%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW303+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n032.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 18:06:56 EDT 2024 % Result : Theorem 181.55s 181.52s % Output : CNFRefutation 181.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.10 % Problem : SWW303+1 : TPTP v8.2.0. Released v5.2.0. % 0.05/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 300 % 0.10/0.29 % DateTime : Wed Jun 19 04:31:08 EDT 2024 % 0.10/0.29 % CPUTime : % 0.14/0.48 start to proof:theBenchmark % 181.25/181.41 %------------------------------------------- % 181.25/181.41 % File :CSE---1.7 % 181.25/181.41 % Problem :theBenchmark % 181.25/181.41 % Transform :cnf % 181.25/181.41 % Format :tptp:raw % 181.25/181.41 % Command :java -jar mcs_scs.jar %d %s % 181.25/181.41 % 181.25/181.41 % Result :Theorem 157.560000s % 181.25/181.41 % Output :CNFRefutation 157.560000s % 181.25/181.41 %------------------------------------------- % 181.25/181.42 %------------------------------------------------------------------------------ % 181.25/181.42 % File : SWW303+1 : TPTP v8.2.0. Released v5.2.0. % 181.25/181.42 % Domain : Software Verification % 181.25/181.42 % Problem : Hoare's Logic with Procedures 434852, 5000 axioms selected % 181.25/181.42 % Version : Especial. % 181.25/181.42 % English : % 181.25/181.42 % 181.25/181.42 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 181.25/181.42 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 181.25/181.42 % Source : [Bla11] % 181.25/181.42 % Names : hoare_434852.5000.p [Bla11] % 181.25/181.42 % 181.25/181.42 % Status : ContradictoryAxioms % 181.25/181.42 % Rating : 0.83 v8.2.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.83 v7.0.0, 0.90 v6.4.0, 0.85 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 0.96 v5.3.0, 1.00 v5.2.0 % 181.25/181.42 % Syntax : Number of formulae : 5243 (1738 unt; 0 def) % 181.25/181.42 % Number of atoms : 12577 (4571 equ) % 181.25/181.42 % Maximal formula atoms : 13 ( 2 avg) % 181.25/181.42 % Number of connectives : 8329 ( 995 ~; 148 |; 695 &) % 181.25/181.42 % ( 888 <=>;5603 =>; 0 <=; 0 <~>) % 181.25/181.42 % Maximal formula depth : 22 ( 6 avg) % 181.25/181.42 % Maximal term depth : 19 ( 2 avg) % 181.25/181.42 % Number of predicates : 144 ( 143 usr; 0 prp; 1-6 aty) % 181.25/181.42 % Number of functors : 383 ( 383 usr; 58 con; 0-7 aty) % 181.25/181.42 % Number of variables : 16742 (16601 !; 141 ?) % 181.25/181.42 % SPC : FOF_CAX_RFO_SEQ % 181.25/181.42 % 181.25/181.42 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 181.25/181.42 % 2011-03-01 11:33:15 % 181.25/181.42 %------------------------------------------------------------------------------ % 181.25/181.42 %----Relevant facts (4987) % 181.25/181.42 fof(fact_ext,axiom, % 181.25/181.42 ! [V_g_2,V_f_2] : % 181.25/181.42 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 181.25/181.42 => V_f_2 = V_g_2 ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_empty,axiom, % 181.25/181.42 ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ). % 181.25/181.42 % 181.25/181.42 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 181.25/181.42 ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ). % 181.25/181.42 % 181.25/181.42 fof(fact_triple_Oinject,axiom, % 181.25/181.42 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] : % 181.25/181.42 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 181.25/181.42 <=> ( V_fun1_2 = V_fun1_H_2 % 181.25/181.42 & V_com_2 = V_com_H_2 % 181.25/181.42 & V_fun2_2 = V_fun2_H_2 ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_cut,axiom, % 181.25/181.42 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] : % 181.25/181.42 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) % 181.25/181.42 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2) % 181.25/181.42 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_hoare__derivs_Oinsert,axiom, % 181.25/181.42 ! [V_ts_2,V_t_2,V_Ga_2,T_b] : % 181.25/181.42 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.42 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) % 181.25/181.42 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_image__eqI,axiom, % 181.25/181.42 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] : % 181.25/181.42 ( V_b_2 = hAPP(V_f_2,V_x_2) % 181.25/181.42 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 181.25/181.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insertE,axiom, % 181.25/181.42 ! [V_A_2,V_b_2,V_a_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) % 181.25/181.42 => ( V_a_2 != V_b_2 % 181.25/181.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insertCI,axiom, % 181.25/181.42 ! [V_b_2,V_B_2,V_a_2,T_b] : % 181.25/181.42 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 181.25/181.42 => V_a_2 = V_b_2 ) % 181.25/181.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_emptyE,axiom, % 181.25/181.42 ! [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)))) ). % 181.25/181.42 % 181.25/181.42 fof(fact_image__constant,axiom, % 181.25/181.42 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.42 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_image__constant__conv,axiom, % 181.25/181.42 ! [V_c_2,T_c,T_b,V_A_2] : % 181.25/181.42 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.42 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 181.25/181.42 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.42 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insert__image,axiom, % 181.25/181.42 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.42 => 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) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_singleton__iff,axiom, % 181.25/181.42 ! [V_a_2,V_b_2,T_b] : % 181.25/181.42 ( 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))))) % 181.25/181.42 <=> V_b_2 = V_a_2 ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_singletonE,axiom, % 181.25/181.42 ! [V_a_2,V_b_2,T_b] : % 181.25/181.42 ( 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))))) % 181.25/181.42 => V_b_2 = V_a_2 ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_equalityCE,axiom, % 181.25/181.42 ! [V_c_2,T_b,V_B_2,V_A_2] : % 181.25/181.42 ( V_A_2 = V_B_2 % 181.25/181.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.42 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) % 181.25/181.42 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_bot__fun__def,axiom, % 181.25/181.42 ! [V_x_2,T_c,T_b] : % 181.25/181.42 ( class_Orderings_Obot(T_b) % 181.25/181.42 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_triple_Orecs,axiom, % 181.25/181.42 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 181.25/181.42 % 181.25/181.42 fof(fact_eq__mem__trans,axiom, % 181.25/181.42 ! [V_A_2,T_b,V_b_2,V_a_2] : % 181.25/181.42 ( V_a_2 = V_b_2 % 181.25/181.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 181.25/181.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_eqelem__imp__iff,axiom, % 181.25/181.42 ! [V_A_2,T_b,V_y_2,V_x_2] : % 181.25/181.42 ( V_x_2 = V_y_2 % 181.25/181.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.42 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_eqset__imp__iff,axiom, % 181.25/181.42 ! [V_x_2,T_b,V_B_2,V_A_2] : % 181.25/181.42 ( V_A_2 = V_B_2 % 181.25/181.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.42 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_mem__def,axiom, % 181.25/181.42 ! [V_A_2,V_x_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.42 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insert__code,axiom, % 181.25/181.42 ! [V_x_2,V_A_2,V_y_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) % 181.25/181.42 <=> ( V_y_2 = V_x_2 % 181.25/181.42 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insert__commute,axiom, % 181.25/181.42 ! [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)) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insert__absorb2,axiom, % 181.25/181.42 ! [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) ). % 181.25/181.42 % 181.25/181.42 fof(fact_image__image,axiom, % 181.25/181.42 ! [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) ). % 181.25/181.42 % 181.25/181.42 fof(fact_equals0D,axiom, % 181.25/181.42 ! [V_a_2,T_b,V_A_2] : % 181.25/181.42 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.42 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_empty__iff,axiom, % 181.25/181.42 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 181.25/181.42 % 181.25/181.42 fof(fact_ex__in__conv,axiom, % 181.25/181.42 ! [V_A_2,T_b] : % 181.25/181.42 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.42 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_all__not__in__conv,axiom, % 181.25/181.42 ! [V_A_2,T_b] : % 181.25/181.42 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.42 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insert__absorb,axiom, % 181.25/181.42 ! [V_A_2,V_a_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.42 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insertI2,axiom, % 181.25/181.42 ! [V_b_2,V_B_2,V_a_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 181.25/181.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insert__ident,axiom, % 181.25/181.42 ! [V_B_2,V_A_2,V_x_2,T_b] : % 181.25/181.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 181.25/181.42 => ( 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) % 181.25/181.42 <=> V_A_2 = V_B_2 ) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insert__iff,axiom, % 181.25/181.42 ! [V_A_2,V_b_2,V_a_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) % 181.25/181.42 <=> ( V_a_2 = V_b_2 % 181.25/181.42 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_insertI1,axiom, % 181.25/181.42 ! [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))) ). % 181.25/181.42 % 181.25/181.42 fof(fact_bot__apply,axiom, % 181.25/181.42 ! [V_x_2,T_c,T_b] : % 181.25/181.42 ( class_Orderings_Obot(T_b) % 181.25/181.42 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_rev__image__eqI,axiom, % 181.25/181.42 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.42 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 181.25/181.42 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_imageI,axiom, % 181.25/181.42 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.42 => 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))) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_image__iff,axiom, % 181.25/181.42 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 181.25/181.42 <=> ? [B_x] : % 181.25/181.42 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.42 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_singleton__inject,axiom, % 181.25/181.42 ! [V_b_2,V_a_2,T_b] : % 181.25/181.42 ( 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))) % 181.25/181.42 => V_a_2 = V_b_2 ) ). % 181.25/181.42 % 181.25/181.42 fof(fact_doubleton__eq__iff,axiom, % 181.25/181.42 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.42 ( 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_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 181.25/181.43 <=> ( ( V_a_2 = V_c_2 % 181.25/181.43 & V_b_2 = V_d_2 ) % 181.25/181.43 | ( V_a_2 = V_d_2 % 181.25/181.43 & V_b_2 = V_c_2 ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_insert__not__empty,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_empty__not__insert,axiom, % 181.25/181.43 ! [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) ). % 181.25/181.43 % 181.25/181.43 fof(fact_image__is__empty,axiom, % 181.25/181.43 ! [V_A_2,V_f_2,T_b,T_c] : % 181.25/181.43 ( 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)) % 181.25/181.43 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_image__empty,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_empty__is__image,axiom, % 181.25/181.43 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( 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) % 181.25/181.43 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_image__insert,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_the__elem__eq,axiom, % 181.25/181.43 ! [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 ). % 181.25/181.43 % 181.25/181.43 fof(fact_triple_Osimps_I2_J,axiom, % 181.25/181.43 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_bot__empty__eq,axiom, % 181.25/181.43 ! [V_x_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) % 181.25/181.43 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 181.25/181.43 ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_hoare__derivs_OSkip,axiom, % 181.25/181.43 ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_conseq1,axiom, % 181.25/181.43 ! [V_Pa_2,V_Qa_2,V_c_2,V_P_H_2,V_Ga_2,T_b] : % 181.25/181.43 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.43 => ( ! [B_Z,B_s] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 181.25/181.43 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 181.25/181.43 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_conseq2,axiom, % 181.25/181.43 ! [V_Qa_2,V_Q_H_2,V_c_2,V_Pa_2,V_Ga_2,T_b] : % 181.25/181.43 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.43 => ( ! [B_Z,B_s] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 181.25/181.43 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s)) ) % 181.25/181.43 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Comp,axiom, % 181.25/181.43 ! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_2,V_Ga_2,T_b] : % 181.25/181.43 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.43 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Qa_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.43 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_image__ident,axiom, % 181.25/181.43 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 181.25/181.43 % 181.25/181.43 fof(fact_pred__equals__eq,axiom, % 181.25/181.43 ! [V_S_2,V_R_2,T_b] : % 181.25/181.43 ( 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) % 181.25/181.43 <=> V_R_2 = V_S_2 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I6_J,axiom, % 181.25/181.43 ! [V_pname_H_2,V_pname_2] : % 181.25/181.43 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 181.25/181.43 <=> V_pname_2 = V_pname_H_2 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_imageE,axiom, % 181.25/181.43 ! [V_A_2,V_f_2,T_c,V_b_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 181.25/181.43 => ~ ! [B_x] : % 181.25/181.43 ( V_b_2 = hAPP(V_f_2,B_x) % 181.25/181.43 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I3_J,axiom, % 181.25/181.43 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 181.25/181.43 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 181.25/181.43 <=> ( V_com1_2 = V_com1_H_2 % 181.25/181.43 & V_com2_2 = V_com2_H_2 ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I13_J,axiom, % 181.25/181.43 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I12_J,axiom, % 181.25/181.43 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I49_J,axiom, % 181.25/181.43 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I48_J,axiom, % 181.25/181.43 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I18_J,axiom, % 181.25/181.43 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I19_J,axiom, % 181.25/181.43 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 181.25/181.43 % 181.25/181.43 fof(fact_eq__mem,axiom, % 181.25/181.43 ! [V_y_2,V_x_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) % 181.25/181.43 <=> V_x_2 = V_y_2 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_the__elem__def,axiom, % 181.25/181.43 ! [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))))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_override__on__def,axiom, % 181.25/181.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 181.25/181.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.43 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) % 181.25/181.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.43 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_override__on__emptyset,axiom, % 181.25/181.43 ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2 ). % 181.25/181.43 % 181.25/181.43 fof(fact_override__on__apply__notin,axiom, % 181.25/181.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 181.25/181.43 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.43 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_override__on__apply__in,axiom, % 181.25/181.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.43 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimage__singleton__eq,axiom, % 181.25/181.43 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] : % 181.25/181.43 ( 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)))))) % 181.25/181.43 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Diff__insert__absorb,axiom, % 181.25/181.43 ! [V_A_2,V_x_2,T_b] : % 181.25/181.43 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.43 => 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 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_insert__Diff,axiom, % 181.25/181.43 ! [V_A_2,V_a_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.43 => 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 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_swap__image__eq,axiom, % 181.25/181.43 ! [V_f_2,T_c,V_b_2,V_A_2,V_a_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 181.25/181.43 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,V_f_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_conseq12,axiom, % 181.25/181.43 ! [V_Qa_2,V_Pa_2,V_Q_H_2,V_c_2,V_P_H_2,V_Ga_2,T_b] : % 181.25/181.43 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.43 => ( ! [B_Z,B_s] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 181.25/181.43 => ! [B_s_H] : % 181.25/181.43 ( ! [B_Z_H] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s)) % 181.25/181.43 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) ) % 181.25/181.43 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) % 181.25/181.43 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Ass,axiom, % 181.25/181.43 ! [V_a_2,V_X_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_hoare__derivs_Oequations_I8_J,axiom, % 181.25/181.43 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_DiffE,axiom, % 181.25/181.43 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.43 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_DiffI,axiom, % 181.25/181.43 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimageI,axiom, % 181.25/181.43 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] : % 181.25/181.43 ( hAPP(V_f_2,V_a_2) = V_b_2 % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_swap__triple,axiom, % 181.25/181.43 ! [V_f_2,T_c,T_b,V_b_2,V_c_2,V_a_2] : % 181.25/181.43 ( V_a_2 != V_c_2 % 181.25/181.43 => ( V_b_2 != V_c_2 % 181.25/181.43 => c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,c_Fun_Oswap(T_b,T_c,V_b_2,V_c_2,c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,V_f_2))) = c_Fun_Oswap(T_b,T_c,V_a_2,V_c_2,V_f_2) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_swap__nilpotent,axiom, % 181.25/181.43 ! [V_f_2,V_b_2,V_a_2,T_c,T_b] : c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,V_f_2)) = V_f_2 ). % 181.25/181.43 % 181.25/181.43 fof(fact_swap__commute,axiom, % 181.25/181.43 ! [V_f_2,V_b_2,V_a_2,T_c,T_b] : c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,V_f_2) = c_Fun_Oswap(T_b,T_c,V_b_2,V_a_2,V_f_2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_swap__self,axiom, % 181.25/181.43 ! [V_f_2,V_a_2,T_c,T_b] : c_Fun_Oswap(T_b,T_c,V_a_2,V_a_2,V_f_2) = V_f_2 ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I1_J,axiom, % 181.25/181.43 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] : % 181.25/181.43 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) % 181.25/181.43 <=> ( V_vname_2 = V_vname_H_2 % 181.25/181.43 & V_fun_2 = V_fun_H_2 ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimage__code,axiom, % 181.25/181.43 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) % 181.25/181.43 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Diff__idemp,axiom, % 181.25/181.43 ! [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) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimage__Diff,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimage__ident,axiom, % 181.25/181.43 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 181.25/181.43 % 181.25/181.43 fof(fact_DiffD2,axiom, % 181.25/181.43 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.43 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_DiffD1,axiom, % 181.25/181.43 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Diff__iff,axiom, % 181.25/181.43 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.43 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.43 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimageI2,axiom, % 181.25/181.43 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimageD,axiom, % 181.25/181.43 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimage__eq,axiom, % 181.25/181.43 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 181.25/181.43 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Diff__cancel,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Diff__empty,axiom, % 181.25/181.43 ! [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 ). % 181.25/181.43 % 181.25/181.43 fof(fact_empty__Diff,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimage__empty,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I30_J,axiom, % 181.25/181.43 ! [V_pname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I31_J,axiom, % 181.25/181.43 ! [V_fun_2,V_vname_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I24_J,axiom, % 181.25/181.43 ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I25_J,axiom, % 181.25/181.43 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I8_J,axiom, % 181.25/181.43 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_com_Osimps_I9_J,axiom, % 181.25/181.43 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 181.25/181.43 % 181.25/181.43 fof(fact_insert__Diff1,axiom, % 181.25/181.43 ! [V_A_2,V_B_2,V_x_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 181.25/181.43 => 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) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_insert__Diff__if,axiom, % 181.25/181.43 ! [V_A_2,V_B_2,V_x_2,T_b] : % 181.25/181.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 181.25/181.43 => 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) ) % 181.25/181.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 181.25/181.43 => 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)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_insert__Diff__single,axiom, % 181.25/181.43 ! [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) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Diff__insert2,axiom, % 181.25/181.43 ! [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) ). % 181.25/181.43 % 181.25/181.43 fof(fact_Diff__insert,axiom, % 181.25/181.43 ! [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)))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__diff__def,axiom, % 181.25/181.43 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 181.25/181.43 ( class_Groups_Ominus(T_b) % 181.25/181.43 => 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)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_minus__apply,axiom, % 181.25/181.43 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 181.25/181.43 ( class_Groups_Ominus(T_b) % 181.25/181.43 => 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)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__image,axiom, % 181.25/181.43 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.43 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(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)))))) ) % 181.25/181.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.43 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(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) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_the__sym__eq__trivial,axiom, % 181.25/181.43 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 181.25/181.43 % 181.25/181.43 fof(fact_the__eq__trivial,axiom, % 181.25/181.43 ! [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 ). % 181.25/181.43 % 181.25/181.43 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 181.25/181.43 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.43 => ( 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) % 181.25/181.43 => 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)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_inj__on__insert,axiom, % 181.25/181.43 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) % 181.25/181.43 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.43 & ~ 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))))))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_the__inv__into__def,axiom, % 181.25/181.43 ! [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))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_diff__single__insert,axiom, % 181.25/181.43 ! [V_B_2,V_x_2,V_A_2,T_b] : % 181.25/181.43 ( 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)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.43 => 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))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_subset__insert__iff,axiom, % 181.25/181.43 ! [V_B_2,V_x_2,V_A_2,T_b] : % 181.25/181.43 ( 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))) % 181.25/181.43 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.43 => 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)) ) % 181.25/181.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimage__const,axiom, % 181.25/181.43 ! [T_c,V_A_2,V_c_2,T_b] : % 181.25/181.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.43 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 181.25/181.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.43 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_vimageE,axiom, % 181.25/181.43 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_order__refl,axiom, % 181.25/181.43 ! [V_x,T_a] : % 181.25/181.43 ( class_Orderings_Opreorder(T_a) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_equalityI,axiom, % 181.25/181.43 ! [V_B_2,V_A_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.43 => V_A_2 = V_B_2 ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_top1I,axiom, % 181.25/181.43 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__triv,axiom, % 181.25/181.43 ! [V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ). % 181.25/181.43 % 181.25/181.43 fof(fact_subsetD,axiom, % 181.25/181.43 ! [V_c_2,V_B_2,V_A_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_UNIV__I,axiom, % 181.25/181.43 ! [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)))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_empty__subsetI,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_inj__on__empty,axiom, % 181.25/181.43 ! [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))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_subset__UNIV,axiom, % 181.25/181.43 ! [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)))) ). % 181.25/181.43 % 181.25/181.43 fof(fact_top__greatest,axiom, % 181.25/181.43 ! [V_x,T_a] : % 181.25/181.43 ( class_Orderings_Otop(T_a) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_subset__refl,axiom, % 181.25/181.43 ! [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)) ). % 181.25/181.43 % 181.25/181.43 fof(fact_top__apply,axiom, % 181.25/181.43 ! [V_x_2,T_c,T_b] : % 181.25/181.43 ( class_Orderings_Otop(T_b) % 181.25/181.43 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_le__fun__def,axiom, % 181.25/181.43 ! [V_g_2,V_f_2,T_b,T_c] : % 181.25/181.43 ( class_Orderings_Oord(T_c) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.25/181.43 <=> ! [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))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_linorder__linear,axiom, % 181.25/181.43 ! [V_y,V_x,T_a] : % 181.25/181.43 ( class_Orderings_Olinorder(T_a) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_set__eq__subset,axiom, % 181.25/181.43 ! [T_b,V_B_2,V_A_2] : % 181.25/181.43 ( V_A_2 = V_B_2 % 181.25/181.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_order__eq__iff,axiom, % 181.25/181.43 ! [V_y_2,V_x_2,T_b] : % 181.25/181.43 ( class_Orderings_Oorder(T_b) % 181.25/181.43 => ( V_x_2 = V_y_2 % 181.25/181.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_equalityD1,axiom, % 181.25/181.43 ! [T_b,V_B_2,V_A_2] : % 181.25/181.43 ( V_A_2 = V_B_2 % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_equalityD2,axiom, % 181.25/181.43 ! [T_b,V_B_2,V_A_2] : % 181.25/181.43 ( V_A_2 = V_B_2 % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_order__eq__refl,axiom, % 181.25/181.43 ! [V_y,V_x,T_a] : % 181.25/181.43 ( class_Orderings_Opreorder(T_a) % 181.25/181.43 => ( V_x = V_y % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_le__funD,axiom, % 181.25/181.43 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 181.25/181.43 ( class_Orderings_Oord(T_c) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.25/181.43 => 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))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_order__antisym__conv,axiom, % 181.25/181.43 ! [V_x_2,V_y_2,T_b] : % 181.25/181.43 ( class_Orderings_Oorder(T_b) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.43 <=> V_x_2 = V_y_2 ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_ord__eq__le__trans,axiom, % 181.25/181.43 ! [V_c,V_b,V_a,T_a] : % 181.25/181.43 ( class_Orderings_Oord(T_a) % 181.25/181.43 => ( V_a = V_b % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_xt1_I3_J,axiom, % 181.25/181.43 ! [V_c,V_b,V_a,T_a] : % 181.25/181.43 ( class_Orderings_Oorder(T_a) % 181.25/181.43 => ( V_a = V_b % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_subset__trans,axiom, % 181.25/181.43 ! [V_C_2,V_B_2,V_A_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_ord__le__eq__trans,axiom, % 181.25/181.43 ! [V_c,V_b,V_a,T_a] : % 181.25/181.43 ( class_Orderings_Oord(T_a) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.43 => ( V_b = V_c % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_xt1_I4_J,axiom, % 181.25/181.43 ! [V_c,V_a,V_b,T_a] : % 181.25/181.43 ( class_Orderings_Oorder(T_a) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 181.25/181.43 => ( V_b = V_c % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_order__antisym,axiom, % 181.25/181.43 ! [V_y,V_x,T_a] : % 181.25/181.43 ( class_Orderings_Oorder(T_a) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.43 => V_x = V_y ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_order__trans,axiom, % 181.25/181.43 ! [V_z,V_y,V_x,T_a] : % 181.25/181.43 ( class_Orderings_Opreorder(T_a) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_xt1_I5_J,axiom, % 181.25/181.43 ! [V_x,V_y,T_a] : % 181.25/181.43 ( class_Orderings_Oorder(T_a) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.43 => V_x = V_y ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_xt1_I6_J,axiom, % 181.25/181.43 ! [V_z,V_x,V_y,T_a] : % 181.25/181.43 ( class_Orderings_Oorder(T_a) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_equalityE,axiom, % 181.25/181.43 ! [T_b,V_B_2,V_A_2] : % 181.25/181.43 ( V_A_2 = V_B_2 % 181.25/181.43 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.43 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_le__funE,axiom, % 181.25/181.43 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 181.25/181.43 ( class_Orderings_Oord(T_c) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.25/181.43 => 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))) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_linorder__le__cases,axiom, % 181.25/181.43 ! [V_y,V_x,T_a] : % 181.25/181.43 ( class_Orderings_Olinorder(T_a) % 181.25/181.43 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_inj__on__def,axiom, % 181.25/181.43 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.43 <=> ! [B_x] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.43 => ! [B_xa] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 181.25/181.43 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 181.25/181.43 => B_x = B_xa ) ) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__idem__iff,axiom, % 181.25/181.43 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2 % 181.25/181.43 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__upd,axiom, % 181.25/181.43 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__same,axiom, % 181.25/181.43 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__apply,axiom, % 181.25/181.43 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 181.25/181.43 ( ( V_z_2 = V_x_2 % 181.25/181.43 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) % 181.25/181.43 & ( V_z_2 != V_x_2 % 181.25/181.43 => hAPP(hAPP(hAPP(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) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__twist,axiom, % 181.25/181.43 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] : % 181.25/181.43 ( V_a_2 != V_c_2 % 181.25/181.43 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__other,axiom, % 181.25/181.43 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 181.25/181.43 ( V_z_2 != V_x_2 % 181.25/181.43 => hAPP(hAPP(hAPP(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) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_rev__predicate1D,axiom, % 181.25/181.43 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] : % 181.25/181.43 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) % 181.25/181.43 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_inj__fun,axiom, % 181.25/181.43 ! [T_d,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.43 => 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))) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_inj__eq,axiom, % 181.25/181.43 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.43 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 181.25/181.43 <=> V_x_2 = V_y_2 ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_the__inv__f__f,axiom, % 181.25/181.43 ! [V_x_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.43 => 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 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_injD,axiom, % 181.25/181.43 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.43 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 181.25/181.43 => V_x_2 = V_y_2 ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_predicate1D,axiom, % 181.25/181.43 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] : % 181.25/181.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) % 181.25/181.43 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.25/181.43 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_subset__inj__on,axiom, % 181.25/181.43 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 181.25/181.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.43 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_fun__upd__idem,axiom, % 181.25/181.43 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] : % 181.25/181.43 ( hAPP(V_f_2,V_x_2) = V_y_2 % 181.25/181.43 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_inj__image__subset__iff,axiom, % 181.25/181.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.43 => ( 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))) % 181.25/181.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 181.25/181.43 % 181.25/181.43 fof(fact_inj__image__eq__iff,axiom, % 181.25/181.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.43 => ( 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) % 181.25/181.44 <=> V_A_2 = V_B_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__id2,axiom, % 181.25/181.44 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_the__inv__into__f__f,axiom, % 181.25/181.44 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => 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 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_the__inv__into__f__eq,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__the__inv__into,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_the__inv__into__onto,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__subsetI,axiom, % 181.25/181.44 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => ( 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))) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_the__inv__into__into,axiom, % 181.25/181.44 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => 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)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__upd__def,axiom, % 181.25/181.44 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] : % 181.25/181.44 ( ( V_x_2 = V_a_2 % 181.25/181.44 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 ) % 181.25/181.44 & ( V_x_2 != V_a_2 % 181.25/181.44 => hAPP(hAPP(hAPP(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) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_range__ex1__eq,axiom, % 181.25/181.44 ! [V_b_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => ( 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))))) % 181.25/181.44 <=> ? [B_x] : % 181.25/181.44 ( V_b_2 = hAPP(V_f_2,B_x) % 181.25/181.44 & ! [B_y] : % 181.25/181.44 ( V_b_2 = hAPP(V_f_2,B_y) % 181.25/181.44 => B_y = B_x ) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__image__mem__iff,axiom, % 181.25/181.44 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => ( 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))) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__image__set__diff,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 181.25/181.44 => 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)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__set__diff,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__contraD,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( V_x_2 != V_y_2 % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 181.25/181.44 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__iff,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 181.25/181.44 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 181.25/181.44 <=> V_x_2 = V_y_2 ) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__onD,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 181.25/181.44 => V_x_2 = V_y_2 ) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__vimage__image__eq,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__fun__updI,axiom, % 181.25/181.44 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 181.25/181.44 => c_Fun_Oinj__on(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__diff,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__subsetD,axiom, % 181.25/181.44 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => ( 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)) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 181.25/181.44 ! [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) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 181.25/181.44 ! [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) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__singleton,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_f__the__inv__into__f,axiom, % 181.25/181.44 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 181.25/181.44 => 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 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_in__mono,axiom, % 181.25/181.44 ! [V_x_2,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_set__rev__mp,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_x_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_set__mp,axiom, % 181.25/181.44 ! [V_x_2,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bot__least,axiom, % 181.25/181.44 ! [V_x,T_a] : % 181.25/181.44 ( class_Orderings_Obot(T_a) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__empty,axiom, % 181.25/181.44 ! [V_A_2,T_b] : % 181.25/181.44 ( 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)))) % 181.25/181.44 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UNIV__not__empty,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__insertI,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__insertI2,axiom, % 181.25/181.44 ! [V_b_2,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_insert__mono,axiom, % 181.25/181.44 ! [V_a_2,V_D_2,V_C_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__image__iff,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 <=> ? [B_AA] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) % 181.25/181.44 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__mono,axiom, % 181.25/181.44 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Diff__subset,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Diff__mono,axiom, % 181.25/181.44 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_double__diff,axiom, % 181.25/181.44 ! [V_C_2,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 181.25/181.44 => 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 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__mono,axiom, % 181.25/181.44 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__UNIV,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_asm,axiom, % 181.25/181.44 ! [V_Ga_2,V_ts_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2)) % 181.25/181.44 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_weaken,axiom, % 181.25/181.44 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] : % 181.25/181.44 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 181.25/181.44 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__vimage__singleton,axiom, % 181.25/181.44 ! [V_a_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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))))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_pred__subset__eq,axiom, % 181.25/181.44 ! [V_S_2,V_R_2,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_range__composition,axiom, % 181.25/181.44 ! [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)))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_swap__def,axiom, % 181.25/181.44 ! [V_f_2,V_b_2,V_a_2,T_c,T_b] : c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,V_f_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),hAPP(V_f_2,V_b_2))),V_b_2),hAPP(V_f_2,V_a_2)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__swap__iff,axiom, % 181.25/181.44 ! [V_f_2,T_c,V_b_2,V_A_2,V_a_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 181.25/181.44 => ( c_Fun_Oinj__on(T_b,T_c,c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,V_f_2),V_A_2) % 181.25/181.44 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__imp__inj__on__swap,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 181.25/181.44 => c_Fun_Oinj__on(T_b,T_c,c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,V_f_2),V_A_2) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_insert__subset,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_x_2,T_b] : % 181.25/181.44 ( 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)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 181.25/181.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__insert,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_x_2,T_b] : % 181.25/181.44 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => ( 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))) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_rangeI,axiom, % 181.25/181.44 ! [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))))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_range__eqI,axiom, % 181.25/181.44 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] : % 181.25/181.44 ( V_b_2 = hAPP(V_f_2,V_x_2) % 181.25/181.44 => 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))))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__singletonD,axiom, % 181.25/181.44 ! [V_x_2,V_A_2,T_b] : % 181.25/181.44 ( 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))))) % 181.25/181.44 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.44 | 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Diff__UNIV,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__diff__subset,axiom, % 181.25/181.44 ! [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)))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__vimage__subset,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__image__vimage__eq,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__swap__iff,axiom, % 181.25/181.44 ! [V_f_2,V_b_2,V_a_2,T_b,T_c] : % 181.25/181.44 ( hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Oswap(T_c,T_b,V_a_2,V_b_2,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)) % 181.25/181.44 <=> 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__imp__surj__swap,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Oswap(T_c,T_b,V_a_2,V_b_2,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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__iff__surj,axiom, % 181.25/181.44 ! [V_A_H_2,T_c,T_b,V_A_2] : % 181.25/181.44 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.44 => ( ? [B_f] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 181.25/181.44 & 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)) ) % 181.25/181.44 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_flat__lub__def,axiom, % 181.25/181.44 ! [V_b_2,V_A_2,T_b] : % 181.25/181.44 ( ( 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))))) % 181.25/181.44 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 ) % 181.25/181.44 & ( ~ 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))))) % 181.25/181.44 => 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)))))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_iso__tuple__UNIV__I,axiom, % 181.25/181.44 ! [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)))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 181.25/181.44 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] : % 181.25/181.44 ( 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)) % 181.25/181.44 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.44 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 181.25/181.44 | ? [B_x,B_y] : % 181.25/181.44 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 181.25/181.44 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) % 181.25/181.44 & 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) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_diff__eq__diff__less__eq,axiom, % 181.25/181.44 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => ( 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_c_2),V_d_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_psubset__insert__iff,axiom, % 181.25/181.44 ! [V_B_2,V_x_2,V_A_2,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 181.25/181.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 181.25/181.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => 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)) ) % 181.25/181.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__if,axiom, % 181.25/181.44 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] : % 181.25/181.44 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 181.25/181.44 => 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_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 181.25/181.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 181.25/181.44 => 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_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 181.25/181.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 181.25/181.44 => 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_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) % 181.25/181.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 181.25/181.44 => 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_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_rangeE,axiom, % 181.25/181.44 ! [V_f_2,T_c,V_b_2,T_b] : % 181.25/181.44 ( 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))))) % 181.25/181.44 => ~ ! [B_x] : V_b_2 != hAPP(V_f_2,B_x) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__subset__eq,axiom, % 181.25/181.44 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => ( 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)) % 181.25/181.44 <=> 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__image__Compl__subset,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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)))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_the__inv__into__comp,axiom, % 181.25/181.44 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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)) % 181.25/181.44 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 181.25/181.44 => ( 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)))) % 181.25/181.44 => 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) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__uminus,axiom, % 181.25/181.44 ! [V_A_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_ComplI,axiom, % 181.25/181.44 ! [V_A_2,V_c_2,T_b] : % 181.25/181.44 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_compl__eq__compl__iff,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Lattices_Oboolean__algebra(T_b) % 181.25/181.44 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) % 181.25/181.44 <=> V_x_2 = V_y_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_uminus__apply,axiom, % 181.25/181.44 ! [V_x_2,V_A_2,T_c,T_b] : % 181.25/181.44 ( class_Groups_Ouminus(T_b) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_double__compl,axiom, % 181.25/181.44 ! [V_x,T_a] : % 181.25/181.44 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.44 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__Compl__def,axiom, % 181.25/181.44 ! [V_x_2,V_A_2,T_c,T_b] : % 181.25/181.44 ( class_Groups_Ouminus(T_b) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__trans,axiom, % 181.25/181.44 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 181.25/181.44 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2) % 181.25/181.44 => 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) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__comp__iff,axiom, % 181.25/181.44 ! [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] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 181.25/181.44 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2) % 181.25/181.44 <=> 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) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__eq__elim,axiom, % 181.25/181.44 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] : % 181.25/181.44 ( 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_c_2),V_d_2) % 181.25/181.44 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__eq__dest,axiom, % 181.25/181.44 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] : % 181.25/181.44 ( 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_c_2),V_d_2) % 181.25/181.44 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__apply,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__assoc,axiom, % 181.25/181.44 ! [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) ). % 181.25/181.44 % 181.25/181.44 fof(fact_minus__minus,axiom, % 181.25/181.44 ! [V_a,T_a] : % 181.25/181.44 ( class_Groups_Ogroup__add(T_a) % 181.25/181.44 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_equation__minus__iff,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Ogroup__add(T_b) % 181.25/181.44 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 181.25/181.44 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_less__minus__iff,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_K__record__comp,axiom, % 181.25/181.44 ! [V_x_2,V_f_2,V_c_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_c_2)),V_f_2),V_x_2) = V_c_2 ). % 181.25/181.44 % 181.25/181.44 fof(fact_minus__equation__iff,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Ogroup__add(T_b) % 181.25/181.44 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2 % 181.25/181.44 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_minus__less__iff,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_neg__equal__iff__equal,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Ogroup__add(T_b) % 181.25/181.44 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 181.25/181.44 <=> V_a_2 = V_b_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_neg__less__iff__less,axiom, % 181.25/181.44 ! [V_a_2,V_b_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => ( 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))) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__eq__dest__lhs,axiom, % 181.25/181.44 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] : % 181.25/181.44 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2 % 181.25/181.44 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__cases,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Olinorder(T_a) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => ( V_x != V_y % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__asym,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_xt1_I10_J,axiom, % 181.25/181.44 ! [V_z,V_x,V_y,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__trans,axiom, % 181.25/181.44 ! [V_z,V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_xt1_I2_J,axiom, % 181.25/181.44 ! [V_c,V_a,V_b,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 181.25/181.44 => ( V_b = V_c % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_ord__less__eq__trans,axiom, % 181.25/181.44 ! [V_c,V_b,V_a,T_a] : % 181.25/181.44 ( class_Orderings_Oord(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.44 => ( V_b = V_c % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_psubset__trans,axiom, % 181.25/181.44 ! [V_C_2,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_xt1_I1_J,axiom, % 181.25/181.44 ! [V_c,V_b,V_a,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( V_a = V_b % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_ord__eq__less__trans,axiom, % 181.25/181.44 ! [V_c,V_b,V_a,T_a] : % 181.25/181.44 ( class_Orderings_Oord(T_a) % 181.25/181.44 => ( V_a = V_b % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_xt1_I9_J,axiom, % 181.25/181.44 ! [V_a,V_b,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__asym_H,axiom, % 181.25/181.44 ! [V_b,V_a,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__imp__not__eq2,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => V_y != V_x ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__imp__not__eq,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => V_x != V_y ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__imp__not__less,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__not__sym,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_less__imp__neq,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => V_x != V_y ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__neqE,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Olinorder(T_a) % 181.25/181.44 => ( V_x != V_y % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__antisym__conv3,axiom, % 181.25/181.44 ! [V_x_2,V_y_2,T_b] : % 181.25/181.44 ( class_Orderings_Olinorder(T_b) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> V_x_2 = V_y_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Compl__eq__Compl__iff,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( 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) % 181.25/181.44 <=> V_A_2 = V_B_2 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__less__linear,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Olinorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 | V_x = V_y % 181.25/181.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_not__less__iff__gr__or__eq,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Olinorder(T_b) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 181.25/181.44 | V_x_2 = V_y_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__neq__iff,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Olinorder(T_b) % 181.25/181.44 => ( V_x_2 != V_y_2 % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_double__complement,axiom, % 181.25/181.44 ! [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 ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__irrefl,axiom, % 181.25/181.44 ! [V_x,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__comp,axiom, % 181.25/181.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => ( 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))) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__def,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_le__minus__iff,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => ( 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))) % 181.25/181.44 <=> 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_minus__le__iff,axiom, % 181.25/181.44 ! [V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => ( 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)) % 181.25/181.44 <=> 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_neg__le__iff__le,axiom, % 181.25/181.44 ! [V_a_2,V_b_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => ( 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))) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_le__imp__neg__le,axiom, % 181.25/181.44 ! [V_b,V_a,T_a] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_minus__diff__eq,axiom, % 181.25/181.44 ! [V_b,V_a,T_a] : % 181.25/181.44 ( class_Groups_Oab__group__add(T_a) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_diff__eq__diff__less,axiom, % 181.25/181.44 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.44 => ( 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_c_2),V_d_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__comp__iff2,axiom, % 181.25/181.44 ! [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] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2) % 181.25/181.44 => ( 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)) % 181.25/181.44 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2) % 181.25/181.44 <=> 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) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__image__Compl__eq,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__compose,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_compl__le__compl__iff,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Lattices_Oboolean__algebra(T_b) % 181.25/181.44 => ( 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))) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_compl__mono,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__imageI2,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] : % 181.25/181.44 ( 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) % 181.25/181.44 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_ComplE,axiom, % 181.25/181.44 ! [V_A_2,V_c_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_ComplD,axiom, % 181.25/181.44 ! [V_A_2,V_c_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Compl__iff,axiom, % 181.25/181.44 ! [V_A_2,V_c_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 181.25/181.44 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__empty2,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__empty1,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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) % 181.25/181.44 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_less__fun__def,axiom, % 181.25/181.44 ! [V_g_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( class_Orderings_Oord(T_c) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.25/181.44 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Compl__anti__mono,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Compl__subset__Compl__iff,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_xt1_I8_J,axiom, % 181.25/181.44 ! [V_z,V_x,V_y,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__le__less__trans,axiom, % 181.25/181.44 ! [V_z,V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_xt1_I7_J,axiom, % 181.25/181.44 ! [V_z,V_x,V_y,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__le__trans,axiom, % 181.25/181.44 ! [V_z,V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_xt1_I11_J,axiom, % 181.25/181.44 ! [V_a,V_b,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 181.25/181.44 => ( V_a != V_b % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__le__neq__trans,axiom, % 181.25/181.44 ! [V_b,V_a,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.44 => ( V_a != V_b % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__le__imp__less__or__eq,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 | V_x = V_y ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__antisym__conv2,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Olinorder(T_b) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> V_x_2 = V_y_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__imp__le,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Opreorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_leD,axiom, % 181.25/181.44 ! [V_x,V_y,T_a] : % 181.25/181.44 ( class_Orderings_Olinorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_xt1_I12_J,axiom, % 181.25/181.44 ! [V_b,V_a,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( V_a != V_b % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__neq__le__trans,axiom, % 181.25/181.44 ! [V_b,V_a,T_a] : % 181.25/181.44 ( class_Orderings_Oorder(T_a) % 181.25/181.44 => ( V_a != V_b % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__antisym__conv1,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Olinorder(T_b) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> V_x_2 = V_y_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_not__leE,axiom, % 181.25/181.44 ! [V_x,V_y,T_a] : % 181.25/181.44 ( class_Orderings_Olinorder(T_a) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_leI,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Olinorder(T_a) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__le__less,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Oorder(T_b) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 | V_x_2 = V_y_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_less__le__not__le,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Opreorder(T_b) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.44 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_order__less__le,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Oorder(T_b) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.44 & V_x_2 != V_y_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__le__less__linear,axiom, % 181.25/181.44 ! [V_y,V_x,T_a] : % 181.25/181.44 ( class_Orderings_Olinorder(T_a) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__not__le,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Olinorder(T_b) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_linorder__not__less,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,T_b] : % 181.25/181.44 ( class_Orderings_Olinorder(T_b) % 181.25/181.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 181.25/181.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_psubsetD,axiom, % 181.25/181.44 ! [V_c_2,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__upd__comp,axiom, % 181.25/181.44 ! [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),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_d),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__compose,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__imp__inj__on,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 181.25/181.44 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_not__psubset__empty,axiom, % 181.25/181.44 ! [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)))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__psubset__trans,axiom, % 181.25/181.44 ! [V_C_2,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_psubset__subset__trans,axiom, % 181.25/181.44 ! [V_C_2,V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_psubset__imp__subset,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__iff__psubset__eq,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 | V_A_2 = V_B_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_psubset__eq,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 & V_A_2 != V_B_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__Compl,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_comp__swap,axiom, % 181.25/181.44 ! [V_g_2,V_b_2,V_a_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_Oswap(T_b,T_d,V_a_2,V_b_2,V_g_2)) = c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__the__inv__into,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_comp__surj,axiom, % 181.25/181.44 ! [V_g_2,T_d,V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => ( 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)) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__comp,axiom, % 181.25/181.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__imageI,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] : % 181.25/181.44 ( 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) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_comp__inj__on,axiom, % 181.25/181.44 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( 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)) % 181.25/181.44 => 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) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_comp__inj__on__iff,axiom, % 181.25/181.44 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( 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)) % 181.25/181.44 <=> 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) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_compl__top__eq,axiom, % 181.25/181.44 ! [T_a] : % 181.25/181.44 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.44 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_compl__bot__eq,axiom, % 181.25/181.44 ! [T_a] : % 181.25/181.44 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.44 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subset__Compl__self__eq,axiom, % 181.25/181.44 ! [V_A_2,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Compl__empty__eq,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Compl__UNIV__eq,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__subset,axiom, % 181.25/181.44 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.44 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2 % 181.25/181.44 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__imp__surj,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__is__surj,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Compl__eq__Diff__UNIV,axiom, % 181.25/181.44 ! [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) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__is__inj,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__imp__bij__betw,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__def,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 181.25/181.44 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__strict__subset,axiom, % 181.25/181.44 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__swap__iff,axiom, % 181.25/181.44 ! [V_B_2,V_f_2,T_c,V_y_2,V_A_2,V_x_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 181.25/181.44 => ( c_Fun_Obij__betw(T_b,T_c,c_Fun_Oswap(T_b,T_c,V_x_2,V_y_2,V_f_2),V_A_2,V_B_2) % 181.25/181.44 <=> c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__swap__iff,axiom, % 181.25/181.44 ! [V_f_2,V_b_2,V_a_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,c_Fun_Oswap(T_b,T_c,V_a_2,V_b_2,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 181.25/181.44 <=> 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__Compl__image__subset,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => 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)))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__def,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 & 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bijI,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => ( 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)) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_diff__eq__diff__eq,axiom, % 181.25/181.44 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.44 ( class_Groups_Oab__group__add(T_b) % 181.25/181.44 => ( 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_c_2),V_d_2) % 181.25/181.44 => ( V_a_2 = V_b_2 % 181.25/181.44 <=> V_c_2 = V_d_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Cantor__Bernstein,axiom, % 181.25/181.44 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( 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)) % 181.25/181.44 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 181.25/181.44 => ( 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)) % 181.25/181.44 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__vimage__eq__inv__image,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__into__comp,axiom, % 181.25/181.44 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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)) % 181.25/181.44 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 181.25/181.44 => ( 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)))) % 181.25/181.44 => 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) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_mk__less__def,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_R_2,T_b] : % 181.25/181.44 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 181.25/181.44 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_psubset__imp__ex__mem,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => ? [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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__subsetI,axiom, % 181.25/181.44 ! [V_B_2,V_f_2,T_c,V_A_2,T_b] : % 181.25/181.44 ( ! [B_x] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,B_x)),V_B_2)) ) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_quotient__diff1,axiom, % 181.25/181.44 ! [V_a_2,V_A_2,V_r_2,T_b] : % 181.25/181.44 ( 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) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_hoare__derivs_OIf,axiom, % 181.25/181.44 ! [V_d_2,V_Qa_2,V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_b] : % 181.25/181.44 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.44 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.44 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Loop,axiom, % 181.25/181.44 ! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_b] : % 181.25/181.44 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 181.25/181.44 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_comp__cong,axiom, % 181.25/181.44 ! [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] : % 181.25/181.44 ( 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)) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__inv__distrib,axiom, % 181.25/181.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => ( 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))) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I53_J,axiom, % 181.25/181.44 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I52_J,axiom, % 181.25/181.44 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I5_J,axiom, % 181.25/181.44 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 181.25/181.44 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 181.25/181.44 <=> ( V_fun_2 = V_fun_H_2 % 181.25/181.44 & V_com_2 = V_com_H_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I4_J,axiom, % 181.25/181.44 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 181.25/181.44 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) % 181.25/181.44 <=> ( V_fun_2 = V_fun_H_2 % 181.25/181.44 & V_com1_2 = V_com1_H_2 % 181.25/181.44 & V_com2_2 = V_com2_H_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_quotient__empty,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_quotient__is__empty2,axiom, % 181.25/181.44 ! [V_r_2,V_A_2,T_b] : % 181.25/181.44 ( 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) % 181.25/181.44 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_quotient__is__empty,axiom, % 181.25/181.44 ! [V_r_2,V_A_2,T_b] : % 181.25/181.44 ( 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)) % 181.25/181.44 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__inv__into,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I59_J,axiom, % 181.25/181.44 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I58_J,axiom, % 181.25/181.44 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_peek__and__def,axiom, % 181.25/181.44 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) % 181.25/181.44 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) % 181.25/181.44 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I28_J,axiom, % 181.25/181.44 ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I29_J,axiom, % 181.25/181.44 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I47_J,axiom, % 181.25/181.44 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I46_J,axiom, % 181.25/181.44 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I17_J,axiom, % 181.25/181.44 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I16_J,axiom, % 181.25/181.44 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I55_J,axiom, % 181.25/181.44 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I54_J,axiom, % 181.25/181.44 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I26_J,axiom, % 181.25/181.44 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I27_J,axiom, % 181.25/181.44 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I45_J,axiom, % 181.25/181.44 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I44_J,axiom, % 181.25/181.44 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I15_J,axiom, % 181.25/181.44 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ). % 181.25/181.44 % 181.25/181.44 fof(fact_com_Osimps_I14_J,axiom, % 181.25/181.44 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_f__inv__into__f,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__into__into,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__into__injective,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] : % 181.25/181.44 ( 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) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 181.25/181.44 => V_x_2 = V_y_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__into__f__f,axiom, % 181.25/181.44 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => 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 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__into__f__eq,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 181.25/181.44 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__inv__into__cancel,axiom, % 181.25/181.44 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2)) % 181.25/181.44 => 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 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__iff__all,axiom, % 181.25/181.44 ! [V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 <=> ! [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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__f__inv__f,axiom, % 181.25/181.44 ! [V_y_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__surj__f__inv__f,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__f__eq,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 181.25/181.44 => 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 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__f__f,axiom, % 181.25/181.44 ! [V_x_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__into__inv__into__eq,axiom, % 181.25/181.44 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => 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) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__inv__eq,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__imp__bij__inv,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__into__image__cancel,axiom, % 181.25/181.44 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2)) % 181.25/181.44 => 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 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__inv__into,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__imp__surj__inv,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__inv__f__f,axiom, % 181.25/181.44 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__image__comp,axiom, % 181.25/181.44 ! [V_X_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__imp__inj__inv,axiom, % 181.25/181.44 ! [V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__inv__o__cancel,axiom, % 181.25/181.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__transfer,axiom, % 181.25/181.44 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => ( ! [B_y] : % 181.25/181.44 ( 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))))) % 181.25/181.44 => 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))) ) % 181.25/181.44 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__o__cancel,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__iff,axiom, % 181.25/181.44 ! [V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 <=> 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__iff,axiom, % 181.25/181.44 ! [V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 <=> 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__image__Collect__eq,axiom, % 181.25/181.44 ! [V_Pa_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_quotientI,axiom, % 181.25/181.44 ! [V_r_2,V_A_2,V_x_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__imp__inv__eq,axiom, % 181.25/181.44 ! [V_g_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.44 => ( ! [B_x] : hAPP(V_f_2,hAPP(V_g_2,B_x)) = B_x % 181.25/181.44 => 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_g_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__def,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__imp__inv__eq,axiom, % 181.25/181.44 ! [V_g_2,V_f_2,T_b,T_c] : % 181.25/181.44 ( 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)) % 181.25/181.44 => ( ! [B_x] : hAPP(V_g_2,hAPP(V_f_2,B_x)) = B_x % 181.25/181.44 => 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_g_2 ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__into__def,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__id,axiom, % 181.25/181.44 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_CollectI,axiom, % 181.25/181.44 ! [T_b,V_a_2,V_Pa_2] : % 181.25/181.44 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_id__apply,axiom, % 181.25/181.44 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 181.25/181.44 % 181.25/181.44 fof(fact_Collect__def,axiom, % 181.25/181.44 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ). % 181.25/181.44 % 181.25/181.44 fof(fact_someI,axiom, % 181.25/181.44 ! [T_b,V_x_2,V_Pa_2] : % 181.25/181.44 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.25/181.44 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_tfl__some,axiom, % 181.25/181.44 ! [T_b,B_P] : % 181.25/181.44 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 181.25/181.44 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_id__def,axiom, % 181.25/181.44 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 181.25/181.44 % 181.25/181.44 fof(fact_some__sym__eq__trivial,axiom, % 181.25/181.44 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 181.25/181.44 % 181.25/181.44 fof(fact_some__eq__trivial,axiom, % 181.25/181.44 ! [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 ). % 181.25/181.44 % 181.25/181.44 fof(fact_some__eq__ex,axiom, % 181.25/181.44 ! [T_b,V_Pa_2] : % 181.25/181.44 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) % 181.25/181.44 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_someI__ex,axiom, % 181.25/181.44 ! [T_b,V_Pa_2] : % 181.25/181.44 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 181.25/181.44 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Collect__empty__eq,axiom, % 181.25/181.44 ! [V_Pa_2,T_b] : % 181.25/181.44 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.44 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_empty__Collect__eq,axiom, % 181.25/181.44 ! [V_Pa_2,T_b] : % 181.25/181.44 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) % 181.25/181.44 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__id,axiom, % 181.25/181.44 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__id,axiom, % 181.25/181.44 ! [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 ). % 181.25/181.44 % 181.25/181.44 fof(fact_id__o,axiom, % 181.25/181.44 ! [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 ). % 181.25/181.44 % 181.25/181.44 fof(fact_o__eq__id__dest,axiom, % 181.25/181.44 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] : % 181.25/181.44 ( 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_c_2) % 181.25/181.44 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inj__on__id,axiom, % 181.25/181.44 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__betw__id__iff,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2) % 181.25/181.44 <=> V_A_2 = V_B_2 ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__id,axiom, % 181.25/181.44 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ). % 181.25/181.44 % 181.25/181.44 fof(fact_CollectE,axiom, % 181.25/181.44 ! [V_Pa_2,V_a_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 181.25/181.44 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_CollectD,axiom, % 181.25/181.44 ! [V_Pa_2,V_a_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 181.25/181.44 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_mem__Collect__eq,axiom, % 181.25/181.44 ! [V_Pa_2,V_a_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 181.25/181.44 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Collect__mem__eq,axiom, % 181.25/181.44 ! [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 ). % 181.25/181.44 % 181.25/181.44 fof(fact_empty__def,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_insert__Collect,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UNIV__def,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Collect__neg__eq,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__Collect__eq,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_insert__compr__raw,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_insert__compr,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_surj__id,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Collect__conv__if,axiom, % 181.25/181.44 ! [T_b,V_a_2,V_Pa_2] : % 181.25/181.44 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 181.25/181.44 => 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))) ) % 181.25/181.44 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Collect__conv__if2,axiom, % 181.25/181.44 ! [T_b,V_a_2,V_Pa_2] : % 181.25/181.44 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 181.25/181.44 => 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))) ) % 181.25/181.44 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_singleton__conv,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_singleton__conv2,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_set__diff__eq,axiom, % 181.25/181.44 ! [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)))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Compl__eq,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_bij__id,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__def,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_inv__id,axiom, % 181.25/181.44 ! [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) ). % 181.25/181.44 % 181.25/181.44 fof(fact_singleton__quotient,axiom, % 181.25/181.44 ! [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))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_quotientE,axiom, % 181.25/181.44 ! [V_r_2,V_A_2,V_X_2,T_b] : % 181.25/181.44 ( 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))) % 181.25/181.44 => ~ ! [B_x] : % 181.25/181.44 ( 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)))) % 181.25/181.44 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Image__mono,axiom, % 181.25/181.44 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] : % 181.25/181.44 ( 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)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Image__empty,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_quotient__def,axiom, % 181.25/181.44 ! [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)))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_equiv__class__self,axiom, % 181.25/181.44 ! [V_a_2,V_r_2,V_A_2,T_b] : % 181.25/181.44 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => 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)))))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__left__comm__idem__remove,axiom, % 181.25/181.44 ! [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))))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Powp__mono,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__upd__restrict__conv,axiom, % 181.25/181.44 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 181.25/181.44 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_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),V_y_2) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_restrict__fun__upd,axiom, % 181.25/181.44 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] : % 181.25/181.44 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 181.25/181.44 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_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),V_y_2) ) % 181.25/181.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 181.25/181.44 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_subsetI,axiom, % 181.25/181.44 ! [V_B_2,V_A_2,T_b] : % 181.25/181.44 ( ! [B_x] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) ) % 181.25/181.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_SUP1__I,axiom, % 181.25/181.44 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_less__by__empty,axiom, % 181.25/181.44 ! [V_B_2,T_b,V_A_2] : % 181.25/181.44 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 181.25/181.44 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 181.25/181.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_SUP1__iff,axiom, % 181.25/181.44 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] : % 181.25/181.44 ( 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)) % 181.25/181.44 <=> ? [B_x] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.44 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_restrict__in,axiom, % 181.25/181.44 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.44 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_restrict__map__insert,axiom, % 181.25/181.44 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Image__UN,axiom, % 181.25/181.44 ! [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)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__left__comm__idem__insert,axiom, % 181.25/181.44 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 181.25/181.44 ! [V_x_2,V_f_2,T_c,T_b] : % 181.25/181.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 181.25/181.44 => 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) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__o,axiom, % 181.25/181.44 ! [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) ). % 181.25/181.44 % 181.25/181.44 fof(fact_SUP__UN__eq,axiom, % 181.25/181.44 ! [V_x_2,V_r_2,T_c,T_b] : % 181.25/181.44 ( 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)) % 181.25/181.44 <=> 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_Image__eq__UN,axiom, % 181.25/181.44 ! [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))))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_fun__upd__restrict,axiom, % 181.25/181.44 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_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),V_y_2) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__I,axiom, % 181.25/181.44 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 181.25/181.44 => 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))) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_vimage__eq__UN,axiom, % 181.25/181.44 ! [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))))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_image__eq__UN,axiom, % 181.25/181.44 ! [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)))) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__equiv__class,axiom, % 181.25/181.44 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 181.25/181.44 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.44 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => 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) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__equiv__class2,axiom, % 181.25/181.44 ! [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] : % 181.25/181.44 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 181.25/181.44 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 181.25/181.44 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) % 181.25/181.44 => 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) ) ) ) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__simps_I1_J,axiom, % 181.25/181.44 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 181.25/181.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.44 => 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)) ) % 181.25/181.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__singleton,axiom, % 181.25/181.44 ! [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 ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__extend__simps_I1_J,axiom, % 181.25/181.44 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 181.25/181.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.44 => 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))) ) % 181.25/181.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.44 => 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)) ) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__upper,axiom, % 181.25/181.44 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => 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))) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_UN__insert__distrib,axiom, % 181.25/181.44 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 181.25/181.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 181.25/181.44 => 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)) ) ). % 181.25/181.44 % 181.25/181.44 fof(fact_congruent2__implies__congruent,axiom, % 181.25/181.44 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] : % 181.25/181.44 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) % 181.25/181.44 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 181.25/181.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.44 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ball__UN,axiom, % 181.25/181.45 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] : % 181.25/181.45 ( ! [B_x] : % 181.25/181.45 ( 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))) % 181.25/181.45 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.25/181.45 <=> ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.45 => ! [B_xa] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) % 181.25/181.45 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_SUP__commute,axiom, % 181.25/181.45 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 181.25/181.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__extend__simps_I9_J,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__simps_I9_J,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__UN__flatten,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_congruent2__implies__congruent__UN,axiom, % 181.25/181.45 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 181.25/181.45 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 181.25/181.45 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) % 181.25/181.45 => 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)) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_SUP__le__iff,axiom, % 181.25/181.45 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] : % 181.25/181.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.25/181.45 => ( 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)) % 181.25/181.45 <=> ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__SUP__iff,axiom, % 181.25/181.45 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] : % 181.25/181.45 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.25/181.45 & class_Orderings_Olinorder(T_b) ) % 181.25/181.45 => ( 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))) % 181.25/181.45 <=> ? [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__iff,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] : % 181.25/181.45 ( 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))) % 181.25/181.45 <=> ? [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.45 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_SUP__const,axiom, % 181.25/181.45 ! [V_M_2,T_b,V_A_2,T_c] : % 181.25/181.45 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.25/181.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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 ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UNION__empty__conv_I2_J,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b,T_c] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.45 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__constant,axiom, % 181.25/181.45 ! [V_c_2,T_c,T_b,V_A_2] : % 181.25/181.45 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 181.25/181.45 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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_c_2)) = V_c_2 ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__empty2,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UNION__empty__conv_I1_J,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_c,T_b] : % 181.25/181.45 ( 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) % 181.25/181.45 <=> ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.45 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__subset__iff,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__simps_I10_J,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_image__UN,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__extend__simps_I10_J,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_SUPR__apply,axiom, % 181.25/181.45 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 181.25/181.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__simps_I6_J,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__extend__simps_I6_J,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_vimage__UN,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_SUP__subset,axiom, % 181.25/181.45 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.45 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__SUPI,axiom, % 181.25/181.45 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 181.25/181.45 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__equiv__class__type2,axiom, % 181.25/181.45 ! [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] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 181.25/181.45 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 181.25/181.45 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( ! [B_x1] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) % 181.25/181.45 => ! [B_x2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 181.25/181.45 => 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)) ) ) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__equiv__class__type,axiom, % 181.25/181.45 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 181.25/181.45 => 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)) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_subset__equiv__class,axiom, % 181.25/181.45 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( 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)))))) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 181.25/181.45 => 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)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fun__upd__None__restrict,axiom, % 181.25/181.45 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] : % 181.25/181.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 181.25/181.45 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) % 181.25/181.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 181.25/181.45 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_eq__equiv__class__iff2,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 181.25/181.45 => ( 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) % 181.25/181.45 <=> 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)) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_restrict__complement__singleton__eq,axiom, % 181.25/181.45 ! [V_x_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_c)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equiv__class__subset,axiom, % 181.25/181.45 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( 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)) % 181.25/181.45 => 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)))))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__Pow__subset,axiom, % 181.25/181.45 ! [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)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_eq__equiv__class,axiom, % 181.25/181.45 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] : % 181.25/181.45 ( 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)))) % 181.25/181.45 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 181.25/181.45 => 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)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_SUP2__I,axiom, % 181.25/181.45 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 181.25/181.45 => 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_c_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_PowI,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Cantors__paradox,axiom, % 181.25/181.45 ! [V_A_2,T_b] : % 181.25/181.45 ~ ? [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_pred__equals__eq2,axiom, % 181.25/181.45 ! [V_S_2,V_R_2,T_c,T_b] : % 181.25/181.45 ( 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) % 181.25/181.45 <=> V_R_2 = V_S_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_SUP__UN__eq2,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__UNIV,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_image__Pow__surj,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : % 181.25/181.45 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__top,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_congruentD,axiom, % 181.25/181.45 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 181.25/181.45 => ( 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)) % 181.25/181.45 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_congruent2D,axiom, % 181.25/181.45 ! [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] : % 181.25/181.45 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 181.25/181.45 => ( 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)) % 181.25/181.45 => ( 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)) % 181.25/181.45 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_empty__upd__none,axiom, % 181.25/181.45 ! [V_xa_2,V_x_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2),c_Option_Ooption_ONone(T_b)),V_xa_2) = c_Option_Ooption_ONone(T_b) ). % 181.25/181.45 % 181.25/181.45 fof(fact_pred__subset__eq2,axiom, % 181.25/181.45 ! [V_S_2,V_R_2,T_c,T_b] : % 181.25/181.45 ( 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))) % 181.25/181.45 <=> 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_bot__empty__eq2,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> 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)))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_restrict__map__empty,axiom, % 181.25/181.45 ! [V_x_2,V_D_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_b) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__not__empty,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__def,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Image__iff,axiom, % 181.25/181.45 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 181.25/181.45 <=> ? [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.45 & 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_rev__ImageI,axiom, % 181.25/181.45 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => ( 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)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_restrict__out,axiom, % 181.25/181.45 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__bottom,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__iff,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 181.25/181.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_PowD,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_restrict__map__def,axiom, % 181.25/181.45 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) % 181.25/181.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_restrict__map__to__empty,axiom, % 181.25/181.45 ! [V_x_2,V_m_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_b) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__mono,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_image__Pow__mono,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Image__singleton__iff,axiom, % 181.25/181.45 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] : % 181.25/181.45 ( 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)))))) % 181.25/181.45 <=> 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equiv__class__eq,axiom, % 181.25/181.45 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( 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)) % 181.25/181.45 => 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)))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__empty,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_quotient__eq__iff,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 181.25/181.45 => ( V_X_2 = V_Y_2 % 181.25/181.45 <=> 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)) ) ) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_quotient__eqI,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 181.25/181.45 => ( 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)) % 181.25/181.45 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Image__singleton,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Powp__Pow__eq,axiom, % 181.25/181.45 ! [V_x_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equiv__class__eq__iff,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( 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)) % 181.25/181.45 <=> ( 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)))) % 181.25/181.45 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_eq__equiv__class__iff,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 181.25/181.45 => ( 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)))) % 181.25/181.45 <=> 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)) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_in__rel__def,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) % 181.25/181.45 <=> 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Nitpick_Orefl_H__def,axiom, % 181.25/181.45 ! [V_r_2,T_b] : % 181.25/181.45 ( c_Nitpick_Orefl_H(T_b,V_r_2) % 181.25/181.45 <=> ! [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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__equiv__class__inject,axiom, % 181.25/181.45 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 181.25/181.45 => ( 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) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 => ! [B_y] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 181.25/181.45 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 181.25/181.45 => 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)) ) ) ) % 181.25/181.45 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_irrefl__def,axiom, % 181.25/181.45 ! [V_r_2,T_b] : % 181.25/181.45 ( c_Relation_Oirrefl(T_b,V_r_2) % 181.25/181.45 <=> ! [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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equiv__class__nondisjoint,axiom, % 181.25/181.45 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( 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))))))) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equivp__equiv,axiom, % 181.25/181.45 ! [V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 181.25/181.45 <=> 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ImageE,axiom, % 181.25/181.45 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 181.25/181.45 => ~ ! [B_x] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__fun__upd,axiom, % 181.25/181.45 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] : % 181.25/181.45 ( ( V_y_2 = c_Option_Ooption_ONone(T_b) % 181.25/181.45 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) % 181.25/181.45 & ( V_y_2 != c_Option_Ooption_ONone(T_b) % 181.25/181.45 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ran__empty,axiom, % 181.25/181.45 ! [T_b,T_c] : c_Map_Oran(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf1E,axiom, % 181.25/181.45 ! [V_x_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 181.25/181.45 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf1I,axiom, % 181.25/181.45 ! [T_b,V_B_2,V_x_2,V_A_2] : % 181.25/181.45 ( hBOOL(hAPP(V_A_2,V_x_2)) % 181.25/181.45 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_IntE,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.45 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.45 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_IntI,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_bot2E,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_SUP2__iff,axiom, % 181.25/181.45 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 181.25/181.45 ( 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_c_2)) % 181.25/181.45 <=> ? [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_predicate2D,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_rev__predicate2D,axiom, % 181.25/181.45 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 181.25/181.45 => ( 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)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equivp__transp,axiom, % 181.25/181.45 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equivp__symp,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_R_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equivp__reflp,axiom, % 181.25/181.45 ! [V_x_2,V_R_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_equivp__def,axiom, % 181.25/181.45 ! [V_R_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 181.25/181.45 <=> ! [B_x,B_y] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 181.25/181.45 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_identity__equivp,axiom, % 181.25/181.45 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__apply,axiom, % 181.25/181.45 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( class_Lattices_Olattice(T_b) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__assoc,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__aci_I2_J,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf_Oassoc,axiom, % 181.25/181.45 ! [V_c,V_b,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__left__commute,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__aci_I3_J,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf_Oleft__commute,axiom, % 181.25/181.45 ! [V_c,V_a,V_b,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__left__idem,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__aci_I4_J,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf_Oleft__idem,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__commute,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__aci_I1_J,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf_Ocommute,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__fun__def,axiom, % 181.25/181.45 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( class_Lattices_Olattice(T_b) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__idem,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf_Oidem,axiom, % 181.25/181.45 ! [V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf1D2,axiom, % 181.25/181.45 ! [V_x_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf1D1,axiom, % 181.25/181.45 ! [V_x_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__assoc,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__left__commute,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__left__absorb,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__commute,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__absorb,axiom, % 181.25/181.45 ! [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 ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__Int__eq,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__restrict,axiom, % 181.25/181.45 ! [V_A_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m_2)),V_A_2) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__ord_I1_J,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__le1,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__ord_I2_J,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__le2,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__iff__inf,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,T_b] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_b) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.45 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__inf__iff,axiom, % 181.25/181.45 ! [V_z_2,V_y_2,V_x_2,T_b] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_b) % 181.25/181.45 => ( 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))) % 181.25/181.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__infI1,axiom, % 181.25/181.45 ! [V_b,V_x,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__infI2,axiom, % 181.25/181.45 ! [V_a,V_x,V_b,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__absorb1,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__absorb2,axiom, % 181.25/181.45 ! [V_x,V_y,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__infI,axiom, % 181.25/181.45 ! [V_b,V_a,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 181.25/181.45 => 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))) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__greatest,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 181.25/181.45 => 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))) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__mono,axiom, % 181.25/181.45 ! [V_d,V_b,V_c,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 181.25/181.45 => 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))) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__infE,axiom, % 181.25/181.45 ! [V_b,V_a,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 181.25/181.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__infI2,axiom, % 181.25/181.45 ! [V_a,V_x,V_b,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__infI1,axiom, % 181.25/181.45 ! [V_b,V_x,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__bot__right,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__bot(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__bot__left,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__bot(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__top__left,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__top(T_a) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__top__right,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__top(T_a) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__eq__top__iff,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,T_b] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__top(T_b) % 181.25/181.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) % 181.25/181.45 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b) % 181.25/181.45 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_IntD2,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_IntD1,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__iff,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.45 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_disjoint__iff__not__equal,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 => ! [B_xa] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) % 181.25/181.45 => B_x != B_xa ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__empty__right,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__empty__left,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_insert__inter__insert,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__mono,axiom, % 181.25/181.45 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__greatest,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_C_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__absorb1,axiom, % 181.25/181.45 ! [V_A_2,V_B_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__absorb2,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__lower2,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__lower1,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__UNIV__right,axiom, % 181.25/181.45 ! [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 ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__UNIV__left,axiom, % 181.25/181.45 ! [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 ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__Int2,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__Int__distrib2,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__Diff,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__Int__distrib,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inj__on__Int,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.45 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_vimage__Int,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_restrict__restrict,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fun__left__comm__idem__inf,axiom, % 181.25/181.45 ! [T_b] : % 181.25/181.45 ( class_Lattices_Osemilattice__inf(T_b) % 181.25/181.45 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__Int__eq,axiom, % 181.25/181.45 ! [V_x_2,V_S_2,V_R_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Collect__conj__eq,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__simps_I5_J,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__simps_I4_J,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__extend__simps_I5_J,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__UN__distrib,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__extend__simps_I4_J,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__UN__distrib2,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_compl__inf__bot,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__compl__bot,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__eq,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__insert__left__if1,axiom, % 181.25/181.45 ! [V_B_2,V_C_2,V_a_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__insert__right__if1,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_a_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__insert__left__if0,axiom, % 181.25/181.45 ! [V_B_2,V_C_2,V_a_2,T_b] : % 181.25/181.