x25741,x25742)+E(f334(x25743,x25741,x25744,x25745),f334(x25743,x25742,x25744,x25745)) % 14.98/14.68 [2575]~E(x25751,x25752)+E(f334(x25753,x25754,x25751,x25755),f334(x25753,x25754,x25752,x25755)) % 14.98/14.68 [2576]~E(x25761,x25762)+E(f334(x25763,x25764,x25765,x25761),f334(x25763,x25764,x25765,x25762)) % 14.98/14.68 [2577]~E(x25771,x25772)+E(f885(x25771,x25773),f885(x25772,x25773)) % 14.98/14.68 [2578]~E(x25781,x25782)+E(f885(x25783,x25781),f885(x25783,x25782)) % 14.98/14.68 [2579]~E(x25791,x25792)+E(f438(x25791,x25793,x25794),f438(x25792,x25793,x25794)) % 14.98/14.68 [2580]~E(x25801,x25802)+E(f438(x25803,x25801,x25804),f438(x25803,x25802,x25804)) % 14.98/14.68 [2581]~E(x25811,x25812)+E(f438(x25813,x25814,x25811),f438(x25813,x25814,x25812)) % 14.98/14.68 [2582]~E(x25821,x25822)+E(f876(x25821,x25823,x25824),f876(x25822,x25823,x25824)) % 14.98/14.68 [2583]~E(x25831,x25832)+E(f876(x25833,x25831,x25834),f876(x25833,x25832,x25834)) % 14.98/14.68 [2584]~E(x25841,x25842)+E(f876(x25843,x25844,x25841),f876(x25843,x25844,x25842)) % 14.98/14.68 [2585]~E(x25851,x25852)+E(f410(x25851),f410(x25852)) % 14.98/14.68 [2586]~E(x25861,x25862)+E(f637(x25861,x25863,x25864,x25865),f637(x25862,x25863,x25864,x25865)) % 14.98/14.68 [2587]~E(x25871,x25872)+E(f637(x25873,x25871,x25874,x25875),f637(x25873,x25872,x25874,x25875)) % 14.98/14.68 [2588]~E(x25881,x25882)+E(f637(x25883,x25884,x25881,x25885),f637(x25883,x25884,x25882,x25885)) % 14.98/14.68 [2589]~E(x25891,x25892)+E(f637(x25893,x25894,x25895,x25891),f637(x25893,x25894,x25895,x25892)) % 14.98/14.68 [2590]~E(x25901,x25902)+E(f644(x25901,x25903,x25904,x25905,x25906),f644(x25902,x25903,x25904,x25905,x25906)) % 14.98/14.68 [2591]~E(x25911,x25912)+E(f644(x25913,x25911,x25914,x25915,x25916),f644(x25913,x25912,x25914,x25915,x25916)) % 14.98/14.68 [2592]~E(x25921,x25922)+E(f644(x25923,x25924,x25921,x25925,x25926),f644(x25923,x25924,x25922,x25925,x25926)) % 14.98/14.68 [2593]~E(x25931,x25932)+E(f644(x25933,x25934,x25935,x25931,x25936),f644(x25933,x25934,x25935,x25932,x25936)) % 14.98/14.68 [2594]~E(x25941,x25942)+E(f644(x25943,x25944,x25945,x25946,x25941),f644(x25943,x25944,x25945,x25946,x25942)) % 14.98/14.68 [2595]~E(x25951,x25952)+E(f891(x25951,x25953),f891(x25952,x25953)) % 14.98/14.68 [2596]~E(x25961,x25962)+E(f891(x25963,x25961),f891(x25963,x25962)) % 14.98/14.68 [2597]~E(x25971,x25972)+E(f640(x25971,x25973,x25974,x25975,x25976),f640(x25972,x25973,x25974,x25975,x25976)) % 14.98/14.68 [2598]~E(x25981,x25982)+E(f640(x25983,x25981,x25984,x25985,x25986),f640(x25983,x25982,x25984,x25985,x25986)) % 14.98/14.68 [2599]~E(x25991,x25992)+E(f640(x25993,x25994,x25991,x25995,x25996),f640(x25993,x25994,x25992,x25995,x25996)) % 14.98/14.68 [2600]~E(x26001,x26002)+E(f640(x26003,x26004,x26005,x26001,x26006),f640(x26003,x26004,x26005,x26002,x26006)) % 14.98/14.68 [2601]~E(x26011,x26012)+E(f640(x26013,x26014,x26015,x26016,x26011),f640(x26013,x26014,x26015,x26016,x26012)) % 14.98/14.68 [2602]~E(x26021,x26022)+E(f393(x26021,x26023,x26024),f393(x26022,x26023,x26024)) % 14.98/14.68 [2603]~E(x26031,x26032)+E(f393(x26033,x26031,x26034),f393(x26033,x26032,x26034)) % 14.98/14.68 [2604]~E(x26041,x26042)+E(f393(x26043,x26044,x26041),f393(x26043,x26044,x26042)) % 14.98/14.68 [2605]~E(x26051,x26052)+E(f224(x26051,x26053,x26054,x26055),f224(x26052,x26053,x26054,x26055)) % 14.98/14.68 [2606]~E(x26061,x26062)+E(f224(x26063,x26061,x26064,x26065),f224(x26063,x26062,x26064,x26065)) % 14.98/14.68 [2607]~E(x26071,x26072)+E(f224(x26073,x26074,x26071,x26075),f224(x26073,x26074,x26072,x26075)) % 14.98/14.68 [2608]~E(x26081,x26082)+E(f224(x26083,x26084,x26085,x26081),f224(x26083,x26084,x26085,x26082)) % 14.98/14.68 [2609]~E(x26091,x26092)+E(f855(x26091,x26093,x26094,x26095,x26096,x26097),f855(x26092,x26093,x26094,x26095,x26096,x26097)) % 14.98/14.68 [2610]~E(x26101,x26102)+E(f855(x26103,x26101,x26104,x26105,x26106,x26107),f855(x26103,x26102,x26104,x26105,x26106,x26107)) % 14.98/14.68 [2611]~E(x26111,x26112)+E(f855(x26113,x26114,x26111,x26115,x26116,x26117),f855(x26113,x26114,x26112,x26115,x26116,x26117)) % 14.98/14.68 [2612]~E(x26121,x26122)+E(f855(x26123,x26124,x26125,x26121,x26126,x26127),f855(x26123,x26124,x26125,x26122,x26126,x26127)) % 14.98/14.68 [2613]~E(x26131,x26132)+E(f855(x26133,x26134,x26135,x26136,x26131,x26137),f855(x26133,x26134,x26135,x26136,x26132,x26137)) % 14.98/14.68 [2614]~E(x26141,x26142)+E(f855(x26143,x26144,x26145,x26146,x26147,x26141),f855(x26143,x26144,x26145,x26146,x26147,x26142)) % 14.98/14.68 [2615]~E(x26151,x26152)+E(f483(x26151,x26153,x26154,x26155,x26156),f483(x26152,x26153,x26154,x26155,x26156)) % 14.98/14.68 [2616]~E(x26161,x26162)+E(f483(x26163,x26161,x26164,x26165,x26166),f483(x26163,x26162,x26164,x26165,x26166)) % 14.98/14.68 [2617]~E(x26171,x26172)+E(f483(x26173,x26174,x26171,x26175,x26176),f483(x26173,x26174,x26172,x26175,x26176)) % 14.98/14.68 [2618]~E(x26181,x26182)+E(f483(x26183,x26184,x26185,x26181,x26186),f483(x26183,x26184,x26185,x26182,x26186)) % 14.98/14.68 [2619]~E(x26191,x26192)+E(f483(x26193,x26194,x26195,x26196,x26191),f483(x26193,x26194,x26195,x26196,x26192)) % 14.98/14.68 [2620]~E(x26201,x26202)+E(f347(x26201,x26203),f347(x26202,x26203)) % 14.98/14.68 [2621]~E(x26211,x26212)+E(f347(x26213,x26211),f347(x26213,x26212)) % 14.98/14.68 [2622]~E(x26221,x26222)+E(f825(x26221,x26223,x26224),f825(x26222,x26223,x26224)) % 14.98/14.68 [2623]~E(x26231,x26232)+E(f825(x26233,x26231,x26234),f825(x26233,x26232,x26234)) % 14.98/14.68 [2624]~E(x26241,x26242)+E(f825(x26243,x26244,x26241),f825(x26243,x26244,x26242)) % 14.98/14.68 [2625]~E(x26251,x26252)+E(f832(x26251,x26253,x26254,x26255,x26256),f832(x26252,x26253,x26254,x26255,x26256)) % 14.98/14.68 [2626]~E(x26261,x26262)+E(f832(x26263,x26261,x26264,x26265,x26266),f832(x26263,x26262,x26264,x26265,x26266)) % 14.98/14.68 [2627]~E(x26271,x26272)+E(f832(x26273,x26274,x26271,x26275,x26276),f832(x26273,x26274,x26272,x26275,x26276)) % 14.98/14.68 [2628]~E(x26281,x26282)+E(f832(x26283,x26284,x26285,x26281,x26286),f832(x26283,x26284,x26285,x26282,x26286)) % 14.98/14.68 [2629]~E(x26291,x26292)+E(f832(x26293,x26294,x26295,x26296,x26291),f832(x26293,x26294,x26295,x26296,x26292)) % 14.98/14.68 [2630]~E(x26301,x26302)+E(f646(x26301,x26303),f646(x26302,x26303)) % 14.98/14.68 [2631]~E(x26311,x26312)+E(f646(x26313,x26311),f646(x26313,x26312)) % 14.98/14.68 [2632]~E(x26321,x26322)+E(f767(x26321,x26323,x26324),f767(x26322,x26323,x26324)) % 14.98/14.68 [2633]~E(x26331,x26332)+E(f767(x26333,x26331,x26334),f767(x26333,x26332,x26334)) % 14.98/14.68 [2634]~E(x26341,x26342)+E(f767(x26343,x26344,x26341),f767(x26343,x26344,x26342)) % 14.98/14.68 [2635]~E(x26351,x26352)+E(f415(x26351,x26353),f415(x26352,x26353)) % 14.98/14.68 [2636]~E(x26361,x26362)+E(f415(x26363,x26361),f415(x26363,x26362)) % 14.98/14.68 [2637]~E(x26371,x26372)+E(f400(x26371,x26373,x26374,x26375),f400(x26372,x26373,x26374,x26375)) % 14.98/14.68 [2638]~E(x26381,x26382)+E(f400(x26383,x26381,x26384,x26385),f400(x26383,x26382,x26384,x26385)) % 14.98/14.68 [2639]~E(x26391,x26392)+E(f400(x26393,x26394,x26391,x26395),f400(x26393,x26394,x26392,x26395)) % 14.98/14.68 [2640]~E(x26401,x26402)+E(f400(x26403,x26404,x26405,x26401),f400(x26403,x26404,x26405,x26402)) % 14.98/14.68 [2641]~E(x26411,x26412)+E(f849(x26411,x26413,x26414,x26415,x26416,x26417,x26418),f849(x26412,x26413,x26414,x26415,x26416,x26417,x26418)) % 14.98/14.68 [2642]~E(x26421,x26422)+E(f849(x26423,x26421,x26424,x26425,x26426,x26427,x26428),f849(x26423,x26422,x26424,x26425,x26426,x26427,x26428)) % 14.98/14.68 [2643]~E(x26431,x26432)+E(f849(x26433,x26434,x26431,x26435,x26436,x26437,x26438),f849(x26433,x26434,x26432,x26435,x26436,x26437,x26438)) % 14.98/14.68 [2644]~E(x26441,x26442)+E(f849(x26443,x26444,x26445,x26441,x26446,x26447,x26448),f849(x26443,x26444,x26445,x26442,x26446,x26447,x26448)) % 14.98/14.68 [2645]~E(x26451,x26452)+E(f849(x26453,x26454,x26455,x26456,x26451,x26457,x26458),f849(x26453,x26454,x26455,x26456,x26452,x26457,x26458)) % 14.98/14.68 [2646]~E(x26461,x26462)+E(f849(x26463,x26464,x26465,x26466,x26467,x26461,x26468),f849(x26463,x26464,x26465,x26466,x26467,x26462,x26468)) % 14.98/14.68 [2647]~E(x26471,x26472)+E(f849(x26473,x26474,x26475,x26476,x26477,x26478,x26471),f849(x26473,x26474,x26475,x26476,x26477,x26478,x26472)) % 14.98/14.68 [2648]~E(x26481,x26482)+E(f252(x26481,x26483,x26484,x26485,x26486),f252(x26482,x26483,x26484,x26485,x26486)) % 14.98/14.68 [2649]~E(x26491,x26492)+E(f252(x26493,x26491,x26494,x26495,x26496),f252(x26493,x26492,x26494,x26495,x26496)) % 14.98/14.68 [2650]~E(x26501,x26502)+E(f252(x26503,x26504,x26501,x26505,x26506),f252(x26503,x26504,x26502,x26505,x26506)) % 14.98/14.68 [2651]~E(x26511,x26512)+E(f252(x26513,x26514,x26515,x26511,x26516),f252(x26513,x26514,x26515,x26512,x26516)) % 14.98/14.68 [2652]~E(x26521,x26522)+E(f252(x26523,x26524,x26525,x26526,x26521),f252(x26523,x26524,x26525,x26526,x26522)) % 14.98/14.68 [2653]~E(x26531,x26532)+E(f391(x26531,x26533,x26534,x26535),f391(x26532,x26533,x26534,x26535)) % 14.98/14.68 [2654]~E(x26541,x26542)+E(f391(x26543,x26541,x26544,x26545),f391(x26543,x26542,x26544,x26545)) % 14.98/14.68 [2655]~E(x26551,x26552)+E(f391(x26553,x26554,x26551,x26555),f391(x26553,x26554,x26552,x26555)) % 14.98/14.68 [2656]~E(x26561,x26562)+E(f391(x26563,x26564,x26565,x26561),f391(x26563,x26564,x26565,x26562)) % 14.98/14.68 [2657]~E(x26571,x26572)+E(f424(x26571),f424(x26572)) % 14.98/14.68 [2658]~E(x26581,x26582)+E(f903(x26581,x26583),f903(x26582,x26583)) % 14.98/14.68 [2659]~E(x26591,x26592)+E(f903(x26593,x26591),f903(x26593,x26592)) % 14.98/14.68 [2660]~E(x26601,x26602)+E(f595(x26601,x26603,x26604),f595(x26602,x26603,x26604)) % 14.98/14.68 [2661]~E(x26611,x26612)+E(f595(x26613,x26611,x26614),f595(x26613,x26612,x26614)) % 14.98/14.68 [2662]~E(x26621,x26622)+E(f595(x26623,x26624,x26621),f595(x26623,x26624,x26622)) % 14.98/14.68 [2663]~E(x26631,x26632)+E(f828(x26631,x26633),f828(x26632,x26633)) % 14.98/14.68 [2664]~E(x26641,x26642)+E(f828(x26643,x26641),f828(x26643,x26642)) % 14.98/14.68 [2665]~E(x26651,x26652)+E(f882(x26651,x26653,x26654,x26655),f882(x26652,x26653,x26654,x26655)) % 14.98/14.68 [2666]~E(x26661,x26662)+E(f882(x26663,x26661,x26664,x26665),f882(x26663,x26662,x26664,x26665)) % 14.98/14.68 [2667]~E(x26671,x26672)+E(f882(x26673,x26674,x26671,x26675),f882(x26673,x26674,x26672,x26675)) % 14.98/14.68 [2668]~E(x26681,x26682)+E(f882(x26683,x26684,x26685,x26681),f882(x26683,x26684,x26685,x26682)) % 14.98/14.68 [2669]~E(x26691,x26692)+E(f608(x26691,x26693,x26694),f608(x26692,x26693,x26694)) % 14.98/14.68 [2670]~E(x26701,x26702)+E(f608(x26703,x26701,x26704),f608(x26703,x26702,x26704)) % 14.98/14.68 [2671]~E(x26711,x26712)+E(f608(x26713,x26714,x26711),f608(x26713,x26714,x26712)) % 14.98/14.68 [2672]~E(x26721,x26722)+E(f476(x26721,x26723,x26724),f476(x26722,x26723,x26724)) % 14.98/14.68 [2673]~E(x26731,x26732)+E(f476(x26733,x26731,x26734),f476(x26733,x26732,x26734)) % 14.98/14.68 [2674]~E(x26741,x26742)+E(f476(x26743,x26744,x26741),f476(x26743,x26744,x26742)) % 14.98/14.68 [2675]~E(x26751,x26752)+E(f196(x26751,x26753,x26754),f196(x26752,x26753,x26754)) % 14.98/14.68 [2676]~E(x26761,x26762)+E(f196(x26763,x26761,x26764),f196(x26763,x26762,x26764)) % 14.98/14.68 [2677]~E(x26771,x26772)+E(f196(x26773,x26774,x26771),f196(x26773,x26774,x26772)) % 14.98/14.68 [2678]~E(x26781,x26782)+E(f390(x26781,x26783,x26784,x26785),f390(x26782,x26783,x26784,x26785)) % 14.98/14.68 [2679]~E(x26791,x26792)+E(f390(x26793,x26791,x26794,x26795),f390(x26793,x26792,x26794,x26795)) % 14.98/14.68 [2680]~E(x26801,x26802)+E(f390(x26803,x26804,x26801,x26805),f390(x26803,x26804,x26802,x26805)) % 14.98/14.68 [2681]~E(x26811,x26812)+E(f390(x26813,x26814,x26815,x26811),f390(x26813,x26814,x26815,x26812)) % 14.98/14.68 [2682]~E(x26821,x26822)+E(f559(x26821,x26823,x26824,x26825),f559(x26822,x26823,x26824,x26825)) % 14.98/14.68 [2683]~E(x26831,x26832)+E(f559(x26833,x26831,x26834,x26835),f559(x26833,x26832,x26834,x26835)) % 14.98/14.68 [2684]~E(x26841,x26842)+E(f559(x26843,x26844,x26841,x26845),f559(x26843,x26844,x26842,x26845)) % 14.98/14.68 [2685]~E(x26851,x26852)+E(f559(x26853,x26854,x26855,x26851),f559(x26853,x26854,x26855,x26852)) % 14.98/14.68 [2686]~E(x26861,x26862)+E(f363(x26861,x26863,x26864),f363(x26862,x26863,x26864)) % 14.98/14.68 [2687]~E(x26871,x26872)+E(f363(x26873,x26871,x26874),f363(x26873,x26872,x26874)) % 14.98/14.68 [2688]~E(x26881,x26882)+E(f363(x26883,x26884,x26881),f363(x26883,x26884,x26882)) % 14.98/14.68 [2689]~E(x26891,x26892)+E(f571(x26891,x26893,x26894,x26895),f571(x26892,x26893,x26894,x26895)) % 14.98/14.68 [2690]~E(x26901,x26902)+E(f571(x26903,x26901,x26904,x26905),f571(x26903,x26902,x26904,x26905)) % 14.98/14.68 [2691]~E(x26911,x26912)+E(f571(x26913,x26914,x26911,x26915),f571(x26913,x26914,x26912,x26915)) % 14.98/14.68 [2692]~E(x26921,x26922)+E(f571(x26923,x26924,x26925,x26921),f571(x26923,x26924,x26925,x26922)) % 14.98/14.68 [2693]~E(x26931,x26932)+E(f814(x26931),f814(x26932)) % 14.98/14.68 [2694]~E(x26941,x26942)+E(f698(x26941,x26943,x26944),f698(x26942,x26943,x26944)) % 14.98/14.68 [2695]~E(x26951,x26952)+E(f698(x26953,x26951,x26954),f698(x26953,x26952,x26954)) % 