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__insert__right__if0,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_a_2,T_b] : % 181.25/181.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__insert__left,axiom, % 181.25/181.45 ! [V_B_2,V_C_2,V_a_2,T_b] : % 181.25/181.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 181.25/181.45 => 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)) ) % 181.25/181.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 181.25/181.45 => 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) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__insert__right,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_a_2,T_b] : % 181.25/181.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => 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)) ) % 181.25/181.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => 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) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_image__Int__subset,axiom, % 181.25/181.45 ! [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)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__disjoint,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__triv,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Compl__disjoint,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Compl__disjoint2,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Image__Int__subset,axiom, % 181.25/181.45 ! [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)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__Compl,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__eq,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_domIff,axiom, % 181.25/181.45 ! [V_m_2,T_c,V_a_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2))) % 181.25/181.45 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__def,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__Collect,axiom, % 181.25/181.45 ! [V_Pa_2,V_A_2,V_x_2,T_b] : % 181.25/181.45 ( 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)))) % 181.25/181.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__eq__empty__conv,axiom, % 181.25/181.45 ! [V_f_2,T_c,T_b] : % 181.25/181.45 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__empty,axiom, % 181.25/181.45 ! [T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__def,axiom, % 181.25/181.45 ! [V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,V_m_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_Option_Ooption(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_c)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inj__on__image__Int,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 181.25/181.45 => 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)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_image__Int,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_disjoint__eq__subset__Compl,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_image__vimage__eq,axiom, % 181.25/181.45 ! [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)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__minus,axiom, % 181.25/181.45 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] : % 181.25/181.45 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b) % 181.25/181.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),V_A_2) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_quotient__disj,axiom, % 181.25/181.45 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 181.25/181.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( 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))) % 181.25/181.45 => ( V_X_2 = V_Y_2 % 181.25/181.45 | 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)) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Id__on__def,axiom, % 181.25/181.45 ! [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)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__override__on,axiom, % 181.25/181.45 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Fun_Ooverride__on(T_b,tc_Option_Ooption(T_c),V_f_2,V_g_2,V_A_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)),c_Map_Odom(T_b,T_c,V_f_2)),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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2)))))),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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2))))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__eq__singleton__conv,axiom, % 181.25/181.45 ! [V_x_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( c_Map_Odom(T_b,T_c,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))) % 181.25/181.45 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inj__on__Un,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.45 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 181.25/181.45 & 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_restrict__upd__same,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__Collect__mono,axiom, % 181.25/181.45 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => ( ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.25/181.45 => hBOOL(hAPP(V_Qa_2,B_x)) ) ) % 181.25/181.45 => 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)))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__Compl,axiom, % 181.25/181.45 ! [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))))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_same__fstI,axiom, % 181.25/181.45 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] : % 181.25/181.45 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.25/181.45 => ( 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))) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff1__fold__graph,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup1E,axiom, % 181.25/181.45 ! [V_x_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 181.25/181.45 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup1CI,axiom, % 181.25/181.45 ! [T_b,V_A_2,V_x_2,V_B_2] : % 181.25/181.45 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 181.25/181.45 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UnE,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UnCI,axiom, % 181.25/181.45 ! [V_A_2,V_B_2,V_c_2,T_b] : % 181.25/181.45 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__absorb,axiom, % 181.25/181.45 ! [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 ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__commute,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__left__absorb,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__left__commute,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__assoc,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_bex__Un,axiom, % 181.25/181.45 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( ? [B_x] : % 181.25/181.45 ( 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))) % 181.25/181.45 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.25/181.45 <=> ( ? [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.25/181.45 | ? [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 181.25/181.45 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ball__Un,axiom, % 181.25/181.45 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( ! [B_x] : % 181.25/181.45 ( 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))) % 181.25/181.45 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.25/181.45 <=> ( ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.25/181.45 & ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 181.25/181.45 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup1I1,axiom, % 181.25/181.45 ! [V_B_2,T_b,V_x_2,V_A_2] : % 181.25/181.45 ( hBOOL(hAPP(V_A_2,V_x_2)) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup1I2,axiom, % 181.25/181.45 ! [V_A_2,T_b,V_x_2,V_B_2] : % 181.25/181.45 ( hBOOL(hAPP(V_B_2,V_x_2)) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup_Oidem,axiom, % 181.25/181.45 ! [V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__idem,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__fun__def,axiom, % 181.25/181.45 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( class_Lattices_Olattice(T_b) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup_Ocommute,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__aci_I5_J,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__commute,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup_Oleft__idem,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__aci_I8_J,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__left__idem,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup_Oleft__commute,axiom, % 181.25/181.45 ! [V_c,V_a,V_b,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__aci_I7_J,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__left__commute,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup_Oassoc,axiom, % 181.25/181.45 ! [V_c,V_b,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__aci_I6_J,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__assoc,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__apply,axiom, % 181.25/181.45 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( class_Lattices_Olattice(T_b) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Image,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__supE,axiom, % 181.25/181.45 ! [V_x,V_b,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( 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)) % 181.25/181.45 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 181.25/181.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__mono,axiom, % 181.25/181.45 ! [V_d,V_b,V_c,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 181.25/181.45 => 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))) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__least,axiom, % 181.25/181.45 ! [V_z,V_x,V_y,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 181.25/181.45 => 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)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__supI,axiom, % 181.25/181.45 ! [V_b,V_x,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 181.25/181.45 => 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)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__absorb1,axiom, % 181.25/181.45 ! [V_x,V_y,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__absorb2,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__supI2,axiom, % 181.25/181.45 ! [V_a,V_b,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__supI1,axiom, % 181.25/181.45 ! [V_b,V_a,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__sup__iff,axiom, % 181.25/181.45 ! [V_z_2,V_y_2,V_x_2,T_b] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_b) % 181.25/181.45 => ( 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)) % 181.25/181.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 181.25/181.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__iff__sup,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,T_b] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_b) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.45 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__ge2,axiom, % 181.25/181.45 ! [V_x,V_y,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__ord_I4_J,axiom, % 181.25/181.45 ! [V_x,V_y,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__ge1,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__ord_I3_J,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__supI1,axiom, % 181.25/181.45 ! [V_b,V_a,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__supI2,axiom, % 181.25/181.45 ! [V_a,V_b,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_a) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__bot__left,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__bot(T_a) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__bot__right,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__bot(T_a) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__eq__bot__iff,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,T_b] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__bot(T_b) % 181.25/181.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) % 181.25/181.45 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b) % 181.25/181.45 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__absorb,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__inf__absorb,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__distrib1,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Odistrib__lattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__inf__distrib1,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Odistrib__lattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__sup__distrib2,axiom, % 181.25/181.45 ! [V_x,V_z,V_y,T_a] : % 181.25/181.45 ( class_Lattices_Odistrib__lattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__inf__distrib2,axiom, % 181.25/181.45 ! [V_x,V_z,V_y,T_a] : % 181.25/181.45 ( class_Lattices_Odistrib__lattice(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__top__right,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__top(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__top__left,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Obounded__lattice__top(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__iff,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 181.25/181.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.45 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UnI1,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UnI2,axiom, % 181.25/181.45 ! [V_A_2,V_B_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__empty__left,axiom, % 181.25/181.45 ! [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 ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__empty__right,axiom, % 181.25/181.45 ! [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 ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__empty,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__insert__right,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__insert__left,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__upper1,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__upper2,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_subset__Un__eq,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__absorb1,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__absorb2,axiom, % 181.25/181.45 ! [V_A_2,V_B_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__least,axiom, % 181.25/181.45 ! [V_B_2,V_C_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__mono,axiom, % 181.25/181.45 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__UNIV__left,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__UNIV__right,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_image__Un,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__Un__distrib,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Int__distrib,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Int__Un__distrib2,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Int__distrib2,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Int__crazy,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Diff__cancel,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Diff__cancel2,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Diff,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_map__upd__Some__unfold,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] : % 181.25/181.45 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 181.25/181.45 <=> ( ( V_x_2 = V_a_2 % 181.25/181.45 & V_b_2 = V_y_2 ) % 181.25/181.45 | ( V_x_2 != V_a_2 % 181.25/181.45 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_map__upd__triv,axiom, % 181.25/181.45 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] : % 181.25/181.45 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 181.25/181.45 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_map__upd__eqD1,axiom, % 181.25/181.45 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] : % 181.25/181.45 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) % 181.25/181.45 => V_x_2 = V_y_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Pow__subset,axiom, % 181.25/181.45 ! [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)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Image__Un,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_vimage__Un,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ran__def,axiom, % 181.25/181.45 ! [V_m_2,T_b,T_c] : c_Map_Oran(T_c,T_b,V_m_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_Option_Ooption(T_b),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_b)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fun__left__comm__idem__sup,axiom, % 181.25/181.45 ! [T_b] : % 181.25/181.45 ( class_Lattices_Osemilattice__sup(T_b) % 181.25/181.45 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold__graph_Oequations_I1_J,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold__graph_OemptyI,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_empty__fold__graphE,axiom, % 181.25/181.45 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => V_x_2 = V_z_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_exE__some,axiom, % 181.25/181.45 ! [T_b,V_c_2,V_Pa_2] : % 181.25/181.45 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 181.25/181.45 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) % 181.25/181.45 => hBOOL(hAPP(V_Pa_2,V_c_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__Un__eq,axiom, % 181.25/181.45 ! [V_x_2,V_S_2,V_R_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Collect__disj__eq,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__Un,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__Un__distrib,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_distrib__inf__le,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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)))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_distrib__sup__le,axiom, % 181.25/181.45 ! [V_z,V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Olattice(T_a) % 181.25/181.45 => 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)))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_compl__sup,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_compl__inf,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_compl__sup__top,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__compl__top,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_domI,axiom, % 181.25/181.45 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] : % 181.25/181.45 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_image__map__upd,axiom, % 181.25/181.45 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 => hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),V_m_2),V_A_2) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_insert__dom,axiom, % 181.25/181.45 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] : % 181.25/181.45 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 181.25/181.45 => hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) = c_Map_Odom(T_c,T_b,V_f_2) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_insert__is__Un,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Int__assoc__eq,axiom, % 181.25/181.45 ! [V_C_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__subset__conv,axiom, % 181.25/181.45 ! [V_C_2,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__partition,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => 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 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__Diff__Int,axiom, % 181.25/181.45 ! [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 ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__Un,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Diff__Int,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inj__on__Un__image__eq__iff,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ( 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) % 181.25/181.45 <=> V_A_2 = V_B_2 ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf__Int__eq2,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Compl__partition,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Compl__partition2,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Compl__Un,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Compl__Int,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Compl__Diff__eq,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ranI,axiom, % 181.25/181.45 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] : % 181.25/181.45 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__const,axiom, % 181.25/181.45 ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Un__def,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__absorb,axiom, % 181.25/181.45 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_insert__def,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold__graph_OinsertI,axiom, % 181.25/181.45 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 181.25/181.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.45 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_map__upd__nonempty,axiom, % 181.25/181.45 ! [V_x_2,V_k_2,V_t_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__simps_I3_J,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.25/181.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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)) ) % 181.25/181.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__simps_I2_J,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.25/181.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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)) ) % 181.25/181.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__extend__simps_I3_J,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.25/181.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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 ) % 181.25/181.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__extend__simps_I2_J,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.25/181.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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 ) % 181.25/181.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UN__insert,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Collect__imp__eq,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_vimage__insert,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_bij__betw__combine,axiom, % 181.25/181.45 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 181.25/181.45 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2) % 181.25/181.45 => ( 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)) % 181.25/181.45 => 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)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_bij__betw__Disj__Un,axiom, % 181.25/181.45 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ( 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)) % 181.25/181.45 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 181.25/181.45 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) % 181.25/181.45 => 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)) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Id__on__empty,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Image__Id__on,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_if__image__distrib,axiom, % 181.25/181.45 ! [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))))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_dom__if,axiom, % 181.25/181.45 ! [V_g_2,V_f_2,V_Pa_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_Pa_2)),V_f_2)),V_g_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)),c_Map_Odom(T_b,T_c,V_f_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)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Pow__insert,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_compl__unique,axiom, % 181.25/181.45 ! [V_y,V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oboolean__algebra(T_a) % 181.25/181.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 181.25/181.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 181.25/181.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ran__map__upd,axiom, % 181.25/181.45 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] : % 181.25/181.45 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b) % 181.25/181.45 => c_Map_Oran(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Id__on__eqI,axiom, % 181.25/181.45 ! [V_A_2,T_b,V_b_2,V_a_2] : % 181.25/181.45 ( V_a_2 = V_b_2 % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Id__on__iff,axiom, % 181.25/181.45 ! [V_A_2,V_y_2,V_x_2,T_b] : % 181.25/181.45 ( 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))) % 181.25/181.45 <=> ( V_x_2 = V_y_2 % 181.25/181.45 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_UNIV__option__conv,axiom, % 181.25/181.45 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold1Set_Ointros,axiom, % 181.25/181.45 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) % 181.25/181.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Field__insert,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_not__None__eq,axiom, % 181.25/181.45 ! [T_b,V_x_2] : % 181.25/181.45 ( V_x_2 != c_Option_Ooption_ONone(T_b) % 181.25/181.45 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_not__Some__eq,axiom, % 181.25/181.45 ! [T_b,V_x_2] : % 181.25/181.45 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y) % 181.25/181.45 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_option_Osimps_I3_J,axiom, % 181.25/181.45 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 181.25/181.45 % 181.25/181.45 fof(fact_option_Osimps_I2_J,axiom, % 181.25/181.45 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 181.25/181.45 % 181.25/181.45 fof(fact_in__lex__prod,axiom, % 181.25/181.45 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 181.25/181.45 ( 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))) % 181.25/181.45 <=> ( 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)) % 181.25/181.45 | ( V_a_2 = V_a_H_2 % 181.25/181.45 & 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)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Id__onE,axiom, % 181.25/181.45 ! [V_A_2,V_c_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2))) % 181.25/181.45 => ~ ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf2E,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 181.25/181.45 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf2I,axiom, % 181.25/181.45 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 181.25/181.45 => 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)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf2D2,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inf2D1,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Field__Un,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold1Set__nonempty,axiom, % 181.25/181.45 ! [V_x_2,V_A_2,V_f_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) % 181.25/181.45 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_empty__fold1SetE,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup__Un__eq2,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Field__empty,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_mono__Field,axiom, % 181.25/181.45 ! [V_s_2,V_r_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_inj__Some,axiom, % 181.25/181.45 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b),V_A_2) ). % 181.25/181.45 % 181.25/181.45 fof(fact_option_Oinject,axiom, % 181.25/181.45 ! [V_a_H_2,V_a_2,T_b] : % 181.25/181.45 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2) % 181.25/181.45 <=> V_a_2 = V_a_H_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold1Set__sing,axiom, % 181.25/181.45 ! [V_b_2,V_a_2,V_f_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> V_a_2 = V_b_2 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 181.25/181.45 ! [V_x_2,T_b] : c_Option_Oset(T_b,hAPP(c_Option_Ooption_OSome(T_b),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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_in__measure,axiom, % 181.25/181.45 ! [V_f_2,V_y_2,V_x_2,T_b] : % 181.25/181.45 ( 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))) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ran__restrictD,axiom, % 181.25/181.45 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2)))) % 181.25/181.45 => ? [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.25/181.45 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_insert__fold1SetE,axiom, % 181.25/181.45 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ~ ! [B_a,B_A] : % 181.25/181.45 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 181.25/181.45 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold1Set_Oequations,axiom, % 181.25/181.45 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 <=> ? [B_a,B_A] : % 181.25/181.45 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 181.25/181.45 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) % 181.25/181.45 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_mlex__leq,axiom, % 181.25/181.45 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 181.25/181.45 ( 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))) % 181.25/181.45 => ( 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)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_mlex__less,axiom, % 181.25/181.45 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 181.25/181.45 ( 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))) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 181.25/181.45 ! [T_b] : c_Option_Oset(T_b,c_Option_Ooption_ONone(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup2E,axiom, % 181.25/181.45 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 181.25/181.45 ( 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)) % 181.25/181.45 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup2CI,axiom, % 181.25/181.45 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] : % 181.25/181.45 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup2I1,axiom, % 181.25/181.45 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_sup2I2,axiom, % 181.25/181.45 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_termination__basic__simps_I5_J,axiom, % 181.25/181.45 ! [V_y,V_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_elem__set,axiom, % 181.25/181.45 ! [V_xo_2,V_x_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2))) % 181.25/181.45 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_set__empty__eq,axiom, % 181.25/181.45 ! [V_xo_2,T_b] : % 181.25/181.45 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.45 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_nat__less__le,axiom, % 181.25/181.45 ! [V_n_2,V_m_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.45 & V_m_2 != V_n_2 ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__eq__less__or__eq,axiom, % 181.25/181.45 ! [V_n_2,V_m_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.45 | V_m_2 = V_n_2 ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__imp__le__nat,axiom, % 181.25/181.45 ! [V_n,V_m] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__neq__implies__less,axiom, % 181.25/181.45 ! [V_n,V_m] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.45 => ( V_m != V_n % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__or__eq__imp__le,axiom, % 181.25/181.45 ! [V_n,V_m] : % 181.25/181.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.45 | V_m = V_n ) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__diff__iff,axiom, % 181.25/181.45 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 181.25/181.45 => ( 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))) % 181.25/181.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__less__mono,axiom, % 181.25/181.45 ! [V_c,V_b,V_a] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold__graph__permute__diff,axiom, % 181.25/181.45 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] : % 181.25/181.45 ( class_Groups_Oab__semigroup__mult(T_b) % 181.25/181.45 => ( 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)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 181.25/181.45 => 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)) ) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_mult__le__mono,axiom, % 181.25/181.45 ! [V_l,V_k,V_j,V_i] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_mult__le__mono2,axiom, % 181.25/181.45 ! [V_k,V_j,V_i] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_mult__le__mono1,axiom, % 181.25/181.45 ! [V_k,V_j,V_i] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__cube,axiom, % 181.25/181.45 ! [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)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__square,axiom, % 181.25/181.45 ! [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))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__mult__distrib,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__commute,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__mult__distrib2,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_mult__left__idem,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_mult__idem,axiom, % 181.25/181.45 ! [V_x,T_a] : % 181.25/181.45 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 181.25/181.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_times_Oidem,axiom, % 181.25/181.45 ! [V_a,T_a] : % 181.25/181.45 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 181.25/181.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 181.25/181.45 ! [V_c,V_b,V_a,T_a] : % 181.25/181.45 ( class_Groups_Oab__semigroup__mult(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fun__left__comm__idem,axiom, % 181.25/181.45 ! [T_b] : % 181.25/181.45 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 181.25/181.45 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold__graph__insert__swap,axiom, % 181.25/181.45 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] : % 181.25/181.45 ( class_Groups_Oab__semigroup__mult(T_b) % 181.25/181.45 => ( 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)) % 181.25/181.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 181.25/181.45 => 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))) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__imp__diff__less,axiom, % 181.25/181.45 ! [V_n,V_k,V_j] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__less__mono2,axiom, % 181.25/181.45 ! [V_l,V_n,V_m] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__not__refl,axiom, % 181.25/181.45 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_nat__neq__iff,axiom, % 181.25/181.45 ! [V_n_2,V_m_2] : % 181.25/181.45 ( V_m_2 != V_n_2 % 181.25/181.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_linorder__neqE__nat,axiom, % 181.25/181.45 ! [V_y,V_x] : % 181.25/181.45 ( V_x != V_y % 181.25/181.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__irrefl__nat,axiom, % 181.25/181.45 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__not__refl2,axiom, % 181.25/181.45 ! [V_m,V_n] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 181.25/181.45 => V_m != V_n ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_less__not__refl3,axiom, % 181.25/181.45 ! [V_t,V_s] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 181.25/181.45 => V_s != V_t ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_nat__less__cases,axiom, % 181.25/181.45 ! [V_Pa_2,V_n_2,V_m_2] : % 181.25/181.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 181.25/181.45 => ( ( V_m_2 = V_n_2 % 181.25/181.45 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 181.25/181.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 181.25/181.45 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__le__self,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__le__mono2,axiom, % 181.25/181.45 ! [V_l,V_n,V_m] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__le__mono,axiom, % 181.25/181.45 ! [V_l,V_n,V_m] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_diff__diff__cancel,axiom, % 181.25/181.45 ! [V_n,V_i] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 181.25/181.45 => 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 ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_eq__diff__iff,axiom, % 181.25/181.45 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 181.25/181.45 => ( 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) % 181.25/181.45 <=> V_m_2 = V_n_2 ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_Nat_Odiff__diff__eq,axiom, % 181.25/181.45 ! [V_n,V_m,V_k] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 181.25/181.45 => 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) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__diff__iff,axiom, % 181.25/181.45 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 181.25/181.45 => ( 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))) % 181.25/181.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__refl,axiom, % 181.25/181.45 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_nat__le__linear,axiom, % 181.25/181.45 ! [V_n,V_m] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_eq__imp__le,axiom, % 181.25/181.45 ! [V_n,V_m] : % 181.25/181.45 ( V_m = V_n % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__trans,axiom, % 181.25/181.45 ! [V_k,V_j,V_i] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 181.25/181.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_le__antisym,axiom, % 181.25/181.45 ! [V_n,V_m] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.45 => V_m = V_n ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_square__eq__iff,axiom, % 181.25/181.45 ! [V_b_2,V_a_2,T_b] : % 181.25/181.45 ( class_Rings_Oidom(T_b) % 181.25/181.45 => ( 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) % 181.25/181.45 <=> ( V_a_2 = V_b_2 % 181.25/181.45 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_minus__mult__minus,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Rings_Oring(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_minus__mult__commute,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Rings_Oring(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_minus__mult__left,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Rings_Oring(T_a) % 181.25/181.45 => 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) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_minus__mult__right,axiom, % 181.25/181.45 ! [V_b,V_a,T_a] : % 181.25/181.45 ( class_Rings_Oring(T_a) % 181.25/181.45 => 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)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__range__updI,axiom, % 181.25/181.45 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_option_Orecs_I2_J,axiom, % 181.25/181.45 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 181.25/181.45 % 181.25/181.45 fof(fact_option_Osimps_I5_J,axiom, % 181.25/181.45 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite_OemptyI,axiom, % 181.25/181.45 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite_OinsertI,axiom, % 181.25/181.45 ! [V_a_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__imageI,axiom, % 181.25/181.45 ! [V_h_2,T_c,V_F_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Int,axiom, % 181.25/181.45 ! [V_Ga_2,V_F_2,T_b] : % 181.25/181.45 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.25/181.45 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Diff,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.45 => 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Collect__conjI,axiom, % 181.25/181.45 ! [V_Qa_2,V_Pa_2,T_b] : % 181.25/181.45 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 181.25/181.45 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) % 181.25/181.45 => 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)))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Collect__subsets,axiom, % 181.25/181.45 ! [V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.45 => 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)))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_nat__mult__commute,axiom, % 181.25/181.45 ! [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) ). % 181.25/181.45 % 181.25/181.45 fof(fact_nat__mult__assoc,axiom, % 181.25/181.45 ! [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)) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Field,axiom, % 181.25/181.45 ! [V_r_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Plus__UNIV__iff,axiom, % 181.25/181.45 ! [T_c,T_b] : % 181.25/181.45 ( 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)))) % 181.25/181.45 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 181.25/181.45 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Prod__UNIV,axiom, % 181.25/181.45 ! [T_c,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 181.25/181.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 181.25/181.45 => 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)))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite,axiom, % 181.25/181.45 ! [V_A_2,T_b] : % 181.25/181.45 ( class_Finite__Set_Ofinite(T_b) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__code,axiom, % 181.25/181.45 ! [V_A_2,T_b] : % 181.25/181.45 ( class_Finite__Set_Ofinite(T_b) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Pow__iff,axiom, % 181.25/181.45 ! [V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) % 181.25/181.45 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite_Oequations_I1_J,axiom, % 181.25/181.45 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__insert,axiom, % 181.25/181.45 ! [V_A_2,V_a_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) % 181.25/181.45 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__fun__UNIVD2,axiom, % 181.25/181.45 ! [T_c,T_b] : % 181.25/181.45 ( 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)))) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__subset,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_rev__finite__subset,axiom, % 181.25/181.45 ! [V_A_2,V_B_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__UNIV,axiom, % 181.25/181.45 ! [T_b] : % 181.25/181.45 ( class_Finite__Set_Ofinite(T_b) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Un,axiom, % 181.25/181.45 ! [V_Ga_2,V_F_2,T_b] : % 181.25/181.45 ( 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))) % 181.25/181.45 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.25/181.45 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__UnI,axiom, % 181.25/181.45 ! [V_Ga_2,V_F_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.25/181.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) % 181.25/181.45 => 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))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Diff2,axiom, % 181.25/181.45 ! [V_A_2,V_B_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.45 => ( 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))) % 181.25/181.45 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__UN,axiom, % 181.25/181.45 ! [V_B_2,T_c,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.45 => ( 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))) % 181.25/181.45 <=> ! [B_x] : % 181.25/181.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_bij__betw__finite,axiom, % 181.25/181.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 181.25/181.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.45 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_fold__graph__imp__finite,axiom, % 181.25/181.45 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_nat__seg__image__imp__finite,axiom, % 181.25/181.45 ! [V_n_2,V_f_2,T_b,V_A_2] : % 181.25/181.45 ( 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))) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__option__UNIV,axiom, % 181.25/181.45 ! [T_b] : % 181.25/181.45 ( 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)))) % 181.25/181.45 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Collect__disjI,axiom, % 181.25/181.45 ! [V_Qa_2,V_Pa_2,T_b] : % 181.25/181.45 ( 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)))) % 181.25/181.45 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 181.25/181.45 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__surj,axiom, % 181.25/181.45 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.45 => ( 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))) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__Diff__insert,axiom, % 181.25/181.45 ! [V_B_2,V_a_2,V_A_2,T_b] : % 181.25/181.45 ( 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)))) % 181.25/181.45 <=> 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))) ) ). % 181.25/181.45 % 181.25/181.45 fof(fact_finite__imageD,axiom, % 181.25/181.45 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 181.25/181.45 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) % 181.25/181.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__compl,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 181.25/181.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__image__set,axiom, % 181.25/181.46 ! [V_f_2,T_c,V_Pa_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 181.25/181.46 => 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))))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__Collect__bounded__ex,axiom, % 181.25/181.46 ! [V_Qa_2,T_c,V_Pa_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 181.25/181.46 => ( 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))))) % 181.25/181.46 <=> ! [B_y] : % 181.25/181.46 ( hBOOL(hAPP(V_Pa_2,B_y)) % 181.25/181.46 => 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)))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__Collect__not,axiom, % 181.25/181.46 ! [V_Pa_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 181.25/181.46 => ( 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)))) % 181.25/181.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__range__imageI,axiom, % 181.25/181.46 ! [V_f_2,T_d,V_g_2,T_c,T_b] : % 181.25/181.46 ( 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))))) % 181.25/181.46 => 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))))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_linorder__neqE__linordered__idom,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.46 => ( V_x != V_y % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__surj__inj,axiom, % 181.25/181.46 ! [V_f_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( 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))) % 181.25/181.46 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_endo__inj__surj,axiom, % 181.25/181.46 ! [V_f_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) % 181.25/181.46 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__UNIV__inj__surj,axiom, % 181.25/181.46 ! [V_f_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 181.25/181.46 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__UNIV__surj__inj,axiom, % 181.25/181.46 ! [V_f_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 181.25/181.46 => ( 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)) % 181.25/181.46 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__vimageD,axiom, % 181.25/181.46 ! [V_F_2,V_h_2,T_c,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 181.25/181.46 => ( 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)) % 181.25/181.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__vimageI,axiom, % 181.25/181.46 ! [V_h_2,T_c,V_F_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.25/181.46 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 181.25/181.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__vimage__iff,axiom, % 181.25/181.46 ! [V_F_2,V_h_2,T_c,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 181.25/181.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_option_Osimps_I4_J,axiom, % 181.25/181.46 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_c)) = V_f1_2 ). % 181.25/181.46 % 181.25/181.46 fof(fact_option_Orecs_I1_J,axiom, % 181.25/181.46 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_c)) = V_f1_2 ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Oremove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one_Oremove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( ( 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)) % 181.25/181.46 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 181.25/181.46 & ( 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)) % 181.25/181.46 => 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)))))) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image__simple_Oremove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 181.25/181.46 => 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)))))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image_Oreindex,axiom, % 181.25/181.46 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 181.25/181.46 => 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) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ounion,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Oinsert__remove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one_Ounion__disjoint,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__Collect__less__nat,axiom, % 181.25/181.46 ! [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)))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__Collect__le__nat,axiom, % 181.25/181.46 ! [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)))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 181.25/181.46 ! [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] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ocommute__comp,axiom, % 181.25/181.46 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ocommute__left__comp,axiom, % 181.25/181.46 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image__simple_Oempty,axiom, % 181.25/181.46 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.25/181.46 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image_Odistrib,axiom, % 181.25/181.46 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 181.25/181.46 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ocommute__comp_H_H,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ocommute__left__comp_H,axiom, % 181.25/181.46 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ocommute__comp_H,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Oempty,axiom, % 181.25/181.46 ! [V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one_Osingleton,axiom, % 181.25/181.46 ! [V_x_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image__simple_Oinsert,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image__simple_Ounion__inter,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Oinsert,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding_Ounion__inter,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one_Oinsert,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => 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)))))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one_Oinsert__remove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ( 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)) % 181.25/181.46 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 181.25/181.46 & ( 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)) % 181.25/181.46 => 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)))))) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one_Ounion__inter,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__M__bounded__by__nat,axiom, % 181.25/181.46 ! [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))))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_in__finite__psubset,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.46 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__idem_Ounion__idem,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.46 => 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) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__idem_Oinsert__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one_Oclosed,axiom, % 181.25/181.46 ! [V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( ! [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)))))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__idem_Oin__comp__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__empty__induct,axiom, % 181.25/181.46 ! [V_Pa_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 181.25/181.46 => ( ! [B_a,B_A] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) % 181.25/181.46 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 181.25/181.46 => 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)))))) ) ) ) % 181.25/181.46 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_infinite__UNIV__nat,axiom, % 181.25/181.46 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__idem_Oidem__left__comp,axiom, % 181.25/181.46 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__idem_Oidem__comp,axiom, % 181.25/181.46 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__nat__set__iff__bounded,axiom, % 181.25/181.46 ! [V_N_2] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 181.25/181.46 <=> ? [B_m] : % 181.25/181.46 ! [B_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 181.25/181.46 ! [V_N_2] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 181.25/181.46 <=> ? [B_m] : % 181.25/181.46 ! [B_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ord_OatMost__iff,axiom, % 181.25/181.46 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ord_OatLeast__iff,axiom, % 181.25/181.46 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ord_OlessThan__iff,axiom, % 181.25/181.46 ! [V_k_2,V_less_2,V_i_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ord_OgreaterThan__iff,axiom, % 181.25/181.46 ! [V_k_2,V_less_2,V_i_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ord_OatLeastAtMost__iff,axiom, % 181.25/181.46 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 181.25/181.46 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ord_OatLeastLessThan__iff,axiom, % 181.25/181.46 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 181.25/181.46 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_max__ext__additive,axiom, % 181.25/181.46 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 => ( 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))) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one__idem_Ounion__idem,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__subset__induct,axiom, % 181.25/181.46 ! [V_Pa_2,V_A_2,V_F_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 181.25/181.46 => ( ! [B_a,B_F] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) % 181.25/181.46 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 181.25/181.46 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) ) % 181.25/181.46 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one__idem_Osubset__idem,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.46 => 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) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_finite__conv__nat__seg__image,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 <=> ? [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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one__idem_Oidem,axiom, % 181.25/181.46 ! [V_x_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 181.25/181.46 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one__idem_Oin__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_max__extp__max__ext__eq,axiom, % 181.25/181.46 ! [V_xa_2,V_x_2,V_R_2,T_b] : % 181.25/181.46 ( 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) % 181.25/181.46 <=> 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_max__ext_Ointros,axiom, % 181.25/181.46 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 181.25/181.46 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( ! [B_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 181.25/181.46 => ? [B_xa] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 181.25/181.46 & 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)) ) ) % 181.25/181.46 => 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))) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__Un,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Groups_Oab__semigroup__mult(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Diff1__less,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Diff2__less,axiom, % 181.25/181.46 ! [V_y_2,V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one__idem_Ohom__commute,axiom, % 181.25/181.46 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( ! [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)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.46 => ( ! [B_x] : % 181.25/181.46 ( 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))) % 181.25/181.46 => hAPP(V_g_2,B_x) = V_z_2 ) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_bij__betw__same__card,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 181.25/181.46 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 181.25/181.46 => ( 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))) % 181.25/181.46 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__image,axiom, % 181.25/181.46 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_BIJ,axiom, % 181.25/181.46 ! [V_B_2,T_c,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.46 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2) % 181.25/181.46 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__singleton__def,axiom, % 181.25/181.46 ! [V_a_2,V_f_2,T_b,V_g_2] : % 181.25/181.46 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__singleton,axiom, % 181.25/181.46 ! [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 ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__one_Oeq__fold,axiom, % 181.25/181.46 ! [V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__insert__le,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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)))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__mono,axiom, % 181.25/181.46 ! [V_A_2,V_B_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__seteq,axiom, % 181.25/181.46 ! [V_A_2,V_B_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.46 => ( 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))) % 181.25/181.46 => V_A_2 = V_B_2 ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__image__le,axiom, % 181.25/181.46 ! [V_f_2,T_c,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_eq__card__imp__inj__on,axiom, % 181.25/181.46 ! [V_f_2,T_c,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( 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) % 181.25/181.46 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_inj__on__iff__eq__card,axiom, % 181.25/181.46 ! [V_f_2,T_c,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.46 <=> 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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_pigeonhole,axiom, % 181.25/181.46 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__quotient__disjoint,axiom, % 181.25/181.46 ! [V_r_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( 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) % 181.25/181.46 => 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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_psubset__card__mono,axiom, % 181.25/181.46 ! [V_A_2,V_B_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__def,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__bij__eq,axiom, % 181.25/181.46 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.46 => ( 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)) % 181.25/181.46 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 181.25/181.46 => ( 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)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.46 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Diff__subset,axiom, % 181.25/181.46 ! [V_A_2,V_B_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Diff__subset__Int,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( 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))) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__card__le__card__Diff,axiom, % 181.25/181.46 ! [V_A_2,V_B_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => 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)))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__psubset,axiom, % 181.25/181.46 ! [V_A_2,V_B_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.46 => ( 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))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__insert__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__Un2,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Diff1__le,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__inj__on__le,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.46 => ( 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)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_inj__on__iff__card__le,axiom, % 181.25/181.46 ! [V_B_2,T_c,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.46 => ( ? [B_f] : % 181.25/181.46 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 181.25/181.46 & 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)) ) % 181.25/181.46 <=> 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__insert,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Groups_Oab__semigroup__mult(T_b) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_below__fold1__iff,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Osemilattice__inf(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> ! [B_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__belowI,axiom, % 181.25/181.46 ! [V_a_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Osemilattice__inf(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold1__in,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( class_Groups_Oab__semigroup__mult(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( ! [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)))))) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Diff__singleton,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Diff__singleton__if,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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)) ) % 181.25/181.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_hom__fold1__commute,axiom, % 181.25/181.46 ! [V_N_2,V_h_2,T_b] : % 181.25/181.46 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 181.25/181.46 => ( ! [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)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Diff__insert,axiom, % 181.25/181.46 ! [V_B_2,V_a_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__UNIV__unit,axiom, % 181.25/181.46 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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_one__reorient,axiom, % 181.25/181.46 ! [V_x_2,T_b] : % 181.25/181.46 ( class_Groups_Oone(T_b) % 181.25/181.46 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2 % 181.25/181.46 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_mult__1__left,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_mult__1,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Groups_Ocomm__monoid__mult(T_a) % 181.25/181.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_mult__1__right,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_mult_Ocomm__neutral,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Groups_Ocomm__monoid__mult(T_a) % 181.25/181.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__mult__1,axiom, % 181.25/181.46 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__1__eq__mult__iff,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 181.25/181.46 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 181.25/181.46 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__mult__1__right,axiom, % 181.25/181.46 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__mult__eq__1__iff,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 181.25/181.46 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 181.25/181.46 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__1__mult,axiom, % 181.25/181.46 ! [V_n,V_m,T_a] : % 181.25/181.46 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_square__eq__1__iff,axiom, % 181.25/181.46 ! [V_x_2,T_b] : % 181.25/181.46 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 181.25/181.46 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 181.25/181.46 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b) % 181.25/181.46 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Oidem,axiom, % 181.25/181.46 ! [V_x,T_a] : % 181.25/181.46 ( class_Lattices_Olattice(T_a) % 181.25/181.46 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Oidem,axiom, % 181.25/181.46 ! [V_x,T_a] : % 181.25/181.46 ( class_Lattices_Olattice(T_a) % 181.25/181.46 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_semilattice__big_OF__eq,axiom, % 181.25/181.46 ! [V_A_2,V_F_2,V_f_2,T_b] : % 181.25/181.46 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 181.25/181.46 ! [V_x,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__ring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_inf__Sup1__distrib,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Odistrib__lattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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))))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_inf__Sup2__distrib,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Odistrib__lattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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))))))) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_sup__Inf1__distrib,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Odistrib__lattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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))))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_sup__Inf2__distrib,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Odistrib__lattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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))))))) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card_Oremove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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)))))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_crossproduct__noteq,axiom, % 181.25/181.46 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.46 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 181.25/181.46 => ( ( V_a_2 != V_b_2 % 181.25/181.46 & V_c_2 != V_d_2 ) % 181.25/181.46 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_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_c_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 181.25/181.46 ! [V_b,V_m,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_crossproduct__eq,axiom, % 181.25/181.46 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] : % 181.25/181.46 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 181.25/181.46 => ( 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)) % 181.25/181.46 <=> ( V_w_2 = V_x_2 % 181.25/181.46 | V_y_2 = V_z_2 ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 181.25/181.46 ! [V_c,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 181.25/181.46 ! [V_d,V_c,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 181.25/181.46 ! [V_d,V_c,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 181.25/181.46 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__right__imp__eq,axiom, % 181.25/181.46 ! [V_c,V_a,V_b,T_a] : % 181.25/181.46 ( class_Groups_Ocancel__semigroup__add(T_a) % 181.25/181.46 => ( 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) % 181.25/181.46 => V_b = V_c ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__imp__eq,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 181.25/181.46 => ( 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) % 181.25/181.46 => V_b = V_c ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__left__imp__eq,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ocancel__semigroup__add(T_a) % 181.25/181.46 => ( 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) % 181.25/181.46 => V_b = V_c ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__right__cancel,axiom, % 181.25/181.46 ! [V_c_2,V_a_2,V_b_2,T_b] : % 181.25/181.46 ( class_Groups_Ocancel__semigroup__add(T_b) % 181.25/181.46 => ( 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_c_2),V_a_2) % 181.25/181.46 <=> V_b_2 = V_c_2 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__left__cancel,axiom, % 181.25/181.46 ! [V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.46 ( class_Groups_Ocancel__semigroup__add(T_b) % 181.25/181.46 => ( 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_c_2) % 181.25/181.46 <=> V_b_2 = V_c_2 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oab__semigroup__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__add__right__cancel,axiom, % 181.25/181.46 ! [V_n_2,V_k_2,V_m_2] : % 181.25/181.46 ( 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) % 181.25/181.46 <=> V_m_2 = V_n_2 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__add__left__cancel,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.46 ( 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) % 181.25/181.46 <=> V_m_2 = V_n_2 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__add__assoc,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__add__left__commute,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__add__commute,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_inj__on__add__nat,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__le__cancel__right,axiom, % 181.25/181.46 ! [V_b_2,V_c_2,V_a_2,T_b] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__le__cancel__left,axiom, % 181.25/181.46 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__right__mono,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__left__mono,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__mono,axiom, % 181.25/181.46 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__le__imp__le__right,axiom, % 181.25/181.46 ! [V_b,V_c,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 181.25/181.46 => ( 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))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__le__imp__le__left,axiom, % 181.25/181.46 ! [V_b,V_a,V_c,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 181.25/181.46 => ( 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))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__less__cancel__right,axiom, % 181.25/181.46 ! [V_b_2,V_c_2,V_a_2,T_b] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__less__cancel__left,axiom, % 181.25/181.46 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__strict__right__mono,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__strict__left__mono,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__strict__mono,axiom, % 181.25/181.46 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__less__imp__less__right,axiom, % 181.25/181.46 ! [V_b,V_c,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 181.25/181.46 => ( 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))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__less__imp__less__left,axiom, % 181.25/181.46 ! [V_b,V_a,V_c,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 181.25/181.46 => ( 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))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_combine__common__factor,axiom, % 181.25/181.46 ! [V_c,V_b,V_e,V_a,T_a] : % 181.25/181.46 ( class_Rings_Osemiring(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__class_Odistrib,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__add__cancel,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ogroup__add(T_a) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__diff__cancel,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ogroup__add(T_a) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_minus__add__distrib,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oab__group__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_minus__add,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ogroup__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__minus__cancel,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ogroup__add(T_a) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_minus__add__cancel,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ogroup__add(T_a) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__lessD1,axiom, % 181.25/181.46 ! [V_k,V_j,V_i] : % 181.25/181.46 ( 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)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__add__eq__less,axiom, % 181.25/181.46 ! [V_n,V_m,V_l,V_k] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 181.25/181.46 => ( 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) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__less__mono,axiom, % 181.25/181.46 ! [V_l,V_k,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__less__mono1,axiom, % 181.25/181.46 ! [V_k,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_trans__less__add2,axiom, % 181.25/181.46 ! [V_m,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_trans__less__add1,axiom, % 181.25/181.46 ! [V_m,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__add__left__cancel__less,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_not__add__less2,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_not__add__less1,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_termination__basic__simps_I1_J,axiom, % 181.25/181.46 ! [V_z,V_y,V_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_termination__basic__simps_I2_J,axiom, % 181.25/181.46 ! [V_y,V_z,V_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__leE,axiom, % 181.25/181.46 ! [V_n,V_k,V_m] : % 181.25/181.46 ( 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)) % 181.25/181.46 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__leD1,axiom, % 181.25/181.46 ! [V_n,V_k,V_m] : % 181.25/181.46 ( 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)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__leD2,axiom, % 181.25/181.46 ! [V_n,V_k,V_m] : % 181.25/181.46 ( 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)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__le__mono,axiom, % 181.25/181.46 ! [V_l,V_k,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__le__mono1,axiom, % 181.25/181.46 ! [V_k,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_trans__le__add2,axiom, % 181.25/181.46 ! [V_m,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_trans__le__add1,axiom, % 181.25/181.46 ! [V_m,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__add__left__cancel__le,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__iff__add,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.46 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__add1,axiom, % 181.25/181.46 ! [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))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__add2,axiom, % 181.25/181.46 ! [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))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_termination__basic__simps_I4_J,axiom, % 181.25/181.46 ! [V_y,V_z,V_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_termination__basic__simps_I3_J,axiom, % 181.25/181.46 ! [V_z,V_y,V_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__cancel2,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__cancel,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__diff__left,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__add__inverse,axiom, % 181.25/181.46 ! [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 ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__add__inverse2,axiom, % 181.25/181.46 ! [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 ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__mult__distrib,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__mult__distrib2,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 181.25/181.46 ! [V_m,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 181.25/181.46 ! [V_a,V_m,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 181.25/181.46 ! [V_m,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__ring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__le__Sup,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__le__less__mono,axiom, % 181.25/181.46 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__less__le__mono,axiom, % 181.25/181.46 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__add__one,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.46 => 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)))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_eq__add__iff1,axiom, % 181.25/181.46 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 181.25/181.46 ( class_Rings_Oring(T_b) % 181.25/181.46 => ( 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_c_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) % 181.25/181.46 <=> 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_c_2) = V_d_2 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_eq__add__iff2,axiom, % 181.25/181.46 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 181.25/181.46 ( class_Rings_Oring(T_b) % 181.25/181.46 => ( 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_c_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) % 181.25/181.46 <=> V_c_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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__def,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ogroup__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_ab__diff__minus,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Oab__group__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__minus__eq__add,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Groups_Ogroup__add(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__diff__inverse,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__diff__conv,axiom, % 181.25/181.46 ! [V_k_2,V_j_2,V_i_2] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__add__assoc2,axiom, % 181.25/181.46 ! [V_i,V_j,V_k] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__diff__assoc2,axiom, % 181.25/181.46 ! [V_i,V_j,V_k] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__add__assoc,axiom, % 181.25/181.46 ! [V_i,V_j,V_k] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__imp__diff__is__add,axiom, % 181.25/181.46 ! [V_k_2,V_j_2,V_i_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 181.25/181.46 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 181.25/181.46 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__add__diff__inverse2,axiom, % 181.25/181.46 ! [V_m,V_n] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__diff__conv2,axiom, % 181.25/181.46 ! [V_i_2,V_j_2,V_k_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__diff__assoc,axiom, % 181.25/181.46 ! [V_i,V_j,V_k] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__add__diff__inverse,axiom, % 181.25/181.46 ! [V_m,V_n] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__add__diff,axiom, % 181.25/181.46 ! [V_m,V_n,V_k] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__diff__conv,axiom, % 181.25/181.46 ! [V_i_2,V_k_2,V_j_2] : % 181.25/181.46 ( 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)) % 181.25/181.46 <=> 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__diff__right,axiom, % 181.25/181.46 ! [V_i,V_j,V_k] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Osingleton,axiom, % 181.25/181.46 ! [V_x_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Osingleton,axiom, % 181.25/181.46 ! [V_x_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__add__iff1,axiom, % 181.25/181.46 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 181.25/181.46 ( class_Rings_Oordered__ring(T_b) % 181.25/181.46 => ( 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_c_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))) % 181.25/181.46 <=> 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_c_2)),V_d_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__add__iff2,axiom, % 181.25/181.46 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 181.25/181.46 ( class_Rings_Oordered__ring(T_b) % 181.25/181.46 => ( 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_c_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))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__add__iff2,axiom, % 181.25/181.46 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 181.25/181.46 ( class_Rings_Oordered__ring(T_b) % 181.25/181.46 => ( 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_c_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))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__add__iff1,axiom, % 181.25/181.46 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 181.25/181.46 ( class_Rings_Oordered__ring(T_b) % 181.25/181.46 => ( 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_c_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))) % 181.25/181.46 <=> 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_c_2)),V_d_2)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 181.25/181.46 ! [V_ry,V_rx,V_lx,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 181.25/181.46 ! [V_ry,V_rx,V_lx,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 181.25/181.46 ! [V_rx,V_ly,V_lx,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 181.25/181.46 ! [V_rx,V_ly,V_lx,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 181.25/181.46 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 181.25/181.46 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 181.25/181.46 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Oin__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_sup__Inf__absorb,axiom, % 181.25/181.46 ! [V_a_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.46 => 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 ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Oin__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_inf__Sup__absorb,axiom, % 181.25/181.46 ! [V_a_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.46 => 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 ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_OF__eq,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_OF__eq,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card_Ounion__inter,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Un__Int,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Oinsert__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Oinsert__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Osubset__idem,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.46 => 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) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Osubset__idem,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.46 => 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) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Ounion__idem,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Ounion__idem,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Un__disjoint,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card_Oinsert,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Oinsert,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Oinsert,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Oinsert__remove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ( 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)) % 181.25/181.46 => 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 ) % 181.25/181.46 & ( 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)) % 181.25/181.46 => 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)))))) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Oinsert__remove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ( 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)) % 181.25/181.46 => 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 ) % 181.25/181.46 & ( 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)) % 181.25/181.46 => 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)))))) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Ounion__inter,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Ounion__inter,axiom, % 181.25/181.46 ! [V_B_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card_Oinsert__remove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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)))))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Oremove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( ( 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)) % 181.25/181.46 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) % 181.25/181.46 & ( 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)) % 181.25/181.46 => 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)))))) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Oremove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( ( 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)) % 181.25/181.46 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) % 181.25/181.46 & ( 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)) % 181.25/181.46 => 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)))))) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__less__add__iff2,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__less__add__iff1,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__le__add__iff1,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__diff__add__eq1,axiom, % 181.25/181.46 ! [V_n,V_m,V_u,V_i,V_j] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__eq__add__iff1,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 181.25/181.46 => ( 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) % 181.25/181.46 <=> 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 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__le__add__iff2,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__diff__add__eq2,axiom, % 181.25/181.46 ! [V_n,V_m,V_u,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_left__add__mult__distrib,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__eq__add__iff2,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 181.25/181.46 => ( 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) % 181.25/181.46 <=> 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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Oclosed,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( ! [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)))))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Oclosed,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( ! [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)))))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__Max__commute,axiom, % 181.25/181.46 ! [V_k_2,V_N_2,T_b] : % 181.25/181.46 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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))))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__Min__commute,axiom, % 181.25/181.46 ! [V_k_2,V_N_2,T_b] : % 181.25/181.46 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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))))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold__Un__disjoint,axiom, % 181.25/181.46 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.46 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => ( 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)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Inf__fin_Ohom__commute,axiom, % 181.25/181.46 ! [V_N_2,V_h_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( ! [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)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Sup__fin_Ohom__commute,axiom, % 181.25/181.46 ! [V_N_2,V_h_2,T_b] : % 181.25/181.46 ( class_Lattices_Olattice(T_b) % 181.25/181.46 => ( ! [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)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold__image__empty,axiom, % 181.25/181.46 ! [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 ). % 181.25/181.46 % 181.25/181.46 fof(fact_minus__Min__eq__Max,axiom, % 181.25/181.46 ! [V_S_2,T_b] : % 181.25/181.46 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.46 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_minus__Max__eq__Min,axiom, % 181.25/181.46 ! [V_S_2,T_b] : % 181.25/181.46 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.46 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Min_Osingleton,axiom, % 181.25/181.46 ! [V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Max_Osingleton,axiom, % 181.25/181.46 ! [V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 181.25/181.46 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => 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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_folding__image_Oeq__fold,axiom, % 181.25/181.46 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => 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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Min__le,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Max__ge,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Min__in,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Max__in,axiom, % 181.25/181.46 ! [V_A_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold__image__distrib,axiom, % 181.25/181.46 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 181.25/181.46 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold__image__insert,axiom, % 181.25/181.46 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] : % 181.25/181.46 ( class_Groups_Oab__semigroup__mult(T_c) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Min__antimono,axiom, % 181.25/181.46 ! [V_N_2,V_M_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 181.25/181.46 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.46 => 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))) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Max__mono,axiom, % 181.25/181.46 ! [V_N_2,V_M_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 181.25/181.46 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.46 => 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))) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold__image__Un__Int,axiom, % 181.25/181.46 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.46 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold__image__reindex,axiom, % 181.25/181.46 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] : % 181.25/181.46 ( class_Groups_Oab__semigroup__mult(T_d) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) % 181.25/181.46 => 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) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_image__eq__fold__image,axiom, % 181.25/181.46 ! [V_f_2,T_c,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_comm__monoid__big_OF__eq,axiom, % 181.25/181.46 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.46 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 181.25/181.46 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => 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) ) % 181.25/181.46 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.46 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_fold__image__Un__one,axiom, % 181.25/181.46 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 181.25/181.46 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 181.25/181.46 => ( ! [B_x] : % 181.25/181.46 ( 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))) % 181.25/181.46 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 181.25/181.46 => 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)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_card__Suc__Diff1,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => 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) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Min_Oremove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( ( 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)) % 181.25/181.46 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) % 181.25/181.46 & ( 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)) % 181.25/181.46 => 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)))))) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Max_Oremove,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.46 => ( ( 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)) % 181.25/181.46 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) % 181.25/181.46 & ( 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)) % 181.25/181.46 => 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)))))) ) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_max__extp_Oequations,axiom, % 181.25/181.46 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 181.25/181.46 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 181.25/181.46 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 181.25/181.46 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 181.25/181.46 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.46 & ! [B_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 181.25/181.46 => ? [B_xa] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_pigeonhole__infinite,axiom, % 181.25/181.46 ! [V_f_2,T_c,V_A_2,T_b] : % 181.25/181.46 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 181.25/181.46 => ? [B_x] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.46 & ~ 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)))))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__mono,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_lessI,axiom, % 181.25/181.46 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_n__not__Suc__n,axiom, % 181.25/181.46 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__n__not__n,axiom, % 181.25/181.46 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 181.25/181.46 % 181.25/181.46 fof(fact_max__Suc__Suc,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__Suc__Suc,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat_Oinject,axiom, % 181.25/181.46 ! [V_nat_H_2,V_nat_2] : % 181.25/181.46 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 181.25/181.46 <=> V_nat_2 = V_nat_H_2 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__inject,axiom, % 181.25/181.46 ! [V_y,V_x] : % 181.25/181.46 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 181.25/181.46 => V_x = V_y ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup_Oidem,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf_Oidem,axiom, % 181.25/181.46 ! [V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup_Ocommute,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__commute,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf_Ocommute,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__commute,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__inf__absorb,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__sup__absorb,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup_Oleft__idem,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__left__idem,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 181.25/181.46 ! [V_b,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__left__idem,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup_Oleft__commute,axiom, % 181.25/181.46 ! [V_c,V_a,V_b,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__left__commute,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 181.25/181.46 ! [V_c,V_a,V_b,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__left__commute,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__inf__distrib1,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup_Oassoc,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__assoc,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf_Oassoc,axiom, % 181.25/181.46 ! [V_c,V_b,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__assoc,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__inf__distrib2,axiom, % 181.25/181.46 ! [V_x,V_z,V_y,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 181.25/181.46 ! [V_x,V_z,V_y,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_minus__max__eq__min,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Groups_Olinordered__ab__group__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_minus__min__eq__max,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Groups_Olinordered__ab__group__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Odistrib__inf__le,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Odistrib__sup__le,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Max_Oidem,axiom, % 181.25/181.46 ! [V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Min_Oidem,axiom, % 181.25/181.46 ! [V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__max__iff__disj,axiom, % 181.25/181.46 ! [V_y_2,V_x_2,V_z_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) % 181.25/181.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__supE,axiom, % 181.25/181.46 ! [V_x,V_b,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( 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)) % 181.25/181.46 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 181.25/181.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__mono,axiom, % 181.25/181.46 ! [V_d,V_b,V_c,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__least,axiom, % 181.25/181.46 ! [V_z,V_x,V_y,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__supI,axiom, % 181.25/181.46 ! [V_b,V_x,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 181.25/181.46 => 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)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__absorb1,axiom, % 181.25/181.46 ! [V_x,V_y,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.46 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Osup__absorb2,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.46 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__supI2,axiom, % 181.25/181.46 ! [V_a,V_b,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__supI1,axiom, % 181.25/181.46 ! [V_b,V_a,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__sup__iff,axiom, % 181.25/181.46 ! [V_z_2,V_y_2,V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( 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)) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__iff__sup,axiom, % 181.25/181.46 ! [V_y_2,V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.46 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__maxI2,axiom, % 181.25/181.46 ! [V_x,V_y,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__maxI1,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__le__iff__disj,axiom, % 181.25/181.46 ! [V_z_2,V_y_2,V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( 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)) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 181.25/181.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__infE,axiom, % 181.25/181.46 ! [V_b,V_a,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( 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))) % 181.25/181.46 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 181.25/181.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__mono,axiom, % 181.25/181.46 ! [V_d,V_b,V_c,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__greatest,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__infI,axiom, % 181.25/181.46 ! [V_b,V_a,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 181.25/181.46 => 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))) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__absorb2,axiom, % 181.25/181.46 ! [V_x,V_y,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 181.25/181.46 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__absorb1,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.46 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__infI2,axiom, % 181.25/181.46 ! [V_a,V_x,V_b,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__infI1,axiom, % 181.25/181.46 ! [V_b,V_x,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__inf__iff,axiom, % 181.25/181.46 ! [V_z_2,V_y_2,V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ole__iff__inf,axiom, % 181.25/181.46 ! [V_y_2,V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.25/181.46 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__le2,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oinf__le1,axiom, % 181.25/181.46 ! [V_y,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__max__iff__disj,axiom, % 181.25/181.46 ! [V_y_2,V_x_2,V_z_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 181.25/181.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_max__less__iff__conj,axiom, % 181.25/181.46 ! [V_z_2,V_y_2,V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( 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)) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oless__supI1,axiom, % 181.25/181.46 ! [V_b,V_a,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oless__supI2,axiom, % 181.25/181.46 ! [V_a,V_b,V_x,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 181.25/181.46 => 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))) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__less__iff__conj,axiom, % 181.25/181.46 ! [V_y_2,V_x_2,V_z_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( 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))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 181.25/181.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__less__iff__disj,axiom, % 181.25/181.46 ! [V_z_2,V_y_2,V_x_2,T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => ( 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)) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 181.25/181.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oless__infI1,axiom, % 181.25/181.46 ! [V_b,V_x,V_a,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Oless__infI2,axiom, % 181.25/181.46 ! [V_a,V_x,V_b,T_a] : % 181.25/181.46 ( class_Orderings_Olinorder(T_a) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 181.25/181.46 => 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)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_max__add__distrib__left,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__add__distrib__left,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_max__diff__distrib__left,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__group__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__diff__distrib__left,axiom, % 181.25/181.46 ! [V_z,V_y,V_x,T_a] : % 181.25/181.46 ( class_Groups_Oordered__ab__group__add(T_a) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_sup__max,axiom, % 181.25/181.46 ! [T_b] : % 181.25/181.46 ( ( class_Lattices_Osemilattice__sup(T_b) % 181.25/181.46 & class_Orderings_Olinorder(T_b) ) % 181.25/181.46 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_inf__min,axiom, % 181.25/181.46 ! [T_b] : % 181.25/181.46 ( ( class_Lattices_Osemilattice__inf(T_b) % 181.25/181.46 & class_Orderings_Olinorder(T_b) ) % 181.25/181.46 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__diff,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_not__less__eq,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__Suc__eq,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.46 | V_m_2 = V_n_2 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__less__eq,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_not__less__less__Suc__eq,axiom, % 181.25/181.46 ! [V_m_2,V_n_2] : % 181.25/181.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 181.25/181.46 <=> V_n_2 = V_m_2 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__antisym,axiom, % 181.25/181.46 ! [V_m,V_n] : % 181.25/181.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 181.25/181.46 => V_m = V_n ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__SucI,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__lessI,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__trans__Suc,axiom, % 181.25/181.46 ! [V_k,V_j,V_i] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__SucE,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => V_m = V_n ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__lessD,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__less__SucD,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__Suc__right,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__Suc,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_add__Suc__shift,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__n__not__le__n,axiom, % 181.25/181.46 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_not__less__eq__eq,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__Suc__eq,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 181.25/181.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.46 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__le__mono,axiom, % 181.25/181.46 ! [V_m_2,V_n_2] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__SucI,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__SucE,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 181.25/181.46 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__leD,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__Suc__Suc,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__diff__diff,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__mult__cancel1,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.46 ( 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) % 181.25/181.46 <=> V_m_2 = V_n_2 ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 181.25/181.46 ! [T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 181.25/181.46 ! [T_b] : % 181.25/181.46 ( class_Orderings_Olinorder(T_b) % 181.25/181.46 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_inj__Suc,axiom, % 181.25/181.46 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 181.25/181.46 % 181.25/181.46 fof(fact_nat__minus__add__max,axiom, % 181.25/181.46 ! [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) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__iff__Suc__add,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.46 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__add__Suc2,axiom, % 181.25/181.46 ! [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)))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__add__Suc1,axiom, % 181.25/181.46 ! [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)))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__eq__Suc__le,axiom, % 181.25/181.46 ! [V_m_2,V_n_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__Suc__eq__le,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__le__eq,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__imp__less__Suc,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__leI,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_le__less__Suc__eq,axiom, % 181.25/181.46 ! [V_n_2,V_m_2] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 181.25/181.46 <=> V_n_2 = V_m_2 ) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__le__lessD,axiom, % 181.25/181.46 ! [V_n,V_m] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 181.25/181.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__less__Suc,axiom, % 181.25/181.46 ! [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))) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__mult__less__cancel1,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_mult__Suc,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_mult__Suc__right,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__diff__le,axiom, % 181.25/181.46 ! [V_m,V_n] : % 181.25/181.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.46 => 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)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Suc__mult__le__cancel1,axiom, % 181.25/181.46 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.46 ( 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))) % 181.25/181.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.46 % 181.25/181.46 fof(fact_diff__Suc__1,axiom, % 181.25/181.46 ! [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 ). % 181.25/181.46 % 181.25/181.46 fof(fact_less__eq__Suc__le__raw,axiom, % 181.25/181.46 ! [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)) ). % 181.25/181.46 % 181.25/181.46 fof(fact_Max_Oin__idem,axiom, % 181.25/181.46 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => 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) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_Oin__idem,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => 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) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__Suc__diff__eq1,axiom, % 181.25/181.47 ! [V_m,V_j,V_k] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__Suc__diff__eq2,axiom, % 181.25/181.47 ! [V_m,V_j,V_k] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max_OF__eq,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_OF__eq,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_Ofold1__belowI,axiom, % 181.25/181.47 ! [V_a_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_Obelow__fold1__iff,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> ! [B_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_fold1__below__iff,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( 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)) % 181.25/181.47 <=> ? [B_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_strict__below__fold1__iff,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> ! [B_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_fold1__strict__below__iff,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( 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)) % 181.25/181.47 <=> ? [B_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max__insert,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min__insert,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max_Osubset__idem,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.47 => 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) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_Osubset__idem,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.47 => 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) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max__Un,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min__Un,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__insert__disjoint,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__insert__if,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => 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) ) % 181.25/181.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__monoid__big_Oinfinite,axiom, % 181.25/181.47 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 181.25/181.47 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 181.25/181.47 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.25/181.47 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max_Oinsert,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_Oinsert,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_fold1__antimono,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => 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))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max_Oinsert__remove,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ( 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)) % 181.25/181.47 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 181.25/181.47 & ( 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)) % 181.25/181.47 => 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)))))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max_Ounion__disjoint,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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)) ) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max_Ounion__inter,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_Oinsert__remove,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ( 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)) % 181.25/181.47 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 181.25/181.47 & ( 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)) % 181.25/181.47 => 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)))))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_Ounion__disjoint,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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)) ) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_Ounion__inter,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__insert,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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)))))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__Suc__eq__diff__pred,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Suc__eq__plus1__left,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Suc__eq__plus1,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_dual__min,axiom, % 181.25/181.47 ! [T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_dual__max,axiom, % 181.25/181.47 ! [T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_max__ord__max,axiom, % 181.25/181.47 ! [T_b] : % 181.25/181.47 ( class_Orderings_Oord(T_b) % 181.25/181.47 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_sup__nat__def,axiom, % 181.25/181.47 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_inf__nat__def,axiom, % 181.25/181.47 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__ord__min,axiom, % 181.25/181.47 ! [T_b] : % 181.25/181.47 ( class_Orderings_Oord(T_b) % 181.25/181.47 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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))))))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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))))))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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))))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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))))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max_Oclosed,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( ! [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)))))) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_Oclosed,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( ! [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)))))) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__le__Sup,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => 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) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => 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) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 181.25/181.47 ! [V_x_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => 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 ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 181.25/181.47 ! [V_x_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => 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 ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.47 => 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) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.47 => 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) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 181.25/181.47 ! [V_a_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.47 => 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 ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_Osup__Inf__absorb,axiom, % 181.25/181.47 ! [V_a_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.47 => 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 ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ( 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)) % 181.25/181.47 => 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 ) % 181.25/181.47 & ( 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)) % 181.25/181.47 => 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)))))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ( 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)) % 181.25/181.47 => 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 ) % 181.25/181.47 & ( 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)) % 181.25/181.47 => 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)))))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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)) ) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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)) ) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Oremove,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => ( ( 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)) % 181.25/181.47 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) % 181.25/181.47 & ( 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)) % 181.25/181.47 => 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)))))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Oremove,axiom, % 181.25/181.47 ! [V_x_2,V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => ( ( 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)) % 181.25/181.47 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) % 181.25/181.47 & ( 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)) % 181.25/181.47 => 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)))))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( ! [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)))))) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => ( ! [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)))))) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_finite__fun__UNIVD1,axiom, % 181.25/181.47 ! [T_c,T_b] : % 181.25/181.47 ( 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)))) % 181.25/181.47 => ( 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)) % 181.25/181.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 181.25/181.47 ! [V_N_2,V_h_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( ! [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)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.47 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 181.25/181.47 ! [V_N_2,V_h_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( ! [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)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.47 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Max_Ohom__commute,axiom, % 181.25/181.47 ! [V_N_2,V_h_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( ! [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)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.47 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_less__zeroE,axiom, % 181.25/181.47 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_le0,axiom, % 181.25/181.47 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__less__Suc,axiom, % 181.25/181.47 ! [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))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__reorient,axiom, % 181.25/181.47 ! [V_x_2,T_b] : % 181.25/181.47 ( class_Groups_Ozero(T_b) % 181.25/181.47 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2 % 181.25/181.47 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_bot__nat__def,axiom, % 181.25/181.47 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__0__iff,axiom, % 181.25/181.47 ! [V_a_2,V_b_2,T_b] : % 181.25/181.47 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 181.25/181.47 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) % 181.25/181.47 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add_Ocomm__neutral,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__add(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__0__right,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Omonoid__add(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_double__zero__sym,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) % 181.25/181.47 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__0,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__add(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__0__left,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Omonoid__add(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_divisors__zero,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Ono__zero__divisors(T_a) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.47 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.47 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_no__zero__divisors,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Ono__zero__divisors(T_a) % 181.25/181.47 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.47 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__eq__0__iff,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Oring__no__zero__divisors(T_b) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__zero__right,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Rings_Omult__zero(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__zero__left,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Rings_Omult__zero(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__0__right,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__self,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_a) % 181.25/181.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_eq__iff__diff__eq__0,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Oab__group__add(T_b) % 181.25/181.47 => ( V_a_2 = V_b_2 % 181.25/181.47 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_right__minus__eq,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_b) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 <=> V_a_2 = V_b_2 ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__neq__one,axiom, % 181.25/181.47 ! [T_a] : % 181.25/181.47 ( class_Rings_Ozero__neq__one(T_a) % 181.25/181.47 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_one__neq__zero,axiom, % 181.25/181.47 ! [T_a] : % 181.25/181.47 ( class_Rings_Ozero__neq__one(T_a) % 181.25/181.47 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_minus__zero,axiom, % 181.25/181.47 ! [T_a] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_a) % 181.25/181.47 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neg__0__equal__iff__equal,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_b) % 181.25/181.47 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 181.25/181.47 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_equal__neg__zero,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 181.25/181.47 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neg__equal__0__iff__equal,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_b) % 181.25/181.47 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neg__equal__zero,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 % 181.25/181.47 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Suc__neq__Zero,axiom, % 181.25/181.47 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Zero__neq__Suc,axiom, % 181.25/181.47 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat_Osimps_I3_J,axiom, % 181.25/181.47 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Suc__not__Zero,axiom, % 181.25/181.47 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat_Osimps_I2_J,axiom, % 181.25/181.47 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Zero__not__Suc,axiom, % 181.25/181.47 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 181.25/181.47 % 181.25/181.47 fof(fact_gr0I,axiom, % 181.25/181.47 ! [V_n] : % 181.25/181.47 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_gr__implies__not0,axiom, % 181.25/181.47 ! [V_n,V_m] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.47 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_less__nat__zero__code,axiom, % 181.25/181.47 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neq0__conv,axiom, % 181.25/181.47 ! [V_n_2] : % 181.25/181.47 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_not__less0,axiom, % 181.25/181.47 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__eq__self__zero,axiom, % 181.25/181.47 ! [V_n,V_m] : % 181.25/181.47 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 181.25/181.47 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__is__0,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Nat_Oadd__0__right,axiom, % 181.25/181.47 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 181.25/181.47 % 181.25/181.47 fof(fact_plus__nat_Oadd__0,axiom, % 181.25/181.47 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 181.25/181.47 % 181.25/181.47 fof(fact_le__0__eq,axiom, % 181.25/181.47 ! [V_n_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 181.25/181.47 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 181.25/181.47 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diffs0__imp__equal,axiom, % 181.25/181.47 ! [V_n,V_m] : % 181.25/181.47 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => V_m = V_n ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__self__eq__0,axiom, % 181.25/181.47 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_minus__nat_Odiff__0,axiom, % 181.25/181.47 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__0__eq__0,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__cancel2,axiom, % 181.25/181.47 ! [V_n_2,V_k_2,V_m_2] : % 181.25/181.47 ( 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) % 181.25/181.47 <=> ( V_m_2 = V_n_2 % 181.25/181.47 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__cancel1,axiom, % 181.25/181.47 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.47 ( 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) % 181.25/181.47 <=> ( V_m_2 = V_n_2 % 181.25/181.47 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__is__0,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__0__right,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__0,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__mult__eq__cancel__disj,axiom, % 181.25/181.47 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.47 ( 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) % 181.25/181.47 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 | V_m_2 = V_n_2 ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__0L,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__0R,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_max__0L,axiom, % 181.25/181.47 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 181.25/181.47 % 181.25/181.47 fof(fact_max__0R,axiom, % 181.25/181.47 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__nonpos__nonpos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__increasing2,axiom, % 181.25/181.47 ! [V_a,V_b,V_c,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__increasing,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__nonneg__eq__0__iff,axiom, % 181.25/181.47 ! [V_y_2,V_x_2,T_b] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__nonneg__nonneg,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_split__mult__neg__le,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__cancel__semiring(T_a) % 181.25/181.47 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 181.25/181.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_split__mult__pos__le,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__ring(T_a) % 181.25/181.47 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 181.25/181.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__mono,axiom, % 181.25/181.47 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__mono_H,axiom, % 181.25/181.47 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__left__mono__neg,axiom, % 181.25/181.47 ! [V_c,V_a,V_b,T_a] : % 181.25/181.47 ( class_Rings_Oordered__ring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__right__mono__neg,axiom, % 181.25/181.47 ! [V_c,V_a,V_b,T_a] : % 181.25/181.47 ( class_Rings_Oordered__ring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__mult__left__mono,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__comm__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__left__mono,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__right__mono,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__nonpos__nonpos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__ring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__nonpos__nonneg,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__cancel__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__nonneg__nonpos2,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__cancel__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__nonneg__nonpos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__cancel__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__nonneg__nonneg,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oordered__cancel__semiring(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__le__0__iff,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 181.25/181.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__le__mult__iff,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 181.25/181.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__le__square,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__ring(T_a) % 181.25/181.47 => 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_pos__add__strict,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__pos__pos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__neg__neg,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__strict__left__mono__neg,axiom, % 181.25/181.47 ! [V_c,V_a,V_b,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__strict__right__mono__neg,axiom, % 181.25/181.47 ! [V_c,V_a,V_b,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__mult__strict__left__mono,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__strict__left__mono,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__strict__right__mono,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__neg__neg,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__neg__pos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__cancel__left__neg,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__less__mult__pos2,axiom, % 181.25/181.47 ! [V_a,V_b,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__less__mult__pos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__pos__neg2,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__pos__neg,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__pos__pos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__cancel__left__pos,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__cancel__left__disj,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 181.25/181.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) % 181.25/181.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__cancel__right__disj,axiom, % 181.25/181.47 ! [V_b_2,V_c_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) % 181.25/181.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) % 181.25/181.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_not__square__less__zero,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__ring(T_a) % 181.25/181.47 => ~ 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_le__iff__diff__le__0,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 181.25/181.47 <=> 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_less__iff__diff__less__0,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 181.25/181.47 <=> 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_sum__squares__eq__zero__iff,axiom, % 181.25/181.47 ! [V_y_2,V_x_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( 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) % 181.25/181.47 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__scale__eq__noteq,axiom, % 181.25/181.47 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 181.25/181.47 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 181.25/181.47 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.47 => ( ( V_a = V_b % 181.25/181.47 & V_c != V_d ) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_not__one__le__zero,axiom, % 181.25/181.47 ! [T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ~ 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__le__one,axiom, % 181.25/181.47 ! [T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_not__one__less__zero,axiom, % 181.25/181.47 ! [T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__less__one,axiom, % 181.25/181.47 ! [T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_minus__le__self__iff,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( 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)) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neg__le__0__iff__le,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_le__minus__self__iff,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neg__0__le__iff__le,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neg__0__less__iff__less,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neg__less__0__iff__less,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_neg__less__nonneg,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_less__minus__self__iff,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_minus__unique,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_a) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.47 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_ab__left__minus,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Oab__group__add(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_left__minus,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_eq__neg__iff__add__eq__0,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_b) % 181.25/181.47 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 181.25/181.47 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_right__minus,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__0,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Ogroup__add(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_gr0__conv__Suc,axiom, % 181.25/181.47 ! [V_n_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 181.25/181.47 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_less__Suc0,axiom, % 181.25/181.47 ! [V_n_2] : % 181.25/181.47 ( 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)))) % 181.25/181.47 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_less__Suc__eq__0__disj,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 181.25/181.47 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 | ? [B_j] : % 181.25/181.47 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__is__1,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( 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)) % 181.25/181.47 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 181.25/181.47 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.25/181.47 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_one__is__add,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( 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) % 181.25/181.47 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 181.25/181.47 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.25/181.47 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__gr__0,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 181.25/181.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card_Oempty,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__infinite,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__eq__1__iff,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( 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)) % 181.25/181.47 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 181.25/181.47 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__less,axiom, % 181.25/181.47 ! [V_m,V_n] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 181.25/181.47 => 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__less__diff,axiom, % 181.25/181.47 ! [V_m_2,V_n_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__mono2,axiom, % 181.25/181.47 ! [V_k,V_j,V_i] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__mono1,axiom, % 181.25/181.47 ! [V_k,V_j,V_i] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__cancel2,axiom, % 181.25/181.47 ! [V_n_2,V_k_2,V_m_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__cancel1,axiom, % 181.25/181.47 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__0__less__mult__iff,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 181.25/181.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__mult__eq__cancel1,axiom, % 181.25/181.47 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 181.25/181.47 => ( 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) % 181.25/181.47 <=> V_m_2 = V_n_2 ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__mult__less__cancel1,axiom, % 181.25/181.47 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__add__0,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__is__0__eq_H,axiom, % 181.25/181.47 ! [V_n,V_m] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__is__0__eq,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_One__nat__def,axiom, % 181.25/181.47 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__eq__self__implies__10,axiom, % 181.25/181.47 ! [V_n,V_m] : % 181.25/181.47 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 181.25/181.47 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 181.25/181.47 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__nonpos__neg,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__neg__nonpos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__strict__increasing2,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__strict__increasing,axiom, % 181.25/181.47 ! [V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__nonneg__pos,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__pos__nonneg,axiom, % 181.25/181.47 ! [V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Oordered__comm__monoid__add(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__left__le__imp__le,axiom, % 181.25/181.47 ! [V_b,V_a,V_c,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__right__le__imp__le,axiom, % 181.25/181.47 ! [V_b,V_c,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__imp__less__left,axiom, % 181.25/181.47 ! [V_b,V_a,V_c,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__left__less__imp__less,axiom, % 181.25/181.47 ! [V_b,V_a,V_c,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__imp__less__right,axiom, % 181.25/181.47 ! [V_b,V_c,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__right__less__imp__less,axiom, % 181.25/181.47 ! [V_b,V_c,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__le__less__imp__less,axiom, % 181.25/181.47 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__less__le__imp__less,axiom, % 181.25/181.47 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__strict__mono_H,axiom, % 181.25/181.47 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__strict__mono,axiom, % 181.25/181.47 ! [V_d,V_c,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.47 => 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))) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__le__cancel__left__neg,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__le__cancel__left__pos,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_sum__squares__le__zero__iff,axiom, % 181.25/181.47 ! [V_y_2,V_x_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_sum__squares__ge__zero,axiom, % 181.25/181.47 ! [V_y,V_x,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__ring(T_a) % 181.25/181.47 => 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)))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_sum__squares__gt__zero__iff,axiom, % 181.25/181.47 ! [V_y_2,V_x_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__ring__strict(T_b) % 181.25/181.47 => ( 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)))) % 181.25/181.47 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_not__sum__squares__lt__zero,axiom, % 181.25/181.47 ! [V_y,V_x,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__ring(T_a) % 181.25/181.47 => ~ 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__right__le__one__le,axiom, % 181.25/181.47 ! [V_y,V_x,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__left__le__one__le,axiom, % 181.25/181.47 ! [V_y,V_x,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__less__two,axiom, % 181.25/181.47 ! [T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => 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)))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__eq__0__iff,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__ge__0__finite,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( 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))) % 181.25/181.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__Suc__less,axiom, % 181.25/181.47 ! [V_i,V_n] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Suc__pred,axiom, % 181.25/181.47 ! [V_n] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.47 => 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 ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_n__less__m__mult__n,axiom, % 181.25/181.47 ! [V_m,V_n] : % 181.25/181.47 ( 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)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_n__less__n__mult__m,axiom, % 181.25/181.47 ! [V_m,V_n] : % 181.25/181.47 ( 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)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_one__less__mult,axiom, % 181.25/181.47 ! [V_m,V_n] : % 181.25/181.47 ( 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)) % 181.25/181.47 => ( 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)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__diff__split,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_Pa_2] : % 181.25/181.47 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 181.25/181.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 181.25/181.47 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 181.25/181.47 & ! [B_d] : % 181.25/181.47 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 181.25/181.47 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__diff__split__asm,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_Pa_2] : % 181.25/181.47 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 181.25/181.47 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 181.25/181.47 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 181.25/181.47 | ? [B_d] : % 181.25/181.47 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 181.25/181.47 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_one__le__mult__iff,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( 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)) % 181.25/181.47 & 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__le__cancel2,axiom, % 181.25/181.47 ! [V_n_2,V_k_2,V_m_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__le__cancel1,axiom, % 181.25/181.47 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__mult__le__cancel1,axiom, % 181.25/181.47 ! [V_n_2,V_m_2,V_k_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__less__Suc,axiom, % 181.25/181.47 ! [V_i_2,V_M_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 181.25/181.47 => 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))))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__less,axiom, % 181.25/181.47 ! [V_i_2,V_M_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__less__Suc2,axiom, % 181.25/181.47 ! [V_i_2,V_M_2] : % 181.25/181.47 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 181.25/181.47 => 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))))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_convex__bound__le,axiom, % 181.25/181.47 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__1(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 181.25/181.47 => 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)) ) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__gt__0__iff,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_finite__UNIV__card__ge__0,axiom, % 181.25/181.47 ! [T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 181.25/181.47 => 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))))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Suc__pred_H,axiom, % 181.25/181.47 ! [V_n] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.47 => 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Suc__diff__1,axiom, % 181.25/181.47 ! [V_n] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.47 => 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 ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add__eq__if,axiom, % 181.25/181.47 ! [V_n,V_m] : % 181.25/181.47 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 181.25/181.47 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_mult__eq__if,axiom, % 181.25/181.47 ! [V_n,V_m] : % 181.25/181.47 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.25/181.47 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card_Oeq__fold__g,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__def,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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) ) % 181.25/181.47 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_convex__bound__lt,axiom, % 181.25/181.47 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 181.25/181.47 => 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)) ) ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_option_Osize_I2_J,axiom, % 181.25/181.47 ! [V_a_2,V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_triple_Osize_I1_J,axiom, % 181.25/181.47 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_even__less__0__iff,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat_Osize_I2_J,axiom, % 181.25/181.47 ! [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))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_triple_Osize_I2_J,axiom, % 181.25/181.47 ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card_Ounion__inter__neutral,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.47 => ( ( ? [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))) % 181.25/181.47 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat_Osize_I1_J,axiom, % 181.25/181.47 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_double__eq__0__iff,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Groups_Olinordered__ab__group__add(T_b) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_option_Osize_I1_J,axiom, % 181.25/181.47 ! [V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,c_Option_Ooption_ONone(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat_Osize_I4_J,axiom, % 181.25/181.47 ! [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))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__Suc__eq,axiom, % 181.25/181.47 ! [V_k_2,V_A_2,T_b] : % 181.25/181.47 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 181.25/181.47 <=> ? [B_b,B_B] : % 181.25/181.47 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) % 181.25/181.47 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) % 181.25/181.47 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 % 181.25/181.47 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_option_Osize_I4_J,axiom, % 181.25/181.47 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_option_Osize_I3_J,axiom, % 181.25/181.47 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__odd__less__0,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__size,axiom, % 181.25/181.47 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__0,axiom, % 181.25/181.47 ! [T_b] : % 181.25/181.47 ( class_Rings_Oring__1(T_b) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__add,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Oring__1(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__mult,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Oring__1(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat_Osize_I3_J,axiom, % 181.25/181.47 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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__diff,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Oring__1(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__1,axiom, % 181.25/181.47 ! [T_b] : % 181.25/181.47 ( class_Rings_Oring__1(T_b) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__minus,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Oring__1(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__double__eq__0__iff,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Int_Oring__char__0(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__odd__nonzero,axiom, % 181.25/181.47 ! [V_a_2,T_b] : % 181.25/181.47 ( class_Int_Oring__char__0(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I4_J,axiom, % 181.25/181.47 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__Pow,axiom, % 181.25/181.47 ! [V_A_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I5_J,axiom, % 181.25/181.47 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I6_J,axiom, % 181.25/181.47 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__Plus__conv__if,axiom, % 181.25/181.47 ! [V_B_2,T_c,V_A_2,T_b] : % 181.25/181.47 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 181.25/181.47 => 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)) ) % 181.25/181.47 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 181.25/181.47 ! [V_q,V_y,V_x,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 181.25/181.47 ! [V_q,V_p,V_x,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 181.25/181.47 ! [V_x,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 181.25/181.47 ! [V_q,V_x,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 181.25/181.47 ! [V_q,V_x,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 181.25/181.47 ! [V_q,V_x,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 181.25/181.47 ! [V_x,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 181.25/181.47 ! [V_q,V_p,V_x,T_a] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Ints__power,axiom, % 181.25/181.47 ! [V_n_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Oring__1(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I7_J,axiom, % 181.25/181.47 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I2_J,axiom, % 181.25/181.47 ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I1_J,axiom, % 181.25/181.47 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__eq__if,axiom, % 181.25/181.47 ! [V_p,V_m] : % 181.25/181.47 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 181.25/181.47 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => 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)))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_finite__Plus__iff,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_c,T_b] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_finite__Plus,axiom, % 181.25/181.47 ! [V_B_2,T_c,V_A_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_finite__PlusD_I1_J,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_c,T_b] : % 181.25/181.47 ( 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))) % 181.25/181.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_finite__PlusD_I2_J,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_c,T_b] : % 181.25/181.47 ( 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))) % 181.25/181.47 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_card__Plus,axiom, % 181.25/181.47 ! [V_B_2,T_c,V_A_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.25/181.47 => 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__strict__mono,axiom, % 181.25/181.47 ! [V_n,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.47 => 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))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_one__less__power,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__le__imp__le__exp,axiom, % 181.25/181.47 ! [V_n,V_m,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => ( 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))) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__increasing__iff,axiom, % 181.25/181.47 ! [V_y_2,V_x_2,V_b_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__decreasing,axiom, % 181.25/181.47 ! [V_a,V_N,V_n,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 181.25/181.47 => 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))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zpower__zadd__distrib,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zpower__zpower,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_field__power__not__zero,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 181.25/181.47 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.47 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__commutes,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__mult__distrib,axiom, % 181.25/181.47 ! [V_n,V_b,V_a,T_a] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__one,axiom, % 181.25/181.47 ! [V_n,T_a] : % 181.25/181.47 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__mult,axiom, % 181.25/181.47 ! [V_n,V_m,V_a,T_a] : % 181.25/181.47 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__one__right,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.47 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__mono,axiom, % 181.25/181.47 ! [V_n,V_b,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__le__power,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zero__less__power,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__eq__0__iff,axiom, % 181.25/181.47 ! [V_n_2,V_a_2,T_b] : % 181.25/181.47 ( ( class_Power_Opower(T_b) % 181.25/181.47 & class_Rings_Omult__zero(T_b) % 181.25/181.47 & class_Rings_Ono__zero__divisors(T_b) % 181.25/181.47 & class_Rings_Ozero__neq__one(T_b) ) % 181.25/181.47 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.47 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_one__le__power,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__0__Suc,axiom, % 181.25/181.47 ! [V_n,T_a] : % 181.25/181.47 ( ( class_Power_Opower(T_a) % 181.25/181.47 & class_Rings_Osemiring__0(T_a) ) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__inject__exp,axiom, % 181.25/181.47 ! [V_n_2,V_m_2,V_a_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) % 181.25/181.47 => ( 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) % 181.25/181.47 <=> V_m_2 = V_n_2 ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__Suc,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Power_Opower(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__Suc2,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__0,axiom, % 181.25/181.47 ! [V_a,T_a] : % 181.25/181.47 ( class_Power_Opower(T_a) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__add,axiom, % 181.25/181.47 ! [V_n,V_m,V_a,T_a] : % 181.25/181.47 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 181.25/181.47 ! [V_m_2,V_x_2] : % 181.25/181.47 ( 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)) % 181.25/181.47 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__Suc__0,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__power__less__imp__less,axiom, % 181.25/181.47 ! [V_n,V_m,V_i] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 181.25/181.47 => ( 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))) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__zero__less__power__iff,axiom, % 181.25/181.47 ! [V_n_2,V_x_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 181.25/181.47 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__less__imp__less__base,axiom, % 181.25/181.47 ! [V_b,V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( 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))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__le__imp__le__base,axiom, % 181.25/181.47 ! [V_b,V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( 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)))) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__inject__base,axiom, % 181.25/181.47 ! [V_b,V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( 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)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => V_a = V_b ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__less__power__Suc,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => 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)))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__gt1__lemma,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => 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)))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__0__left,axiom, % 181.25/181.47 ! [V_n,T_a] : % 181.25/181.47 ( ( class_Power_Opower(T_a) % 181.25/181.47 & class_Rings_Osemiring__0(T_a) ) % 181.25/181.47 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => 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) ) % 181.25/181.47 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.47 => 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) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__gt1,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => 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)))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__strict__increasing,axiom, % 181.25/181.47 ! [V_a,V_N,V_n,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__less__imp__less__exp,axiom, % 181.25/181.47 ! [V_n,V_m,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => ( 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))) % 181.25/181.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__strict__increasing__iff,axiom, % 181.25/181.47 ! [V_y_2,V_x_2,V_b_2,T_b] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_b) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__increasing,axiom, % 181.25/181.47 ! [V_a,V_N,V_n,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__minus,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Oring__1(T_a) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__one__le__power,axiom, % 181.25/181.47 ! [V_n,V_i] : % 181.25/181.47 ( 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)) % 181.25/181.47 => 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__Suc__less,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__eq__imp__eq__base,axiom, % 181.25/181.47 ! [V_b,V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( 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) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.47 => V_a = V_b ) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__Suc__less__one,axiom, % 181.25/181.47 ! [V_n,V_a,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__strict__decreasing,axiom, % 181.25/181.47 ! [V_a,V_N,V_n,T_a] : % 181.25/181.47 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 181.25/181.47 => 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))) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_UNIV__Plus__UNIV,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Plus__eq__empty__conv,axiom, % 181.25/181.47 ! [V_B_2,V_A_2,T_c,T_b] : % 181.25/181.47 ( 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)) % 181.25/181.47 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power__power__power,axiom, % 181.25/181.47 ! [T_b] : % 181.25/181.47 ( class_Power_Opower(T_b) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I12_J,axiom, % 181.25/181.47 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I13_J,axiom, % 181.25/181.47 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__zmult__distrib2,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__zmult__distrib,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zmult__zminus,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zdiff__zmult__distrib,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zdiff__zmult__distrib2,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zmult__commute,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zmult__assoc,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zmult__1,axiom, % 181.25/181.47 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 181.25/181.47 % 181.25/181.47 fof(fact_zmult__1__right,axiom, % 181.25/181.47 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 181.25/181.47 % 181.25/181.47 fof(fact_pos__zmult__eq__1__iff,axiom, % 181.25/181.47 ! [V_n_2,V_m_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 181.25/181.47 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 181.25/181.47 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 181.25/181.47 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zmult__zless__mono2,axiom, % 181.25/181.47 ! [V_k,V_j,V_i] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_power_Opower_Opower__0,axiom, % 181.25/181.47 ! [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 ). % 181.25/181.47 % 181.25/181.47 fof(fact_power_Opower_Opower__Suc,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I15_J,axiom, % 181.25/181.47 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I10_J,axiom, % 181.25/181.47 ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I9_J,axiom, % 181.25/181.47 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.47 % 181.25/181.47 fof(fact_com_Osize_I14_J,axiom, % 181.25/181.47 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__gen__delta,axiom, % 181.25/181.47 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.47 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.47 => 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_c_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_c_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)))) ) % 181.25/181.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.47 => 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_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_Min_Ohom__commute,axiom, % 181.25/181.47 ! [V_N_2,V_h_2,T_b] : % 181.25/181.47 ( class_Orderings_Olinorder(T_b) % 181.25/181.47 => ( ! [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)) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 181.25/181.47 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.25/181.47 => 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)) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_ex__least__nat__less,axiom, % 181.25/181.47 ! [V_n_2,V_Pa_2] : % 181.25/181.47 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 181.25/181.47 => ( hBOOL(hAPP(V_Pa_2,V_n_2)) % 181.25/181.47 => ? [B_k] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 181.25/181.47 & ! [B_i] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 181.25/181.47 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 181.25/181.47 & 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)))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__Suc2,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_min__Suc1,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_odd__nonzero,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_odd__less__0,axiom, % 181.25/181.47 ! [V_z_2] : % 181.25/181.47 ( 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))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_le__imp__0__less,axiom, % 181.25/181.47 ! [V_z] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.47 => 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__zminus__inverse2,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__0,axiom, % 181.25/181.47 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__0__right,axiom, % 181.25/181.47 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 181.25/181.47 % 181.25/181.47 fof(fact_zminus__0,axiom, % 181.25/181.47 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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_less__bin__lemma,axiom, % 181.25/181.47 ! [V_l_2,V_k_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 181.25/181.47 <=> 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_int__one__le__iff__zero__less,axiom, % 181.25/181.47 ! [V_z_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_int__0__less__1,axiom, % 181.25/181.47 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))) ). % 181.25/181.47 % 181.25/181.47 fof(fact_int__0__neq__1,axiom, % 181.25/181.47 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zle__diff1__eq,axiom, % 181.25/181.47 ! [V_z_2,V_w_2] : % 181.25/181.47 ( 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)))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zminus__zminus,axiom, % 181.25/181.47 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 181.25/181.47 % 181.25/181.47 fof(fact_zless__linear,axiom, % 181.25/181.47 ! [V_y,V_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 181.25/181.47 | V_x = V_y % 181.25/181.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zless__le,axiom, % 181.25/181.47 ! [V_w_2,V_z_2] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 181.25/181.47 & V_z_2 != V_w_2 ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__int__def,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_diff__int__def__symmetric,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__assoc,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__left__commute,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__commute,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zminus__zadd__distrib,axiom, % 181.25/181.47 ! [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)) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__strict__right__mono,axiom, % 181.25/181.47 ! [V_k,V_j,V_i] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 181.25/181.47 => 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__zless__mono,axiom, % 181.25/181.47 ! [V_z,V_z_H,V_w,V_w_H] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 181.25/181.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 181.25/181.47 => 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))) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zadd__left__mono,axiom, % 181.25/181.47 ! [V_k,V_j,V_i] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 181.25/181.47 => 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))) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zle__add1__eq__le,axiom, % 181.25/181.47 ! [V_z_2,V_w_2] : % 181.25/181.47 ( 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)))) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_add1__zle__eq,axiom, % 181.25/181.47 ! [V_z_2,V_w_2] : % 181.25/181.47 ( 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)) % 181.25/181.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zless__imp__add1__zle,axiom, % 181.25/181.47 ! [V_z,V_w] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_zless__add1__eq,axiom, % 181.25/181.47 ! [V_z_2,V_w_2] : % 181.25/181.47 ( 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)))) % 181.25/181.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 181.25/181.47 | V_w_2 = V_z_2 ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__timesf,axiom, % 181.25/181.47 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_b) % 181.25/181.47 => 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)) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__1,axiom, % 181.25/181.47 ! [V_A_2,T_c,T_b] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_b) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__zero__iff,axiom, % 181.25/181.47 ! [V_f_2,V_A_2,T_b,T_c] : % 181.25/181.47 ( ( class_Rings_Ocomm__semiring__1(T_c) % 181.25/181.47 & class_Rings_Ono__zero__divisors(T_c) ) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( 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) % 181.25/181.47 <=> ? [B_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.47 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__zero,axiom, % 181.25/181.47 ! [V_f_2,V_A_2,T_b,T_c] : % 181.25/181.47 ( class_Rings_Ocomm__semiring__1(T_c) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ? [B_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.47 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 181.25/181.47 => 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) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__empty,axiom, % 181.25/181.47 ! [V_f_2,T_c,T_b] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_b) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod_Oempty,axiom, % 181.25/181.47 ! [V_g_2,T_c,T_b] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_b) % 181.25/181.47 => 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) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod_Oinfinite,axiom, % 181.25/181.47 ! [V_g_2,V_A_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__infinite,axiom, % 181.25/181.47 ! [V_f_2,V_A_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__eq__1__iff,axiom, % 181.25/181.47 ! [V_f_2,V_F_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.25/181.47 => ( 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) % 181.25/181.47 <=> ! [B_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 181.25/181.47 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod_Odistrib,axiom, % 181.25/181.47 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__case__0,axiom, % 181.25/181.47 ! [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 ). % 181.25/181.47 % 181.25/181.47 fof(fact_nat__case__Suc,axiom, % 181.25/181.47 ! [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) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__pos__nat__iff,axiom, % 181.25/181.47 ! [V_f_2,V_S_2,T_b] : % 181.25/181.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.47 => ( 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))) % 181.25/181.47 <=> ! [B_x] : % 181.25/181.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 181.25/181.47 => 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))) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__reindex__cong,axiom, % 181.25/181.47 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_d) % 181.25/181.47 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.47 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 181.25/181.47 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) % 181.25/181.47 => 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) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__reindex,axiom, % 181.25/181.47 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_d) % 181.25/181.47 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 181.25/181.47 => 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) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__reindex__id,axiom, % 181.25/181.47 ! [V_B_2,V_f_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 181.25/181.47 => 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__delta,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.47 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.47 => 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) ) % 181.25/181.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.47 => 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) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__delta_H,axiom, % 181.25/181.47 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.47 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.47 => 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) ) % 181.25/181.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.47 => 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) ) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__constant,axiom, % 181.25/181.47 ! [V_y_2,V_A_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => 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)) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod_Oinsert,axiom, % 181.25/181.47 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__insert,axiom, % 181.25/181.47 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 181.25/181.47 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.47 => 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)) ) ) ) ). % 181.25/181.47 % 181.25/181.47 fof(fact_setprod__Un__Int,axiom, % 181.25/181.47 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod_Ounion__inter,axiom, % 181.25/181.48 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod_Oreindex,axiom, % 181.25/181.48 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 181.25/181.48 => 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) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod_OF__eq,axiom, % 181.25/181.48 ! [V_g_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => 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) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => 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) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod_Oeq__fold,axiom, % 181.25/181.48 ! [V_g_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod_Oinsert__remove,axiom, % 181.25/181.48 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => 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)))))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod__Un__disjoint,axiom, % 181.25/181.48 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.48 => ( 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)) % 181.25/181.48 => 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)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod_Ounion__disjoint,axiom, % 181.25/181.48 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.48 => ( 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)) % 181.25/181.48 => 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)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_max__Suc1,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_max__Suc2,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod_Oremove,axiom, % 181.25/181.48 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.48 => 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)))))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_diff__Suc,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_self__quotient__aux1,axiom, % 181.25/181.48 ! [V_q,V_r,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( 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)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_self__quotient__aux2,axiom, % 181.25/181.48 ! [V_q,V_r,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( 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)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_q__pos__lemma,axiom, % 181.25/181.48 ! [V_r_H,V_q_H,V_b_H] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_q__neg__lemma,axiom, % 181.25/181.48 ! [V_r_H,V_q_H,V_b_H] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_unique__quotient__lemma,axiom, % 181.25/181.48 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zle__antisym,axiom, % 181.25/181.48 ! [V_w,V_z] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 181.25/181.48 => V_z = V_w ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zle__trans,axiom, % 181.25/181.48 ! [V_k,V_j,V_i] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zle__linear,axiom, % 181.25/181.48 ! [V_w,V_z] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 181.25/181.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zle__refl,axiom, % 181.25/181.48 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 181.25/181.48 ! [V_n_2,V_m_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 181.25/181.48 <=> 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__mono2__neg__lemma,axiom, % 181.25/181.48 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 181.25/181.48 ( 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) % 181.25/181.48 => ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_unique__quotient__lemma__neg,axiom, % 181.25/181.48 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__mono2__lemma,axiom, % 181.25/181.48 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 181.25/181.48 ( 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) % 181.25/181.48 => ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 181.25/181.48 ! [V_n,V_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 181.25/181.48 ! [V_y,V_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 181.25/181.48 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))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 181.25/181.48 ! [V_y,V_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod_Ounion__inter__neutral,axiom, % 181.25/181.48 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.48 => ( ! [B_x] : % 181.25/181.48 ( 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))) % 181.25/181.48 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 181.25/181.48 => 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)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 181.25/181.48 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))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod__Un__one,axiom, % 181.25/181.48 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 181.25/181.48 => ( ! [B_x] : % 181.25/181.48 ( 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))) % 181.25/181.48 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 181.25/181.48 => 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)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_tsub__def,axiom, % 181.25/181.48 ! [V_x,V_y] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 181.25/181.48 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 181.25/181.48 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_int__power__div__base,axiom, % 181.25/181.48 ! [V_k,V_m] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 181.25/181.48 => 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)))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__relI,axiom, % 181.25/181.48 ! [V_r,V_q,V_b,V_a] : % 181.25/181.48 ( 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) % 181.25/181.48 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod__diff1,axiom, % 181.25/181.48 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Fields_Ofield(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.48 => 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)) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.48 => 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) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_minus__divide__left,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_diff__divide__distrib,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__zero__left,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__zero,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_add__divide__distrib,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__1,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_power__divide,axiom, % 181.25/181.48 ! [V_n,V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_times__divide__eq__right,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zminus__zminus,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zminus2,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zero,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__rel__div,axiom, % 181.25/181.48 ! [V_r,V_q,V_b,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__0,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__by__0,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__by__1,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_unique__remainder,axiom, % 181.25/181.48 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( 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))) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => V_r = V_r_H ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_unique__quotient,axiom, % 181.25/181.48 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( 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))) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => V_q = V_q_H ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_self__remainder,axiom, % 181.25/181.48 ! [V_r,V_q,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__rel__0,axiom, % 181.25/181.48 ! [V_b] : % 181.25/181.48 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_eq__divide__imp,axiom, % 181.25/181.48 ! [V_b,V_a,V_c,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 181.25/181.48 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__eq__imp,axiom, % 181.25/181.48 ! [V_a,V_b,V_c,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 181.25/181.48 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_nonzero__divide__eq__eq,axiom, % 181.25/181.48 ! [V_a_2,V_b_2,V_c_2,T_b] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_b) % 181.25/181.48 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2 % 181.25/181.48 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_nonzero__eq__divide__eq,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_b) % 181.25/181.48 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) % 181.25/181.48 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__self__if,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 181.25/181.48 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 181.25/181.48 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__self,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_right__inverse__eq,axiom, % 181.25/181.48 ! [V_a_2,V_b_2,T_b] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_b) % 181.25/181.48 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b) % 181.25/181.48 <=> V_a_2 = V_b_2 ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_nonzero__minus__divide__right,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_nonzero__minus__divide__divide,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Rings_Odivision__ring(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_nonzero__power__divide,axiom, % 181.25/181.48 ! [V_n,V_a,V_b,T_a] : % 181.25/181.48 ( class_Fields_Ofield(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 181.25/181.48 ! [V_y,V_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 181.25/181.48 ! [V_a_2,V_b_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 181.25/181.48 ! [V_a_2,V_b_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__neg__pos__less0,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_power__one__over,axiom, % 181.25/181.48 ! [V_n,V_a,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__self,axiom, % 181.25/181.48 ! [V_a] : % 181.25/181.48 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__mult1,axiom, % 181.25/181.48 ! [V_b,V_a,V_c,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__mult2,axiom, % 181.25/181.48 ! [V_b,V_a,V_c,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__self1__is__id,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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 ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__self2__is__id,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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 ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__mult1__if,axiom, % 181.25/181.48 ! [V_b,V_a,V_c,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) % 181.25/181.48 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__self,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod__dividef,axiom, % 181.25/181.48 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_self__quotient,axiom, % 181.25/181.48 ! [V_r,V_q,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__mono1__neg,axiom, % 181.25/181.48 ! [V_b,V_a_H,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__mono1,axiom, % 181.25/181.48 ! [V_b,V_a_H,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__neg__neg__trivial,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__mono2__neg,axiom, % 181.25/181.48 ! [V_b,V_b_H,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__nonpos__pos__le0,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 181.25/181.48 ! [V_a_2,V_b_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__pos__pos__trivial,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__nonneg__neg__le0,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__mono2,axiom, % 181.25/181.48 ! [V_b,V_b_H,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 181.25/181.48 ! [V_b_2,V_a_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 181.25/181.48 ! [V_i_2,V_k_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 181.25/181.48 ! [V_a_2,V_b_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__eq__0__iff,axiom, % 181.25/181.48 ! [V_k_2,V_i_2] : % 181.25/181.48 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 181.25/181.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_int__div__less__self,axiom, % 181.25/181.48 ! [V_k,V_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zmult2__eq,axiom, % 181.25/181.48 ! [V_b,V_a,V_c] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__self1,axiom, % 181.25/181.48 ! [V_c,V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__self2,axiom, % 181.25/181.48 ! [V_c,V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__add__self2,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__add__self1,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_power__diff,axiom, % 181.25/181.48 ! [V_m,V_n,V_a,T_a] : % 181.25/181.48 ( class_Fields_Ofield(T_a) % 181.25/181.48 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__zdiv,axiom, % 181.25/181.48 ! [V_k_2,V_n_2,V_Pa_2] : % 181.25/181.48 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 181.25/181.48 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.48 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 181.25/181.48 => ! [B_i] : % 181.25/181.48 ( ? [B_j] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 181.25/181.48 & 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) ) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 181.25/181.48 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ! [B_i] : % 181.25/181.48 ( ? [B_j] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 & 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) ) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__rel__div__eq,axiom, % 181.25/181.48 ! [V_r_1,V_y,V_b_1,V_a_1] : % 181.25/181.48 ( 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) % 181.25/181.48 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 181.25/181.48 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 181.25/181.48 ! [V_y,V_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_tsub__eq,axiom, % 181.25/181.48 ! [V_x,V_y] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 181.25/181.48 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zminus1__lemma,axiom, % 181.25/181.48 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 181.25/181.48 ( 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))) % 181.25/181.48 => 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))))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__left__mono__neg,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => ( 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))) % 181.25/181.48 => 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))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__left__mono,axiom, % 181.25/181.48 ! [V_c,V_a,V_b,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.48 => ( 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))) % 181.25/181.48 => 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))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__divide__le__eq,axiom, % 181.25/181.48 ! [V_a_2,V_b_2,V_c_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__le__divide__eq,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => ( 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_c_2))) % 181.25/181.48 <=> 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_c_2))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mult__imp__le__div__pos,axiom, % 181.25/181.48 ! [V_x,V_z,V_y,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.48 => ( 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)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult2__eq,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__le__mono,axiom, % 181.25/181.48 ! [V_k,V_n,V_m] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__le__dividend,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__1,axiom, % 181.25/181.48 ! [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 ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__less,axiom, % 181.25/181.48 ! [V_n,V_m] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_nat__mult__div__cancel__disj,axiom, % 181.25/181.48 ! [V_n,V_m,V_k] : % 181.25/181.48 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 => 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) ) % 181.25/181.48 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__le__mono2,axiom, % 181.25/181.48 ! [V_k,V_n,V_m] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_nat__mult__div__cancel1,axiom, % 181.25/181.48 ! [V_n,V_m,V_k] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__self1__is__m,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.48 => 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 ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult__self__is__m,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.48 => 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 ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__less__dividend,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__if,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__geq,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.48 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__div,axiom, % 181.25/181.48 ! [V_k_2,V_n_2,V_Pa_2] : % 181.25/181.48 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 181.25/181.48 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 181.25/181.48 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 => ! [B_i,B_j] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 181.25/181.48 => ( 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) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_le__div__geq,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__div_H,axiom, % 181.25/181.48 ! [V_n_2,V_m_2,V_Pa_2] : % 181.25/181.48 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 181.25/181.48 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 181.25/181.48 | ? [B_q] : % 181.25/181.48 ( 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)) % 181.25/181.48 & 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)))) % 181.25/181.48 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__div__lemma,axiom, % 181.25/181.48 ! [V_m_2,V_q_2,V_n_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 181.25/181.48 => ( ( 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)) % 181.25/181.48 & 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)))) ) % 181.25/181.48 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_times__divide__times__eq,axiom, % 181.25/181.48 ! [V_w,V_z,V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_minus__divide__right,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_minus__divide__divide,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__right__mono__neg,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__right__mono,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__le__0__iff,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 181.25/181.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zero__le__divide__iff,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 181.25/181.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__strict__right__mono__neg,axiom, % 181.25/181.48 ! [V_c,V_a,V_b,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__strict__right__mono,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__neg__neg,axiom, % 181.25/181.48 ! [V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__neg__pos,axiom, % 181.25/181.48 ! [V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__pos__neg,axiom, % 181.25/181.48 ! [V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__pos__pos,axiom, % 181.25/181.48 ! [V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__less__0__iff,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 181.25/181.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zero__less__divide__iff,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 181.25/181.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_eq__divide__eq,axiom, % 181.25/181.48 ! [V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_b) % 181.25/181.48 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) % 181.25/181.48 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) % 181.25/181.48 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__eq__eq,axiom, % 181.25/181.48 ! [V_a_2,V_c_2,V_b_2,T_b] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_b) % 181.25/181.48 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2 % 181.25/181.48 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) % 181.25/181.48 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mult__divide__mult__cancel__right,axiom, % 181.25/181.48 ! [V_b,V_a,V_c,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mult__divide__mult__cancel__left,axiom, % 181.25/181.48 ! [V_b,V_a,V_c,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_frac__eq__eq,axiom, % 181.25/181.48 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] : % 181.25/181.48 ( class_Fields_Ofield(T_b) % 181.25/181.48 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.48 => ( 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) % 181.25/181.48 <=> 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) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__nonpos__neg,axiom, % 181.25/181.48 ! [V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__nonpos__pos,axiom, % 181.25/181.48 ! [V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_frac__le,axiom, % 181.25/181.48 ! [V_z,V_w,V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 181.25/181.48 => 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))) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_frac__less,axiom, % 181.25/181.48 ! [V_z,V_w,V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 181.25/181.48 => 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))) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_frac__less2,axiom, % 181.25/181.48 ! [V_z,V_w,V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 181.25/181.48 => 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))) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__nonneg__neg,axiom, % 181.25/181.48 ! [V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__nonneg__pos,axiom, % 181.25/181.48 ! [V_y,V_x,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__strict__left__mono__neg,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.48 => ( 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))) % 181.25/181.48 => 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))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__strict__left__mono,axiom, % 181.25/181.48 ! [V_c,V_a,V_b,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 181.25/181.48 => ( 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))) % 181.25/181.48 => 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))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__divide__less__eq,axiom, % 181.25/181.48 ! [V_a_2,V_b_2,V_c_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__less__divide__eq,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => ( 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_c_2))) % 181.25/181.48 <=> 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_c_2))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mult__imp__less__div__pos,axiom, % 181.25/181.48 ! [V_x,V_z,V_y,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.48 => ( 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)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mult__imp__div__pos__less,axiom, % 181.25/181.48 ! [V_z,V_x,V_y,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.48 => ( 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))) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__divide__less__eq,axiom, % 181.25/181.48 ! [V_a_2,V_b_2,V_c_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 181.25/181.48 <=> 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_c_2))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__less__divide__eq,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => ( 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_c_2))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__less__eq,axiom, % 181.25/181.48 ! [V_a_2,V_c_2,V_b_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 181.25/181.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => 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_c_2))) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_less__divide__eq,axiom, % 181.25/181.48 ! [V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.48 => ( 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_c_2))) % 181.25/181.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => 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_c_2))) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_add__num__frac,axiom, % 181.25/181.48 ! [V_x,V_z,V_y,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_add__divide__eq__iff,axiom, % 181.25/181.48 ! [V_y,V_x,V_z,T_a] : % 181.25/181.48 ( class_Fields_Ofield(T_a) % 181.25/181.48 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_add__frac__num,axiom, % 181.25/181.48 ! [V_z,V_x,V_y,T_a] : % 181.25/181.48 ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.48 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__add__eq__iff,axiom, % 181.25/181.48 ! [V_y,V_x,V_z,T_a] : % 181.25/181.48 ( class_Fields_Ofield(T_a) % 181.25/181.48 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_add__frac__eq,axiom, % 181.25/181.48 ! [V_w,V_x,V_z,V_y,T_a] : % 181.25/181.48 ( class_Fields_Ofield(T_a) % 181.25/181.48 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_diff__frac__eq,axiom, % 181.25/181.48 ! [V_w,V_x,V_z,V_y,T_a] : % 181.25/181.48 ( class_Fields_Ofield(T_a) % 181.25/181.48 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__diff__eq__iff,axiom, % 181.25/181.48 ! [V_y,V_x,V_z,T_a] : % 181.25/181.48 ( class_Fields_Ofield(T_a) % 181.25/181.48 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_diff__divide__eq__iff,axiom, % 181.25/181.48 ! [V_y,V_x,V_z,T_a] : % 181.25/181.48 ( class_Fields_Ofield(T_a) % 181.25/181.48 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_less__half__sum,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.48 => 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))))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_gt__half__sum,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_le__divide__eq,axiom, % 181.25/181.48 ! [V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.48 => ( 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_c_2))) % 181.25/181.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => 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_c_2))) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divide__le__eq,axiom, % 181.25/181.48 ! [V_a_2,V_c_2,V_b_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 181.25/181.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => 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_c_2))) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__le__divide__eq,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,V_c_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => ( 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_c_2))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__divide__le__eq,axiom, % 181.25/181.48 ! [V_a_2,V_b_2,V_c_2,T_b] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_b) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 181.25/181.48 <=> 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_c_2))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mult__imp__div__pos__le,axiom, % 181.25/181.48 ! [V_z,V_x,V_y,T_a] : % 181.25/181.48 ( class_Fields_Olinordered__field(T_a) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.48 => ( 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))) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_z3div__def,axiom, % 181.25/181.48 ! [V_k,V_l] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 181.25/181.48 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_setprod__Un,axiom, % 181.25/181.48 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.48 ( class_Fields_Ofield(T_c) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.48 => ( ! [B_x] : % 181.25/181.48 ( 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))) % 181.25/181.48 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) ) % 181.25/181.48 => 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))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_norm__frac_Osimps,axiom, % 181.25/181.48 ! [V_a_2,V_b_2] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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)) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 181.25/181.48 => 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)) ) % 181.25/181.48 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 181.25/181.48 => 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))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmult2__lemma,axiom, % 181.25/181.48 ! [V_c,V_r,V_q,V_b,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 181.25/181.48 => 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)))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_strong__setprod__reindex__cong,axiom, % 181.25/181.48 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 181.25/181.48 ( class_Groups_Ocomm__monoid__mult(T_d) % 181.25/181.48 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.25/181.48 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 181.25/181.48 => ( ! [B_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.48 => 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) ) % 181.25/181.48 => 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) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiff__zmod__left,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiff__zmod__right,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zminus__zmod,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zminus__zminus,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zminus2,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__cong,axiom, % 181.25/181.48 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 181.25/181.48 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 181.25/181.48 => 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) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__simps_I4_J,axiom, % 181.25/181.48 ! [V_b,V_c,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__simps_I3_J,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__mult2,axiom, % 181.25/181.48 ! [V_b,V_c,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__mult1,axiom, % 181.25/181.48 ! [V_b,V_a,V_c,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__left__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zmult1__eq,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__right__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mod__trivial,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__diff__cong,axiom, % 181.25/181.48 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 181.25/181.48 ( class_Divides_Oring__div(T_a) % 181.25/181.48 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 181.25/181.48 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 181.25/181.48 => 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) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__diff__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Oring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__diff__left__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Oring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__diff__right__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Oring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__minus__eq,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Oring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__minus__cong,axiom, % 181.25/181.48 ! [V_a_H,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Oring__div(T_a) % 181.25/181.48 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__add__cong,axiom, % 181.25/181.48 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 181.25/181.48 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 181.25/181.48 => 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) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__simps_I1_J,axiom, % 181.25/181.48 ! [V_b,V_c,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__simps_I2_J,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__add__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__add__left__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__add__right__eq,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__add__self1,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__add__self2,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__self,axiom, % 181.25/181.48 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__self,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__by__0,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zero,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__0,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zpower__zmod,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__self1__is__0,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__self2__is__0,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__self1,axiom, % 181.25/181.48 ! [V_b,V_c,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__self2,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__by__1,axiom, % 181.25/181.48 ! [V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__div__trivial,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 181.25/181.48 ! [V_y,V_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__le__nonneg__dividend,axiom, % 181.25/181.48 ! [V_k,V_m] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__mod__bound,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__mod__bound,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__eq__0__iff,axiom, % 181.25/181.48 ! [V_d_2,V_m_2] : % 181.25/181.48 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zminus1__not__zero,axiom, % 181.25/181.48 ! [V_l,V_k] : % 181.25/181.48 ( 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) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zminus2__not__zero,axiom, % 181.25/181.48 ! [V_l,V_k] : % 181.25/181.48 ( 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) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zdiv__trivial,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_DIVISION__BY__ZERO,axiom, % 181.25/181.48 ! [V_a] : % 181.25/181.48 ( 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) % 181.25/181.48 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zadd1__eq,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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 ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__div__equality2,axiom, % 181.25/181.48 ! [V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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 ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__div__equality,axiom, % 181.25/181.48 ! [V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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 ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mod__equality2,axiom, % 181.25/181.48 ! [V_c,V_a,V_b,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mod__equality,axiom, % 181.25/181.48 ! [V_c,V_b,V_a,T_a] : % 181.25/181.48 ( class_Divides_Osemiring__div(T_a) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__neg__neg__trivial,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__mod__conj,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( 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))) % 181.25/181.48 & 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_neg__mod__sign,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__pos__pos__trivial,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__mod__conj,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => ( 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))) % 181.25/181.48 & 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pos__mod__sign,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zminus2__eq__if,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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) ) % 181.25/181.48 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zminus1__eq__if,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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) ) % 181.25/181.48 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zdiv__equality,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zmult1__eq,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zmod__equality,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zmod__equality2,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmult__div__cancel,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zdiv__equality_H,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__rel__mod,axiom, % 181.25/181.48 ! [V_r,V_q,V_b,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__pos__neg__trivial,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( 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))) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__rel__div__mod,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__zmod,axiom, % 181.25/181.48 ! [V_k_2,V_n_2,V_Pa_2] : % 181.25/181.48 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 181.25/181.48 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 181.25/181.48 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 181.25/181.48 => ! [B_i,B_j] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 181.25/181.48 & 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) ) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 181.25/181.48 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ! [B_i,B_j] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 & 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) ) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmult2__lemma__aux3,axiom, % 181.25/181.48 ! [V_q,V_b,V_r,V_c] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmult2__lemma__aux4,axiom, % 181.25/181.48 ! [V_q,V_b,V_r,V_c] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmult2__lemma__aux1,axiom, % 181.25/181.48 ! [V_q,V_r,V_b,V_c] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmult2__lemma__aux2,axiom, % 181.25/181.48 ! [V_q,V_r,V_b,V_c] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__rel__mod__eq,axiom, % 181.25/181.48 ! [V_y,V_q_1,V_b_1,V_a_1] : % 181.25/181.48 ( 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) % 181.25/181.48 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 181.25/181.48 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmod__zmult2__eq,axiom, % 181.25/181.48 ! [V_b,V_a,V_c] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zminus2__eq__if,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)) ) % 181.25/181.48 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zdiv__zminus1__eq__if,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)) ) % 181.25/181.48 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zadd1__lemma,axiom, % 181.25/181.48 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( 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))) % 181.25/181.48 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__pos__lemma,axiom, % 181.25/181.48 ! [V_n_2,V_Pa_2,V_k_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> ! [B_i,B_j] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 181.25/181.48 & 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) ) % 181.25/181.48 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__neg__lemma,axiom, % 181.25/181.48 ! [V_n_2,V_Pa_2,V_k_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> ! [B_i,B_j] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 181.25/181.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 & 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) ) % 181.25/181.48 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_zmult1__lemma,axiom, % 181.25/181.48 ! [V_a,V_r,V_q,V_c,V_b] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_z3mod__def,axiom, % 181.25/181.48 ! [V_k,V_l] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 181.25/181.48 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_norm__frac_Opsimps,axiom, % 181.25/181.48 ! [V_b_2,V_a_2] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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)) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 181.25/181.48 => 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)) ) % 181.25/181.48 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 181.25/181.48 => 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))) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_negDivAlg__div__mod,axiom, % 181.25/181.48 ! [V_l,V_k] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_posDivAlg__div__mod,axiom, % 181.25/181.48 ! [V_l,V_k] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__mod__div,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__distrib,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__distrib2,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__less__eq__dividend,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__less,axiom, % 181.25/181.48 ! [V_n,V_m] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_accp__downward,axiom, % 181.25/181.48 ! [V_a_2,V_b_2,V_r_2,T_b] : % 181.25/181.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 181.25/181.48 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_accp_Oequations,axiom, % 181.25/181.48 ! [V_a_2,V_r_2,T_b] : % 181.25/181.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 181.25/181.48 <=> ! [B_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 181.25/181.48 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_accp_Osimps,axiom, % 181.25/181.48 ! [V_a_2,V_r_2,T_b] : % 181.25/181.48 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 181.25/181.48 <=> ! [B_x] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 181.25/181.48 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__Suc,axiom, % 181.25/181.48 ! [V_n,V_m] : % 181.25/181.48 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.25/181.48 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__1,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__less__divisor,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__eq__0__iff,axiom, % 181.25/181.48 ! [V_d_2,V_m_2] : % 181.25/181.48 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__geq,axiom, % 181.25/181.48 ! [V_n,V_m] : % 181.25/181.48 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__if,axiom, % 181.25/181.48 ! [V_n,V_m] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => 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) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__self3,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_le__mod__geq,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__add1__eq,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__le__divisor,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult__self4,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_posDivAlg__0,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__mult2__eq,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mult1__eq,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__mod__equality_H,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mult__div__cancel,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Divides_Omod__div__equality_H,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_accp__subset,axiom, % 181.25/181.48 ! [V_R2_2,V_R1_2,T_b] : % 181.25/181.48 ( 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)) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__lemma,axiom, % 181.25/181.48 ! [V_q,V_b,V_r,V_c] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 181.25/181.48 => 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__mod,axiom, % 181.25/181.48 ! [V_k_2,V_n_2,V_Pa_2] : % 181.25/181.48 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 181.25/181.48 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 181.25/181.48 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 => ! [B_i,B_j] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 181.25/181.48 => ( 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) % 181.25/181.48 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Suc__times__mod__eq,axiom, % 181.25/181.48 ! [V_m,V_k] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_negDivAlg__correct,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__correct,axiom, % 181.25/181.48 ! [V_a,V_b] : % 181.25/181.48 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_posDivAlg__correct,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__def,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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)) ) % 181.25/181.48 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.48 => 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))) ) ) ) ) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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))) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__step,axiom, % 181.25/181.48 ! [V_m,V_n] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_norm__frac_Opinduct,axiom, % 181.25/181.48 ! [V_Pa_2,V_a1_2,V_a0_2] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( ! [B_a,B_b] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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))) ) % 181.25/181.48 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 181.25/181.48 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 181.25/181.48 ! [V_a,V_r,V_q,V_c,V_b] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 181.25/181.48 => 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)))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__eq,axiom, % 181.25/181.48 ! [V_r,V_q,V_n,V_m] : % 181.25/181.48 ( 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))) % 181.25/181.48 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 181.25/181.48 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__eq,axiom, % 181.25/181.48 ! [V_qr,V_n,V_m] : % 181.25/181.48 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 181.25/181.48 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__rel__unique,axiom, % 181.25/181.48 ! [V_qr_H,V_qr,V_n,V_m] : % 181.25/181.48 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 181.25/181.48 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 181.25/181.48 => V_qr = V_qr_H ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__def,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__eq,axiom, % 181.25/181.48 ! [V_r,V_q,V_n,V_m] : % 181.25/181.48 ( 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))) % 181.25/181.48 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__rel,axiom, % 181.25/181.48 ! [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)))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__zero,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__div__mod,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__base,axiom, % 181.25/181.48 ! [V_n,V_m] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.48 => 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) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_negateSnd__eq,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__rel__neg,axiom, % 181.25/181.48 ! [V_qr,V_b,V_a] : % 181.25/181.48 ( 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)) % 181.25/181.48 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__rel__add1__eq,axiom, % 181.25/181.48 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 181.25/181.48 => 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)))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 181.25/181.48 ! [V_c,V_r,V_q,V_b,V_a] : % 181.25/181.48 ( 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))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 181.25/181.48 => 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)))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__neg__neg,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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)))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__neg__neg,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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)))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__if,axiom, % 181.25/181.48 ! [V_m_2,V_n_2] : % 181.25/181.48 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 181.25/181.48 => 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) ) % 181.25/181.48 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__pos__neg,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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)))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__int__def,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__int__def,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__neg__pos,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__neg__pos,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__pos__pos,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__pos__pos,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.48 => 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)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__pos__neg,axiom, % 181.25/181.48 ! [V_b,V_a] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.48 => 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)))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pair__imageI,axiom, % 181.25/181.48 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 181.25/181.48 ( 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)) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_prod__size__simp,axiom, % 181.25/181.48 ! [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))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__comp,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__def,axiom, % 181.25/181.48 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_splitI,axiom, % 181.25/181.48 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_prod__caseI,axiom, % 181.25/181.48 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mem__splitI,axiom, % 181.25/181.48 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) % 181.25/181.48 => 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_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_splitD_H,axiom, % 181.25/181.48 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] : % 181.25/181.48 ( 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_c_2)) % 181.25/181.48 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_splitD,axiom, % 181.25/181.48 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 181.25/181.48 ( 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))) % 181.25/181.48 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Eps__split__eq,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__paired__Eps,axiom, % 181.25/181.48 ! [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)))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Id__on__def_H,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_The__split__eq,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__paired__The,axiom, % 181.25/181.48 ! [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)))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_inj__graph,axiom, % 181.25/181.48 ! [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))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Eps__split,axiom, % 181.25/181.48 ! [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))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__nat__def,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__nat__def,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_The__split,axiom, % 181.25/181.48 ! [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))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__nat__rel__def,axiom, % 181.25/181.48 ! [V_qr_2,V_n_2,V_m_2] : % 181.25/181.48 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 181.25/181.48 <=> ( 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)) % 181.25/181.48 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.25/181.48 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 181.25/181.48 => ( 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))) % 181.25/181.48 & 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)) ) ) % 181.25/181.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 181.25/181.48 => ( 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))) % 181.25/181.48 & 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))) ) ) ) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Pair__inject,axiom, % 181.25/181.48 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 181.25/181.48 ( 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) % 181.25/181.48 => ~ ( V_a = V_a_H % 181.25/181.48 => V_b != V_b_H ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Pair__eq,axiom, % 181.25/181.48 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 181.25/181.48 ( 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) % 181.25/181.48 <=> ( V_a_2 = V_a_H_2 % 181.25/181.48 & V_b_2 = V_b_H_2 ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__paired__All,axiom, % 181.25/181.48 ! [T_c,T_b,V_Pa_2] : % 181.25/181.48 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 181.25/181.48 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__weak__cong,axiom, % 181.25/181.48 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] : % 181.25/181.48 ( V_p_2 = V_q_2 % 181.25/181.48 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_finite__psubset__def,axiom, % 181.25/181.48 ! [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)))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_divmod__int__rel__def,axiom, % 181.25/181.48 ! [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))))))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_prod_Osimps_I2_J,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__conv,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_fst__eqD,axiom, % 181.25/181.48 ! [V_a,V_y,V_x,T_b,T_a] : % 181.25/181.48 ( 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 % 181.25/181.48 => V_x = V_a ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_fst__conv,axiom, % 181.25/181.48 ! [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 ). % 181.25/181.48 % 181.25/181.48 fof(fact_snd__eqD,axiom, % 181.25/181.48 ! [V_a,V_y,V_x,T_a,T_b] : % 181.25/181.48 ( 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 % 181.25/181.48 => V_y = V_a ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_snd__conv,axiom, % 181.25/181.48 ! [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 ). % 181.25/181.48 % 181.25/181.48 fof(fact_prod__eqI,axiom, % 181.25/181.48 ! [V_q,V_p,T_b,T_a] : % 181.25/181.48 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 181.25/181.48 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 181.25/181.48 => V_p = V_q ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Pair__fst__snd__eq,axiom, % 181.25/181.48 ! [T_c,T_b,V_t_2,V_s_2] : % 181.25/181.48 ( V_s_2 = V_t_2 % 181.25/181.48 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) % 181.25/181.48 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__eta,axiom, % 181.25/181.48 ! [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 ). % 181.25/181.48 % 181.25/181.48 fof(fact_fst__def,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_snd__def,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_swap__inj__on,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__Pair,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__twice,axiom, % 181.25/181.48 ! [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) ). % 181.25/181.48 % 181.25/181.48 fof(fact_surjective__pairing,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_pair__collapse,axiom, % 181.25/181.48 ! [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 ). % 181.25/181.48 % 181.25/181.48 fof(fact_prod__case__beta,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__beta,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_split__comp__eq,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Nitpick_OFrac__def,axiom, % 181.25/181.48 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)))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_conjI__realizer,axiom, % 181.25/181.48 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] : % 181.25/181.48 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 181.25/181.48 => ( hBOOL(hAPP(V_Qa_2,V_q_2)) % 181.25/181.48 => ( 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)))) % 181.25/181.48 & 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)))) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_exI__realizer,axiom, % 181.25/181.48 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] : % 181.25/181.48 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 181.25/181.48 => 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)))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_int__ge__less__than2__def,axiom, % 181.25/181.48 ! [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)))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_int__ge__less__than__def,axiom, % 181.25/181.48 ! [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)))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_Nitpick_Oprod__def,axiom, % 181.25/181.48 ! [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)))) ). % 181.25/181.48 % 181.25/181.48 fof(fact_div__pos__neg__1__number__of,axiom, % 181.25/181.48 ! [V_w] : % 181.25/181.48 ( 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))) % 181.25/181.48 => 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))))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_mod__pos__neg__1__number__of,axiom, % 181.25/181.48 ! [V_w] : % 181.25/181.48 ( 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))) % 181.25/181.48 => 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))))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_plus__numeral__code_I9_J,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_times__numeral__code_I5_J,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_less__eq__number__of__int__code,axiom, % 181.25/181.48 ! [V_l_2,V_k_2] : % 181.25/181.48 ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_number__of__is__id,axiom, % 181.25/181.48 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 181.25/181.48 % 181.25/181.48 fof(fact_number__of__reorient,axiom, % 181.25/181.48 ! [V_x_2,V_w_2,T_b] : % 181.25/181.48 ( class_Int_Onumber(T_b) % 181.25/181.48 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 % 181.25/181.48 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_eq__number__of,axiom, % 181.25/181.48 ! [V_y_2,V_x_2,T_b] : % 181.25/181.48 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.48 & class_Int_Oring__char__0(T_b) ) % 181.25/181.48 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 181.25/181.48 <=> V_x_2 = V_y_2 ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_less__number__of__int__code,axiom, % 181.25/181.48 ! [V_l_2,V_k_2] : % 181.25/181.48 ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_minus__numeral__code_I5_J,axiom, % 181.25/181.48 ! [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)) ). % 181.25/181.48 % 181.25/181.48 fof(fact_le__number__of__eq__not__less,axiom, % 181.25/181.48 ! [V_w_2,V_v_2,T_b] : % 181.25/181.48 ( ( class_Int_Onumber(T_b) % 181.25/181.48 & class_Orderings_Olinorder(T_b) ) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> ~ 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))) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_left__distrib__number__of,axiom, % 181.25/181.48 ! [V_v,V_b,V_a,T_b] : % 181.25/181.48 ( ( class_Int_Onumber(T_b) % 181.25/181.48 & class_Rings_Osemiring(T_b) ) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_right__distrib__number__of,axiom, % 181.25/181.48 ! [V_c,V_b,V_v,T_b] : % 181.25/181.48 ( ( class_Int_Onumber(T_b) % 181.25/181.48 & class_Rings_Osemiring(T_b) ) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_right__diff__distrib__number__of,axiom, % 181.25/181.48 ! [V_c,V_b,V_v,T_b] : % 181.25/181.48 ( ( class_Int_Onumber(T_b) % 181.25/181.48 & class_Rings_Oring(T_b) ) % 181.25/181.48 => 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)) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_left__diff__distrib__number__of,axiom, % 181.25/181.48 ! [V_v,V_b,V_a,T_b] : % 181.25/181.48 ( ( class_Int_Onumber(T_b) % 181.25/181.48 & class_Rings_Oring(T_b) ) % 181.25/181.48 => 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))) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_le__number__of,axiom, % 181.25/181.48 ! [V_y_2,V_x_2,T_b] : % 181.25/181.48 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.48 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_less__number__of,axiom, % 181.25/181.48 ! [V_y_2,V_x_2,T_b] : % 181.25/181.48 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.48 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.48 => ( 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))) % 181.25/181.