14.98/14.68 [2696]~E(x26961,x26962)+E(f698(x26963,x26964,x26961),f698(x26963,x26964,x26962)) % 14.98/14.68 [2697]~E(x26971,x26972)+E(f890(x26971,x26973),f890(x26972,x26973)) % 14.98/14.68 [2698]~E(x26981,x26982)+E(f890(x26983,x26981),f890(x26983,x26982)) % 14.98/14.68 [2699]~E(x26991,x26992)+E(f396(x26991,x26993,x26994,x26995),f396(x26992,x26993,x26994,x26995)) % 14.98/14.68 [2700]~E(x27001,x27002)+E(f396(x27003,x27001,x27004,x27005),f396(x27003,x27002,x27004,x27005)) % 14.98/14.68 [2701]~E(x27011,x27012)+E(f396(x27013,x27014,x27011,x27015),f396(x27013,x27014,x27012,x27015)) % 14.98/14.68 [2702]~E(x27021,x27022)+E(f396(x27023,x27024,x27025,x27021),f396(x27023,x27024,x27025,x27022)) % 14.98/14.68 [2703]~E(x27031,x27032)+E(f827(x27031,x27033),f827(x27032,x27033)) % 14.98/14.68 [2704]~E(x27041,x27042)+E(f827(x27043,x27041),f827(x27043,x27042)) % 14.98/14.68 [2705]~E(x27051,x27052)+E(f520(x27051,x27053,x27054,x27055,x27056,x27057),f520(x27052,x27053,x27054,x27055,x27056,x27057)) % 14.98/14.68 [2706]~E(x27061,x27062)+E(f520(x27063,x27061,x27064,x27065,x27066,x27067),f520(x27063,x27062,x27064,x27065,x27066,x27067)) % 14.98/14.68 [2707]~E(x27071,x27072)+E(f520(x27073,x27074,x27071,x27075,x27076,x27077),f520(x27073,x27074,x27072,x27075,x27076,x27077)) % 14.98/14.68 [2708]~E(x27081,x27082)+E(f520(x27083,x27084,x27085,x27081,x27086,x27087),f520(x27083,x27084,x27085,x27082,x27086,x27087)) % 14.98/14.68 [2709]~E(x27091,x27092)+E(f520(x27093,x27094,x27095,x27096,x27091,x27097),f520(x27093,x27094,x27095,x27096,x27092,x27097)) % 14.98/14.68 [2710]~E(x27101,x27102)+E(f520(x27103,x27104,x27105,x27106,x27107,x27101),f520(x27103,x27104,x27105,x27106,x27107,x27102)) % 14.98/14.68 [2711]~E(x27111,x27112)+E(f816(x27111,x27113,x27114),f816(x27112,x27113,x27114)) % 14.98/14.68 [2712]~E(x27121,x27122)+E(f816(x27123,x27121,x27124),f816(x27123,x27122,x27124)) % 14.98/14.68 [2713]~E(x27131,x27132)+E(f816(x27133,x27134,x27131),f816(x27133,x27134,x27132)) % 14.98/14.68 [2714]~E(x27141,x27142)+E(f691(x27141,x27143,x27144,x27145),f691(x27142,x27143,x27144,x27145)) % 14.98/14.68 [2715]~E(x27151,x27152)+E(f691(x27153,x27151,x27154,x27155),f691(x27153,x27152,x27154,x27155)) % 14.98/14.68 [2716]~E(x27161,x27162)+E(f691(x27163,x27164,x27161,x27165),f691(x27163,x27164,x27162,x27165)) % 14.98/14.68 [2717]~E(x27171,x27172)+E(f691(x27173,x27174,x27175,x27171),f691(x27173,x27174,x27175,x27172)) % 14.98/14.68 [2718]~E(x27181,x27182)+E(f745(x27181,x27183),f745(x27182,x27183)) % 14.98/14.68 [2719]~E(x27191,x27192)+E(f745(x27193,x27191),f745(x27193,x27192)) % 14.98/14.68 [2720]~E(x27201,x27202)+E(f468(x27201,x27203),f468(x27202,x27203)) % 14.98/14.68 [2721]~E(x27211,x27212)+E(f468(x27213,x27211),f468(x27213,x27212)) % 14.98/14.68 [2722]~E(x27221,x27222)+E(f408(x27221,x27223,x27224),f408(x27222,x27223,x27224)) % 14.98/14.68 [2723]~E(x27231,x27232)+E(f408(x27233,x27231,x27234),f408(x27233,x27232,x27234)) % 14.98/14.68 [2724]~E(x27241,x27242)+E(f408(x27243,x27244,x27241),f408(x27243,x27244,x27242)) % 14.98/14.68 [2725]~E(x27251,x27252)+E(f328(x27251),f328(x27252)) % 14.98/14.68 [2726]~E(x27261,x27262)+E(f200(x27261,x27263,x27264,x27265,x27266,x27267,x27268),f200(x27262,x27263,x27264,x27265,x27266,x27267,x27268)) % 14.98/14.68 [2727]~E(x27271,x27272)+E(f200(x27273,x27271,x27274,x27275,x27276,x27277,x27278),f200(x27273,x27272,x27274,x27275,x27276,x27277,x27278)) % 14.98/14.68 [2728]~E(x27281,x27282)+E(f200(x27283,x27284,x27281,x27285,x27286,x27287,x27288),f200(x27283,x27284,x27282,x27285,x27286,x27287,x27288)) % 14.98/14.68 [2729]~E(x27291,x27292)+E(f200(x27293,x27294,x27295,x27291,x27296,x27297,x27298),f200(x27293,x27294,x27295,x27292,x27296,x27297,x27298)) % 14.98/14.68 [2730]~E(x27301,x27302)+E(f200(x27303,x27304,x27305,x27306,x27301,x27307,x27308),f200(x27303,x27304,x27305,x27306,x27302,x27307,x27308)) % 14.98/14.68 [2731]~E(x27311,x27312)+E(f200(x27313,x27314,x27315,x27316,x27317,x27311,x27318),f200(x27313,x27314,x27315,x27316,x27317,x27312,x27318)) % 14.98/14.68 [2732]~E(x27321,x27322)+E(f200(x27323,x27324,x27325,x27326,x27327,x27328,x27321),f200(x27323,x27324,x27325,x27326,x27327,x27328,x27322)) % 14.98/14.68 [2733]~E(x27331,x27332)+E(f495(x27331,x27333,x27334),f495(x27332,x27333,x27334)) % 14.98/14.68 [2734]~E(x27341,x27342)+E(f495(x27343,x27341,x27344),f495(x27343,x27342,x27344)) % 14.98/14.68 [2735]~E(x27351,x27352)+E(f495(x27353,x27354,x27351),f495(x27353,x27354,x27352)) % 14.98/14.68 [2736]~E(x27361,x27362)+E(f491(x27361,x27363,x27364,x27365,x27366),f491(x27362,x27363,x27364,x27365,x27366)) % 14.98/14.68 [2737]~E(x27371,x27372)+E(f491(x27373,x27371,x27374,x27375,x27376),f491(x27373,x27372,x27374,x27375,x27376)) % 14.98/14.68 [2738]~E(x27381,x27382)+E(f491(x27383,x27384,x27381,x27385,x27386),f491(x27383,x27384,x27382,x27385,x27386)) % 14.98/14.68 [2739]~E(x27391,x27392)+E(f491(x27393,x27394,x27395,x27391,x27396),f491(x27393,x27394,x27395,x27392,x27396)) % 14.98/14.68 [2740]~E(x27401,x27402)+E(f491(x27403,x27404,x27405,x27406,x27401),f491(x27403,x27404,x27405,x27406,x27402)) % 14.98/14.68 [2741]~E(x27411,x27412)+E(f222(x27411,x27413,x27414,x27415),f222(x27412,x27413,x27414,x27415)) % 14.98/14.68 [2742]~E(x27421,x27422)+E(f222(x27423,x27421,x27424,x27425),f222(x27423,x27422,x27424,x27425)) % 14.98/14.68 [2743]~E(x27431,x27432)+E(f222(x27433,x27434,x27431,x27435),f222(x27433,x27434,x27432,x27435)) % 14.98/14.68 [2744]~E(x27441,x27442)+E(f222(x27443,x27444,x27445,x27441),f222(x27443,x27444,x27445,x27442)) % 14.98/14.68 [2745]~E(x27451,x27452)+E(f523(x27451,x27453,x27454),f523(x27452,x27453,x27454)) % 14.98/14.68 [2746]~E(x27461,x27462)+E(f523(x27463,x27461,x27464),f523(x27463,x27462,x27464)) % 14.98/14.68 [2747]~E(x27471,x27472)+E(f523(x27473,x27474,x27471),f523(x27473,x27474,x27472)) % 14.98/14.68 [2748]~E(x27481,x27482)+E(f631(x27481,x27483,x27484),f631(x27482,x27483,x27484)) % 14.98/14.68 [2749]~E(x27491,x27492)+E(f631(x27493,x27491,x27494),f631(x27493,x27492,x27494)) % 14.98/14.68 [2750]~E(x27501,x27502)+E(f631(x27503,x27504,x27501),f631(x27503,x27504,x27502)) % 14.98/14.68 [2751]~E(x27511,x27512)+E(f680(x27511,x27513,x27514),f680(x27512,x27513,x27514)) % 14.98/14.68 [2752]~E(x27521,x27522)+E(f680(x27523,x27521,x27524),f680(x27523,x27522,x27524)) % 14.98/14.68 [2753]~E(x27531,x27532)+E(f680(x27533,x27534,x27531),f680(x27533,x27534,x27532)) % 14.98/14.68 [2754]~E(x27541,x27542)+E(f354(x27541,x27543,x27544,x27545,x27546),f354(x27542,x27543,x27544,x27545,x27546)) % 14.98/14.68 [2755]~E(x27551,x27552)+E(f354(x27553,x27551,x27554,x27555,x27556),f354(x27553,x27552,x27554,x27555,x27556)) % 