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_min__number__of,axiom, % 181.25/181.48 ! [V_v,V_u,T_b] : % 181.25/181.48 ( ( class_Int_Onumber(T_b) % 181.25/181.48 & class_Orderings_Oord(T_b) ) % 181.25/181.48 => ( ( 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))) % 181.25/181.48 => 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) ) % 181.25/181.48 & ( ~ 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))) % 181.25/181.48 => 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) ) ) ) ). % 181.25/181.48 % 181.25/181.48 fof(fact_max__number__of,axiom, % 181.25/181.48 ! [V_v,V_u,T_b] : % 181.25/181.48 ( ( class_Int_Onumber(T_b) % 181.25/181.49 & class_Orderings_Oord(T_b) ) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__add,axiom, % 181.25/181.49 ! [V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__number__of__eq,axiom, % 181.25/181.49 ! [V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__number__of__left,axiom, % 181.25/181.49 ! [V_z,V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__mult,axiom, % 181.25/181.49 ! [V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_arith__simps_I32_J,axiom, % 181.25/181.49 ! [V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__number__of__left,axiom, % 181.25/181.49 ! [V_z,V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__diff,axiom, % 181.25/181.49 ! [V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_arith__simps_I30_J,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__minus,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Ints__number__of,axiom, % 181.25/181.49 ! [V_w_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__eq__eq__number__of1,axiom, % 181.25/181.49 ! [V_a_2,V_w_2,V_b_2,T_b] : % 181.25/181.49 ( ( class_Fields_Ofield__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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 % 181.25/181.49 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__eq__eq__number__of,axiom, % 181.25/181.49 ! [V_w_2,V_c_2,V_b_2,T_b] : % 181.25/181.49 ( ( class_Fields_Ofield__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) % 181.25/181.49 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 => 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_c_2) ) % 181.25/181.49 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__divide__eq__number__of,axiom, % 181.25/181.49 ! [V_c_2,V_b_2,V_w_2,T_b] : % 181.25/181.49 ( ( class_Fields_Ofield__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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_c_2) % 181.25/181.49 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 ) % 181.25/181.49 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__divide__eq__number__of1,axiom, % 181.25/181.49 ! [V_w_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( ( class_Fields_Ofield__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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)) % 181.25/181.49 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 => 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 ) % 181.25/181.49 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__number__of__diff1,axiom, % 181.25/181.49 ! [V_c,V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus__number__of__mult,axiom, % 181.25/181.49 ! [V_z,V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__number__of__eq,axiom, % 181.25/181.49 ! [V_w,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus__numeral__code_I6_J,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__divide__eq__number__of1,axiom, % 181.25/181.49 ! [V_w_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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)))) % 181.25/181.49 <=> ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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)))) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__divide__eq__number__of,axiom, % 181.25/181.49 ! [V_c_2,V_b_2,V_w_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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_c_2))) % 181.25/181.49 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.49 => 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_c_2)),V_b_2)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.49 => 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_c_2))) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.49 => 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))) ) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__less__eq__number__of,axiom, % 181.25/181.49 ! [V_w_2,V_c_2,V_b_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 181.25/181.49 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.49 => 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_c_2))) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.49 => 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_c_2)),V_b_2)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.49 => 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))) ) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__less__eq__number__of1,axiom, % 181.25/181.49 ! [V_a_2,V_w_2,V_b_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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)) % 181.25/181.49 <=> ( ( 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))) % 181.25/181.49 => 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)))) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__number__of__diff2,axiom, % 181.25/181.49 ! [V_w,V_c,V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__le__eq__number__of1,axiom, % 181.25/181.49 ! [V_a_2,V_w_2,V_b_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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)) % 181.25/181.49 <=> ( ( 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))) % 181.25/181.49 => 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)))) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__le__eq__number__of,axiom, % 181.25/181.49 ! [V_w_2,V_c_2,V_b_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 181.25/181.49 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.49 => 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_c_2))) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.49 => 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_c_2)),V_b_2)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.49 => 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))) ) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__divide__eq__number__of,axiom, % 181.25/181.49 ! [V_c_2,V_b_2,V_w_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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_c_2))) % 181.25/181.49 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.49 => 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_c_2)),V_b_2)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.49 => 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_c_2))) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 181.25/181.49 => 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))) ) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__divide__eq__number__of1,axiom, % 181.25/181.49 ! [V_w_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => ( 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)))) % 181.25/181.49 <=> ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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)))) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mod__pos__pos__1__number__of,axiom, % 181.25/181.49 ! [V_w] : % 181.25/181.49 ( 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))) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_div__pos__pos__1__number__of,axiom, % 181.25/181.49 ! [V_w] : % 181.25/181.49 ( 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))) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_inv__image__def,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_prod_Orecs,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__number__of__odd__number__of,axiom, % 181.25/181.49 ! [V_v_2,V_w_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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))) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pair__lessI2,axiom, % 181.25/181.49 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__eq__int__code_I16_J,axiom, % 181.25/181.49 ! [V_k2_2,V_k1_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I34_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__int__code_I16_J,axiom, % 181.25/181.49 ! [V_k2_2,V_k1_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I17_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I51_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 181.25/181.49 <=> V_k_2 = V_l_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_bin__less__0__simps_I4_J,axiom, % 181.25/181.49 ! [V_w_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Bit1__def,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__Bit1,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__number__of__odd,axiom, % 181.25/181.49 ! [V_z_2,V_w_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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))) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zpower__number__of__odd,axiom, % 181.25/181.49 ! [V_z_2,V_w_2] : % 181.25/181.49 ( ( 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))) % 181.25/181.49 => 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))) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_in__inv__image,axiom, % 181.25/181.49 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pair__lessI1,axiom, % 181.25/181.49 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_expand__Suc,axiom, % 181.25/181.49 ! [V_v] : % 181.25/181.49 ( 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))) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pair__leqI2,axiom, % 181.25/181.49 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_smax__insertI,axiom, % 181.25/181.49 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => 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)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_smin__insertI,axiom, % 181.25/181.49 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => 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)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pair__leqI1,axiom, % 181.25/181.49 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_smax__emptyI,axiom, % 181.25/181.49 ! [V_Y_2] : % 181.25/181.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 181.25/181.49 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_smin__emptyI,axiom, % 181.25/181.49 ! [V_X_2] : % 181.25/181.49 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_max__strict__def,axiom, % 181.25/181.49 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 181.25/181.49 % 181.25/181.49 fof(fact_wmin__insertI,axiom, % 181.25/181.49 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => 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)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_wmax__insertI,axiom, % 181.25/181.49 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => 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)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rp__inv__image__def,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_max__weak__def,axiom, % 181.25/181.49 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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_wmin__emptyI,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_wmax__emptyI,axiom, % 181.25/181.49 ! [V_X_2] : % 181.25/181.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_min__weak__def,axiom, % 181.25/181.49 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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of__Bit1,axiom, % 181.25/181.49 ! [V_w_2] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 181.25/181.49 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 181.25/181.49 => 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)))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_min__rpair__set,axiom, % 181.25/181.49 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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_max__rpair__set,axiom, % 181.25/181.49 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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__neg__1,axiom, % 181.25/181.49 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__neg__0,axiom, % 181.25/181.49 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__neg__eq__ge__0,axiom, % 181.25/181.49 ! [V_x_2] : % 181.25/181.49 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__def,axiom, % 181.25/181.49 ! [V_Z_2] : % 181.25/181.49 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__number__of__Bit1,axiom, % 181.25/181.49 ! [V_w_2] : % 181.25/181.49 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 181.25/181.49 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__imp__number__of__eq__0,axiom, % 181.25/181.49 ! [V_v] : % 181.25/181.49 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__nat__number__of,axiom, % 181.25/181.49 ! [V_v_H_2,V_v_2] : % 181.25/181.49 ( 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) % 181.25/181.49 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 181.25/181.49 => 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))) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 181.25/181.49 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 181.25/181.49 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 181.25/181.49 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of__add__left,axiom, % 181.25/181.49 ! [V_k,V_v_H,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 181.25/181.49 => 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) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rp__inv__image__rp,axiom, % 181.25/181.49 ! [V_f_2,T_c,V_Pa_2,T_b] : % 181.25/181.49 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 181.25/181.49 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_min__strict__def,axiom, % 181.25/181.49 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__nat__number__of__add,axiom, % 181.25/181.49 ! [V_n,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__nat__number__of,axiom, % 181.25/181.49 ! [V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_one__mod__nat__number__of,axiom, % 181.25/181.49 ! [V_v_H] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_equiv__intrel__iff,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( 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)))) % 181.25/181.49 <=> 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_equiv__intrel,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 181.25/181.49 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__0,axiom, % 181.25/181.49 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ex__nat,axiom, % 181.25/181.49 ! [V_Pa_2] : % 181.25/181.49 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 181.25/181.49 <=> ? [B_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 181.25/181.49 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_all__nat,axiom, % 181.25/181.49 ! [V_Pa_2] : % 181.25/181.49 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 181.25/181.49 <=> ! [B_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 181.25/181.49 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 181.25/181.49 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 181.25/181.49 <=> V_x_2 = V_y_2 ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__nat__nat__iff,axiom, % 181.25/181.49 ! [V_z_H_2,V_z_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 181.25/181.49 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 181.25/181.49 <=> V_z_2 = V_z_H_2 ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of__def,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 181.25/181.49 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__nat,axiom, % 181.25/181.49 ! [V_z] : % 181.25/181.49 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 181.25/181.49 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__le__0,axiom, % 181.25/181.49 ! [V_z] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__0__iff,axiom, % 181.25/181.49 ! [V_i_2] : % 181.25/181.49 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__mono__iff,axiom, % 181.25/181.49 ! [V_w_2,V_z_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zless__nat__conj,axiom, % 181.25/181.49 ! [V_z_2,V_w_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 181.25/181.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__1,axiom, % 181.25/181.49 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_succ__def,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__less__nat__eq,axiom, % 181.25/181.49 ! [V_z_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__less__eq__zless,axiom, % 181.25/181.49 ! [V_z_2,V_w_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__le__eq__zle,axiom, % 181.25/181.49 ! [V_z_2,V_w_2] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__add__distrib,axiom, % 181.25/181.49 ! [V_z_H,V_z] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__mult__distrib,axiom, % 181.25/181.49 ! [V_z_H,V_z] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__diff__distrib,axiom, % 181.25/181.49 ! [V_z,V_z_H] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__mod__distrib,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__div__distrib,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 181.25/181.49 ! [V_n,V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__power__eq,axiom, % 181.25/181.49 ! [V_n,V_z] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__nat__eq__if,axiom, % 181.25/181.49 ! [V_z_2,V_z_H_2] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_one__less__nat__eq,axiom, % 181.25/181.49 ! [V_z_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 181.25/181.49 ! [V_z] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__succ,axiom, % 181.25/181.49 ! [V_k,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__mult__distrib__neg,axiom, % 181.25/181.49 ! [V_z_H,V_z] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mod__nat__number__of,axiom, % 181.25/181.49 ! [V_v_H,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 181.25/181.49 => 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))) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_div__nat__number__of,axiom, % 181.25/181.49 ! [V_v_H,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__nat__number__of__number__of,axiom, % 181.25/181.49 ! [V_w,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__nat__number__of,axiom, % 181.25/181.49 ! [V_n,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_intrel__iff,axiom, % 181.25/181.49 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 181.25/181.49 ( 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)) % 181.25/181.49 <=> 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_one__div__nat__number__of,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__aux__def,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_One__int__def,axiom, % 181.25/181.49 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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult,axiom, % 181.25/181.49 ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le,axiom, % 181.25/181.49 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 181.25/181.49 ( 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))))))) % 181.25/181.49 <=> 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus,axiom, % 181.25/181.49 ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Zero__int__def,axiom, % 181.25/181.49 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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add,axiom, % 181.25/181.49 ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less,axiom, % 181.25/181.49 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 181.25/181.49 ( 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))))))) % 181.25/181.49 <=> 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus__int__def,axiom, % 181.25/181.49 ! [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))))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__nat__number__of,axiom, % 181.25/181.49 ! [V_v_2,V_v_H_2] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_min__number__of__Suc,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_min__Suc__number__of,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__Pls,axiom, % 181.25/181.49 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__Pls__right,axiom, % 181.25/181.49 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__Pls,axiom, % 181.25/181.49 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 181.25/181.49 % 181.25/181.49 fof(fact_Rep__Integ__inject,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 181.25/181.49 <=> V_x_2 = V_y_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I2_J,axiom, % 181.25/181.49 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I19_J,axiom, % 181.25/181.49 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Pls__def,axiom, % 181.25/181.49 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus__Pls,axiom, % 181.25/181.49 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I1_J,axiom, % 181.25/181.49 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I39_J,axiom, % 181.25/181.49 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I46_J,axiom, % 181.25/181.49 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 181.25/181.49 % 181.25/181.49 fof(fact_succ__pred,axiom, % 181.25/181.49 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 181.25/181.49 % 181.25/181.49 fof(fact_semiring__norm_I112_J,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__Pls,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__numeral__0__right,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__numeral__0,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_bin__less__0__simps_I1_J,axiom, % 181.25/181.49 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of__Pls,axiom, % 181.25/181.49 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.25/181.49 % 181.25/181.49 fof(fact_semiring__norm_I113_J,axiom, % 181.25/181.49 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__is__num__zero,axiom, % 181.25/181.49 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I22_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I12_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__diff__number__of,axiom, % 181.25/181.49 ! [V_m,V_v] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__neg__number__of__Pls,axiom, % 181.25/181.49 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Rep__Integ__inverse,axiom, % 181.25/181.49 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 181.25/181.49 % 181.25/181.49 fof(fact_succ__Pls,axiom, % 181.25/181.49 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__iff__pred__less,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus__Bit1,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pred__def,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of__diff__1,axiom, % 181.25/181.49 ! [V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__numeral__1,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__numeral__1__right,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__Numeral0,axiom, % 181.25/181.49 ! [V_x,T_a] : % 181.25/181.49 ( ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.49 & class_Int_Onumber__ring(T_a) ) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_numeral__1__eq__1,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_semiring__norm_I110_J,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__number__of__0,axiom, % 181.25/181.49 ! [V_v_2] : % 181.25/181.49 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__0__number__of,axiom, % 181.25/181.49 ! [V_v_2] : % 181.25/181.49 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I29_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I5_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__nat__number__of,axiom, % 181.25/181.49 ! [V_v_H_2,V_v_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 181.25/181.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__Numeral1,axiom, % 181.25/181.49 ! [V_x,T_a] : % 181.25/181.49 ( ( class_Fields_Ofield(T_a) % 181.25/181.49 & class_Int_Onumber__ring(T_a) ) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__numeral__1,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( ( class_Fields_Ofield(T_a) % 181.25/181.49 & class_Int_Onumber__ring(T_a) ) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__nat__number__of,axiom, % 181.25/181.49 ! [V_v_H_2,V_v_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_one__is__num__one,axiom, % 181.25/181.49 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__numeral__1__eq__1,axiom, % 181.25/181.49 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Numeral1__eq1__nat,axiom, % 181.25/181.49 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__special_I1_J,axiom, % 181.25/181.49 ! [V_y_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__special_I3_J,axiom, % 181.25/181.49 ! [V_x_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__special_I3_J,axiom, % 181.25/181.49 ! [V_x_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__special_I1_J,axiom, % 181.25/181.49 ! [V_y_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__0__number__of,axiom, % 181.25/181.49 ! [V_v_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_numeral__1__eq__Suc__0,axiom, % 181.25/181.49 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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_numeral__3__eq__3,axiom, % 181.25/181.49 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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power3__eq__cube,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 181.25/181.49 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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc3__eq__add__3,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__nat__number__of,axiom, % 181.25/181.49 ! [V_v_H,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 181.25/181.49 => 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)) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 181.25/181.49 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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__pred,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__special_I2_J,axiom, % 181.25/181.49 ! [V_y_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__special_I4_J,axiom, % 181.25/181.49 ! [V_x_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__special_I4_J,axiom, % 181.25/181.49 ! [V_x_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__special_I2_J,axiom, % 181.25/181.49 ! [V_y_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Rings_Olinordered__idom(T_b) ) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__special_I3_J,axiom, % 181.25/181.49 ! [V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__special_I2_J,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__diff__eq__diff__pred,axiom, % 181.25/181.49 ! [V_m,V_n] : % 181.25/181.49 ( 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)) % 181.25/181.49 => 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)))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of__mult__left,axiom, % 181.25/181.49 ! [V_k,V_v_H,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__nat__number__of,axiom, % 181.25/181.49 ! [V_v_H,V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__number__of__pred__iff__0,axiom, % 181.25/181.49 ! [V_v_2] : % 181.25/181.49 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 181.25/181.49 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__mod__eq__add3__mod,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mod__Suc__eq__mod__add3,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__div__eq__add3__div,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_div__Suc__eq__div__add3,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of__add__1,axiom, % 181.25/181.49 ! [V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__1__add__number__of,axiom, % 181.25/181.49 ! [V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__special_I1_J,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__special_I2_J,axiom, % 181.25/181.49 ! [V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__def,axiom, % 181.25/181.49 ! [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)))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__number__of__Suc,axiom, % 181.25/181.49 ! [V_n_2,V_v_2] : % 181.25/181.49 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 181.25/181.49 <=> 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))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__eq__number__of,axiom, % 181.25/181.49 ! [V_v_2,V_n_2] : % 181.25/181.49 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 181.25/181.49 <=> 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))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__case__number__of,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__Suc__number__of,axiom, % 181.25/181.49 ! [V_v_2,V_n_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> 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))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__number__of__Suc,axiom, % 181.25/181.49 ! [V_n_2,V_v_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> 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)))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__Suc__number__of,axiom, % 181.25/181.49 ! [V_v_2,V_n_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> 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))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_le__number__of__Suc,axiom, % 181.25/181.49 ! [V_n_2,V_v_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> 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)))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_max__number__of__Suc,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_max__Suc__number__of,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__case__add__eq__if,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of2,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__rec__add__eq__if,axiom, % 181.25/181.49 ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__special_I4_J,axiom, % 181.25/181.49 ! [V_x_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 181.25/181.49 <=> 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))))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__special_I2_J,axiom, % 181.25/181.49 ! [V_y_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 181.25/181.49 <=> 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)))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_iszero__0,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_iszero__def,axiom, % 181.25/181.49 ! [V_z_2,T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => ( c_Int_Oiszero(T_b,V_z_2) % 181.25/181.49 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__iszero__1,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__rec__0,axiom, % 181.25/181.49 ! [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 ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__rec__Suc,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_iszero__Numeral0,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_iszero__number__of__Bit1,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_a) % 181.25/181.49 & class_Int_Oring__char__0(T_a) ) % 181.25/181.49 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__iszero__Numeral1,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__number__of__eq,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 181.25/181.49 <=> 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)))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__special_I1_J,axiom, % 181.25/181.49 ! [V_y_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 181.25/181.49 <=> 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)))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__special_I3_J,axiom, % 181.25/181.49 ! [V_x_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 <=> 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)))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__rec__number__of,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zmod__number__of__Bit1,axiom, % 181.25/181.49 ! [V_v,V_w] : % 181.25/181.49 ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__zmod__mult__2,axiom, % 181.25/181.49 ! [V_b,V_a] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__morphism__nat__int,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__Abs__Integ,axiom, % 181.25/181.49 ! [V_z_2] : % 181.25/181.49 ~ ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I7_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus__Bit0,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__eq__int__code_I13_J,axiom, % 181.25/181.49 ! [V_k2_2,V_k1_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I31_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Bit0__def,axiom, % 181.25/181.49 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__Bit0__Bit0,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__Bit0,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I48_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 181.25/181.49 <=> V_k_2 = V_l_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__int__code_I13_J,axiom, % 181.25/181.49 ! [V_k2_2,V_k1_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I14_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I49_J,axiom, % 181.25/181.49 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I50_J,axiom, % 181.25/181.49 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Bit0__Pls,axiom, % 181.25/181.49 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I38_J,axiom, % 181.25/181.49 ! [V_l_2] : % 181.25/181.49 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 181.25/181.49 <=> c_Int_OPls = V_l_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I44_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 181.25/181.49 <=> V_k_2 = c_Int_OPls ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_bin__less__0__simps_I3_J,axiom, % 181.25/181.49 ! [V_w_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I27_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I21_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__eq__int__code_I14_J,axiom, % 181.25/181.49 ! [V_k2_2,V_k1_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I32_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I10_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I4_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__int__code_I15_J,axiom, % 181.25/181.49 ! [V_k2_2,V_k1_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I16_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__Bit0__Bit1,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__Bit1__Bit0,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I3_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I9_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I10_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zdiv__number__of__Bit0,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__number__of__Bit0,axiom, % 181.25/181.49 ! [V_w_2] : % 181.25/181.49 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 181.25/181.49 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pred__Bit1,axiom, % 181.25/181.49 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pred__Bit0,axiom, % 181.25/181.49 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_iszero__number__of__Bit0,axiom, % 181.25/181.49 ! [V_w_2,T_b] : % 181.25/181.49 ( ( class_Int_Onumber__ring(T_b) % 181.25/181.49 & class_Int_Oring__char__0(T_b) ) % 181.25/181.49 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) % 181.25/181.49 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_succ__Bit0,axiom, % 181.25/181.49 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 181.25/181.49 % 181.25/181.49 fof(fact_succ__Bit1,axiom, % 181.25/181.49 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__number__of__Bit0,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__Bit0,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__eq__int__code_I15_J,axiom, % 181.25/181.49 ! [V_k2_2,V_k1_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I33_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__int__code_I14_J,axiom, % 181.25/181.49 ! [V_k2_2,V_k1_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I15_J,axiom, % 181.25/181.49 ! [V_l_2,V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__UNIV__bool,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__Bit1,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I8_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__Bit1__Bit1,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__number__of__even,axiom, % 181.25/181.49 ! [V_w_2,V_z_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zpower__number__of__even,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_double__number__of__Bit0,axiom, % 181.25/181.49 ! [V_w,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of1,axiom, % 181.25/181.49 ! [V_n] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( 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)))) % 181.25/181.49 & 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)))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__number__of__even__number__of,axiom, % 181.25/181.49 ! [V_w_2,V_v_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__2__right,axiom, % 181.25/181.49 ! [V_z,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__2,axiom, % 181.25/181.49 ! [V_z,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_one__add__one__is__two,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__power2,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__eq__power2,axiom, % 181.25/181.49 ! [V_a_2,T_b] : % 181.25/181.49 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 181.25/181.49 => ( 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) % 181.25/181.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_semiring__norm_I115_J,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_numeral__2__eq__2,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 181.25/181.49 ! [V_x,T_a] : % 181.25/181.49 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.49 => 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)))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__eq__square,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 181.25/181.49 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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__2__eq__Suc_H,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__2__eq__Suc,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_one__power2,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__minus,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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)))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__mult__2__right,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__mult__2,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__even__eq,axiom, % 181.25/181.49 ! [V_n,V_a,T_a] : % 181.25/181.49 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.49 => 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)))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 181.25/181.49 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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__1__add__1,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mod2__Suc__Suc,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_div2__Suc__Suc,axiom, % 181.25/181.49 ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zmod__number__of__Bit0,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__self__div__2,axiom, % 181.25/181.49 ! [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 ). % 181.25/181.49 % 181.25/181.49 fof(fact_half__gt__zero__iff,axiom, % 181.25/181.49 ! [V_r_2,T_b] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 181.25/181.49 & class_Int_Onumber__ring(T_b) ) % 181.25/181.49 => ( 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)))))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_half__gt__zero,axiom, % 181.25/181.49 ! [V_r,T_a] : % 181.25/181.49 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 181.25/181.49 & class_Int_Onumber__ring(T_a) ) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 181.25/181.49 => 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)))))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__le__power2,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.49 => 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)))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__le__imp__le,axiom, % 181.25/181.49 ! [V_y,V_x,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.49 => ( 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)))))) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__eq__imp__eq,axiom, % 181.25/181.49 ! [V_y,V_x,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.49 => ( 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)))) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.49 => V_x = V_y ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__less__power2,axiom, % 181.25/181.49 ! [V_a_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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)))))) % 181.25/181.49 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__less__0,axiom, % 181.25/181.49 ! [V_a,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.49 => ~ 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_sum__power2__eq__zero__iff,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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) % 181.25/181.49 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__eq__square__number__of,axiom, % 181.25/181.49 ! [V_w,T_b] : % 181.25/181.49 ( ( class_Groups_Omonoid__mult(T_b) % 181.25/181.49 & class_Int_Onumber(T_b) ) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__2__cases,axiom, % 181.25/181.49 ! [V_n] : % 181.25/181.49 ( 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))))) % 181.25/181.49 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.49 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__2,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__eq__1__iff,axiom, % 181.25/181.49 ! [V_a_2,T_b] : % 181.25/181.49 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 181.25/181.49 => ( 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) % 181.25/181.49 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b) % 181.25/181.49 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 181.25/181.49 ! [V_n,V_x,T_a] : % 181.25/181.49 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__minus__even,axiom, % 181.25/181.49 ! [V_n,V_a,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__less__imp__less,axiom, % 181.25/181.49 ! [V_y,V_x,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.49 => ( 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)))))) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_sum__power2__ge__zero,axiom, % 181.25/181.49 ! [V_y,V_x,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.49 => 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))))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_sum__power2__le__zero__iff,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_sum__power2__gt__zero__iff,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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))))))) % 181.25/181.49 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__sum__power2__lt__zero,axiom, % 181.25/181.49 ! [V_y,V_x,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.49 => ~ 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__sum,axiom, % 181.25/181.49 ! [V_y,V_x,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__le__even__power_H,axiom, % 181.25/181.49 ! [V_n,V_a,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.49 => 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)))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 181.25/181.49 ! [V_n,V_x,T_a] : % 181.25/181.49 ( class_Rings_Ocomm__semiring__1(T_a) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__odd__eq,axiom, % 181.25/181.49 ! [V_n,V_a,T_a] : % 181.25/181.49 ( class_Groups_Omonoid__mult(T_a) % 181.25/181.49 => 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))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__minus1__even,axiom, % 181.25/181.49 ! [V_n,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zdiv__number__of__Bit1,axiom, % 181.25/181.49 ! [V_v,V_w] : % 181.25/181.49 ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mod2__gr__0,axiom, % 181.25/181.49 ! [V_m_2] : % 181.25/181.49 ( 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)))))) % 181.25/181.49 <=> 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_div__2__gt__zero,axiom, % 181.25/181.49 ! [V_n] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 181.25/181.49 => 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)))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power2__diff,axiom, % 181.25/181.49 ! [V_y,V_x,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_odd__0__le__power__imp__0__le,axiom, % 181.25/181.49 ! [V_n,V_a,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.49 => ( 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))))) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_odd__power__less__zero,axiom, % 181.25/181.49 ! [V_n,V_a,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_a) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__minus1__odd,axiom, % 181.25/181.49 ! [V_n,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__n__div__2__gt__zero,axiom, % 181.25/181.49 ! [V_n] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 181.25/181.49 => 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)))))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pos__zmod__mult__2,axiom, % 181.25/181.49 ! [V_b,V_a] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__zdiv__mult__2,axiom, % 181.25/181.49 ! [V_b,V_a] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pos__zdiv__mult__2,axiom, % 181.25/181.49 ! [V_b,V_a] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_adjust__eq,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_adjust__def,axiom, % 181.25/181.49 ! [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))))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 181.25/181.49 ! [V_w] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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)))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_posDivAlg_Osimps,axiom, % 181.25/181.49 ! [V_b,V_a] : % 181.25/181.49 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_posDivAlg__eqn__number__of,axiom, % 181.25/181.49 ! [V_w,V_v] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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)))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_posDivAlg__eqn,axiom, % 181.25/181.49 ! [V_a,V_b] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 181.25/181.49 => 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_posDivAlg_Opsimps,axiom, % 181.25/181.49 ! [V_b_2,V_a_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__num,axiom, % 181.25/181.49 ! [V_k_2,T_b] : % 181.25/181.49 ( class_Rings_Oring__1(T_b) % 181.25/181.49 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.49 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) % 181.25/181.49 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => 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))) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => 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))))) ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 181.25/181.49 ! [V_w] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ( 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)))) % 181.25/181.49 => 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))) ) % 181.25/181.49 & ( ~ 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)))) % 181.25/181.49 => 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)))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negDivAlg__eqn,axiom, % 181.25/181.49 ! [V_a,V_b] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I24_J,axiom, % 181.25/181.49 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I7_J,axiom, % 181.25/181.49 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__eq__iff,axiom, % 181.25/181.49 ! [V_z_2,V_w_2,T_b] : % 181.25/181.49 ( class_Int_Oring__char__0(T_b) % 181.25/181.49 => ( 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) % 181.25/181.49 <=> V_w_2 = V_z_2 ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Bit1__Min,axiom, % 181.25/181.49 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I43_J,axiom, % 181.25/181.49 ! [V_l_2] : % 181.25/181.49 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 181.25/181.49 <=> c_Int_OMin = V_l_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I47_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 181.25/181.49 <=> V_k_2 = c_Int_OMin ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__m1,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__number__of__def,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__eq,axiom, % 181.25/181.49 ! [V_k,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I40_J,axiom, % 181.25/181.49 c_Int_OMin != c_Int_OPls ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I37_J,axiom, % 181.25/181.49 c_Int_OPls != c_Int_OMin ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I42_J,axiom, % 181.25/181.49 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I45_J,axiom, % 181.25/181.49 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__setprod,axiom, % 181.25/181.49 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.49 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 181.25/181.49 & class_Rings_Oring__1(T_b) ) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_bin__less__0__simps_I2_J,axiom, % 181.25/181.49 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I20_J,axiom, % 181.25/181.49 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I23_J,axiom, % 181.25/181.49 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I30_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I26_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I3_J,axiom, % 181.25/181.49 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I6_J,axiom, % 181.25/181.49 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I13_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I9_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I28_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I8_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_eq__number__of__Pls__Min,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Int_OMin__def,axiom, % 181.25/181.49 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__Min,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__number__of__Min,axiom, % 181.25/181.49 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pred__Pls,axiom, % 181.25/181.49 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__Min,axiom, % 181.25/181.49 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 181.25/181.49 % 181.25/181.49 fof(fact_add__Min__right,axiom, % 181.25/181.49 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pred__Min,axiom, % 181.25/181.49 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__eq__0__iff,axiom, % 181.25/181.49 ! [V_z_2,T_b] : % 181.25/181.49 ( class_Int_Oring__char__0(T_b) % 181.25/181.49 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.49 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__0__eq__iff,axiom, % 181.25/181.49 ! [V_z_2,T_b] : % 181.25/181.49 ( class_Int_Oring__char__0(T_b) % 181.25/181.49 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 181.25/181.49 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__0,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__le__iff,axiom, % 181.25/181.49 ! [V_z_2,V_w_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__less__iff,axiom, % 181.25/181.49 ! [V_z_2,V_w_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nonzero__number__of__Min,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__add,axiom, % 181.25/181.49 ! [V_z,V_w,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__number__of__eq,axiom, % 181.25/181.49 ! [V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__mult,axiom, % 181.25/181.49 ! [V_z,V_w,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_succ__Min,axiom, % 181.25/181.49 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__1,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__diff,axiom, % 181.25/181.49 ! [V_z,V_w,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I2_J,axiom, % 181.25/181.49 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__minus,axiom, % 181.25/181.49 ! [V_z,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Ints__of__int,axiom, % 181.25/181.49 ! [V_z_2,T_b] : % 181.25/181.49 ( class_Rings_Oring__1(T_b) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__power,axiom, % 181.25/181.49 ! [V_n,V_z,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__minus1,axiom, % 181.25/181.49 ! [V_z,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mult__minus1__right,axiom, % 181.25/181.49 ! [V_z,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_arith__simps_I31_J,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_number__of__Min,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_divide__minus1,axiom, % 181.25/181.49 ! [V_x,T_a] : % 181.25/181.49 ( ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.49 & class_Int_Onumber__ring(T_a) ) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I11_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_rel__simps_I25_J,axiom, % 181.25/181.49 ! [V_k_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zmod__minus1__right,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I4_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus__Min,axiom, % 181.25/181.49 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 181.25/181.49 ! [V_n,V_m] : % 181.25/181.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 181.25/181.49 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 181.25/181.49 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zmult__eq__1__iff,axiom, % 181.25/181.49 ! [V_n_2,V_m_2] : % 181.25/181.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 181.25/181.49 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 181.25/181.49 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 181.25/181.49 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 181.25/181.49 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I6_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_diff__bin__simps_I5_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zdiv__minus1__right,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_minus1__divide,axiom, % 181.25/181.49 ! [V_x,T_a] : % 181.25/181.49 ( ( class_Fields_Ofield__inverse__zero(T_a) % 181.25/181.49 & class_Int_Onumber__ring(T_a) ) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_div__eq__minus1,axiom, % 181.25/181.49 ! [V_b] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__le__0__iff,axiom, % 181.25/181.49 ! [V_z_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__0__le__iff,axiom, % 181.25/181.49 ! [V_z_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__less__0__iff,axiom, % 181.25/181.49 ! [V_z_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__0__less__iff,axiom, % 181.25/181.49 ! [V_z_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__idom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negDivAlg__minus1,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_div__pos__neg__trivial,axiom, % 181.25/181.49 ! [V_b,V_a] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 181.25/181.49 => ( 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))) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zmod__minus1,axiom, % 181.25/181.49 ! [V_b] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__m1__even,axiom, % 181.25/181.49 ! [V_n,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_power__m1__odd,axiom, % 181.25/181.49 ! [V_n,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negDivAlg_Osimps,axiom, % 181.25/181.49 ! [V_b,V_a] : % 181.25/181.49 ( ( ( 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))) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ ( 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))) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negDivAlg__eqn__number__of,axiom, % 181.25/181.49 ! [V_w,V_v] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ( 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)))) % 181.25/181.49 => 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))) ) % 181.25/181.49 & ( ~ 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)))) % 181.25/181.49 => 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)))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negDivAlg_Opsimps,axiom, % 181.25/181.49 ! [V_b_2,V_a_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ( ( 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))) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ ( 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))) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_posDivAlg_Opinduct,axiom, % 181.25/181.49 ! [V_Pa_2,V_a1_2,V_a0_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ! [B_a,B_b] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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))) ) % 181.25/181.49 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 181.25/181.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__of__code,axiom, % 181.25/181.49 ! [V_k] : % 181.25/181.49 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.25/181.49 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 181.25/181.49 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.25/181.49 => ( ( 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) % 181.25/181.49 => 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)))))) ) % 181.25/181.49 & ( 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) % 181.25/181.49 => 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)) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int,axiom, % 181.25/181.49 ! [V_j_2,V_i_2,T_b] : % 181.25/181.49 ( class_Rings_Oring__1(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negative__zle,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negative__zless,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__int__eq,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__of__nat__eq,axiom, % 181.25/181.49 ! [V_n,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__eq__id,axiom, % 181.25/181.49 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 181.25/181.49 ! [V_A_2,V_f_2,T_b] : % 181.25/181.49 ( ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.49 & class_Groups_Ocomm__monoid__mult(T_b) ) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__int,axiom, % 181.25/181.49 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 181.25/181.49 % 181.25/181.49 fof(fact_code__numeral__zero__minus__one,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__eq__iff,axiom, % 181.25/181.49 ! [V_n_2,V_m_2,T_b] : % 181.25/181.49 ( class_Nat_Osemiring__char__0(T_b) % 181.25/181.49 => ( 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) % 181.25/181.49 <=> V_m_2 = V_n_2 ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__neg__int,axiom, % 181.25/181.49 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 181.25/181.49 ! [V_A_2,V_x_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 181.25/181.49 <=> 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 181.25/181.49 ! [V_A_2] : % 181.25/181.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 181.25/181.49 <=> 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_inj__int,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__setprod,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__eq__0__conv,axiom, % 181.25/181.49 ! [V_n_2] : % 181.25/181.49 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.25/181.49 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__0,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 181.25/181.49 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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__zle__int,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 181.25/181.49 ! [V_Pa_2] : % 181.25/181.49 ( ! [B_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 181.25/181.49 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.25/181.49 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 181.25/181.49 ! [V_Pa_2] : % 181.25/181.49 ( ? [B_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 181.25/181.49 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.25/181.49 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__less__0__conv,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zless__int,axiom, % 181.25/181.49 ! [V_n_2,V_m_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zle__int,axiom, % 181.25/181.49 ! [V_n_2,V_m_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zadd__int__left,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zadd__int,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zle__iff__zadd,axiom, % 181.25/181.49 ! [V_z_2,V_w_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 181.25/181.49 <=> ? [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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__0__le__iff,axiom, % 181.25/181.49 ! [V_n,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__le__imp__of__nat,axiom, % 181.25/181.49 ! [V_m,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negative__eq__positive,axiom, % 181.25/181.49 ! [V_m_2,V_n_2] : % 181.25/181.49 ( 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) % 181.25/181.49 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.49 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__less__0__iff,axiom, % 181.25/181.49 ! [V_m,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.49 => ~ 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__int__zless__negative,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zmult__int,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__mult,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__0,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__less__iff,axiom, % 181.25/181.49 ! [V_n_2,V_m_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__imp__of__nat__less,axiom, % 181.25/181.49 ! [V_n,V_m,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__less__imp__less,axiom, % 181.25/181.49 ! [V_n,V_m,T_a] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_a) % 181.25/181.49 => ( 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))) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__1,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 181.25/181.49 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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__le__iff,axiom, % 181.25/181.49 ! [V_n_2,V_m_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__add,axiom, % 181.25/181.49 ! [V_n,V_m,T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__mult,axiom, % 181.25/181.49 ! [V_n,V_m,T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zmod__int,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__neg__nat,axiom, % 181.25/181.49 ! [V_z] : % 181.25/181.49 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 181.25/181.49 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zdiv__int,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__1,axiom, % 181.25/181.49 ! [T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__set__return__embed,axiom, % 181.25/181.49 ! [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 ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Ints__of__nat,axiom, % 181.25/181.49 ! [V_n_2,T_b] : % 181.25/181.49 ( class_Rings_Oring__1(T_b) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__power,axiom, % 181.25/181.49 ! [V_n,V_m,T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zpower__int,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__power,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_inj__of__nat,axiom, % 181.25/181.49 ! [T_b] : % 181.25/181.49 ( class_Nat_Osemiring__char__0(T_b) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 181.25/181.49 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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__le__0__conv,axiom, % 181.25/181.49 ! [V_n_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__Suc0__eq__1,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zless__iff__Suc__zadd,axiom, % 181.25/181.49 ! [V_z_2,V_w_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 181.25/181.49 <=> ? [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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__nat__eq,axiom, % 181.25/181.49 ! [V_z] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.49 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__eq__iff,axiom, % 181.25/181.49 ! [V_z_2,V_m_2] : % 181.25/181.49 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 181.25/181.49 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 181.25/181.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__0__le,axiom, % 181.25/181.49 ! [V_z] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.49 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zless__nat__eq__int__zless,axiom, % 181.25/181.49 ! [V_z_2,V_m_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 181.25/181.49 <=> 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__zle__neg,axiom, % 181.25/181.49 ! [V_m_2,V_n_2] : % 181.25/181.49 ( 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)))) % 181.25/181.49 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.25/181.49 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__Suc,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negative__zle__0,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__zminus__int,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__setprod,axiom, % 181.25/181.49 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.49 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 181.25/181.49 & class_Rings_Osemiring__1(T_b) ) % 181.25/181.49 => 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zdiff__int,axiom, % 181.25/181.49 ! [V_m,V_n] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__Suc,axiom, % 181.25/181.49 ! [V_m,T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_neg__zminus__int,axiom, % 181.25/181.49 ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__diff,axiom, % 181.25/181.49 ! [V_m,V_n,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__code__numeral__code,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__less__int__conv,axiom, % 181.25/181.49 ! [V_n_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__eq__iff2,axiom, % 181.25/181.49 ! [V_w_2,V_m_2] : % 181.25/181.49 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 181.25/181.49 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 181.25/181.49 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 181.25/181.49 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__eq__iff,axiom, % 181.25/181.49 ! [V_m_2,V_w_2] : % 181.25/181.49 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 181.25/181.49 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 181.25/181.49 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 181.25/181.49 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_split__nat,axiom, % 181.25/181.49 ! [V_i_2,V_Pa_2] : % 181.25/181.49 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 181.25/181.49 <=> ( ! [B_n] : % 181.25/181.49 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 181.25/181.49 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 181.25/181.49 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zmult__zless__mono2__lemma,axiom, % 181.25/181.49 ! [V_k,V_j,V_i] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_not__zle__0__negative,axiom, % 181.25/181.49 ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negative__zless__0,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__eq__iff__number__of,axiom, % 181.25/181.49 ! [V_v_2,V_m_2] : % 181.25/181.49 ( 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) % 181.25/181.49 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 181.25/181.49 & 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 181.25/181.49 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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__0__less__iff,axiom, % 181.25/181.49 ! [V_n_2,T_b] : % 181.25/181.49 ( class_Rings_Olinordered__semidom(T_b) % 181.25/181.49 => ( 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))) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__nat__number__of,axiom, % 181.25/181.49 ! [V_v] : % 181.25/181.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__nat,axiom, % 181.25/181.49 ! [V_z,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__less__iff,axiom, % 181.25/181.49 ! [V_m_2,V_w_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 181.25/181.49 <=> 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zdiff__int__split,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,V_Pa_2] : % 181.25/181.49 ( 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)))) % 181.25/181.49 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 181.25/181.49 => 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)))) ) % 181.25/181.49 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 181.25/181.49 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 181.25/181.49 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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__number__of__eq,axiom, % 181.25/181.49 ! [V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__number__of__lemma,axiom, % 181.25/181.49 ! [V_v,T_a] : % 181.25/181.49 ( class_Int_Onumber__ring(T_a) % 181.25/181.49 => ( ( 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))) % 181.25/181.49 => 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) ) % 181.25/181.49 & ( ~ 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))) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__int__of__nat,axiom, % 181.25/181.49 ! [V_k,T_a] : % 181.25/181.49 ( class_Rings_Oring__1(T_a) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => 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)))) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => 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)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_one__code__numeral__code,axiom, % 181.25/181.49 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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__def,axiom, % 181.25/181.49 ! [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))))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__double,axiom, % 181.25/181.49 ! [V_x,T_a] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_a) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_div__mod__code__numeral__def,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negDivAlg_Opinduct,axiom, % 181.25/181.49 ! [V_Pa_2,V_a1_2,V_a0_2] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ! [B_a,B_b] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ( ( ~ ( 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))) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 181.25/181.49 => 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))) ) % 181.25/181.49 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 181.25/181.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 181.25/181.49 ! [V_n_2,T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Integ__def,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( 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) % 181.25/181.49 <=> V_x_2 = V_y_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_int__int__eq,axiom, % 181.25/181.49 ! [V_n_2,V_m_2] : % 181.25/181.49 ( 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) % 181.25/181.49 <=> V_m_2 = V_n_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.49 <=> 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( V_A_2 = V_B_2 % 181.25/181.49 <=> 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) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.49 <=> 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_infinite__UNIV__int,axiom, % 181.25/181.49 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 181.25/181.49 ! [V_i_2,V_inc_2,T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 181.25/181.49 ! [V_i_2,V_n_2,V_inc_2,T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Rep__Integ,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__of__aux__code,axiom, % 181.25/181.49 ! [V_n,V_i] : % 181.25/181.49 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.25/181.49 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 181.25/181.49 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 181.25/181.49 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_nat__set__def,axiom, % 181.25/181.49 ! [V_S_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_S_2) % 181.25/181.49 <=> ! [B_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.49 <=> 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.25/181.49 => ( V_A_2 = V_B_2 % 181.25/181.49 <=> 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 181.25/181.49 ! [V_B_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.49 <=> 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 181.25/181.49 ! [V_x_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__nat__int__set__return__embed,axiom, % 181.25/181.49 ! [V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 181.25/181.49 ! [V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 181.25/181.49 <=> 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 181.25/181.49 ! [V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 181.25/181.49 ! [V_f_2,V_A_2,T_b] : % 181.25/181.49 ( ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.49 & class_Groups_Ocomm__monoid__mult(T_b) ) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 181.25/181.49 ! [V_A_2,V_x_2] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x_2) % 181.25/181.49 => ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 181.25/181.49 <=> 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_code__numeral_Osize_I1_J,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__greaterThanLessThan__int,axiom, % 181.25/181.49 ! [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)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__greaterThanLessThan__int,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 181.25/181.49 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x) % 181.25/181.49 => ( c_Nat__Transfer_Ois__nat(V_y) % 181.25/181.49 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x) % 181.25/181.49 => ( c_Nat__Transfer_Ois__nat(V_y) % 181.25/181.49 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x) % 181.25/181.49 => ( c_Nat__Transfer_Ois__nat(V_y) % 181.25/181.49 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x) % 181.25/181.49 => ( c_Nat__Transfer_Ois__nat(V_y) % 181.25/181.49 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 181.25/181.49 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 181.25/181.49 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 181.25/181.49 ! [V_n,V_x] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x) % 181.25/181.49 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 181.25/181.49 ! [V_y,V_x] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x) % 181.25/181.49 => ( c_Nat__Transfer_Ois__nat(V_y) % 181.25/181.49 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_is__nat__def,axiom, % 181.25/181.49 ! [V_x_2] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x_2) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_greaterThanLessThan__empty,axiom, % 181.25/181.49 ! [V_k_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__uminus__greaterThanLessThan,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,T_b] : % 181.25/181.49 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 181.25/181.49 ! [V_x_2,V_A_2] : % 181.25/181.49 ( c_Nat__Transfer_Onat__set(V_A_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 181.25/181.49 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 181.25/181.49 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Int__greaterThanLessThan,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 181.25/181.49 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 181.25/181.49 ! [V_f_2,V_A_2,T_b] : % 181.25/181.49 ( ! [B_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.25/181.49 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_code__numeral_Osize_I2_J,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nats__number__of,axiom, % 181.25/181.49 ! [V_w_2,T_b] : % 181.25/181.49 ( class_Int_Onumber__ring(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__greaterThanLessThan,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_code__numeral_Oinject,axiom, % 181.25/181.49 ! [V_code__numeral_H_2,V_code__numeral_2] : % 181.25/181.49 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 181.25/181.49 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_code__numeral_Osimps_I2_J,axiom, % 181.25/181.49 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 181.25/181.49 % 181.25/181.49 fof(fact_code__numeral_Osimps_I3_J,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nats__0,axiom, % 181.25/181.49 ! [T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nats__add,axiom, % 181.25/181.49 ! [V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 181.25/181.49 => 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nats__mult,axiom, % 181.25/181.49 ! [V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 181.25/181.49 => 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))) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Nats__1,axiom, % 181.25/181.49 ! [T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_of__nat__in__Nats,axiom, % 181.25/181.49 ! [V_n_2,T_b] : % 181.25/181.49 ( class_Rings_Osemiring__1(T_b) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Suc__code__numeral__minus__one,axiom, % 181.25/181.49 ! [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 ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__greaterThanLessThan,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_code__numeral_Osize_I4_J,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I4_J,axiom, % 181.25/181.49 ! [V_u_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_less__than__iff,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( 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)) % 181.25/181.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__greaterThanAtMost,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__greaterThanAtMost__int,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_greaterThanAtMost__empty,axiom, % 181.25/181.49 ! [V_k_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_greaterThanAtMost__empty__iff,axiom, % 181.25/181.49 ! [V_l_2,V_k_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( 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)) % 181.25/181.49 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 181.25/181.49 ! [V_l_2,V_k_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( 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) % 181.25/181.49 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I20_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__int_I14_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_pair__less__def,axiom, % 181.25/181.49 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__greaterThanAtMost,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_measure__def,axiom, % 181.25/181.49 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Int__greaterThanAtMost,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__int_I10_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__greaterThanAtMost__int,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I16_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_mlex__prod__def,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_code__numeral_Osize_I3_J,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_type__definition__Integ,axiom, % 181.25/181.49 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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_decr__mult__lemma,axiom, % 181.25/181.49 ! [V_k_2,V_Pa_2,V_d_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 181.25/181.49 => ( ! [B_x] : % 181.25/181.49 ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.25/181.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 181.25/181.49 => ! [B_x] : % 181.25/181.49 ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.25/181.49 => 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)))) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_negD,axiom, % 181.25/181.49 ! [V_x] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.25/181.49 => ? [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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_type__definition_ORep__range,axiom, % 181.25/181.49 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 181.25/181.49 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 181.25/181.49 => 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 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_type__definition_OAbs__image,axiom, % 181.25/181.49 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 181.25/181.49 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_type__definition_ORep,axiom, % 181.25/181.49 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 181.25/181.49 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 181.25/181.49 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_type__definition_ORep__inverse,axiom, % 181.25/181.49 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 181.25/181.49 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 181.25/181.49 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_type__definition_ORep__inject,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 181.25/181.49 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 181.25/181.49 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 181.25/181.49 <=> V_x_2 = V_y_2 ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_type__definition_OAbs__inject,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 181.25/181.49 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 181.25/181.49 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 181.25/181.49 <=> V_x_2 = V_y_2 ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_type__definition_OAbs__inverse,axiom, % 181.25/181.49 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 181.25/181.49 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 181.25/181.49 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_incr__mult__lemma,axiom, % 181.25/181.49 ! [V_k_2,V_Pa_2,V_d_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 181.25/181.49 => ( ! [B_x] : % 181.25/181.49 ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.25/181.49 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 181.25/181.49 => ! [B_x] : % 181.25/181.49 ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.25/181.49 => 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)))) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_setprod__mono__one__left,axiom, % 181.25/181.49 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 181.25/181.49 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 181.25/181.49 => ( ! [B_x] : % 181.25/181.49 ( 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))) % 181.25/181.49 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 181.25/181.49 => 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) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_setprod__mono__one__right,axiom, % 181.25/181.49 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 181.25/181.49 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.25/181.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 181.25/181.49 => ( ! [B_x] : % 181.25/181.49 ( 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))) % 181.25/181.49 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 181.25/181.49 => 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) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_zero__less__imp__eq__int,axiom, % 181.25/181.49 ! [V_k] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 181.25/181.49 => ? [B_n] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 181.25/181.49 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I19_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I3_J,axiom, % 181.25/181.49 ! [V_u_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__atLeastAtMost,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__atLeastLessThan,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__atLeastAtMost__int,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__atLeastLessThan__int,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I21_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__eq__iff,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 181.25/181.49 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 181.25/181.49 <=> ( V_a_2 = V_c_2 % 181.25/181.49 & V_b_2 = V_d_2 ) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 181.25/181.49 => V_a_2 = V_c_2 ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 181.25/181.49 => V_b_2 = V_d_2 ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__add__atLeastLessThan,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__Suc__atLeastLessThan,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__Suc__atLeastAtMost,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__int_I15_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__add__atLeastAtMost,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 181.25/181.49 ! [V_n_2,V_m_2] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_m_2) % 181.25/181.49 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan0,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I6_J,axiom, % 181.25/181.49 ! [V_u_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__atLeastLessThan,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( c_Nat__Transfer_Ois__nat(V_x_2) % 181.25/181.49 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I18_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastatMost__empty__iff,axiom, % 181.25/181.49 ! [V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( 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)) % 181.25/181.49 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastatMost__empty__iff2,axiom, % 181.25/181.49 ! [V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( 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) % 181.25/181.49 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastatMost__empty,axiom, % 181.25/181.49 ! [V_a_2,V_b_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastatMost__subset__iff,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( 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_c_2,V_d_2))) % 181.25/181.49 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 181.25/181.49 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 181.25/181.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__empty,axiom, % 181.25/181.49 ! [V_a_2,V_b_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__empty__iff,axiom, % 181.25/181.49 ! [V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( 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)) % 181.25/181.49 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__empty__iff2,axiom, % 181.25/181.49 ! [V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( 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) % 181.25/181.49 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastAtMost__singleton_H,axiom, % 181.25/181.49 ! [V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( V_a_2 = V_b_2 % 181.25/181.49 => 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))) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastAtMost__singleton__iff,axiom, % 181.25/181.49 ! [V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 181.25/181.49 <=> ( V_a_2 = V_b_2 % 181.25/181.49 & V_b_2 = V_c_2 ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastAtMost__singleton,axiom, % 181.25/181.49 ! [V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__subset__iff,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( 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_c_2),V_d_2))) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) % 181.25/181.49 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 181.25/181.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I17_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__uminus__atLeastAtMost,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,T_b] : % 181.25/181.49 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__diff,axiom, % 181.25/181.49 ! [V_m_2,V_n_2,V_i_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2)) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_UN__UN__finite__eq,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__int_I11_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 181.25/181.49 ! [V_y_2,V_x_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 181.25/181.49 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__atLeastAtMost,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastAtMostSuc__conv,axiom, % 181.25/181.49 ! [V_n_2,V_m_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__singleton,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Int__atLeastAtMost,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastatMost__psubset__iff,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => ( 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_c_2,V_d_2))) % 181.25/181.49 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 181.25/181.49 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 181.25/181.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) % 181.25/181.49 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) % 181.25/181.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) ) % 181.25/181.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThan__add__Un,axiom, % 181.25/181.49 ! [V_k_2,V_j_2,V_i_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_Int__atLeastLessThan,axiom, % 181.25/181.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => 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_c_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_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I22_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__int_I16_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__int_I13_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__int_I12_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_subset__card__intvl__is__intvl,axiom, % 181.25/181.49 ! [V_k_2,V_A_2] : % 181.25/181.49 ( 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))))) % 181.25/181.49 => 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))) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__int_I9_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Oorder(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__uminus__greaterThanAtMost,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,T_b] : % 181.25/181.49 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__uminus__atLeastLessThan,axiom, % 181.25/181.49 ! [V_y_2,V_x_2,T_b] : % 181.25/181.49 ( class_Groups_Oordered__ab__group__add(T_b) % 181.25/181.49 => 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)) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__add__int__atLeastLessThan,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__atLeastZeroLessThan__int,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__atLeastLessThan__int,axiom, % 181.25/181.49 ! [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)) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 181.25/181.49 ! [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) ). % 181.25/181.49 % 181.25/181.49 fof(fact_atLeastLessThanSuc,axiom, % 181.25/181.49 ! [V_n_2,V_m_2] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_simp__from__to,axiom, % 181.25/181.49 ! [V_i_2,V_j_2] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 181.25/181.49 => 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)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 181.25/181.49 => 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)) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I15_J,axiom, % 181.25/181.49 ! [V_u_2,V_m_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 181.25/181.49 => 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) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_card__atLeastAtMost__int,axiom, % 181.25/181.49 ! [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))) ). % 181.25/181.49 % 181.25/181.49 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 181.25/181.49 ! [V_x_2,V_y_2,V_c_2] : % 181.25/181.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 181.25/181.49 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 181.25/181.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 181.25/181.49 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 181.25/181.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 181.25/181.49 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_ivl__disj__un_I5_J,axiom, % 181.25/181.49 ! [V_u_2,V_l_2,T_b] : % 181.25/181.49 ( class_Orderings_Olinorder(T_b) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 181.25/181.49 => 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) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_bset_I8_J,axiom, % 181.25/181.49 ! [V_B_2,V_t_2,V_D_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => ! [B_x] : % 181.25/181.49 ( ! [B_xa] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ! [B_xb] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 181.25/181.49 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 181.25/181.49 => 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))) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_aset_I6_J,axiom, % 181.25/181.49 ! [V_A_2,V_t_2,V_D_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.49 => ( 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)) % 181.25/181.49 => ! [B_x] : % 181.25/181.49 ( ! [B_xa] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ! [B_xb] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 181.25/181.49 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 181.25/181.49 => 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)) ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_aset_I4_J,axiom, % 181.25/181.49 ! [V_A_2,V_t_2,V_D_2] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.49 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 181.25/181.49 => ! [B_x] : % 181.25/181.49 ( ! [B_xa] : % 181.25/181.49 ( 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))) % 181.25/181.49 => ! [B_xb] : % 181.25/181.49 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 181.25/181.49 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.49 => ( B_x != V_t_2 % 181.25/181.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 181.25/181.49 % 181.25/181.49 fof(fact_all__nat__less,axiom, % 181.25/181.49 ! [V_Pa_2,V_n_2] : % 181.25/181.49 ( ! [B_m] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 181.25/181.50 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 181.25/181.50 <=> ! [B_x] : % 181.25/181.50 ( 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))) % 181.25/181.50 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_ex__nat__less,axiom, % 181.25/181.50 ! [V_Pa_2,V_n_2] : % 181.25/181.50 ( ? [B_m] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 181.25/181.50 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 181.25/181.50 <=> ? [B_x] : % 181.25/181.50 ( 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))) % 181.25/181.50 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_all__nat__less__eq,axiom, % 181.25/181.50 ! [V_Pa_2,V_n_2] : % 181.25/181.50 ( ! [B_m] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 181.25/181.50 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 181.25/181.50 <=> ! [B_x] : % 181.25/181.50 ( 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))) % 181.25/181.50 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_ex__nat__less__eq,axiom, % 181.25/181.50 ! [V_Pa_2,V_n_2] : % 181.25/181.50 ( ? [B_m] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 181.25/181.50 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 181.25/181.50 <=> ? [B_x] : % 181.25/181.50 ( 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))) % 181.25/181.50 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_bset_I4_J,axiom, % 181.25/181.50 ! [V_B_2,V_t_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 181.25/181.50 => ! [B_x] : % 181.25/181.50 ( ! [B_xa] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xb] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 181.25/181.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.50 => ( B_x != V_t_2 % 181.25/181.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_bset_I7_J,axiom, % 181.25/181.50 ! [V_B_2,V_t_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 181.25/181.50 => ! [B_x] : % 181.25/181.50 ( ! [B_xa] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xb] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 181.25/181.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 181.25/181.50 => 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))) ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_aset_I5_J,axiom, % 181.25/181.50 ! [V_A_2,V_t_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 181.25/181.50 => ! [B_x] : % 181.25/181.50 ( ! [B_xa] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xb] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 181.25/181.50 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 181.25/181.50 => 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)) ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_bset_I3_J,axiom, % 181.25/181.50 ! [V_B_2,V_t_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ( 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)) % 181.25/181.50 => ( ! [B_x] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xa] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 181.25/181.50 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 181.25/181.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_aset_I3_J,axiom, % 181.25/181.50 ! [V_A_2,V_t_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ( 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)) % 181.25/181.50 => ( ! [B_x] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xa] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 181.25/181.50 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 181.25/181.50 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_aset_I8_J,axiom, % 181.25/181.50 ! [V_t_2,V_A_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ! [B_x] : % 181.25/181.50 ( ! [B_xa] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xb] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 181.25/181.50 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 181.25/181.50 => 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))) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_bset_I6_J,axiom, % 181.25/181.50 ! [V_t_2,V_B_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ! [B_x] : % 181.25/181.50 ( ! [B_xa] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xb] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 181.25/181.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_UN__finite2__subset,axiom, % 181.25/181.50 ! [V_B_2,V_k_2,V_A_2,T_b] : % 181.25/181.50 ( ! [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))) % 181.25/181.50 => 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))) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_periodic__finite__ex,axiom, % 181.25/181.50 ! [V_Pa_2,V_d_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 181.25/181.50 => ( ! [B_x,B_k] : % 181.25/181.50 ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.25/181.50 <=> 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)))) ) % 181.25/181.50 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 181.25/181.50 <=> ? [B_x] : % 181.25/181.50 ( 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))) % 181.25/181.50 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_aset_I7_J,axiom, % 181.25/181.50 ! [V_t_2,V_A_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ! [B_x] : % 181.25/181.50 ( ! [B_xa] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xb] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 181.25/181.50 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 181.25/181.50 => 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))) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_bset_I5_J,axiom, % 181.25/181.50 ! [V_t_2,V_B_2,V_D_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 181.25/181.50 => ! [B_x] : % 181.25/181.50 ( ! [B_xa] : % 181.25/181.50 ( 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))) % 181.25/181.50 => ! [B_xb] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 181.25/181.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_image__atLeastZeroLessThan__int,axiom, % 181.25/181.50 ! [V_u_2] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 181.25/181.50 => 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))) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_finite__lessThan,axiom, % 181.25/181.50 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 181.25/181.50 % 181.25/181.50 fof(fact_lessThan__eq__iff,axiom, % 181.25/181.50 ! [V_y_2,V_x_2,T_b] : % 181.25/181.50 ( class_Orderings_Olinorder(T_b) % 181.25/181.50 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) % 181.25/181.50 <=> V_x_2 = V_y_2 ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_card__lessThan,axiom, % 181.25/181.50 ! [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 ). % 181.25/181.50 % 181.25/181.50 fof(fact_UN__lessThan__UNIV,axiom, % 181.25/181.50 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)) ). % 181.25/181.50 % 181.25/181.50 fof(fact_atLeast0LessThan,axiom, % 181.25/181.50 ! [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) ). % 181.25/181.50 % 181.25/181.50 fof(fact_lessThan__0,axiom, % 181.25/181.50 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)) ). % 181.25/181.50 % 181.25/181.50 fof(fact_lessThan__Suc,axiom, % 181.25/181.50 ! [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)) ). % 181.25/181.50 % 181.25/181.50 fof(fact_lessThan__iff,axiom, % 181.25/181.50 ! [V_k_2,V_i_2,T_b] : % 181.25/181.50 ( class_Orderings_Oord(T_b) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) % 181.25/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_lessThan__subset__iff,axiom, % 181.25/181.50 ! [V_y_2,V_x_2,T_b] : % 181.25/181.50 ( class_Orderings_Olinorder(T_b) % 181.25/181.50 => ( 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))) % 181.25/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_lessThan__strict__subset__iff,axiom, % 181.25/181.50 ! [V_n_2,V_m_2,T_b] : % 181.25/181.50 ( class_Orderings_Olinorder(T_b) % 181.25/181.50 => ( 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))) % 181.25/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_single__Diff__lessThan,axiom, % 181.25/181.50 ! [V_k_2,T_b] : % 181.25/181.50 ( class_Orderings_Oorder(T_b) % 181.25/181.50 => 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))) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_ivl__disj__un_I8_J,axiom, % 181.25/181.50 ! [V_u_2,V_l_2,T_b] : % 181.25/181.50 ( class_Orderings_Olinorder(T_b) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 181.25/181.50 => 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) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_ivl__disj__int_I4_J,axiom, % 181.25/181.50 ! [V_u_2,V_l_2,T_b] : % 181.25/181.50 ( class_Orderings_Oorder(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_ivl__disj__int_I2_J,axiom, % 181.25/181.50 ! [V_u_2,V_l_2,T_b] : % 181.25/181.50 ( class_Orderings_Oorder(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 181.25/181.50 ! [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))) ). % 181.25/181.50 % 181.25/181.50 fof(fact_arith__series__int,axiom, % 181.25/181.50 ! [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)))) ). % 181.25/181.50 % 181.25/181.50 fof(fact_UN__finite2__eq,axiom, % 181.25/181.50 ! [V_B_2,V_k_2,V_A_2,T_b] : % 181.25/181.50 ( ! [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) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_UN__finite__subset,axiom, % 181.25/181.50 ! [V_C_2,V_A_2,T_b] : % 181.25/181.50 ( ! [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)) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_of__nat__setsum,axiom, % 181.25/181.50 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Rings_Osemiring__1(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__subtractf,axiom, % 181.25/181.50 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Groups_Oab__group__add(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__negf,axiom, % 181.25/181.50 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Groups_Oab__group__add(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__addf,axiom, % 181.25/181.50 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__right__distrib,axiom, % 181.25/181.50 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] : % 181.25/181.50 ( class_Rings_Osemiring__0(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__left__distrib,axiom, % 181.25/181.50 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Rings_Osemiring__0(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__product,axiom, % 181.25/181.50 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Rings_Osemiring__0(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__commute,axiom, % 181.25/181.50 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__divide__distrib,axiom, % 181.25/181.50 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Fields_Ofield(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__0,axiom, % 181.25/181.50 ! [V_A_2,T_c,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_of__int__setsum,axiom, % 181.25/181.50 ! [V_A_2,V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Rings_Oring__1(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__empty,axiom, % 181.25/181.50 ! [V_f_2,T_c,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_Oempty,axiom, % 181.25/181.50 ! [V_g_2,T_c,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_Oinfinite,axiom, % 181.25/181.50 ! [V_g_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__infinite,axiom, % 181.25/181.50 ! [V_f_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_Odistrib,axiom, % 181.25/181.50 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 181.25/181.50 ! [V_n_2,V_m_2,V_f_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 181.25/181.50 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 181.25/181.50 ! [V_n_2,V_m_2,V_f_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 181.25/181.50 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__reindex,axiom, % 181.25/181.50 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_d) % 181.25/181.50 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 181.25/181.50 => 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) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__reindex__id,axiom, % 181.25/181.50 ! [V_B_2,V_f_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 181.25/181.50 => 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)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__add__nat__ivl,axiom, % 181.25/181.50 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__diff__nat__ivl,axiom, % 181.25/181.50 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 181.25/181.50 ( class_Groups_Oab__group__add(T_b) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__delta,axiom, % 181.25/181.50 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.50 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.50 => 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) ) % 181.25/181.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.50 => 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) ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__delta_H,axiom, % 181.25/181.50 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.50 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.50 => 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) ) % 181.25/181.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 181.25/181.50 => 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) ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__setsum__restrict,axiom, % 181.25/181.50 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_d) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 181.25/181.50 => 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) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__constant,axiom, % 181.25/181.50 ! [V_A_2,V_y_2,T_c,T_b] : % 181.25/181.50 ( class_Rings_Osemiring__1(T_b) % 181.25/181.50 => 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) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__lessThan__Suc,axiom, % 181.25/181.50 ! [V_n_2,V_f_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => 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)) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_Oinsert,axiom, % 181.25/181.50 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__insert,axiom, % 181.25/181.50 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.25/181.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__Un__Int,axiom, % 181.25/181.50 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__diff,axiom, % 181.25/181.50 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Oab__group__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_Oreindex,axiom, % 181.25/181.50 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 181.25/181.50 => 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) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_Oeq__fold,axiom, % 181.25/181.50 ! [V_g_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_OF__eq,axiom, % 181.25/181.50 ! [V_g_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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) ) % 181.25/181.50 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 181.25/181.50 ! [V_k_2,V_f_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) % 181.25/181.50 => 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)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__head__upt__Suc,axiom, % 181.25/181.50 ! [V_f_2,V_n_2,V_m_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.50 => 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))) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__head__Suc,axiom, % 181.25/181.50 ! [V_f_2,V_n_2,V_m_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.50 => 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))) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__restrict__set_H,axiom, % 181.25/181.50 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__restrict__set,axiom, % 181.25/181.50 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__image__gen,axiom, % 181.25/181.50 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.25/181.50 => 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)) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_Oinsert__remove,axiom, % 181.25/181.50 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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)))))) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__Un__disjoint,axiom, % 181.25/181.50 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.50 => ( 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)) % 181.25/181.50 => 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)) ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__Un,axiom, % 181.25/181.50 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Oab__group__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.50 => 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))) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__op__ivl__Suc,axiom, % 181.25/181.50 ! [V_f_2,V_m_2,V_n_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 181.25/181.50 => 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) ) % 181.25/181.