14.98/14.68 [2756]~E(x27561,x27562)+E(f354(x27563,x27564,x27561,x27565,x27566),f354(x27563,x27564,x27562,x27565,x27566)) % 14.98/14.68 [2757]~E(x27571,x27572)+E(f354(x27573,x27574,x27575,x27571,x27576),f354(x27573,x27574,x27575,x27572,x27576)) % 14.98/14.68 [2758]~E(x27581,x27582)+E(f354(x27583,x27584,x27585,x27586,x27581),f354(x27583,x27584,x27585,x27586,x27582)) % 14.98/14.68 [2759]~E(x27591,x27592)+E(f116(x27591),f116(x27592)) % 14.98/14.68 [2760]~E(x27601,x27602)+E(f570(x27601,x27603),f570(x27602,x27603)) % 14.98/14.68 [2761]~E(x27611,x27612)+E(f570(x27613,x27611),f570(x27613,x27612)) % 14.98/14.68 [2762]~E(x27621,x27622)+E(f858(x27621,x27623,x27624),f858(x27622,x27623,x27624)) % 14.98/14.68 [2763]~E(x27631,x27632)+E(f858(x27633,x27631,x27634),f858(x27633,x27632,x27634)) % 14.98/14.68 [2764]~E(x27641,x27642)+E(f858(x27643,x27644,x27641),f858(x27643,x27644,x27642)) % 14.98/14.68 [2765]~E(x27651,x27652)+E(f818(x27651,x27653,x27654,x27655,x27656),f818(x27652,x27653,x27654,x27655,x27656)) % 14.98/14.68 [2766]~E(x27661,x27662)+E(f818(x27663,x27661,x27664,x27665,x27666),f818(x27663,x27662,x27664,x27665,x27666)) % 14.98/14.68 [2767]~E(x27671,x27672)+E(f818(x27673,x27674,x27671,x27675,x27676),f818(x27673,x27674,x27672,x27675,x27676)) % 14.98/14.68 [2768]~E(x27681,x27682)+E(f818(x27683,x27684,x27685,x27681,x27686),f818(x27683,x27684,x27685,x27682,x27686)) % 14.98/14.68 [2769]~E(x27691,x27692)+E(f818(x27693,x27694,x27695,x27696,x27691),f818(x27693,x27694,x27695,x27696,x27692)) % 14.98/14.68 [2770]~E(x27701,x27702)+E(f730(x27701,x27703,x27704,x27705),f730(x27702,x27703,x27704,x27705)) % 14.98/14.68 [2771]~E(x27711,x27712)+E(f730(x27713,x27711,x27714,x27715),f730(x27713,x27712,x27714,x27715)) % 14.98/14.68 [2772]~E(x27721,x27722)+E(f730(x27723,x27724,x27721,x27725),f730(x27723,x27724,x27722,x27725)) % 14.98/14.68 [2773]~E(x27731,x27732)+E(f730(x27733,x27734,x27735,x27731),f730(x27733,x27734,x27735,x27732)) % 14.98/14.68 [2774]~E(x27741,x27742)+E(f829(x27741,x27743,x27744,x27745),f829(x27742,x27743,x27744,x27745)) % 14.98/14.68 [2775]~E(x27751,x27752)+E(f829(x27753,x27751,x27754,x27755),f829(x27753,x27752,x27754,x27755)) % 14.98/14.68 [2776]~E(x27761,x27762)+E(f829(x27763,x27764,x27761,x27765),f829(x27763,x27764,x27762,x27765)) % 14.98/14.68 [2777]~E(x27771,x27772)+E(f829(x27773,x27774,x27775,x27771),f829(x27773,x27774,x27775,x27772)) % 14.98/14.68 [2778]~E(x27781,x27782)+E(f426(x27781),f426(x27782)) % 14.98/14.68 [2779]~E(x27791,x27792)+E(f381(x27791,x27793,x27794,x27795),f381(x27792,x27793,x27794,x27795)) % 14.98/14.68 [2780]~E(x27801,x27802)+E(f381(x27803,x27801,x27804,x27805),f381(x27803,x27802,x27804,x27805)) % 14.98/14.68 [2781]~E(x27811,x27812)+E(f381(x27813,x27814,x27811,x27815),f381(x27813,x27814,x27812,x27815)) % 14.98/14.68 [2782]~E(x27821,x27822)+E(f381(x27823,x27824,x27825,x27821),f381(x27823,x27824,x27825,x27822)) % 14.98/14.68 [2783]~E(x27831,x27832)+E(f653(x27831,x27833,x27834,x27835,x27836,x27837),f653(x27832,x27833,x27834,x27835,x27836,x27837)) % 14.98/14.68 [2784]~E(x27841,x27842)+E(f653(x27843,x27841,x27844,x27845,x27846,x27847),f653(x27843,x27842,x27844,x27845,x27846,x27847)) % 14.98/14.68 [2785]~E(x27851,x27852)+E(f653(x27853,x27854,x27851,x27855,x27856,x27857),f653(x27853,x27854,x27852,x27855,x27856,x27857)) % 14.98/14.68 [2786]~E(x27861,x27862)+E(f653(x27863,x27864,x27865,x27861,x27866,x27867),f653(x27863,x27864,x27865,x27862,x27866,x27867)) % 14.98/14.68 [2787]~E(x27871,x27872)+E(f653(x27873,x27874,x27875,x27876,x27871,x27877),f653(x27873,x27874,x27875,x27876,x27872,x27877)) % 14.98/14.68 [2788]~E(x27881,x27882)+E(f653(x27883,x27884,x27885,x27886,x27887,x27881),f653(x27883,x27884,x27885,x27886,x27887,x27882)) % 14.98/14.68 [2789]~E(x27891,x27892)+E(f596(x27891,x27893,x27894),f596(x27892,x27893,x27894)) % 14.98/14.68 [2790]~E(x27901,x27902)+E(f596(x27903,x27901,x27904),f596(x27903,x27902,x27904)) % 14.98/14.68 [2791]~E(x27911,x27912)+E(f596(x27913,x27914,x27911),f596(x27913,x27914,x27912)) % 14.98/14.68 [2792]~E(x27921,x27922)+E(f406(x27921),f406(x27922)) % 14.98/14.68 [2793]~E(x27931,x27932)+E(f856(x27931,x27933,x27934,x27935,x27936,x27937),f856(x27932,x27933,x27934,x27935,x27936,x27937)) % 14.98/14.68 [2794]~E(x27941,x27942)+E(f856(x27943,x27941,x27944,x27945,x27946,x27947),f856(x27943,x27942,x27944,x27945,x27946,x27947)) % 14.98/14.68 [2795]~E(x27951,x27952)+E(f856(x27953,x27954,x27951,x27955,x27956,x27957),f856(x27953,x27954,x27952,x27955,x27956,x27957)) % 14.98/14.68 [2796]~E(x27961,x27962)+E(f856(x27963,x27964,x27965,x27961,x27966,x27967),f856(x27963,x27964,x27965,x27962,x27966,x27967)) % 14.98/14.68 [2797]~E(x27971,x27972)+E(f856(x27973,x27974,x27975,x27976,x27971,x27977),f856(x27973,x27974,x27975,x27976,x27972,x27977)) % 14.98/14.68 [2798]~E(x27981,x27982)+E(f856(x27983,x27984,x27985,x27986,x27987,x27981),f856(x27983,x27984,x27985,x27986,x27987,x27982)) % 14.98/14.68 [2799]~E(x27991,x27992)+E(f822(x27991,x27993,x27994,x27995,x27996),f822(x27992,x27993,x27994,x27995,x27996)) % 14.98/14.68 [2800]~E(x28001,x28002)+E(f822(x28003,x28001,x28004,x28005,x28006),f822(x28003,x28002,x28004,x28005,x28006)) % 14.98/14.68 [2801]~E(x28011,x28012)+E(f822(x28013,x28014,x28011,x28015,x28016),f822(x28013,x28014,x28012,x28015,x28016)) % 14.98/14.68 [2802]~E(x28021,x28022)+E(f822(x28023,x28024,x28025,x28021,x28026),f822(x28023,x28024,x28025,x28022,x28026)) % 14.98/14.68 [2803]~E(x28031,x28032)+E(f822(x28033,x28034,x28035,x28036,x28031),f822(x28033,x28034,x28035,x28036,x28032)) % 14.98/14.68 [2804]~E(x28041,x28042)+E(f764(x28041,x28043,x28044),f764(x28042,x28043,x28044)) % 14.98/14.68 [2805]~E(x28051,x28052)+E(f764(x28053,x28051,x28054),f764(x28053,x28052,x28054)) % 14.98/14.68 [2806]~E(x28061,x28062)+E(f764(x28063,x28064,x28061),f764(x28063,x28064,x28062)) % 14.98/14.68 [2807]~E(x28071,x28072)+E(f770(x28071,x28073,x28074),f770(x28072,x28073,x28074)) % 14.98/14.68 [2808]~E(x28081,x28082)+E(f770(x28083,x28081,x28084),f770(x28083,x28082,x28084)) % 14.98/14.68 [2809]~E(x28091,x28092)+E(f770(x28093,x28094,x28091),f770(x28093,x28094,x28092)) % 14.98/14.68 [2810]~E(x28101,x28102)+E(f606(x28101,x28103),f606(x28102,x28103)) % 14.98/14.68 [2811]~E(x28111,x28112)+E(f606(x28113,x28111),f606(x28113,x28112)) % 14.98/14.68 [2812]~E(x28121,x28122)+E(f253(x28121,x28123,x28124,x28125,x28126),f253(x28122,x28123,x28124,x28125,x28126)) % 14.98/14.68 [2813]~E(x28131,x28132)+E(f253(x28133,x28131,x28134,x28135,x28136),f253(x28133,x28132,x28134,x28135,x28136)) % 14.98/14.68 [2814]~E(x28141,x28142)+E(f253(x28143,x28144,x28141,x28145,x28146),f253(x28143,x28144,x28142,x28145,x28146)) % 14.98/14.68 [2815]~E(x28151,x28152)+E(f253(x28153,x28154,x28155,x28151,x28156),f253(x28153,x28154,x28155,x28152,x28156)) % 14.98/14.68 [2816]~E(x28161,x28162)+E(f253(x28163,x28164,x28165,x28166,x28161),f253(x28163,x28164,x28165,x28166,x28162)) % 14.98/14.68 [2817]~E(x28171,x28172)+E(f268(x28171,x28173,x28174,x28175),f268(x28172,x28173,x28174,x28175)) % 14.98/14.68 [2818]~E(x28181,x28182)+E(f268(x28183,x28181,x28184,x28185),f268(x28183,x28182,x28184,x28185)) % 14.98/14.68 [2819]~E(x28191,x28192)+E(f268(x28193,x28194,x28191,x28195),f268(x28193,x28194,x28192,x28195)) % 14.98/14.68 [2820]~E(x28201,x28202)+E(f268(x28203,x28204,x28205,x28201),f268(x28203,x28204,x28205,x28202)) % 14.98/14.68 [2821]~E(x28211,x28212)+E(f554(x28211,x28213,x28214),f554(x28212,x28213,x28214)) % 14.98/14.68 [2822]~E(x28221,x28222)+E(f554(x28223,x28221,x28224),f554(x28223,x28222,x28224)) % 14.98/14.68 [2823]~E(x28231,x28232)+E(f554(x28233,x28234,x28231),f554(x28233,x28234,x28232)) % 14.98/14.68 [2824]~E(x28241,x28242)+E(f647(x28241,x28243,x28244,x28245),f647(x28242,x28243,x28244,x28245)) % 14.98/14.68 [2825]~E(x28251,x28252)+E(f647(x28253,x28251,x28254,x28255),f647(x28253,x28252,x28254,x28255)) % 14.98/14.68 [2826]~E(x28261,x28262)+E(f647(x28263,x28264,x28261,x28265),f647(x28263,x28264,x28262,x28265)) % 14.98/14.68 [2827]~E(x28271,x28272)+E(f647(x28273,x28274,x28275,x28271),f647(x28273,x28274,x28275,x28272)) % 14.98/14.68 [2828]~E(x28281,x28282)+E(f721(x28281,x28283,x28284),f721(x28282,x28283,x28284)) % 14.98/14.68 [2829]~E(x28291,x28292)+E(f721(x28293,x28291,x28294),f721(x28293,x28292,x28294)) % 14.98/14.68 [2830]~E(x28301,x28302)+E(f721(x28303,x28304,x28301),f721(x28303,x28304,x28302)) % 14.98/14.68 [2831]~E(x28311,x28312)+E(f768(x28311,x28313,x28314),f768(x28312,x28313,x28314)) % 14.98/14.68 [2832]~E(x28321,x28322)+E(f768(x28323,x28321,x28324),f768(x28323,x28322,x28324)) % 14.98/14.68 [2833]~E(x28331,x28332)+E(f768(x28333,x28334,x28331),f768(x28333,x28334,x28332)) % 14.98/14.68 [2834]~E(x28341,x28342)+E(f879(x28341,x28343),f879(x28342,x28343)) % 14.98/14.68 [2835]~E(x28351,x28352)+E(f879(x28353,x28351),f879(x28353,x28352)) % 14.98/14.68 [2836]~E(x28361,x28362)+E(f326(x28361),f326(x28362)) % 14.98/14.68 [2837]~E(x28371,x28372)+E(f817(x28371,x28373),f817(x28372,x28373)) % 14.98/14.68 [2838]~E(x28381,x28382)+E(f817(x28383,x28381),f817(x28383,x28382)) % 14.98/14.68 [2839]~P1(x28391)+P1(x28392)+~E(x28391,x28392) % 14.98/14.68 [2840]~P2(x28401)+P2(x28402)+~E(x28401,x28402) % 14.98/14.68 [2841]~P104(x28411)+P104(x28412)+~E(x28411,x28412) % 14.98/14.68 [2842]~P109(x28421)+P109(x28422)+~E(x28421,x28422) % 14.98/14.68 [2843]P49(x28432,x28433)+~E(x28431,x28432)+~P49(x28431,x28433) % 14.98/14.68 [2844]P49(x28443,x28442)+~E(x28441,x28442)+~P49(x28443,x28441) % 14.98/14.68 [2845]P35(x28452,x28453)+~E(x28451,x28452)+~P35(x28451,x28453) % 14.98/14.68 [2846]P35(x28463,x28462)+~E(x28461,x28462)+~P35(x28463,x28461) % 14.98/14.68 [2847]~P61(x28471)+P61(x28472)+~E(x28471,x28472) % 14.98/14.68 [2848]~P4(x28481)+P4(x28482)+~E(x28481,x28482) % 14.98/14.68 [2849]~P112(x28491)+P112(x28492)+~E(x28491,x28492) % 14.98/14.68 [2850]~P3(x28501)+P3(x28502)+~E(x28501,x28502) % 14.98/14.68 [2851]~P91(x28511)+P91(x28512)+~E(x28511,x28512) % 14.98/14.68 [2852]~P78(x28521)+P78(x28522)+~E(x28521,x28522) % 14.98/14.68 [2853]~P67(x28531)+P67(x28532)+~E(x28531,x28532) % 14.98/14.68 [2854]~P66(x28541)+P66(x28542)+~E(x28541,x28542) % 14.98/14.68 [2855]~P111(x28551)+P111(x28552)+~E(x28551,x28552) % 14.98/14.68 [2856]~P92(x28561)+P92(x28562)+~E(x28561,x28562) % 14.98/14.68 [2857]~P86(x28571)+P86(x28572)+~E(x28571,x28572) % 14.98/14.68 [2858]~P108(x28581)+P108(x28582)+~E(x28581,x28582) % 14.98/14.68 [2859]P52(x28592,x28593,x28594)+~E(x28591,x28592)+~P52(x28591,x28593,x28594) % 14.98/14.68 [2860]P52(x28603,x28602,x28604)+~E(x28601,x28602)+~P52(x28603,x28601,x28604) % 14.98/14.68 [2861]P52(x28613,x28614,x28612)+~E(x28611,x28612)+~P52(x28613,x28614,x28611) % 14.98/14.68 [2862]~P99(x28621)+P99(x28622)+~E(x28621,x28622) % 14.98/14.68 [2863]~P113(x28631)+P113(x28632)+~E(x28631,x28632) % 14.98/14.68 [2864]~P38(x28641)+P38(x28642)+~E(x28641,x28642) % 14.98/14.68 [2865]~P93(x28651)+P93(x28652)+~E(x28651,x28652) % 14.98/14.68 [2866]P16(x28662,x28663,x28664)+~E(x28661,x28662)+~P16(x28661,x28663,x28664) % 14.98/14.68 [2867]P16(x28673,x28672,x28674)+~E(x28671,x28672)+~P16(x28673,x28671,x28674) % 14.98/14.68 [2868]P16(x28683,x28684,x28682)+~E(x28681,x28682)+~P16(x28683,x28684,x28681) % 14.98/14.68 [2869]~P110(x28691)+P110(x28692)+~E(x28691,x28692) % 14.98/14.68 [2870]P149(x28702,x28703,x28704)+~E(x28701,x28702)+~P149(x28701,x28703,x28704) % 14.98/14.68 [2871]P149(x28713,x28712,x28714)+~E(x28711,x28712)+~P149(x28713,x28711,x28714) % 14.98/14.68 [2872]P149(x28723,x28724,x28722)+~E(x28721,x28722)+~P149(x28723,x28724,x28721) % 14.98/14.68 [2873]P148(x28732,x28733,x28734)+~E(x28731,x28732)+~P148(x28731,x28733,x28734) % 14.98/14.68 [2874]P148(x28743,x28742,x28744)+~E(x28741,x28742)+~P148(x28743,x28741,x28744) % 14.98/14.68 [2875]P148(x28753,x28754,x28752)+~E(x28751,x28752)+~P148(x28753,x28754,x28751) % 14.98/14.68 [2876]~P81(x28761)+P81(x28762)+~E(x28761,x28762) % 14.98/14.68 [2877]~P127(x28771)+P127(x28772)+~E(x28771,x28772) % 14.98/14.68 [2878]~P135(x28781)+P135(x28782)+~E(x28781,x28782) % 14.98/14.68 [2879]~P131(x28791)+P131(x28792)+~E(x28791,x28792) % 14.98/14.68 [2880]~P58(x28801)+P58(x28802)+~E(x28801,x28802) % 14.98/14.68 [2881]P55(x28812,x28813)+~E(x28811,x28812)+~P55(x28811,x28813) % 14.98/14.68 [2882]P55(x28823,x28822)+~E(x28821,x28822)+~P55(x28823,x28821) % 14.98/14.68 [2883]P22(x28832,x28833,x28834,x28835)+~E(x28831,x28832)+~P22(x28831,x28833,x28834,x28835) % 14.98/14.68 [2884]P22(x28843,x28842,x28844,x28845)+~E(x28841,x28842)+~P22(x28843,x28841,x28844,x28845) % 14.98/14.68 [2885]P22(x28853,x28854,x28852,x28855)+~E(x28851,x28852)+~P22(x28853,x28854,x28851,x28855) % 14.98/14.68 [2886]P22(x28863,x28864,x28865,x28862)+~E(x28861,x28862)+~P22(x28863,x28864,x28865,x28861) % 14.98/14.68 [2887]~P69(x28871)+P69(x28872)+~E(x28871,x28872) % 14.98/14.68 [2888]~P94(x28881)+P94(x28882)+~E(x28881,x28882) % 14.98/14.68 [2889]~P103(x28891)+P103(x28892)+~E(x28891,x28892) % 14.98/14.68 [2890]P29(x28902,x28903,x28904)+~E(x28901,x28902)+~P29(x28901,x28903,x28904) % 14.98/14.68 [2891]P29(x28913,x28912,x28914)+~E(x28911,x28912)+~P29(x28913,x28911,x28914) % 14.98/14.68 [2892]P29(x28923,x28924,x28922)+~E(x28921,x28922)+~P29(x28923,x28924,x28921) % 