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__cl__ivl__Suc,axiom, % 181.25/181.50 ! [V_f_2,V_m_2,V_n_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 181.25/181.50 => 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) ) % 181.25/181.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 181.25/181.50 => 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))) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__head,axiom, % 181.25/181.50 ! [V_Pa_2,V_n_2,V_m_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.50 => 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))) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__ub__add__nat,axiom, % 181.25/181.50 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.25/181.50 => ( 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)))) % 181.25/181.50 => 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)))) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__cases,axiom, % 181.25/181.50 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => 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))))) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__diff1_H,axiom, % 181.25/181.50 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.50 => 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)))))) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum_Oremove,axiom, % 181.25/181.50 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.25/181.50 => 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)))))) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__diff1,axiom, % 181.25/181.50 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Oab__group__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.50 => 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)) ) % 181.25/181.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.50 => 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) ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__diff1__ring,axiom, % 181.25/181.50 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( class_Rings_Oring(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.25/181.50 => 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)) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_geometric__sum,axiom, % 181.25/181.50 ! [V_n_2,V_x_2,T_b] : % 181.25/181.50 ( class_Fields_Ofield(T_b) % 181.25/181.50 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b) % 181.25/181.50 => 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))) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_gauss__sum,axiom, % 181.25/181.50 ! [V_n_2,T_b] : % 181.25/181.50 ( class_Rings_Ocomm__semiring__1(T_b) % 181.25/181.50 => 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))) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__natinterval__difff,axiom, % 181.25/181.50 ! [V_f_2,V_n_2,V_m_2,T_b] : % 181.25/181.50 ( class_Groups_Oab__group__add(T_b) % 181.25/181.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.50 => 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)))) ) % 181.25/181.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.25/181.50 => 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) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_arith__series__general,axiom, % 181.25/181.50 ! [V_n_2,V_d_2,V_a_2,T_b] : % 181.25/181.50 ( class_Rings_Ocomm__semiring__1(T_b) % 181.25/181.50 => 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)))) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__mono2,axiom, % 181.25/181.50 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 181.25/181.50 ( class_Groups_Oordered__comm__monoid__add(T_c) % 181.25/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.25/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.25/181.50 => ( ! [B_b] : % 181.25/181.50 ( 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))) % 181.25/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) ) % 181.25/181.50 => 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))) ) ) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__mult__setsum__if__inj,axiom, % 181.25/181.50 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : % 181.25/181.50 ( class_Rings_Osemiring__0(T_d) % 181.25/181.50 => ( 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))) % 181.25/181.50 => 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))))))) ) ) ). % 181.25/181.50 % 181.25/181.50 fof(fact_setsum__bounded,axiom, % 181.25/181.50 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] : % 181.25/181.50 ( ( class_Groups_Oordered__ab__semigroup__add(T_c) % 181.25/181.50 & class_Rings_Osemiring__1(T_c) ) % 181.25/181.50 => ( ! [B_i] : % 181.25/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) % 181.25/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) ) % 181.25/181.50 => 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))) ) ) ). % 181.25/181.50 % 181.55/181.50 fof(fact_SigmaI,axiom, % 181.55/181.50 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Times__eq__cancel2,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 181.55/181.50 => ( 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)) % 181.55/181.50 <=> V_A_2 = V_B_2 ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__Diff__distrib2,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Times__Diff__distrib1,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__Diff__distrib1,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__eq__0__iff,axiom, % 181.55/181.50 ! [V_f_2,V_F_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.55/181.50 => ( 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) % 181.55/181.50 <=> ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 181.55/181.50 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__empty1,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_card__cartesian__product,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__cartesian__product,axiom, % 181.55/181.50 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Times__empty,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__empty2,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Compl__Times__UNIV2,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Compl__Times__UNIV1,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setprod__cartesian__product,axiom, % 181.55/181.50 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__mult(T_b) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__Un__distrib2,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Times__Un__distrib1,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__Un__distrib1,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_swap__product,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_card__eq__setsum,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__cartesian__product,axiom, % 181.55/181.50 ! [V_B_2,T_c,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.55/181.50 => 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)))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_equiv__type,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__Int__distrib2,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Times__Int__distrib1,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__Int__distrib1,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Id__on__subset__Times,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_UNIV__Times__UNIV,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_mem__Sigma__iff,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.50 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_SigmaD1,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_SigmaD2,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_SigmaE2,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.50 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_int__setsum,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__eq__Suc0__iff,axiom, % 181.55/181.50 ! [V_f_2,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( 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)) % 181.55/181.50 <=> ? [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 181.55/181.50 & ! [B_xa] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 181.55/181.50 => ( B_x != B_xa % 181.55/181.50 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__eq__1__iff,axiom, % 181.55/181.50 ! [V_f_2,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( 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) % 181.55/181.50 <=> ? [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 181.55/181.50 & ! [B_xa] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 181.55/181.50 => ( B_x != B_xa % 181.55/181.50 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 181.55/181.50 ! [V_k_2,V_f_2] : % 181.55/181.50 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_card__cartesian__product__singleton,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Times__subset__cancel2,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 181.55/181.50 => ( 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)))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Image__subset,axiom, % 181.55/181.50 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__cartesian__productD1,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,T_c,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__cartesian__productD2,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,T_c,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_SetCompr__Sigma__eq,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Collect__split,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fst__image__times,axiom, % 181.55/181.50 ! [V_A_2,T_c,T_b,V_B_2] : % 181.55/181.50 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 => 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)) ) % 181.55/181.50 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 => 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 ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_snd__image__times,axiom, % 181.55/181.50 ! [V_B_2,T_c,T_b,V_A_2] : % 181.55/181.50 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 => 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)) ) % 181.55/181.50 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 => 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 ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__diff__nat,axiom, % 181.55/181.50 ! [V_f_2,V_A_2,V_B_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_insert__times__insert,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__equiv__class,axiom, % 181.55/181.50 ! [V_X_2,V_r_2,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( 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)))) % 181.55/181.50 => ( 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))) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_vimage__Times,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_UN__Times__distrib,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__def,axiom, % 181.55/181.50 ! [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))))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 181.55/181.50 ! [V_A_2,V_f_2,T_b] : % 181.55/181.50 ( ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.50 & class_Groups_Ocomm__monoid__mult(T_b) ) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__quotient,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( 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)))) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__diff1__nat,axiom, % 181.55/181.50 ! [V_f_2,V_A_2,V_a_2,T_b] : % 181.55/181.50 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.50 => 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)) ) % 181.55/181.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__Un__nat,axiom, % 181.55/181.50 ! [V_f_2,V_B_2,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 181.55/181.50 ! [V_f_2,V_A_2,T_b] : % 181.55/181.50 ( ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.50 & class_Groups_Ocomm__monoid__mult(T_b) ) % 181.55/181.50 => ( c_Nat__Transfer_Onat__set(V_A_2) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_image__split__eq__Sigma,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_arith__series__nat,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 181.55/181.50 ! [V_f_2,V_A_2,T_b] : % 181.55/181.50 ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fold__image__Sigma,axiom, % 181.55/181.50 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__mult(T_d) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__multicount,axiom, % 181.55/181.50 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) % 181.55/181.50 => 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 ) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 181.55/181.50 ! [V_A_2,V_I_2,T_c,T_b] : % 181.55/181.50 ? [B_f] : % 181.55/181.50 ( 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)) % 181.55/181.50 & 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setprod__Sigma,axiom, % 181.55/181.50 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__mult(T_d) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__Sigma,axiom, % 181.55/181.50 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_d) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_card__SigmaI,axiom, % 181.55/181.50 ! [V_B_2,T_c,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum_Ounion__inter__neutral,axiom, % 181.55/181.50 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( 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))) % 181.55/181.50 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 181.55/181.50 => 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)) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__Un__zero,axiom, % 181.55/181.50 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( 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))) % 181.55/181.50 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 181.55/181.50 => 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)) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__mono3,axiom, % 181.55/181.50 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 181.55/181.50 ( ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.50 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( 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))) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 181.55/181.50 => 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))) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__reindex__nonzero,axiom, % 181.55/181.50 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_d) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 181.55/181.50 => ! [B_y] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) % 181.55/181.50 => ( B_x != B_y % 181.55/181.50 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 181.55/181.50 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) % 181.55/181.50 => 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) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__SigmaI,axiom, % 181.55/181.50 ! [V_B_2,T_c,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_a] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_UN__le__eq__Un0,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__multicount__gen,axiom, % 181.55/181.50 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) % 181.55/181.50 => 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) ) % 181.55/181.50 => 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) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__atMost,axiom, % 181.55/181.50 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atMost__eq__iff,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) % 181.55/181.50 <=> V_x_2 = V_y_2 ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atLeast0AtMost,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_lessThan__Suc__atMost,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_card__atMost,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atMost__Suc,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atMost__iff,axiom, % 181.55/181.50 ! [V_k_2,V_i_2,T_b] : % 181.55/181.50 ( class_Orderings_Oord(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atMost__subset__iff,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => ( 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))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_UN__atMost__UNIV,axiom, % 181.55/181.50 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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__atMost__Suc,axiom, % 181.55/181.50 ! [V_n_2,V_f_2,T_b] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atMost__0,axiom, % 181.55/181.50 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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Int__atLeastAtMostL1,axiom, % 181.55/181.50 ! [V_d_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Int__atLeastAtMostR1,axiom, % 181.55/181.50 ! [V_d_2,V_c_2,V_b_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I9_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_UN__le__add__shift,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__int_I3_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__int_I1_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I2_J,axiom, % 181.55/181.50 ! [V_u_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I10_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I7_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__nonneg__0,axiom, % 181.55/181.50 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add(T_c) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 181.55/181.50 => ( ! [B_i] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 181.55/181.50 => ( 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) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 181.55/181.50 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__nonneg__leq__bound,axiom, % 181.55/181.50 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add(T_c) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 181.55/181.50 => ( ! [B_i] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 181.55/181.50 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_greaterThan__0,axiom, % 181.55/181.50 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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_greaterThan__eq__iff,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) % 181.55/181.50 <=> V_x_2 = V_y_2 ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_greaterThan__iff,axiom, % 181.55/181.50 ! [V_k_2,V_i_2,T_b] : % 181.55/181.50 ( class_Orderings_Oord(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_greaterThan__subset__iff,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( 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))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Compl__atMost,axiom, % 181.55/181.50 ! [V_k_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Compl__greaterThan,axiom, % 181.55/181.50 ! [V_k_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__int_I7_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I11_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_image__uminus__lessThan,axiom, % 181.55/181.50 ! [V_x_2,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_image__uminus__greaterThan,axiom, % 181.55/181.50 ! [V_x_2,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__int_I5_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_greaterThan__Suc,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sum__diff__distrib,axiom, % 181.55/181.50 ! [V_n_2,V_Pa_2,V_Qa_2] : % 181.55/181.50 ( ! [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))) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I12_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_SigmaE,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 181.55/181.50 => ~ ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => ! [B_y] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) % 181.55/181.50 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atLeast__eq__iff,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) % 181.55/181.50 <=> V_x_2 = V_y_2 ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atLeast__iff,axiom, % 181.55/181.50 ! [V_k_2,V_i_2,T_b] : % 181.55/181.50 ( class_Orderings_Oord(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atLeast__subset__iff,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => ( 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))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atLeast__0,axiom, % 181.55/181.50 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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Compl__atLeast,axiom, % 181.55/181.50 ! [V_k_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Compl__lessThan,axiom, % 181.55/181.50 ! [V_k_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atLeast__Suc__greaterThan,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I14_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__int_I8_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Int__atLeastAtMostL2,axiom, % 181.55/181.50 ! [V_c_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Int__atLeastAtMostR2,axiom, % 181.55/181.50 ! [V_d_2,V_c_2,V_a_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_UN__atLeast__UNIV,axiom, % 181.55/181.50 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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__int_I6_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_image__uminus__atMost,axiom, % 181.55/181.50 ! [V_x_2,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_image__uminus__atLeast,axiom, % 181.55/181.50 ! [V_x_2,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add(T_b) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atLeast__Suc,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_atMost__Int__atLeast,axiom, % 181.55/181.50 ! [V_n_2,T_b] : % 181.55/181.50 ( class_Orderings_Oorder(T_b) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I1_J,axiom, % 181.55/181.50 ! [V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ivl__disj__un_I13_J,axiom, % 181.55/181.50 ! [V_u_2,V_l_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair__surj,axiom, % 181.55/181.50 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__mono__zero__left,axiom, % 181.55/181.50 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( 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))) % 181.55/181.50 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 181.55/181.50 => 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) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__mono__zero__right,axiom, % 181.55/181.50 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( 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))) % 181.55/181.50 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 181.55/181.50 => 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) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair__imageI,axiom, % 181.55/181.50 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair_Ocompositionality,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair__compose,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair_Ocomp,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_snd__comp__map__pair,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fst__comp__map__pair,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair__simp,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fst__map__pair,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_snd__prod__fun,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair__ident,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair_Oidentity,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair_Oid,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair__def,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair__surj__on,axiom, % 181.55/181.50 ! [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] : % 181.55/181.50 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 181.55/181.50 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_map__pair__inj__on,axiom, % 181.55/181.50 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.50 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.55/181.50 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_prod__fun__imageE,axiom, % 181.55/181.50 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_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))) % 181.55/181.50 => ~ ! [B_x,B_y] : % 181.55/181.50 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 181.55/181.50 => ~ 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__strict__mono,axiom, % 181.55/181.50 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 181.55/181.50 ( ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.50 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) ) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 181.55/181.50 => 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))) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_field__le__mult__one__interval,axiom, % 181.55/181.50 ! [V_y,V_x,T_a] : % 181.55/181.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 181.55/181.50 => ( ! [B_z] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 181.55/181.50 => 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)) ) ) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 181.55/181.50 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 181.55/181.50 ( ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.50 & class_Groups_Ocomm__monoid__mult(T_b) ) % 181.55/181.50 => ( V_A_2 = V_B_2 % 181.55/181.50 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 181.55/181.50 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 181.55/181.50 => 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) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__if,axiom, % 181.55/181.50 ! [V_x,T_a] : % 181.55/181.50 ( class_Groups_Osgn__if(T_a) % 181.55/181.50 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 181.55/181.50 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 181.55/181.50 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 181.55/181.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.55/181.50 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 181.55/181.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.55/181.50 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__1__neg,axiom, % 181.55/181.50 ! [V_a_2,T_b] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_b) % 181.55/181.50 => ( 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)) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__times,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn0,axiom, % 181.55/181.50 ! [T_a] : % 181.55/181.50 ( class_Groups_Osgn__if(T_a) % 181.55/181.50 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__0__0,axiom, % 181.55/181.50 ! [V_a_2,T_b] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_b) % 181.55/181.50 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.55/181.50 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__sgn,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__greater,axiom, % 181.55/181.50 ! [V_a_2,T_b] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_b) % 181.55/181.50 => ( 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))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__less,axiom, % 181.55/181.50 ! [V_a_2,T_b] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_b) % 181.55/181.50 => ( 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))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__1__pos,axiom, % 181.55/181.50 ! [V_a_2,T_b] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_b) % 181.55/181.50 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__pos,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.55/181.50 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_zsgn__def,axiom, % 181.55/181.50 ! [V_i] : % 181.55/181.50 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 181.55/181.50 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 181.55/181.50 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 181.55/181.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 181.55/181.50 => 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)) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sgn__neg,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.55/181.50 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Body__triple__valid__0,axiom, % 181.55/181.50 ! [V_Qa_2,V_pna_2,V_Pa_2,T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pna_2)),V_Qa_2)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_code__numeral_Osimps_I5_J,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_decr__lemma,axiom, % 181.55/181.50 ! [V_z,V_x,V_d] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__abs,axiom, % 181.55/181.50 ! [V_A_2,V_f_2,T_c,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__abs__ge__zero,axiom, % 181.55/181.50 ! [V_A_2,V_f_2,T_c,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__power__minus,axiom, % 181.55/181.50 ! [V_n,V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_nonzero__abs__divide,axiom, % 181.55/181.50 ! [V_a,V_b,T_a] : % 181.55/181.50 ( class_Fields_Olinordered__field(T_a) % 181.55/181.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__of__nonneg,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__le__zero__iff,axiom, % 181.55/181.50 ! [V_a_2,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 181.55/181.50 => ( 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))) % 181.55/181.50 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__ge__zero,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__not__less__zero,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => ~ 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_zero__less__abs__iff,axiom, % 181.55/181.50 ! [V_a_2,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 181.55/181.50 => ( 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))) % 181.55/181.50 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__of__pos,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__triangle__ineq,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__mult__less,axiom, % 181.55/181.50 ! [V_d,V_b,V_c,V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 181.55/181.50 => 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))) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__of__nat,axiom, % 181.55/181.50 ! [V_n,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__int__eq,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__one,axiom, % 181.55/181.50 ! [T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__divide,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__add__abs,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__idempotent,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__mult,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__mult__self,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_power__abs,axiom, % 181.55/181.50 ! [V_n,V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__eq__0,axiom, % 181.55/181.50 ! [V_a_2,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 181.55/181.50 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 181.55/181.50 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__zero,axiom, % 181.55/181.50 ! [T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__ge__self,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__le__D1,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__less__iff,axiom, % 181.55/181.50 ! [V_b_2,V_a_2,T_b] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_b) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) % 181.55/181.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 181.55/181.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__le__D2,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__leI,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__le__iff,axiom, % 181.55/181.50 ! [V_b_2,V_a_2,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 181.55/181.50 => ( 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)) % 181.55/181.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 181.55/181.50 & 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__ge__minus__self,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__minus__cancel,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__setprod,axiom, % 181.55/181.50 ! [V_A_2,V_f_2,T_c,T_b] : % 181.55/181.50 ( class_Fields_Olinordered__field(T_b) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__setsum__abs,axiom, % 181.55/181.50 ! [V_A_2,V_f_2,T_c,T_b] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__triangle__ineq2__sym,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__triangle__ineq2,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__triangle__ineq3,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__minus__commute,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__zmult__eq__1,axiom, % 181.55/181.50 ! [V_n,V_m] : % 181.55/181.50 ( 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) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_triple__valid__Suc,axiom, % 181.55/181.50 ! [V_t,V_n,T_a] : % 181.55/181.50 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 181.55/181.50 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__sgn,axiom, % 181.55/181.50 ! [V_k,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_mult__sgn__abs,axiom, % 181.55/181.50 ! [V_x,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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 ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__mult__pos,axiom, % 181.55/181.50 ! [V_y,V_x,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__eq__mult,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Rings_Oordered__ring__abs(T_a) % 181.55/181.50 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 181.55/181.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 181.55/181.50 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 181.55/181.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__triangle__ineq4,axiom, % 181.55/181.50 ! [V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__diff__triangle__ineq,axiom, % 181.55/181.50 ! [V_d,V_c,V_b,V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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))))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__of__nonpos,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__minus__le__zero,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__if,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oabs__if(T_a) % 181.55/181.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 181.55/181.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__of__neg,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_zero__le__power__abs,axiom, % 181.55/181.50 ! [V_n,V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__div__pos,axiom, % 181.55/181.50 ! [V_x,V_y,T_a] : % 181.55/181.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__minus__one,axiom, % 181.55/181.50 ! [T_a] : % 181.55/181.50 ( ( class_Int_Onumber__ring(T_a) % 181.55/181.50 & class_Rings_Olinordered__idom(T_a) ) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_zabs__less__one__iff,axiom, % 181.55/181.50 ! [V_z_2] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_zabs__def,axiom, % 181.55/181.50 ! [V_i] : % 181.55/181.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 181.55/181.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 181.55/181.50 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_nat__abs__mult__distrib,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_zero__le__zpower__abs,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__number__of,axiom, % 181.55/181.50 ! [V_x,T_a] : % 181.55/181.50 ( ( class_Int_Onumber__ring(T_a) % 181.55/181.50 & class_Rings_Olinordered__idom(T_a) ) % 181.55/181.50 => ( ( 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))) % 181.55/181.50 => 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)) ) % 181.55/181.50 & ( ~ 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))) % 181.55/181.50 => 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) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__power__minus__one,axiom, % 181.55/181.50 ! [V_n,T_a] : % 181.55/181.50 ( ( class_Int_Onumber__ring(T_a) % 181.55/181.50 & class_Rings_Olinordered__idom(T_a) ) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_zero__less__zpower__abs__iff,axiom, % 181.55/181.50 ! [V_n_2,V_x_2] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_power2__abs,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_abs__power2,axiom, % 181.55/181.50 ! [V_a,T_a] : % 181.55/181.50 ( class_Rings_Olinordered__idom(T_a) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_code__numeral_Osimps_I4_J,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_incr__lemma,axiom, % 181.55/181.50 ! [V_x,V_z,V_d] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_divmod__int__pdivmod,axiom, % 181.55/181.50 ! [V_l_2,V_k_2] : % 181.55/181.50 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => 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)) ) % 181.55/181.50 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => 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) ) % 181.55/181.50 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => 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)))) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Nitpick_Oint__gcd__def,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_divmod__int__code,axiom, % 181.55/181.50 ! [V_l_2,V_k_2] : % 181.55/181.50 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => 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)) ) % 181.55/181.50 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => 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) ) % 181.55/181.50 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => 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)))) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apsnd__compose,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_snd__apsnd,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apsnd__eq__conv,axiom, % 181.55/181.50 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] : % 181.55/181.50 ( 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) % 181.55/181.50 <=> 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apsnd__conv,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fst__apsnd,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_negateSnd__def,axiom, % 181.55/181.50 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apsnd__def,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apsnd__id,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_nat__gcd_Osimps,axiom, % 181.55/181.50 ! [V_x,V_y] : % 181.55/181.50 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.50 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 181.55/181.50 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pdivmod__def,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pdivmod__posDivAlg,axiom, % 181.55/181.50 ! [V_k,V_l] : % 181.55/181.50 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => 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)) ) % 181.55/181.50 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_nat__gcd_Opsimps,axiom, % 181.55/181.50 ! [V_y_2,V_x_2] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.50 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 181.55/181.50 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Nitpick_Onat__lcm__def,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Nitpick_Oint__lcm__def,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_nat__gcd_Opinduct,axiom, % 181.55/181.50 ! [V_Pa_2,V_a1_2,V_a0_2] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( ! [B_x,B_y] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.50 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 181.55/181.50 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 181.55/181.50 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apfst__apsnd,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apsnd__apfst,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apfst__compose,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fst__apfst,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apfst__eq__conv,axiom, % 181.55/181.50 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] : % 181.55/181.50 ( 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) % 181.55/181.50 <=> 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apfst__conv,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_snd__apfst,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apsnd__apfst__commute,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apfst__def,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_apfst__id,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 181.55/181.50 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 181.55/181.50 ( ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.50 & class_Groups_Ocomm__monoid__mult(T_b) ) % 181.55/181.50 => ( V_A_2 = V_B_2 % 181.55/181.50 => ( c_Nat__Transfer_Onat__set(V_B_2) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 181.55/181.50 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 181.55/181.50 => 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) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_accp__acc__eq,axiom, % 181.55/181.50 ! [V_x_2,V_r_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__def,axiom, % 181.55/181.50 ! [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))))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__compI,axiom, % 181.55/181.50 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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_c_2)),V_s_2)) % 181.55/181.50 => 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_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__distrib,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__distrib2,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_O__assoc,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__empty2,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__empty1,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__mono,axiom, % 181.55/181.50 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__UNION__distrib2,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__UNION__distrib,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_union__comp__emptyR,axiom, % 181.55/181.50 ! [V_C_2,V_B_2,V_A_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_union__comp__emptyL,axiom, % 181.55/181.50 ! [V_B_2,V_C_2,V_A_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__comp__subset__Sigma,axiom, % 181.55/181.50 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => ( 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)))) % 181.55/181.50 => 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)))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acc__subset,axiom, % 181.55/181.50 ! [V_R2_2,V_R1_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acc__downward,axiom, % 181.55/181.50 ! [V_a_2,V_r_2,V_b_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 181.55/181.50 => ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acc_Osimps,axiom, % 181.55/181.50 ! [V_r_2,V_a_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 181.55/181.50 <=> ! [B_x] : % 181.55/181.50 ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_max__ext__compat,axiom, % 181.55/181.50 ! [V_S_2,V_R_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_min__ext__compat,axiom, % 181.55/181.50 ! [V_S_2,V_R_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pred__comp__rel__comp__eq,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_reduction__pairI,axiom, % 181.55/181.50 ! [V_S_2,V_R_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_R_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Nitpick_Ozero__frac__def,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__less__than,axiom, % 181.55/181.50 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pred__comp_Ointros,axiom, % 181.55/181.50 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__empty,axiom, % 181.55/181.50 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__inv__image,axiom, % 181.55/181.50 ! [V_f_2,T_c,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__lex__prod,axiom, % 181.55/181.50 ! [V_rb_2,T_c,V_ra_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_ra_2) % 181.55/181.50 => ( c_Wellfounded_Owf(T_c,V_rb_2) % 181.55/181.50 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__measure,axiom, % 181.55/181.50 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__comp__self,axiom, % 181.55/181.50 ! [V_R_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_R_2) % 181.55/181.50 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__irrefl,axiom, % 181.55/181.50 ! [V_a_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => ~ 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__asym,axiom, % 181.55/181.50 ! [V_x_2,V_a_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => ~ 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__not__sym,axiom, % 181.55/181.50 ! [V_x_2,V_a_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => ~ 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__not__refl,axiom, % 181.55/181.50 ! [V_a_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => ~ 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__less,axiom, % 181.55/181.50 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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__finite__psubset,axiom, % 181.55/181.50 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__mlex,axiom, % 181.55/181.50 ! [V_f_2,V_R_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_R_2) % 181.55/181.50 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__subset,axiom, % 181.55/181.50 ! [V_p_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__pair__less,axiom, % 181.55/181.50 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 181.55/181.50 % 181.55/181.50 fof(fact_min__ext__wf,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pred__comp_Oequations,axiom, % 181.55/181.50 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> ? [B_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 181.55/181.50 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_max__ext__wf,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__Int1,axiom, % 181.55/181.50 ! [V_r_H_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__Int2,axiom, % 181.55/181.50 ! [V_r_H_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__int__ge__less__than2,axiom, % 181.55/181.50 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__int__ge__less__than,axiom, % 181.55/181.50 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acc__wfD,axiom, % 181.55/181.50 ! [V_x_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__acc__iff,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__no__loop,axiom, % 181.55/181.50 ! [V_R_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__union__merge,axiom, % 181.55/181.50 ! [V_S_2,V_R_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 <=> ~ ? [B_f] : % 181.55/181.50 ! [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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfE__pf,axiom, % 181.55/181.50 ! [V_A_2,V_R_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_R_2) % 181.55/181.50 => ( 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))) % 181.55/181.50 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__union__compatible,axiom, % 181.55/181.50 ! [V_S_2,V_R_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_R_2) % 181.55/181.50 => ( c_Wellfounded_Owf(T_b,V_S_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf,axiom, % 181.55/181.50 ! [T_b] : % 181.55/181.50 ( class_Orderings_Owellorder(T_b) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_reduction__pair__def,axiom, % 181.55/181.50 ! [V_Pa_2,T_b] : % 181.55/181.50 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 181.55/181.50 <=> ( 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)) % 181.55/181.50 & 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_reduction__pair__lemma,axiom, % 181.55/181.50 ! [V_S_2,V_R_2,V_Pa_2,T_b] : % 181.55/181.50 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 181.55/181.50 => ( 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))) % 181.55/181.50 => ( 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))) % 181.55/181.50 => ( c_Wellfounded_Owf(T_b,V_S_2) % 181.55/181.50 => 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)) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__map__pair__image,axiom, % 181.55/181.50 ! [V_f_2,T_c,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Nitpick_Oone__frac__def,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Nitpick_Ofrac__def,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pred__nat__def,axiom, % 181.55/181.50 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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__lenlex,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__same__fst,axiom, % 181.55/181.50 ! [T_b,V_R_2,T_c,V_Pa_2] : % 181.55/181.50 ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.55/181.50 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) ) % 181.55/181.50 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__pred__nat,axiom, % 181.55/181.50 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__lex,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__lexn,axiom, % 181.55/181.50 ! [V_n_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__if__measure,axiom, % 181.55/181.50 ! [T_b,V_g_2,V_f_2,V_Pa_2] : % 181.55/181.50 ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.55/181.50 => 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))) ) % 181.55/181.50 => 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))))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_lex__def,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_lexn_Osimps_I1_J,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__Collect__split,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__on__def,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.50 <=> ( 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)))) % 181.55/181.50 & ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_nat0__intermed__int__val,axiom, % 181.55/181.50 ! [V_k_2,V_f_2,V_n_2] : % 181.55/181.50 ( ! [B_i] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 181.55/181.50 => 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))) ) % 181.55/181.50 => ( 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)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 181.55/181.50 => ? [B_i] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 181.55/181.50 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_RangeI,axiom, % 181.55/181.50 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__on__Id__on,axiom, % 181.55/181.50 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__Id__on,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__empty__iff,axiom, % 181.55/181.50 ! [V_r_2,T_b,T_c] : % 181.55/181.50 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__empty,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__Un__eq,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__on__empty,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__on__Un,axiom, % 181.55/181.50 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.50 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__Range,axiom, % 181.55/181.50 ! [V_r_2,T_c,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__on__Int,axiom, % 181.55/181.50 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.50 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_snd__eq__Range,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__iff,axiom, % 181.55/181.50 ! [V_r_2,T_c,V_a_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 181.55/181.50 <=> ? [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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__onD2,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__onD1,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__onD,axiom, % 181.55/181.50 ! [V_a_2,V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__insert,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__Int__subset,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__Diff__subset,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_reflp__def,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Predicate_Oreflp(T_b,V_r_2) % 181.55/181.50 <=> 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_RangeP__Range__eq,axiom, % 181.55/181.50 ! [V_x_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__onI,axiom, % 181.55/181.50 ! [V_A_2,V_r_2,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => 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)) ) % 181.55/181.50 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_RangeP_Ointros,axiom, % 181.55/181.50 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 181.55/181.50 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_reflpE,axiom, % 181.55/181.50 ! [V_x_2,V_r_2,T_b] : % 181.55/181.50 ( c_Predicate_Oreflp(T_b,V_r_2) % 181.55/181.50 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_RangeP_Oequations,axiom, % 181.55/181.50 ! [V_a2_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) % 181.55/181.50 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_RangeE,axiom, % 181.55/181.50 ! [V_r_2,T_c,V_b_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 181.55/181.50 => ~ ! [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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__Un,axiom, % 181.55/181.50 ! [V_s_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => ( c_Wellfounded_Owf(T_b,V_s_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_int__val__lemma,axiom, % 181.55/181.50 ! [V_k_2,V_f_2,V_n_2] : % 181.55/181.50 ( ! [B_i] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 181.55/181.50 => 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))) ) % 181.55/181.50 => ( 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)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 181.55/181.50 => ? [B_i] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 181.55/181.50 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_DomainI,axiom, % 181.55/181.50 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__Id__on,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__empty__iff,axiom, % 181.55/181.50 ! [V_r_2,T_c,T_b] : % 181.55/181.50 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__empty,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__mono,axiom, % 181.55/181.50 ! [V_s_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__Un__eq,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__Domain,axiom, % 181.55/181.50 ! [V_r_2,T_c,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fst__eq__Domain,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__iff,axiom, % 181.55/181.50 ! [V_r_2,T_c,V_a_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 181.55/181.50 <=> ? [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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__insert,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__Int__subset,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__Diff__subset,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Field__def,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__Collect__split,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_DomainP__Domain__eq,axiom, % 181.55/181.50 ! [V_x_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_DomainE,axiom, % 181.55/181.50 ! [V_r_2,T_c,V_a_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 181.55/181.50 => ~ ! [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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfP__def,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_OwfP(T_b,V_r_2) % 181.55/181.50 <=> 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_DomainP_Ointros,axiom, % 181.55/181.50 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 181.55/181.50 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfP__empty,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfP__accp__iff,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_OwfP(T_b,V_r_2) % 181.55/181.50 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_accp__wfPD,axiom, % 181.55/181.50 ! [V_x_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_OwfP(T_b,V_r_2) % 181.55/181.50 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfP__subset,axiom, % 181.55/181.50 ! [V_p_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_OwfP(T_b,V_r_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_DomainP_Oequations,axiom, % 181.55/181.50 ! [V_a1_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) % 181.55/181.50 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__in__rel,axiom, % 181.55/181.50 ! [V_R_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_R_2) % 181.55/181.50 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfP__wf__eq,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfP__acyclicP,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_OwfP(T_b,V_r_2) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setprod__pos__nat,axiom, % 181.55/181.50 ! [V_f_2,V_S_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 181.55/181.50 => 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))) ) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Rep__Integ__induct,axiom, % 181.55/181.50 ! [V_Pa_2,V_y_2] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 181.55/181.50 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 181.55/181.50 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acyclic__subset,axiom, % 181.55/181.50 ! [V_r_2,V_s_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Oacyclic(T_b,V_s_2) % 181.55/181.50 => ( 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)) % 181.55/181.50 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__acyclic,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__acyclic__wf,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 181.55/181.50 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__iff__acyclic__if__finite,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 181.55/181.50 => ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Nitpick_Owf_H__def,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Nitpick_Owf_H(T_b,V_r_2) % 181.55/181.50 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 181.55/181.50 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 181.55/181.50 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Rep__Integ__cases,axiom, % 181.55/181.50 ! [V_y_2] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 181.55/181.50 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__on__def_H,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.50 <=> ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 181.55/181.50 => 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)) ) % 181.55/181.50 & ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => 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)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ball__empty,axiom, % 181.55/181.50 ! [V_Pa_2,T_b,B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 181.55/181.50 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Powp__def,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) % 181.55/181.50 <=> ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 181.55/181.50 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_congruent__def,axiom, % 181.55/181.50 ! [V_f_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 181.55/181.50 <=> ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Abs__Integ__cases,axiom, % 181.55/181.50 ! [V_x_2] : % 181.55/181.50 ~ ! [B_y] : % 181.55/181.50 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 181.55/181.50 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Abs__Integ__induct,axiom, % 181.55/181.50 ! [V_x_2,V_Pa_2] : % 181.55/181.50 ( ! [B_y] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 181.55/181.50 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 181.55/181.50 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__UN__I,axiom, % 181.55/181.50 ! [V_B_2,T_c,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_a] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_triples__valid__Suc,axiom, % 181.55/181.50 ! [V_n_2,V_ts_2,T_b] : % 181.55/181.50 ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 181.55/181.50 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 181.55/181.50 => ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 181.55/181.50 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_hoare__valids__def,axiom, % 181.55/181.50 ! [V_ts_2,V_Ga_2,T_b] : % 181.55/181.50 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2) % 181.55/181.50 <=> ! [B_n] : % 181.55/181.50 ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2)) % 181.55/181.50 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) % 181.55/181.50 => ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 181.55/181.50 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ex__bij__betw__nat__finite__1,axiom, % 181.55/181.50 ! [V_M_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 181.55/181.50 => ? [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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_inj__on__diff__nat,axiom, % 181.55/181.50 ! [V_k_2,V_N_2] : % 181.55/181.50 ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 181.55/181.50 => 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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ex__bij__betw__nat__finite,axiom, % 181.55/181.50 ! [V_M_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 181.55/181.50 => ? [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) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfP__SUP,axiom, % 181.55/181.50 ! [T_b,V_r_2,T_c] : % 181.55/181.50 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) % 181.55/181.50 => ( ! [B_i,B_j] : % 181.55/181.50 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 181.55/181.50 => 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)) ) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__map__freshness,axiom, % 181.55/181.50 ! [V_f_2,T_c,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2))) % 181.55/181.50 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 181.55/181.50 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_mem__splitE,axiom, % 181.55/181.50 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] : % 181.55/181.50 ( 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_c_2),V_p_2))) % 181.55/181.50 => ~ ! [B_x,B_y] : % 181.55/181.50 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) % 181.55/181.50 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_mem__splitI2,axiom, % 181.55/181.50 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] : % 181.55/181.50 ( ! [B_a,B_b] : % 181.55/181.50 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) ) % 181.55/181.50 => 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_c_2),V_p_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__SucD,axiom, % 181.55/181.50 ! [V_n_2,V_A_2,V_f_2,T_b] : % 181.55/181.50 ( 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) % 181.55/181.50 => ? [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 & 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_nat__mod__eq__lemma,axiom, % 181.55/181.50 ! [V_y,V_n,V_x] : % 181.55/181.50 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 181.55/181.50 => ? [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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wfI__pf,axiom, % 181.55/181.50 ! [V_R_2,T_b] : % 181.55/181.50 ( ! [B_A] : % 181.55/181.50 ( 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))) % 181.55/181.50 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 181.55/181.50 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_ex__bij__betw__finite__nat,axiom, % 181.55/181.50 ! [V_M_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 181.55/181.50 => ? [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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Sigma__mono,axiom, % 181.55/181.50 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => 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))) ) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_not__acc__down,axiom, % 181.55/181.50 ! [V_R_2,V_x_2,T_b] : % 181.55/181.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) % 181.55/181.50 => ~ ! [B_z] : % 181.55/181.50 ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acc_OaccI,axiom, % 181.55/181.50 ! [V_r_2,V_x_2,T_b] : % 181.55/181.50 ( ! [B_y] : % 181.55/181.50 ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) ) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fold__image__1,axiom, % 181.55/181.50 ! [V_f_2,V_S_2,T_b,T_c] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__mult(T_c) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 181.55/181.50 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 181.55/181.50 => 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) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_card_Oneutral,axiom, % 181.55/181.50 ! [V_A_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.55/181.50 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_max__ext_Osimps,axiom, % 181.55/181.50 ! [V_R_2,V_a2_2,V_a1_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 181.55/181.50 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 181.55/181.50 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.50 & ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 181.55/181.50 => ? [B_xa] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 181.55/181.50 & 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)) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_mod__induct__0,axiom, % 181.55/181.50 ! [V_i_2,V_Pa_2,V_p_2] : % 181.55/181.50 ( ! [B_i] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 181.55/181.50 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 181.55/181.50 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 181.55/181.50 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 181.55/181.50 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_fold__image__cong,axiom, % 181.55/181.50 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] : % 181.55/181.50 ( class_Groups_Oab__semigroup__mult(T_c) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 181.55/181.50 => 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) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Min__eqI,axiom, % 181.55/181.50 ! [V_x_2,V_A_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_y] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) ) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.50 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Max__eqI,axiom, % 181.55/181.50 ! [V_x_2,V_A_2,T_b] : % 181.55/181.50 ( class_Orderings_Olinorder(T_b) % 181.55/181.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.50 => ( ! [B_y] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) ) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.50 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__no__infinite__down__chainE,axiom, % 181.55/181.50 ! [V_f_2,V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => ~ ! [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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osize_I11_J,axiom, % 181.55/181.50 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I41_J,axiom, % 181.55/181.50 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I40_J,axiom, % 181.55/181.50 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I39_J,axiom, % 181.55/181.50 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I38_J,axiom, % 181.55/181.50 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I37_J,axiom, % 181.55/181.50 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I36_J,axiom, % 181.55/181.50 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I22_J,axiom, % 181.55/181.50 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I23_J,axiom, % 181.55/181.50 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I34_J,axiom, % 181.55/181.50 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I35_J,axiom, % 181.55/181.50 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I11_J,axiom, % 181.55/181.50 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I10_J,axiom, % 181.55/181.50 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osimps_I2_J,axiom, % 181.55/181.50 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 181.55/181.50 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) % 181.55/181.50 <=> ( V_loc_2 = V_loc_H_2 % 181.55/181.50 & V_fun_2 = V_fun_H_2 % 181.55/181.50 & V_com_2 = V_com_H_2 ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_com_Osize_I3_J,axiom, % 181.55/181.50 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__reindex__cong,axiom, % 181.55/181.50 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 181.55/181.50 ( class_Groups_Ocomm__monoid__add(T_d) % 181.55/181.50 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 181.55/181.50 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 181.55/181.50 => ( ! [B_a] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 181.55/181.50 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 181.55/181.50 => 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) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_scomp__unfold,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_setsum__ivl__cong,axiom, % 181.55/181.50 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] : % 181.55/181.50 ( ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.50 & class_Orderings_Oord(T_b) ) % 181.55/181.50 => ( V_a_2 = V_c_2 % 181.55/181.50 => ( V_b_2 = V_d_2 % 181.55/181.50 => ( ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) % 181.55/181.50 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 181.55/181.50 => 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_c_2),V_d_2)) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Pair__scomp,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_scomp__scomp,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_scomp__Pair,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_scomp__apply,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_scomp__def,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_iterate_Osimps,axiom, % 181.55/181.50 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 181.55/181.50 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.55/181.50 => 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) ) % 181.55/181.50 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_less__eq,axiom, % 181.55/181.50 ! [V_n_2,V_m_2] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_nat__intermed__int__val,axiom, % 181.55/181.50 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 181.55/181.50 ( ! [B_i] : % 181.55/181.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 181.55/181.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 181.55/181.50 => 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))) ) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 181.55/181.50 => ? [B_i] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 181.55/181.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 181.55/181.50 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__trancl,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_less__than__def,axiom, % 181.55/181.50 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acyclic__def,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 181.55/181.50 <=> ! [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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl_Or__into__trancl,axiom, % 181.55/181.50 ! [V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__subset__Field2,axiom, % 181.55/181.50 ! [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))))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__Int__subset,axiom, % 181.55/181.50 ! [V_s_2,V_r_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_r__into__trancl_H,axiom, % 181.55/181.50 ! [V_r_2,V_p_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__empty,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__domain,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__range,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__trancl,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 181.55/181.50 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__trans,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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_c_2)),V_r_2)) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__into__trancl2,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_r__r__into__trancl,axiom, % 181.55/181.50 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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_c_2)),V_R_2)) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__mono,axiom, % 181.55/181.50 ! [V_s_2,V_r_2,V_p_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 181.55/181.50 => ( 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)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__unfold,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__subset__Sigma,axiom, % 181.55/181.50 ! [V_A_2,V_r_2,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_log_Osimps,axiom, % 181.55/181.50 ! [V_i,V_b] : % 181.55/181.50 ( ( ( 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))) % 181.55/181.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 181.55/181.50 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 181.55/181.50 & ( ~ ( 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))) % 181.55/181.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_minus__shift__def,axiom, % 181.55/181.50 ! [V_r,V_l,V_k] : % 181.55/181.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 181.55/181.50 => 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) ) % 181.55/181.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 181.55/181.50 => 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) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_inc__shift__def,axiom, % 181.55/181.50 ! [V_k,V_v] : % 181.55/181.50 ( ( V_v = V_k % 181.55/181.50 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 181.55/181.50 & ( V_v != V_k % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_range,axiom, % 181.55/181.50 ! [V_s,V_k] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__insert,axiom, % 181.55/181.50 ! [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)))))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_r__into__rtrancl,axiom, % 181.55/181.50 ! [V_r_2,V_p_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl_Ortrancl__refl,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__into__rtrancl,axiom, % 181.55/181.50 ! [V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__Un__subset,axiom, % 181.55/181.50 ! [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)))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Image__closed__trancl,axiom, % 181.55/181.50 ! [V_X_2,V_r_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__mono,axiom, % 181.55/181.50 ! [V_s_2,V_r_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__subset,axiom, % 181.55/181.50 ! [V_S_2,V_R_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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))) % 181.55/181.50 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__subset__rtrancl,axiom, % 181.55/181.50 ! [V_s_2,V_r_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__trans,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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_c_2)),V_r_2)) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__idemp,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__Un__rtrancl,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_in__rtrancl__UnI,axiom, % 181.55/181.50 ! [V_S_2,V_R_2,V_x_2,T_b] : % 181.55/181.50 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 181.55/181.50 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) ) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_r__comp__rtrancl__eq,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__idemp__self__comp,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__rtrancl,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__rtrancl,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__rtrancl,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__unfold__right,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__unfold__left,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__rtrancl__absorb,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__trancl__absorb,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__eq__or__trancl,axiom, % 181.55/181.50 ! [V_R_2,V_y_2,V_x_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> ( V_x_2 = V_y_2 % 181.55/181.50 | ( V_x_2 != V_y_2 % 181.55/181.50 & 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))) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__into__trancl2,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtranclD,axiom, % 181.55/181.50 ! [V_R_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( V_a_2 = V_b_2 % 181.55/181.50 | ( V_a_2 != V_b_2 % 181.55/181.50 & 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))) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__into__trancl1,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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_c_2)),V_r_2)) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__rtrancl__trancl,axiom, % 181.55/181.50 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 181.55/181.50 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__trancl__trancl,axiom, % 181.55/181.50 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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))) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Not__Domain__rtrancl,axiom, % 181.55/181.50 ! [V_y_2,V_R_2,V_x_2,T_b] : % 181.55/181.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) % 181.55/181.50 => ( 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))) % 181.55/181.50 <=> V_x_2 = V_y_2 ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acc__downwards__aux,axiom, % 181.55/181.50 ! [V_r_2,V_a_2,V_b_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acc__downwards,axiom, % 181.55/181.50 ! [V_b_2,V_r_2,V_a_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 181.55/181.50 => ( 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))) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__insert,axiom, % 181.55/181.50 ! [V_r_2,V_x_2,V_y_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.50 & ~ 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acyclic__insert,axiom, % 181.55/181.50 ! [V_r_2,V_x_2,V_y_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 181.55/181.50 & ~ 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pred__nat__trancl__eq__le,axiom, % 181.55/181.50 ! [V_n_2,V_m_2] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__subset__Sigma__aux,axiom, % 181.55/181.50 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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)))) % 181.55/181.50 => ( V_a_2 = V_b_2 % 181.55/181.50 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_irrefl__tranclI,axiom, % 181.55/181.50 ! [V_x_2,V_r_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ~ 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_sequence__trans,axiom, % 181.55/181.50 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] : % 181.55/181.50 ( ! [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))) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__converse,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__converse,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__iff,axiom, % 181.55/181.50 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converseI,axiom, % 181.55/181.50 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converseD,axiom, % 181.55/181.50 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => 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)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__inv__image,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__Id__on,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Field__converse,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__converse,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__Int,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__converse,axiom, % 181.55/181.50 ! [V_r_2,T_c,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 181.55/181.50 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__Un,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__rel__comp,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__on__converse,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 181.55/181.50 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__UNION,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_acyclic__converse,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 181.55/181.50 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__converse__trancl,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 181.55/181.50 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_equiv__comp__eq,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.55/181.50 => 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 ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__converse,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__converse,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__def,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__converseD,axiom, % 181.55/181.50 ! [V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__converseI,axiom, % 181.55/181.50 ! [V_r_2,V_x_2,V_y_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__converseD,axiom, % 181.55/181.50 ! [V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__converseI,axiom, % 181.55/181.50 ! [V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.50 ( 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)))) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Image__subset__eq,axiom, % 181.55/181.50 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> 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))))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__on__comp__subset,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.50 => 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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_comp__equivI,axiom, % 181.55/181.50 ! [V_A_2,V_r_2,T_b] : % 181.55/181.50 ( 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 % 181.55/181.50 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 % 181.55/181.50 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_finite__acyclic__wf__converse,axiom, % 181.55/181.50 ! [V_r_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 181.55/181.50 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 181.55/181.50 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__def,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_reflcl__set__eq,axiom, % 181.55/181.50 ! [V_y_2,V_x_2,V_r_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 <=> 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 181.55/181.50 ! [V_R_2,V_p_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 181.55/181.50 => 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)))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_IdI,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_converse__Id,axiom, % 181.55/181.50 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ). % 181.55/181.50 % 181.55/181.50 fof(fact_wf__exp,axiom, % 181.55/181.50 ! [V_R_2,V_n_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Id__O__R,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_R__O__Id,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_funpow__swap1,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Image__Id,axiom, % 181.55/181.50 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ). % 181.55/181.50 % 181.55/181.50 fof(fact_funpow__mult,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_comp__funpow,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_relpow_Osimps_I1_J,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__1,axiom, % 181.55/181.50 ! [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 ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__commute,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__power,axiom, % 181.55/181.50 ! [V_R_2,V_p_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 181.55/181.50 <=> ? [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))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__imp__rtrancl,axiom, % 181.55/181.50 ! [V_R_2,V_n_2,V_p_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_relpow_Osimps_I2_J,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__add,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pair__in__Id__conv,axiom, % 181.55/181.50 ! [V_b_2,V_a_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> V_a_2 = V_b_2 ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Domain__Id,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__empty,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Range__Id,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__reflcl__absorb,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__reflcl,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__Id,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__r__diff__Id,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__0__I,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__0__E,axiom, % 181.55/181.50 ! [V_R_2,V_y_2,V_x_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => V_x_2 = V_y_2 ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__Suc__I2,axiom, % 181.55/181.50 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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))) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__Suc__I,axiom, % 181.55/181.50 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_funpow_Osimps_I2_J,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_funpow__add,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_funpow_Osimps_I1_J,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_pair__leq__def,axiom, % 181.55/181.50 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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__reflcl,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_reflcl__trancl,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__unfold,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_refl__reflcl,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_trancl__power,axiom, % 181.55/181.50 ! [V_R_2,V_p_2,T_b] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 181.55/181.50 <=> ? [B_n] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 181.55/181.50 & 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))) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_Id__def,axiom, % 181.55/181.50 ! [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))))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_irrefl__diff__Id,axiom, % 181.55/181.50 ! [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))) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 181.55/181.50 ! [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)) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rtrancl__Int__subset,axiom, % 181.55/181.50 ! [V_r_2,V_s_2,T_b] : % 181.55/181.50 ( 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)) % 181.55/181.50 => ( 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)) % 181.55/181.50 => 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)) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_funpow__code__def,axiom, % 181.55/181.50 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__E2,axiom, % 181.55/181.50 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.50 => V_x_2 != V_z_2 ) % 181.55/181.50 => ~ ! [B_y,B_m] : % 181.55/181.50 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 181.55/181.50 => ( 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)) % 181.55/181.50 => ~ 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))) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_rel__pow__E,axiom, % 181.55/181.50 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.50 => V_x_2 != V_z_2 ) % 181.55/181.50 => ~ ! [B_y,B_m] : % 181.55/181.50 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 181.55/181.50 => ( 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))) % 181.55/181.50 => ~ 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)) ) ) ) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_total__on__diff__Id,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( 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))) % 181.55/181.50 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_total__on__empty,axiom, % 181.55/181.50 ! [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) ). % 181.55/181.50 % 181.55/181.50 fof(fact_total__on__converse,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 181.55/181.50 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 181.55/181.50 % 181.55/181.50 fof(fact_total__on__def,axiom, % 181.55/181.50 ! [V_r_2,V_A_2,T_b] : % 181.55/181.50 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2) % 181.55/181.50 <=> ! [B_x] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.50 => ! [B_xa] : % 181.55/181.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 181.55/181.50 => ( B_x != B_xa % 181.55/181.50 => ( 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)) % 181.55/181.50 | 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)) ) ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_acyclicI,axiom, % 181.55/181.51 ! [V_r_2,T_b] : % 181.55/181.51 ( ! [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))) % 181.55/181.51 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Image__Int__eq,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : % 181.55/181.51 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_single__valued__rel__comp,axiom, % 181.55/181.51 ! [V_s_2,T_d,V_r_2,T_c,T_b] : % 181.55/181.51 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 181.55/181.51 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_single__valued__subset,axiom, % 181.55/181.51 ! [V_s_2,V_r_2,T_c,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 181.55/181.51 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_single__valued__rel__pow,axiom, % 181.55/181.51 ! [V_n_2,V_R_2,T_b] : % 181.55/181.51 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_single__valued__Id,axiom, % 181.55/181.51 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_single__valued__Id__on,axiom, % 181.55/181.51 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_single__valuedD,axiom, % 181.55/181.51 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] : % 181.55/181.51 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 181.55/181.51 => ( 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)) % 181.55/181.51 => ( 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)) % 181.55/181.51 => V_y_2 = V_z_2 ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_single__valued__def,axiom, % 181.55/181.51 ! [V_r_2,T_c,T_b] : % 181.55/181.51 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 181.55/181.51 <=> ! [B_x,B_y] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ! [B_z] : % 181.55/181.51 ( 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)) % 181.55/181.51 => B_y = B_z ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_single__valued__confluent,axiom, % 181.55/181.51 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 181.55/181.51 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2) % 181.55/181.51 => ( 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))) % 181.55/181.51 => ( 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))) % 181.55/181.51 => ( 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))) % 181.55/181.51 | 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))) ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rtrancl__Un__separatorE,axiom, % 181.55/181.51 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ! [B_y] : % 181.55/181.51 ( 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)) % 181.55/181.51 => B_x = B_y ) ) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rtrancl__Un__separator__converseE,axiom, % 181.55/181.51 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ! [B_y] : % 181.55/181.51 ( 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)) % 181.55/181.51 => B_y = B_x ) ) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rel__pow__Suc__D2,axiom, % 181.55/181.51 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ? [B_y] : % 181.55/181.51 ( 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)) % 181.55/181.51 & 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rel__pow__Suc__E2,axiom, % 181.55/181.51 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ ! [B_y] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ~ 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rel__pow__Suc__E,axiom, % 181.55/181.51 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ ! [B_y] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_tranclD2,axiom, % 181.55/181.51 ! [V_R_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ? [B_z] : % 181.55/181.51 ( 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))) % 181.55/181.51 & 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_tranclD,axiom, % 181.55/181.51 ! [V_R_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ? [B_z] : % 181.55/181.51 ( 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)) % 181.55/181.51 & 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_IdE,axiom, % 181.55/181.51 ! [V_p_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) % 181.55/181.51 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold__empty,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold__image__def,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_folding_Oeq__fold,axiom, % 181.55/181.51 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold__def,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_union__fold__insert,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold__sup__insert,axiom, % 181.55/181.51 ! [V_a_2,V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Osemilattice__sup(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold__inf__insert,axiom, % 181.55/181.51 ! [V_a_2,V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Osemilattice__inf(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_Ofold__inf__insert,axiom, % 181.55/181.51 ! [V_a_2,V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_Ofold__sup__insert,axiom, % 181.55/181.51 ! [V_a_2,V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 181.55/181.51 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 181.55/181.51 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sup__SUPR__fold__sup,axiom, % 181.55/181.51 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sup__le__fold__sup,axiom, % 181.55/181.51 ! [V_b_2,V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Osemilattice__sup(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold__inf__le__inf,axiom, % 181.55/181.51 ! [V_b_2,V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Osemilattice__inf(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 181.55/181.51 ! [V_b_2,V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_Osup__le__fold__sup,axiom, % 181.55/181.51 ! [V_b_2,V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold1__eq__fold__idem,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Olattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Olattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Min_Oeq__fold__idem_H,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Max_Oeq__fold__idem_H,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_minus__fold__remove,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_folding__one_Oeq__fold_H,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_SUPR__fold__sup,axiom, % 181.55/181.51 ! [V_f_2,V_A_2,T_b,T_c] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold1__eq__fold,axiom, % 181.55/181.51 ! [V_a_2,V_A_2,T_b] : % 181.55/181.51 ( class_Groups_Oab__semigroup__mult(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Olattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Olattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Min_Oeq__fold_H,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Max_Oeq__fold_H,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__rec,axiom, % 181.55/181.51 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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)))))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 181.55/181.51 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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)))))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm,axiom, % 181.55/181.51 ! [T_b] : % 181.55/181.51 ( class_Groups_Oab__semigroup__mult(T_b) % 181.55/181.51 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 181.55/181.51 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 181.55/181.51 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 181.55/181.51 => V_y_2 = V_x_2 ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 181.55/181.51 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__equality,axiom, % 181.55/181.51 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 181.55/181.51 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 181.55/181.51 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 181.55/181.51 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__insert,axiom, % 181.55/181.51 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 181.55/181.51 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => ? [B_y_H] : % 181.55/181.51 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 181.55/181.51 & 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)) ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INFI__fold__inf,axiom, % 181.55/181.51 ! [V_f_2,V_A_2,T_b,T_c] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__E,axiom, % 181.55/181.51 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 181.55/181.51 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__D,axiom, % 181.55/181.51 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF1__E,axiom, % 181.55/181.51 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 181.55/181.51 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF1__D,axiom, % 181.55/181.51 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF2__D,axiom, % 181.55/181.51 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 181.55/181.51 ( 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_c_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF2__E,axiom, % 181.55/181.51 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 181.55/181.51 ( 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_c_2)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 181.55/181.51 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__INT,axiom, % 181.55/181.51 ! [V_A_2,T_c,V_I_2,T_b] : % 181.55/181.51 ( ? [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 181.55/181.51 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__Un,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Un__INT__distrib2,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I6_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Un__INT__distrib,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I7_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I6_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I7_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Compl__INT,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Compl__UN,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_converse__INTER,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Image__INT__subset,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF__less__iff,axiom, % 181.55/181.51 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] : % 181.55/181.51 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 & class_Orderings_Olinorder(T_b) ) % 181.55/181.51 => ( 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)) % 181.55/181.51 <=> ? [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.55/181.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_le__INF__iff,axiom, % 181.55/181.51 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( 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))) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__subset__iff,axiom, % 181.55/181.51 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__lower,axiom, % 181.55/181.51 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Collect__ball__eq,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__insert,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I2_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.55/181.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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 ) % 181.55/181.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I1_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.55/181.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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 ) % 181.55/181.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF__INT__eq,axiom, % 181.55/181.51 ! [V_x_2,V_r_2,T_c,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 <=> 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I5_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I5_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__Int__distrib,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF__commute,axiom, % 181.55/181.51 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INFI__apply,axiom, % 181.55/181.51 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Pow__INT__eq,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_b,T_c] : % 181.55/181.51 ( 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)) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.55/181.51 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.55/181.51 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__iff,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF__INT__eq2,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 <=> 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I10_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I10_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_vimage__INT,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__insert__distrib,axiom, % 181.55/181.51 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF__const,axiom, % 181.55/181.51 ! [V_M_2,T_b,V_A_2,T_c] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.55/181.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__absorb,axiom, % 181.55/181.51 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__empty,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__constant,axiom, % 181.55/181.51 ! [V_c_2,T_c,T_b,V_A_2] : % 181.55/181.51 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 181.55/181.51 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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_c_2)) = V_c_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INFI__bool__eq,axiom, % 181.55/181.51 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I9_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I9_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_UN__simps_I7_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_UN__extend__simps_I7_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF__subset,axiom, % 181.55/181.51 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INTER__def,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I2_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.55/181.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I1_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.55/181.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I3_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.55/181.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I3_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.55/181.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I4_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.55/181.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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 ) % 181.55/181.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_bij__image__INT,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF__leI,axiom, % 181.55/181.51 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__greaterThan__UNIV,axiom, % 181.55/181.51 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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I4_J,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 181.55/181.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Image__INT__eq,axiom, % 181.55/181.51 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] : % 181.55/181.51 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) % 181.55/181.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inf__INFI__fold__inf,axiom, % 181.55/181.51 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__fold__inf,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__fold__sup,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__Inter,axiom, % 181.55/181.51 ! [V_M_2,T_b] : % 181.55/181.51 ( ? [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) % 181.55/181.51 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 181.55/181.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_UnionI,axiom, % 181.55/181.51 ! [V_A_2,V_C_2,V_X_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_InterE,axiom, % 181.55/181.51 ! [V_X_2,V_C_2,V_A_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_InterD,axiom, % 181.55/181.51 ! [V_X_2,V_C_2,V_A_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Un__Inter,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF2__iff,axiom, % 181.55/181.51 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 181.55/181.51 ( 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_c_2)) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INF1__iff,axiom, % 181.55/181.51 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__simps_I8_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INT__extend__simps_I8_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INTER__eq__Inter__image,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__image__eq,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__empty,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Domain__Union,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sigma__Union,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_image__Union,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Int__Union,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Int__Union2,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Range__Union,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_UN__extend__simps_I8_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_UN__simps_I8_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_vimage__Union,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Field__Union,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__Pow__eq,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__disjoint,axiom, % 181.55/181.51 ! [V_A_2,V_C_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_le__Inf__iff,axiom, % 181.55/181.51 ! [V_A_2,V_b_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( 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))) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__le__iff,axiom, % 181.55/181.51 ! [V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( 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)) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_less__Sup__iff,axiom, % 181.55/181.51 ! [V_S_2,V_a_2,T_b] : % 181.55/181.51 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 & class_Orderings_Olinorder(T_b) ) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) % 181.55/181.51 <=> ? [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 181.55/181.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__less__iff,axiom, % 181.55/181.51 ! [V_a_2,V_S_2,T_b] : % 181.55/181.51 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 & class_Orderings_Olinorder(T_b) ) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) % 181.55/181.51 <=> ? [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 181.55/181.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__upper,axiom, % 181.55/181.51 ! [V_A_2,V_B_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__lower,axiom, % 181.55/181.51 ! [V_A_2,V_B_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__Inf,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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)))))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__Sup,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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))))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__mono,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__quotient,axiom, % 181.55/181.51 ! [V_r_2,V_A_2,T_b] : % 181.55/181.51 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.55/181.51 => 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 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__insert,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__UnionD,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) % 181.55/181.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_subset__Pow__Union,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__anti__mono,axiom, % 181.55/181.51 ! [V_A_2,V_B_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__empty,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__eq,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__UNIV,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__insert,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__Un__distrib,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_UNION__eq__Union__image,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__image__eq,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__upper,axiom, % 181.55/181.51 ! [V_A_2,V_x_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__UNIV,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__lower,axiom, % 181.55/181.51 ! [V_A_2,V_x_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__Un__distrib,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__empty,axiom, % 181.55/181.51 ! [T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__singleton,axiom, % 181.55/181.51 ! [V_a_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__insert,axiom, % 181.55/181.51 ! [V_A_2,V_a_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Int__Inter__image,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__UNIV,axiom, % 181.55/181.51 ! [T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__singleton,axiom, % 181.55/181.51 ! [V_a_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__empty,axiom, % 181.55/181.51 ! [T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__UNIV,axiom, % 181.55/181.51 ! [T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__insert,axiom, % 181.55/181.51 ! [V_A_2,V_a_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Un__eq__Union,axiom, % 181.55/181.51 ! [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))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Un__Union__image,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__Int__subset,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Int__eq__Inter,axiom, % 181.55/181.51 ! [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))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__Un__subset,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__binary,axiom, % 181.55/181.51 ! [V_b_2,V_a_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__binary,axiom, % 181.55/181.51 ! [V_b_2,V_a_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sup__Sup__fold__sup,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__fin__Sup,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inf__Inf__fold__inf,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__fin__Inf,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_image__INT,axiom, % 181.55/181.51 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 181.55/181.51 => 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)) ) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) % 181.55/181.51 => 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)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_card__partition,axiom, % 181.55/181.51 ! [V_k_2,V_C_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 181.55/181.51 => ( ! [B_c] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) % 181.55/181.51 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 ) % 181.55/181.51 => ( ! [B_c1] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) % 181.55/181.51 => ! [B_c2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) % 181.55/181.51 => ( B_c1 != B_c2 % 181.55/181.51 => 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)) ) ) ) % 181.55/181.51 => 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)) ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Union__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__Union,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) % 181.55/181.51 => ( ! [B_M] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) ) % 181.55/181.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_insert__partition,axiom, % 181.55/181.51 ! [V_F_2,V_x_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ! [B_xa] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( B_x != B_xa % 181.55/181.51 => 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)) ) ) ) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__on__Inter,axiom, % 181.55/181.51 ! [V_f_2,T_c,T_b,V_S_2] : % 181.55/181.51 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 181.55/181.51 => ( ! [B_A] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) % 181.55/181.51 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) ) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inter__subset,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_b] : % 181.55/181.51 ( ! [B_X] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) ) % 181.55/181.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__on__INTER,axiom, % 181.55/181.51 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] : % 181.55/181.51 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => ( ! [B_i] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) % 181.55/181.51 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) ) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 181.55/181.51 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.51 => ( 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)) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => ~ ! [B_y] : % 181.55/181.51 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 181.55/181.51 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 181.55/181.51 ! [V_c_2,V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) % 181.55/181.51 => 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_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 181.55/181.51 ! [V_c_2,V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_InterI,axiom, % 181.55/181.51 ! [V_A_2,V_C_2,T_b] : % 181.55/181.51 ( ! [B_X] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) ) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inf__le__fold__inf,axiom, % 181.55/181.51 ! [V_c_2,V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Osemilattice__inf(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) % 181.55/181.51 => 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_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold__sup__le__sup,axiom, % 181.55/181.51 ! [V_c_2,V_b_2,V_A_2,T_b] : % 181.55/181.51 ( class_Lattices_Osemilattice__sup(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) % 181.55/181.51 => 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_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_mod__div__decomp,axiom, % 181.55/181.51 ! [V_b,V_a,T_a] : % 181.55/181.51 ( class_Divides_Osemiring__div(T_a) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_wf__eq__minimal,axiom, % 181.55/181.51 ! [V_r_2,T_b] : % 181.55/181.51 ( c_Wellfounded_Owf(T_b,V_r_2) % 181.55/181.51 <=> ! [B_Q] : % 181.55/181.51 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 181.55/181.51 => ? [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 181.55/181.51 & ! [B_y] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 181.55/181.51 => 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)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_folding__image__simple__idem_Oidem,axiom, % 181.55/181.51 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.55/181.51 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_transfer__nat__int__set__cong,axiom, % 181.55/181.51 ! [V_P_H_2,V_Pa_2] : % 181.55/181.51 ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 181.55/181.51 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.55/181.51 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 181.55/181.51 => 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_H_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_UnionE,axiom, % 181.55/181.51 ! [V_C_2,V_A_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ ! [B_X] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) % 181.55/181.51 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__upd__left,axiom, % 181.55/181.51 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2))) % 181.55/181.51 => c_Map_Omap__add(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rel__compE,axiom, % 181.55/181.51 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ ! [B_x,B_y,B_z] : % 181.55/181.51 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) % 181.55/181.51 => ( 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)) % 181.55/181.51 => ~ 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)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__empty,axiom, % 181.55/181.51 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = V_m_2 ). % 181.55/181.51 % 181.55/181.51 fof(fact_empty__map__add,axiom, % 181.55/181.51 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),V_m_2) = V_m_2 ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__def,axiom, % 181.55/181.51 ! [V_x_2,V_m2_2,V_m1_2,T_b,T_c] : hAPP(c_Map_Omap__add(T_c,T_b,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_b)),hAPP(V_m2_2,V_x_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__None,axiom, % 181.55/181.51 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] : % 181.55/181.51 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b) % 181.55/181.51 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 181.55/181.51 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__assoc,axiom, % 181.55/181.51 ! [V_m3_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__add(T_b,T_c,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_m3_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__find__right,axiom, % 181.55/181.51 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] : % 181.55/181.51 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) % 181.55/181.51 => hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 181.55/181.51 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) % 181.55/181.51 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 181.55/181.51 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) % 181.55/181.51 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 181.55/181.51 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2))) % 181.55/181.51 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__Some__iff,axiom, % 181.55/181.51 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] : % 181.55/181.51 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 181.55/181.51 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 181.55/181.51 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 181.55/181.51 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__SomeD,axiom, % 181.55/181.51 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] : % 181.55/181.51 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 181.55/181.51 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 181.55/181.51 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 181.55/181.51 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_dom__map__add,axiom, % 181.55/181.51 ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__upd,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__on__map__add__dom,axiom, % 181.55/181.51 ! [V_m_H_2,V_m_2,T_c,T_b] : % 181.55/181.51 ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2)) % 181.55/181.51 <=> c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__comm,axiom, % 181.55/181.51 ! [V_m2_2,V_m1_2,T_c,T_b] : % 181.55/181.51 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m1_2)),c_Map_Odom(T_b,T_c,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 => c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2) = c_Map_Omap__add(T_b,T_c,V_m2_2,V_m1_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__range__map__of__map__add,axiom, % 181.55/181.51 ! [V_l_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 181.55/181.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__add(T_c,T_b,V_f_2,hAPP(c_Map_Omap__of(T_c,T_b),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_converseE,axiom, % 181.55/181.51 ! [V_r_2,V_yx_2,T_c,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ ! [B_x,B_y] : % 181.55/181.51 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) % 181.55/181.51 => ~ 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__dom__map__of,axiom, % 181.55/181.51 ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_l_2)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__range__map__of,axiom, % 181.55/181.51 ! [V_xys_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__map__of__foldr,axiom, % 181.55/181.51 ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_Map_Omap__of(T_b,T_c),V_ps_2)) = c_List_Ofoldr(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)))))),c_Option_Ooption_OSome(T_c))),V_ps_2,V_m_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,T_b] : c_Smallcheck_Oorelse(T_b,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,V_y_2,c_Option_Ooption_OSome(T_b)),V_x_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_full__small__int__def,axiom, % 181.55/181.51 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_small_H_Osimps,axiom, % 181.55/181.51 ! [V_f_2,V_i_2,V_d_2] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 181.55/181.51 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 181.55/181.51 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_small_H_Opsimps,axiom, % 181.55/181.51 ! [V_i_2,V_d_2,V_f_2] : % 181.55/181.51 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))) % 181.55/181.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 181.55/181.51 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 181.55/181.51 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_small__int__def,axiom, % 181.55/181.51 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_small__prod__def,axiom, % 181.55/181.51 ! [V_d_2,V_f_2,T_b,T_c] : % 181.55/181.51 ( ( class_Smallcheck_Osmall(T_c) % 181.55/181.51 & class_Smallcheck_Osmall(T_b) ) % 181.55/181.51 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_b,T_c)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_b),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),c_Smallcheck_Osmall__class_Osmall(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c)))),V_d_2)),V_d_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_small_H_Opinduct,axiom, % 181.55/181.51 ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] : % 181.55/181.51 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2)))) % 181.55/181.51 => ( ! [B_f,B_d,B_i] : % 181.55/181.51 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))) % 181.55/181.51 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 181.55/181.51 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 181.55/181.51 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) % 181.55/181.51 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i)) ) ) % 181.55/181.51 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__mapk__SomeI,axiom, % 181.55/181.51 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.55/181.51 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_d),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) % 181.55/181.51 => hAPP(hAPP(c_Map_Omap__of(T_c,T_d),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_b),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__mapI,axiom, % 181.55/181.51 ! [V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldr__map,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__injective,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.51 ( 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) % 181.55/181.51 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 181.55/181.51 => V_xs_2 = V_ys_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__mapD,axiom, % 181.55/181.51 ! [V_f_2,T_c,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__map__eq__map,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.55/181.51 => ( 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) % 181.55/181.51 <=> V_xs_2 = V_ys_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__map,axiom, % 181.55/181.51 ! [V_f_2,T_c,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__ident,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ). % 181.55/181.51 % 181.55/181.51 fof(fact_List_Omap_Oidentity,axiom, % 181.55/181.51 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_List_Omap_Oid,axiom, % 181.55/181.51 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_List_Omap_Ocomp,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__comp__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_List_Omap_Ocompositionality,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__map,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__map,axiom, % 181.55/181.51 ! [V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),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))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Map_Omap__of(T_b,T_d),V_xs_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__comp__def,axiom, % 181.55/181.51 ! [V_k_2,V_g_2,V_f_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_c,c_Option_Ooption_ONone(T_b),V_f_2),hAPP(V_g_2,V_k_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__comp__simps_I2_J,axiom, % 181.55/181.51 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] : % 181.55/181.51 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2) % 181.55/181.51 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__comp__Some__iff,axiom, % 181.55/181.51 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] : % 181.55/181.51 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) % 181.55/181.51 <=> ? [B_k_H] : % 181.55/181.51 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) % 181.55/181.51 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_option__map__o__empty,axiom, % 181.55/181.51 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_d,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c))),V_x_2) = c_Option_Ooption_ONone(T_b) ). % 181.55/181.51 % 181.55/181.51 fof(fact_option__map__Some,axiom, % 181.55/181.51 ! [V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_option__map__eq__Some,axiom, % 181.55/181.51 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] : % 181.55/181.51 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 181.55/181.51 <=> ? [B_z] : % 181.55/181.51 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z) % 181.55/181.51 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_option__map__None,axiom, % 181.55/181.51 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),c_Option_Ooption_ONone(T_c)) = c_Option_Ooption_ONone(T_b) ). % 181.55/181.51 % 181.55/181.51 fof(fact_option__map__is__None,axiom, % 181.55/181.51 ! [V_opt_2,V_f_2,T_b,T_c] : % 181.55/181.51 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b) % 181.55/181.51 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__comp__simps_I1_J,axiom, % 181.55/181.51 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] : % 181.55/181.51 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 181.55/181.51 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_d) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Option_Omap_Ocomp,axiom, % 181.55/181.51 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Option_Omap(T_b,T_d),V_g_2)) = hAPP(c_Option_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Option_Omap_Ocompositionality,axiom, % 181.55/181.51 ! [V_option_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_option_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_option__map__comp,axiom, % 181.55/181.51 ! [V_opt_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_opt_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Option_Omap_Oid,axiom, % 181.55/181.51 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Option_Omap_Oidentity,axiom, % 181.55/181.51 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_infinite__UNIV__listI,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_dom__option__map,axiom, % 181.55/181.51 ! [V_m_2,V_f_2,T_d,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),T_b),c_Option_Omap(T_d,T_c)),V_f_2)),V_m_2)) = c_Map_Odom(T_b,T_d,V_m_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_option__map__o__map__upd,axiom, % 181.55/181.51 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_d)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_d),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_b_2))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__comp__empty_I2_J,axiom, % 181.55/181.51 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_b) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__comp__empty_I1_J,axiom, % 181.55/181.51 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c)),V_x_2) = c_Option_Ooption_ONone(T_b) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__comp__None__iff,axiom, % 181.55/181.51 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] : % 181.55/181.51 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 181.55/181.51 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) % 181.55/181.51 | ? [B_k_H] : % 181.55/181.51 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) % 181.55/181.51 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Option_Omap__def,axiom, % 181.55/181.51 ! [V_f_2,T_c,T_b] : hAPP(c_Option_Omap(T_b,T_c),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_c),T_b,c_Option_Ooption_ONone(T_c),hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__map__restrict,axiom, % 181.55/181.51 ! [V_ks_2,V_f_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_b,T_c,hAPP(c_Fun_Ocomp(T_c,tc_Option_Ooption(T_c),T_b,c_Option_Ooption_OSome(T_c)),V_f_2),hAPP(c_List_Oset(T_b),V_ks_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of_Osimps_I2_J,axiom, % 181.55/181.51 ! [V_ps_2,V_p_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Map_Omap__of(T_b,T_c),V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__set,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map_Osimps_I2_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__eq__conv,axiom, % 181.55/181.51 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 181.55/181.51 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldr_Osimps_I2_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__subset__Cons,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_List_Oset_Osimps_I2_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__ConsD,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,V_y_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => ( V_y_2 = V_x_2 % 181.55/181.51 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_not__Cons__self,axiom, % 181.55/181.51 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 181.55/181.51 % 181.55/181.51 fof(fact_not__Cons__self2,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Oinject,axiom, % 181.55/181.51 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> ( V_a_2 = V_a_H_2 % 181.55/181.51 & V_list_2 = V_list_H_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__on__map__eq__map,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( 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) % 181.55/181.51 <=> V_xs_2 = V_ys_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__inj__on,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.51 ( 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) % 181.55/181.51 => ( 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))) % 181.55/181.51 => V_xs_2 = V_ys_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__fun__upd,axiom, % 181.55/181.51 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hAPP(hAPP(c_List_Omap(T_b,T_c),hAPP(hAPP(hAPP(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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__Cons__code_I2_J,axiom, % 181.55/181.51 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 181.55/181.51 ( ( V_l = V_k % 181.55/181.51 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) ) % 181.55/181.51 & ( V_l != V_k % 181.55/181.51 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__eq__dom,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_c,T_b] : % 181.55/181.51 ( hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2) % 181.55/181.51 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__is__SomeD,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] : % 181.55/181.51 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 181.55/181.51 => 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_List_Oset(tc_prod(T_c,T_b)),V_xys_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__SomeD,axiom, % 181.55/181.51 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] : % 181.55/181.51 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xs_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_dom__map__of__conv__image__fst,axiom, % 181.55/181.51 ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_inj__on__mapI,axiom, % 181.55/181.51 ! [V_A_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__eq__None__iff,axiom, % 181.55/181.51 ! [V_x_2,V_xys_2,T_b,T_c] : % 181.55/181.51 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b) % 181.55/181.51 <=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__map__keys,axiom, % 181.55/181.51 ! [V_m_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2) % 181.55/181.51 => hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),T_c,T_b),c_Option_Othe(T_c)),V_m_2))),V_xs_2)) = V_m_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__Cons__def,axiom, % 181.55/181.51 ! [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)))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_the_Osimps,axiom, % 181.55/181.51 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 181.55/181.51 % 181.55/181.51 fof(fact_pick_Osimps,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a,V_i] : % 181.55/181.51 ( ( 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))) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( ~ 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))) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hoare__derivs_OBody,axiom, % 181.55/181.51 ! [V_Procsa_2,V_Qa_2,V_Pa_2,V_Ga_2,T_b] : % 181.55/181.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Qa_2)),V_Procsa_2)) % 181.55/181.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__dom__body,axiom, % 181.55/181.51 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Body__triple__valid__Suc,axiom, % 181.55/181.51 ! [V_Qa_2,V_pna_2,V_Pa_2,V_n_2,T_b] : % 181.55/181.51 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pna_2))),V_Qa_2)) % 181.55/181.51 <=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pna_2)),V_Qa_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_select__weight__cons__zero,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_pick__member,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_i_2] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__simps_I2_J,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a] : % 181.55/181.51 ( class_Groups_Omonoid__add(T_a) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__0,axiom, % 181.55/181.51 ! [V_xs_2,T_c,T_b] : % 181.55/181.51 ( class_Groups_Omonoid__add(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__addf,axiom, % 181.55/181.51 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__mult__const,axiom, % 181.55/181.51 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( class_Rings_Osemiring__0(T_b) % 181.55/181.51 => 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_c_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_c_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__const__mult,axiom, % 181.55/181.51 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] : % 181.55/181.51 ( class_Rings_Osemiring__0(T_b) % 181.55/181.51 => 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_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__subtractf,axiom, % 181.55/181.51 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( class_Groups_Oab__group__add(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__abs,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_uminus__listsum__map,axiom, % 181.55/181.51 ! [V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( class_Groups_Oab__group__add(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_select__weight__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_select__weight__member,axiom, % 181.55/181.51 ! [V_s_2,V_xs_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_ran__distinct,axiom, % 181.55/181.51 ! [V_al_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_al_2))) % 181.55/181.51 => c_Map_Oran(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_al_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__map__of__compr,axiom, % 181.55/181.51 ! [V_xs_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2))) % 181.55/181.51 => hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_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_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2)))),c_Option_Ooption_OSome(T_c)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 181.55/181.51 ! [V_ns_2] : % 181.55/181.51 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 181.55/181.51 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct_Osimps_I2_J,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) % 181.55/181.51 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__map,axiom, % 181.55/181.51 ! [V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 181.55/181.51 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 181.55/181.51 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__listsum__conv__Setsum,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 181.55/181.51 ! [V_f_2,V_xs_2,T_b,T_c] : % 181.55/181.51 ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.51 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__inject__set,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2))) % 181.55/181.51 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2))) % 181.55/181.51 => ( hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2) % 181.55/181.51 <=> hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__is__SomeI,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) % 181.55/181.51 => ( 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)),V_xys_2))) % 181.55/181.51 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__eq__Some__iff,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) % 181.55/181.51 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) % 181.55/181.51 <=> 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)),V_xys_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Some__eq__map__of__iff,axiom, % 181.55/181.51 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2))) % 181.55/181.51 => ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2) % 181.55/181.51 <=> 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)),V_xys_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Nitpick_Osetsum_H__def,axiom, % 181.55/181.51 ! [V_f_2,V_A_2,T_b,T_c] : % 181.55/181.51 ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.51 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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))))) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__lists__length__le,axiom, % 181.55/181.51 ! [V_n_2,V_A_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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))))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__map,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__eq__imp__length__eq,axiom, % 181.55/181.51 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.51 ( 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) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexn__length,axiom, % 181.55/181.51 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 % 181.55/181.51 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_impossible__Cons,axiom, % 181.55/181.51 ! [V_x,V_ys,V_xs,T_a] : % 181.55/181.51 ( 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))) % 181.55/181.51 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_neq__if__length__neq,axiom, % 181.55/181.51 ! [V_ys,V_xs,T_a] : % 181.55/181.51 ( 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) % 181.55/181.51 => V_xs != V_ys ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_card__length,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__card,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_card__distinct,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexn_Osimps_I2_J,axiom, % 181.55/181.51 ! [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)))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__pos__if__in__set,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Osize_I4_J,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Cons__in__lex,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( ( 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)) % 181.55/181.51 & 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) ) % 181.55/181.51 | ( V_x_2 = V_y_2 % 181.55/181.51 & 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__triv,axiom, % 181.55/181.51 ! [V_xs_2,V_r_2,T_c,T_b] : % 181.55/181.51 ( class_Rings_Osemiring__1(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lenlex__conv,axiom, % 181.55/181.51 ! [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)))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lenlex__def,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_finite__lists__length__eq,axiom, % 181.55/181.51 ! [V_n_2,V_A_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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))))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Nitpick_Ocard_H__def,axiom, % 181.55/181.51 ! [V_A_2,T_b] : % 181.55/181.51 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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)))) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__sublist,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__sublistI,axiom, % 181.55/181.51 ! [V_I_2,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_notin__set__sublistI,axiom, % 181.55/181.51 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => ~ 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__set__sublistD,axiom, % 181.55/181.51 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__sublist__subset,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__cons__cons,axiom, % 181.55/181.51 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( 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)) % 181.55/181.51 | ( V_a_2 = V_b_2 % 181.55/181.51 & 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( 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)))) % 181.55/181.51 => 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)))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Cons__acc__listrel1I,axiom, % 181.55/181.51 ! [V_xs_2,V_r_2,V_x_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 181.55/181.51 => ( 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)))) % 181.55/181.51 => 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)))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1__mono,axiom, % 181.55/181.51 ! [V_s_2,V_r_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1__converse,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1I2,axiom, % 181.55/181.51 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 181.55/181.51 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rtrancl__listrel1__eq__len,axiom, % 181.55/181.51 ! [V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1__eq__len,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__listrel1__converse,axiom, % 181.55/181.51 ! [V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 <=> 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Cons__listrel1__Cons,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( ( 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)) % 181.55/181.51 & V_xs_2 = V_ys_2 ) % 181.55/181.51 | ( V_x_2 = V_y_2 % 181.55/181.51 & 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1I1,axiom, % 181.55/181.51 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__lex,axiom, % 181.55/181.51 ! [V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( 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))) % 181.55/181.51 & 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Osize_I2_J,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__Cons,axiom, % 181.55/181.51 ! [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))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__rtrancl__refl,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__mono,axiom, % 181.55/181.51 ! [V_s_2,V_r_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__size__map,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__eq__len,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__rtrancl__trans,axiom, % 181.55/181.51 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => ( 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)))) % 181.55/181.51 => 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)))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__size__estimation,axiom, % 181.55/181.51 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__size__estimation_H,axiom, % 181.55/181.51 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__reflcl__if__listrel1,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1__subset__listrel,axiom, % 181.55/181.51 ! [V_r_H_2,V_r_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel_OCons,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ( 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))) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__size__conv__listsum,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrelp__listrel__eq,axiom, % 181.55/181.51 ! [V_xa_2,V_x_2,V_r_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__iff__zip,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( 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) % 181.55/181.51 & ! [B_x] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__same__conv__map,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__zipI1,axiom, % 181.55/181.51 ! [V_ys,T_b,V_xs,T_a] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__zipI2,axiom, % 181.55/181.51 ! [V_xs,T_b,V_ys,T_a] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrelp_Oequations_I2_J,axiom, % 181.55/181.51 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 181.55/181.51 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrelp_OCons,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 181.55/181.51 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__zip,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__zip__inject,axiom, % 181.55/181.51 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] : % 181.55/181.51 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 181.55/181.51 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 181.55/181.51 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 181.55/181.51 => ( hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) % 181.55/181.51 => V_ys_2 = V_zs_2 ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__fst__zip,axiom, % 181.55/181.51 ! [V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => 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 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__snd__zip,axiom, % 181.55/181.51 ! [V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => 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 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__map__fst__snd,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__Cons__Cons,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__eq__conv,axiom, % 181.55/181.51 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 % 181.55/181.51 <=> ( 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 % 181.55/181.51 & 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 ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__zip__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__zip__map2,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__eq__iff__zip__eq,axiom, % 181.55/181.51 ! [T_b,V_ys_2,V_xs_2] : % 181.55/181.51 ( V_xs_2 = V_ys_2 % 181.55/181.51 <=> ( 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) % 181.55/181.51 & ! [B_x] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__same,axiom, % 181.55/181.51 ! [V_xs_2,V_b_2,V_a_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 & V_a_2 = V_b_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__zip__leftD,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__zip__rightD,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__set__zipE,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__zip__is__None,axiom, % 181.55/181.51 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c) % 181.55/181.51 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__zip__is__Some,axiom, % 181.55/181.51 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__map__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__map1,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__map2,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_dom__map__of__zip,axiom, % 181.55/181.51 ! [V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__zip__upd,axiom, % 181.55/181.51 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] : % 181.55/181.51 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 181.55/181.51 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 181.55/181.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 181.55/181.51 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_z_2)) % 181.55/181.51 => hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__zip__map,axiom, % 181.55/181.51 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_x_2)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__Cons2,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ ! [B_x,B_xs] : % 181.55/181.51 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 181.55/181.51 => ( 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)) % 181.55/181.51 => ~ 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__Cons1,axiom, % 181.55/181.51 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ ! [B_y,B_ys] : % 181.55/181.51 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) % 181.55/181.51 => ( 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)) % 181.55/181.51 => ~ 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__zip,axiom, % 181.55/181.51 ! [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)))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__subset,axiom, % 181.55/181.51 ! [V_A_2,V_r_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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))))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__zip,axiom, % 181.55/181.51 ! [V_ys,T_b,V_xs,T_a,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( 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))) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__eq__iff__nth__eq,axiom, % 181.55/181.51 ! [T_b,V_ys_2,V_xs_2] : % 181.55/181.51 ( V_xs_2 = V_ys_2 % 181.55/181.51 <=> ( 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) % 181.55/181.51 & ! [B_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lists__mono,axiom, % 181.55/181.51 ! [V_B_2,V_A_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__Cons__0,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth_Osimps,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__Cons__Suc,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_all__set__conv__all__nth,axiom, % 181.55/181.51 ! [V_Pa_2,V_xs_2,T_b] : % 181.55/181.51 ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.51 <=> ! [B_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__map,axiom, % 181.55/181.51 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__conv__nth,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 <=> ! [B_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ! [B_j] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( B_i != B_j % 181.55/181.51 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__eq__iff__index__eq,axiom, % 181.55/181.51 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => ( 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))) % 181.55/181.51 => ( 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))) % 181.55/181.51 => ( 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) % 181.55/181.51 <=> V_i_2 = V_j_2 ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lists__UNIV,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_equiv__listrel,axiom, % 181.55/181.51 ! [V_r_2,V_A_2,T_b] : % 181.55/181.51 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__refl__on,axiom, % 181.55/181.51 ! [V_r_2,V_A_2,T_b] : % 181.55/181.51 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_elem__le__listsum__nat,axiom, % 181.55/181.51 ! [V_ns,V_k] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__mem,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_n_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__set__conv__nth,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 <=> ? [B_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__Cons_H,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a,V_n] : % 181.55/181.51 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 181.55/181.51 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__conv__nth,axiom, % 181.55/181.51 ! [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))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Cons__in__lists__iff,axiom, % 181.55/181.51 ! [V_A_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__lists__conv__set,axiom, % 181.55/181.51 ! [V_A_2,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__Cons__number__of,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a,V_v] : % 181.55/181.51 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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 ) % 181.55/181.51 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lists__eq__set,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__setsum__nth,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__sublist,axiom, % 181.55/181.51 ! [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))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__iff__nth,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( 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) % 181.55/181.51 & ! [B_n] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lists__accD,axiom, % 181.55/181.51 ! [V_r_2,V_xs_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lists__accI,axiom, % 181.55/181.51 ! [V_r_2,V_xs_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__take__index__conv,axiom, % 181.55/181.51 ! [V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( ( 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))) % 181.55/181.51 & 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 ) % 181.55/181.51 | ? [B_i] : % 181.55/181.51 ( 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)))) % 181.55/181.51 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) % 181.55/181.51 & 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)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_pick__same,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_l_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__take,axiom, % 181.55/181.51 ! [V_xs,T_a,V_n,V_i] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__zip,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__take,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 181.55/181.51 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.51 % 181.55/181.51 fof(fact_times__code__numeral__code,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 181.55/181.51 ! [V_m_2,V_n_2] : % 181.55/181.51 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 181.55/181.51 <=> V_n_2 = V_m_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__Suc__Cons,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zero__code__numeral__def,axiom, % 181.55/181.51 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sublist__upt__eq__take,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__set__takeD,axiom, % 181.55/181.51 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__take__subset,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__all,axiom, % 181.55/181.51 ! [V_n,V_xs,T_a] : % 181.55/181.51 ( 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)) % 181.55/181.51 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__take,axiom, % 181.55/181.51 ! [V_i,V_xs,T_a] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__take,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_one__code__numeral__def,axiom, % 181.55/181.51 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_less__code__numeral__code,axiom, % 181.55/181.51 ! [V_m_2,V_n_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_code__numeral_Oof__nat__inject,axiom, % 181.55/181.51 ! [V_y_2,V_x_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 181.55/181.51 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 181.55/181.51 <=> V_x_2 = V_y_2 ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_number__of__code__numeral__def,axiom, % 181.55/181.51 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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__take__subset__set__take,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_n_2,V_m_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_plus__code__numeral__code,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_less__eq__code__numeral__code,axiom, % 181.55/181.51 ! [V_m_2,V_n_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_code__numeral__not__eq__zero,axiom, % 181.55/181.51 ! [V_i_2] : % 181.55/181.51 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 181.55/181.51 <=> 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__update__nat,axiom, % 181.55/181.51 ! [V_n,V_ns,V_k] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__list__update,axiom, % 181.55/181.51 ! [V_i_2,V_a_2,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => ( ~ 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)))))) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__list__update__neq,axiom, % 181.55/181.51 ! [V_x,V_xs,T_a,V_j,V_i] : % 181.55/181.51 ( V_i != V_j % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__id,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__update,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__beyond,axiom, % 181.55/181.51 ! [V_x,V_i,V_xs,T_a] : % 181.55/181.51 ( 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)) % 181.55/181.51 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__list__update,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__code_I2_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update_Osimps_I2_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__code_I3_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__swap,axiom, % 181.55/181.51 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 181.55/181.51 ( V_i != V_i_H % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__overwrite,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_update__zip,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__update,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__update__subsetI,axiom, % 181.55/181.51 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__update__subset__insert,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__list__update,axiom, % 181.55/181.51 ! [V_x,V_j,V_xs,T_a,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( ( V_i = V_j % 181.55/181.51 => 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 ) % 181.55/181.51 & ( V_i != V_j % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__same__conv,axiom, % 181.55/181.51 ! [V_x_2,V_xs_2,T_b,V_i_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 181.55/181.51 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__list__update__eq,axiom, % 181.55/181.51 ! [V_x,V_xs,T_a,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__update__memI,axiom, % 181.55/181.51 ! [V_x_2,V_xs_2,T_b,V_n_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1__iff__update,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ? [B_y,B_n] : % 181.55/181.51 ( 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)) % 181.55/181.51 & 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))) % 181.55/181.51 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upd__upds__conv__if,axiom, % 181.55/181.51 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2)))) % 181.55/181.51 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2)))) % 181.55/181.51 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__add__upds,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upds__apply__nontin,axiom, % 181.55/181.51 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upds__Cons,axiom, % 181.55/181.51 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upds__list__update2__drop,axiom, % 181.55/181.51 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] : % 181.55/181.51 ( 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_i_2)) % 181.55/181.51 => ( 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))) % 181.55/181.51 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upds__twist,axiom, % 181.55/181.51 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2))) % 181.55/181.51 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_restrict__map__upds,axiom, % 181.55/181.51 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => ( 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_D_2)) % 181.55/181.51 => c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_dom__map__upds,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,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),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_select__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_subtract__code__numeral__code,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nat__of__of__nat,axiom, % 181.55/181.51 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 181.55/181.51 % 181.55/181.51 fof(fact_of__nat__nat__of,axiom, % 181.55/181.51 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 181.55/181.51 % 181.55/181.51 fof(fact_nat__of__inverse,axiom, % 181.55/181.51 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 181.55/181.51 % 181.55/181.51 fof(fact_code__numeral_Onat__of__inject,axiom, % 181.55/181.51 ! [V_y_2,V_x_2] : % 181.55/181.51 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 181.55/181.51 <=> V_x_2 = V_y_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 181.55/181.51 ! [V_l_2,V_k_2] : % 181.55/181.51 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 181.55/181.51 <=> V_k_2 = V_l_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_type__definition__code__numeral,axiom, % 181.55/181.51 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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_less__code__numeral__def,axiom, % 181.55/181.51 ! [V_m_2,V_n_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 181.55/181.51 <=> 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nat__of,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nat__of__number,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_int__of__def,axiom, % 181.55/181.51 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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_less__eq__code__numeral__def,axiom, % 181.55/181.51 ! [V_m_2,V_n_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 181.55/181.51 <=> 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nat__of__code,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nat__of__aux__def,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Suc__code__numeral__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_minus__code__numeral__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_of__nat__inverse,axiom, % 181.55/181.51 ! [V_y_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 181.55/181.51 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_plus__code__numeral__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_div__code__numeral__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_subtract__code__numeral__def,axiom, % 181.55/181.51 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.51 % 181.55/181.51 fof(fact_minus__code__numeral__code,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_times__code__numeral__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_mod__code__numeral__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_code__numeral__decr,axiom, % 181.55/181.51 ! [V_k] : % 181.55/181.51 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_select__weigth__select,axiom, % 181.55/181.51 ! [T_b,V_xs_2] : % 181.55/181.51 ( V_xs_2 != c_List_Olist_ONil(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_greaterThanLessThan__upto,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lists_ONil,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__Nil1,axiom, % 181.55/181.51 ! [V_r_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__Nil2,axiom, % 181.55/181.51 ! [V_r_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__0,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__eq__Nil,axiom, % 181.55/181.51 ! [V_xs_2,V_n_2,T_b] : % 181.55/181.51 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 181.55/181.51 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__Nil,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrelp_ONil,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrelp_Oequations_I1_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip_Osimps_I1_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__Nil,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__simps_I1_J,axiom, % 181.55/181.51 ! [T_a] : % 181.55/181.51 ( class_Groups_Omonoid__add(T_a) % 181.55/181.51 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_atLeastAtMost__upto,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__upto,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldr_Osimps_I1_J,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_upto__empty,axiom, % 181.55/181.51 ! [V_i,V_j] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 181.55/181.51 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__Cons__code_I1_J,axiom, % 181.55/181.51 ! [V_k,T_a,T_b] : hAPP(hAPP(c_Map_Omap__of(T_b,T_a),c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Osimps_I3_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Osimps_I2_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sublist__nil,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sublist__empty,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Osize_I1_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_List_Oset_Osimps_I1_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__empty2,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__empty,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__upto,axiom, % 181.55/181.51 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct_Osimps_I1_J,axiom, % 181.55/181.51 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of_Osimps_I1_J,axiom, % 181.55/181.51 ! [V_x_1,T_b,T_a] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Osize_I3_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__0__conv,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upto_Osimps,axiom, % 181.55/181.51 ! [V_j,V_i] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 181.55/181.51 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upto__rec__number__of,axiom, % 181.55/181.51 ! [V_n,V_m] : % 181.55/181.51 ( ( 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))) % 181.55/181.51 => 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))) ) % 181.55/181.51 & ( ~ 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))) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__is__Nil__conv,axiom, % 181.55/181.51 ! [V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.51 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map_Osimps_I1_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Nil__is__map__conv,axiom, % 181.55/181.51 ! [V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upds__Nil2,axiom, % 181.55/181.51 ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2 ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upds__Nil1,axiom, % 181.55/181.51 ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2 ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__nonempty,axiom, % 181.55/181.51 ! [V_x_2,V_k_2,V_xs_2,T_b] : % 181.55/181.51 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update_Osimps_I1_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__code_I1_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__greater__0__conv,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__1__Cons,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_not__Nil__listrel1,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_not__listrel1__Nil,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel_ONil,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__Nil__right,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Nil__notin__lex,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Nil2__notin__lex,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 181.55/181.51 ! [V_j_2,V_i_2,V_f_2,T_b] : % 181.55/181.51 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 181.55/181.51 ! [V_l_2,V_k_2,V_f_2,T_b] : % 181.55/181.51 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__Cons,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sublist__singleton,axiom, % 181.55/181.51 ! [V_x_2,T_b,V_A_2] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_atLeastLessThan__upto,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lists__empty,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__Cons_H,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a,V_n] : % 181.55/181.51 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_greaterThanAtMost__upto,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_select,axiom, % 181.55/181.51 ! [V_s_2,T_b,V_xs_2] : % 181.55/181.51 ( V_xs_2 != c_List_Olist_ONil(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel__Nil,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__Cons__sing__Nil,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__Cons__number__of,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a,V_v] : % 181.55/181.51 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upto_Opsimps,axiom, % 181.55/181.51 ! [V_j_2,V_i_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 181.55/181.51 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_anamorph_Osimps,axiom, % 181.55/181.51 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 181.55/181.51 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.55/181.51 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listset_Osimps_I1_J,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nat__list__def,axiom, % 181.55/181.51 ! [V_l_2] : % 181.55/181.51 ( c_List_Onat__list(V_l_2) % 181.55/181.51 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listset_Osimps_I2_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__Cons1,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__Cons,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Osimps_I5_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list_Osimps_I4_J,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_upto_Opinduct,axiom, % 181.55/181.51 ! [V_Pa_2,V_a1_2,V_a0_2] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( ! [B_i,B_j] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 181.55/181.51 => 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)) ) % 181.55/181.51 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 181.55/181.51 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upds__append1,axiom, % 181.55/181.51 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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))) % 181.55/181.51 => c_Map_Omap__upds(T_b,T_c,V_m_2,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) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append1__eq__conv,axiom, % 181.55/181.51 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( V_xs_2 = V_ys_2 % 181.55/181.51 & V_x_2 = V_y_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Cons__eq__append__conv,axiom, % 181.55/181.51 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 181.55/181.51 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 ) % 181.55/181.51 | ? [B_ys_H] : % 181.55/181.51 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 % 181.55/181.51 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__eq__Cons__conv,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 181.55/181.51 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) % 181.55/181.51 | ? [B_ys_H] : % 181.55/181.51 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) % 181.55/181.51 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Cons__eq__appendI,axiom, % 181.55/181.51 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 181.55/181.51 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 181.55/181.51 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 181.55/181.51 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__Cons,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__append,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__in__lists__conv,axiom, % 181.55/181.51 ! [V_A_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 181.55/181.51 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__append,axiom, % 181.55/181.51 ! [V_ys,V_xs,T_a] : % 181.55/181.51 ( class_Groups_Omonoid__add(T_a) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldr__append,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__assoc,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__eq__append__conv2,axiom, % 181.55/181.51 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> ? [B_us] : % 181.55/181.51 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) % 181.55/181.51 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 ) % 181.55/181.51 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 % 181.55/181.51 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_same__append__eq,axiom, % 181.55/181.51 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> V_ys_2 = V_zs_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__same__eq,axiom, % 181.55/181.51 ! [V_zs_2,V_xs_2,V_ys_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> V_ys_2 = V_zs_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__eq__appendI,axiom, % 181.55/181.51 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 181.55/181.51 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 181.55/181.51 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 181.55/181.51 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__append,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2),hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__append,axiom, % 181.55/181.51 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 181.55/181.51 ( 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) % 181.55/181.51 => ( 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) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__append,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__upds__append2__drop,axiom, % 181.55/181.51 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__upds__append__drop,axiom, % 181.55/181.51 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.51 ( 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) % 181.55/181.51 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__append,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_eq__Nil__appendI,axiom, % 181.55/181.51 ! [T_a,V_ys,V_xs] : % 181.55/181.51 ( V_xs = V_ys % 181.55/181.51 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__self__conv2,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__self__conv,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 % 181.55/181.51 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__is__Nil__conv,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) % 181.55/181.51 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 181.55/181.51 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_self__append__conv2,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_ys_2] : % 181.55/181.51 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_self__append__conv,axiom, % 181.55/181.51 ! [V_ys_2,T_b,V_xs_2] : % 181.55/181.51 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 181.55/181.51 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__Nil2,axiom, % 181.55/181.51 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 181.55/181.51 % 181.55/181.51 fof(fact_Nil__is__append__conv,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 181.55/181.51 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 181.55/181.51 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__Nil,axiom, % 181.55/181.51 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__append__length,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__append__length__plus,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__append,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__append1,axiom, % 181.55/181.51 ! [V_x,V_ys,V_xs,T_a,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__length,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__listrel1I,axiom, % 181.55/181.51 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( ( ( 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))) % 181.55/181.51 & V_us_2 = V_vs_2 ) % 181.55/181.51 | ( V_xs_2 = V_ys_2 % 181.55/181.51 & 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))) ) ) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__append__leftI,axiom, % 181.55/181.51 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__append,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 181.55/181.51 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 181.55/181.51 & 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__append,axiom, % 181.55/181.51 ! [V_ys,V_xs,T_a,V_n] : % 181.55/181.51 ( ( 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))) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( ~ 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))) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__update__append,axiom, % 181.55/181.51 ! [V_x,V_ys,V_xs,T_a,V_n] : % 181.55/181.51 ( ( 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))) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( ~ 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))) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sublist__append,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1I,axiom, % 181.55/181.51 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ( 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)) % 181.55/181.51 => ( 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)) % 181.55/181.51 => 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))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__append__left__rightI,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__Suc__conv__app__nth,axiom, % 181.55/181.51 ! [V_xs,T_a,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_snoc__listrel1__snoc__iff,axiom, % 181.55/181.51 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ( ( 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))) % 181.55/181.51 & V_x_2 = V_y_2 ) % 181.55/181.51 | ( V_xs_2 = V_ys_2 % 181.55/181.51 & 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)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sublist__Cons,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listrel1E,axiom, % 181.55/181.51 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ~ ! [B_x,B_y] : % 181.55/181.51 ( 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)) % 181.55/181.51 => ! [B_us,B_vs] : % 181.55/181.51 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) % 181.55/181.51 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__append__leftD,axiom, % 181.55/181.51 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( ! [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)) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate1__def,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upd__conv__take__nth__drop,axiom, % 181.55/181.51 ! [V_a,V_xs,T_a,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__take__drop__id,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__1__Cons,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__Suc__Cons,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__via__drop,axiom, % 181.55/181.51 ! [V_ys,V_y,V_xs,V_n,T_a] : % 181.55/181.51 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 181.55/181.51 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__drop,axiom, % 181.55/181.51 ! [V_i,V_xs,T_a] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct1__rotate,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) % 181.55/181.51 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__drop,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__take,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__zip,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__drop,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__0,axiom, % 181.55/181.51 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__drop,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__rotate1,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__drop__subset,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__set__dropD,axiom, % 181.55/181.51 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__rotate1,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate1__is__Nil__conv,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__Nil,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__drop__subset__set__drop,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_m_2,V_n_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__all,axiom, % 181.55/181.51 ! [V_n,V_xs,T_a] : % 181.55/181.51 ( 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)) % 181.55/181.51 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__eq__Nil,axiom, % 181.55/181.51 ! [V_xs_2,V_n_2,T_b] : % 181.55/181.51 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 181.55/181.51 <=> 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__append,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__eq__conv__conj,axiom, % 181.55/181.51 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 181.55/181.51 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 % 181.55/181.51 <=> ( 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) % 181.55/181.51 & 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__Cons,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__Cons_H,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a,V_n] : % 181.55/181.51 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__drop,axiom, % 181.55/181.51 ! [V_xs,T_a,V_i,V_n] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__eq__append__conv__if,axiom, % 181.55/181.51 ! [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] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> ( ( 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))) % 181.55/181.51 => ( 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) % 181.55/181.51 & 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) ) ) % 181.55/181.51 & ( ~ 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))) % 181.55/181.51 => ( 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 % 181.55/181.51 & 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 ) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__drop_H,axiom, % 181.55/181.51 ! [V_xs,T_a,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__simps,axiom, % 181.55/181.51 ! [V_xs,V_x,T_b,T_a] : % 181.55/181.51 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 181.55/181.51 & 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__Cons__number__of,axiom, % 181.55/181.51 ! [V_xs,V_x,T_a,V_v] : % 181.55/181.51 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__add,axiom, % 181.55/181.51 ! [V_xs,T_a,V_j,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate1__length01,axiom, % 181.55/181.51 ! [V_xs,T_a] : % 181.55/181.51 ( 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))) % 181.55/181.51 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__append1,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_zip__append2,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_id__take__nth__drop,axiom, % 181.55/181.51 ! [V_xs,T_a,V_i] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__hd__drop,axiom, % 181.55/181.51 ! [V_xs,T_a,V_n] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd__drop__conv__nth,axiom, % 181.55/181.51 ! [V_n,T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => ( 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))) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd_Osimps,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd__map,axiom, % 181.55/181.51 ! [V_f_2,T_c,T_b,V_xs_2] : % 181.55/181.51 ( V_xs_2 != c_List_Olist_ONil(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd__append,axiom, % 181.55/181.51 ! [V_ys,T_a,V_xs] : % 181.55/181.51 ( ( V_xs = c_List_Olist_ONil(T_a) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd__append2,axiom, % 181.55/181.51 ! [V_ys,T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd__in__set,axiom, % 181.55/181.51 ! [T_b,V_xs_2] : % 181.55/181.51 ( V_xs_2 != c_List_Olist_ONil(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd__conv__nth,axiom, % 181.55/181.51 ! [T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate1__hd__tl,axiom, % 181.55/181.51 ! [T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd__rotate__conv__nth,axiom, % 181.55/181.51 ! [V_n,T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__Suc,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_tl__drop,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__tl,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_tl__append2,axiom, % 181.55/181.51 ! [V_ys,T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__tl,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__conv__mod,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_tl_Osimps_I2_J,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__tl,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__tl,axiom, % 181.55/181.51 ! [V_xs,T_a] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__rotate,axiom, % 181.55/181.51 ! [V_xs_2,V_n_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) % 181.55/181.51 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__rotate,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__rotate,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__rotate,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__is__Nil__conv,axiom, % 181.55/181.51 ! [V_xs_2,V_n_2,T_b] : % 181.55/181.51 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 181.55/181.51 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_tl_Osimps_I1_J,axiom, % 181.55/181.51 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate1__rotate__swap,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__def,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__Suc,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_tl__append,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate0,axiom, % 181.55/181.51 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__add,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__id,axiom, % 181.55/181.51 ! [V_xs,T_a,V_n] : % 181.55/181.51 ( 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) % 181.55/181.51 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__length01,axiom, % 181.55/181.51 ! [V_n,V_xs,T_a] : % 181.55/181.51 ( 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))) % 181.55/181.51 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__tl,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_tl__take,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__Suc,axiom, % 181.55/181.51 ! [V_n,T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_rotate__drop__take,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fold1__set,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 181.55/181.51 => ( V_xs_2 != c_List_Olist_ONil(T_b) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__append__rightI,axiom, % 181.55/181.51 ! [V_r_2,V_x_2,T_b,V_y_2] : % 181.55/181.51 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldl__Nil,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_start__le__sum,axiom, % 181.55/181.51 ! [V_ns_2,V_n_2,V_m_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldl__assoc,axiom, % 181.55/181.51 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 181.55/181.51 ( class_Groups_Osemigroup__add(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldl__absorb0,axiom, % 181.55/181.51 ! [V_zs_2,V_x_2,T_b] : % 181.55/181.51 ( class_Groups_Omonoid__add(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldr__conv__foldl,axiom, % 181.55/181.51 ! [V_a_2,V_xs_2,T_b] : % 181.55/181.51 ( class_Groups_Oab__semigroup__add(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldl__map,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldl__Cons,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldl__append,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__foldl,axiom, % 181.55/181.51 ! [T_b] : % 181.55/181.51 ( class_Groups_Omonoid__add(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldl__foldr1,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( class_Groups_Omonoid__add(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_foldl__foldr1__lemma,axiom, % 181.55/181.51 ! [V_xs_2,V_a_2,T_b] : % 181.55/181.51 ( class_Groups_Omonoid__add(T_b) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sum__eq__0__conv,axiom, % 181.55/181.51 ! [V_ns_2,V_m_2] : % 181.55/181.51 ( 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) % 181.55/181.51 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 & ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 181.55/181.51 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 181.55/181.51 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 181.55/181.51 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__set__fold,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__set__fold,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Sup__fin__set__fold,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( class_Lattices_Olattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Inf__fin__set__fold,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( class_Lattices_Olattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Min__fin__set__fold,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_Max__fin__set__fold,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_OInf__fin__set__fold,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_min__max_OSup__fin__set__fold,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_SUPR__set__fold,axiom, % 181.55/181.51 ! [V_f_2,V_xs_2,T_c,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_INFI__set__fold,axiom, % 181.55/181.51 ! [V_f_2,V_xs_2,T_c,T_b] : % 181.55/181.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__upds__fold__map__upd,axiom, % 181.55/181.51 ! [V_vs_2,V_ks_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),T_c))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c))))),c_Option_Ooption_OSome(T_c))),V_m_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_ks_2),V_vs_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_elem__le__sum,axiom, % 181.55/181.51 ! [V_ns_2,V_n_2] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__Nil__left,axiom, % 181.55/181.51 ! [V_r_2,V_y_2,T_b] : % 181.55/181.51 ( 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))) % 181.55/181.51 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__list__update,axiom, % 181.55/181.51 ! [V_x,V_k,T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => ( ( 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)) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 181.55/181.51 & ( 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)) % 181.55/181.51 => 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) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__appendL,axiom, % 181.55/181.51 ! [V_xs,T_a,V_ys] : % 181.55/181.51 ( V_ys = c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__appendR,axiom, % 181.55/181.51 ! [V_xs,T_a,V_ys] : % 181.55/181.51 ( V_ys != c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__append,axiom, % 181.55/181.51 ! [V_xs,T_a,V_ys] : % 181.55/181.51 ( ( V_ys = c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 181.55/181.51 & ( V_ys != c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__ConsL,axiom, % 181.55/181.51 ! [V_x,T_a,V_xs] : % 181.55/181.51 ( V_xs = c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__ConsR,axiom, % 181.55/181.51 ! [V_x,T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last_Osimps,axiom, % 181.55/181.51 ! [V_x,T_a,V_xs] : % 181.55/181.51 ( ( V_xs = c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 181.55/181.51 & ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__map,axiom, % 181.55/181.51 ! [V_f_2,T_c,T_b,V_xs_2] : % 181.55/181.51 ( V_xs_2 != c_List_Olist_ONil(T_b) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__in__set,axiom, % 181.55/181.51 ! [T_b,V_as_2] : % 181.55/181.51 ( V_as_2 != c_List_Olist_ONil(T_b) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__snoc,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__drop,axiom, % 181.55/181.51 ! [V_xs,T_a,V_n] : % 181.55/181.51 ( 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))) % 181.55/181.51 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_last__conv__nth,axiom, % 181.55/181.51 ! [T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__mono,axiom, % 181.55/181.51 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] : % 181.55/181.51 ( ( class_Groups_Omonoid__add(T_c) % 181.55/181.51 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 181.55/181.51 => ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 181.55/181.51 => 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)))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__linear,axiom, % 181.55/181.51 ! [V_y_2,V_x_2,V_r_2,T_b] : % 181.55/181.51 ( ! [B_a,B_b] : % 181.55/181.51 ( 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)) % 181.55/181.51 | B_a = B_b % 181.55/181.51 | 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)) ) % 181.55/181.51 => ( 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))) % 181.55/181.51 | V_x_2 = V_y_2 % 181.55/181.51 | 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lexord__irreflexive,axiom, % 181.55/181.51 ! [V_y_2,V_r_2,T_b] : % 181.55/181.51 ( ! [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)) % 181.55/181.51 => ~ 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_lists_Osimps,axiom, % 181.55/181.51 ! [V_A_2,V_a_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) % 181.55/181.51 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 181.55/181.51 | ? [B_a,B_l] : % 181.55/181.51 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) % 181.55/181.51 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 181.55/181.51 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_weak__map__of__SomeI,axiom, % 181.55/181.51 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_l_2))) % 181.55/181.51 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_list__size__pointwise,axiom, % 181.55/181.51 ! [V_g_2,V_f_2,V_xs_2,T_b] : % 181.55/181.51 ( ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_butlast__take,axiom, % 181.55/181.51 ! [V_xs,T_a,V_n] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_butlast__drop,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__butlast,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_butlast__append,axiom, % 181.55/181.51 ! [V_xs,T_a,V_ys] : % 181.55/181.51 ( ( V_ys = c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 181.55/181.51 & ( V_ys != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_butlast_Osimps_I2_J,axiom, % 181.55/181.51 ! [V_x,T_a,V_xs] : % 181.55/181.51 ( ( V_xs = c_List_Olist_ONil(T_a) % 181.55/181.51 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 181.55/181.51 & ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__butlast,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__set__butlastD,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 181.55/181.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__butlast,axiom, % 181.55/181.51 ! [T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_butlast_Osimps_I1_J,axiom, % 181.55/181.51 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__set__butlast__appendI,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 181.55/181.51 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) ) % 181.55/181.51 => 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))))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_butlast__snoc,axiom, % 181.55/181.51 ! [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 ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__butlast,axiom, % 181.55/181.51 ! [V_xs,T_a,V_n] : % 181.55/181.51 ( 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))) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__butlast,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_butlast__conv__take,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_butlast__list__update,axiom, % 181.55/181.51 ! [V_x,V_xs,T_a,V_k] : % 181.55/181.51 ( ( 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)) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( 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)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_append__butlast__last__id,axiom, % 181.55/181.51 ! [T_a,V_xs] : % 181.55/181.51 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.51 => 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 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_snoc__eq__iff__butlast,axiom, % 181.55/181.51 ! [V_ys_2,V_x_2,V_xs_2,T_b] : % 181.55/181.51 ( 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 % 181.55/181.51 <=> ( V_ys_2 != c_List_Olist_ONil(T_b) % 181.55/181.51 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 % 181.55/181.51 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__take__lemma,axiom, % 181.55/181.51 ! [V_ys,V_xs,T_a,V_k] : % 181.55/181.51 ( 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))) % 181.55/181.51 => ( 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))) % 181.55/181.51 => ( ! [B_i] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 181.55/181.51 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 181.55/181.51 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_body__def,axiom, % 181.55/181.51 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 181.55/181.51 % 181.55/181.51 fof(fact_transpose__aux__max,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_listsum__map__remove1,axiom, % 181.55/181.51 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] : % 181.55/181.51 ( class_Groups_Ocomm__monoid__add(T_c) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => 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)))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter__append,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_remove1_Osimps_I2_J,axiom, % 181.55/181.51 ! [V_xs,T_a,V_y,V_x] : % 181.55/181.51 ( ( V_x = V_y % 181.55/181.51 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 181.55/181.51 & ( V_x != V_y % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter_Osimps_I2_J,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 181.55/181.51 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__remove1,axiom, % 181.55/181.51 ! [V_x,V_xs,T_a] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__filter,axiom, % 181.55/181.51 ! [V_Pa_2,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter__filter,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter__remove1,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_remove1__commute,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_remove1__filter__not,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 181.55/181.51 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sum__length__filter__compl,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__filter__le,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__remove1__subset,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter__is__subset,axiom, % 181.55/181.51 ! [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))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_in__set__remove1,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_b_2,V_a_2] : % 181.55/181.51 ( V_a_2 != V_b_2 % 181.55/181.51 => ( 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)))) % 181.55/181.51 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_notin__set__remove1,axiom, % 181.55/181.51 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => ~ 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_remove1__idem,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter__id__conv,axiom, % 181.55/181.51 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.51 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_remove1_Osimps_I1_J,axiom, % 181.55/181.51 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter_Osimps_I1_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter__empty__conv,axiom, % 181.55/181.51 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.51 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__filter,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__filter__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_remove1__append,axiom, % 181.55/181.51 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => 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) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__filter__less,axiom, % 181.55/181.51 ! [V_Pa_2,V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.51 => 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))) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__minus__filter__out,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_filter__in__sublist,axiom, % 181.55/181.51 ! [V_s_2,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => 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) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__filter__conv__card,axiom, % 181.55/181.51 ! [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))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__remove1,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__remove1__eq,axiom, % 181.55/181.51 ! [V_x_2,V_xs_2,T_b] : % 181.55/181.51 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.51 => 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)))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__filter__def,axiom, % 181.55/181.51 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),V_f_2)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_b)))),V_xs_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_transpose__max__length,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_transpose__empty,axiom, % 181.55/181.51 ! [V_xs_2,T_b] : % 181.55/181.51 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) % 181.55/181.51 <=> ! [B_x] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 181.55/181.51 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_transpose_Osimps_I1_J,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__filter__simps_I2_J,axiom, % 181.55/181.51 ! [V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ). % 181.55/181.51 % 181.55/181.51 fof(fact_transpose__map__map,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_transpose_Osimps_I2_J,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__of__filter__in,axiom, % 181.55/181.51 ! [V_Pa_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] : % 181.55/181.51 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) % 181.55/181.51 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_k_2),V_z_2)) % 181.55/181.51 => hAPP(hAPP(c_Map_Omap__of(T_c,T_b),hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__filter__simps_I1_J,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_b),T_b,c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sublist__shift__lemma__Suc,axiom, % 181.55/181.51 ! [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)))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_select__weigth__drop__zero,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_pick__drop__zero,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_nth__transpose,axiom, % 181.55/181.51 ! [V_xs_2,T_b,V_i_2] : % 181.55/181.51 ( 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)))) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__transpose,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__filter__map__filter,axiom, % 181.55/181.51 ! [V_xs_2,V_Pa_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_Pa_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sorted__list__of__set__remove,axiom, % 181.55/181.51 ! [V_x_2,V_A_2,T_b] : % 181.55/181.51 ( class_Orderings_Olinorder(T_b) % 181.55/181.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.51 => 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)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sublist__def,axiom, % 181.55/181.51 ! [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))))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_drop__upt,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_hd__upt,axiom, % 181.55/181.51 ! [V_j,V_i] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.55/181.51 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__Suc__append,axiom, % 181.55/181.51 ! [V_j,V_i] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__Suc,axiom, % 181.55/181.51 ! [V_j,V_i] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.55/181.51 => 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))) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.55/181.51 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__add__eq__append,axiom, % 181.55/181.51 ! [V_k,V_j,V_i] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.55/181.51 => 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))) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__rec,axiom, % 181.55/181.51 ! [V_j,V_i] : % 181.55/181.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.55/181.51 => 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)) ) % 181.55/181.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.55/181.51 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__conv__Cons,axiom, % 181.55/181.51 ! [V_j,V_i] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_map__Suc__upt,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_distinct__upt,axiom, % 181.55/181.51 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 181.55/181.51 % 181.55/181.51 fof(fact_take__upt,axiom, % 181.55/181.51 ! [V_n,V_m,V_i] : % 181.55/181.51 ( 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)) % 181.55/181.51 => 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)) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_sorted__list__of__set__range,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_set__upt,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_atLeastLessThan__upt,axiom, % 181.55/181.51 ! [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)) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__eq__Nil__conv,axiom, % 181.55/181.51 ! [V_j_2,V_i_2] : % 181.55/181.51 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 181.55/181.51 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__conv__Nil,axiom, % 181.55/181.51 ! [V_i,V_j] : % 181.55/181.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 181.55/181.51 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__0,axiom, % 181.55/181.51 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 181.55/181.51 % 181.55/181.51 fof(fact_length__upt,axiom, % 181.55/181.51 ! [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) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__rec__number__of,axiom, % 181.55/181.51 ! [V_n,V_m] : % 181.55/181.51 ( ( 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))) % 181.55/181.51 => 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))) ) % 181.55/181.51 & ( ~ 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))) % 181.55/181.51 => 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) ) ) ). % 181.55/181.51 % 181.55/181.51 fof(fact_upt__eq__Cons__conv,axiom, % 181.55/181.51 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 181.55/181.51 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 181.55/181.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 181.55/181.52 & V_i_2 = V_x_2 % 181.55/181.52 & 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 ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_last__upt,axiom, % 181.55/181.52 ! [V_j,V_i] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__nth,axiom, % 181.55/181.52 ! [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 ). % 181.55/181.52 % 181.55/181.52 fof(fact_atLeastAtMost__upt,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_atLeast__upt,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 181.55/181.52 ! [V_n_2,V_m_2,V_f_2,T_b] : % 181.55/181.52 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 181.55/181.52 ! [V_n_2,V_m_2,V_f_2,T_b] : % 181.55/181.52 ( class_Groups_Ocomm__monoid__add(T_b) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__list__of__set__empty,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_nth__upt,axiom, % 181.55/181.52 ! [V_j,V_k,V_i] : % 181.55/181.52 ( 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)) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_greaterThanAtMost__upt,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_greaterThanLessThan__upt,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_nth__map__upt,axiom, % 181.55/181.52 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_atMost__upto,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sublist__shift__lemma,axiom, % 181.55/181.52 ! [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))))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose__rectangle,axiom, % 181.55/181.52 ! [V_n_2,T_b,V_xs_2] : % 181.55/181.52 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 181.55/181.52 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 181.55/181.52 => ( ! [B_i] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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 ) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose_Opsimps_I2_J,axiom, % 181.55/181.52 ! [V_xss_2,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose_Opsimps_I1_J,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose__aux__filter__head,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose__aux__filter__tail,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_filter__concat,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat_Osimps_I2_J,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__concat,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat_Osimps_I1_J,axiom, % 181.55/181.52 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nil__eq__concat__conv,axiom, % 181.55/181.52 ! [V_xss_2,T_b] : % 181.55/181.52 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 181.55/181.52 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat__eq__Nil__conv,axiom, % 181.55/181.52 ! [V_xss_2,T_b] : % 181.55/181.52 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 181.55/181.52 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat__conv__foldl,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_foldl__conv__concat,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat__append,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__concat,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__concat,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose_Osimps_I3_J,axiom, % 181.55/181.52 ! [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))))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat__eq__concat__iff,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.52 ( ! [B_x] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => 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)) ) % 181.55/181.52 => ( 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) % 181.55/181.52 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 181.55/181.52 <=> V_xs_2 = V_ys_2 ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat__injective,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.52 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 181.55/181.52 => ( 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) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => 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)) ) % 181.55/181.52 => V_xs_2 = V_ys_2 ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat__map__singleton,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose_Opsimps_I3_J,axiom, % 181.55/181.52 ! [V_xss_2,V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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))))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 181.55/181.52 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsum__map__filter,axiom, % 181.55/181.52 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] : % 181.55/181.52 ( class_Groups_Omonoid__add(T_c) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => ( ~ hBOOL(hAPP(V_Pa_2,B_x)) % 181.55/181.52 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_return__list__def,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transfer__nat__int__list__return__embed,axiom, % 181.55/181.52 ! [V_l] : % 181.55/181.52 ( c_List_Onat__list(V_l) % 181.55/181.52 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__remdups__concat,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__remdups,axiom, % 181.55/181.52 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__remdups__leq,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remdups__map__remdups,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__remdups,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remdups__eq__nil__iff,axiom, % 181.55/181.52 ! [V_x_2,T_b] : % 181.55/181.52 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b) % 181.55/181.52 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remdups__eq__nil__right__iff,axiom, % 181.55/181.52 ! [V_x_2,T_b] : % 181.55/181.52 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2) % 181.55/181.52 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remdups_Osimps_I1_J,axiom, % 181.55/181.52 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remove1__remdups,axiom, % 181.55/181.52 ! [V_x,V_xs,T_a] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remdups__id__iff__distinct,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2 % 181.55/181.52 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__remdups__id,axiom, % 181.55/181.52 ! [V_xs,T_a] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.52 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__remdups__eq,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remdups__remdups,axiom, % 181.55/181.52 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remdups__filter,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_embed__list__def,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remdups_Osimps_I2_J,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => 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) ) % 181.55/181.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__remdups__card__conv,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 181.55/181.52 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_n__lists_Osimps_I2_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_partition__filter__conv,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_partition__filter1,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__n__lists,axiom, % 181.55/181.52 ! [V_n,V_xs,T_a] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__n__lists,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__n__lists__elem,axiom, % 181.55/181.52 ! [V_xs_2,V_n_2,V_ys_2,T_b] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_partition__P,axiom, % 181.55/181.52 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.52 & ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) % 181.55/181.52 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_partition_Osimps_I1_J,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_n__lists__Nil,axiom, % 181.55/181.52 ! [T_a,V_n] : % 181.55/181.52 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.52 => 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))) ) % 181.55/181.52 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.52 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_n__lists_Osimps_I1_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_partition_Osimps_I2_J,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_partition__filter2,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_partition__set,axiom, % 181.55/181.52 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__n__lists,axiom, % 181.55/181.52 ! [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)))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sublists__powset,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__sublists,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__set__sublists,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.52 => 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)))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sublists_Osimps_I1_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sublists_Osimps_I2_J,axiom, % 181.55/181.52 ! [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))))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_product_Osimps_I2_J,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__the__def,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ). % 181.55/181.52 % 181.55/181.52 fof(fact_product_Osimps_I1_J,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__product,axiom, % 181.55/181.52 ! [V_ys,T_b,V_xs,T_a] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_product__list__set,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__of__zip__enum__inject,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,T_b,T_c] : % 181.55/181.52 ( ( class_Enum_Oenum(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => ( 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)),c_Enum_Oenum__class_Oenum(T_c)) % 181.55/181.52 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_Enum_Oenum__class_Oenum(T_c)) % 181.55/181.52 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),c_Enum_Oenum__class_Oenum(T_c)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),c_Enum_Oenum__class_Oenum(T_c)),V_ys_2))) % 181.55/181.52 => V_xs_2 = V_ys_2 ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__list__of__set__insert,axiom, % 181.55/181.52 ! [V_x_2,V_A_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.52 => 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)))))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__distinct,axiom, % 181.55/181.52 ! [T_a] : % 181.55/181.52 ( class_Enum_Oenum(T_a) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__prod__def,axiom, % 181.55/181.52 ! [T_b,T_a] : % 181.55/181.52 ( ( class_Enum_Oenum(T_a) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__option__def,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_b)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_Option_Ooption(T_b)),c_Option_Ooption_OSome(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__UNIV,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_UNIV__enum,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_in__enum,axiom, % 181.55/181.52 ! [V_x_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__insort,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__key_Osimps_I1_J,axiom, % 181.55/181.52 ! [V_x_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__key_Osimps_I2_J,axiom, % 181.55/181.52 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( ( 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))) % 181.55/181.52 => 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)) ) % 181.55/181.52 & ( ~ 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))) % 181.55/181.52 => 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)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__not__Nil,axiom, % 181.55/181.52 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__insort,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_fun__left__comm__insort,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__left__comm,axiom, % 181.55/181.52 ! [V_xs_2,V_y_2,V_x_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__key__left__comm,axiom, % 181.55/181.52 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_remove1__insort,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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 ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_filter__insort__triv,axiom, % 181.55/181.52 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__insort,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => ( 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))) % 181.55/181.52 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__fun__def,axiom, % 181.55/181.52 ! [T_c,T_b] : % 181.55/181.52 ( ( class_Enum_Oenum(T_b) % 181.55/181.52 & class_Enum_Oenum(T_c) ) % 181.55/181.52 => c_Enum_Oenum__class_Oenum(tc_fun(T_b,T_c)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),c_Enum_On__lists(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)),c_Enum_Oenum__class_Oenum(T_c))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__fun__code,axiom, % 181.55/181.52 ! [T_c,T_b] : % 181.55/181.52 ( ( class_Enum_Oenum(T_b) % 181.55/181.52 & class_HOL_Oequal(T_b) % 181.55/181.52 & class_Enum_Oenum(T_c) ) % 181.55/181.52 => c_Enum_Oenum__class_Oenum(tc_fun(T_b,T_c)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),c_Enum_On__lists(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)),c_Enum_Oenum__class_Oenum(T_c))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_ex__n__lists__def,axiom, % 181.55/181.52 ! [V_n_2,V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( c_Enum_Oex__n__lists(T_b,V_Pa_2,V_n_2) % 181.55/181.52 <=> ? [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,c_Enum_Oenum__class_Oenum(T_b))))) % 181.55/181.52 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_all__n__lists__def,axiom, % 181.55/181.52 ! [V_n_2,V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( c_Enum_Oall__n__lists(T_b,V_Pa_2,V_n_2) % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,c_Enum_Oenum__class_Oenum(T_b))))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__all__fun__def,axiom, % 181.55/181.52 ! [V_Pa_2,T_b,T_c] : % 181.55/181.52 ( ( class_Enum_Oenum(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_b,T_c)),V_Pa_2)) % 181.55/181.52 <=> c_Enum_Oall__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__ex__fun__def,axiom, % 181.55/181.52 ! [V_Pa_2,T_b,T_c] : % 181.55/181.52 ( ( class_Enum_Oenum(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_b,T_c)),V_Pa_2)) % 181.55/181.52 <=> c_Enum_Oex__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__all__option__def,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_b)),V_Pa_2)) % 181.55/181.52 <=> ( hBOOL(hAPP(V_Pa_2,c_Option_Ooption_ONone(T_b))) % 181.55/181.52 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b),V_Pa_2),c_Option_Ooption_OSome(T_b)))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__ex__option__def,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_b)),V_Pa_2)) % 181.55/181.52 <=> ( hBOOL(hAPP(V_Pa_2,c_Option_Ooption_ONone(T_b))) % 181.55/181.52 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b),V_Pa_2),c_Option_Ooption_OSome(T_b)))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__ex,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) % 181.55/181.52 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__all,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) % 181.55/181.52 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_exists__code,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 181.55/181.52 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_all__code,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 181.55/181.52 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__all__prod__def,axiom, % 181.55/181.52 ! [V_Pa_2,T_b,T_c] : % 181.55/181.52 ( ( class_Enum_Oenum(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2)) % 181.55/181.52 <=> 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))))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__ex__prod__def,axiom, % 181.55/181.52 ! [V_Pa_2,T_b,T_c] : % 181.55/181.52 ( ( class_Enum_Oenum(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2)) % 181.55/181.52 <=> 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))))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_order__fun_I1_J,axiom, % 181.55/181.52 ! [V_g_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( ( class_Orderings_Oorder(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.55/181.52 <=> 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_order__fun_I2_J,axiom, % 181.55/181.52 ! [V_g_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( ( class_Orderings_Oorder(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.55/181.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.55/181.52 & 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)))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__ex__fun__code,axiom, % 181.55/181.52 ! [V_Pa_2,T_b,T_c] : % 181.55/181.52 ( ( class_Enum_Oenum(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) % 181.55/181.52 & class_HOL_Oequal(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_b,T_c)),V_Pa_2)) % 181.55/181.52 <=> c_Enum_Oex__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_enum__all__fun__code,axiom, % 181.55/181.52 ! [V_Pa_2,T_b,T_c] : % 181.55/181.52 ( ( class_Enum_Oenum(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) % 181.55/181.52 & class_HOL_Oequal(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_b,T_c)),V_Pa_2)) % 181.55/181.52 <=> c_Enum_Oall__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__key__remove1,axiom, % 181.55/181.52 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 181.55/181.52 => ( 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 % 181.55/181.52 => 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 ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__insert__insort__key,axiom, % 181.55/181.52 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( ~ 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)))) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted_ONil,axiom, % 181.55/181.52 ! [T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__single,axiom, % 181.55/181.52 ! [V_x,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__insort,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( 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)) % 181.55/181.52 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__remdups,axiom, % 181.55/181.52 ! [V_l,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__same,axiom, % 181.55/181.52 ! [V_xs_2,V_g_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__upt,axiom, % 181.55/181.52 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__remove1,axiom, % 181.55/181.52 ! [V_a,V_xs,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__tl,axiom, % 181.55/181.52 ! [V_xs,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__upto,axiom, % 181.55/181.52 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__insort__insert,axiom, % 181.55/181.52 ! [V_x_2,V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__drop,axiom, % 181.55/181.52 ! [V_n,V_xs,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__take,axiom, % 181.55/181.52 ! [V_n,V_xs,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__butlast,axiom, % 181.55/181.52 ! [V_xs,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted_Oequations_I1_J,axiom, % 181.55/181.52 ! [T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__insort__insert,axiom, % 181.55/181.52 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__distinct__set__unique,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 181.55/181.52 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 181.55/181.52 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__map__remove1,axiom, % 181.55/181.52 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__insort__insert__key,axiom, % 181.55/181.52 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__filter,axiom, % 181.55/181.52 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__map__same,axiom, % 181.55/181.52 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__many__eq,axiom, % 181.55/181.52 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( 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))) % 181.55/181.