14.98/14.68 [2893]P50(x28932,x28933,x28934)+~E(x28931,x28932)+~P50(x28931,x28933,x28934) % 14.98/14.68 [2894]P50(x28943,x28942,x28944)+~E(x28941,x28942)+~P50(x28943,x28941,x28944) % 14.98/14.68 [2895]P50(x28953,x28954,x28952)+~E(x28951,x28952)+~P50(x28953,x28954,x28951) % 14.98/14.68 [2896]~P146(x28961)+P146(x28962)+~E(x28961,x28962) % 14.98/14.68 [2897]P6(x28972,x28973,x28974)+~E(x28971,x28972)+~P6(x28971,x28973,x28974) % 14.98/14.68 [2898]P6(x28983,x28982,x28984)+~E(x28981,x28982)+~P6(x28983,x28981,x28984) % 14.98/14.68 [2899]P6(x28993,x28994,x28992)+~E(x28991,x28992)+~P6(x28993,x28994,x28991) % 14.98/14.68 [2900]~P102(x29001)+P102(x29002)+~E(x29001,x29002) % 14.98/14.68 [2901]~P95(x29011)+P95(x29012)+~E(x29011,x29012) % 14.98/14.68 [2902]P5(x29022,x29023)+~E(x29021,x29022)+~P5(x29021,x29023) % 14.98/14.68 [2903]P5(x29033,x29032)+~E(x29031,x29032)+~P5(x29033,x29031) % 14.98/14.68 [2904]~P68(x29041)+P68(x29042)+~E(x29041,x29042) % 14.98/14.68 [2905]~P121(x29051)+P121(x29052)+~E(x29051,x29052) % 14.98/14.68 [2906]~P140(x29061)+P140(x29062)+~E(x29061,x29062) % 14.98/14.68 [2907]~P59(x29071)+P59(x29072)+~E(x29071,x29072) % 14.98/14.68 [2908]~P96(x29081)+P96(x29082)+~E(x29081,x29082) % 14.98/14.68 [2909]~P125(x29091)+P125(x29092)+~E(x29091,x29092) % 14.98/14.68 [2910]~P82(x29101)+P82(x29102)+~E(x29101,x29102) % 14.98/14.68 [2911]P19(x29112,x29113,x29114,x29115,x29116)+~E(x29111,x29112)+~P19(x29111,x29113,x29114,x29115,x29116) % 14.98/14.68 [2912]P19(x29123,x29122,x29124,x29125,x29126)+~E(x29121,x29122)+~P19(x29123,x29121,x29124,x29125,x29126) % 14.98/14.68 [2913]P19(x29133,x29134,x29132,x29135,x29136)+~E(x29131,x29132)+~P19(x29133,x29134,x29131,x29135,x29136) % 14.98/14.68 [2914]P19(x29143,x29144,x29145,x29142,x29146)+~E(x29141,x29142)+~P19(x29143,x29144,x29145,x29141,x29146) % 14.98/14.68 [2915]P19(x29153,x29154,x29155,x29156,x29152)+~E(x29151,x29152)+~P19(x29153,x29154,x29155,x29156,x29151) % 14.98/14.68 [2916]P26(x29162,x29163)+~E(x29161,x29162)+~P26(x29161,x29163) % 14.98/14.68 [2917]P26(x29173,x29172)+~E(x29171,x29172)+~P26(x29173,x29171) % 14.98/14.68 [2918]P28(x29182,x29183,x29184)+~E(x29181,x29182)+~P28(x29181,x29183,x29184) % 14.98/14.68 [2919]P28(x29193,x29192,x29194)+~E(x29191,x29192)+~P28(x29193,x29191,x29194) % 14.98/14.68 [2920]P28(x29203,x29204,x29202)+~E(x29201,x29202)+~P28(x29203,x29204,x29201) % 14.98/14.68 [2921]~P97(x29211)+P97(x29212)+~E(x29211,x29212) % 14.98/14.68 [2922]~P119(x29221)+P119(x29222)+~E(x29221,x29222) % 14.98/14.68 [2923]P23(x29232,x29233,x29234,x29235,x29236)+~E(x29231,x29232)+~P23(x29231,x29233,x29234,x29235,x29236) % 14.98/14.68 [2924]P23(x29243,x29242,x29244,x29245,x29246)+~E(x29241,x29242)+~P23(x29243,x29241,x29244,x29245,x29246) % 14.98/14.68 [2925]P23(x29253,x29254,x29252,x29255,x29256)+~E(x29251,x29252)+~P23(x29253,x29254,x29251,x29255,x29256) % 14.98/14.68 [2926]P23(x29263,x29264,x29265,x29262,x29266)+~E(x29261,x29262)+~P23(x29263,x29264,x29265,x29261,x29266) % 14.98/14.68 [2927]P23(x29273,x29274,x29275,x29276,x29272)+~E(x29271,x29272)+~P23(x29273,x29274,x29275,x29276,x29271) % 14.98/14.68 [2928]~P137(x29281)+P137(x29282)+~E(x29281,x29282) % 14.98/14.68 [2929]~P60(x29291)+P60(x29292)+~E(x29291,x29292) % 14.98/14.68 [2930]~P100(x29301)+P100(x29302)+~E(x29301,x29302) % 14.98/14.68 [2931]~P71(x29311)+P71(x29312)+~E(x29311,x29312) % 14.98/14.68 [2932]~P72(x29321)+P72(x29322)+~E(x29321,x29322) % 14.98/14.68 [2933]P37(x29332,x29333)+~E(x29331,x29332)+~P37(x29331,x29333) % 14.98/14.68 [2934]P37(x29343,x29342)+~E(x29341,x29342)+~P37(x29343,x29341) % 14.98/14.68 [2935]~P147(x29351)+P147(x29352)+~E(x29351,x29352) % 14.98/14.68 [2936]~P98(x29361)+P98(x29362)+~E(x29361,x29362) % 14.98/14.68 [2937]P31(x29372,x29373,x29374)+~E(x29371,x29372)+~P31(x29371,x29373,x29374) % 14.98/14.68 [2938]P31(x29383,x29382,x29384)+~E(x29381,x29382)+~P31(x29383,x29381,x29384) % 14.98/14.68 [2939]P31(x29393,x29394,x29392)+~E(x29391,x29392)+~P31(x29393,x29394,x29391) % 14.98/14.68 [2940]~P83(x29401)+P83(x29402)+~E(x29401,x29402) % 14.98/14.68 [2941]P33(x29412,x29413,x29414)+~E(x29411,x29412)+~P33(x29411,x29413,x29414) % 14.98/14.68 [2942]P33(x29423,x29422,x29424)+~E(x29421,x29422)+~P33(x29423,x29421,x29424) % 14.98/14.68 [2943]P33(x29433,x29434,x29432)+~E(x29431,x29432)+~P33(x29433,x29434,x29431) % 14.98/14.68 [2944]P56(x29442,x29443,x29444,x29445)+~E(x29441,x29442)+~P56(x29441,x29443,x29444,x29445) % 14.98/14.68 [2945]P56(x29453,x29452,x29454,x29455)+~E(x29451,x29452)+~P56(x29453,x29451,x29454,x29455) % 14.98/14.68 [2946]P56(x29463,x29464,x29462,x29465)+~E(x29461,x29462)+~P56(x29463,x29464,x29461,x29465) % 14.98/14.68 [2947]P56(x29473,x29474,x29475,x29472)+~E(x29471,x29472)+~P56(x29473,x29474,x29475,x29471) % 14.98/14.68 [2948]~P70(x29481)+P70(x29482)+~E(x29481,x29482) % 14.98/14.68 [2949]P32(x29492,x29493,x29494,x29495,x29496)+~E(x29491,x29492)+~P32(x29491,x29493,x29494,x29495,x29496) % 14.98/14.68 [2950]P32(x29503,x29502,x29504,x29505,x29506)+~E(x29501,x29502)+~P32(x29503,x29501,x29504,x29505,x29506) % 14.98/14.68 [2951]P32(x29513,x29514,x29512,x29515,x29516)+~E(x29511,x29512)+~P32(x29513,x29514,x29511,x29515,x29516) % 14.98/14.68 [2952]P32(x29523,x29524,x29525,x29522,x29526)+~E(x29521,x29522)+~P32(x29523,x29524,x29525,x29521,x29526) % 14.98/14.68 [2953]P32(x29533,x29534,x29535,x29536,x29532)+~E(x29531,x29532)+~P32(x29533,x29534,x29535,x29536,x29531) % 14.98/14.68 [2954]~P128(x29541)+P128(x29542)+~E(x29541,x29542) % 14.98/14.68 [2955]~P73(x29551)+P73(x29552)+~E(x29551,x29552) % 14.98/14.68 [2956]P11(x29562,x29563)+~E(x29561,x29562)+~P11(x29561,x29563) % 14.98/14.68 [2957]P11(x29573,x29572)+~E(x29571,x29572)+~P11(x29573,x29571) % 14.98/14.68 [2958]~P117(x29581)+P117(x29582)+~E(x29581,x29582) % 14.98/14.68 [2959]~P74(x29591)+P74(x29592)+~E(x29591,x29592) % 14.98/14.68 [2960]~P138(x29601)+P138(x29602)+~E(x29601,x29602) % 14.98/14.68 [2961]~P65(x29611)+P65(x29612)+~E(x29611,x29612) % 14.98/14.68 [2962]~P84(x29621)+P84(x29622)+~E(x29621,x29622) % 14.98/14.68 [2963]~P142(x29631)+P142(x29632)+~E(x29631,x29632) % 14.98/14.68 [2964]P53(x29642,x29643,x29644)+~E(x29641,x29642)+~P53(x29641,x29643,x29644) % 14.98/14.68 [2965]P53(x29653,x29652,x29654)+~E(x29651,x29652)+~P53(x29653,x29651,x29654) % 14.98/14.68 [2966]P53(x29663,x29664,x29662)+~E(x29661,x29662)+~P53(x29663,x29664,x29661) % 14.98/14.68 [2967]~P85(x29671)+P85(x29672)+~E(x29671,x29672) % 14.98/14.68 [2968]P36(x29682,x29683)+~E(x29681,x29682)+~P36(x29681,x29683) % 14.98/14.68 [2969]P36(x29693,x29692)+~E(x29691,x29692)+~P36(x29693,x29691) % 14.98/14.68 [2970]P24(x29702,x29703)+~E(x29701,x29702)+~P24(x29701,x29703) % 14.98/14.68 [2971]P24(x29713,x29712)+~E(x29711,x29712)+~P24(x29713,x29711) % 14.98/14.68 [2972]~P87(x29721)+P87(x29722)+~E(x29721,x29722) % 14.98/14.68 [2973]~P64(x29731)+P64(x29732)+~E(x29731,x29732) % 14.98/14.68 [2974]~P139(x29741)+P139(x29742)+~E(x29741,x29742) % 14.98/14.68 [2975]~P114(x29751)+P114(x29752)+~E(x29751,x29752) % 14.98/14.68 [2976]~P63(x29761)+P63(x29762)+~E(x29761,x29762) % 14.98/14.68 [2977]~P143(x29771)+P143(x29772)+~E(x29771,x29772) % 14.98/14.68 [2978]~P126(x29781)+P126(x29782)+~E(x29781,x29782) % 14.98/14.68 [2979]~P115(x29791)+P115(x29792)+~E(x29791,x29792) % 14.98/14.68 [2980]~P132(x29801)+P132(x29802)+~E(x29801,x29802) % 14.98/14.68 [2981]~P130(x29811)+P130(x29812)+~E(x29811,x29812) % 14.98/14.68 [2982]P17(x29822,x29823,x29824,x29825)+~E(x29821,x29822)+~P17(x29821,x29823,x29824,x29825) % 14.98/14.68 [2983]P17(x29833,x29832,x29834,x29835)+~E(x29831,x29832)+~P17(x29833,x29831,x29834,x29835) % 14.98/14.68 [2984]P17(x29843,x29844,x29842,x29845)+~E(x29841,x29842)+~P17(x29843,x29844,x29841,x29845) % 14.98/14.68 [2985]P17(x29853,x29854,x29855,x29852)+~E(x29851,x29852)+~P17(x29853,x29854,x29855,x29851) % 14.98/14.68 [2986]~P144(x29861)+P144(x29862)+~E(x29861,x29862) % 14.98/14.68 [2987]P13(x29872,x29873)+~E(x29871,x29872)+~P13(x29871,x29873) % 14.98/14.68 [2988]P13(x29883,x29882)+~E(x29881,x29882)+~P13(x29883,x29881) % 14.98/14.68 [2989]~P79(x29891)+P79(x29892)+~E(x29891,x29892) % 14.98/14.68 [2990]~P145(x29901)+P145(x29902)+~E(x29901,x29902) % 14.98/14.68 [2991]~P106(x29911)+P106(x29912)+~E(x29911,x29912) % 14.98/14.68 [2992]~P80(x29921)+P80(x29922)+~E(x29921,x29922) % 14.98/14.68 [2993]P12(x29932,x29933,x29934)+~E(x29931,x29932)+~P12(x29931,x29933,x29934) % 14.98/14.68 [2994]P12(x29943,x29942,x29944)+~E(x29941,x29942)+~P12(x29943,x29941,x29944) % 14.98/14.68 [2995]P12(x29953,x29954,x29952)+~E(x29951,x29952)+~P12(x29953,x29954,x29951) % 14.98/14.68 [2996]P9(x29962,x29963,x29964,x29965)+~E(x29961,x29962)+~P9(x29961,x29963,x29964,x29965) % 14.98/14.68 [2997]P9(x29973,x29972,x29974,x29975)+~E(x29971,x29972)+~P9(x29973,x29971,x29974,x29975) % 14.98/14.68 [2998]P9(x29983,x29984,x29982,x29985)+~E(x29981,x29982)+~P9(x29983,x29984,x29981,x29985) % 14.98/14.68 [2999]P9(x29993,x29994,x29995,x29992)+~E(x29991,x29992)+~P9(x29993,x29994,x29995,x29991) % 14.98/14.68 [3000]P27(x30002,x30003,x30004)+~E(x30001,x30002)+~P27(x30001,x30003,x30004) % 14.98/14.68 [3001]P27(x30013,x30012,x30014)+~E(x30011,x30012)+~P27(x30013,x30011,x30014) % 14.98/14.68 [3002]P27(x30023,x30024,x30022)+~E(x30021,x30022)+~P27(x30023,x30024,x30021) % 14.98/14.68 [3003]~P134(x30031)+P134(x30032)+~E(x30031,x30032) % 14.98/14.68 [3004]P43(x30042,x30043)+~E(x30041,x30042)+~P43(x30041,x30043) % 14.98/14.68 [3005]P43(x30053,x30052)+~E(x30051,x30052)+~P43(x30053,x30051) % 14.98/14.68 [3006]~P141(x30061)+P141(x30062)+~E(x30061,x30062) % 14.98/14.68 [3007]~P88(x30071)+P88(x30072)+~E(x30071,x30072) % 14.98/14.68 [3008]~P90(x30081)+P90(x30082)+~E(x30081,x30082) % 14.98/14.68 [3009]P14(x30092,x30093,x30094)+~E(x30091,x30092)+~P14(x30091,x30093,x30094) % 14.98/14.68 [3010]P14(x30103,x30102,x30104)+~E(x30101,x30102)+~P14(x30103,x30101,x30104) % 14.98/14.68 [3011]P14(x30113,x30114,x30112)+~E(x30111,x30112)+~P14(x30113,x30114,x30111) % 14.98/14.68 [3012]~P120(x30121)+P120(x30122)+~E(x30121,x30122) % 14.98/14.68 [3013]~P129(x30131)+P129(x30132)+~E(x30131,x30132) % 14.98/14.68 [3014]~P76(x30141)+P76(x30142)+~E(x30141,x30142) % 14.98/14.68 [3015]P46(x30152,x30153)+~E(x30151,x30152)+~P46(x30151,x30153) % 14.98/14.68 [3016]P46(x30163,x30162)+~E(x30161,x30162)+~P46(x30163,x30161) % 14.98/14.68 [3017]~P124(x30171)+P124(x30172)+~E(x30171,x30172) % 14.98/14.68 [3018]~P133(x30181)+P133(x30182)+~E(x30181,x30182) % 14.98/14.68 [3019]P20(x30192,x30193,x30194,x30195,x30196,x30197)+~E(x30191,x30192)+~P20(x30191,x30193,x30194,x30195,x30196,x30197) % 14.98/14.68 [3020]P20(x30203,x30202,x30204,x30205,x30206,x30207)+~E(x30201,x30202)+~P20(x30203,x30201,x30204,x30205,x30206,x30207) % 14.98/14.68 [3021]P20(x30213,x30214,x30212,x30215,x30216,x30217)+~E(x30211,x30212)+~P20(x30213,x30214,x30211,x30215,x30216,x30217) % 14.98/14.68 [3022]P20(x30223,x30224,x30225,x30222,x30226,x30227)+~E(x30221,x30222)+~P20(x30223,x30224,x30225,x30221,x30226,x30227) % 14.98/14.68 [3023]P20(x30233,x30234,x30235,x30236,x30232,x30237)+~E(x30231,x30232)+~P20(x30233,x30234,x30235,x30236,x30231,x30237) % 14.98/14.68 [3024]P20(x30243,x30244,x30245,x30246,x30247,x30242)+~E(x30241,x30242)+~P20(x30243,x30244,x30245,x30246,x30247,x30241) % 14.98/14.68 [3025]P40(x30252,x30253,x30254,x30255,x30256,x30257)+~E(x30251,x30252)+~P40(x30251,x30253,x30254,x30255,x30256,x30257) % 14.98/14.68 [3026]P40(x30263,x30262,x30264,x30265,x30266,x30267)+~E(x30261,x30262)+~P40(x30263,x30261,x30264,x30265,x30266,x30267) % 14.98/14.68 [3027]P40(x30273,x30274,x30272,x30275,x30276,x30277)+~E(x30271,x30272)+~P40(x30273,x30274,x30271,x30275,x30276,x30277) % 14.98/14.68 [3028]P40(x30283,x30284,x30285,x30282,x30286,x30287)+~E(x30281,x30282)+~P40(x30283,x30284,x30285,x30281,x30286,x30287) % 14.98/14.68 [3029]P40(x30293,x30294,x30295,x30296,x30292,x30297)+~E(x30291,x30292)+~P40(x30293,x30294,x30295,x30296,x30291,x30297) % 14.98/14.68 [3030]P40(x30303,x30304,x30305,x30306,x30307,x30302)+~E(x30301,x30302)+~P40(x30303,x30304,x30305,x30306,x30307,x30301) % 14.98/14.68 [3031]~P101(x30311)+P101(x30312)+~E(x30311,x30312) % 14.98/14.68 [3032]P54(x30322,x30323,x30324,x30325,x30326)+~E(x30321,x30322)+~P54(x30321,x30323,x30324,x30325,x30326) % 14.98/14.68 [3033]P54(x30333,x30332,x30334,x30335,x30336)+~E(x30331,x30332)+~P54(x30333,x30331,x30334,x30335,x30336) % 14.98/14.68 [3034]P54(x30343,x30344,x30342,x30345,x30346)+~E(x30341,x30342)+~P54(x30343,x30344,x30341,x30345,x30346) % 14.98/14.68 [3035]P54(x30353,x30354,x30355,x30352,x30356)+~E(x30351,x30352)+~P54(x30353,x30354,x30355,x30351,x30356) % 14.98/14.68 [3036]P54(x30363,x30364,x30365,x30366,x30362)+~E(x30361,x30362)+~P54(x30363,x30364,x30365,x30366,x30361) % 14.98/14.68 [3037]~P123(x30371)+P123(x30372)+~E(x30371,x30372) % 14.98/14.68 [3038]P7(x30382,x30383,x30384)+~E(x30381,x30382)+~P7(x30381,x30383,x30384) % 14.98/14.68 [3039]P7(x30393,x30392,x30394)+~E(x30391,x30392)+~P7(x30393,x30391,x30394) % 14.98/14.68 [3040]P7(x30403,x30404,x30402)+~E(x30401,x30402)+~P7(x30403,x30404,x30401) % 14.98/14.68 [3041]~P105(x30411)+P105(x30412)+~E(x30411,x30412) % 14.98/14.68 [3042]P151(x30422,x30423)+~E(x30421,x30422)+~P151(x30421,x30423) % 14.98/14.68 [3043]P151(x30433,x30432)+~E(x30431,x30432)+~P151(x30433,x30431) % 14.98/14.68 [3044]~P118(x30441)+P118(x30442)+~E(x30441,x30442) % 14.98/14.68 [3045]~P122(x30451)+P122(x30452)+~E(x30451,x30452) % 14.98/14.68 [3046]P10(x30462,x30463,x30464,x30465,x30466,x30467)+~E(x30461,x30462)+~P10(x30461,x30463,x30464,x30465,x30466,x30467) % 14.98/14.68 [3047]P10(x30473,x30472,x30474,x30475,x30476,x30477)+~E(x30471,x30472)+~P10(x30473,x30471,x30474,x30475,x30476,x30477) % 14.98/14.68 [3048]P10(x30483,x30484,x30482,x30485,x30486,x30487)+~E(x30481,x30482)+~P10(x30483,x30484,x30481,x30485,x30486,x30487) % 14.98/14.68 [3049]P10(x30493,x30494,x30495,x30492,x30496,x30497)+~E(x30491,x30492)+~P10(x30493,x30494,x30495,x30491,x30496,x30497) % 14.98/14.68 [3050]P10(x30503,x30504,x30505,x30506,x30502,x30507)+~E(x30501,x30502)+~P10(x30503,x30504,x30505,x30506,x30501,x30507) % 14.98/14.68 [3051]P10(x30513,x30514,x30515,x30516,x30517,x30512)+~E(x30511,x30512)+~P10(x30513,x30514,x30515,x30516,x30517,x30511) % 14.98/14.68 [3052]P18(x30522,x30523,x30524,x30525)+~E(x30521,x30522)+~P18(x30521,x30523,x30524,x30525) % 14.98/14.68 [3053]P18(x30533,x30532,x30534,x30535)+~E(x30531,x30532)+~P18(x30533,x30531,x30534,x30535) % 14.98/14.68 [3054]P18(x30543,x30544,x30542,x30545)+~E(x30541,x30542)+~P18(x30543,x30544,x30541,x30545) % 14.98/14.68 [3055]P18(x30553,x30554,x30555,x30552)+~E(x30551,x30552)+~P18(x30553,x30554,x30555,x30551) % 14.98/14.68 [3056]~P136(x30561)+P136(x30562)+~E(x30561,x30562) % 14.98/14.68 [3057]P15(x30572,x30573,x30574)+~E(x30571,x30572)+~P15(x30571,x30573,x30574) % 14.98/14.68 [3058]P15(x30583,x30582,x30584)+~E(x30581,x30582)+~P15(x30583,x30581,x30584) % 14.98/14.68 [3059]P15(x30593,x30594,x30592)+~E(x30591,x30592)+~P15(x30593,x30594,x30591) % 14.98/14.68 [3060]P51(x30602,x30603)+~E(x30601,x30602)+~P51(x30601,x30603) % 14.98/14.68 [3061]P51(x30613,x30612)+~E(x30611,x30612)+~P51(x30613,x30611) % 14.98/14.68 [3062]P21(x30622,x30623,x30624,x30625,x30626,x30627)+~E(x30621,x30622)+~P21(x30621,x30623,x30624,x30625,x30626,x30627) % 14.98/14.68 [3063]P21(x30633,x30632,x30634,x30635,x30636,x30637)+~E(x30631,x30632)+~P21(x30633,x30631,x30634,x30635,x30636,x30637) % 14.98/14.68 [3064]P21(x30643,x30644,x30642,x30645,x30646,x30647)+~E(x30641,x30642)+~P21(x30643,x30644,x30641,x30645,x30646,x30647) % 14.98/14.68 [3065]P21(x30653,x30654,x30655,x30652,x30656,x30657)+~E(x30651,x30652)+~P21(x30653,x30654,x30655,x30651,x30656,x30657) % 14.98/14.68 [3066]P21(x30663,x30664,x30665,x30666,x30662,x30667)+~E(x30661,x30662)+~P21(x30663,x30664,x30665,x30666,x30661,x30667) % 14.98/14.68 [3067]P21(x30673,x30674,x30675,x30676,x30677,x30672)+~E(x30671,x30672)+~P21(x30673,x30674,x30675,x30676,x30677,x30671) % 14.98/14.68 [3068]~P116(x30681)+P116(x30682)+~E(x30681,x30682) % 14.98/14.68 [3069]P47(x30692,x30693)+~E(x30691,x30692)+~P47(x30691,x30693) % 14.98/14.68 [3070]P47(x30703,x30702)+~E(x30701,x30702)+~P47(x30703,x30701) % 14.98/14.68 [3071]P57(x30712,x30713)+~E(x30711,x30712)+~P57(x30711,x30713) % 14.98/14.68 [3072]P57(x30723,x30722)+~E(x30721,x30722)+~P57(x30723,x30721) % 14.98/14.68 [3073]~P62(x30731)+P62(x30732)+~E(x30731,x30732) % 14.98/14.68 [3074]P48(x30742,x30743)+~E(x30741,x30742)+~P48(x30741,x30743) % 14.98/14.68 [3075]P48(x30753,x30752)+~E(x30751,x30752)+~P48(x30753,x30751) % 14.98/14.68 [3076]P30(x30762,x30763,x30764,x30765)+~E(x30761,x30762)+~P30(x30761,x30763,x30764,x30765) % 14.98/14.68 [3077]P30(x30773,x30772,x30774,x30775)+~E(x30771,x30772)+~P30(x30773,x30771,x30774,x30775) % 14.98/14.68 [3078]P30(x30783,x30784,x30782,x30785)+~E(x30781,x30782)+~P30(x30783,x30784,x30781,x30785) % 14.98/14.68 [3079]P30(x30793,x30794,x30795,x30792)+~E(x30791,x30792)+~P30(x30793,x30794,x30795,x30791) % 14.98/14.68 [3080]P41(x30802,x30803)+~E(x30801,x30802)+~P41(x30801,x30803) % 14.98/14.68 [3081]P41(x30813,x30812)+~E(x30811,x30812)+~P41(x30813,x30811) % 14.98/14.68 [3082]P150(x30822,x30823)+~E(x30821,x30822)+~P150(x30821,x30823) % 14.98/14.68 [3083]P150(x30833,x30832)+~E(x30831,x30832)+~P150(x30833,x30831) % 14.98/14.68 [3084]~P34(x30841)+P34(x30842)+~E(x30841,x30842) % 14.98/14.68 [3085]P152(x30852,x30853)+~E(x30851,x30852)+~P152(x30851,x30853) % 14.98/14.68 [3086]P152(x30863,x30862)+~E(x30861,x30862)+~P152(x30863,x30861) % 14.98/14.68 [3087]P8(x30872,x30873,x30874,x30875,x30876)+~E(x30871,x30872)+~P8(x30871,x30873,x30874,x30875,x30876) % 14.98/14.68 [3088]P8(x30883,x30882,x30884,x30885,x30886)+~E(x30881,x30882)+~P8(x30883,x30881,x30884,x30885,x30886) % 14.98/14.68 [3089]P8(x30893,x30894,x30892,x30895,x30896)+~E(x30891,x30892)+~P8(x30893,x30894,x30891,x30895,x30896) % 14.98/14.68 [3090]P8(x30903,x30904,x30905,x30902,x30906)+~E(x30901,x30902)+~P8(x30903,x30904,x30905,x30901,x30906) % 14.98/14.68 [3091]P8(x30913,x30914,x30915,x30916,x30912)+~E(x30911,x30912)+~P8(x30913,x30914,x30915,x30916,x30911) % 14.98/14.68 [3092]P45(x30922,x30923,x30924)+~E(x30921,x30922)+~P45(x30921,x30923,x30924) % 14.98/14.68 [3093]P45(x30933,x30932,x30934)+~E(x30931,x30932)+~P45(x30933,x30931,x30934) % 14.98/14.68 [3094]P45(x30943,x30944,x30942)+~E(x30941,x30942)+~P45(x30943,x30944,x30941) % 14.98/14.68 [3095]~P107(x30951)+P107(x30952)+~E(x30951,x30952) % 14.98/14.68 [3096]~P77(x30961)+P77(x30962)+~E(x30961,x30962) % 14.98/14.68 [3097]~P89(x30971)+P89(x30972)+~E(x30971,x30972) % 14.98/14.68 [3098]~P75(x30981)+P75(x30982)+~E(x30981,x30982) % 14.98/14.68 [3099]~P25(x30991)+P25(x30992)+~E(x30991,x30992) % 14.98/14.68 [3100]P44(x31002,x31003,x31004)+~E(x31001,x31002)+~P44(x31001,x31003,x31004) % 14.98/14.68 [3101]P44(x31013,x31012,x31014)+~E(x31011,x31012)+~P44(x31013,x31011,x31014) % 14.98/14.68 [3102]P44(x31023,x31024,x31022)+~E(x31021,x31022)+~P44(x31023,x31024,x31021) % 14.98/14.68 [3103]~P42(x31031)+P42(x31032)+~E(x31031,x31032) % 14.98/14.68 [3104]P39(x31042,x31043,x31044,x31045)+~E(x31041,x31042)+~P39(x31041,x31043,x31044,x31045) % 14.98/14.68 [3105]P39(x31053,x31052,x31054,x31055)+~E(x31051,x31052)+~P39(x31053,x31051,x31054,x31055) % 14.98/14.68 [3106]P39(x31063,x31064,x31062,x31065)+~E(x31061,x31062)+~P39(x31063,x31064,x31061,x31065) % 14.98/14.68 [3107]P39(x31073,x31074,x31075,x31072)+~E(x31071,x31072)+~P39(x31073,x31074,x31075,x31071) % 14.98/14.68 % 14.98/14.68 %------------------------------------------- % 14.98/14.68 cnf(10489,plain, % 14.98/14.68 ($false), % 14.98/14.68 inference(scs_inference,[],[3330,4669,4667,3309,4773,4750,4777,4799]), % 14.98/14.68 ['proof']). % 14.98/14.68 % SZS output end Proof % 14.98/14.68 % Total time :0.540000s %------------------------------------------------------------------------------