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 181.55/181.52 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__many,axiom, % 181.55/181.52 ! [V_zs,V_y,V_x,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 181.55/181.52 => 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))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__insort__key,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( 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))) % 181.55/181.52 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__Cons,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 181.55/181.52 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 & ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__append,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 181.55/181.52 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 & c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 181.55/181.52 & ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => ! [B_xa] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_filter__insort,axiom, % 181.55/181.52 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 181.55/181.52 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted_Oequations_I2_J,axiom, % 181.55/181.52 ! [V_a1_2,V_a2_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) % 181.55/181.52 <=> ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) % 181.55/181.52 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__insert__triv,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__insort__insert,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__list__of__set,axiom, % 181.55/181.52 ! [V_A_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.52 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 % 181.55/181.52 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) % 181.55/181.52 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__remove1,axiom, % 181.55/181.52 ! [V_xs_2,V_a_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 => 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 ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__nth__mono,axiom, % 181.55/181.52 ! [V_j,V_i,V_xs,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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))) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__equals__nth__mono,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 <=> ! [B_j] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ! [B_i] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 181.55/181.52 => 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))) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__sorted__distinct__set__unique,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => ( 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))) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) % 181.55/181.52 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 181.55/181.52 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__insert__key__triv,axiom, % 181.55/181.52 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( 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)))) % 181.55/181.52 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__insert__insort,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose__column,axiom, % 181.55/181.52 ! [V_i_2,V_xs_2,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_nth__nth__transpose__sorted,axiom, % 181.55/181.52 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ( 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)))) % 181.55/181.52 => ( 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)))) % 181.55/181.52 => 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) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_inj__on__rev,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__singleton__conv,axiom, % 181.55/181.52 ! [V_x_2,V_xs_2,T_b] : % 181.55/181.52 ( 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)) % 181.55/181.52 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_singleton__rev__conv,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__concat,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__map,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev_Osimps_I2_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__eq__Cons__iff,axiom, % 181.55/181.52 ! [V_ys_2,V_y_2,V_xs_2,T_b] : % 181.55/181.52 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 181.55/181.52 <=> 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__rev,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) % 181.55/181.52 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__append,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_zip__rev,axiom, % 181.55/181.52 ! [V_ys,T_b,V_xs,T_a] : % 181.55/181.52 ( 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) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__rev,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_foldl__foldr,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_foldr__foldl,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__is__Nil__conv,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 181.55/181.52 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nil__is__rev__conv,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) % 181.55/181.52 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev_Osimps_I1_J,axiom, % 181.55/181.52 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__rev,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsum__rev,axiom, % 181.55/181.52 ! [V_xs,T_a] : % 181.55/181.52 ( class_Groups_Ocomm__monoid__add(T_a) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__rev__ident,axiom, % 181.55/181.52 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__swap,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.52 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 % 181.55/181.52 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__is__rev__conv,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,T_b] : % 181.55/181.52 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) % 181.55/181.52 <=> V_xs_2 = V_ys_2 ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__filter,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_hd__rev,axiom, % 181.55/181.52 ! [T_a,V_xs] : % 181.55/181.52 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.52 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_last__rev,axiom, % 181.55/181.52 ! [T_a,V_xs] : % 181.55/181.52 ( V_xs != c_List_Olist_ONil(T_a) % 181.55/181.52 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__transpose,axiom, % 181.55/181.52 ! [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)))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__foldl__cons,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__drop,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__take,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rotate__rev,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__nth,axiom, % 181.55/181.52 ! [V_xs,T_a,V_n] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_rev__update,axiom, % 181.55/181.52 ! [V_y,V_xs,T_a,V_k] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__rev__nth__mono,axiom, % 181.55/181.52 ! [V_j,V_i,V_xs,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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))) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_foldr__max__sorted,axiom, % 181.55/181.52 ! [V_y_2,V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) % 181.55/181.52 => ( ( V_xs_2 = c_List_Olist_ONil(T_b) % 181.55/181.52 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) % 181.55/181.52 & ( V_xs_2 != c_List_Olist_ONil(T_b) % 181.55/181.52 => 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) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__transpose__sorted,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 181.55/181.52 => 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) ) % 181.55/181.52 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) % 181.55/181.52 => 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))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose__column__length,axiom, % 181.55/181.52 ! [V_i_2,V_xs_2,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transpose__transpose,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__nth__monoI,axiom, % 181.55/181.52 ! [V_xs,T_a] : % 181.55/181.52 ( class_Orderings_Olinorder(T_a) % 181.55/181.52 => ( ! [B_i,B_j] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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))) ) ) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__takeWhile,axiom, % 181.55/181.52 ! [V_Pa_2,V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_zip__takeWhile__fst,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_zip__takeWhile__snd,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__takeWhile__le,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__eq__take,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile_Osimps_I1_J,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__eq__all__conv,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__takeWhileD,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,V_x_2,T_b] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__takeWhile,axiom, % 181.55/181.52 ! [V_Pa_2,V_xs_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__map,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__tail,axiom, % 181.55/181.52 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile_Osimps_I2_J,axiom, % 181.55/181.52 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 181.55/181.52 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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)) ) % 181.55/181.52 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__append1,axiom, % 181.55/181.52 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_nth__length__takeWhile,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ~ 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))))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__nth,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__upds__def,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_Map_Omap__of(T_b,T_c),hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__not__last,axiom, % 181.55/181.52 ! [T_b,V_xs_2] : % 181.55/181.52 ( V_xs_2 != c_List_Olist_ONil(T_b) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 181.55/181.52 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__neq__rev,axiom, % 181.55/181.52 ! [V_x_2,V_xs_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile__neq__rev,axiom, % 181.55/181.52 ! [V_x_2,V_xs_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__dropWhile__id,axiom, % 181.55/181.52 ! [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 ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile_Osimps_I2_J,axiom, % 181.55/181.52 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 181.55/181.52 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) % 181.55/181.52 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__dropWhile,axiom, % 181.55/181.52 ! [V_Pa_2,V_xs_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile__eq__Nil__conv,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b) % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile_Osimps_I1_J,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_hd__dropWhile,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b) % 181.55/181.52 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__dropWhile__le,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile__map,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__dropWhile,axiom, % 181.55/181.52 ! [V_Pa_2,V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile__append1,axiom, % 181.55/181.52 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile__eq__Cons__conv,axiom, % 181.55/181.52 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 <=> ( 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)) % 181.55/181.52 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile__eq__drop,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile__nth,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => 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)))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sort__foldl__insort,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__of__zip__enum__is__Some,axiom, % 181.55/181.52 ! [V_x,V_ys,T_b,T_a] : % 181.55/181.52 ( class_Enum_Oenum(T_a) % 181.55/181.52 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)) % 181.55/181.52 => ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__sort,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_filter__sort,axiom, % 181.55/181.52 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__sort,axiom, % 181.55/181.52 ! [V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sort__key__simps_I1_J,axiom, % 181.55/181.52 ! [V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__sort,axiom, % 181.55/181.52 ! [V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__sort,axiom, % 181.55/181.52 ! [V_xs_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2))) % 181.55/181.52 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__sort__key,axiom, % 181.55/181.52 ! [V_xs_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sort__key__simps_I2_J,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__eq__filter,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( ! [B_x] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.52 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__eq__take__P__nth,axiom, % 181.55/181.52 ! [V_Pa_2,V_xs_2,T_b,V_n_2] : % 181.55/181.52 ( ! [B_i] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 181.55/181.52 => ( 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))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) % 181.55/181.52 => ( ( 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))) % 181.55/181.52 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) % 181.55/181.52 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__takeWhile__less__P__nth,axiom, % 181.55/181.52 ! [V_xs_2,T_b,V_Pa_2,V_j_2] : % 181.55/181.52 ( ! [B_i] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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)))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_lists__IntI,axiom, % 181.55/181.52 ! [V_B_2,V_A_2,V_l_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2))) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2))) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsp_ONil,axiom, % 181.55/181.52 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsp__infI,axiom, % 181.55/181.52 ! [V_B_2,V_l_2,V_A_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2)) % 181.55/181.52 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2)) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsp__inf__eq,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsp__conj__eq,axiom, % 181.55/181.52 ! [V_x_2,V_B_2,V_A_2,T_b] : % 181.55/181.52 ( 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)) % 181.55/181.52 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) % 181.55/181.52 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsp_Oequations_I1_J,axiom, % 181.55/181.52 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_in__listsp__conv__set,axiom, % 181.55/181.52 ! [V_xs_2,V_A_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_append__in__listsp__conv,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_A_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 181.55/181.52 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 181.55/181.52 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsp_Oequations_I2_J,axiom, % 181.55/181.52 ! [V_a2_2,V_a1_2,V_A_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2))) % 181.55/181.52 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 181.55/181.52 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsp__mono,axiom, % 181.55/181.52 ! [V_B_2,V_A_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_listsp__lists__eq,axiom, % 181.55/181.52 ! [V_x_2,V_A_2,T_b] : % 181.55/181.52 ( 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)) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_lists__Int__eq,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__def,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 <=> ( 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) % 181.55/181.52 & ! [B_x] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted_Osimps,axiom, % 181.55/181.52 ! [V_a_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2) % 181.55/181.52 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 181.55/181.52 | ? [B_xs,B_x] : % 181.55/181.52 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 181.55/181.52 & ! [B_xa] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs))) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) % 181.55/181.52 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__rev1,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2) % 181.55/181.52 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__rev,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( 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)) % 181.55/181.52 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__Cons,axiom, % 181.55/181.52 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( 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)) % 181.55/181.52 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 181.55/181.52 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__map1,axiom, % 181.55/181.52 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 <=> 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__map2,axiom, % 181.55/181.52 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( 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)) % 181.55/181.52 <=> 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__appendI,axiom, % 181.55/181.52 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) % 181.55/181.52 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_c_2,V_d_2) % 181.55/181.52 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__append,axiom, % 181.55/181.52 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 => ( 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)) % 181.55/181.52 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__Nil2,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c)) % 181.55/181.52 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__Nil,axiom, % 181.55/181.52 ! [V_ys_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2) % 181.55/181.52 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__takeI,axiom, % 181.55/181.52 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__dropI,axiom, % 181.55/181.52 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__lengthD,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__eq,axiom, % 181.55/181.52 ! [T_b,V_ys_2,V_xs_2] : % 181.55/181.52 ( V_xs_2 = V_ys_2 % 181.55/181.52 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__nthD2,axiom, % 181.55/181.52 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__nthD,axiom, % 181.55/181.52 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__conv__all__nth,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 <=> ( 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) % 181.55/181.52 & ! [B_i] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__update__cong,axiom, % 181.55/181.52 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 181.55/181.52 => 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)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__update__cong2,axiom, % 181.55/181.52 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 181.55/181.52 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2I,axiom, % 181.55/181.52 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] : % 181.55/181.52 ( ! [B_x] : % 181.55/181.52 ( 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)))) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) % 181.55/181.52 => ( 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) % 181.55/181.52 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_all__nth__imp__all__set,axiom, % 181.55/181.52 ! [V_x_2,V_Pa_2,V_xs_2,T_b] : % 181.55/181.52 ( ! [B_i] : % 181.55/181.52 ( 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))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__removeAll__inj__on,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_not__in__set__insert,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_removeAll_Osimps_I2_J,axiom, % 181.55/181.52 ! [V_xs,T_a,V_y,V_x] : % 181.55/181.52 ( ( V_x = V_y % 181.55/181.52 => 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) ) % 181.55/181.52 & ( V_x != V_y % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__insert,axiom, % 181.55/181.52 ! [V_x,V_xs,T_a] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__removeAll,axiom, % 181.55/181.52 ! [V_x,V_xs,T_a] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_removeAll__append,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_removeAll__id,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_removeAll_Osimps_I1_J,axiom, % 181.55/181.52 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 181.55/181.52 % 181.55/181.52 fof(fact_removeAll__filter__not,axiom, % 181.55/181.52 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_removeAll__filter__not__eq,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insert__remdups,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__remove1__removeAll,axiom, % 181.55/181.52 ! [V_x,V_xs,T_a] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 181.55/181.52 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_in__set__insert,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_List_Oset__insert,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insert__Nil,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__removeAll__inj,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 181.55/181.52 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_set__removeAll,axiom, % 181.55/181.52 ! [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)))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_List_Oinsert__def,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) % 181.55/181.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_concat__map__maps,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_maps__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_maps__simps_I2_J,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_maps__simps_I1_J,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_distinct__concat,axiom, % 181.55/181.52 ! [V_xs_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2)) % 181.55/181.52 => ( ! [B_ys] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) ) % 181.55/181.52 => ( ! [B_ys] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 181.55/181.52 => ! [B_zs] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 181.55/181.52 => ( B_ys != B_zs % 181.55/181.52 => 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)) ) ) ) % 181.55/181.52 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_measures__lesseq,axiom, % 181.55/181.52 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ( 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))) % 181.55/181.52 => 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)))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_wf__measures,axiom, % 181.55/181.52 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_in__measures_I1_J,axiom, % 181.55/181.52 ! [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))))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_measures__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_measures__less,axiom, % 181.55/181.52 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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)))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_in__measures_I2_J,axiom, % 181.55/181.52 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] : % 181.55/181.52 ( 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)))) % 181.55/181.52 <=> ( 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))) % 181.55/181.52 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 181.55/181.52 & 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))) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_foldl__apply,axiom, % 181.55/181.52 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] : % 181.55/181.52 ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => 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)) ) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_zip__obtain__same__length,axiom, % 181.55/181.52 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 181.55/181.52 ( ( 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)) % 181.55/181.52 => 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)))) ) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_map__of__eqI,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,T_c,T_b] : % 181.55/181.52 ( hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)) = hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2)) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))) % 181.55/181.52 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2),B_x) ) % 181.55/181.52 => hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_pos__not__random__dseq__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_dropWhile__append2,axiom, % 181.55/181.52 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 181.55/181.52 ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all2__all__nthI,axiom, % 181.55/181.52 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 => ( ! [B_n] : % 181.55/181.52 ( 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))) % 181.55/181.52 => 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))) ) % 181.55/181.52 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_finite__sorted__distinct__unique,axiom, % 181.55/181.52 ! [V_A_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 181.55/181.52 => ? [B_x] : % 181.55/181.52 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2 % 181.55/181.52 & c_List_Olinorder__class_Osorted(T_b,B_x) % 181.55/181.52 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x)) % 181.55/181.52 & ! [B_y] : % 181.55/181.52 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2 % 181.55/181.52 & c_List_Olinorder__class_Osorted(T_b,B_y) % 181.55/181.52 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) ) % 181.55/181.52 => B_y = B_x ) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_takeWhile__append2,axiom, % 181.55/181.52 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 181.55/181.52 ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.52 => 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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_insort__is__Cons,axiom, % 181.55/181.52 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] : % 181.55/181.52 ( class_Orderings_Olinorder(T_c) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 181.55/181.52 => 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) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Cons__eq__filter__iff,axiom, % 181.55/181.52 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 <=> ? [B_us,B_vs] : % 181.55/181.52 ( 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)) % 181.55/181.52 & ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 181.55/181.52 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.52 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_filter__eq__Cons__iff,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 <=> ? [B_us,B_vs] : % 181.55/181.52 ( 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)) % 181.55/181.52 & ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 181.55/181.52 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.52 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ball__nth,axiom, % 181.55/181.52 ! [V_Pa_2,V_xs_2,T_b,V_n_2] : % 181.55/181.52 ( 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))) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_sorted_OCons,axiom, % 181.55/181.52 ! [V_x_2,V_xs_2,T_b] : % 181.55/181.52 ( class_Orderings_Olinorder(T_b) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) % 181.55/181.52 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 181.55/181.52 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex__length,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 181.55/181.52 <=> ? [B_n] : % 181.55/181.52 ( 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))) % 181.55/181.52 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex__simps_I1_J,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 181.55/181.52 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex__iff,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 181.55/181.52 <=> ? [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex__append,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 181.55/181.52 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 181.55/181.52 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex__rev,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 181.55/181.52 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex__simps_I2_J,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_in__set__conv__decomp__first,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 <=> ? [B_ys] : % 181.55/181.52 ( ? [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)) % 181.55/181.52 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_in__set__conv__decomp__last,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 <=> ? [B_ys,B_zs] : % 181.55/181.52 ( 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)) % 181.55/181.52 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_in__set__conv__decomp,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 <=> ? [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)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Oplus__frac__def,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Otimes__frac__def,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Oof__frac__def,axiom, % 181.55/181.52 ! [V_q,T_a,T_b] : % 181.55/181.52 ( ( class_Rings_Oinverse(T_b) % 181.55/181.52 & class_Rings_Oring__1(T_b) ) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Oless__frac__def,axiom, % 181.55/181.52 ! [V_r_2,V_q_2,T_b] : % 181.55/181.52 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) % 181.55/181.52 <=> 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 181.55/181.52 ! [V_r_2,V_q_2,T_b] : % 181.55/181.52 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) % 181.55/181.52 <=> 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Odenom__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Nitpick_Onum__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_setprod__pos,axiom, % 181.55/181.52 ! [V_f_2,V_A_2,T_b,T_c] : % 181.55/181.52 ( class_Rings_Olinordered__semidom(T_c) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all__length,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 181.55/181.52 <=> ! [B_n] : % 181.55/181.52 ( 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))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all__simps_I2_J,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all__rev,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 181.55/181.52 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all__append,axiom, % 181.55/181.52 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 181.55/181.52 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 181.55/181.52 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all__iff,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_Ball__set__list__all,axiom, % 181.55/181.52 ! [V_Pa_2,V_xs_2,T_b] : % 181.55/181.52 ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 181.55/181.52 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all__simps_I1_J,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 181.55/181.52 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__all__iff__raw,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex1__simps_I2_J,axiom, % 181.55/181.52 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 181.55/181.52 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => 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) ) % 181.55/181.52 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 181.55/181.52 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_internal__split__def,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_exists1__code,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : % 181.55/181.52 ( class_Enum_Oenum(T_b) % 181.55/181.52 => ( ? [B_x] : % 181.55/181.52 ( hBOOL(hAPP(V_Pa_2,B_x)) % 181.55/181.52 & ! [B_y] : % 181.55/181.52 ( hBOOL(hAPP(V_Pa_2,B_y)) % 181.55/181.52 => B_y = B_x ) ) % 181.55/181.52 <=> c_List_Olist__ex1(T_b,V_Pa_2,c_Enum_Oenum__class_Oenum(T_b)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex1__simps_I1_J,axiom, % 181.55/181.52 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_internal__split__conv,axiom, % 181.55/181.52 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ). % 181.55/181.52 % 181.55/181.52 fof(fact_list__ex1__iff,axiom, % 181.55/181.52 ! [V_xs_2,V_Pa_2,T_b] : % 181.55/181.52 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 181.55/181.52 <=> ? [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 & hBOOL(hAPP(V_Pa_2,B_x)) % 181.55/181.52 & ! [B_y] : % 181.55/181.52 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 181.55/181.52 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 181.55/181.52 => B_y = B_x ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_setprod__nonneg,axiom, % 181.55/181.52 ! [V_f_2,V_A_2,T_b,T_c] : % 181.55/181.52 ( class_Rings_Olinordered__semidom(T_c) % 181.55/181.52 => ( ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 181.55/181.52 => 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))) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_bool_Osize_I2_J,axiom, % 181.55/181.52 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(fact_bool_Osize_I1_J,axiom, % 181.55/181.52 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(fact_finite__less__ub,axiom, % 181.55/181.52 ! [V_u_2,V_f_2] : % 181.55/181.52 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 181.55/181.52 => 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)))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_finite__induct,axiom, % 181.55/181.52 ! [V_Pa_2,V_F_2,T_b] : % 181.55/181.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 181.55/181.52 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 181.55/181.52 => ( ! [B_x,B_F] : % 181.55/181.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 181.55/181.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F)) % 181.55/181.52 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) ) % 181.55/181.52 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_measure__function__int,axiom, % 181.55/181.52 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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_equal__fun__def,axiom, % 181.55/181.52 ! [V_g_2,V_f_2,T_b,T_c] : % 181.55/181.52 ( ( class_HOL_Oequal(T_c) % 181.55/181.52 & class_Enum_Oenum(T_b) ) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 181.55/181.52 <=> ! [B_x] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)))) % 181.55/181.52 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_measure__size,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( class_Nat_Osize(T_b) % 181.55/181.52 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_is__measure_Ointros,axiom, % 181.55/181.52 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ). % 181.55/181.52 % 181.55/181.52 fof(fact_is__measure_Oequations,axiom, % 181.55/181.52 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 181.55/181.52 % 181.55/181.52 fof(fact_is__measure_Osimps,axiom, % 181.55/181.52 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 181.55/181.52 % 181.55/181.52 fof(fact_equal,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( class_HOL_Oequal(T_b) % 181.55/181.52 => c_HOL_Oequal__class_Oequal(T_b) = c_fequal ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_equal__refl,axiom, % 181.55/181.52 ! [V_x,T_a] : % 181.55/181.52 ( class_HOL_Oequal(T_a) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_equal__eq,axiom, % 181.55/181.52 ! [V_y_2,V_x_2,T_b] : % 181.55/181.52 ( class_HOL_Oequal(T_b) % 181.55/181.52 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2)) % 181.55/181.52 <=> V_x_2 = V_y_2 ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__equal,axiom, % 181.55/181.52 ! [T_b] : % 181.55/181.52 ( class_HOL_Oequal(T_b) % 181.55/181.52 => c_fequal = c_HOL_Oequal__class_Oequal(T_b) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_measure__snd,axiom, % 181.55/181.52 ! [T_c,V_f_2,T_b] : % 181.55/181.52 ( c_FunDef_Ois__measure(T_b,V_f_2) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_measure__fst,axiom, % 181.55/181.52 ! [T_c,V_f_2,T_b] : % 181.55/181.52 ( c_FunDef_Ois__measure(T_b,V_f_2) % 181.55/181.52 => 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_transfer__morphism__int__nat,axiom, % 181.55/181.52 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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 181.55/181.52 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 181.55/181.52 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.55/181.52 => 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) ) % 181.55/181.52 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.55/181.52 => 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I5_J,axiom, % 181.55/181.52 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I2_J,axiom, % 181.55/181.52 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I8_J,axiom, % 181.55/181.52 ! [V_k2_2] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I12_J,axiom, % 181.55/181.52 ! [V_k1_2] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I6_J,axiom, % 181.55/181.52 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I13_J,axiom, % 181.55/181.52 ! [V_k2_2,V_k1_2] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I16_J,axiom, % 181.55/181.52 ! [V_k2_2,V_k1_2] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I1_J,axiom, % 181.55/181.52 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__number__of__int__code,axiom, % 181.55/181.52 ! [V_l_2,V_k_2] : % 181.55/181.52 ( 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))) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_equal__int__def,axiom, % 181.55/181.52 ! [V_l_2,V_k_2] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 181.55/181.52 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I14_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I15_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I3_J,axiom, % 181.55/181.52 ! [V_k2_2] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I9_J,axiom, % 181.55/181.52 ! [V_k1_2] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I4_J,axiom, % 181.55/181.52 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I10_J,axiom, % 181.55/181.52 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I7_J,axiom, % 181.55/181.52 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__code_I11_J,axiom, % 181.55/181.52 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_bool_Osize_I4_J,axiom, % 181.55/181.52 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(fact_bool_Osize_I3_J,axiom, % 181.55/181.52 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_eq__int__refl,axiom, % 181.55/181.52 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_neg__bind__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_size__code,axiom, % 181.55/181.52 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = hAPP(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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_lazy__sequence__size__code,axiom, % 181.55/181.52 ! [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) = hAPP(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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_seq__case,axiom, % 181.55/181.52 ! [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) = hAPP(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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_yieldn__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_lazy__sequence_Oinject,axiom, % 181.55/181.52 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] : % 181.55/181.52 ( 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) % 181.55/181.52 <=> ( V_a_2 = V_a_H_2 % 181.55/181.52 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact__01,axiom, % 181.55/181.52 ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_neg__map__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 181.55/181.52 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 181.55/181.52 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.55/181.52 => 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) ) % 181.55/181.52 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 181.55/181.52 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = 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)) ) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_neg__single__def,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_New__DSequence_Oneg__single__def,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_New__DSequence_Opos__empty__def,axiom, % 181.55/181.52 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 181.55/181.52 % 181.55/181.52 fof(fact_pos__empty__def,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_New__DSequence_Opos__bind__def,axiom, % 181.55/181.52 ! [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) = 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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_pos__bind__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__splice,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_splice_Osimps_I1_J,axiom, % 181.55/181.52 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 181.55/181.52 % 181.55/181.52 fof(fact_splice__Nil2,axiom, % 181.55/181.52 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 181.55/181.52 % 181.55/181.52 fof(fact_splice_Osimps_I3_J,axiom, % 181.55/181.52 ! [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))) ). % 181.55/181.52 % 181.55/181.52 fof(fact_splice_Osimps_I2_J,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_pos__map__def,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_acyclicP__converse,axiom, % 181.55/181.52 ! [V_r_2,T_b] : % 181.55/181.52 ( 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)))) % 181.55/181.52 <=> 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_converse__meet,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_converse__join,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_conversep__noteq,axiom, % 181.55/181.52 ! [V_y_2,V_x_2,T_b] : % 181.55/181.52 ( 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)) % 181.55/181.52 <=> V_x_2 != V_y_2 ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_conversepD,axiom, % 181.55/181.52 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) % 181.55/181.52 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_conversep_Ointros,axiom, % 181.55/181.52 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 181.55/181.52 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_conversep_Oequations,axiom, % 181.55/181.52 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2)) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_conversep__iff,axiom, % 181.55/181.52 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] : % 181.55/181.52 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) % 181.55/181.52 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_conversep__conversep,axiom, % 181.55/181.52 ! [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 ). % 181.55/181.52 % 181.55/181.52 fof(fact_conversep__eq,axiom, % 181.55/181.52 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ). % 181.55/181.52 % 181.55/181.52 fof(fact_converse__pred__comp,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(fact_conversep__converse__eq,axiom, % 181.55/181.52 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] : % 181.55/181.52 ( 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)) % 181.55/181.52 <=> 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))) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_pos__single__def,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_tl__replicate,axiom, % 181.55/181.52 ! [V_x,T_a,V_n] : % 181.55/181.52 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 181.55/181.52 => 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) ) ). % 181.55/181.52 % 181.55/181.52 fof(fact_replicate__length__filter,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(fact_length__replicate,axiom, % 181.55/181.52 ! [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 ). % 181.55/181.52 % 181.55/181.52 %----Arity declarations (233) % 181.55/181.52 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 181.55/181.52 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Lattices_Obounded__lattice(T_1) % 181.55/181.52 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 181.55/181.52 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Lattices_Obounded__lattice(T_1) % 181.55/181.52 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Lattices_Obounded__lattice(T_1) % 181.55/181.52 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Lattices_Olattice(T_1) % 181.55/181.52 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Lattices_Olattice(T_1) % 181.55/181.52 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Lattices_Odistrib__lattice(T_1) % 181.55/181.52 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Lattices_Oboolean__algebra(T_1) % 181.55/181.52 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Orderings_Opreorder,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Orderings_Opreorder(T_1) % 181.55/181.52 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Finite__Set_Ofinite,axiom, % 181.55/181.52 ! [T_1,T_2] : % 181.55/181.52 ( ( class_Finite__Set_Ofinite(T_2) % 181.55/181.52 & class_Finite__Set_Ofinite(T_1) ) % 181.55/181.52 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Lattices_Olattice,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Lattices_Olattice(T_1) % 181.55/181.52 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Orderings_Oorder,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Orderings_Oorder(T_1) % 181.55/181.52 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Orderings_Otop,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Orderings_Otop(T_1) % 181.55/181.52 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Orderings_Oord,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Orderings_Oord(T_1) % 181.55/181.52 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Orderings_Obot,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Orderings_Obot(T_1) % 181.55/181.52 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Groups_Ouminus,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Groups_Ouminus(T_1) % 181.55/181.52 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Groups_Ominus,axiom, % 181.55/181.52 ! [T_2,T_1] : % 181.55/181.52 ( class_Groups_Ominus(T_1) % 181.55/181.52 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__HOL_Oequal,axiom, % 181.55/181.52 ! [T_1,T_2] : % 181.55/181.52 ( ( class_Enum_Oenum(T_2) % 181.55/181.52 & class_HOL_Oequal(T_1) ) % 181.55/181.52 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_fun__Enum_Oenum,axiom, % 181.55/181.52 ! [T_1,T_2] : % 181.55/181.52 ( ( class_Enum_Oenum(T_2) % 181.55/181.52 & class_Enum_Oenum(T_1) ) % 181.55/181.52 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_Com_Ocom) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Com__Ocom__Nat_Osize,axiom, % 181.55/181.52 class_Nat_Osize(tc_Com_Ocom) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 181.55/181.52 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 181.55/181.52 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 181.55/181.52 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 181.55/181.52 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 181.55/181.52 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 181.55/181.52 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 181.55/181.52 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 181.55/181.52 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 181.55/181.52 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 181.55/181.52 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 181.55/181.52 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 181.55/181.52 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 181.55/181.52 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 181.55/181.52 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 181.55/181.52 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 181.55/181.52 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 181.55/181.52 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 181.55/181.52 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 181.55/181.52 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 181.55/181.52 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 181.55/181.52 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 181.55/181.52 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 181.55/181.52 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 181.55/181.52 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 181.55/181.52 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 181.55/181.52 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 181.55/181.52 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 181.55/181.52 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 181.55/181.52 class_Divides_Osemiring__div(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 181.55/181.52 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 181.55/181.52 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 181.55/181.52 class_Groups_Oab__group__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 181.55/181.52 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 181.55/181.52 class_Rings_Oordered__ring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 181.55/181.52 class_Orderings_Opreorder(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 181.55/181.52 class_Orderings_Olinorder(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 181.55/181.52 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 181.55/181.52 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 181.55/181.52 class_Groups_Omonoid__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 181.55/181.52 class_Smallcheck_Osmall(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 181.55/181.52 class_Rings_Osemiring__1(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 181.55/181.52 class_Rings_Osemiring__0(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 181.55/181.52 class_Lattices_Olattice(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 181.55/181.52 class_Groups_Ogroup__add(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 181.55/181.52 class_Divides_Oring__div(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 181.55/181.52 class_Rings_Omult__zero(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 181.55/181.52 class_Orderings_Oorder(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 181.55/181.52 class_Int_Oring__char__0(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 181.55/181.52 class_Int_Onumber__ring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 181.55/181.52 class_Rings_Osemiring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Orderings_Oord,axiom, % 181.55/181.52 class_Orderings_Oord(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 181.55/181.52 class_Groups_Ouminus(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 181.55/181.52 class_Groups_Osgn__if(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 181.55/181.52 class_Groups_Oabs__if(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 181.55/181.52 class_Rings_Oring__1(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Ominus,axiom, % 181.55/181.52 class_Groups_Ominus(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Power_Opower,axiom, % 181.55/181.52 class_Power_Opower(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Ozero,axiom, % 181.55/181.52 class_Groups_Ozero(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oring,axiom, % 181.55/181.52 class_Rings_Oring(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Rings_Oidom,axiom, % 181.55/181.52 class_Rings_Oidom(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Int_Onumber,axiom, % 181.55/181.52 class_Int_Onumber(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__Groups_Oone,axiom, % 181.55/181.52 class_Groups_Oone(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Int__Oint__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_Int_Oint) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 181.55/181.52 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 181.55/181.52 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 181.55/181.52 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 181.55/181.52 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 181.55/181.52 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 181.55/181.52 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 181.55/181.52 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 181.55/181.52 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 181.55/181.52 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 181.55/181.52 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 181.55/181.52 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 181.55/181.52 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 181.55/181.52 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 181.55/181.52 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 181.55/181.52 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 181.55/181.52 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 181.55/181.52 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 181.55/181.52 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 181.55/181.52 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 181.55/181.52 class_Orderings_Owellorder(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 181.55/181.52 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 181.55/181.52 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 181.55/181.52 class_Orderings_Opreorder(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 181.55/181.52 class_Orderings_Olinorder(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 181.55/181.52 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 181.55/181.52 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 181.55/181.52 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 181.55/181.52 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 181.55/181.52 class_Lattices_Olattice(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 181.55/181.52 class_Rings_Omult__zero(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 181.55/181.52 class_Orderings_Oorder(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 181.55/181.52 class_Rings_Osemiring(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 181.55/181.52 class_Orderings_Oord(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 181.55/181.52 class_Orderings_Obot(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 181.55/181.52 class_Groups_Ominus(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Power_Opower,axiom, % 181.55/181.52 class_Power_Opower(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 181.55/181.52 class_Groups_Ozero(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Int_Onumber,axiom, % 181.55/181.52 class_Int_Onumber(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Groups_Oone,axiom, % 181.55/181.52 class_Groups_Oone(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Nat__Onat__Nat_Osize,axiom, % 181.55/181.52 class_Nat_Osize(tc_Nat_Onat) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 181.55/181.52 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 181.55/181.52 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 181.55/181.52 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 181.55/181.52 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 181.55/181.52 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 181.55/181.52 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 181.55/181.52 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 181.55/181.52 class_Orderings_Opreorder(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 181.55/181.52 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 181.55/181.52 class_Lattices_Olattice(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 181.55/181.52 class_Orderings_Oorder(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 181.55/181.52 class_Orderings_Otop(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 181.55/181.52 class_Orderings_Oord(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 181.55/181.52 class_Orderings_Obot(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 181.55/181.52 class_Groups_Ouminus(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 181.55/181.52 class_Groups_Ominus(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 181.55/181.52 class_Enum_Oenum(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_HOL__Obool__Nat_Osize,axiom, % 181.55/181.52 class_Nat_Osize(tc_HOL_Obool) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_Com_Ostate) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Com__Ostate__Nat_Osize,axiom, % 181.55/181.52 class_Nat_Osize(tc_Com_Ostate) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Com__Ovname__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_Com_Ovname) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Com__Ovname__Nat_Osize,axiom, % 181.55/181.52 class_Nat_Osize(tc_Com_Ovname) ). % 181.55/181.52 % 181.55/181.52 fof(arity_List__Olist__HOL_Oequal,axiom, % 181.55/181.52 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_List__Olist__Nat_Osize,axiom, % 181.55/181.52 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_sum__Finite__Set_Ofinite,axiom, % 181.55/181.52 ! [T_1,T_2] : % 181.55/181.52 ( ( class_Finite__Set_Ofinite(T_2) % 181.55/181.52 & class_Finite__Set_Ofinite(T_1) ) % 181.55/181.52 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_sum__HOL_Oequal,axiom, % 181.55/181.52 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_sum__Enum_Oenum,axiom, % 181.55/181.52 ! [T_1,T_2] : % 181.55/181.52 ( ( class_Enum_Oenum(T_2) % 181.55/181.52 & class_Enum_Oenum(T_1) ) % 181.55/181.52 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_sum__Nat_Osize,axiom, % 181.55/181.52 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 181.55/181.52 ! [T_1] : % 181.55/181.52 ( class_Finite__Set_Ofinite(T_1) % 181.55/181.52 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 181.55/181.52 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 181.55/181.52 ! [T_1] : % 181.55/181.52 ( class_Enum_Oenum(T_1) % 181.55/181.52 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Option__Ooption__Nat_Osize,axiom, % 181.55/181.52 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_prod__Finite__Set_Ofinite,axiom, % 181.55/181.52 ! [T_1,T_2] : % 181.55/181.52 ( ( class_Finite__Set_Ofinite(T_2) % 181.55/181.52 & class_Finite__Set_Ofinite(T_1) ) % 181.55/181.52 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_prod__Smallcheck_Osmall,axiom, % 181.55/181.52 ! [T_1,T_2] : % 181.55/181.52 ( ( class_Smallcheck_Osmall(T_2) % 181.55/181.52 & class_Smallcheck_Osmall(T_1) ) % 181.55/181.52 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_prod__HOL_Oequal,axiom, % 181.55/181.52 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_prod__Enum_Oenum,axiom, % 181.55/181.52 ! [T_1,T_2] : % 181.55/181.52 ( ( class_Enum_Oenum(T_2) % 181.55/181.52 & class_Enum_Oenum(T_1) ) % 181.55/181.52 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 181.55/181.52 % 181.55/181.52 fof(arity_prod__Nat_Osize,axiom, % 181.55/181.52 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 181.55/181.52 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 181.55/181.52 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 181.55/181.52 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 181.55/181.52 class_Nat_Osize(tc_Product__Type_Ounit) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 181.55/181.52 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 181.55/181.52 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 181.55/181.52 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 181.55/181.52 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 181.55/181.52 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 181.55/181.52 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 181.55/181.52 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 181.55/181.52 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 181.55/181.52 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 181.55/181.52 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 181.55/181.52 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 181.55/181.52 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 181.55/181.52 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 181.55/181.52 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 181.55/181.52 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 181.55/181.52 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 181.55/181.52 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 181.55/181.52 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 181.55/181.52 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 181.55/181.52 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 181.55/181.52 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 181.55/181.52 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 181.55/181.52 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 181.55/181.52 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 181.55/181.52 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 181.55/181.52 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 181.55/181.52 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 181.55/181.52 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 181.55/181.52 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 181.55/181.52 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 181.55/181.52 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 181.55/181.52 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 181.55/181.52 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 181.55/181.52 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 181.55/181.52 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 181.55/181.52 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 181.55/181.52 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 181.55/181.52 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 181.55/181.52 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 181.55/181.52 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 181.55/181.52 % 181.55/181.52 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 181.55/181.52 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 181.55/181.52 % 181.55/181.52 %----Helper facts (20) % 181.55/181.52 fof(help_c__COMBI__1,axiom, % 181.55/181.52 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 181.55/181.52 % 181.55/181.52 fof(help_c__COMBK__1,axiom, % 181.55/181.52 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 181.55/181.52 % 181.55/181.52 fof(help_c__COMBB__1,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__COMBC__1,axiom, % 181.55/181.52 ! [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) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__COMBS__1,axiom, % 181.55/181.52 ! [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)) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fequal__1,axiom, % 181.55/181.52 ! [V_y_2,V_x_2] : % 181.55/181.52 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 181.55/181.52 | V_x_2 = V_y_2 ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fequal__2,axiom, % 181.55/181.52 ! [V_y_2,V_x_2] : % 181.55/181.52 ( V_x_2 != V_y_2 % 181.55/181.52 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fFalse__1,axiom, % 181.55/181.52 ~ hBOOL(c_fFalse) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fTrue__1,axiom, % 181.55/181.52 hBOOL(c_fTrue) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fNot__1,axiom, % 181.55/181.52 ! [V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 181.55/181.52 | ~ hBOOL(V_Pa_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fNot__2,axiom, % 181.55/181.52 ! [V_Pa_2] : % 181.55/181.52 ( ~ ~ hBOOL(V_Pa_2) % 181.55/181.52 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fconj__1,axiom, % 181.55/181.52 ! [V_Qa_2,V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(V_Pa_2) % 181.55/181.52 | ~ hBOOL(V_Qa_2) % 181.55/181.52 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fconj__2,axiom, % 181.55/181.52 ! [V_Qa_2,V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) % 181.55/181.52 | hBOOL(V_Pa_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fconj__3,axiom, % 181.55/181.52 ! [V_Qa_2,V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) % 181.55/181.52 | hBOOL(V_Qa_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fdisj__1,axiom, % 181.55/181.52 ! [V_Qa_2,V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(V_Pa_2) % 181.55/181.52 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fdisj__2,axiom, % 181.55/181.52 ! [V_Pa_2,V_Qa_2] : % 181.55/181.52 ( ~ hBOOL(V_Qa_2) % 181.55/181.52 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fdisj__3,axiom, % 181.55/181.52 ! [V_Qa_2,V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) % 181.55/181.52 | hBOOL(V_Pa_2) % 181.55/181.52 | hBOOL(V_Qa_2) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fimplies__1,axiom, % 181.55/181.52 ! [V_Qa_2,V_Pa_2] : % 181.55/181.52 ( hBOOL(V_Pa_2) % 181.55/181.52 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fimplies__2,axiom, % 181.55/181.52 ! [V_Pa_2,V_Qa_2] : % 181.55/181.52 ( ~ hBOOL(V_Qa_2) % 181.55/181.52 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ). % 181.55/181.52 % 181.55/181.52 fof(help_c__fimplies__3,axiom, % 181.55/181.52 ! [V_Qa_2,V_Pa_2] : % 181.55/181.52 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) % 181.55/181.52 | ~ hBOOL(V_Pa_2) % 181.55/181.52 | hBOOL(V_Qa_2) ) ). % 181.55/181.52 % 181.55/181.52 %----Conjectures (3) % 181.55/181.52 fof(conj_0,hypothesis, % 181.55/181.52 hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_Procs)) ). % 181.55/181.52 % 181.55/181.52 fof(conj_1,hypothesis, % 181.55/181.52 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(hAPP(c_COMBB(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(t_a)),v_P)),c_Com_Ocom_OBODY)),v_Q)),v_Procs)) ). % 181.55/181.52 % 181.55/181.52 fof(conj_2,conjecture, % 181.55/181.52 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ). % 181.55/181.52 % 181.55/181.52 %------------------------------------------------------------------------------ % 181.55/181.52 %------------------------------------------- % 181.55/181.52 % Proof found % 181.55/181.52 % SZS status Theorem for theBenchmark % 181.55/181.52 % SZS output start Proof % 181.55/181.52 %ClaNum:10144(EqnAxiom:2858) % 181.55/181.52 %VarNum:70026(SingletonVarNum:20442) % 181.55/181.52 %MaxLitNum:8 % 181.55/181.52 %MaxfuncDepth:13 % 181.55/181.52 %SharedTerms:1063 % 181.55/181.53 %goalClause: 4562 % 181.55/181.53 %singleGoalClaCount:1 % 181.55/181.53 [2862]P1(a188) % 181.55/181.53 [2863]P2(a859) % 181.55/181.53 [2864]P2(a865) % 181.55/181.53 [2865]P3(a859) % 181.55/181.53 [2866]P3(a865) % 181.55/181.53 [2867]P3(a1) % 181.55/181.53 [2868]P3(a102) % 181.55/181.53 [2869]P103(a859) % 181.55/181.53 [2870]P103(a865) % 181.55/181.53 [2871]P103(a1) % 181.55/181.53 [2872]P103(a102) % 181.55/181.53 [2873]P107(a859) % 181.55/181.53 [2874]P104(a859) % 181.55/181.53 [2875]P104(a865) % 181.55/181.53 [2876]P104(a1) % 181.55/181.53 [2877]P104(a102) % 181.55/181.53 [2878]P105(a865) % 181.55/181.53 [2879]P105(a1) % 181.55/181.53 [2880]P105(a102) % 181.55/181.53 [2881]P106(a859) % 181.55/181.53 [2882]P106(a865) % 181.55/181.53 [2883]P106(a1) % 181.55/181.53 [2884]P106(a102) % 181.55/181.53 [2885]P75(a1) % 181.55/181.53 [2886]P79(a859) % 181.55/181.53 [2887]P80(a859) % 181.55/181.53 [2888]P80(a1) % 181.55/181.53 [2889]P4(a1) % 181.55/181.53 [2890]P5(a1) % 181.55/181.53 [2891]P6(a859) % 181.55/181.53 [2892]P94(a859) % 181.55/181.53 [2893]P94(a865) % 181.55/181.53 [2894]P94(a1) % 181.55/181.53 [2895]P99(a859) % 181.55/181.53 [2896]P99(a865) % 181.55/181.53 [2897]P99(a1) % 181.55/181.53 [2898]P95(a859) % 181.55/181.53 [2899]P97(a859) % 181.55/181.53 [2900]P100(a859) % 181.55/181.53 [2901]P100(a865) % 181.55/181.53 [2902]P100(a1) % 181.55/181.53 [2903]P98(a859) % 181.55/181.53 [2904]P98(a865) % 181.55/181.53 [2905]P98(a1) % 181.55/181.53 [2906]P66(a865) % 181.55/181.53 [2907]P66(a1) % 181.55/181.53 [2908]P66(a102) % 181.55/181.53 [2909]P108(a1) % 181.55/181.53 [2910]P116(a1) % 181.55/181.53 [2911]P58(a859) % 181.55/181.53 [2912]P58(a868) % 181.55/181.53 [2913]P117(a1) % 181.55/181.53 [2914]P76(a865) % 181.55/181.53 [2915]P76(a1) % 181.55/181.53 [2916]P76(a102) % 181.55/181.53 [2917]P77(a865) % 181.55/181.53 [2918]P77(a1) % 181.55/181.53 [2919]P77(a102) % 181.55/181.53 [2920]P68(a865) % 181.55/181.53 [2921]P68(a1) % 181.55/181.53 [2922]P68(a102) % 181.55/181.53 [2923]P120(a865) % 181.55/181.53 [2924]P120(a1) % 181.55/181.53 [2925]P120(a102) % 181.55/181.53 [2926]P134(a1) % 181.55/181.53 [2927]P109(a1) % 181.55/181.53 [2928]P112(a865) % 181.55/181.53 [2929]P112(a1) % 181.55/181.53 [2930]P112(a102) % 181.55/181.53 [2931]P136(a865) % 181.55/181.53 [2932]P136(a1) % 181.55/181.53 [2933]P69(a865) % 181.55/181.53 [2934]P69(a1) % 181.55/181.53 [2935]P69(a102) % 181.55/181.53 [2936]P70(a865) % 181.55/181.53 [2937]P70(a1) % 181.55/181.53 [2938]P70(a102) % 181.55/181.53 [2939]P67(a865) % 181.55/181.53 [2940]P67(a1) % 181.55/181.53 [2941]P67(a102) % 181.55/181.53 [2942]P81(a865) % 181.55/181.53 [2943]P81(a1) % 181.55/181.53 [2944]P81(a102) % 181.55/181.53 [2945]P82(a865) % 181.55/181.53 [2946]P82(a1) % 181.55/181.53 [2947]P82(a102) % 181.55/181.53 [2948]P84(a865) % 181.55/181.53 [2949]P84(a1) % 181.55/181.53 [2950]P84(a102) % 181.55/181.53 [2951]P137(a865) % 181.55/181.53 [2952]P137(a1) % 181.55/181.53 [2953]P137(a102) % 181.55/181.53 [2954]P113(a865) % 181.55/181.53 [2955]P113(a1) % 181.55/181.53 [2956]P113(a102) % 181.55/181.53 [2957]P123(a1) % 181.55/181.53 [2958]P73(a865) % 181.55/181.53 [2959]P73(a1) % 181.55/181.53 [2960]P73(a102) % 181.55/181.53 [2961]P74(a1) % 181.55/181.53 [2962]P88(a865) % 181.55/181.53 [2963]P88(a1) % 181.55/181.53 [2964]P88(a102) % 181.55/181.53 [2965]P72(a865) % 181.55/181.53 [2966]P72(a1) % 181.55/181.53 [2967]P72(a102) % 181.55/181.53 [2968]P78(a865) % 181.55/181.53 [2969]P78(a1) % 181.55/181.53 [2970]P78(a102) % 181.55/181.53 [2971]P124(a865) % 181.55/181.53 [2972]P124(a1) % 181.55/181.53 [2973]P124(a102) % 181.55/181.53 [2974]P138(a1) % 181.55/181.53 [2975]P125(a865) % 181.55/181.53 [2976]P125(a1) % 181.55/181.53 [2977]P125(a102) % 181.55/181.53 [2978]P139(a865) % 181.55/181.53 [2979]P139(a1) % 181.55/181.53 [2980]P139(a102) % 181.55/181.53 [2981]P85(a865) % 181.55/181.53 [2982]P85(a1) % 181.55/181.53 [2983]P85(a102) % 181.55/181.53 [2984]P130(a865) % 181.55/181.53 [2985]P130(a1) % 181.55/181.53 [2986]P130(a102) % 181.55/181.53 [2987]P132(a865) % 181.55/181.53 [2988]P132(a1) % 181.55/181.53 [2989]P132(a102) % 181.55/181.53 [2990]P131(a865) % 181.55/181.53 [2991]P131(a1) % 181.55/181.53 [2992]P131(a102) % 181.55/181.53 [2993]P121(a1) % 181.55/181.53 [2994]P122(a1) % 181.55/181.53 [2995]P118(a865) % 181.55/181.53 [2996]P118(a1) % 181.55/181.53 [2997]P118(a102) % 181.55/181.53 [2998]P126(a865) % 181.55/181.53 [2999]P126(a1) % 181.55/181.53 [3000]P126(a102) % 181.55/181.53 [3001]P127(a865) % 181.55/181.53 [3002]P127(a1) % 181.55/181.53 [3003]P127(a102) % 181.55/181.53 [3004]P128(a1) % 181.55/181.53 [3005]P129(a1) % 181.55/181.53 [3006]P135(a1) % 181.55/181.53 [3007]P89(a1) % 181.55/181.53 [3008]P110(a865) % 181.55/181.53 [3009]P110(a1) % 181.55/181.53 [3010]P110(a102) % 181.55/181.53 [3011]P140(a865) % 181.55/181.53 [3012]P140(a1) % 181.55/181.53 [3013]P140(a102) % 181.55/181.53 [3014]P59(a865) % 181.55/181.53 [3015]P59(a1) % 181.55/181.53 [3016]P59(a102) % 181.55/181.53 [3017]P60(a1) % 181.55/181.53 [3018]P90(a865) % 181.55/181.53 [3019]P90(a1) % 181.55/181.53 [3020]P90(a102) % 181.55/181.53 [3021]P92(a1) % 181.55/181.53 [3022]P141(a865) % 181.55/181.53 [3023]P141(a1) % 181.55/181.53 [3024]P141(a102) % 181.55/181.53 [3025]P101(a865) % 181.55/181.53 [3026]P101(a1) % 181.55/181.53 [3027]P101(a102) % 181.55/181.53 [3028]P86(a1) % 181.55/181.53 [3029]P83(a1) % 181.55/181.53 [3030]P133(a1) % 181.55/181.53 [3031]P71(a1) % 181.55/181.53 [3032]P111(a865) % 181.55/181.53 [3033]P142(a868) % 181.55/181.53 [3034]P142(a1) % 181.55/181.53 [3035]P87(a865) % 181.55/181.53 [3036]P87(a1) % 181.55/181.53 [3037]P87(a102) % 181.55/181.53 [3038]P61(a859) % 181.55/181.53 [3039]P61(a868) % 181.55/181.53 [3040]P91(a859) % 181.55/181.53 [3041]P91(a860) % 181.55/181.53 [3042]P91(a865) % 181.55/181.53 [3043]P91(a863) % 181.55/181.53 [3044]P91(a868) % 181.55/181.53 [3045]P91(a1) % 181.55/181.53 [3046]P91(a861) % 181.55/181.53 [3047]P91(a102) % 181.55/181.53 [3048]P91(a320) % 181.55/181.53 [3049]P102(a859) % 181.55/181.53 [3050]P102(a860) % 181.55/181.53 [3051]P102(a865) % 181.55/181.53 [3052]P102(a863) % 181.55/181.53 [3053]P102(a868) % 181.55/181.53 [3054]P102(a861) % 181.55/181.53 [3055]P102(a102) % 181.55/181.53 [3056]P102(a320) % 181.55/181.53 [3057]P96(a859) % 181.55/181.53 [3077]P39(a865,a243) % 181.55/181.53 [3078]P39(a865,a314) % 181.55/181.53 [4443]~E(a100,a84) % 181.55/181.53 [4444]~P1(a242) % 181.55/181.53 [2859]E(f2(a1),a84) % 181.55/181.53 [2860]E(f103(a102),a3) % 181.55/181.53 [2861]E(f22(a102),a23) % 181.55/181.53 [3058]E(f104(a865),f189(a865)) % 181.55/181.53 [3059]E(f113(a865),f190(a865)) % 181.55/181.53 [3060]E(f191(a865),f2(a865)) % 181.55/181.53 [3061]E(f31(a24),f2(a865)) % 181.55/181.53 [3062]E(f105(a1),f34(a1)) % 181.55/181.53 [3063]E(f85(a242),f2(a865)) % 181.55/181.53 [3064]E(f85(a188),f2(a865)) % 181.55/181.53 [3065]P7(f79(a1)) % 181.55/181.53 [3066]P7(f2(a1)) % 181.55/181.53 [3127]P39(f870(a865,a865),a35) % 181.55/181.53 [3477]E(f316(a865,a865,a243,a243),a35) % 181.55/181.53 [4445]~E(f79(a1),f2(a1)) % 181.55/181.53 [3067]E(f114(f2(a865)),f2(a865)) % 181.55/181.53 [3068]E(f4(f2(a102)),f2(a865)) % 181.55/181.53 [3080]E(f324(f80(a1),a84),a84) % 181.55/181.53 [3083]E(f324(a115,f2(a865)),f79(a865)) % 181.55/181.53 [3084]E(f324(a107,f79(a1)),f79(a865)) % 181.55/181.53 [3085]E(f324(a3,f79(a865)),f79(a102)) % 181.55/181.53 [3087]E(f324(a3,f2(a865)),f2(a102)) % 181.55/181.53 [3089]E(f324(f106(a1),a84),f2(a1)) % 181.55/181.53 [3090]E(f324(f106(a102),a84),f2(a102)) % 181.55/181.53 [3091]E(f324(a107,f2(a1)),f2(a865)) % 181.55/181.53 [3092]E(f324(f192(a859),a242),f2(a865)) % 181.55/181.53 [3093]E(f324(f192(a859),a188),f2(a865)) % 181.55/181.53 [3094]E(f324(f192(a861),a24),f2(a865)) % 181.55/181.53 [3095]E(f324(f106(a865),a84),f2(a865)) % 181.55/181.53 [3099]E(f324(f80(a1),f79(a1)),a100) % 181.55/181.53 [3106]E(f324(f80(a1),f2(a1)),f2(a1)) % 181.55/181.53 [3108]E(f324(f192(a102),f2(a102)),f2(a865)) % 181.55/181.53 [3109]E(f324(f103(a1),f79(a865)),f79(a1)) % 181.55/181.53 [3110]E(f324(f103(a1),f2(a865)),f2(a1)) % 181.55/181.53 [3122]E(f324(a107,f79(a1)),f324(a115,f2(a865))) % 181.55/181.53 [3124]E(f315(f870(a865,a865),a35),a36) % 181.55/181.53 [3125]E(f317(f870(a865,a865),a35),a68) % 181.55/181.53 [3126]E(f324(f173(a862,a861),a27),a28) % 181.55/181.53 [3148]E(f324(f245(a865),f2(a865)),f191(f871(a865,a859))) % 181.55/181.53 [3149]E(f324(f246(a865),f2(a865)),f247(f871(a865,a859))) % 181.55/181.53 [3158]P40(f191(f871(a1,a859))) % 181.55/181.53 [3194]E(f324(f324(f22(a102),f2(a102)),f79(a102)),f2(a102)) % 181.55/181.53 [3271]P1(f324(f324(f239(a1),a100),f2(a1))) % 181.55/181.53 [3296]P1(f324(f324(f238(a1),f2(a1)),f79(a1))) % 181.55/181.53 [3298]P1(f324(f324(f239(a1),f2(a1)),f79(a1))) % 181.55/181.53 [3470]P1(f324(f61(a862),f179(a862,a861,a28))) % 181.55/181.53 [3507]E(f324(f324(f281(a865,a865,a865),a314),f300(a865,a314)),a243) % 181.55/181.53 [3545]P42(a1,a865,a107,f324(f238(a1),f2(a1))) % 181.55/181.53 [3549]E(f324(f324(f41(a865,f871(a865,a859)),f247(f871(a865,a859))),f245(a865)),f247(f871(a865,a859))) % 181.55/181.53 [3550]E(f324(f324(f41(a865,f871(a865,a859)),f247(f871(a865,a859))),f293(a865)),f247(f871(a865,a859))) % 181.55/181.53 [3551]E(f324(f324(f41(a865,f871(a865,a859)),f247(f871(a865,a859))),f246(a865)),f247(f871(a865,a859))) % 181.55/181.53 [3552]E(f324(f324(f42(a865,f871(a865,a859)),f247(f871(a865,a859))),f296(a865)),f191(f871(a865,a859))) % 181.55/181.53 [3568]P27(a865,a1,f103(a1),f247(f871(a865,a859))) % 181.55/181.53 [3580]P42(a865,a1,f103(a1),f324(f16(a859,a865),a188)) % 181.55/181.53 [3713]E(f324(f73(a865,a102,a1,a3),a107),f106(a102)) % 181.55/181.53 [3936]P54(a102,a865,a19,a3,f247(f871(a865,a859))) % 181.55/181.53 [3945]P54(a1,f871(f870(a865,a865),a859),a110,a90,a101) % 181.55/181.53 [4216]E(f264(a1,a1,a1,a1,f34(a1),f80(a1)),a50) % 181.55/181.53 [4476]~E(f324(f106(a1),a100),f324(f106(a1),a84)) % 181.55/181.53 [4477]~P1(f324(a196,f79(a1))) % 181.55/181.53 [4478]~P1(f324(a196,f2(a1))) % 181.55/181.53 [4523]~P1(f324(f324(f239(a1),a84),f2(a1))) % 181.55/181.53 [3140]E(f324(f324(f22(a1),a100),a100),a84) % 181.55/181.53 [3156]E(f324(f103(a1),f324(a115,f2(a865))),f79(a1)) % 181.55/181.53 [3221]E(f324(f37(a868),f247(f871(a868,a859))),f79(a865)) % 181.55/181.53 [3242]P1(f324(a196,f324(f106(a1),a100))) % 181.55/181.53 [3243]P1(f324(f324(f326(a862),a873),a874)) % 181.55/181.53 [3245]P1(f324(f324(f238(a1),a100),a84)) % 181.55/181.53 [3247]P1(f324(f324(f239(a1),a100),a84)) % 181.55/181.53 [3307]E(f324(f324(f302(a865),f2(a865)),f191(f871(a865,a859))),f324(f293(a865),f2(a865))) % 181.55/181.53 [3363]P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),a84))) % 181.55/181.53 [3375]E(f324(f303(a865,a865,a115),f247(f871(a865,a859))),f324(f296(a865),f2(a865))) % 181.55/181.53 [3414]P9(f870(a865,a865),f247(f871(f870(a865,a865),a859)),a111) % 181.55/181.53 [3721]E(f324(f73(a865,a1,a102,f103(a1)),a19),a20) % 181.55/181.53 [3781]P39(a865,f324(f244(f870(a865,a865)),f324(f263(a865,a865,a859),f239(a865)))) % 181.55/181.53 [4512]~P1(f324(a196,f324(f106(a1),a84))) % 181.55/181.53 [4513]~P1(f324(f324(f238(a1),a84),a100)) % 181.55/181.53 [4514]~P1(f324(f324(f239(a1),a84),a84)) % 181.55/181.53 [4515]~P1(f324(f324(f239(a1),a84),a100)) % 181.55/181.53 [4516]~P1(f324(f324(f239(a1),a100),a100)) % 181.55/181.53 [4517]~P1(f324(f324(f92(a1),a84),a100)) % 181.55/181.53 [4518]~P1(f324(f324(f92(a1),a100),a84)) % 181.55/181.53 [4529]~P1(f324(f61(a865),f247(f871(a865,a859)))) % 181.55/181.53 [4530]~P1(f324(f61(a1),f247(f871(a1,a859)))) % 181.55/181.53 [4387]E(f324(f263(a1,a1,a859),f324(f324(f8(f871(a1,a859),f871(a1,a859),a1),f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f239(a1),f2(a1))))),f324(f324(f7(a1,a1,f871(a1,a859)),f324(f324(f8(f871(a1,f871(a1,a859)),f871(a1,f871(a1,a859)),a1),f7(a1,a1,a859)),f324(f324(f8(f871(a1,a1),f871(a1,f871(a1,a859)),a1),f324(f8(a1,f871(a1,a859),a1),a321)),a222))),f79(a1)))),a218) % 181.55/181.53 [4562]~P26(a858,a875,f324(f324(f302(f864(a858)),f324(f324(f324(f93(a858),f324(a876,a873)),f324(a25,a873)),f324(a877,a873))),f191(f871(f864(a858),a859)))) % 181.55/181.53 [3452]E(f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100),f324(f80(a1),a100)) % 181.55/181.53 [3490]E(f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100),f324(f324(f22(a1),a84),a100)) % 181.55/181.53 [3647]E(f324(f324(f60(f870(a865,a865)),f247(f871(f870(a865,a865),a859))),a111),a101) % 181.55/181.53 [3676]E(f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f79(a1)) % 181.55/181.53 [3677]E(f324(f106(a102),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f79(a102)) % 181.55/181.53 [3678]E(f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f79(a865)) % 181.55/181.53 [3682]E(f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(a115,f2(a865))) % 181.55/181.53 [4072]E(f324(f324(f113(f871(f870(f870(a865,a865),f870(a865,a865)),a859)),a35),f300(f870(a865,a865),f191(f871(f870(f870(a865,a865),f870(a865,a865)),a859)))),a70) % 181.55/181.53 [4143]E(f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),f79(a865)),f2(a865))),f191(f871(f870(a865,a865),a859))))),f79(a1)) % 181.55/181.53 [4144]E(f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),f2(a865)),f2(a865))),f191(f871(f870(a865,a865),a859))))),f2(a1)) % 181.55/181.53 [4160]E(f324(f244(f870(a865,a865)),f324(f263(a865,a865,a859),f324(f324(f8(a865,f871(a865,a859),a865),f324(f7(a865,a865,a859),a321)),a115))),a314) % 181.55/181.53 [4129]E(f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),f324(a115,f324(a115,f2(a865)))) % 181.55/181.53 [4132]E(f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),f324(f324(f81(a865),f79(a865)),f79(a865))) % 181.55/181.53 [4133]E(f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),f324(f37(a859),f247(f871(a859,a859)))) % 181.55/181.53 [4202]P7(f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))) % 181.55/181.53 [4274]P29(f871(f870(a865,a865),a859),f324(f324(f259(f871(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a859),f871(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a859)),a36),a69)) % 181.55/181.53 [4275]P29(f871(f870(a865,a865),a859),f324(f324(f259(f871(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a859),f871(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a859)),a68),a71)) % 181.55/181.53 [4314]E(f324(f324(f113(f871(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a859)),f317(f870(a865,a865),a70)),f324(f324(f302(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),f191(f871(f870(a865,a865),a859))),f191(f871(f870(a865,a865),a859)))),f191(f871(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a859)))),a71) % 181.55/181.53 [4315]E(f324(f324(f113(f871(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a859)),f315(f870(a865,a865),a70)),f324(f324(f302(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),f191(f871(f870(a865,a865),a859))),f191(f871(f870(a865,a865),a859)))),f191(f871(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a859)))),a69) % 181.55/181.53 [4204]E(f324(a107,f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(a115,f324(a115,f2(a865)))) % 181.55/181.53 [4251]E(f324(f103(a1),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))) % 181.55/181.53 [4286]P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.53 [4287]E(f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100)),f324(a115,f324(a115,f324(a115,f2(a865))))) % 181.55/181.53 [4329]P7(f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))) % 181.55/181.53 [4417]P26(a858,a875,f324(f303(a862,f864(a858),f324(f324(f18(a862,f871(a858,f871(a860,a859)),f864(a858)),f324(f324(f18(a862,a861,f871(f871(a858,f871(a860,a859)),f864(a858))),f324(f324(f8(f871(a858,f871(a860,a859)),f871(a861,f871(f871(a858,f871(a860,a859)),f864(a858))),a862),f93(a858)),a876)),a25)),a877)),a874)) % 181.55/181.53 [4357]E(f324(f103(a1),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))),f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))) % 181.55/181.53 [4372]P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100)))) % 181.55/181.53 [3079]P8(x30791,a321) % 181.55/181.53 [3478]P27(a865,a865,a115,x34781) % 181.55/181.53 [3069]P91(f864(x30691)) % 181.55/181.53 [3070]P91(f869(x30701)) % 181.55/181.53 [3071]P91(f866(x30711)) % 181.55/181.53 [3072]P91(f867(x30721)) % 181.55/181.53 [3073]P102(f864(x30731)) % 181.55/181.53 [3074]P102(f869(x30741)) % 181.55/181.53 [3075]P102(f866(x30751)) % 181.55/181.53 [3076]P102(f867(x30761)) % 181.55/181.53 [3096]P39(a1,f108(x30961)) % 181.55/181.53 [3097]P39(a1,f109(x30971)) % 181.55/181.53 [3145]P39(f871(x31451,a859),f299(x31451)) % 181.55/181.53 [3170]E(f248(x31701,x31701,a321),a321) % 181.55/181.53 [3185]E(f44(a1,x31851,x31851),f2(a1)) % 181.55/181.53 [3239]P17(x32391,f871(x32391,a859),f302(x32391)) % 181.55/181.53 [4447]~E(f324(a25,x44471),a24) % 181.55/181.53 [4449]~E(f324(a115,x44491),x44491) % 181.55/181.53 [4461]~E(f324(a115,x44611),f2(a865)) % 181.55/181.53 [3081]E(f324(f192(a865),x30811),x30811) % 181.55/181.53 [3082]E(f324(f106(a1),x30821),x30821) % 181.55/181.53 [3098]E(f324(a90,f325(x30981)),x30981) % 181.55/181.53 [3111]E(f117(x31111,f116(x31111)),f116(x31111)) % 181.55/181.53 [3112]E(f146(x31121,f116(x31121)),f116(x31121)) % 181.55/181.53 [3114]E(f31(f324(a25,x31141)),f2(a865)) % 181.55/181.53 [3119]E(f324(f162(x31191),f116(x31191)),f116(x31191)) % 181.55/181.53 [3120]E(f324(f166(x31201),f116(x31201)),f116(x31201)) % 181.55/181.53 [3121]E(f324(f163(x31211),f116(x31211)),f116(x31211)) % 181.55/181.53 [3128]E(f324(f106(a1),x31281),f324(f105(a1),x31281)) % 181.55/181.53 [3129]E(f324(a90,f324(a110,x31291)),x31291) % 181.55/181.53 [3131]E(f324(a3,f324(a19,x31311)),x31311) % 181.55/181.53 [3132]E(f324(a19,f324(a3,x31321)),x31321) % 181.55/181.53 [3133]P7(f324(f103(a1),x31331)) % 181.55/181.53 [3138]E(f324(f192(f869(x31381)),f203(x31381)),f2(a865)) % 181.55/181.53 [3139]E(f324(f192(f866(x31391)),f116(x31391)),f2(a865)) % 181.55/181.53 [3144]E(f324(f192(a861),f324(a25,x31441)),f2(a865)) % 181.55/181.53 [3154]E(f232(x31541,f203(x31541)),f191(f871(x31541,a859))) % 181.55/181.53 [3161]E(f324(f324(f22(a865),x31611),f2(a865)),x31611) % 181.55/181.53 [3162]E(f324(f324(f82(a865),x31621),f79(a865)),x31621) % 181.55/181.53 [3163]E(f324(f324(f82(a1),x31631),f79(a1)),x31631) % 181.55/181.53 [3164]E(f324(f324(f81(a865),x31641),f2(a865)),x31641) % 181.55/181.53 [3165]E(f324(f324(f81(a1),x31651),f2(a1)),x31651) % 181.55/181.53 [3166]E(f324(f324(f190(a865),x31661),f2(a865)),x31661) % 181.55/181.53 [3167]E(f324(f324(f82(a865),x31671),f2(a865)),f2(a865)) % 181.55/181.53 [3168]E(f324(f324(f189(a865),x31681),f2(a865)),f2(a865)) % 181.55/181.53 [3169]E(f324(f324(f38(a1),x31691),f2(a1)),f2(a1)) % 181.55/181.53 [3176]E(f324(f167(x31761),f116(x31761)),f191(f871(x31761,a859))) % 181.55/181.53 [3180]P1(f324(f131(x31801),f116(x31801))) % 181.55/181.53 [3186]E(f324(f148(x31861,x31861),f5(x31861)),f34(f866(x31861))) % 181.55/181.53 [3187]E(f324(f148(x31871,x31871),f34(x31871)),f34(f866(x31871))) % 181.55/181.53 [3188]E(f324(f204(x31881,x31881),f5(x31881)),f34(f869(x31881))) % 181.55/181.53 [3189]E(f324(f204(x31891,x31891),f34(x31891)),f34(f869(x31891))) % 181.55/181.53 [3190]E(f44(a1,x31901,f2(a1)),x31901) % 181.55/181.53 [3191]E(f324(f238(a865),f324(a115,x31911)),f324(f239(a865),x31911)) % 181.55/181.53 [3192]E(f324(f245(a865),f324(a115,x31921)),f324(f293(a865),x31921)) % 181.55/181.53 [3193]E(f324(f246(a865),f324(a115,x31931)),f324(f296(a865),x31931)) % 181.55/181.53 [3195]E(f44(a1,f2(a1),x31951),f2(a1)) % 181.55/181.53 [3205]E(f324(f324(f81(a865),x32051),f79(a865)),f324(a115,x32051)) % 181.55/181.53 [3215]E(f324(f294(a865,x32151),f2(a865)),f191(f871(a865,a859))) % 181.55/181.53 [3227]E(f295(a865,f2(a865),x32271),f324(f293(a865),x32271)) % 181.55/181.53 [3274]E(f324(f324(f22(a865),f324(a115,x32741)),f79(a865)),x32741) % 181.55/181.53 [3287]E(f46(f2(a1),x32871),f324(f324(f259(a1,a1),f2(a1)),f2(a1))) % 181.55/181.53 [3337]P1(f324(f324(f239(a865),x33371),f324(a115,x33371))) % 181.55/181.53 [3349]P1(f324(f324(f239(a865),f2(a865)),f324(a115,x33491))) % 181.55/181.53 [3579]E(f94(x35791,x35791,f247(f871(x35791,a859)),f34(x35791)),f34(x35791)) % 181.55/181.53 [3633]E(f324(f324(f22(a102),f324(a3,f324(a115,f324(a19,x36331)))),f79(a102)),x36331) % 181.55/181.53 [3705]P1(f324(f324(f238(a1),f324(f80(a1),f324(f103(a1),x37051))),f2(a1))) % 181.55/181.53 [3852]P1(f324(f324(f239(a1),f324(f80(a1),f324(f103(a1),f324(a115,x38521)))),f2(a1))) % 181.55/181.53 [4483]~E(f247(f871(x44831,a859)),f191(f871(x44831,a859))) % 181.55/181.53 [4526]~P1(f324(f324(f239(a865),x45261),f2(a865))) % 181.55/181.53 [4538]~P1(f324(f324(f239(a1),f324(f103(a1),x45381)),f2(a1))) % 181.55/181.53 [3143]E(f175(x31431,f116(f866(x31431))),f116(f866(x31431))) % 181.55/181.53 [3146]E(f324(f324(f82(a1),a84),x31461),a84) % 181.55/181.53 [3147]E(f324(f324(f81(a1),a84),x31471),x31471) % 181.55/181.53 [3150]E(f324(a107,f324(f103(a1),x31501)),x31501) % 181.55/181.53 [3151]E(f324(f324(f22(a1),x31511),a84),x31511) % 181.55/181.53 [3152]E(f324(f324(f81(a1),x31521),a84),x31521) % 181.55/181.53 [3155]E(f324(f324(f22(a865),x31551),x31551),f2(a865)) % 181.55/181.53 [3159]E(f324(f80(a1),f324(f80(a1),x31591)),x31591) % 181.55/181.53 [3160]E(f324(f37(a865),f324(f245(a865),x31601)),x31601) % 181.55/181.53 [3171]E(f324(f324(f82(a865),f79(a865)),x31711),x31711) % 181.55/181.53 [3172]E(f324(f324(f82(a1),f79(a1)),x31721),x31721) % 181.55/181.53 [3173]E(f324(f324(f81(a865),f2(a865)),x31731),x31731) % 181.55/181.53 [3174]E(f324(f324(f81(a1),f2(a1)),x31741),x31741) % 181.55/181.53 [3175]E(f324(f324(f190(a865),f2(a865)),x31751),x31751) % 181.55/181.53 [3181]E(f324(f324(f22(a865),f2(a865)),x31811),f2(a865)) % 181.55/181.53 [3182]E(f324(f324(f82(a865),f2(a865)),x31821),f2(a865)) % 181.55/181.53 [3183]E(f324(f324(f189(a865),f2(a865)),x31831),f2(a865)) % 181.55/181.53 [3184]E(f324(f324(f38(a1),f2(a1)),x31841),f2(a1)) % 181.55/181.53 [3200]E(f324(f294(a865,f2(a865)),x32001),f324(f245(a865),x32001)) % 181.55/181.53 [3201]E(f324(f324(f82(a1),a100),x32011),f324(f80(a1),x32011)) % 181.55/181.53 [3207]E(f324(a107,f324(f106(a1),x32071)),f324(f106(a865),x32071)) % 181.55/181.53 [3208]E(f324(a19,f324(f106(a102),x32081)),f324(f106(a865),x32081)) % 181.55/181.53 [3209]E(f324(f37(a865),f324(f293(a865),x32091)),f324(a115,x32091)) % 181.55/181.53 [3219]E(f324(f324(f81(a865),f79(a865)),x32191),f324(a115,x32191)) % 181.55/181.53 [3223]E(f324(f105(a1),f324(f103(a1),x32231)),f324(f103(a1),x32231)) % 181.55/181.53 [3224]E(f324(f75(a1),f324(f103(a1),x32241)),f324(f103(a1),x32241)) % 181.55/181.53 [3229]E(f324(f37(x32291),f191(f871(x32291,a859))),f2(a865)) % 181.55/181.53 [3231]E(f324(f324(f38(a865),x32311),f324(a115,f2(a865))),x32311) % 181.55/181.53 [3240]E(f44(a865,x32401,f324(a115,f2(a865))),f2(a865)) % 181.55/181.53 [3241]E(f44(a1,x32411,f324(f106(a1),a100)),f2(a1)) % 181.55/181.53 [3258]E(f324(f324(f38(a1),x32581),f324(f106(a1),a100)),f324(f80(a1),x32581)) % 181.55/181.53 [3262]E(f133(a865,f324(f294(a865,x32621),f2(a865))),f116(a865)) % 181.55/181.53 [3263]E(f324(f324(f81(a1),x32631),f79(a1)),f324(f324(f22(a1),x32631),a100)) % 181.55/181.53 [3264]E(f324(f324(f22(a1),x32641),f79(a1)),f324(f324(f81(a1),x32641),a100)) % 181.55/181.53 [3268]P1(f324(f324(f238(a865),x32681),x32681)) % 181.55/181.53 [3269]P1(f324(f324(f238(a1),x32691),x32691)) % 181.55/181.53 [3270]P1(f324(f324(f92(a1),x32701),x32701)) % 181.55/181.53 [3275]E(f324(f80(a1),f324(f106(a1),x32751)),f324(f106(a1),f324(f80(a1),x32751))) % 181.55/181.53 [3276]P1(f324(f61(a865),f324(f245(a865),x32761))) % 181.55/181.53 [3277]P1(f324(f61(a865),f324(f293(a865),x32771))) % 181.55/181.53 [3285]E(f155(x32851,f247(f871(x32851,a859))),f247(f871(f866(x32851),a859))) % 181.55/181.53 [3290]P1(f324(f324(f238(a865),f2(a865)),x32901)) % 181.55/181.53 [3300]E(f324(f324(f81(a865),f114(x33001)),f324(a115,f2(a865))),f114(f324(a115,x33001))) % 181.55/181.53 [3301]E(f324(f244(x33011),f324(f16(a859,x33011),a242)),f191(f871(x33011,a859))) % 181.55/181.53 [3302]E(f324(f244(x33021),f324(f16(a859,x33021),a188)),f247(f871(x33021,a859))) % 181.55/181.53 [3306]E(f324(f324(f302(a865),x33061),f324(f245(a865),x33061)),f324(f245(a865),f324(a115,x33061))) % 181.55/181.53 [3318]E(f324(f324(f81(a1),f79(a1)),f324(f103(a1),x33181)),f324(f103(a1),f324(a115,x33181))) % 181.55/181.53 [3320]E(f324(f324(f145(f866(x33201)),f116(x33201)),f116(f866(x33201))),f53(x33201,f116(x33201))) % 181.55/181.53 [3340]E(f191(f871(f870(x33401,x33401),a859)),f256(x33401,f191(f871(x33401,a859)))) % 181.55/181.53 [3341]E(f324(f301(x33411),f247(f871(x33411,a859))),f247(f871(f871(x33411,a859),a859))) % 181.55/181.53 [3342]E(f324(f80(f871(x33421,a859)),f191(f871(x33421,a859))),f247(f871(x33421,a859))) % 181.55/181.53 [3343]E(f324(f80(f871(x33431,a859)),f247(f871(x33431,a859))),f191(f871(x33431,a859))) % 181.55/181.53 [3345]P1(f324(f61(x33451),f191(f871(x33451,a859)))) % 181.55/181.53 [3347]E(f324(f294(a865,x33471),f324(a115,x33471)),f324(f324(f302(a865),x33471),f191(f871(a865,a859)))) % 181.55/181.53 [3348]E(f86(f870(a865,a865),f47(x33481,f2(a865))),f324(f324(f259(a865,a865),f2(a865)),x33481)) % 181.55/181.53 [3362]E(f324(f324(f302(a865),f324(a115,x33621)),f324(f293(a865),x33621)),f324(f293(a865),f324(a115,x33621))) % 181.55/181.53 [3366]P39(x33661,f191(f871(f870(x33661,x33661),a859))) % 181.55/181.53 [3369]P1(f324(f324(f238(a1),f2(a1)),f324(f103(a1),x33691))) % 181.55/181.53 [3377]E(f324(f324(f81(a865),f324(f192(a865),x33771)),f324(a115,f2(a865))),f324(f192(a865),f324(a115,x33771))) % 181.55/181.53 [3485]P40(f324(f303(a865,a1,f103(a1)),x34851)) % 181.55/181.53 [3523]P41(x35231,f191(f871(x35231,a859)),f191(f871(f870(x35231,x35231),a859))) % 181.55/181.53 [3542]E(f324(f324(f259(a1,a1),f324(f106(a1),a100)),f324(f324(f22(a1),x35421),f79(a1))),f49(f324(f106(a1),a100),x35421)) % 181.55/181.53 [3592]P57(x35921,f324(f16(f871(x35921,a859),x35921),f324(f16(a859,x35921),a242))) % 181.55/181.53 [3793]P1(f324(f324(f326(f871(f870(a865,a865),a859)),f325(x37931)),a101)) % 181.55/181.53 [3818]P1(f324(f324(f326(f871(f870(a865,a865),a859)),f324(a110,x38181)),a101)) % 181.55/181.53 [3956]P27(x39561,f871(x39561,a859),f324(f324(f7(x39561,f871(x39561,a859),f871(x39561,a859)),f302(x39561)),f191(f871(x39561,a859))),f247(f871(x39561,a859))) % 181.55/181.53 [4480]~E(f324(f324(f81(a1),x44801),x44801),a100) % 181.55/181.53 [4511]~E(f324(a3,f324(a115,f324(a19,x45111))),f2(a102)) % 181.55/181.53 [4519]~P1(f324(a196,f324(f103(a1),x45191))) % 181.55/181.53 [4522]~P1(f324(f324(f239(a865),x45221),x45221)) % 181.55/181.53 [4531]~P1(f324(f324(f238(a865),f324(a115,x45311)),x45311)) % 181.55/181.53 [3292]E(f324(a107,f324(f80(a1),f324(f103(a1),x32921))),f2(a865)) % 181.55/181.53 [3295]E(f324(f324(f81(a1),f324(f80(a1),x32951)),x32951),f2(a1)) % 181.55/181.53 [3299]E(f324(f37(a1),f324(f294(a1,f2(a1)),x32991)),f324(a107,x32991)) % 181.55/181.53 [3311]E(f324(f324(f249(a865),f324(a115,f2(a865))),x33111),f324(a115,f2(a865))) % 181.55/181.53 [3411]E(f324(f277(x34111),f191(f871(f870(x34111,x34111),a859))),f191(f871(x34111,a859))) % 181.55/181.53 [3419]E(f40(f871(x34191,a859),f191(f871(f871(x34191,a859),a859))),f247(f871(x34191,a859))) % 181.55/181.53 [3420]E(f40(f871(x34201,a859),f247(f871(f871(x34201,a859),a859))),f191(f871(x34201,a859))) % 181.55/181.53 [3421]E(f39(f871(x34211,a859),f191(f871(f871(x34211,a859),a859))),f191(f871(x34211,a859))) % 181.55/181.53 [3422]E(f39(f871(x34221,a859),f247(f871(f871(x34221,a859),a859))),f247(f871(x34221,a859))) % 181.55/181.53 [3468]E(f324(f324(f302(f866(x34681)),f116(x34681)),f191(f871(f866(x34681),a859))),f155(x34681,f191(f871(x34681,a859)))) % 181.55/181.53 [3469]E(f324(f324(f302(f866(x34691)),f116(x34691)),f191(f871(f866(x34691),a859))),f156(x34691,f116(f871(x34691,a859)))) % 181.55/181.53 [3506]E(f324(f324(f81(a865),f4(x35061)),f324(a115,f2(a865))),f4(f324(a3,f324(a115,f324(a19,x35061))))) % 181.55/181.53 [3534]E(f324(f37(a1),f324(f303(a865,a1,f103(a1)),x35341)),f324(f37(a865),x35341)) % 181.55/181.53 [3535]P1(f324(f324(f238(a865),x35351),f324(f324(f82(a865),x35351),x35351))) % 181.55/181.53 [3572]E(f324(f303(a1,a865,a107),f295(a1,f2(a1),f324(f103(a1),x35721))),f324(f293(a865),x35721)) % 181.55/181.53 [3587]E(f324(f324(f38(a865),f324(a115,f2(a865))),f324(f106(a865),x35871)),f324(a107,f324(f324(f38(a1),f79(a1)),f324(f106(a1),x35871)))) % 181.55/181.53 [3589]E(f324(f167(a865),f133(a865,f324(f294(a865,f2(a865)),f324(a115,x35891)))),f324(f293(a865),x35891)) % 181.55/181.53 [3590]E(f324(f324(f81(a865),f324(f192(a102),x35901)),f324(a115,f2(a865))),f324(f192(a102),f324(a3,f324(a115,f324(a19,x35901))))) % 181.55/181.53 [3607]E(f324(f303(a1,a865,a107),f324(f303(a865,a1,f103(a1)),x36071)),x36071) % 181.55/181.53 [3639]E(f324(f324(f302(a865),f2(a865)),f324(f303(a865,a865,a115),f324(f245(a865),x36391))),f324(f245(a865),f324(a115,x36391))) % 181.55/181.53 [3646]P52(x36461,x36461,f300(x36461,f191(f871(f870(x36461,x36461),a859)))) % 181.55/181.53 [3652]P1(f324(a196,f324(f80(a1),f324(f103(a1),f324(a115,x36521))))) % 181.55/181.53 [3663]E(f324(f324(f22(f871(a865,a859)),f324(f246(a865),x36631)),f324(f324(f302(a865),x36631),f191(f871(a865,a859)))),f324(f246(a865),f324(a115,x36631))) % 181.55/181.53 [3679]E(f324(f324(f81(a1),f324(f324(f22(a1),a84),x36791)),f324(f324(f22(a1),a84),x36791)),f324(f324(f22(a1),a84),f324(f324(f81(a1),x36791),x36791))) % 181.55/181.53 [3695]E(f324(f324(f302(f871(x36951,a859)),f191(f871(x36951,a859))),f191(f871(f871(x36951,a859),a859))),f324(f301(x36951),f191(f871(x36951,a859)))) % 181.55/181.53 [3722]E(f324(f324(f22(f871(a865,a859)),f324(f296(a865),x37221)),f324(f324(f302(a865),f324(a115,x37221)),f191(f871(a865,a859)))),f324(f296(a865),f324(a115,x37221))) % 181.55/181.53 [3730]E(f324(f324(f302(f869(x37301)),f203(x37301)),f324(f303(x37301,f869(x37301),f233(x37301)),f247(f871(x37301,a859)))),f247(f871(f869(x37301),a859))) % 181.55/181.53 [3830]E(f324(f106(a865),f324(f324(f81(a1),x38301),x38301)),f324(f324(f87(a865,a865),f324(f106(a865),x38301)),f324(f324(f18(a865,a865,a865),f81(a865)),f5(a865)))) % 181.55/181.53 [4225]P17(x42251,f871(x42251,a859),f324(f324(f8(f871(x42251,a859),f871(f871(x42251,a859),f871(x42251,a859)),x42251),f324(f7(f871(x42251,a859),f871(x42251,a859),f871(x42251,a859)),f22(f871(x42251,a859)))),f324(f324(f7(x42251,f871(x42251,a859),f871(x42251,a859)),f302(x42251)),f191(f871(x42251,a859))))) % 181.55/181.53 [4313]E(f324(f244(f870(a1,a1)),f324(f263(a1,a1,a859),f324(f324(f8(f871(a1,a859),f871(a1,a859),a1),f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),x43131)))),f239(a1)))),f108(x43131)) % 181.55/181.53 [4347]E(f324(f244(f870(a1,a1)),f324(f263(a1,a1,a859),f324(f324(f18(a1,f871(a1,a859),f871(a1,a859)),f324(f324(f8(f871(a859,a859),f871(f871(a1,a859),f871(a1,a859)),a1),f8(a859,a859,a1)),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),x43471)))),f239(a1)))),f109(x43471)) % 181.55/181.53 [4402]E(f324(f244(f870(f871(x44021,a859),f871(x44021,a859))),f324(f263(f871(x44021,a859),f871(x44021,a859),a859),f324(f324(f7(f871(x44021,a859),f871(f871(x44021,a859),a859),f871(f871(x44021,a859),a859)),f324(f324(f8(f871(f871(x44021,a859),f871(a859,a859)),f871(f871(f871(x44021,a859),a859),f871(f871(x44021,a859),a859)),f871(x44021,a859)),f18(f871(x44021,a859),a859,a859)),f324(f324(f8(f871(f871(x44021,a859),a859),f871(f871(x44021,a859),f871(a859,a859)),f871(x44021,a859)),f324(f8(a859,f871(a859,a859),f871(x44021,a859)),a322)),f239(f871(x44021,a859))))),f61(x44021)))),f299(x44021)) % 181.55/181.53 [4535]~P1(f324(f61(f866(x45351)),f247(f871(f866(x45351),a859)))) % 181.55/181.53 [4540]~P1(f324(f324(f92(a1),a100),f324(f324(f81(a1),x45401),x45401))) % 181.55/181.53 [4550]~P1(f324(f324(f238(a1),f2(a1)),f324(f80(a1),f324(f103(a1),f324(a115,x45501))))) % 181.55/181.53 [3446]E(f324(f324(f22(a1),f324(f324(f81(a1),x34461),a100)),a100),x34461) % 181.55/181.53 [3462]E(f324(f167(a865),f133(a865,f324(f294(a865,f2(a865)),x34621))),f324(f245(a865),x34621)) % 181.55/181.53 [3701]E(f324(f324(f81(a1),f324(f324(f81(a1),f79(a1)),x37011)),x37011),f324(f324(f22(a1),f324(f324(f81(a1),x37011),x37011)),a100)) % 181.55/181.53 [3748]E(f324(f279(x37481,x37481),f300(x37481,f191(f871(f870(x37481,x37481),a859)))),f300(x37481,f191(f871(f870(x37481,x37481),a859)))) % 181.55/181.53 [3796]P1(f324(f324(f238(a865),x37961),f324(f324(f82(a865),x37961),f324(f324(f82(a865),x37961),x37961)))) % 181.55/181.53 [4076]P1(f324(f61(a865),f324(f244(a865),f324(f324(f7(a865,a865,a859),f238(a865)),x40761)))) % 181.55/181.53 [4077]P1(f324(f61(a865),f324(f244(a865),f324(f324(f7(a865,a865,a859),f239(a865)),x40771)))) % 181.55/181.53 [4367]E(f324(f244(f870(x43671,x43671)),f324(f324(f8(f871(x43671,a859),a859,f870(x43671,x43671)),f88(x43671)),f324(f324(f7(f870(x43671,x43671),f871(x43671,f870(x43671,x43671)),f871(x43671,a859)),f324(f324(f8(f871(f870(x43671,x43671),a859),f871(f871(x43671,f870(x43671,x43671)),f871(x43671,a859)),f870(x43671,x43671)),f8(f870(x43671,x43671),a859,x43671)),a321)),f324(f324(f18(x43671,x43671,f870(x43671,x43671)),f259(x43671,x43671)),f5(x43671))))),f300(x43671,f191(f871(f870(x43671,x43671),a859)))) % 181.55/181.53 [4537]~E(f324(f324(f22(a1),f324(f324(f81(a1),x45371),x45371)),a100),a84) % 181.55/181.53 [4539]~E(f324(f324(f81(a1),f324(f324(f81(a1),f79(a1)),x45391)),x45391),f2(a1)) % 181.55/181.53 [4547]~P1(f324(f324(f92(a1),f324(f324(f81(a1),x45471),x45471)),a100)) % 181.55/181.53 [3841]E(f324(f324(f81(a1),f324(f324(f22(a1),a100),x38411)),f324(f324(f22(a1),a100),x38411)),f324(f324(f22(a1),a100),f324(f324(f22(a1),f324(f324(f81(a1),x38411),x38411)),a100))) % 181.55/181.53 [3965]E(f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),a100),x39651)),f324(f324(f22(a1),a100),x39651))),a100),f324(f324(f22(a1),a100),f324(f324(f81(a1),x39651),x39651))) % 181.55/181.53 [4000]E(f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f81(a1),x40001),a100)),f324(f324(f81(a1),x40001),a100))),a100),f324(f324(f81(a1),f324(f324(f81(a1),x40001),x40001)),a100)) % 181.55/181.53 [4038]E(f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),a100),x40381)),f324(f324(f22(a1),a100),x40381))),a100),f324(f324(f22(a1),a84),f324(f324(f22(a1),f324(f324(f81(a1),x40381),x40381)),a100))) % 181.55/181.53 [4139]E(f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x41391),f2(a865))),f191(f871(f870(a865,a865),a859))))),f324(f103(a1),x41391)) % 181.55/181.53 [4149]E(f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),f329(x41491)),f409(x41491))),f191(f871(f870(a865,a865),a859))))),x41491) % 181.55/181.53 [4186]E(f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),x41861)),f324(f303(a865,a1,f103(a1)),f324(f244(a865),f324(f324(f8(a1,a859,a865),x41861),f103(a1))))) % 181.55/181.53 [4233]P40(f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),x42331))) % 181.55/181.53 [4254]P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),x42541),f191(f871(f870(a865,a865),a859)))),a71)) % 181.55/181.53 [4260]E(f324(f303(a1,a865,a107),f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),f324(f324(f8(a865,a859,a1),x42601),a107)))),f324(f244(a865),x42601)) % 181.55/181.53 [4416]E(f305(a865,f324(f324(f41(f870(a865,a865),f871(a865,a859)),f324(a110,x44161)),f324(f263(a865,a865,f871(a865,a859)),f324(f324(f7(a865,f871(a865,a859),f871(a865,f871(a865,a859))),f324(f324(f8(f871(a865,f871(f871(a865,a859),f871(a865,a859))),f871(f871(a865,a859),f871(a865,f871(a865,a859))),a865),f7(a865,f871(a865,a859),f871(a865,a859))),f324(f324(f8(f871(a865,a865),f871(a865,f871(f871(a865,a859),f871(a865,a859))),a865),f324(f8(a865,f871(f871(a865,a859),f871(a865,a859)),a865),f302(a865))),f22(a865)))),f191(f871(a865,a859)))))),f324(a107,x44161)) % 181.55/181.53 [4552]~P1(f324(f324(f92(a1),a84),f324(f324(f22(a1),f324(f324(f81(a1),x45521),x45521)),a100))) % 181.55/181.53 [3885]E(f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),x38851),x38851)),a100)),a100),f324(f324(f81(a1),x38851),x38851)) % 181.55/181.53 [3937]E(f324(f324(f22(a1),f324(f324(f22(a1),f324(f324(f81(a1),x39371),x39371)),a100)),a100),f324(f324(f81(a1),f324(f324(f22(a1),x39371),a100)),f324(f324(f22(a1),x39371),a100))) % 181.55/181.53 [4158]E(f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f81(a1),f324(f80(a1),x41581)),a100)),f324(f324(f81(a1),f324(f80(a1),x41581)),a100))),a100),f324(f80(a1),f324(f324(f22(a1),f324(f324(f81(a1),x41581),x41581)),a100))) % 181.55/181.53 [4560]~P1(f324(f324(f92(a1),f324(f324(f22(a1),f324(f324(f81(a1),x45601),x45601)),a100)),a84)) % 181.55/181.53 [4205]E(f324(f324(f81(a865),x42051),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(a115,f324(a115,x42051))) % 181.55/181.53 [4206]E(f324(f324(f82(a865),x42061),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f81(a865),x42061),x42061)) % 181.55/181.53 [4207]E(f324(f324(f38(a865),f324(f324(f81(a865),x42071),x42071)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x42071) % 181.55/181.53 [4289]E(f44(a865,f324(a115,f324(a115,x42891)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f44(a865,x42891,f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.53 [4433]E(f324(a90,f324(f324(f41(f870(a865,a865),f871(f870(a865,a865),a859)),f324(a110,x44331)),f324(f263(a865,a865,f871(f870(a865,a865),a859)),f324(f324(f8(f871(a865,f871(f870(a865,a865),a859)),f871(a865,f871(f870(a865,a865),a859)),a865),f324(f8(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859),a865),f278(f870(a865,a865),f870(a865,a865),a111))),f324(f324(f7(a865,f871(f870(a865,a865),a859),f871(a865,f871(f870(a865,a865),a859))),f324(f324(f8(f871(a865,f871(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f871(f871(f870(a865,a865),a859),f871(a865,f871(f870(a865,a865),a859))),a865),f7(a865,f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f8(f871(a865,f870(a865,a865)),f871(a865,f871(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),a865),f324(f8(f870(a865,a865),f871(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),a865),f302(f870(a865,a865)))),f324(f7(a865,a865,f870(a865,a865)),f259(a865,a865))))),f191(f871(f870(a865,a865),a859))))))),f324(f80(a1),x44331)) % 181.55/181.53 [4284]E(f324(f324(f81(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x42841),f324(a115,f324(a115,x42841))) % 181.55/181.53 [4285]E(f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x42851),f324(f324(f81(a865),x42851),x42851)) % 181.55/181.53 [4319]E(f324(f324(f38(a865),f324(a115,f324(a115,x43191))),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(a115,f324(f324(f38(a865),x43191),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.53 [4373]E(f324(f324(f81(a865),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))),x43731),f324(a115,f324(a115,f324(a115,x43731)))) % 181.55/181.53 [4441]E(f324(f263(a1,a1,f870(a1,a1)),f324(f324(f18(a1,f871(a1,f870(a1,a1)),f871(a1,f870(a1,a1))),f324(f324(f8(f871(a1,f871(f870(a1,a1),f870(a1,a1))),f871(f871(a1,f870(a1,a1)),f871(a1,f870(a1,a1))),a1),f18(a1,f870(a1,a1),f870(a1,a1))),f324(f324(f8(f871(a1,f870(a1,a1)),f871(a1,f871(f870(a1,a1),f870(a1,a1))),a1),f324(f18(a1,f870(a1,a1),f871(f870(a1,a1),f870(a1,a1))),f324(f324(f8(a859,f871(f870(a1,a1),f871(f870(a1,a1),f870(a1,a1))),a1),f99(f870(a1,a1))),f324(f324(f8(a1,a859,a1),f324(f238(a1),f2(a1))),f324(f324(f7(a1,a1,a1),f22(a1)),x44411))))),f324(f324(f7(a1,f871(a1,a1),f871(a1,f870(a1,a1))),f324(f324(f8(f871(a1,f870(a1,a1)),f871(f871(a1,a1),f871(a1,f870(a1,a1))),a1),f8(a1,f870(a1,a1),a1)),f324(f324(f8(a1,f871(a1,f870(a1,a1)),a1),f259(a1,a1)),f324(f324(f7(a1,a1,a1),f324(f324(f8(a1,f871(a1,a1),a1),f81(a1)),f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))),f79(a1))))),f324(f324(f7(a1,a1,a1),f22(a1)),x44411))))),f324(f324(f8(a1,f871(a1,f870(a1,a1)),a1),f259(a1,a1)),f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))))),f43(x44411)) % 181.55/181.53 [3115]P91(f870(x31151,x31152)) % 181.55/181.53 [3116]P91(f872(x31161,x31162)) % 181.55/181.53 [3117]P102(f870(x31171,x31172)) % 181.55/181.53 [3118]P102(f872(x31181,x31182)) % 181.55/181.53 [3136]P16(a1,f174(x31361,x31362)) % 181.55/181.53 [3137]P39(x31371,f147(x31371,x31372)) % 181.55/181.53 [3202]P33(x32021,x32022,f116(x32021)) % 181.55/181.53 [3235]P41(x32351,x32352,f256(x32351,x32352)) % 181.55/181.53 [3236]P52(x32361,x32361,f256(x32361,x32362)) % 181.55/181.53 [3509]P27(x35091,x35091,f5(x35091),x35092) % 181.55/181.53 [3510]P27(x35101,x35101,f34(x35101),x35102) % 181.55/181.53 [3518]P34(x35181,x35182,f116(x35181),f116(x35181)) % 181.55/181.53 [3519]P27(x35191,f869(x35191),f233(x35191),x35192) % 181.55/181.53 [3528]P27(f866(x35281),f866(x35281),f163(x35281),x35282) % 181.55/181.53 [3929]P28(x39291,x39291,f34(x39291),x39292,x39292) % 181.55/181.53 [4453]~E(f33(x44531,x44532),a24) % 181.55/181.53 [4454]~E(f26(x44541,x44542),a24) % 181.55/181.53 [4455]~E(f32(x44551,x44552),a24) % 181.55/181.53 [4490]~P35(x44901,x44902,f116(x44901)) % 181.55/181.53 [4491]~P37(x44911,x44912,f116(x44911)) % 181.55/181.53 [3100]E(f324(f5(x31001),x31002),x31002) % 181.55/181.53 [3102]E(f324(f34(x31021),x31022),x31022) % 181.55/181.53 [3103]E(f324(f244(x31031),x31032),x31032) % 181.55/181.53 [3113]E(f324(f194(x31131),x31132),f118(x31131)) % 181.55/181.53 [3123]E(f31(f26(x31231,x31232)),f2(a865)) % 181.55/181.53 [3134]E(f86(x31341,f324(a321,x31342)),x31342) % 181.55/181.53 [3135]E(f91(x31351,f324(a321,x31352)),x31352) % 181.55/181.53 [3153]E(f324(f192(a861),f26(x31531,x31532)),f2(a865)) % 181.55/181.53 [3157]E(f324(f130(x31571,x31572),f116(x31571)),f116(x31571)) % 181.55/181.53 [3177]E(f300(x31771,f300(x31771,x31772)),f300(x31771,x31772)) % 181.55/181.53 [3178]E(f146(x31781,f146(x31781,x31782)),f146(x31781,x31782)) % 181.55/181.53 [3198]E(f324(f324(f124(x31981),x31982),f116(x31981)),x31982) % 181.55/181.53 [3203]E(f168(x32031,x32032,f116(x32031)),x32032) % 181.55/181.53 [3204]E(f168(x32041,f116(x32041),x32042),x32042) % 181.55/181.53 [3210]E(f324(f324(f170(x32101),x32102),f116(x32101)),f116(x32101)) % 181.55/181.53 [3211]E(f324(f324(f132(x32111),x32112),f116(x32111)),f116(x32111)) % 181.55/181.53 [3213]E(f234(x32131,x32132,f203(x32131)),f2(a865)) % 181.55/181.53 [3214]E(f149(x32141,x32142,f116(x32141)),f2(a865)) % 181.55/181.53 [3216]E(f164(x32161,x32162,f116(x32161)),f116(x32161)) % 181.55/181.53 [3217]E(f172(x32171,x32172,f116(x32171)),f116(x32171)) % 181.55/181.53 [3218]E(f171(x32181,f116(x32181),x32182),f116(x32181)) % 181.55/181.53 [3222]E(f324(f167(x32221),f146(x32221,x32222)),f324(f167(x32221),x32222)) % 181.55/181.53 [3225]E(f324(f255(x32251,x32251),f256(x32251,x32252)),x32252) % 181.55/181.53 [3226]E(f324(f257(x32261,x32261),f256(x32261,x32262)),x32262) % 181.55/181.53 [3234]E(f324(f279(x32341,x32341),f256(x32341,x32342)),f256(x32341,x32342)) % 181.55/181.53 [3250]E(f300(f866(x32501),f151(x32501,x32502)),f152(x32501,f300(x32501,x32502))) % 181.55/181.53 [3252]P1(f324(f131(a1),f174(x32521,x32522))) % 181.55/181.53 [3260]E(f324(f255(x32601,x32601),f300(x32601,x32602)),f247(f871(x32601,a859))) % 181.55/181.53 [3261]E(f324(f257(x32611,x32611),f300(x32611,x32612)),f247(f871(x32611,a859))) % 181.55/181.53 [3265]P1(f324(f131(x32651),f146(x32651,x32652))) % 181.55/181.53 [3267]P1(f324(f154(x32671,x32672),f116(x32671))) % 181.55/181.53 [3273]E(f324(f167(a1),f174(x32731,x32732)),f295(a1,x32731,x32732)) % 181.55/181.53 [3288]P53(x32881,f191(f871(x32881,a859)),x32882) % 181.55/181.53 [3293]E(f324(f262(a1,a1),f45(x32931,x32932)),f44(a1,x32931,x32932)) % 181.55/181.53 [3294]E(f324(f294(a865,x32941),f324(a115,x32942)),f295(a865,x32941,x32942)) % 181.55/181.53 [3310]E(f324(f324(f145(x33101),x33102),f116(x33101)),f134(x33101,x33102,f116(x33101))) % 181.55/181.53 [3322]E(f295(a865,f324(a115,x33221),x33222),f297(a865,x33221,x33222)) % 181.55/181.53 [3325]P41(x33251,f247(f871(x33251,a859)),f300(x33251,x33252)) % 181.55/181.53 [3388]E(f324(f324(f22(a865),x33881),f324(a115,x33882)),f324(f37(a865),f298(a865,x33882,x33881))) % 181.55/181.53 [3447]E(f161(x34471,x34472,f116(x34471)),f324(f324(f259(f866(x34471),f866(x34471)),f116(x34471)),f116(x34471))) % 181.55/181.53 [3466]E(f324(f263(x34661,x34662,f870(x34661,x34662)),f259(x34661,x34662)),f34(f870(x34661,x34662))) % 181.55/181.53 [3471]P1(f324(f324(f326(f866(x34711)),f116(x34711)),f155(x34711,x34712))) % 181.55/181.53 [3472]E(f324(f192(f866(x34721)),f117(x34721,x34722)),f324(f324(f22(a865),f324(f192(f866(x34721)),x34722)),f79(a865))) % 181.55/181.53 [3479]P1(f324(f61(a865),f298(a865,x34791,x34792))) % 181.55/181.53 [3480]P1(f324(f61(a865),f297(a865,x34801,x34802))) % 181.55/181.53 [3481]P1(f324(f61(a865),f295(a865,x34811,x34812))) % 181.55/181.53 [3482]P1(f324(f61(a1),f298(a1,x34821,x34822))) % 181.55/181.53 [3483]P1(f324(f61(a1),f297(a1,x34831,x34832))) % 181.55/181.53 [3484]P1(f324(f61(a1),f295(a1,x34841,x34842))) % 181.55/181.53 [3586]E(f324(f303(a865,a865,a115),f295(a865,x35861,x35862)),f295(a865,f324(a115,x35861),f324(a115,x35862))) % 181.55/181.53 [3604]E(f324(f324(f281(x36041,x36041,x36041),f300(x36041,x36042)),f300(x36041,x36042)),f300(x36041,x36042)) % 181.55/181.53 [3637]E(f324(f324(f259(a1,a1),f324(f324(f38(a1),x36371),x36372)),f44(a1,x36371,x36372)),f45(x36371,x36372)) % 181.55/181.53 [3638]E(f324(f324(f259(a102,a102),f324(f324(f38(a102),x36381),x36382)),f44(a102,x36381,x36382)),f21(x36381,x36382)) % 181.55/181.53 [3667]E(f324(f324(f259(a865,a865),f324(f324(f38(a865),x36671),x36672)),f44(a865,x36671,x36672)),f86(f870(a865,a865),f47(x36671,x36672))) % 181.55/181.53 [3718]P1(f324(f324(f239(a865),f324(f324(f22(a865),x37181),x37182)),f324(a115,x37181))) % 181.55/181.53 [3817]E(f324(f324(f81(a1),f324(f324(f82(a1),x38171),f324(f324(f38(a1),x38172),x38171))),f44(a1,x38172,x38171)),x38172) % 181.55/181.53 [3821]E(f324(f324(f41(a865,f871(f870(f866(x38211),f866(x38211)),a859)),f247(f871(a865,a859))),f137(x38211,x38212)),f139(x38211,x38212)) % 181.55/181.53 [4051]P1(f324(f324(f326(f870(f866(x40511),f866(x40511))),f324(f324(f259(f866(x40511),f866(x40511)),f116(x40511)),f116(x40511))),f152(x40511,x40512))) % 181.55/181.53 [4218]E(f264(x42181,x42181,x42182,x42182,f5(x42181),f5(x42182)),f34(f870(x42181,x42182))) % 181.55/181.53 [4220]E(f264(x42201,x42201,x42202,x42202,f34(x42201),f34(x42202)),f34(f870(x42201,x42202))) % 181.55/181.53 [4463]~E(f324(f233(x44631),x44632),f203(x44631)) % 181.55/181.53 [3196]E(f324(f237(x31961),f324(f233(x31961),x31962)),x31962) % 181.55/181.53 [3197]E(f324(f163(x31971),f324(f163(x31971),x31972)),x31972) % 181.55/181.53 [3199]E(f324(f324(f132(x31991),f2(a865)),x31992),x31992) % 181.55/181.53 [3212]E(f324(f324(f170(x32121),f2(a865)),x32122),f116(x32121)) % 181.55/181.53 [3220]E(f324(f324(f124(x32201),f116(x32201)),x32202),x32202) % 181.55/181.53 [3228]E(f324(f192(f869(x32281)),f324(f233(x32281),x32282)),f2(a865)) % 181.55/181.53 [3230]E(f39(f871(x32301,a859),f324(f301(x32301),x32302)),x32302) % 181.55/181.53 [3232]E(f324(f167(x32321),f324(f162(x32321),x32322)),f324(f167(x32321),x32322)) % 181.55/181.53 [3233]E(f324(f167(x32331),f324(f163(x32331),x32332)),f324(f167(x32331),x32332)) % 181.55/181.53 [3238]E(f324(f324(f22(a102),x32381),x32382),f324(f324(a23,x32381),x32382)) % 181.55/181.53 [3254]E(f324(f324(f82(a865),x32541),x32542),f324(f324(f82(a865),x32542),x32541)) % 181.55/181.53 [3255]E(f324(f324(f82(a1),x32551),x32552),f324(f324(f82(a1),x32552),x32551)) % 181.55/181.53 [3256]E(f324(f324(f81(a865),x32561),x32562),f324(f324(f81(a865),x32562),x32561)) % 181.55/181.53 [3257]E(f324(f324(f81(a1),x32571),x32572),f324(f324(f81(a1),x32572),x32571)) % 181.55/181.53 [3280]E(f324(f324(f184(x32801,x32801),f2(a865)),x32802),f34(x32801)) % 181.55/181.53 [3281]E(f324(f192(f866(x32811)),f324(f162(x32811),x32812)),f324(f192(f866(x32811)),x32812)) % 181.55/181.53 [3282]E(f324(f192(f866(x32821)),f324(f163(x32821),x32822)),f324(f192(f866(x32821)),x32822)) % 181.55/181.53 [3283]E(f171(x32831,x32832,f191(f871(a865,a859))),f116(x32831)) % 181.55/181.53 [3284]E(f324(f324(f148(x32841,x32841),f5(x32841)),x32842),x32842) % 181.55/181.53 [3286]E(f324(f258(a1,a1),f45(x32861,x32862)),f324(f324(f38(a1),x32861),x32862)) % 181.55/181.53 [3303]E(f324(f192(f866(x33031)),f146(x33031,x33032)),f324(f37(x33031),f324(f167(x33031),x33032))) % 181.55/181.53 [3304]E(f31(f32(x33041,x33042)),f324(f324(f81(a865),f31(x33042)),f324(a115,f2(a865)))) % 181.55/181.53 [3305]E(f324(f277(x33051),f324(f279(x33051,x33051),x33052)),f324(f277(x33051),x33052)) % 181.55/181.53 [3309]P1(f324(f61(x33091),f324(f167(x33091),x33092))) % 181.55/181.53 [3317]E(f324(f324(f81(a1),x33171),f324(f80(a1),x33172)),f324(f324(f22(a1),x33171),x33172)) % 181.55/181.53 [3324]P26(x33241,x33242,f191(f871(f864(x33241),a859))) % 181.55/181.53 [3326]E(f324(f303(x33261,x33261,f5(x33261)),x33262),x33262) % 181.55/181.53 [3327]E(f324(f303(x33271,x33271,f34(x33271)),x33272),x33272) % 181.55/181.53 [3328]E(f324(f304(x33281,x33281,f5(x33281)),x33282),x33282) % 181.55/181.53 [3329]E(f324(f304(x33291,x33291,f34(x33291)),x33292),x33292) % 181.55/181.53 [3330]P1(f324(f247(f871(x33301,a859)),x33302)) % 181.55/181.53 [3332]E(f324(f37(a865),f324(f294(a865,x33321),x33322)),f324(f324(f22(a865),x33322),x33321)) % 181.55/181.53 [3333]E(f324(f294(a865,f324(a115,x33331)),x33332),f298(a865,x33331,x33332)) % 181.55/181.53 [3346]E(f324(f324(f302(x33461),x33462),f191(f871(x33461,a859))),f324(f244(x33461),f324(a321,x33462))) % 181.55/181.53 [3350]E(f324(f324(f302(x33501),x33502),f191(f871(x33501,a859))),f232(x33501,f324(f233(x33501),x33502))) % 181.55/181.53 [3352]E(f300(x33521,f324(f279(x33521,x33521),x33522)),f324(f279(x33521,x33521),f300(x33521,x33522))) % 181.55/181.53 [3357]E(f324(f324(f81(a865),f324(a115,x33571)),x33572),f324(f324(f81(a865),x33571),f324(a115,x33572))) % 181.55/181.53 [3358]E(f324(f324(f22(a865),f324(a115,x33581)),f324(a115,x33582)),f324(f324(f22(a865),x33581),x33582)) % 181.55/181.53 [3364]E(f54(x33641,f2(a865),x33642),f324(f324(f145(f866(x33641)),f116(x33641)),f116(f866(x33641)))) % 181.55/181.53 [3365]E(f324(f37(a865),f297(a865,x33651,x33652)),f324(f324(f22(a865),x33652),x33651)) % 181.55/181.53 [3374]P39(x33741,f324(f324(f280(a865,x33741),a243),x33742)) % 181.55/181.53 [3376]P16(a865,f133(a865,f324(f294(a865,x33761),x33762))) % 181.55/181.53 [3378]P1(f324(f61(a865),f324(f294(a865,x33781),x33782))) % 181.55/181.53 [3379]P1(f324(f61(a1),f324(f294(a1,x33791),x33792))) % 181.55/181.53 [3381]E(f324(f279(f866(x33811),f866(x33811)),f151(x33811,x33812)),f151(x33811,f324(f279(x33811,x33811),x33812))) % 181.55/181.53 [3382]E(f324(f192(a861),f32(x33821,x33822)),f324(f324(f81(a865),f324(f192(a861),x33822)),f324(a115,f2(a865)))) % 181.55/181.53 [3384]E(f324(f294(a1,x33841),f324(f324(f81(a1),x33842),f79(a1))),f295(a1,x33841,x33842)) % 181.55/181.53 [3387]E(f324(f324(f38(a1),f324(f80(a1),x33871)),f324(f80(a1),x33872)),f324(f324(f38(a1),x33871),x33872)) % 181.55/181.53 [3395]E(f179(x33951,x33952,f324(f16(f869(x33952),x33951),f203(x33952))),f191(f871(x33951,a859))) % 181.55/181.53 [3396]E(f181(x33961,x33962,f324(f16(f869(x33962),x33961),f203(x33962))),f191(f871(x33962,a859))) % 181.55/181.53 [3397]E(f324(f324(f184(f870(x33971,x33971),a859),f79(a865)),x33972),x33972) % 181.55/181.53 [3399]E(f324(f324(f22(f871(x33991,a859)),x33992),f191(f871(x33991,a859))),x33992) % 181.55/181.53 [3400]E(f324(f324(f104(f871(x34001,a859)),x34002),f247(f871(x34001,a859))),x34002) % 181.55/181.53 [3401]E(f324(f324(f113(f871(x34011,a859)),x34012),f191(f871(x34011,a859))),x34012) % 181.55/181.53 [3402]E(f324(f258(a865,a865),f86(f870(a865,a865),f47(x34021,x34022))),f324(f324(f38(a865),x34021),x34022)) % 181.55/181.53 [3409]E(f306(x34091,f324(a20,x34092),f324(f80(a1),f324(a20,x34092))),f324(f324(f309(a1),x34091),x34092)) % 181.55/181.53 [3410]E(f295(a1,f324(f324(f81(a1),x34101),f79(a1)),x34102),f297(a1,x34101,x34102)) % 181.55/181.53 [3415]E(f324(f262(a865,a865),f86(f870(a865,a865),f47(x34151,x34152))),f44(a865,x34151,x34152)) % 181.55/181.53 [3423]E(f307(x34231,f324(a20,x34232),f324(f80(a1),f324(a20,x34232))),f308(a1,x34231,x34232)) % 181.55/181.53 [3426]P1(f324(f324(f326(x34261),x34262),f247(f871(x34261,a859)))) % 181.55/181.53 [3431]E(f324(f324(f22(a865),f324(a115,x34311)),x34312),f324(f37(a865),f295(a865,x34312,x34311))) % 181.55/181.53 [3458]E(f324(f324(f22(f871(x34581,a859)),x34582),f247(f871(x34581,a859))),f191(f871(x34581,a859))) % 181.55/181.53 [3459]E(f324(f324(f104(f871(x34591,a859)),x34592),f191(f871(x34591,a859))),f191(f871(x34591,a859))) % 181.55/181.53 [3460]E(f324(f324(f113(f871(x34601,a859)),x34602),f247(f871(x34601,a859))),f247(f871(x34601,a859))) % 181.55/181.53 [3474]E(f44(a1,f324(f80(a1),x34741),f324(f80(a1),x34742)),f324(f80(a1),f44(a1,x34741,x34742))) % 181.55/181.53 [3475]E(f44(a1,f324(f103(a1),x34751),f324(f103(a1),x34752)),f324(f103(a1),f44(a865,x34751,x34752))) % 181.55/181.53 [3486]E(f324(f192(f866(x34861)),f324(f166(x34861),x34862)),f324(f324(f22(a865),f324(f192(f866(x34861)),x34862)),f79(a865))) % 181.55/181.53 [3511]E(f324(f324(f38(a1),f44(a1,x35111,x35112)),x35112),f2(a1)) % 181.55/181.53 [3521]E(f324(a3,f44(a865,f324(a19,x35211),f324(a19,x35212))),f44(a102,x35211,x35212)) % 181.55/181.53 [3554]E(f324(a3,f324(f324(f22(a865),f324(a19,x35541)),f324(a19,x35542))),f324(f324(f22(a102),x35541),x35542)) % 181.55/181.53 [3555]E(f324(a3,f324(f324(f82(a865),f324(a19,x35551)),f324(a19,x35552))),f324(f324(f82(a102),x35551),x35552)) % 181.55/181.53 [3556]E(f324(a3,f324(f324(f81(a865),f324(a19,x35561)),f324(a19,x35562))),f324(f324(f81(a102),x35561),x35562)) % 181.55/181.53 [3557]E(f324(a3,f324(f324(f38(a865),f324(a19,x35571)),f324(a19,x35572))),f324(f324(f38(a102),x35571),x35572)) % 181.55/181.53 [3566]E(f324(f303(a865,a865,a115),f324(f294(a865,x35661),x35662)),f324(f294(a865,f324(a115,x35661)),f324(a115,x35662))) % 181.55/181.53 [3591]P1(f324(f47(x35911,x35912),f86(f870(a865,a865),f47(x35911,x35912)))) % 181.55/181.53 [3610]E(f324(f324(f81(a865),f324(f324(f81(a865),f31(x36101)),f31(x36102))),f324(a115,f2(a865))),f31(f33(x36101,x36102))) % 181.55/181.53 [3611]E(f44(a865,f324(a115,f44(a865,x36111,x36112)),x36112),f44(a865,f324(a115,x36111),x36112)) % 181.55/181.53 [3625]E(f324(f324(f42(f871(x36251,a859),f871(x36251,a859)),x36252),f5(f871(x36251,a859))),f40(f871(x36251,a859),x36252)) % 181.55/181.53 [3626]E(f324(f324(f41(f871(x36261,a859),f871(x36261,a859)),x36262),f5(f871(x36261,a859))),f39(f871(x36261,a859),x36262)) % 181.55/181.53 [3627]E(f324(f303(f866(x36271),f871(x36271,a859),f167(x36271)),f324(f167(f866(x36271)),f53(x36271,x36272))),f324(f301(x36271),f324(f167(x36271),x36272))) % 181.55/181.53 [3630]P1(f324(f324(f326(f871(x36301,a859)),x36302),f324(f301(x36301),x36302))) % 181.55/181.53 [3636]E(f44(a1,f324(f80(a1),f44(a1,x36361,x36362)),x36362),f44(a1,f324(f80(a1),x36361),x36362)) % 181.55/181.53 [3648]P1(f324(f324(f238(f871(x36481,a859)),x36482),f247(f871(x36481,a859)))) % 181.55/181.53 [3650]E(f324(f324(f281(x36501,x36501,x36501),f300(x36501,x36502)),f300(x36501,f300(x36501,x36502))),f300(x36501,x36502)) % 181.55/181.53 [3651]E(f324(f324(f113(f871(x36511,a859)),f324(f257(x36511,x36511),x36512)),f324(f255(x36511,x36511),x36512)),f324(f277(x36511),x36512)) % 181.55/181.53 [3672]E(f311(x36721,x36722,f247(f871(x36721,a859)),f247(f871(x36722,a859))),f247(f871(f872(x36721,x36722),a859))) % 181.55/181.53 [3723]P1(f324(f324(f238(a865),f44(a865,x37231,x37232)),x37231)) % 181.55/181.53 [3746]P1(f324(f324(f238(a1),f324(f80(a1),f324(f103(a1),x37461))),f324(f103(a1),x37462))) % 181.55/181.53 [3772]P1(f324(f324(f326(f871(x37721,a859)),f191(f871(x37721,a859))),f324(f301(x37721),x37722))) % 181.55/181.53 [3777]E(f300(x37771,f324(f324(f281(x37771,x37771,x37771),x37772),f300(x37771,x37772))),f300(x37771,x37772)) % 181.55/181.53 [3780]E(f324(f324(f281(x37801,x37801,x37801),f300(x37801,x37802)),x37802),f324(f324(f281(x37801,x37801,x37801),x37802),f300(x37801,x37802))) % 181.55/181.53 [3782]E(f324(a107,f324(f324(f81(a1),f324(f324(f22(a1),x37821),x37822)),f79(a1))),f324(f37(a1),f295(a1,x37822,x37821))) % 181.55/181.53 [3797]E(f324(f255(x37971,x37971),f324(f324(f281(x37971,x37971,x37971),x37972),f300(x37971,x37972))),f324(f255(x37971,x37971),x37972)) % 181.55/181.53 [3798]E(f324(f257(x37981,x37981),f324(f324(f281(x37981,x37981,x37981),x37982),f300(x37981,x37982))),f324(f257(x37981,x37981),x37982)) % 181.55/181.53 [3814]E(f324(f324(f81(a865),f324(f324(f81(a865),f324(f192(a861),x38141)),f324(f192(a861),x38142))),f324(a115,f2(a865))),f324(f192(a861),f33(x38141,x38142))) % 181.55/181.53 [3825]P27(a865,a865,f324(f324(f7(a865,a865,a865),f81(a865)),x38251),x38252) % 181.55/181.53 [3827]P16(a865,f324(f163(a865),f324(f324(f148(f866(x38271),a865),f192(f866(x38271))),f175(x38271,x38272)))) % 181.55/181.53 [3872]P1(f324(f324(f239(a1),f324(f80(a1),f324(f103(a1),f324(a115,x38721)))),f324(f103(a1),x38722))) % 181.55/181.53 [3917]E(f324(f136(f866(x39171),x39171,f324(f7(x39171,f866(x39171),f866(x39171)),f145(x39171)),f116(x39171)),x39172),f324(f163(x39171),x39172)) % 181.55/181.53 [3972]P1(f324(f324(f238(f871(f870(f866(x39721),f866(x39721)),a859)),f152(x39721,x39722)),f300(f866(x39721),f151(x39721,x39722)))) % 181.55/181.53 [4004]P1(f324(f47(x40041,x40042),f324(f324(f259(a865,a865),f324(f324(f38(a865),x40041),x40042)),f44(a865,x40041,x40042)))) % 181.55/181.53 [4015]P1(f324(f324(f238(f871(f870(f866(x40151),f866(x40151)),a859)),f151(x40151,f300(x40151,x40152))),f300(f866(x40151),f151(x40151,x40152)))) % 181.55/181.53 [4244]E(f324(f324(f265(f870(a102,a102),a102,f870(a102,a102),f870(x42441,f870(a102,a102))),f269(f324(f160(a102),f324(f324(f148(f870(a102,x42441),a102),f258(a102,x42441)),x42442)))),f324(f324(f8(x42441,f871(f870(a102,a102),f870(x42441,f870(a102,a102))),a102),f259(x42441,f870(a102,a102))),f270(x42441,x42442))),f268(x42441,x42442)) % 181.55/181.53 [4355]E(f324(f235(a865,f870(x43551,f867(x43551)),f2(a865),f324(f263(x43551,f867(x43551),a865),f324(f16(f871(f867(x43551),a865),x43551),f324(f324(f7(f867(x43551),a865,a865),f324(f324(f8(a865,f871(a865,a865),f867(x43551)),f81(a865)),f192(f867(x43551)))),f79(a865))))),f324(f127(x43551),x43552)),f324(f192(f867(x43551)),x43552)) % 181.55/181.53 [4432]E(f324(f263(f871(f870(x44321,x44321),a859),f871(f870(x44321,x44321),a859),f871(f871(x44322,x44321),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859)))),f324(f324(f7(f871(f870(x44321,x44321),a859),f871(f871(f870(x44321,x44321),a859),f871(f871(x44322,x44321),f871(f870(x44322,x44322),a859))),f871(f871(f870(x44321,x44321),a859),f871(f871(x44322,x44321),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859))))),f324(f324(f8(f871(f871(f871(x44322,x44321),f871(f870(x44322,x44322),a859)),f871(f871(x44322,x44321),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859)))),f871(f871(f871(f870(x44321,x44321),a859),f871(f871(x44322,x44321),f871(f870(x44322,x44322),a859))),f871(f871(f870(x44321,x44321),a859),f871(f871(x44322,x44321),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859))))),f871(f870(x44321,x44321),a859)),f8(f871(f871(x44322,x44321),f871(f870(x44322,x44322),a859)),f871(f871(x44322,x44321),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859))),f871(f870(x44321,x44321),a859))),f324(f324(f8(f871(f871(x44322,x44321),f871(f871(f870(x44322,x44322),a859),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859)))),f871(f871(f871(x44322,x44321),f871(f870(x44322,x44322),a859)),f871(f871(x44322,x44321),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859)))),f871(f870(x44321,x44321),a859)),f18(f871(x44322,x44321),f871(f870(x44322,x44322),a859),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859)))),f324(f324(f8(f871(f871(x44322,x44321),f871(f870(x44322,x44322),a859)),f871(f871(x44322,x44321),f871(f871(f870(x44322,x44322),a859),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859)))),f871(f870(x44321,x44321),a859)),f324(f8(f871(f870(x44322,x44322),a859),f871(f871(f870(x44322,x44322),a859),f870(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859))),f871(x44322,x44321)),f259(f871(f870(x44322,x44322),a859),f871(f870(x44322,x44322),a859)))),f280(x44321,x44322))))),f280(x44321,x44322))),f74(x44321,x44322)) % 181.55/181.53 [4520]~E(f324(f301(x45201),x45202),f191(f871(f871(x45201,a859),a859))) % 181.55/181.53 [4534]~P1(f324(f324(f326(x45341),x45342),f191(f871(x45341,a859)))) % 181.55/181.53 [4544]~P1(f324(f324(f239(f871(x45441,a859)),x45442),f191(f871(x45441,a859)))) % 181.55/181.53 [3335]E(f324(f324(f22(a865),x33351),f324(f324(f81(a865),x33351),x33352)),f2(a865)) % 181.55/181.53 [3338]E(f324(f324(f104(f871(x33381,a859)),x33382),x33382),x33382) % 181.55/181.53 [3339]E(f324(f324(f113(f871(x33391,a859)),x33392),x33392),x33392) % 181.55/181.53 [3367]E(f324(f324(f22(f871(x33671,a859)),x33672),x33672),f191(f871(x33671,a859))) % 181.55/181.53 [3370]E(f324(f137(x33701,x33702),f2(a865)),f191(f871(f870(f866(x33701),f866(x33701)),a859))) % 181.55/181.53 [3371]E(f324(f324(f81(a865),x33711),f324(a115,x33712)),f324(a115,f324(f324(f81(a865),x33711),x33712))) % 181.55/181.53 [3383]E(f197(f324(f103(a1),x33831),f324(f103(a1),x33832)),f324(f103(a1),f324(f324(f22(a865),x33831),x33832))) % 181.55/181.53 [3386]E(f324(f324(f38(a1),f324(f80(a1),x33861)),x33862),f324(f324(f38(a1),x33861),f324(f80(a1),x33862))) % 181.55/181.53 [3390]E(f324(f37(a1),f324(f294(a1,x33901),x33902)),f324(a107,f324(f324(f22(a1),x33902),x33901))) % 181.55/181.53 [3393]E(f324(f324(f81(a865),f324(a115,x33931)),x33932),f324(a115,f324(f324(f81(a865),x33931),x33932))) % 181.55/181.53 [3398]E(f324(f80(f871(x33981,a859)),f324(f80(f871(x33981,a859)),x33982)),x33982) % 181.55/181.53 [3412]E(f175(x34121,f324(f324(f145(f866(x34121)),f116(x34121)),x34122)),f175(x34121,x34122)) % 181.55/181.53 [3416]E(f324(f324(f81(a865),x34161),f324(f324(f82(a865),x34161),x34162)),f324(f324(f82(a865),x34161),f324(a115,x34162))) % 181.55/181.53 [3424]E(f324(f324(a23,f324(a3,x34241)),f324(a3,x34242)),f324(a3,f324(f324(f22(a865),x34241),x34242))) % 181.55/181.53 [3438]E(f324(f324(f82(a1),f324(f80(a1),x34381)),x34382),f324(f80(a1),f324(f324(f82(a1),x34381),x34382))) % 181.55/181.53 [3440]E(f324(f324(f249(a1),f324(f103(a1),x34401)),x34402),f324(f103(a1),f324(f324(f249(a865),x34401),x34402))) % 181.55/181.53 [3441]E(f324(f324(f82(a102),f324(a3,x34411)),f324(a3,x34412)),f324(a3,f324(f324(f82(a865),x34411),x34412))) % 181.55/181.53 [3442]E(f324(f324(f81(a102),f324(a3,x34421)),f324(a3,x34422)),f324(a3,f324(f324(f81(a865),x34421),x34422))) % 181.55/181.53 [3443]E(f324(f324(f189(a865),f324(a115,x34431)),f324(a115,x34432)),f324(a115,f324(f324(f189(a865),x34431),x34432))) % 181.55/181.53 [3444]E(f324(f324(f190(a865),f324(a115,x34441)),f324(a115,x34442)),f324(a115,f324(f324(f190(a865),x34441),x34442))) % 181.55/181.53 [3450]E(f324(f167(a865),f133(a865,f324(f294(a865,x34501),x34502))),f324(f294(a865,x34501),x34502)) % 181.55/181.53 [3451]E(f305(x34511,f324(f324(f302(x34511),x34512),f191(f871(x34511,a859)))),x34512) % 181.55/181.53 [3456]E(f324(f255(x34561,x34562),f191(f871(f870(x34561,x34562),a859))),f191(f871(x34562,a859))) % 181.55/181.53 [3457]E(f324(f257(x34571,x34572),f191(f871(f870(x34571,x34572),a859))),f191(f871(x34571,a859))) % 181.55/181.53 [3461]E(f324(a107,f324(f324(f22(a1),x34611),x34612)),f324(f37(a1),f297(a1,x34612,x34611))) % 181.55/181.53 [3465]E(f324(f324(f81(a865),x34651),f324(f324(f82(a865),x34652),x34651)),f324(f324(f82(a865),f324(a115,x34652)),x34651)) % 181.55/181.53 [3467]E(f324(f324(f60(x34671),f191(f871(x34671,a859))),x34672),f191(f871(f871(x34671,a859),a859))) % 181.55/181.53 [3476]E(f324(f192(f866(a865)),f133(a865,f324(f294(a865,x34761),x34762))),f324(f324(f22(a865),x34762),x34761)) % 181.55/181.53 [3491]E(f324(f324(f104(f871(x34911,a859)),f247(f871(x34911,a859))),x34912),x34912) % 181.55/181.53 [3492]E(f324(f324(f113(f871(x34921,a859)),f191(f871(x34921,a859))),x34922),x34922) % 181.55/181.53 [3493]E(f324(f324(f81(a1),f324(f80(a1),x34931)),f324(f80(a1),x34932)),f324(f80(a1),f324(f324(f81(a1),x34931),x34932))) % 181.55/181.53 [3497]E(f324(f324(f82(a1),f324(f106(a1),x34971)),f324(f106(a1),x34972)),f324(f106(a1),f324(f324(f82(a1),x34971),x34972))) % 181.55/181.53 [3499]E(f324(f324(f82(a1),f324(f103(a1),x34991)),f324(f103(a1),x34992)),f324(f103(a1),f324(f324(f82(a865),x34991),x34992))) % 181.55/181.53 [3500]E(f324(f324(f81(a1),f324(f106(a1),x35001)),f324(f106(a1),x35002)),f324(f106(a1),f324(f324(f81(a1),x35001),x35002))) % 181.55/181.53 [3502]E(f324(f324(f81(a1),f324(f103(a1),x35021)),f324(f103(a1),x35022)),f324(f103(a1),f324(f324(f81(a865),x35021),x35022))) % 181.55/181.53 [3503]E(f324(f324(f38(a1),f324(f103(a1),x35031)),f324(f103(a1),x35032)),f324(f103(a1),f324(f324(f38(a865),x35031),x35032))) % 181.55/181.53 [3522]E(f324(f324(f6(x35221,a865),f324(f16(a865,x35221),f79(a865))),x35222),f324(f37(x35221),x35222)) % 181.55/181.53 [3529]E(f324(f80(a1),f44(a1,f324(f80(a1),x35291),x35292)),f44(a1,x35291,f324(f80(a1),x35292))) % 181.55/181.53 [3531]E(f324(f167(a1),f174(x35311,f324(f324(f22(a1),x35312),f79(a1)))),f324(f294(a1,x35311),x35312)) % 181.55/181.53 [3536]P1(f324(f324(f238(a865),x35361),f324(f324(f81(a865),x35362),x35361))) % 181.55/181.53 [3537]P1(f324(f324(f238(a865),x35371),f324(f324(f81(a865),x35371),x35372))) % 181.55/181.53 [3539]E(f324(f324(f22(f871(x35391,a859)),f191(f871(x35391,a859))),x35392),f191(f871(x35391,a859))) % 181.55/181.53 [3540]E(f324(f324(f104(f871(x35401,a859)),f191(f871(x35401,a859))),x35402),f191(f871(x35401,a859))) % 181.55/181.53 [3541]E(f324(f324(f113(f871(x35411,a859)),f247(f871(x35411,a859))),x35412),f247(f871(x35411,a859))) % 181.55/181.53 [3546]E(f324(f324(f259(a1,a1),x35461),f324(f80(a1),x35462)),f324(a50,f324(f324(f259(a1,a1),x35461),x35462))) % 181.55/181.53 [3547]E(f324(f294(a1,f324(f324(f81(a1),x35471),f79(a1))),x35472),f298(a1,x35471,x35472)) % 181.55/181.53 [3558]E(f324(f324(f82(a865),x35581),f324(f324(f38(a865),x35582),x35581)),f324(f324(f22(a865),x35582),f44(a865,x35582,x35581))) % 181.55/181.53 [3559]E(f324(f324(f82(a1),x35591),f324(f324(f38(a1),x35592),x35591)),f324(f324(f22(a1),x35592),f44(a1,x35592,x35591))) % 181.55/181.53 [3563]E(f324(f167(a1),f174(f324(f324(f81(a1),x35631),f79(a1)),x35632)),f297(a1,x35631,x35632)) % 181.55/181.53 [3567]P1(f324(f324(f238(f871(x35671,a859)),x35672),x35672)) % 181.55/181.53 [3570]E(f324(f324(f104(f871(x35701,a859)),x35702),f324(f80(f871(x35701,a859)),x35702)),f191(f871(x35701,a859))) % 181.55/181.53 [3571]E(f324(f324(f113(f871(x35711,a859)),x35712),f324(f80(f871(x35711,a859)),x35712)),f247(f871(x35711,a859))) % 181.55/181.53 [3577]E(f324(f324(f22(a865),f324(f324(f22(a865),x35771),f79(a865))),x35772),f324(f324(f22(a865),x35771),f324(a115,x35772))) % 181.55/181.53 [3583]E(f324(f324(f22(f871(x35831,a859)),f247(f871(x35831,a859))),x35832),f324(f80(f871(x35831,a859)),x35832)) % 181.55/181.53 [3584]E(f324(f324(f22(a1),f324(f106(a1),x35841)),f324(f106(a1),x35842)),f324(f106(a1),f324(f324(f81(a1),x35841),f324(f80(a1),x35842)))) % 181.55/181.53 [3596]E(f324(f167(a865),f133(a865,f324(f294(a865,x35961),f324(a115,x35962)))),f295(a865,x35961,x35962)) % 181.55/181.53 [3608]E(f324(f192(f866(f866(x36081))),f53(x36081,x36082)),f324(f324(f249(a865),f324(a115,f324(a115,f2(a865)))),f324(f192(f866(x36081)),x36082))) % 181.55/181.53 [3628]E(f324(f324(f184(f870(x36281,x36281),a859),f2(a865)),x36282),f300(x36281,f191(f871(f870(x36281,x36281),a859)))) % 181.55/181.53 [3632]P1(f324(f131(a865),f133(a865,f324(f294(a865,x36321),x36322)))) % 181.55/181.53 [3649]E(f324(f303(a1,a865,a107),f295(a1,f324(f103(a1),x36491),f324(f103(a1),x36492))),f295(a865,x36491,x36492)) % 181.55/181.53 [3659]E(f186(a865,f2(a865),f5(a865),f324(f324(f22(a865),x36591),x36592)),f324(f324(f22(a865),x36591),f324(a115,x36592))) % 181.55/181.53 [3660]E(f324(a107,f324(f324(f22(a1),x36601),f324(f324(f81(a1),x36602),f79(a1)))),f324(f37(a1),f298(a1,x36602,x36601))) % 181.55/181.53 [3696]E(f324(f324(f148(a865,a865),a115),f133(a865,f324(f294(a865,x36961),x36962))),f133(a865,f324(f294(a865,f324(a115,x36961)),f324(a115,x36962)))) % 181.55/181.53 [3703]E(f324(f167(a1),f174(f324(f324(f81(a1),x37031),f79(a1)),f324(f324(f22(a1),x37032),f79(a1)))),f298(a1,x37031,x37032)) % 181.55/181.53 [3714]P1(f324(f324(f238(f871(x37141,a859)),f191(f871(x37141,a859))),x37142)) % 181.55/181.53 [3719]E(f86(x37191,f324(f324(f7(x37191,x37191,a859),a321),x37192)),x37192) % 181.55/181.53 [3720]E(f91(x37201,f324(f324(f7(x37201,x37201,a859),a321),x37202)),x37202) % 181.55/181.53 [3724]E(f324(f167(a865),f133(a865,f324(f294(a865,f324(a115,x37241)),f324(a115,x37242)))),f297(a865,x37241,x37242)) % 181.55/181.53 [3749]E(f324(f324(f261(x37491,x37492),f247(f871(x37491,a859))),f324(f16(f871(x37492,a859),x37491),f247(f871(x37492,a859)))),f247(f871(f870(x37491,x37492),a859))) % 181.55/181.53 [3784]E(f324(f244(x37841),f324(f324(f8(a859,a859,x37841),a319),x37842)),f324(f80(f871(x37841,a859)),f324(f244(x37841),x37842))) % 181.55/181.53 [3787]E(f324(f244(x37871),f324(f324(f7(x37871,x37871,a859),a321),x37872)),f324(f324(f302(x37871),x37872),f191(f871(x37871,a859)))) % 181.55/181.53 [3794]E(f324(f324(f81(a1),f324(f324(f22(a1),x37941),x37942)),f324(f324(f22(a1),x37941),x37942)),f324(f324(f22(a1),f324(f324(f81(a1),x37941),x37941)),f324(f324(f81(a1),x37942),x37942))) % 181.55/181.53 [3795]E(f324(f324(f81(a1),f324(f324(f81(a1),x37951),x37951)),f324(f324(f81(a1),x37952),x37952)),f324(f324(f81(a1),f324(f324(f81(a1),x37951),x37952)),f324(f324(f81(a1),x37951),x37952))) % 181.55/181.53 [3811]P1(f324(f324(f238(a865),f324(f37(x38111),f324(f167(x38111),x38112))),f324(f192(f866(x38111)),x38112))) % 181.55/181.53 [3812]P1(f324(f324(f238(a865),f324(f192(f866(x38121)),f146(x38121,x38122))),f324(f192(f866(x38121)),x38122))) % 181.55/181.53 [3822]E(f324(f244(x38221),f324(f324(f7(x38221,f871(x38221,a859),a859),f326(x38221)),x38222)),x38222) % 181.55/181.53 [3837]E(f324(f324(f170(x38371),f324(f324(f22(a865),f324(f192(f866(x38371)),x38372)),f79(a865))),x38372),f117(x38371,x38372)) % 181.55/181.53 [3859]E(f186(a865,f2(a865),f324(f324(f8(a865,a865,a865),a115),f324(f189(a865),x38591)),x38592),f324(f324(f189(a865),f324(a115,x38591)),x38592)) % 181.55/181.53 [3863]E(f39(f871(x38631,a859),f324(f303(f871(f870(x38631,x38631),a859),f871(x38631,a859),f277(x38631)),x38632)),f324(f277(x38631),f39(f871(f870(x38631,x38631),a859),x38632))) % 181.55/181.53 [3864]E(f186(a865,f324(a115,x38641),f324(f324(f8(a865,a865,a865),a115),f324(f190(a865),x38641)),x38642),f324(f324(f190(a865),f324(a115,x38641)),x38642)) % 181.55/181.53 [3866]E(f324(f324(f259(a1,a1),f324(f324(f38(a1),f324(f75(a1),x38661)),f324(f75(a1),x38662))),f44(a1,f324(f75(a1),x38661),f324(f75(a1),x38662))),f52(x38661,x38662)) % 181.55/181.53 [3888]P1(f324(f324(f238(f871(f871(x38881,a859),a859)),x38882),f324(f301(x38881),f39(f871(x38881,a859),x38882)))) % 181.55/181.53 [3922]E(f324(f324(f41(x39221,f871(x39221,a859)),x39222),f324(f324(f7(x39221,f871(x39221,a859),f871(x39221,a859)),f302(x39221)),f191(f871(x39221,a859)))),x39222) % 181.55/181.53 [3923]E(f324(f324(f281(x39231,x39231,x39231),f324(f279(x39231,x39231),x39232)),f300(x39231,f324(f279(x39231,x39231),x39232))),f324(f279(x39231,x39231),f324(f324(f281(x39231,x39231,x39231),x39232),f300(x39231,x39232)))) % 181.55/181.53 [3995]E(f324(f167(x39951),f324(f136(f866(x39951),f866(x39951),f124(x39951),f116(x39951)),x39952)),f324(f324(f41(f866(x39951),f871(x39951,a859)),f324(f167(f866(x39951)),x39952)),f167(x39951))) % 181.55/181.53 [4027]E(f324(f324(f113(f871(f870(x40271,x40271),a859)),f300(x40271,f191(f871(f870(x40271,x40271),a859)))),f324(f324(f281(x40271,x40271,x40271),f300(x40271,x40272)),x40272)),f300(x40271,x40272)) % 181.55/181.53 [4061]E(f324(f324(f177(x40611,x40611),x40612),x40612),f324(f324(f148(x40611,f870(x40611,x40611)),f324(f324(f18(x40611,x40611,f870(x40611,x40611)),f259(x40611,x40611)),f5(x40611))),x40612)) % 181.55/181.53 [4180]E(f324(f136(a865,f866(x41801),f324(f7(f866(x41801),a865,a865),f324(f324(f8(a865,f871(a865,a865),f866(x41801)),f190(a865)),f192(f866(x41801)))),f2(a865)),f324(f163(f866(x41801)),x41802)),f324(f192(f866(f866(x41801))),f175(x41801,x41802))) % 181.55/181.53 [4259]E(f324(f324(f280(f870(a865,f866(x42591)),f866(x42591)),f316(a865,f866(x42591),a243,f139(x42591,x42592))),f324(f324(f18(f866(x42591),f866(x42591),f870(a865,f866(x42591))),f324(f324(f8(a865,f871(f866(x42591),f870(a865,f866(x42591))),f866(x42591)),f259(a865,f866(x42591))),f192(f866(x42591)))),f5(f866(x42591)))),f140(x42591,x42592)) % 181.55/181.53 [4389]E(f324(f244(x43891),f324(f324(f8(f871(f871(x43891,a859),a859),a859,x43891),f89(f871(x43891,a859))),f324(f324(f8(f871(f871(x43891,a859),a859),f871(f871(x43891,a859),a859),x43891),f324(f18(f871(x43891,a859),a859,a859),f324(f324(f8(a859,f871(a859,a859),f871(x43891,a859)),a327),f324(f324(f7(f871(x43891,a859),f871(f871(x43891,a859),a859),a859),f326(f871(x43891,a859))),x43892)))),f326(x43891)))),f40(f871(x43891,a859),x43892)) % 181.55/181.53 [4545]~P1(f324(f324(f239(a1),f324(f103(a1),x45451)),f324(f80(a1),f324(f103(a1),x45452)))) % 181.55/181.53 [4561]~P1(f324(f324(f92(a1),f324(f324(f22(a1),f324(f324(f81(a1),x45611),x45611)),a100)),f324(f324(f81(a1),x45612),x45612))) % 181.55/181.53 [3463]E(f324(f324(f22(a865),f324(f324(f81(a865),x34631),x34632)),x34632),x34631) % 181.55/181.53 [3464]E(f324(f324(f22(a865),f324(f324(f81(a865),x34641),x34642)),x34641),x34642) % 181.55/181.53 [3530]E(f324(f324(f81(a865),f324(f324(f22(a865),x35301),x35302)),x35302),f324(f324(f190(a865),x35301),x35302)) % 181.55/181.53 [3635]E(f324(f324(f82(a865),f324(f324(f38(a865),x36351),x36352)),x36352),f324(f324(f22(a865),x36351),f44(a865,x36351,x36352))) % 181.55/181.53 [3664]E(f324(f167(a865),f133(a865,f324(f294(a865,f324(a115,x36641)),x36642))),f298(a865,x36641,x36642)) % 181.55/181.53 [3671]E(f324(f103(a1),f221(f324(a107,f324(f75(a1),x36711)),f324(a107,f324(f75(a1),x36712)))),f324(f324(a222,x36711),x36712)) % 181.55/181.53 [3673]E(f324(f324(f104(f871(x36731,a859)),f324(f80(f871(x36731,a859)),x36732)),x36732),f191(f871(x36731,a859))) % 181.55/181.53 [3674]E(f324(f324(f113(f871(x36741,a859)),f324(f80(f871(x36741,a859)),x36742)),x36742),f247(f871(x36741,a859))) % 181.55/181.53 [3692]P1(f324(f324(f238(a865),f324(f324(f22(a865),x36921),x36922)),x36921)) % 181.55/181.53 [3693]P1(f324(f324(f238(a865),f324(f324(f38(a865),x36931),x36932)),x36931)) % 181.55/181.53 [3716]P1(f324(f324(f239(a865),x37161),f324(a115,f324(f324(f81(a865),x37162),x37161)))) % 181.55/181.53 [3717]P1(f324(f324(f239(a865),x37171),f324(a115,f324(f324(f81(a865),x37171),x37172)))) % 181.55/181.53 [3734]E(f324(f324(f82(a865),f324(a107,f324(f75(a1),x37341))),f324(a107,f324(f75(a1),x37342))),f324(a107,f324(f75(a1),f324(f324(f82(a1),x37341),x37342)))) % 181.55/181.53 [3745]P1(f324(f324(f238(a1),f2(a1)),f324(f324(f249(a1),f324(f75(a1),x37451)),x37452))) % 181.55/181.53 [3816]E(f324(f278(f866(x38161),f866(x38161),f152(x38161,x38162)),f324(f324(f302(f866(x38161)),f116(x38161)),f191(f871(f866(x38161),a859)))),f324(f324(f302(f866(x38161)),f116(x38161)),f191(f871(f866(x38161),a859)))) % 181.55/181.53 [3835]E(f324(f324(f113(f871(f870(x38351,x38351),a859)),f300(x38351,x38352)),f300(x38351,f191(f871(f870(x38351,x38351),a859)))),f300(x38351,x38352)) % 181.55/181.53 [3849]E(f324(f324(f38(a1),f324(f106(a1),f324(f324(f81(a1),x38491),x38491))),f324(f106(a1),f324(f324(f81(a1),x38492),x38492))),f324(f324(f38(a1),f324(f106(a1),x38491)),f324(f106(a1),x38492))) % 181.55/181.53 [3912]E(f324(f324(f249(a1),x39121),f324(f106(a865),f324(f324(f81(a1),x39122),x39122))),f324(f324(f87(a1,a1),f324(f324(f249(a1),x39121),f324(f106(a865),x39122))),f324(f324(f18(a1,a1,a1),f82(a1)),f5(a1)))) % 181.55/181.53 [3918]E(f324(f244(f871(x39181,a859)),f324(f324(f7(f871(x39181,a859),f871(x39181,a859),a859),f238(f871(x39181,a859))),x39182)),f324(f301(x39181),x39182)) % 181.55/181.53 [3934]E(f324(f324(f148(a1,a865),a107),f324(f324(f124(a1),f324(f324(f148(a865,a1),f103(a1)),x39341)),f324(f324(f148(a865,a1),f103(a1)),x39342))),f324(f324(f124(a865),x39341),x39342)) % 181.55/181.53 [3971]E(f324(f303(a1,a1,f324(f324(f7(a1,a1,a1),f81(a1)),x39711)),f324(f294(a1,f2(a1)),f324(f324(f22(a1),x39712),x39711))),f324(f294(a1,x39711),x39712)) % 181.55/181.53 [3973]P43(x39731,f324(f324(f22(f871(f870(x39731,x39731),a859)),x39732),f300(x39731,f191(f871(f870(x39731,x39731),a859))))) % 181.55/181.53 [3993]E(f324(f192(f866(x39931)),f324(f136(f866(x39931),f866(x39931),f124(x39931),f116(x39931)),x39932)),f324(f160(a865),f324(f324(f148(f866(x39931),a865),f192(f866(x39931))),x39932))) % 181.55/181.53 [3998]P41(x39981,f247(f871(x39981,a859)),f324(f324(f113(f871(f870(x39981,x39981),a859)),x39982),f300(x39981,f191(f871(f870(x39981,x39981),a859))))) % 181.55/181.53 [4041]E(f186(a865,f2(a865),f324(f324(f8(a865,a865,a865),a115),f324(f324(f7(a865,a865,a865),f189(a865)),x40411)),x40412),f324(f324(f189(a865),x40412),f324(a115,x40411))) % 181.55/181.53 [4044]E(f186(a865,f324(a115,x40441),f324(f324(f8(a865,a865,a865),a115),f324(f324(f7(a865,a865,a865),f190(a865)),x40441)),x40442),f324(f324(f190(a865),x40442),f324(a115,x40441))) % 181.55/181.53 [4047]E(f324(f303(x40471,f866(x40471),f324(f324(f7(x40471,f866(x40471),f866(x40471)),f145(x40471)),f116(x40471))),x40472),f169(x40471,x40472,f324(f324(f302(f866(x40471)),f116(x40471)),f191(f871(f866(x40471),a859))))) % 181.55/181.53 [4048]E(f324(f324(f113(f871(f870(x40481,x40481),a859)),f324(f324(f281(x40481,x40481,x40481),x40482),f300(x40481,x40482))),f300(x40481,f191(f871(f870(x40481,x40481),a859)))),f300(x40481,x40482)) % 181.55/181.53 [4056]P1(f324(f324(f238(f871(f870(x40561,x40561),a859)),f256(x40561,x40562)),f324(f324(f261(x40561,x40561),x40562),f324(f16(f871(x40561,a859),x40561),x40562)))) % 181.55/181.53 [4059]E(f324(f303(a1,a865,a107),f324(f324(f104(f871(a1,a859)),f324(f303(a865,a1,f103(a1)),x40591)),f324(f303(a865,a1,f103(a1)),x40592))),f324(f324(f104(f871(a865,a859)),x40591),x40592)) % 181.55/181.53 [4060]E(f324(f303(a1,a865,a107),f324(f324(f113(f871(a1,a859)),f324(f303(a865,a1,f103(a1)),x40601)),f324(f303(a865,a1,f103(a1)),x40602))),f324(f324(f113(f871(a865,a859)),x40601),x40602)) % 181.55/181.53 [4064]E(f324(f244(x40641),f324(f324(f8(a859,a859,x40641),a319),f324(f324(f7(x40641,f871(x40641,a859),a859),f326(x40641)),x40642))),f324(f80(f871(x40641,a859)),x40642)) % 181.55/181.53 [4091]E(f324(f136(f866(x40911),f866(x40911),f124(x40911),f116(x40911)),f324(f324(f148(f866(x40911),f866(x40911)),f163(x40911)),f324(f163(f866(x40911)),x40912))),f324(f163(x40911),f324(f136(f866(x40911),f866(x40911),f124(x40911),f116(x40911)),x40912))) % 181.55/181.53 [4120]E(f324(f324(f41(a865,f871(f870(x41201,x41201),a859)),f247(f871(a865,a859))),f324(f324(f7(a865,f871(f870(x41201,x41201),a859),f871(f870(x41201,x41201),a859)),f184(f870(x41201,x41201),a859)),x41202)),f300(x41201,x41202)) % 181.55/181.53 [4140]E(f86(x41401,f324(f324(f8(f871(x41401,a859),a859,x41401),f324(a321,x41402)),f324(f324(f7(x41401,f871(x41401,a859),f871(x41401,a859)),f302(x41401)),f191(f871(x41401,a859))))),f305(x41401,x41402)) % 181.55/181.53 [4148]E(f324(f192(f866(x41481)),f146(x41481,f324(f136(f866(x41481),f866(x41481),f124(x41481),f116(x41481)),x41482))),f324(f37(x41481),f324(f324(f41(f866(x41481),f871(x41481,a859)),f324(f167(f866(x41481)),x41482)),f167(x41481)))) % 181.55/181.53 [4165]E(f324(f324(f113(f871(f870(x41651,x41651),a859)),x41652),f324(f324(f281(x41651,x41651,x41651),f324(f324(f281(x41651,x41651,x41651),x41652),f300(x41651,x41652))),x41652)),f324(f324(f281(x41651,x41651,x41651),x41652),f300(x41651,x41652))) % 181.55/181.53 [4190]P1(f324(f324(f238(f871(f870(x41901,x41901),a859)),f324(f324(f281(x41901,x41901,x41901),x41902),f300(x41901,x41902))),f324(f324(f261(x41901,x41901),f324(f277(x41901),x41902)),f324(f16(f871(x41901,a859),x41901),f324(f277(x41901),x41902))))) % 181.55/181.53 [4234]E(f324(f244(f866(x42341)),f324(f324(f7(f866(x42341),f871(x42341,a859),a859),f324(f324(f8(f871(x42341,a859),f871(f871(x42341,a859),a859),f866(x42341)),f238(f871(x42341,a859))),f167(x42341))),x42342)),f155(x42341,x42342)) % 181.55/181.53 [4246]E(f324(f150(f866(x42461),x42461,f116(x42461),f324(f324(f8(f866(x42461),f871(f866(x42461),f866(x42461)),x42461),f324(f7(f866(x42461),f866(x42461),f866(x42461)),f124(x42461))),f324(f324(f7(x42461,f866(x42461),f866(x42461)),f145(x42461)),f116(x42461)))),x42462),f324(f162(x42461),x42462)) % 181.55/181.53 [4288]P27(f871(x42881,x42882),f871(f870(x42881,x42882),a859),f324(f324(f8(f871(f870(x42881,x42882),a859),f871(f870(x42881,x42882),a859),f871(x42881,x42882)),f244(f870(x42881,x42882))),f324(f324(f8(f871(x42881,f871(x42882,a859)),f871(f870(x42881,x42882),a859),f871(x42881,x42882)),f263(x42881,x42882,a859)),f324(f8(x42882,f871(x42882,a859),x42881),f324(f7(x42882,x42882,a859),a321)))),f247(f871(f871(x42881,x42882),a859))) % 181.55/181.53 [4293]E(f44(a1,f324(f106(a1),f324(f324(f81(a1),x42931),x42931)),f324(f106(a1),f324(f324(f81(a1),x42932),x42932))),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f44(a1,f324(f106(a1),x42931),f324(f106(a1),x42932)))) % 181.55/181.53 [4336]E(f324(f324(f41(x43361,f871(f870(x43361,x43361),a859)),x43362),f324(f324(f7(x43361,f871(f870(x43361,x43361),a859),f871(f870(x43361,x43361),a859)),f324(f324(f8(f870(x43361,x43361),f871(f871(f870(x43361,x43361),a859),f871(f870(x43361,x43361),a859)),x43361),f302(f870(x43361,x43361))),f324(f324(f18(x43361,x43361,f870(x43361,x43361)),f259(x43361,x43361)),f5(x43361)))),f191(f871(f870(x43361,x43361),a859)))),f256(x43361,x43362)) % 181.55/181.53 [4344]E(f206(x43441,f324(f324(f259(a1,a1),f324(f80(a1),f324(f324(f73(f870(a1,a1),a1,x43441,f258(a1,a1)),f217(x43441)),x43442))),f324(f324(f73(f870(a1,a1),a1,x43441,f262(a1,a1)),f217(x43441)),x43442))),f225(x43441,x43442)) % 181.55/181.53 [4428]E(f324(f244(f871(x44281,a859)),f324(f324(f8(f871(f871(x44281,a859),a859),a859,f871(x44281,a859)),f88(f871(x44281,a859))),f324(f324(f7(f871(x44281,a859),f871(f871(x44281,a859),a859),f871(f871(x44281,a859),a859)),f324(f324(f8(f871(f871(x44281,a859),f871(a859,a859)),f871(f871(f871(x44281,a859),a859),f871(f871(x44281,a859),a859)),f871(x44281,a859)),f18(f871(x44281,a859),a859,a859)),f324(f324(f8(f871(f871(x44281,a859),a859),f871(f871(x44281,a859),f871(a859,a859)),f871(x44281,a859)),f324(f8(a859,f871(a859,a859),f871(x44281,a859)),a322)),f324(f324(f7(f871(x44281,a859),f871(f871(x44281,a859),f871(x44281,a859)),f871(f871(x44281,a859),a859)),f324(f324(f8(f871(f871(x44281,a859),a859),f871(f871(f871(x44281,a859),f871(x44281,a859)),f871(f871(x44281,a859),a859)),f871(x44281,a859)),f8(f871(x44281,a859),a859,f871(x44281,a859))),a321)),f80(f871(x44281,a859)))))),f324(f324(f8(f871(f871(x44281,a859),a859),a859,f871(x44281,a859)),f324(f326(f871(x44281,a859)),x44282)),f301(x44281))))),f324(f301(x44281),f324(f80(f871(x44281,a859)),x44282))) % 181.55/181.53 [4542]~E(f324(f324(f81(a1),x45421),x45421),f324(f324(f22(a1),f324(f324(f81(a1),x45422),x45422)),a100)) % 181.55/181.53 [4548]~P1(f324(f324(f239(a865),f324(f324(f81(a865),x45481),x45482)),x45482)) % 181.55/181.53 [4549]~P1(f324(f324(f239(a865),f324(f324(f81(a865),x45491),x45492)),x45491)) % 181.55/181.53 [3750]E(f324(f324(f22(a865),x37501),f324(f324(f82(a865),f324(f324(f38(a865),x37501),x37502)),x37502)),f44(a865,x37501,x37502)) % 181.55/181.53 [3751]E(f324(f324(f22(a1),x37511),f324(f324(f82(a1),f324(f324(f38(a1),x37511),x37512)),x37512)),f44(a1,x37511,x37512)) % 181.55/181.53 [3785]E(f324(f324(f148(a865,x37851),f324(f159(x37851),x37852)),f133(a865,f324(f294(a865,f2(a865)),f324(f192(f866(x37851)),x37852)))),x37852) % 181.55/181.53 [3845]E(f324(f278(x38451,x38451,f300(x38451,f191(f871(f870(x38451,x38451),a859)))),x38452),x38452) % 181.55/181.53 [3976]E(f300(x39761,f324(f324(f22(f871(f870(x39761,x39761),a859)),x39762),f300(x39761,f191(f871(f870(x39761,x39761),a859))))),f300(x39761,x39762)) % 181.55/181.53 [3977]E(f300(x39771,f324(f324(f113(f871(f870(x39771,x39771),a859)),x39772),f300(x39771,f191(f871(f870(x39771,x39771),a859))))),f300(x39771,x39772)) % 181.55/181.53 [4030]E(f324(f324(f22(a1),f324(f324(f22(a1),f324(f324(f81(a1),x40301),x40301)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),x40302),x40302)),a100)),f324(f324(f81(a1),f324(f324(f22(a1),x40301),x40302)),f324(f324(f22(a1),x40301),x40302))) % 181.55/181.53 [4069]E(f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f81(a1),x40691),x40692)),f324(f324(f81(a1),x40691),x40692))),a100),f324(f324(f81(a1),f324(f324(f81(a1),x40691),x40691)),f324(f324(f22(a1),f324(f324(f81(a1),x40692),x40692)),a100))) % 181.55/181.53 [4095]E(f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),x40951),x40951)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),x40952),x40952)),a100)),f324(f324(f81(a1),f324(f324(f81(a1),x40951),f324(f324(f22(a1),x40952),a100))),f324(f324(f81(a1),x40951),f324(f324(f22(a1),x40952),a100)))) % 181.55/181.53 [4105]E(f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),x41051),x41052)),f324(f324(f22(a1),x41051),x41052))),a100),f324(f324(f22(a1),f324(f324(f22(a1),f324(f324(f81(a1),x41051),x41051)),a100)),f324(f324(f81(a1),x41052),x41052))) % 181.55/181.53 [4106]E(f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f81(a1),x41061),x41062)),f324(f324(f81(a1),x41061),x41062))),a100),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),x41061),x41061)),a100)),f324(f324(f81(a1),x41062),x41062))) % 181.55/181.53 [4162]E(f324(f103(a1),f324(f324(f38(a865),f324(f324(f82(a865),f324(a107,f324(f75(a1),x41621))),f324(a107,f324(f75(a1),x41622)))),f221(f324(a107,f324(f75(a1),x41621)),f324(a107,f324(f75(a1),x41622))))),f223(x41621,x41622)) % 181.55/181.53 [4211]E(f324(f324(f265(f870(a102,a102),a102,f870(a102,a102),f870(x42111,f870(a102,a102))),f269(f324(a3,f324(f192(f866(x42111)),x42112)))),f324(f324(f8(x42111,f871(f870(a102,a102),f870(x42111,f870(a102,a102))),a102),f259(x42111,f870(a102,a102))),f324(f324(f8(a865,x42111,a102),f324(f159(x42111),x42112)),a19))),f275(x42111,x42112)) % 181.55/181.53 [4294]E(f324(f136(a865,f866(x42941),f324(f7(f866(x42941),a865,a865),f324(f324(f8(a865,f871(a865,a865),f866(x42941)),f190(a865)),f192(f866(x42941)))),f2(a865)),f324(f163(f866(x42941)),f175(x42941,x42942))),f324(f192(f866(f866(x42941))),f324(f130(f866(x42941),f324(f324(f8(a859,a859,f866(x42941)),a319),f324(f324(f7(f866(x42941),f866(x42941),a859),a321),f116(x42941)))),x42942))) % 181.55/181.53 [4300]E(f324(f324(f41(a865,f871(x43001,a859)),f247(f871(a865,a859))),f324(f324(f7(a865,f871(a865,f871(x43001,a859)),f871(x43001,a859)),f324(f324(f8(f871(a865,a859),f871(f871(a865,f871(x43001,a859)),f871(x43001,a859)),a865),f41(a865,f871(x43001,a859))),f294(a865,f2(a865)))),x43002)),f324(f324(f41(a865,f871(x43001,a859)),f247(f871(a865,a859))),x43002)) % 181.55/181.53 [4320]P1(f324(f61(a865),f324(f244(a865),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),x43201)),f324(f324(f7(a865,a865,a859),f239(a865)),x43202))))) % 181.55/181.53 [4438]E(f324(f244(f870(f866(x44381),f866(x44381))),f324(f263(f866(x44381),f866(x44381),a859),f324(f324(f18(f866(x44381),f871(f866(x44381),a859),f871(f866(x44381),a859)),f324(f324(f8(f871(f866(x44381),f871(a859,a859)),f871(f871(f866(x44381),a859),f871(f866(x44381),a859)),f866(x44381)),f18(f866(x44381),a859,a859)),f324(f324(f8(f871(f866(x44381),a859),f871(f866(x44381),f871(a859,a859)),f866(x44381)),f324(f8(a859,f871(a859,a859),f866(x44381)),a323)),f324(f324(f7(f866(x44381),f871(f866(x44381),a865),f871(f866(x44381),a859)),f324(f324(f8(f871(a865,a859),f871(f871(f866(x44381),a865),f871(f866(x44381),a859)),f866(x44381)),f8(a865,a859,f866(x44381))),f324(f324(f8(a865,f871(a865,a859),f866(x44381)),f239(a865)),f192(f866(x44381))))),f192(f866(x44381)))))),f324(f324(f18(f866(x44381),f871(f866(x44381),a859),f871(f866(x44381),a859)),f324(f324(f8(f871(f866(x44381),f871(a859,a859)),f871(f871(f866(x44381),a859),f871(f866(x44381),a859)),f866(x44381)),f18(f866(x44381),a859,a859)),f324(f324(f8(f871(f866(x44381),a859),f871(f866(x44381),f871(a859,a859)),f866(x44381)),f324(f8(a859,f871(a859,a859),f866(x44381)),a322)),f324(f324(f7(f866(x44381),f871(f866(x44381),a865),f871(f866(x44381),a859)),f324(f324(f8(f871(a865,a859),f871(f871(f866(x44381),a865),f871(f866(x44381),a859)),f866(x44381)),f8(a865,a859,f866(x44381))),f324(f324(f8(a865,f871(a865,a859),f866(x44381)),a321),f192(f866(x44381))))),f192(f866(x44381)))))),f324(f324(f7(f866(x44381),f871(f870(f866(x44381),f866(x44381)),a859),f871(f866(x44381),a859)),f324(f324(f8(f871(f866(x44381),f871(f871(f870(f866(x44381),f866(x44381)),a859),a859)),f871(f871(f870(f866(x44381),f866(x44381)),a859),f871(f866(x44381),a859)),f866(x44381)),f7(f866(x44381),f871(f870(f866(x44381),f866(x44381)),a859),a859)),f324(f324(f8(f871(f866(x44381),f870(f866(x44381),f866(x44381))),f871(f866(x44381),f871(f871(f870(f866(x44381),f866(x44381)),a859),a859)),f866(x44381)),f324(f8(f870(f866(x44381),f866(x44381)),f871(f871(f870(f866(x44381),f866(x44381)),a859),a859),f866(x44381)),f326(f870(f866(x44381),f866(x44381))))),f259(f866(x44381),f866(x44381))))),f139(x44381,x44382)))))),f140(x44381,x44382)) % 181.55/181.53 [4554]~P1(f324(f324(f92(a1),f324(f324(f81(a1),x45541),x45541)),f324(f324(f22(a1),f324(f324(f81(a1),x45542),x45542)),a100))) % 181.55/181.53 [4098]E(f324(f324(f81(a1),f324(f324(f81(a1),f324(f324(f82(a1),x40981),x40982)),f324(f324(f82(a1),x40981),x40982))),x40982),f324(f324(f82(a1),f324(f324(f22(a1),f324(f324(f81(a1),x40981),x40981)),a100)),x40982)) % 181.55/181.53 [4209]E(f324(a107,f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x42091),x42092)),f191(f871(f870(a865,a865),a859)))))),f324(f324(f22(a865),x42091),x42092)) % 181.55/181.53 [4214]E(f324(f324(f281(x42141,x42141,x42141),f324(f324(f113(f871(f870(x42141,x42141),a859)),x42142),f300(x42141,f191(f871(f870(x42141,x42141),a859))))),f300(x42141,f324(f324(f113(f871(f870(x42141,x42141),a859)),x42142),f300(x42141,f191(f871(f870(x42141,x42141),a859)))))),f300(x42141,x42142)) % 181.55/181.53 [4252]E(f270(x42521,f324(f130(f870(a102,x42521),f324(f263(a102,x42521,a859),f324(f324(f8(a859,f871(x42521,a859),a102),f16(a859,x42521)),f324(f239(a102),f2(a102))))),x42522)),f270(x42521,x42522)) % 181.55/181.53 [4253]E(f268(x42531,f324(f130(f870(a102,x42531),f324(f263(a102,x42531,a859),f324(f324(f8(a859,f871(x42531,a859),a102),f16(a859,x42531)),f324(f239(a102),f2(a102))))),x42532)),f268(x42531,x42532)) % 181.55/181.53 [4255]E(f324(f80(a1),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x42551),x42552)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x42552),x42551)),f191(f871(f870(a865,a865),a859)))))) % 181.55/181.53 [4311]E(f324(f324(f280(f866(a865),x43111),f139(a865,a243)),f324(f324(f7(x43111,f866(f871(x43111,a865)),f866(a865)),f324(f324(f8(f871(f871(x43111,a865),a865),f871(f866(f871(x43111,a865)),f866(a865)),x43111),f148(f871(x43111,a865),a865)),f324(f7(f871(x43111,a865),x43111,a865),f5(f871(x43111,a865))))),x43112)),f147(x43111,x43112)) % 181.55/181.53 [4333]E(f324(f324(f87(a1,a865),f324(f106(a1),f324(f324(f81(a1),x43331),a100))),f324(f324(f18(a1,a865,a865),f324(f324(f7(a1,a865,f871(a865,a865)),f324(f324(f8(a859,f871(a865,f871(a865,a865)),a1),f99(a865)),a196)),f2(a865))),f324(f324(f8(a865,a865,a1),a115),f324(f324(f8(a865,a865,a1),f324(f189(a865),x43332)),a107)))),f324(f324(f189(a865),f324(a115,x43332)),f324(f106(a865),x43331))) % 181.55/181.53 [4334]E(f324(f324(f87(a1,a865),f324(f106(a1),f324(f324(f81(a1),x43341),a100))),f324(f324(f18(a1,a865,a865),f324(f324(f7(a1,a865,f871(a865,a865)),f324(f324(f8(a859,f871(a865,f871(a865,a865)),a1),f99(a865)),a196)),f324(a115,x43342))),f324(f324(f8(a865,a865,a1),a115),f324(f324(f8(a865,a865,a1),f324(f190(a865),x43342)),a107)))),f324(f324(f190(a865),f324(a115,x43342)),f324(f106(a865),x43341))) % 181.55/181.53 [4354]E(f324(f136(f866(x43541),f866(x43541),f124(x43541),f116(x43541)),f324(f324(f148(f866(x43541),f866(x43541)),f150(f866(x43541),x43541,f116(x43541),f324(f324(f8(f866(x43541),f871(f866(x43541),f866(x43541)),x43541),f16(f866(x43541),f866(x43541))),f324(f324(f7(x43541,f866(x43541),f866(x43541)),f145(x43541)),f116(x43541))))),x43542)),f324(f324(f148(f866(x43541),x43541),f135(x43541)),f324(f130(f866(x43541),f324(f324(f8(a859,a859,f866(x43541)),a319),f324(f324(f7(f866(x43541),f866(x43541),a859),a321),f116(x43541)))),x43542))) % 181.55/181.53 [4418]E(f324(f263(a1,a1,a859),f324(f324(f7(a1,f871(a1,a859),f871(a1,a859)),f324(f324(f8(f871(a1,f871(a859,a859)),f871(f871(a1,a859),f871(a1,a859)),a1),f18(a1,a859,a859)),f324(f324(f8(f871(a1,a859),f871(a1,f871(a859,a859)),a1),f324(f8(a859,f871(a859,a859),a1),a322)),f324(f324(f8(f871(a1,a1),f871(a1,a859),a1),f324(f8(a1,a859,a1),f324(a321,x44181))),f324(f324(f8(a1,f871(a1,a1),a1),f81(a1)),f324(f82(a1),x44182)))))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),f324(a327,f324(f324(f239(a1),f2(a1)),x44182))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),f324(f324(f7(a1,a1,a859),f239(a1)),x44182))))),f324(f324(f8(a859,a859,a1),f324(a327,f324(a319,f324(f324(f239(a1),f2(a1)),x44182)))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f239(a1),x44182))),f324(f324(f7(a1,a1,a859),f238(a1)),f2(a1))))))),f48(x44181,x44182)) % 181.55/181.53 [4420]E(f324(f244(x44201),f324(f324(f8(f871(a865,a859),a859,x44201),f88(a865)),f324(f324(f7(x44201,f871(a865,a859),f871(a865,a859)),f324(f324(f8(f871(a865,f871(a859,a859)),f871(f871(a865,a859),f871(a865,a859)),x44201),f18(a865,a859,a859)),f324(f324(f8(f871(a865,a859),f871(a865,f871(a859,a859)),x44201),f324(f8(a859,f871(a859,a859),a865),a322)),f324(f324(f7(x44201,f871(a865,x44201),f871(a865,a859)),f324(f324(f8(f871(x44201,a859),f871(f871(a865,x44201),f871(a865,a859)),x44201),f8(x44201,a859,a865)),a321)),f324(f159(x44201),x44202))))),f324(f324(f7(a865,a865,a859),f239(a865)),f324(f192(f866(x44201)),x44202))))),f324(f167(x44201),x44202)) % 181.55/181.53 [4224]E(f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),x42241),a100)),x42242)),f324(f324(f22(a1),f324(f324(f81(a1),x42241),a100)),x42242))),a100),f324(f324(f22(a1),f324(f324(f81(a1),x42241),x42241)),f324(f324(f22(a1),f324(f324(f81(a1),x42242),x42242)),a100))) % 181.55/181.53 [4349]E(f324(f136(f866(f866(x43491)),f866(f866(x43491)),f124(f866(x43491)),f116(f866(x43491))),f324(f324(f148(f866(x43491),f866(f866(x43491))),f150(f866(f866(x43491)),x43491,f116(f866(x43491)),f324(f16(f871(f866(x43491),f866(f866(x43491))),x43491),f324(f324(f7(f866(x43491),f866(f866(x43491)),f866(f866(x43491))),f145(f866(x43491))),f116(f866(x43491)))))),x43492)),f324(f324(f148(f866(x43491),f866(x43491)),f166(x43491)),f324(f130(f866(x43491),f324(f324(f8(a859,a859,f866(x43491)),a319),f324(f324(f7(f866(x43491),f866(x43491),a859),a321),f116(x43491)))),x43492))) % 181.55/181.53 [4360]E(f324(f324(f87(a1,a865),f324(f106(a1),f324(f324(f81(a1),x43601),a100))),f324(f324(f18(a1,a865,a865),f324(f324(f7(a1,a865,f871(a865,a865)),f324(f324(f8(a859,f871(a865,f871(a865,a865)),a1),f99(a865)),a196)),f2(a865))),f324(f324(f8(a865,a865,a1),a115),f324(f324(f7(a1,a865,a865),f324(f324(f8(a865,f871(a865,a865),a1),f189(a865)),a107)),x43602)))),f324(f324(f189(a865),f324(f106(a865),x43601)),f324(a115,x43602))) % 181.55/181.53 [4361]E(f324(f324(f87(a1,a865),f324(f106(a1),f324(f324(f81(a1),x43611),a100))),f324(f324(f18(a1,a865,a865),f324(f324(f7(a1,a865,f871(a865,a865)),f324(f324(f8(a859,f871(a865,f871(a865,a865)),a1),f99(a865)),a196)),f324(a115,x43612))),f324(f324(f8(a865,a865,a1),a115),f324(f324(f7(a1,a865,a865),f324(f324(f8(a865,f871(a865,a865),a1),f190(a865)),a107)),x43612)))),f324(f324(f190(a865),f324(f106(a865),x43611)),f324(a115,x43612))) % 181.55/181.53 [4348]E(f324(f263(x43481,x43481,a859),f324(f324(f18(x43481,a859,f871(x43481,a859)),f324(f324(f8(f871(x43481,f871(a859,a859)),f871(a859,f871(x43481,a859)),x43481),f7(x43481,a859,a859)),f324(f324(f8(f871(x43481,a859),f871(x43481,f871(a859,a859)),x43481),f324(f8(a859,f871(a859,a859),x43481),a322)),a321))),x43482)),f256(x43481,x43482)) % 181.55/181.53 [4395]E(f324(f324(f38(a865),x43951),f324(f324(f81(a865),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))),x43952)),f324(f324(f38(a865),x43951),f324(a115,f324(a115,f324(a115,x43952))))) % 181.55/181.53 [4396]E(f44(a865,x43961,f324(f324(f81(a865),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))),x43962)),f44(a865,x43961,f324(a115,f324(a115,f324(a115,x43962))))) % 181.55/181.53 [4397]E(f44(a865,f324(f324(f81(a865),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))),x43971),x43972),f44(a865,f324(a115,f324(a115,f324(a115,x43971))),x43972)) % 181.55/181.53 [4410]E(f123(f324(x44101,f324(f324(f82(a102),f324(f106(a102),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))),x44102))),f324(f209(x44101),x44102)) % 181.55/181.53 [4411]E(f324(f324(f38(a865),f324(f324(f81(a865),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))),x44111)),x44112),f324(f324(f38(a865),f324(a115,f324(a115,f324(a115,x44111)))),x44112)) % 181.55/181.53 [4464]~E(f33(x44641,x44642),f324(a25,x44643)) % 181.55/181.53 [4465]~E(f26(x44651,x44652),f324(a25,x44653)) % 181.55/181.53 [4466]~E(f32(x44661,x44662),f324(a25,x44663)) % 181.55/181.53 [4467]~E(f324(a25,x44671),f33(x44672,x44673)) % 181.55/181.53 [4468]~E(f324(a25,x44681),f26(x44682,x44683)) % 181.55/181.53 [4469]~E(f324(a25,x44691),f32(x44692,x44693)) % 181.55/181.53 [4486]~E(f30(x44861,x44862,x44863),a24) % 181.55/181.53 [4487]~E(f29(x44871,x44872,x44873),a24) % 181.55/181.53 [3179]E(f324(f195(x31791,x31792),x31793),f121(x31791,x31792)) % 181.55/181.53 [3278]E(f324(f324(f148(x32781,x32782),x32783),f116(x32781)),f116(x32782)) % 181.55/181.53 [3279]E(f324(f324(f204(x32791,x32792),x32793),f203(x32791)),f203(x32792)) % 181.55/181.53 [3319]E(f324(f185(x33191,x33192,x33193),f2(a865)),x33192) % 181.55/181.53 [3321]E(f324(f324(f177(x33211,x33212),x33213),f116(x33212)),f116(f870(x33211,x33212))) % 181.55/181.53 [3336]E(f324(f192(f866(x33361)),f165(x33361,x33362,x33363)),x33362) % 181.55/181.53 [3356]E(f86(x33561,f62(x33561,x33562,x33563)),f324(f63(x33561,x33562),x33563)) % 181.55/181.53 [3360]E(f248(x33601,x33602,f248(x33602,x33601,x33603)),x33603) % 181.55/181.53 [3408]E(f134(x34081,x34082,f146(x34081,x34083)),f146(x34081,f134(x34081,x34082,x34083))) % 181.55/181.53 [3427]E(f324(f258(f866(x34271),f866(x34271)),f161(x34271,x34272,x34273)),f324(f130(x34271,x34272),x34273)) % 181.55/181.53 [3504]E(f186(x35041,x35042,x35043,f2(a865)),x35042) % 181.55/181.53 [3505]E(f17(x35051,x35052,x35053,f2(a102)),x35052) % 181.55/181.53 [3512]E(f157(x35121,x35122,x35123,f116(x35121)),f116(x35122)) % 181.55/181.53 [3513]E(f158(x35131,x35132,x35133,f116(x35131)),f116(x35132)) % 181.55/181.53 [3520]E(f324(f324(f159(x35201),f324(f324(f145(x35201),x35202),x35203)),f2(a865)),x35202) % 181.55/181.53 [3548]E(f59(x35481,x35482,f116(x35481),x35483),f116(f870(x35481,x35482))) % 181.55/181.53 [3569]P27(x35691,x35692,x35693,f191(f871(x35691,a859))) % 181.55/181.53 [3725]E(f324(f73(x37251,x37252,x37251,x37253),f34(x37251)),x37253) % 181.55/181.53 [3903]P1(f324(f324(f326(f870(x39031,x39031)),f324(f324(f259(x39031,x39031),x39032),x39032)),f300(x39031,x39033))) % 181.55/181.53 [4555]~P1(f324(f324(f326(f870(f866(x45551),f866(x45551))),f324(f324(f259(f866(x45551),f866(x45551)),x45552),f116(x45551))),f139(x45551,x45553))) % 181.55/181.53 [4556]~P1(f324(f324(f326(f870(f866(x45561),f866(x45561))),f324(f324(f259(f866(x45561),f866(x45561)),x45562),f116(x45561))),f141(x45561,x45563))) % 181.55/181.53 [4557]~P1(f324(f324(f326(f870(f866(x45571),f866(x45571))),f324(f324(f259(f866(x45571),f866(x45571)),x45572),f116(x45571))),f151(x45571,x45573))) % 181.55/181.53 [4558]~P1(f324(f324(f326(f870(f866(x45581),f866(x45581))),f324(f324(f259(f866(x45581),f866(x45581)),f116(x45581)),x45582)),f139(x45581,x45583))) % 181.55/181.53 [4559]~P1(f324(f324(f326(f870(f866(x45591),f866(x45591))),f324(f324(f259(f866(x45591),f866(x45591)),f116(x45591)),x45592)),f151(x45591,x45593))) % 181.55/181.53 [3253]E(f324(f324(f205(x32531),x32532),x32533),f206(x32531,f220(x32532,x32533))) % 181.55/181.53 [3308]E(f324(f279(x33081,x33082),f324(f279(x33082,x33081),x33083)),x33083) % 181.55/181.53 [3331]E(f324(f324(f177(x33311,x33312),f116(x33311)),x33313),f116(f870(x33311,x33312))) % 181.55/181.53 [3334]E(f171(x33341,x33342,f324(f245(a865),x33343)),f324(f324(f170(x33341),x33343),x33342)) % 181.55/181.53 [3353]E(f146(x33531,f324(f130(x33531,x33532),x33533)),f324(f130(x33531,x33532),f146(x33531,x33533))) % 181.55/181.53 [3354]E(f324(f255(x33541,x33542),f324(f279(x33542,x33541),x33543)),f324(f257(x33542,x33541),x33543)) % 181.55/181.53 [3355]E(f324(f257(x33551,x33552),f324(f279(x33552,x33551),x33553)),f324(f255(x33552,x33551),x33553)) % 181.55/181.53 [3372]E(f324(f130(x33721,x33722),f324(f163(x33721),x33723)),f324(f163(x33721),f324(f130(x33721,x33722),x33723))) % 181.55/181.53 [3385]E(f324(f324(f132(x33851),x33852),f324(f166(x33851),x33853)),f324(f324(f132(x33851),f324(a115,x33852)),x33853)) % 181.55/181.53 [3403]E(f31(f29(x34031,x34032,x34033)),f324(f324(f81(a865),f31(x34033)),f324(a115,f2(a865)))) % 181.55/181.53 [3404]E(f324(f303(x34041,x34042,x34043),f191(f871(x34041,a859))),f191(f871(x34042,a859))) % 181.55/181.53 [3405]E(f324(f304(x34051,x34052,x34053),f191(f871(x34052,a859))),f191(f871(x34051,a859))) % 181.55/181.53 [3406]E(f324(f304(x34061,x34062,x34063),f247(f871(x34062,a859))),f247(f871(x34061,a859))) % 181.55/181.53 [3407]E(f324(f278(x34071,x34072,x34073),f191(f871(x34071,a859))),f191(f871(x34072,a859))) % 181.55/181.53 [3436]E(f324(f324(f302(x34361),x34362),f324(f167(x34361),x34363)),f324(f167(x34361),f134(x34361,x34362,x34363))) % 181.55/181.53 [3448]E(f234(x34481,x34482,f324(f233(x34481),x34483)),f324(f324(f81(a865),f324(x34482,x34483)),f324(a115,f2(a865)))) % 181.55/181.53 [3524]E(f324(f192(a861),f29(x35241,x35242,x35243)),f324(f324(f81(a865),f324(f192(a861),x35243)),f324(a115,f2(a865)))) % 181.55/181.53 [3525]E(f324(f303(f870(x35251,x35252),x35252,f262(x35251,x35252)),x35253),f324(f255(x35251,x35252),x35253)) % 181.55/181.53 [3526]E(f324(f303(f870(x35261,x35262),x35261,f258(x35261,x35262)),x35263),f324(f257(x35261,x35262),x35263)) % 181.55/181.53 [3595]E(f324(f324(f259(x35951,x35952),f324(f258(x35951,x35952),x35953)),f324(f262(x35951,x35952),x35953)),x35953) % 181.55/181.53 [3602]E(f324(f192(f867(x36021)),f125(x36021,x36022,x36023)),f324(f324(f81(a865),f324(f192(f867(x36021)),x36023)),f324(a115,f2(a865)))) % 181.55/181.53 [3603]E(f324(f324(f263(x36031,x36032,x36031),f16(x36031,x36032)),x36033),f324(f258(x36031,x36032),x36033)) % 181.55/181.53 [3623]E(f180(x36231,x36232,x36233,f324(f16(f869(x36232),x36231),f203(x36232))),x36233) % 181.55/181.53 [3624]E(f180(x36241,x36242,f324(f16(f869(x36242),x36241),f203(x36242)),x36243),x36243) % 181.55/181.53 [3680]E(f31(f30(x36801,x36802,x36803)),f324(f324(f81(a865),f324(f324(f81(a865),f31(x36802)),f31(x36803))),f324(a115,f2(a865)))) % 181.55/181.53 [3729]E(f324(f73(x37291,x37291,x37292,f34(x37291)),x37293),x37293) % 181.55/181.53 [3838]E(f324(f192(a861),f30(x38381,x38382,x38383)),f324(f324(f81(a865),f324(f324(f81(a865),f324(f192(a861),x38382)),f324(f192(a861),x38383))),f324(a115,f2(a865)))) % 181.55/181.53 [3913]P1(f324(f324(f238(f871(x39131,a859)),f324(f167(x39131),f324(f130(x39131,x39132),x39133))),f324(f167(x39131),x39133))) % 181.55/181.53 [3961]P1(f324(f324(f238(f871(x39611,a859)),f324(f167(x39611),f324(f324(f170(x39611),x39612),x39613))),f324(f167(x39611),x39613))) % 181.55/181.53 [3962]P1(f324(f324(f238(f871(x39621,a859)),f324(f167(x39621),f324(f324(f132(x39621),x39622),x39623))),f324(f167(x39621),x39623))) % 181.55/181.53 [3967]P1(f324(f324(f238(f871(x39671,a859)),f324(f167(x39671),f171(x39671,x39672,x39673))),f324(f167(x39671),x39672))) % 181.55/181.53 [3968]P1(f324(f324(f238(f871(x39681,a859)),f324(f167(x39681),f164(x39681,x39682,x39683))),f324(f167(x39681),x39683))) % 181.55/181.53 [3991]P27(f870(x39911,x39912),f870(x39912,x39911),f324(f263(x39911,x39912,f870(x39912,x39911)),f324(f7(x39912,x39911,f870(x39912,x39911)),f259(x39912,x39911))),x39913) % 181.55/181.53 [4003]E(f324(f324(f324(f184(f866(x40031),f866(x40031)),f44(a865,x40032,f324(f192(f866(x40031)),x40033))),f162(x40031)),x40033),f324(f324(f324(f184(f866(x40031),f866(x40031)),x40032),f162(x40031)),x40033)) % 181.55/181.53 [4045]P1(f324(f324(f326(f870(f866(x40451),f866(x40451))),f324(f324(f259(f866(x40451),f866(x40451)),x40452),x40452)),f152(x40451,f300(x40451,x40453)))) % 181.55/181.53 [4193]E(f86(f870(x41931,x41932),f324(f324(f18(f870(x41931,x41932),x41932,a859),f324(f324(f8(x41931,f871(x41932,a859),f870(x41931,x41932)),x41933),f258(x41931,x41932))),f262(x41931,x41932))),f86(f870(x41931,x41932),f324(f263(x41931,x41932,a859),x41933))) % 181.55/181.53 [4194]E(f91(f870(x41941,x41942),f324(f324(f18(f870(x41941,x41942),x41942,a859),f324(f324(f8(x41941,f871(x41942,a859),f870(x41941,x41942)),x41943),f258(x41941,x41942))),f262(x41941,x41942))),f91(f870(x41941,x41942),f324(f263(x41941,x41942,a859),x41943))) % 181.55/181.53 [4231]E(f324(f324(f280(f870(a865,x42311),x42311),f316(a865,x42311,a243,x42312)),f324(f324(f18(x42311,x42311,f870(a865,x42311)),f324(f324(f8(a865,f871(x42311,f870(a865,x42311)),x42311),f259(a865,x42311)),x42313)),f5(x42311))),f318(x42311,x42313,x42312)) % 181.55/181.53 [4296]E(f324(f264(x42961,x42961,x42962,x42962,f5(x42961),f5(x42962)),x42963),x42963) % 181.55/181.53 [4371]E(f324(f136(f866(f866(x43711)),f866(f866(x43711)),f124(f866(x43711)),f116(f866(x43711))),f324(f324(f148(f866(x43711),f866(f866(x43711))),f324(f324(f7(f866(x43711),f866(x43711),f866(f866(x43711))),f324(f324(f8(f871(x43711,f866(x43711)),f871(f866(x43711),f866(f866(x43711))),f866(x43711)),f148(x43711,f866(x43711))),f324(f7(x43711,f866(x43711),f866(x43711)),f145(x43711)))),x43712)),f54(x43711,x43713,x43712))),f54(x43711,f324(a115,x43713),x43712)) % 181.55/181.53 [4434]E(f324(f235(a865,f870(x44341,f867(x44341)),f2(a865),f324(f263(x44341,f867(x44341),a865),f324(f324(f7(x44341,a865,f871(f867(x44341),a865)),f324(f324(f8(f871(f867(x44341),f871(a865,a865)),f871(a865,f871(f867(x44341),a865)),x44341),f7(f867(x44341),a865,a865)),f324(f324(f8(f871(f867(x44341),a865),f871(f867(x44341),f871(a865,a865)),x44341),f324(f8(a865,f871(a865,a865),f867(x44341)),f81(a865))),f324(f324(f7(x44341,f871(f867(x44341),a865),f871(f867(x44341),a865)),f324(f324(f8(f871(a865,a865),f871(f871(f867(x44341),a865),f871(f867(x44341),a865)),x44341),f8(a865,a865,f867(x44341))),f324(f324(f8(a865,f871(a865,a865),x44341),f81(a865)),x44342))),f128(x44341,x44342))))),f79(a865)))),f324(f127(x44341),x44343)),f324(f128(x44341,x44342),x44343)) % 181.55/181.53 [4437]E(f324(f324(f87(a1,x44371),f223(f324(f324(f73(f870(a1,a1),a1,x44371,f262(a1,a1)),f217(x44371)),x44372),f324(f324(f73(f870(a1,a1),a1,x44371,f262(a1,a1)),f217(x44371)),x44373))),f324(f324(f18(a1,a1,x44371),f324(f324(f8(a1,f871(a1,x44371),a1),f205(x44371)),f324(f324(f18(a1,a1,a1),f324(f324(f8(a1,f871(a1,a1),a1),f81(a1)),f324(f324(f8(a1,a1,a1),f324(f82(a1),f324(f324(f73(f870(a1,a1),a1,x44371,f258(a1,a1)),f217(x44371)),x44372))),f324(f324(f7(a1,a1,a1),f38(a1)),f324(f324(f73(f870(a1,a1),a1,x44371,f262(a1,a1)),f217(x44371)),x44372))))),f324(f324(f8(a1,a1,a1),f324(f82(a1),f324(f324(f73(f870(a1,a1),a1,x44371,f258(a1,a1)),f217(x44371)),x44373))),f324(f324(f7(a1,a1,a1),f38(a1)),f324(f324(f73(f870(a1,a1),a1,x44371,f262(a1,a1)),f217(x44371)),x44373)))))),f5(a1))),f228(x44371,x44372,x44373)) % 181.55/181.53 [4482]~E(f324(f324(f145(x44821),x44822),x44823),x44823) % 181.55/181.53 [4489]~E(f324(f324(f145(x44891),x44892),x44893),f116(x44891)) % 181.55/181.53 [4509]~E(f324(f324(f302(x45091),x45092),x45093),f191(f871(x45091,a859))) % 181.55/181.53 [4532]~E(f324(f303(x45321,f871(x45321,a859),x45322),x45323),f324(f301(x45321),x45323)) % 181.55/181.53 [3313]E(f324(f324(f153(x33131,f116(x33131)),x33132),x33133),f116(x33131)) % 181.55/181.53 [3314]E(f324(f135(x33141),f324(f324(f145(x33141),x33142),x33143)),x33142) % 181.55/181.53 [3315]E(f324(f166(x33151),f324(f324(f145(x33151),x33152),x33153)),x33153) % 181.55/181.53 [3359]E(f324(f324(f132(x33591),f79(a865)),f324(f324(f145(x33591),x33592),x33593)),x33593) % 181.55/181.53 [3392]E(f117(x33921,f324(f324(f132(x33921),x33922),x33923)),f324(f324(f132(x33921),x33922),f117(x33921,x33923))) % 181.55/181.53 [3394]E(f324(f324(f153(x33941,x33942),x33943),f324(f324(f159(x33941),x33942),x33943)),x33942) % 181.55/181.53 [3418]E(f324(f324(f302(x34181),x34182),f324(f324(f302(x34181),x34182),x34183)),f324(f324(f302(x34181),x34182),x34183)) % 181.55/181.53 [3429]E(f324(f324(f173(x34291,x34292),f116(f870(x34291,x34292))),x34293),f203(x34292)) % 181.55/181.53 [3432]E(f324(f324(f302(x34321),x34322),f324(f167(x34321),x34323)),f324(f167(x34321),f324(f324(f145(x34321),x34322),x34323))) % 181.55/181.53 [3434]E(f324(f324(f132(x34341),x34342),f324(f166(x34341),x34343)),f324(f166(x34341),f324(f324(f132(x34341),x34342),x34343))) % 181.55/181.53 [3445]E(f324(f324(f170(x34451),f79(a865)),f324(f324(f145(x34451),x34452),x34453)),f324(f324(f145(x34451),x34452),f116(x34451))) % 181.55/181.53 [3489]E(f324(f63(x34891,x34892),f324(f324(f302(x34891),x34893),f191(f871(x34891,a859)))),x34893) % 181.55/181.53 [3532]E(f324(f324(f81(a865),x35321),f324(f324(f81(a865),x35322),x35323)),f324(f324(f81(a865),x35322),f324(f324(f81(a865),x35321),x35323))) % 181.55/181.53 [3533]E(f324(f324(f81(a1),x35331),f324(f324(f81(a1),x35332),x35333)),f324(f324(f81(a1),x35332),f324(f324(f81(a1),x35331),x35333))) % 181.55/181.53 [3538]E(f324(f324(f261(x35381,x35382),f191(f871(x35381,a859))),x35383),f191(f871(f870(x35381,x35382),a859))) % 181.55/181.53 [3561]E(f324(f324(f104(f871(x35611,a859)),x35612),x35613),f324(f324(f104(f871(x35611,a859)),x35613),x35612)) % 181.55/181.53 [3562]E(f324(f324(f113(f871(x35621,a859)),x35622),x35623),f324(f324(f113(f871(x35621,a859)),x35623),x35622)) % 181.55/181.53 [3564]E(f324(f324(f124(x35641),x35642),f324(f324(f145(x35641),x35643),f116(x35641))),f324(f162(x35641),f324(f324(f145(x35641),x35643),x35642))) % 181.55/181.53 [3565]E(f324(f324(f124(x35651),f324(f163(x35651),x35652)),f324(f163(x35651),x35653)),f324(f163(x35651),f324(f324(f124(x35651),x35653),x35652))) % 181.55/181.53 [3573]E(f324(f166(x35731),f324(f324(f170(x35731),f324(a115,x35732)),x35733)),f324(f324(f170(x35731),x35732),f324(f166(x35731),x35733))) % 181.55/181.53 [3581]P1(f324(f324(f326(x35811),x35812),f324(f324(f302(x35811),x35812),x35813))) % 181.55/181.53 [3585]E(f324(f324(f42(x35851,f871(x35852,a859)),f191(f871(x35851,a859))),x35853),f247(f871(x35852,a859))) % 181.55/181.53 [3588]E(f324(f278(x35881,x35881,f256(x35881,x35882)),x35883),f324(f324(f104(f871(x35881,a859)),x35882),x35883)) % 181.55/181.53 [3601]E(f324(f192(f866(x36011)),f324(f324(f145(x36011),x36012),x36013)),f324(f324(f81(a865),f324(f192(f866(x36011)),x36013)),f324(a115,f2(a865)))) % 181.55/181.53 [3605]E(f138(x36051,f324(f324(f124(x36051),x36052),f324(f324(f145(x36051),x36053),f116(x36051)))),x36053) % 181.55/181.53 [3606]E(f117(x36061,f324(f324(f124(x36061),x36062),f324(f324(f145(x36061),x36063),f116(x36061)))),x36062) % 181.55/181.53 [3612]E(f324(f324(f124(x36121),f324(f324(f170(x36121),x36122),x36123)),f324(f324(f132(x36121),x36122),x36123)),x36123) % 181.55/181.53 [3621]E(f324(f324(f22(a865),f324(f324(f81(a865),x36211),x36212)),f324(f324(f81(a865),x36213),x36212)),f324(f324(f22(a865),x36211),x36213)) % 181.55/181.53 [3622]E(f324(f324(f22(a865),f324(f324(f81(a865),x36221),x36222)),f324(f324(f81(a865),x36221),x36223)),f324(f324(f22(a865),x36222),x36223)) % 181.55/181.53 [3629]E(f324(f324(f124(x36291),f324(f163(x36291),x36292)),f324(f324(f145(x36291),x36293),f116(x36291))),f324(f163(x36291),f324(f324(f145(x36291),x36293),x36292))) % 181.55/181.53 [3631]E(f324(f324(f81(a865),f324(f192(f866(x36311)),x36312)),f324(f192(f866(x36311)),x36313)),f324(f192(f866(x36311)),f324(f324(f124(x36311),x36312),x36313))) % 181.55/181.53 [3634]E(f324(f324(f81(a865),f324(f192(f866(x36341)),x36342)),f324(f192(f866(x36341)),x36343)),f324(f192(f866(x36341)),f168(x36341,x36342,x36343))) % 181.55/181.53 [3642]E(f324(f324(f113(f871(x36421,a859)),f324(f167(x36421),x36422)),f324(f167(x36421),x36423)),f324(f167(x36421),f324(f324(f124(x36421),x36422),x36423))) % 181.55/181.53 [3643]E(f44(a865,f324(f324(f82(a865),x36431),x36432),f324(f324(f82(a865),x36431),x36433)),f324(f324(f82(a865),x36431),f44(a865,x36432,x36433))) % 181.55/181.53 [3656]E(f324(f324(f170(x36561),f324(f324(f22(a865),x36562),f79(a865))),f324(f166(x36561),x36563)),f324(f166(x36561),f324(f324(f170(x36561),x36562),x36563))) % 181.55/181.53 [3661]E(f324(f324(f104(f871(x36611,a859)),x36612),f324(f80(f871(x36611,a859)),x36613)),f324(f324(f22(f871(x36611,a859)),x36612),x36613)) % 181.55/181.53 [3662]E(f324(f324(f22(f871(x36621,a859)),x36622),f324(f80(f871(x36621,a859)),x36623)),f324(f324(f104(f871(x36621,a859)),x36622),x36623)) % 181.55/181.53 [3684]E(f324(f324(f261(x36841,x36842),x36843),f324(f16(f871(x36842,a859),x36841),f191(f871(x36842,a859)))),f191(f871(f870(x36841,x36842),a859))) % 181.55/181.53 [3686]E(f324(f324(f22(a865),f324(f324(f82(a865),x36861),x36862)),f324(f324(f82(a865),x36861),x36863)),f324(f324(f82(a865),x36861),f324(f324(f22(a865),x36862),x36863))) % 181.55/181.53 [3687]E(f324(f324(f81(a865),f324(f324(f82(a865),x36871),x36872)),f324(f324(f82(a865),x36871),x36873)),f324(f324(f82(a865),x36871),f324(f324(f81(a865),x36872),x36873))) % 181.55/181.53 [3688]E(f324(f324(f22(a1),f324(f324(f82(a1),x36881),x36882)),f324(f324(f82(a1),x36881),x36883)),f324(f324(f82(a1),x36881),f324(f324(f22(a1),x36882),x36883))) % 181.55/181.53 [3689]E(f324(f324(f81(a1),f324(f324(f82(a1),x36891),x36892)),f324(f324(f82(a1),x36891),x36893)),f324(f324(f82(a1),x36891),f324(f324(f81(a1),x36892),x36893))) % 181.55/181.53 [3690]E(f324(f324(f82(a1),f324(f324(f249(a1),x36901),x36902)),f324(f324(f249(a1),x36901),x36903)),f324(f324(f249(a1),x36901),f324(f324(f81(a865),x36902),x36903))) % 181.55/181.53 [3704]E(f324(f324(f41(x37041,f871(x37042,a859)),x37043),f324(f16(f871(x37042,a859),x37041),f191(f871(x37042,a859)))),f191(f871(x37042,a859))) % 181.55/181.53 [3706]E(f44(a865,f324(f324(f82(a865),x37061),x37062),f324(f324(f82(a865),x37063),x37062)),f324(f324(f82(a865),f44(a865,x37061,x37063)),x37062)) % 181.55/181.53 [3710]E(f44(a1,f324(f324(f22(a1),x37101),f44(a1,x37102,x37103)),x37103),f44(a1,f324(f324(f22(a1),x37101),x37102),x37103)) % 181.55/181.53 [3711]E(f44(a1,f324(f324(f82(a1),x37111),f44(a1,x37112,x37113)),x37113),f44(a1,f324(f324(f82(a1),x37111),x37112),x37113)) % 181.55/181.53 [3712]P1(f324(f324(f238(f871(x37121,a859)),x37122),f324(f324(f302(x37121),x37123),x37122))) % 181.55/181.53 [3715]E(f324(f303(f870(x37151,x37152),x37151,f258(x37151,x37152)),f324(f167(f870(x37151,x37152)),x37153)),f179(x37151,x37152,f324(f173(x37151,x37152),x37153))) % 181.55/181.53 [3764]P1(f324(f61(x37641),f179(x37641,x37642,f324(f173(x37641,x37642),x37643)))) % 181.55/181.53 [3789]E(f324(f324(f41(f871(x37891,a859),f871(x37891,a859)),x37892),f324(f104(f871(x37891,a859)),x37893)),f324(f324(f104(f871(x37891,a859)),x37893),f39(f871(x37891,a859),x37892))) % 181.55/181.53 [3790]E(f324(f324(f42(f871(x37901,a859),f871(x37901,a859)),x37902),f324(f113(f871(x37901,a859)),x37903)),f324(f324(f113(f871(x37901,a859)),x37903),f40(f871(x37901,a859),x37902))) % 181.55/181.53 [3801]E(f324(f167(x38011),f324(f324(f324(f184(f866(x38011),f866(x38011)),x38012),f162(x38011)),x38013)),f324(f167(x38011),x38013)) % 181.55/181.53 [3805]E(f324(f324(f170(x38051),f324(f192(f866(x38051)),f172(x38051,x38052,x38053))),x38053),f172(x38051,x38052,x38053)) % 181.55/181.53 [3806]E(f179(x38061,x38062,f324(f324(f8(x38062,f869(x38062),x38061),f233(x38062)),x38063)),f247(f871(x38061,a859))) % 181.55/181.53 [3810]E(f324(f192(f866(x38101)),f324(f324(f324(f184(f866(x38101),f866(x38101)),x38102),f162(x38101)),x38103)),f324(f192(f866(x38101)),x38103)) % 181.55/181.53 [3813]E(f324(f324(f263(x38131,x38132,x38132),f324(f16(f871(x38132,x38132),x38131),f5(x38132))),x38133),f324(f262(x38131,x38132),x38133)) % 181.55/181.53 [3819]E(f44(a1,f324(f324(f22(a1),f44(a1,x38191,x38192)),x38193),x38192),f44(a1,f324(f324(f22(a1),x38191),x38193),x38192)) % 181.55/181.53 [3820]E(f44(a1,f324(f324(f249(a1),f44(a1,x38201,x38202)),x38203),x38202),f44(a1,f324(f324(f249(a1),x38201),x38203),x38202)) % 181.55/181.53 [3823]E(f324(f324(f41(f871(f870(x38231,x38232),a859),f871(x38232,a859)),x38233),f255(x38231,x38232)),f324(f255(x38231,x38232),f39(f871(f870(x38231,x38232),a859),x38233))) % 181.55/181.53 [3824]E(f324(f324(f41(f871(f870(x38241,x38242),a859),f871(x38241,a859)),x38243),f257(x38241,x38242)),f324(f257(x38241,x38242),f39(f871(f870(x38241,x38242),a859),x38243))) % 181.55/181.53 [3850]E(f324(f73(x38501,x38501,x38501,x38502),f324(f324(f184(x38501,x38501),x38503),x38502)),f324(f324(f184(x38501,x38501),f324(a115,x38503)),x38502)) % 181.55/181.53 [3860]E(f235(f869(x38601),x38602,f203(x38601),f324(f324(f8(x38601,f869(x38601),x38602),f233(x38601)),x38603)),f324(f204(x38602,x38601),x38603)) % 181.55/181.53 [3867]E(f324(f324(f132(x38671),f324(f324(f22(a865),f324(f192(f866(x38671)),x38672)),x38673)),f324(f163(x38671),x38672)),f324(f163(x38671),f324(f324(f170(x38671),x38673),x38672))) % 181.55/181.53 [3868]E(f324(f324(f170(x38681),f324(f324(f22(a865),f324(f192(f866(x38681)),x38682)),x38683)),f324(f163(x38681),x38682)),f324(f163(x38681),f324(f324(f132(x38681),x38683),x38682))) % 181.55/181.53 [3871]E(f324(f324(f81(a865),f324(f160(a865),f324(f324(f148(x38711,a865),x38712),x38713))),f324(f192(f866(x38711)),x38713)),f149(x38711,x38712,x38713)) % 181.55/181.53 [3889]E(f324(f162(x38891),f324(f324(f324(f184(f866(x38891),f866(x38891)),x38892),f162(x38891)),x38893)),f324(f324(f324(f184(f866(x38891),f866(x38891)),f324(a115,x38892)),f162(x38891)),x38893)) % 181.55/181.53 [3904]P1(f324(f324(f238(a865),f324(f192(f866(x39041)),f324(f130(x39041,x39042),x39043))),f324(f192(f866(x39041)),x39043))) % 181.55/181.53 [3921]E(f324(f324(f113(f871(f871(x39211,a859),a859)),f324(f301(x39211),x39212)),f324(f303(f871(x39211,a859),f871(x39211,a859),f324(f302(x39211),x39213)),f324(f301(x39211),x39212))),f324(f301(x39211),f324(f324(f302(x39211),x39213),x39212))) % 181.55/181.53 [3941]P26(x39411,x39412,f324(f324(f302(f864(x39411)),f324(f324(f324(f93(x39411),x39413),a24),x39413)),f191(f871(f864(x39411),a859)))) % 181.55/181.53 [3958]P1(f324(f324(f238(a865),f324(f192(f866(x39581)),f172(x39581,x39582,x39583))),f324(f192(f866(x39581)),x39583))) % 181.55/181.53 [3966]E(f324(f257(x39661,x39662),f324(f244(f870(x39661,x39662)),f324(f263(x39661,x39662,a859),x39663))),f324(f244(x39661),f324(f324(f8(f871(x39662,a859),a859,x39661),f88(x39662)),x39663))) % 181.55/181.53 [3978]E(f324(f303(a865,a865,f324(f324(f7(a865,a865,a865),f81(a865)),x39781)),f295(a865,x39782,x39783)),f295(a865,f324(f324(f81(a865),x39782),x39781),f324(f324(f81(a865),x39783),x39781))) % 181.55/181.53 [3981]P1(f324(f61(f869(x39811)),f324(f303(x39812,f869(x39811),f324(f173(x39812,x39811),x39813)),f247(f871(x39812,a859))))) % 181.55/181.53 [3994]E(f324(f303(a865,a865,f324(f324(f7(a865,a865,a865),f81(a865)),x39941)),f324(f294(a865,x39942),x39943)),f324(f294(a865,f324(f324(f81(a865),x39942),x39941)),f324(f324(f81(a865),x39943),x39941))) % 181.55/181.53 [4012]E(f324(f324(f177(x40121,x40122),f324(f324(f148(f870(x40121,x40122),x40121),f258(x40121,x40122)),x40123)),f324(f324(f148(f870(x40121,x40122),x40122),f262(x40121,x40122)),x40123)),x40123) % 181.55/181.53 [4017]E(f324(f324(f81(a865),f324(f324(f82(a865),x40171),f44(a865,f324(f324(f38(a865),x40172),x40171),x40173))),f44(a865,x40172,x40171)),f44(a865,x40172,f324(f324(f82(a865),x40171),x40173))) % 181.55/181.53 [4031]E(f324(f324(f124(x40311),x40312),f324(f136(f866(x40311),f866(x40311),f124(x40311),f116(x40311)),x40313)),f324(f136(f866(x40311),f866(x40311),f124(x40311),x40312),x40313)) % 181.55/181.53 [4049]P1(f324(f324(f326(f870(x40491,x40491)),f324(f324(f259(x40491,x40491),x40492),x40492)),f324(f324(f184(f870(x40491,x40491),a859),f2(a865)),x40493))) % 181.55/181.53 [4055]E(f324(f244(x40551),f324(f324(f8(f871(x40552,a859),a859,x40551),f88(x40552)),f324(f7(x40552,x40551,a859),x40553))),f324(f255(x40552,x40551),f324(f244(f870(x40552,x40551)),f324(f263(x40552,x40551,a859),x40553)))) % 181.55/181.53 [4073]E(f324(f324(f113(f871(x40731,a859)),f324(f324(f41(a865,f871(x40731,a859)),f295(a865,f79(a865),x40732)),x40733)),f324(x40733,f2(a865))),f324(f324(f41(a865,f871(x40731,a859)),f324(f293(a865),x40732)),x40733)) % 181.55/181.53 [4088]E(f324(f136(f866(x40881),f866(x40881),f124(x40881),f116(x40881)),f324(f324(f148(f866(x40881),f866(x40881)),f130(x40881,x40882)),x40883)),f324(f130(x40881,x40882),f324(f136(f866(x40881),f866(x40881),f124(x40881),f116(x40881)),x40883))) % 181.55/181.53 [4093]E(f324(f262(f866(x40931),f866(x40931)),f161(x40931,x40932,x40933)),f324(f130(x40931,f324(f73(a859,a859,x40931,a319),x40932)),x40933)) % 181.55/181.53 [4142]E(f324(f324(f81(a1),f324(f324(f81(a1),f324(f324(f82(a1),x41421),f324(f324(f38(a1),x41422),x41421))),f44(a1,x41422,x41421))),x41423),f324(f324(f81(a1),x41422),x41423)) % 181.55/181.53 [4182]E(f324(f324(f81(a1),f324(f324(f81(a1),f324(f324(f82(a1),f324(f324(f38(a1),x41821),x41822)),x41822)),f44(a1,x41821,x41822))),x41823),f324(f324(f81(a1),x41821),x41823)) % 181.55/181.53 [4212]E(f86(f870(x42121,x42122),f324(f263(x42121,x42122,a859),f324(f324(f8(f871(x42122,f870(x42121,x42122)),f871(x42122,a859),x42121),f324(f8(f870(x42121,x42122),a859,x42122),x42123)),f259(x42121,x42122)))),f86(f870(x42121,x42122),x42123)) % 181.55/181.53 [4213]E(f91(f870(x42131,x42132),f324(f263(x42131,x42132,a859),f324(f324(f8(f871(x42132,f870(x42131,x42132)),f871(x42132,a859),x42131),f324(f8(f870(x42131,x42132),a859,x42132),x42133)),f259(x42131,x42132)))),f91(f870(x42131,x42132),x42133)) % 181.55/181.53 [4241]P1(f324(f324(f238(f871(x42411,a859)),f39(f871(x42411,a859),f324(f324(f104(f871(f871(x42411,a859),a859)),x42412),x42413))),f324(f324(f104(f871(x42411,a859)),f39(f871(x42411,a859),x42412)),f39(f871(x42411,a859),x42413)))) % 181.55/181.53 [4242]E(f324(f163(x42421),f324(f324(f324(f184(f866(x42421),f866(x42421)),f324(f324(f22(a865),f324(f192(f866(x42421)),x42422)),f44(a865,x42423,f324(f192(f866(x42421)),x42422)))),f162(x42421)),x42422)),f324(f324(f324(f184(f866(x42421),f866(x42421)),x42423),f162(x42421)),f324(f163(x42421),x42422))) % 181.55/181.53 [4256]E(f324(f244(x42561),f324(f324(f8(a859,a859,x42561),a319),f324(f324(f7(x42561,f869(x42562),a859),f324(f324(f8(f869(x42562),f871(f869(x42562),a859),x42561),a321),x42563)),f203(x42562)))),f179(x42561,x42562,x42563)) % 181.55/181.53 [4281]P1(f324(f324(f238(a865),f324(f192(f866(x42811)),f324(f324(f132(x42811),f324(f192(f866(x42811)),f172(x42811,x42812,x42813))),x42813))),f324(f192(f866(x42811)),x42813))) % 181.55/181.53 [4322]E(f324(f244(x43221),f324(f324(f8(f871(x43222,a859),a859,x43221),f88(x43222)),f324(f324(f8(f869(x43221),f871(x43222,a859),x43221),f324(f7(x43222,f869(x43221),a859),f324(f324(f8(f869(x43221),f871(f869(x43221),a859),x43222),a321),x43223))),f233(x43221)))),f181(x43222,x43221,x43223)) % 181.55/181.53 [4546]~P1(f324(f62(x45461,x45462,f191(f871(x45461,a859))),x45463)) % 181.55/181.53 [4553]~P1(f324(f324(f326(f870(x45531,x45531)),f324(f324(f259(x45531,x45531),x45532),x45533)),f147(x45531,f116(f871(x45531,a865))))) % 181.55/181.53 [3574]E(f324(f192(f866(x35741)),f324(f324(f170(x35741),x35742),x35743)),f324(f324(f189(a865),f324(f192(f866(x35741)),x35743)),x35742)) % 181.55/181.53 [3575]E(f324(f192(f866(x35751)),f324(f324(f132(x35751),x35752),x35753)),f324(f324(f22(a865),f324(f192(f866(x35751)),x35753)),x35752)) % 181.55/181.53 [3600]E(f324(f192(f866(f866(x36001))),f54(x36001,x36002,x36003)),f324(f324(f249(a865),f324(f192(f866(x36001)),x36003)),x36002)) % 181.55/181.53 [3614]E(f324(f324(f38(a865),f324(f324(f38(a865),x36141),x36142)),x36143),f324(f324(f38(a865),x36141),f324(f324(f82(a865),x36142),x36143))) % 181.55/181.53 [3615]E(f324(f324(f22(a865),f324(f324(f22(a865),x36151),x36152)),x36153),f324(f324(f22(a865),x36151),f324(f324(f81(a865),x36152),x36153))) % 181.55/181.53 [3616]E(f324(f324(f82(a865),f324(f324(f82(a865),x36161),x36162)),x36163),f324(f324(f82(a865),x36161),f324(f324(f82(a865),x36162),x36163))) % 181.55/181.53 [3617]E(f324(f324(f82(a1),f324(f324(f82(a1),x36171),x36172)),x36173),f324(f324(f82(a1),x36171),f324(f324(f82(a1),x36172),x36173))) % 181.55/181.53 [3618]E(f324(f324(f81(a865),f324(f324(f81(a865),x36181),x36182)),x36183),f324(f324(f81(a865),x36181),f324(f324(f81(a865),x36182),x36183))) % 181.55/181.53 [3619]E(f324(f324(f81(a1),f324(f324(f81(a1),x36191),x36192)),x36193),f324(f324(f81(a1),x36191),f324(f324(f81(a1),x36192),x36193))) % 181.55/181.53 [3620]E(f324(f324(f249(a1),f324(f324(f249(a1),x36201),x36202)),x36203),f324(f324(f249(a1),x36201),f324(f324(f82(a865),x36202),x36203))) % 181.55/181.53 [3640]E(f156(x36401,f324(f324(f145(f871(x36401,a859)),x36402),x36403)),f169(x36401,x36402,f156(x36401,x36403))) % 181.55/181.53 [3685]E(f324(f324(f22(a865),f324(f324(f22(a865),x36851),x36852)),x36853),f324(f324(f22(a865),f324(f324(f22(a865),x36851),x36853)),x36852)) % 181.55/181.53 [3691]E(f324(f233(f870(x36911,f867(x36911))),f324(f324(f259(x36911,f867(x36911)),x36912),x36913)),f324(f127(x36911),f125(x36911,x36912,x36913))) % 181.55/181.53 [3694]E(f324(f324(f104(f871(x36941,a859)),x36942),f324(f324(f22(f871(x36941,a859)),x36943),x36942)),f191(f871(x36941,a859))) % 181.55/181.53 [3735]E(f40(f871(x37351,a859),f324(f324(f302(f871(x37351,a859)),x37352),x37353)),f324(f324(f104(f871(x37351,a859)),x37352),f40(f871(x37351,a859),x37353))) % 181.55/181.53 [3736]E(f39(f871(x37361,a859),f324(f324(f302(f871(x37361,a859)),x37362),x37363)),f324(f324(f113(f871(x37361,a859)),x37362),f39(f871(x37361,a859),x37363))) % 181.55/181.53 [3737]E(f165(x37371,f324(f192(f866(x37371)),f324(f130(x37371,f324(a321,x37372)),x37373)),x37372),f324(f130(x37371,f324(a321,x37372)),x37373)) % 181.55/181.53 [3739]E(f324(f324(f22(a865),f324(f324(f82(a865),x37391),x37392)),f324(f324(f82(a865),x37393),x37392)),f324(f324(f82(a865),f324(f324(f22(a865),x37391),x37393)),x37392)) % 181.55/181.53 [3740]E(f324(f324(f81(a865),f324(f324(f82(a865),x37401),x37402)),f324(f324(f82(a865),x37403),x37402)),f324(f324(f82(a865),f324(f324(f81(a865),x37401),x37403)),x37402)) % 181.55/181.53 [3741]E(f324(f324(f22(a1),f324(f324(f82(a1),x37411),x37412)),f324(f324(f82(a1),x37413),x37412)),f324(f324(f82(a1),f324(f324(f22(a1),x37411),x37413)),x37412)) % 181.55/181.53 [3742]E(f324(f324(f81(a1),f324(f324(f82(a1),x37421),x37422)),f324(f324(f82(a1),x37423),x37422)),f324(f324(f82(a1),f324(f324(f81(a1),x37421),x37423)),x37422)) % 181.55/181.53 [3744]E(f324(f324(f189(a865),f324(f324(f22(a865),x37441),x37442)),f324(f324(f22(a865),x37443),x37442)),f324(f324(f22(a865),f324(f324(f189(a865),x37441),x37443)),x37442)) % 181.55/181.53 [3767]E(f324(f324(f104(f871(f866(x37671),a859)),f154(x37671,x37672)),f154(x37671,x37673)),f154(x37671,f324(f324(f104(f871(x37671,a859)),x37672),x37673))) % 181.55/181.53 [3769]E(f324(f324(f104(f871(x37691,a859)),x37692),f324(f324(f104(f871(x37691,a859)),x37692),x37693)),f324(f324(f104(f871(x37691,a859)),x37692),x37693)) % 181.55/181.53 [3770]E(f324(f324(f113(f871(x37701,a859)),x37702),f324(f324(f22(f871(x37701,a859)),x37703),x37702)),f324(f324(f113(f871(x37701,a859)),x37702),x37703)) % 181.55/181.53 [3771]E(f324(f324(f113(f871(x37711,a859)),x37712),f324(f324(f113(f871(x37711,a859)),x37712),x37713)),f324(f324(f113(f871(x37711,a859)),x37712),x37713)) % 181.55/181.53 [3783]E(f324(f324(f281(x37831,x37832,x37832),x37833),f300(x37832,f191(f871(f870(x37832,x37832),a859)))),x37833) % 181.55/181.53 [3786]E(f324(f324(f113(f871(x37861,a859)),f324(f324(f302(x37861),x37862),f191(f871(x37861,a859)))),x37863),f324(f324(f302(x37861),x37862),x37863)) % 181.55/181.53 [3804]E(f324(f324(f22(a865),f324(f324(f22(a865),f324(a115,x38041)),x38042)),f324(a115,x38043)),f324(f324(f22(a865),f324(f324(f22(a865),x38041),x38042)),x38043)) % 181.55/181.53 [3832]E(f324(f324(f104(f871(f871(x38321,a859),a859)),f324(f301(x38321),x38322)),f324(f301(x38321),x38323)),f324(f301(x38321),f324(f324(f104(f871(x38321,a859)),x38322),x38323))) % 181.55/181.53 [3836]E(f324(f324(f113(f871(x38361,a859)),f324(f80(f871(x38361,a859)),x38362)),x38363),f324(f80(f871(x38361,a859)),f324(f324(f22(f871(x38361,a859)),x38362),x38363))) % 181.55/181.53 [3847]E(f324(f324(f302(x38471),x38472),f324(f324(f22(f871(x38471,a859)),x38473),f324(f324(f302(x38471),x38472),f191(f871(x38471,a859))))),f324(f324(f302(x38471),x38472),x38473)) % 181.55/181.53 [3857]P1(f324(f324(f238(f871(x38571,a859)),x38572),f324(f324(f113(f871(x38571,a859)),x38573),x38572))) % 181.55/181.53 [3858]P1(f324(f324(f238(f871(x38581,a859)),x38582),f324(f324(f113(f871(x38581,a859)),x38582),x38583))) % 181.55/181.53 [3861]E(f324(f324(f113(f871(x38611,a859)),f324(f80(f871(x38611,a859)),x38612)),f324(f80(f871(x38611,a859)),x38613)),f324(f80(f871(x38611,a859)),f324(f324(f104(f871(x38611,a859)),x38612),x38613))) % 181.55/181.53 [3862]E(f324(f324(f104(f871(x38621,a859)),f324(f80(f871(x38621,a859)),x38622)),f324(f80(f871(x38621,a859)),x38623)),f324(f80(f871(x38621,a859)),f324(f324(f113(f871(x38621,a859)),x38622),x38623))) % 181.55/181.53 [3876]P1(f324(f324(f238(f871(x38761,a859)),f324(f167(x38761),x38762)),f324(f167(x38761),f324(f324(f145(x38761),x38763),x38762)))) % 181.55/181.53 [3886]E(f324(f324(f113(f871(x38861,a859)),f324(f324(f22(f871(x38861,a859)),x38862),x38863)),f324(f324(f104(f871(x38861,a859)),x38862),x38863)),x38862) % 181.55/181.53 [3943]E(f324(f324(f9(x39431,a1),f324(f324(f8(a865,a1,x39431),f103(a1)),x39432)),x39433),f324(f103(a1),f324(f324(f9(x39431,a865),x39432),x39433))) % 181.55/181.53 [3944]E(f324(f324(f6(x39441,a1),f324(f324(f8(a865,a1,x39441),f103(a1)),x39442)),x39443),f324(f103(a1),f324(f324(f6(x39441,a865),x39442),x39443))) % 181.55/181.53 [3996]E(f324(f324(f124(x39961),f172(x39961,x39962,x39963)),f324(f324(f132(x39961),f324(f192(f866(x39961)),f172(x39961,x39962,x39963))),x39963)),x39963) % 181.55/181.53 [4001]E(f324(f80(f871(f870(x40011,x40012),a859)),f324(f324(f261(x40011,x40012),x40013),f324(f16(f871(x40012,a859),x40011),f247(f871(x40012,a859))))),f324(f324(f261(x40011,x40012),f324(f80(f871(x40011,a859)),x40013)),f324(f16(f871(x40012,a859),x40011),f247(f871(x40012,a859))))) % 181.55/181.53 [4002]E(f324(f80(f871(f870(x40021,x40022),a859)),f324(f324(f261(x40021,x40022),f247(f871(x40021,a859))),f324(f16(f871(x40022,a859),x40021),x40023))),f324(f324(f261(x40021,x40022),f247(f871(x40021,a859))),f324(f16(f871(x40022,a859),x40021),f324(f80(f871(x40022,a859)),x40023)))) % 181.55/181.53 [4050]E(f324(f324(f41(f871(x40501,a859),f871(x40501,a859)),x40502),f324(f324(f7(f871(x40501,a859),f871(x40501,a859),f871(x40501,a859)),f104(f871(x40501,a859))),x40503)),f324(f324(f104(f871(x40501,a859)),f39(f871(x40501,a859),x40502)),x40503)) % 181.55/181.53 [4057]E(f324(f136(f866(x40571),f866(x40571),f124(x40571),f116(x40571)),f324(f324(f145(f866(x40571)),x40572),x40573)),f324(f324(f124(x40571),x40572),f324(f136(f866(x40571),f866(x40571),f124(x40571),f116(x40571)),x40573))) % 181.55/181.53 [4079]E(f324(f324(f302(f871(x40791,a859)),f324(f278(x40791,x40791,x40792),f324(f324(f302(x40791),x40793),f191(f871(x40791,a859))))),f191(f871(f871(x40791,a859),a859))),f324(f324(f60(x40791),f324(f324(f302(x40791),x40793),f191(f871(x40791,a859)))),x40792)) % 181.55/181.53 [4089]E(f324(f324(f81(a865),f324(f324(f82(a865),x40891),f324(f324(f38(a865),x40892),x40893))),f324(f324(f38(a865),f324(f324(f82(a865),x40891),f44(a865,x40892,x40893))),x40893)),f324(f324(f38(a865),f324(f324(f82(a865),x40891),x40892)),x40893)) % 181.55/181.53 [4090]E(f324(f324(f81(a1),f324(f324(f82(a1),x40901),f324(f324(f38(a1),x40902),x40903))),f324(f324(f38(a1),f324(f324(f82(a1),x40901),f44(a1,x40902,x40903))),x40903)),f324(f324(f38(a1),f324(f324(f82(a1),x40901),x40902)),x40903)) % 181.55/181.53 [4127]E(f324(f324(f22(f871(x41271,a859)),f324(f167(x41271),x41272)),f324(f324(f302(x41271),x41273),f191(f871(x41271,a859)))),f324(f167(x41271),f324(f130(x41271,f324(f324(f8(a859,a859,x41271),a319),f324(a321,x41273))),x41272))) % 181.55/181.53 [4179]E(f324(f324(f124(x41791),f324(f136(f866(x41791),f866(x41791),f124(x41791),f116(x41791)),x41792)),f324(f136(f866(x41791),f866(x41791),f124(x41791),f116(x41791)),x41793)),f324(f136(f866(x41791),f866(x41791),f124(x41791),f116(x41791)),f324(f324(f124(f866(x41791)),x41792),x41793))) % 181.55/181.53 [4184]E(f324(f324(f259(f866(x41841),f866(x41841)),f324(f130(x41841,x41842),x41843)),f324(f130(x41841,f324(f73(a859,a859,x41841,a319),x41842)),x41843)),f161(x41841,x41842,x41843)) % 181.55/181.53 [4187]E(f324(f324(f81(a865),f324(f324(f81(a865),f324(f324(f38(a865),x41871),x41872)),f324(f324(f38(a865),x41873),x41872))),f324(f324(f38(a865),f324(f324(f81(a865),f44(a865,x41871,x41872)),f44(a865,x41873,x41872))),x41872)),f324(f324(f38(a865),f324(f324(f81(a865),x41871),x41873)),x41872)) % 181.55/181.53 [4188]E(f324(f324(f81(a1),f324(f324(f81(a1),f324(f324(f38(a1),x41881),x41882)),f324(f324(f38(a1),x41883),x41882))),f324(f324(f38(a1),f324(f324(f81(a1),f44(a1,x41881,x41882)),f44(a1,x41883,x41882))),x41882)),f324(f324(f38(a1),f324(f324(f81(a1),x41881),x41883)),x41882)) % 181.55/181.53 [4245]E(f324(f324(f104(f871(f866(x42451),a859)),f324(f324(f7(f866(x42451),f871(f866(x42451),a859),a859),f326(f866(x42451))),f155(x42451,x42452))),f324(f324(f7(f866(x42451),f871(f866(x42451),a859),a859),f326(f866(x42451))),f155(x42451,x42453))),f154(x42451,f324(f324(f104(f871(x42451,a859)),f324(f324(f7(x42451,f871(x42451,a859),a859),f326(x42451)),x42452)),f324(f324(f7(x42451,f871(x42451,a859),a859),f326(x42451)),x42453)))) % 181.55/181.53 [4258]E(f324(f244(x42581),f324(f324(f18(x42581,a859,a859),f324(f324(f8(a859,f871(a859,a859),x42581),a323),f324(f324(f7(x42581,x42581,a859),a321),x42582))),f324(f324(f7(x42581,f871(x42581,a859),a859),f326(x42581)),x42583))),f324(f324(f302(x42581),x42582),x42583)) % 181.55/181.53 [4278]E(f324(f324(f87(f866(f866(x42781)),f866(f866(x42781))),f53(x42781,x42782)),f324(f324(f18(f866(f866(x42781)),f866(f866(x42781)),f866(f866(x42781))),f324(f324(f8(f866(f866(x42781)),f871(f866(f866(x42781)),f866(f866(x42781))),f866(f866(x42781))),f124(f866(x42781))),f324(f148(f866(x42781),f866(x42781)),f324(f145(x42781),x42783)))),f5(f866(f866(x42781))))),f53(x42781,f324(f324(f145(x42781),x42783),x42782))) % 181.55/181.53 [4282]E(f324(f244(x42821),f324(f324(f18(x42821,a859,a859),f324(f324(f8(a859,f871(a859,a859),x42821),a322),f324(f324(f7(x42821,f871(x42821,a859),a859),f326(x42821)),x42822))),f324(f324(f7(x42821,f871(x42821,a859),a859),f326(x42821)),x42823))),f324(f324(f104(f871(x42821,a859)),x42822),x42823)) % 181.55/181.53 [4283]E(f324(f244(x42831),f324(f324(f18(x42831,a859,a859),f324(f324(f8(a859,f871(a859,a859),x42831),a323),f324(f324(f7(x42831,f871(x42831,a859),a859),f326(x42831)),x42832))),f324(f324(f7(x42831,f871(x42831,a859),a859),f326(x42831)),x42833))),f324(f324(f113(f871(x42831,a859)),x42832),x42833)) % 181.55/181.53 [4374]E(f324(f324(f41(x43741,f871(f871(x43741,a859),a859)),x43742),f324(f324(f7(x43741,f871(f871(x43741,a859),a859),f871(f871(x43741,a859),a859)),f324(f324(f8(f871(x43741,a859),f871(f871(f871(x43741,a859),a859),f871(f871(x43741,a859),a859)),x43741),f302(f871(x43741,a859))),f324(f324(f8(f871(x43741,a859),f871(x43741,a859),x43741),f278(x43741,x43741,x43743)),f324(f324(f7(x43741,f871(x43741,a859),f871(x43741,a859)),f302(x43741)),f191(f871(x43741,a859)))))),f191(f871(f871(x43741,a859),a859)))),f324(f324(f60(x43741),x43742),x43743)) % 181.55/181.53 [4376]E(f324(f324(f205(x43761),f324(f324(f82(a1),f324(f324(f73(f870(a1,a1),a1,x43761,f258(a1,a1)),f217(x43761)),x43762)),f324(f324(f73(f870(a1,a1),a1,x43761,f258(a1,a1)),f217(x43761)),x43763))),f324(f324(f82(a1),f324(f324(f73(f870(a1,a1),a1,x43761,f262(a1,a1)),f217(x43761)),x43762)),f324(f324(f73(f870(a1,a1),a1,x43761,f262(a1,a1)),f217(x43761)),x43763))),f226(x43761,x43762,x43763)) % 181.55/181.53 [4379]E(f324(f244(f866(x43791)),f324(f324(f18(f866(x43791),a859,a859),f324(f324(f8(a859,f871(a859,a859),f866(x43791)),a322),f324(f324(f7(f866(x43791),a865,a859),f324(f324(f8(a865,f871(a865,a859),f866(x43791)),a321),f192(f866(x43791)))),x43792))),f324(f324(f7(f866(x43791),f871(x43791,a859),a859),f324(f324(f8(f871(x43791,a859),f871(f871(x43791,a859),a859),f866(x43791)),f238(f871(x43791,a859))),f167(x43791))),f324(f167(x43791),x43793)))),f324(f167(f866(x43791)),f54(x43791,x43792,x43793))) % 181.55/181.53 [3757]E(f44(a865,f324(f324(f81(a865),f324(f324(f82(a865),x37571),x37572)),x37573),x37572),f44(a865,x37573,x37572)) % 181.55/181.53 [3803]E(f133(a865,f324(f294(a865,f324(f324(f81(a865),x38031),x38032)),x38033)),f324(f324(f132(a865),x38032),f133(a865,f324(f294(a865,x38031),x38033)))) % 181.55/181.53 [3846]E(f324(f324(f81(a1),f324(f103(a1),x38461)),f324(f324(f81(a1),f324(f103(a1),x38462)),x38463)),f324(f324(f81(a1),f324(f103(a1),f324(f324(f81(a865),x38461),x38462))),x38463)) % 181.55/181.53 [3853]E(f324(f324(f22(f871(x38531,a859)),f324(f324(f22(f871(x38531,a859)),x38532),x38533)),x38533),f324(f324(f22(f871(x38531,a859)),x38532),x38533)) % 181.55/181.53 [3854]E(f324(f324(f113(f871(x38541,a859)),f324(f324(f22(f871(x38541,a859)),x38542),x38543)),x38543),f324(f324(f113(f871(x38541,a859)),x38542),x38543)) % 181.55/181.53 [3877]E(f324(f324(f281(x38771,x38771,x38772),f300(x38771,f191(f871(f870(x38771,x38771),a859)))),x38773),x38773) % 181.55/181.53 [3883]E(f324(f324(f113(f871(x38831,a859)),f324(f277(x38831),x38832)),f324(f277(x38831),x38833)),f324(f277(x38831),f324(f324(f113(f871(f870(x38831,x38831),a859)),x38832),x38833))) % 181.55/181.53 [3894]E(f268(x38941,f324(f324(f145(f870(a102,x38941)),f324(f324(f259(a102,x38941),f2(a102)),x38942)),x38943)),f268(x38941,x38943)) % 181.55/181.53 [3897]E(f324(f324(f104(f871(x38971,a859)),f40(f871(x38971,a859),x38972)),f40(f871(x38971,a859),x38973)),f40(f871(x38971,a859),f324(f324(f113(f871(f871(x38971,a859),a859)),x38972),x38973))) % 181.55/181.53 [3898]E(f324(f324(f113(f871(x38981,a859)),f39(f871(x38981,a859),x38982)),f39(f871(x38981,a859),x38983)),f39(f871(x38981,a859),f324(f324(f113(f871(f871(x38981,a859),a859)),x38982),x38983))) % 181.55/181.53 [3935]E(f324(f324(f281(x39351,x39351,x39351),f324(f324(f184(f870(x39351,x39351),a859),x39352),x39353)),x39353),f324(f324(f184(f870(x39351,x39351),a859),f324(a115,x39352)),x39353)) % 181.55/181.53 [3987]P1(f324(f324(f238(f871(x39871,a859)),f324(f324(f22(f871(x39871,a859)),x39872),x39873)),x39872)) % 181.55/181.53 [3988]P1(f324(f324(f238(f871(x39881,a859)),f324(f324(f104(f871(x39881,a859)),x39882),x39883)),x39883)) % 181.55/181.53 [3989]P1(f324(f324(f238(f871(x39891,a859)),f324(f324(f104(f871(x39891,a859)),x39892),x39893)),x39892)) % 181.55/181.53 [4014]E(f300(x40141,f324(f324(f113(f871(f870(x40141,x40141),a859)),f300(x40141,x40142)),f300(x40141,x40143))),f300(x40141,f324(f324(f113(f871(f870(x40141,x40141),a859)),x40142),x40143))) % 181.55/181.53 [4018]E(f40(f871(x40181,a859),f324(f324(f302(f871(x40181,a859)),x40182),f324(f324(f302(f871(x40181,a859)),x40183),f191(f871(f871(x40181,a859),a859))))),f324(f324(f104(f871(x40181,a859)),x40182),x40183)) % 181.55/181.53 [4019]E(f39(f871(x40191,a859),f324(f324(f302(f871(x40191,a859)),x40192),f324(f324(f302(f871(x40191,a859)),x40193),f191(f871(f871(x40191,a859),a859))))),f324(f324(f113(f871(x40191,a859)),x40192),x40193)) % 181.55/181.53 [4025]E(f324(f324(f281(x40251,x40251,x40251),f324(f324(f184(f870(x40251,x40251),a859),x40252),x40253)),x40253),f324(f324(f281(x40251,x40251,x40251),x40253),f324(f324(f184(f870(x40251,x40251),a859),x40252),x40253))) % 181.55/181.53 [4094]E(f324(f324(f113(f871(x40941,a859)),f324(f244(x40941),f324(f324(f7(x40941,x40941,a859),a321),x40942))),x40943),f324(f324(f302(x40941),x40942),x40943)) % 181.55/181.53 [4096]E(f324(a107,f324(f324(f9(x40961,a1),f324(f324(f8(a865,a1,x40961),f103(a1)),x40962)),x40963)),f324(f324(f9(x40961,a865),x40962),x40963)) % 181.55/181.53 [4097]E(f324(a107,f324(f324(f6(x40971,a1),f324(f324(f8(a865,a1,x40971),f103(a1)),x40972)),x40973)),f324(f324(f6(x40971,a865),x40972),x40973)) % 181.55/181.53 [4176]E(f324(f150(f866(x41761),x41761,f324(f166(x41761),x41762),f324(f16(f871(f866(x41761),f866(x41761)),x41761),f324(f324(f7(f866(x41761),f866(x41761),f866(x41761)),f124(x41761)),x41762))),x41763),f324(f166(x41761),f324(f324(f124(x41761),x41763),x41762))) % 181.55/181.53 [4208]P1(f324(f324(f238(f871(f871(x42081,a859),a859)),f324(f324(f113(f871(f871(x42081,a859),a859)),f324(f301(x42081),x42082)),f324(f301(x42081),x42083))),f324(f301(x42081),f324(f324(f113(f871(x42081,a859)),x42082),x42083)))) % 181.55/181.53 [4301]E(f324(f244(x43011),f324(f324(f18(x43011,a859,a859),f324(f324(f8(a859,f871(a859,a859),x43011),a322),f324(f324(f7(x43011,f871(x43011,a859),a859),f326(x43011)),x43012))),f324(f324(f8(a859,a859,x43011),a319),f324(f324(f7(x43011,f871(x43011,a859),a859),f326(x43011)),x43013)))),f324(f324(f22(f871(x43011,a859)),x43012),x43013)) % 181.55/181.53 [4323]E(f324(f37(a865),f324(f244(a865),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),f324(f324(f7(a865,a865,a859),f239(a865)),f324(f192(f866(x43231)),x43232)))),f324(f324(f8(x43231,a859,a865),x43233),f324(f159(x43231),x43232))))),f324(f192(f866(x43231)),f324(f130(x43231,x43233),x43232))) % 181.55/181.53 [4325]E(f324(f192(f866(x43251)),f171(x43251,x43252,x43253)),f324(f37(a865),f324(f244(a865),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),f324(f324(f7(a865,a865,a859),f239(a865)),f324(f192(f866(x43251)),x43252)))),f324(f324(f7(a865,f871(a865,a859),a859),f326(a865)),x43253))))) % 181.55/181.53 [4423]E(f324(f324(f104(f871(f870(f866(x44231),f866(x44231)),a859)),f324(f303(f870(f870(x44231,f866(x44231)),f870(x44231,f866(x44231))),f870(f866(x44231),f866(x44231)),f264(f870(x44231,f866(x44231)),f866(x44231),f870(x44231,f866(x44231)),f866(x44231),f324(f263(x44231,f866(x44231),f866(x44231)),f145(x44231)),f324(f263(x44231,f866(x44231),f866(x44231)),f145(x44231)))),f316(x44231,f866(x44231),x44232,f324(f137(x44231,x44232),x44233)))),f324(f244(f870(f866(x44231),f866(x44231))),f324(f263(f866(x44231),f866(x44231),a859),f324(f324(f7(f866(x44231),f871(f866(x44231),a859),f871(f866(x44231),a859)),f324(f324(f8(f871(a859,a859),f871(f871(f866(x44231),a859),f871(f866(x44231),a859)),f866(x44231)),f8(a859,a859,f866(x44231))),f324(f324(f8(a859,f871(a859,a859),f866(x44231)),a322),f324(f324(f7(f866(x44231),a865,a859),f324(f324(f8(a865,f871(a865,a859),f866(x44231)),a321),f192(f866(x44231)))),f324(a115,x44233))))),f324(f324(f7(f866(x44231),a865,a859),f324(f324(f8(a865,f871(a865,a859),f866(x44231)),a321),f192(f866(x44231)))),f324(a115,x44233)))))),f324(f137(x44231,x44232),f324(a115,x44233))) % 181.55/181.53 [3899]E(f44(a865,f324(a115,f324(f324(f81(a865),f324(f324(f82(a865),x38991),x38992)),x38993)),x38992),f44(a865,f324(a115,x38993),x38992)) % 181.55/181.53 [4163]E(f324(f244(x41631),f324(f324(f18(x41631,a859,a859),f324(f324(f8(a859,f871(a859,a859),x41631),a322),x41632)),x41633)),f324(f324(f104(f871(x41631,a859)),f324(f244(x41631),x41632)),f324(f244(x41631),x41633))) % 181.55/181.53 [4164]E(f324(f244(x41641),f324(f324(f18(x41641,a859,a859),f324(f324(f8(a859,f871(a859,a859),x41641),a323),x41642)),x41643)),f324(f324(f113(f871(x41641,a859)),f324(f244(x41641),x41642)),f324(f244(x41641),x41643))) % 181.55/181.53 [4166]E(f324(f324(f124(x41661),f324(f324(f132(x41661),f44(a865,x41662,f324(f192(f866(x41661)),x41663))),x41663)),f324(f324(f170(x41661),f44(a865,x41662,f324(f192(f866(x41661)),x41663))),x41663)),f324(f324(f324(f184(f866(x41661),f866(x41661)),x41662),f162(x41661)),x41663)) % 181.55/181.53 [4172]E(f324(f244(x41721),f324(f324(f18(x41721,a859,a859),f324(f324(f8(a859,f871(a859,a859),x41721),a327),x41722)),x41723)),f324(f324(f113(f871(x41721,a859)),f324(f80(f871(x41721,a859)),f324(f244(x41721),x41722))),f324(f244(x41721),x41723))) % 181.55/181.53 [4189]E(f324(f324(f81(a865),f324(f192(f866(x41891)),f324(f130(x41891,x41892),x41893))),f324(f192(f866(x41891)),f324(f130(x41891,f324(f324(f8(a859,a859,x41891),a319),x41892)),x41893))),f324(f192(f866(x41891)),x41893)) % 181.55/181.53 [4215]P1(f324(f324(f238(f871(x42151,a859)),f324(f324(f113(f871(x42151,a859)),f40(f871(x42151,a859),x42152)),f40(f871(x42151,a859),x42153))),f40(f871(x42151,a859),f324(f324(f104(f871(f871(x42151,a859),a859)),x42152),x42153)))) % 181.55/181.53 [4229]E(f324(f167(x42291),f324(f130(x42291,f324(f324(f8(a859,a859,x42291),a319),f324(f324(f7(x42291,x42291,a859),a321),x42292))),x42293)),f324(f324(f22(f871(x42291,a859)),f324(f167(x42291),x42293)),f324(f324(f302(x42291),x42292),f191(f871(x42291,a859))))) % 181.55/181.53 [4238]P1(f324(f324(f238(f871(f870(x42381,x42381),a859)),f324(f324(f113(f871(f870(x42381,x42381),a859)),f300(x42381,x42382)),f300(x42381,x42383))),f300(x42381,f324(f324(f113(f871(f870(x42381,x42381),a859)),x42382),x42383)))) % 181.55/181.53 [4263]E(f324(f324(f82(a865),f324(a115,f324(a115,f2(a865)))),f324(f324(f6(a865,a865),f324(f324(f8(a865,a865,a865),f324(f81(a865),x42631)),f324(f324(f7(a865,a865,a865),f82(a865)),x42632))),f324(f245(a865),x42633))),f324(f324(f82(a865),x42633),f324(f324(f81(a865),x42631),f324(f324(f81(a865),x42631),f324(f324(f82(a865),f324(f324(f22(a865),x42633),f79(a865))),x42632))))) % 181.55/181.53 [4273]E(f324(f244(x42731),f324(f324(f18(x42731,a859,a859),f324(f324(f8(a859,f871(a859,a859),x42731),a322),f324(f324(f7(x42731,f871(x42731,a859),a859),f326(x42731)),f324(f167(x42731),x42732)))),x42733)),f324(f167(x42731),f324(f130(x42731,x42733),x42732))) % 181.55/181.53 [4422]E(f324(f244(x44221),f324(f324(f8(f871(a865,a859),a859,x44221),f88(a865)),f324(f324(f7(x44221,f871(a865,a859),f871(a865,a859)),f324(f324(f8(f871(a865,f871(a859,a859)),f871(f871(a865,a859),f871(a865,a859)),x44221),f18(a865,a859,a859)),f324(f324(f8(f871(a865,a859),f871(a865,f871(a859,a859)),x44221),f324(f8(a859,f871(a859,a859),a865),a322)),f324(f324(f7(x44221,f871(a865,x44221),f871(a865,a859)),f324(f324(f8(f871(x44221,a859),f871(f871(a865,x44221),f871(a865,a859)),x44221),f8(x44221,a859,a865)),a321)),f324(f159(x44221),x44222))))),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),f324(f324(f7(a865,a865,a859),f239(a865)),f324(f192(f866(x44221)),x44222)))),f324(f324(f7(a865,f871(a865,a859),a859),f326(a865)),x44223))))),f324(f167(x44221),f171(x44221,x44222,x44223))) % 181.55/181.53 [4312]E(f324(f244(x43121),f324(f324(f18(x43121,a859,a859),f324(f324(f8(a859,f871(a859,a859),x43121),a327),f324(f324(f8(a859,a859,x43121),a319),f324(f324(f7(x43121,x43121,a859),a321),x43122)))),x43123)),f324(f324(f302(x43121),x43122),f324(f244(x43121),x43123))) % 181.55/181.53 [4345]E(f324(f324(f148(f870(x43451,a865),x43451),f258(x43451,a865)),f324(f130(f870(x43451,a865),f324(f324(f7(f870(x43451,a865),f871(a865,a859),a859),f324(f324(f8(a865,f871(f871(a865,a859),a859),f870(x43451,a865)),f326(a865)),f262(x43451,a865))),x43452)),f324(f324(f177(x43451,a865),x43453),f133(a865,f324(f294(a865,f2(a865)),f324(f192(f866(x43451)),x43453)))))),f171(x43451,x43453,x43452)) % 181.55/181.53 [4375]E(f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f6(a865,a1),f324(f324(f8(a1,a1,a865),f324(f81(a1),x43751)),f324(f324(f7(a865,a1,a1),f324(f324(f8(a1,f871(a1,a1),a865),f82(a1)),f103(a1))),x43752))),f324(f245(a865),x43753))),f324(f324(f82(a1),f324(f103(a1),x43753)),f324(f324(f81(a1),x43751),f324(f324(f81(a1),x43751),f324(f324(f82(a1),f324(f103(a1),f324(f324(f22(a865),x43753),f79(a865)))),x43752))))) % 181.55/181.53 [4415]E(f324(f244(f870(x44151,x44152)),f324(f263(x44151,x44152,a859),f324(f324(f7(x44151,f871(f870(x44152,x44151),a859),f871(x44152,a859)),f324(f324(f8(f871(x44152,f871(f871(f870(x44152,x44151),a859),a859)),f871(f871(f870(x44152,x44151),a859),f871(x44152,a859)),x44151),f7(x44152,f871(f870(x44152,x44151),a859),a859)),f324(f324(f8(f871(x44152,f870(x44152,x44151)),f871(x44152,f871(f871(f870(x44152,x44151),a859),a859)),x44151),f324(f8(f870(x44152,x44151),f871(f871(f870(x44152,x44151),a859),a859),x44152),f326(f870(x44152,x44151)))),f324(f7(x44152,x44151,f870(x44152,x44151)),f259(x44152,x44151))))),x44153))),f324(f279(x44152,x44151),x44153)) % 181.55/181.53 [4439]E(f324(f244(f866(x44391)),f324(f324(f8(f871(x44391,a859),a859,f866(x44391)),f88(x44391)),f324(f324(f8(f871(x44391,f871(f866(x44391),a859)),f871(x44391,a859),f866(x44391)),f324(f8(f871(f866(x44391),a859),a859,x44391),f88(f866(x44391)))),f324(f324(f7(f866(x44391),f871(x44391,f871(f866(x44391),a859)),f871(x44391,f871(f866(x44391),a859))),f324(f324(f8(f871(x44391,f871(f871(f866(x44391),a859),f871(f866(x44391),a859))),f871(f871(x44391,f871(f866(x44391),a859)),f871(x44391,f871(f866(x44391),a859))),f866(x44391)),f18(x44391,f871(f866(x44391),a859),f871(f866(x44391),a859))),f324(f324(f8(f871(x44391,f871(f866(x44391),f871(a859,a859))),f871(x44391,f871(f871(f866(x44391),a859),f871(f866(x44391),a859))),f866(x44391)),f324(f8(f871(f866(x44391),f871(a859,a859)),f871(f871(f866(x44391),a859),f871(f866(x44391),a859)),x44391),f18(f866(x44391),a859,a859))),f324(f324(f8(f871(x44391,f871(f866(x44391),a859)),f871(x44391,f871(f866(x44391),f871(a859,a859))),f866(x44391)),f324(f8(f871(f866(x44391),a859),f871(f866(x44391),f871(a859,a859)),x44391),f324(f8(a859,f871(a859,a859),f866(x44391)),a322))),f324(f324(f7(f866(x44391),f871(x44391,f871(f866(x44391),f866(x44391))),f871(x44391,f871(f866(x44391),a859))),f324(f324(f8(f871(f871(f866(x44391),f866(x44391)),f871(f866(x44391),a859)),f871(f871(x44391,f871(f866(x44391),f866(x44391))),f871(x44391,f871(f866(x44391),a859))),f866(x44391)),f8(f871(f866(x44391),f866(x44391)),f871(f866(x44391),a859),x44391)),f324(f324(f8(f871(f866(x44391),a859),f871(f871(f866(x44391),f866(x44391)),f871(f866(x44391),a859)),f866(x44391)),f8(f866(x44391),a859,f866(x44391))),a321))),f145(x44391)))))),f324(f324(f7(x44391,f871(f866(x44391),a859),f871(f866(x44391),a859)),f324(f324(f8(f871(a859,a859),f871(f871(f866(x44391),a859),f871(f866(x44391),a859)),x44391),f8(a859,a859,f866(x44391))),f324(f324(f8(a859,f871(a859,a859),x44391),a322),f324(f324(f7(x44391,f871(x44391,a859),a859),f326(x44391)),x44392)))),f324(f324(f7(f866(x44391),f871(f866(x44391),a859),a859),f326(f866(x44391))),x44393)))))),f169(x44391,x44392,x44393)) % 181.55/181.53 [4436]E(f324(f324(f87(a1,f870(a1,a1)),f324(f324(f22(a1),x44361),x44362)),f324(f324(f7(a1,f870(a1,a1),f870(a1,a1)),f324(f324(f18(a1,f870(a1,a1),f871(f870(a1,a1),f870(a1,a1))),f324(f324(f8(a859,f871(f870(a1,a1),f871(f870(a1,a1),f870(a1,a1))),a1),f99(f870(a1,a1))),f324(f238(a1),f2(a1)))),f324(f259(a1,a1),f324(f324(f81(a1),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x44363)),f79(a1))))),f324(f324(f259(a1,a1),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x44363)),x44361))),f324(f43(x44362),f324(f324(f259(a1,a1),x44363),x44361))) % 181.55/181.53 [3926]E(f76(x39261,x39262,x39263,x39263,x39264),x39264) % 181.55/181.53 [4471]~E(f26(x44711,x44712),f33(x44713,x44714)) % 181.55/181.53 [4474]~E(f32(x44741,x44742),f33(x44743,x44744)) % 181.55/181.53 [4475]~E(f32(x44751,x44752),f26(x44753,x44754)) % 181.55/181.53 [4492]~E(f324(a25,x44921),f30(x44922,x44923,x44924)) % 181.55/181.53 [4493]~E(f324(a25,x44931),f29(x44932,x44933,x44934)) % 181.55/181.53 [4494]~E(f30(x44941,x44942,x44943),f324(a25,x44944)) % 181.55/181.53 [4495]~E(f29(x44951,x44952,x44953),f324(a25,x44954)) % 181.55/181.53 [3455]E(f324(f324(f324(f72(x34551,x34552),x34553),x34554),f324(x34553,x34554)),x34553) % 181.55/181.53 [3514]E(f324(f324(f250(x35141,x35142,x35143),x35144),f2(a865)),x35142) % 181.55/181.53 [3553]E(f186(x35531,x35532,x35533,f324(a115,x35534)),f324(x35533,x35534)) % 181.55/181.53 [3593]E(f164(x35931,x35932,f164(x35931,x35933,x35934)),f164(x35931,x35933,f164(x35931,x35932,x35934))) % 181.55/181.53 [3726]E(f324(f235(x37261,x37262,x37263,x37264),f203(x37262)),x37263) % 181.55/181.53 [3727]E(f324(f150(x37271,x37272,x37273,x37274),f116(x37272)),x37273) % 181.55/181.53 [3728]E(f324(f136(x37281,x37282,x37283,x37284),f116(x37282)),x37284) % 181.55/181.53 [3843]E(f324(f235(f869(x38431),x38432,f203(x38431),f324(f16(f869(x38431),x38432),f203(x38431))),f324(x38433,x38434)),f203(x38431)) % 181.55/181.53 [3887]E(f324(f324(f113(f871(x38871,a859)),f179(x38871,x38872,x38873)),f179(x38871,x38872,x38874)),f179(x38871,x38872,f180(x38871,x38872,x38874,x38873))) % 181.55/181.53 [3919]E(f324(f324(f265(x39191,x39192,x39193,f870(x39192,x39193)),x39194),f259(x39192,x39193)),x39194) % 181.55/181.53 [3930]E(f236(x39301,x39302,x39303,x39304,f203(x39302)),x39303) % 181.55/181.53 [3931]E(f182(x39311,x39312,x39313,x39314,f116(x39312)),x39313) % 181.55/181.53 [3932]E(f182(x39321,x39322,x39323,f116(x39321),x39324),x39323) % 181.55/181.53 [4222]P44(x42221,x42222,x42223,x42224,f191(f871(x42221,a859)),x42224) % 181.55/181.53 [3259]E(f324(f324(f16(x32591,x32592),x32593),x32594),x32593) % 181.55/181.53 [3373]E(f324(f324(f204(x33731,x33732),x33733),f324(f233(x33731),x33734)),f324(f233(x33732),f324(x33733,x33734))) % 181.55/181.53 [3544]E(f164(x35441,x35442,f324(f130(x35441,x35443),x35444)),f324(f130(x35441,x35443),f164(x35441,x35442,x35444))) % 181.55/181.53 [3576]E(f324(f324(f64(x35761,x35762,x35763),x35764),f191(f871(x35761,a859))),x35764) % 181.55/181.53 [3599]E(f324(f324(f159(x35991),f324(f324(f145(x35991),x35992),x35993)),f324(a115,x35994)),f324(f324(f159(x35991),x35993),x35994)) % 181.55/181.53 [3641]P30(x36411,f2(a865),f324(f324(f324(f93(x36411),x36412),f324(a25,x36413)),x36414)) % 181.55/181.53 [3666]E(f324(f324(x36661,x36662),f324(f185(x36663,x36664,x36661),x36662)),f324(f185(x36663,x36664,x36661),f324(a115,x36662))) % 181.55/181.53 [3762]E(f324(f324(f153(x37621,f324(f324(f145(x37621),x37622),x37623)),f2(a865)),x37624),f324(f324(f145(x37621),x37624),x37623)) % 181.55/181.53 [3773]E(f324(f324(f41(f871(x37731,a859),f871(x37732,a859)),x37733),f303(x37731,x37732,x37734)),f324(f303(x37731,x37732,x37734),f39(f871(x37731,a859),x37733))) % 181.55/181.53 [3774]E(f324(f324(f41(f871(x37741,a859),f871(x37742,a859)),x37743),f304(x37742,x37741,x37744)),f324(f304(x37742,x37741,x37744),f39(f871(x37741,a859),x37743))) % 181.55/181.53 [3870]E(f179(x38701,x38702,f183(x38701,x38702,x38703,x38704)),f324(f324(f104(f871(x38701,a859)),f179(x38701,x38702,x38703)),x38704)) % 181.55/181.53 [3874]E(f324(f128(x38741,x38742),f125(x38741,x38743,x38744)),f324(f324(f81(a865),f324(f324(f81(a865),f324(x38742,x38743)),f324(f128(x38741,x38742),x38744))),f324(a115,f2(a865)))) % 181.55/181.53 [3893]E(f324(f136(x38931,x38932,f324(f7(x38932,x38931,x38931),x38933),x38934),f324(f163(x38932),f116(x38932))),x38934) % 181.55/181.53 [3942]E(f77(x39421,x39422,x39423,x39424,f191(f871(x39421,a859))),x39423) % 181.55/181.53 [3990]E(f324(f324(f324(f324(f72(x39901,f869(x39902)),f324(f16(f869(x39902),x39901),f203(x39902))),x39903),f203(x39902)),x39904),f203(x39902)) % 181.55/181.53 [4145]E(f324(f263(x41451,x41452,x41453),f324(f324(f8(f871(x41452,f870(x41451,x41452)),f871(x41452,x41453),x41451),f324(f8(f870(x41451,x41452),x41453,x41452),x41454)),f259(x41451,x41452))),x41454) % 181.55/181.53 [3453]E(f324(f262(x34531,x34532),f324(f324(f259(x34531,x34532),x34533),x34534)),x34534) % 181.55/181.53 [3454]E(f324(f258(x34541,x34542),f324(f324(f259(x34541,x34542),x34543),x34544)),x34543) % 181.55/181.53 [3487]E(f324(f192(f866(x34871)),f324(f324(f148(x34872,x34871),x34873),x34874)),f324(f192(f866(x34872)),x34874)) % 181.55/181.53 [3488]E(f324(f192(f866(x34881)),f324(f324(f153(x34881,x34882),x34883),x34884)),f324(f192(f866(x34881)),x34882)) % 181.55/181.53 [3508]E(f324(f324(f132(x35081),f324(a115,x35082)),f324(f324(f145(x35081),x35083),x35084)),f324(f324(f132(x35081),x35082),x35084)) % 181.55/181.53 [3578]E(f324(f324(f302(x35781),x35782),f324(f324(f302(x35781),x35783),x35784)),f324(f324(f302(x35781),x35783),f324(f324(f302(x35781),x35782),x35784))) % 181.55/181.53 [3582]E(f324(f324(f148(x35821,x35822),x35823),f117(x35821,x35824)),f117(x35822,f324(f324(f148(x35821,x35822),x35823),x35824))) % 181.55/181.53 [3597]E(f324(f163(x35971),f324(f324(f148(x35972,x35971),x35973),x35974)),f324(f324(f148(x35972,x35971),x35973),f324(f163(x35972),x35974))) % 181.55/181.53 [3598]E(f324(f324(f148(x35981,x35982),x35983),f324(f166(x35981),x35984)),f324(f166(x35982),f324(f324(f148(x35981,x35982),x35983),x35984))) % 181.55/181.53 [3609]E(f324(f324(f170(x36091),f324(a115,x36092)),f324(f324(f145(x36091),x36093),x36094)),f324(f324(f145(x36091),x36093),f324(f324(f170(x36091),x36092),x36094))) % 181.55/181.53 [3613]E(f324(f167(x36131),f324(f324(f148(x36132,x36131),x36133),x36134)),f324(f303(x36132,x36131,x36133),f324(f167(x36132),x36134))) % 181.55/181.53 [3665]E(f17(x36651,x36652,x36653,f324(a3,f324(a115,f324(a19,x36654)))),f324(x36653,x36654)) % 181.55/181.53 [3668]E(f324(f324(f124(x36681),f324(f130(x36681,x36682),x36683)),f324(f130(x36681,x36682),x36684)),f324(f130(x36681,x36682),f324(f324(f124(x36681),x36683),x36684))) % 181.55/181.53 [3681]E(f146(x36811,f324(f324(f148(x36812,x36811),x36813),f146(x36812,x36814))),f146(x36811,f324(f324(f148(x36812,x36811),x36813),x36814))) % 181.55/181.53 [3697]E(f324(f279(x36971,x36971),f324(f324(f280(x36972,x36971),x36973),x36974)),f324(f324(f280(x36972,x36971),f324(f279(x36972,x36972),x36973)),x36974)) % 181.55/181.53 [3707]E(f324(f324(f281(x37071,x37072,x37073),x37074),f191(f871(f870(x37072,x37073),a859))),f191(f871(f870(x37071,x37073),a859))) % 181.55/181.53 [3708]E(f324(f324(f170(x37081),f324(f324(f22(a865),x37082),x37083)),f324(f324(f132(x37081),x37083),x37084)),f324(f324(f132(x37081),x37083),f324(f324(f170(x37081),x37082),x37084))) % 181.55/181.53 [3754]E(f40(f871(x37541,a859),f324(f303(x37542,f871(x37541,a859),x37543),x37544)),f324(f324(f42(x37542,f871(x37541,a859)),x37544),x37543)) % 181.55/181.53 [3755]E(f39(f871(x37551,a859),f324(f303(x37552,f871(x37551,a859),x37553),x37554)),f324(f324(f41(x37552,f871(x37551,a859)),x37554),x37553)) % 181.55/181.53 [3756]E(f324(f192(f866(f870(x37561,x37562))),f324(f324(f177(x37561,x37562),x37563),x37564)),f324(f324(f189(a865),f324(f192(f866(x37561)),x37563)),f324(f192(f866(x37562)),x37564))) % 181.55/181.53 [3758]E(f324(f304(x37581,x37582,x37583),f324(f80(f871(x37582,a859)),x37584)),f324(f80(f871(x37581,a859)),f324(f304(x37581,x37582,x37583),x37584))) % 181.55/181.53 [3788]E(f324(f183(x37881,x37882,x37883,f191(f871(x37881,a859))),x37884),f203(x37882)) % 181.55/181.53 [3809]E(f324(f304(x38091,x38092,x38093),f324(f244(x38092),x38094)),f324(f244(x38091),f324(f324(f8(x38092,a859,x38091),x38094),x38093))) % 181.55/181.53 [3826]E(f324(f324(f159(x38261),f324(f324(f124(x38261),x38262),f324(f324(f145(x38261),x38263),x38264))),f324(f192(f866(x38261)),x38262)),x38263) % 181.55/181.53 [3831]E(f324(f183(x38311,x38312,f324(f16(f869(x38312),x38311),f203(x38312)),x38313),x38314),f203(x38312)) % 181.55/181.53 [3851]E(f324(f303(x38511,x38512,x38513),f324(f304(x38511,x38512,x38513),x38514)),f324(f324(f104(f871(x38512,a859)),x38514),f324(f303(x38511,x38512,x38513),f247(f871(x38511,a859))))) % 181.55/181.53 [3869]P1(f324(f324(f326(x38691),f324(x38692,x38693)),f324(f303(x38694,x38691,x38692),f247(f871(x38694,a859))))) % 181.55/181.53 [3882]E(f324(f324(f261(x38821,x38822),f324(f167(x38821),x38823)),f324(f16(f871(x38822,a859),x38821),f324(f167(x38822),x38824))),f324(f167(f870(x38821,x38822)),f59(x38821,x38822,x38823,x38824))) % 181.55/181.53 [3896]E(f149(x38961,x38962,f324(f324(f145(x38961),x38963),x38964)),f324(f324(f81(a865),f324(f324(f81(a865),f324(x38962,x38963)),f149(x38961,x38962,x38964))),f324(a115,f2(a865)))) % 181.55/181.53 [3910]E(f186(f866(x39101),f324(f324(f145(x39101),x39102),x39103),f324(f324(f7(a865,f866(x39101),f866(x39101)),f132(x39101)),x39103),x39104),f324(f324(f132(x39101),x39104),f324(f324(f145(x39101),x39102),x39103))) % 181.55/181.53 [3911]P27(x39111,f870(x39112,x39111),f328(x39113,x39114,x39112,x39111),f324(f324(f41(x39112,f871(x39111,a859)),x39114),x39113)) % 181.55/181.53 [3920]E(f324(f324(f22(f871(x39201,a859)),f324(f324(f22(f871(x39201,a859)),x39202),x39203)),f324(f324(f302(x39201),x39204),f191(f871(x39201,a859)))),f324(f324(f22(f871(x39201,a859)),x39202),f324(f324(f302(x39201),x39204),x39203))) % 181.55/181.53 [3933]E(f324(f324(f184(f871(x39331,x39332),f871(x39331,x39332)),x39333),f73(x39332,x39332,x39331,x39334)),f73(x39332,x39332,x39331,f324(f324(f184(x39332,x39332),x39333),x39334))) % 181.55/181.53 [4013]E(f324(f324(f324(f184(f866(x40131),f866(x40131)),x40132),f162(x40131)),f324(f324(f324(f184(f866(x40131),f866(x40131)),x40133),f162(x40131)),x40134)),f324(f324(f324(f184(f866(x40131),f866(x40131)),f324(f324(f81(a865),x40132),x40133)),f162(x40131)),x40134)) % 181.55/181.53 [4099]P1(f324(f324(f238(f871(x40991,a859)),f324(f167(x40991),f324(f324(f153(x40991,x40992),x40993),x40994))),f324(f324(f302(x40991),x40994),f324(f167(x40991),x40992)))) % 181.55/181.53 [4135]E(f324(f324(f41(f871(x41351,a859),f871(f870(x41351,x41352),a859)),x41353),f324(f324(f7(f871(x41351,a859),f871(x41351,f871(x41352,a859)),f871(f870(x41351,x41352),a859)),f261(x41351,x41352)),x41354)),f324(f324(f261(x41351,x41352),f39(f871(x41351,a859),x41353)),x41354)) % 181.55/181.53 [4175]E(f214(x41751,x41752,x41753,f324(f73(x41752,f871(a102,f871(a102,f871(f870(a102,a102),f871(a102,f867(x41752))))),x41751,f213(x41752)),x41754)),f215(x41751,x41752,x41754,x41753)) % 181.55/181.53 [4192]E(f210(x41921,x41922,x41923,f324(f73(x41922,f871(a102,f871(a102,f871(f870(a102,a102),f871(a102,f867(f869(x41922)))))),x41921,f207(x41922)),x41924)),f211(x41921,x41922,x41924,x41923)) % 181.55/181.53 [4197]P1(f324(f66(x41971,x41972,x41973,x41974,f191(f871(x41971,a859))),x41974)) % 181.55/181.53 [4240]E(f324(f324(f41(x42401,f871(x42402,a859)),x42403),f324(f324(f7(x42401,f871(x42402,a859),f871(x42402,a859)),f324(f324(f8(x42402,f871(f871(x42402,a859),f871(x42402,a859)),x42401),f302(x42402)),x42404)),f191(f871(x42402,a859)))),f324(f303(x42401,x42402,x42404),x42403)) % 181.55/181.53 [4247]P1(f324(f324(f238(f871(x42471,a859)),f324(f255(x42472,x42471),f324(f324(f104(f871(f870(x42472,x42471),a859)),x42473),x42474))),f324(f324(f104(f871(x42471,a859)),f324(f255(x42472,x42471),x42473)),f324(f255(x42472,x42471),x42474)))) % 181.55/181.53 [4248]P1(f324(f324(f238(f871(x42481,a859)),f324(f257(x42481,x42482),f324(f324(f104(f871(f870(x42481,x42482),a859)),x42483),x42484))),f324(f324(f104(f871(x42481,a859)),f324(f257(x42481,x42482),x42483)),f324(f257(x42481,x42482),x42484)))) % 181.55/181.53 [4310]P1(f324(f324(f238(f871(f870(x43101,x43102),a859)),f324(f303(x43102,f870(x43101,x43102),f328(x43103,x43104,x43101,x43102)),f324(f324(f41(x43101,f871(x43102,a859)),x43104),x43103))),f324(f324(f261(x43101,x43102),x43104),x43103))) % 181.55/181.53 [4351]E(f86(f870(x43511,x43512),f324(f263(x43511,x43512,a859),f324(f324(f7(x43511,f871(x43512,a859),f871(x43512,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x43512,a859),f871(x43512,a859)),x43511),f8(a859,a859,x43512)),f324(f324(f8(a859,f871(a859,a859),x43511),a322),f324(a321,x43513)))),f324(a321,x43514)))),f324(f324(f259(x43511,x43512),x43513),x43514)) % 181.55/181.53 [4352]E(f91(f870(x43521,x43522),f324(f263(x43521,x43522,a859),f324(f324(f7(x43521,f871(x43522,a859),f871(x43522,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x43522,a859),f871(x43522,a859)),x43521),f8(a859,a859,x43522)),f324(f324(f8(a859,f871(a859,a859),x43521),a322),f324(a321,x43523)))),f324(a321,x43524)))),f324(f324(f259(x43521,x43522),x43523),x43524)) % 181.55/181.53 [4426]E(f324(f324(f263(f866(x44261),f866(x44261),f870(f866(x44261),f866(x44261))),f324(f324(f18(f866(x44261),f871(f866(x44261),f870(f866(x44261),f866(x44261))),f871(f866(x44261),f870(f866(x44261),f866(x44261)))),f324(f324(f8(f871(f866(x44261),f871(f870(f866(x44261),f866(x44261)),f870(f866(x44261),f866(x44261)))),f871(f871(f866(x44261),f870(f866(x44261),f866(x44261))),f871(f866(x44261),f870(f866(x44261),f866(x44261)))),f866(x44261)),f18(f866(x44261),f870(f866(x44261),f866(x44261)),f870(f866(x44261),f866(x44261)))),f324(f324(f8(f871(f866(x44261),f870(f866(x44261),f866(x44261))),f871(f866(x44261),f871(f870(f866(x44261),f866(x44261)),f870(f866(x44261),f866(x44261)))),f866(x44261)),f324(f8(f870(f866(x44261),f866(x44261)),f871(f870(f866(x44261),f866(x44261)),f870(f866(x44261),f866(x44261))),f866(x44261)),f324(f99(f870(f866(x44261),f866(x44261))),f324(x44262,x44263)))),f324(f324(f8(f866(x44261),f871(f866(x44261),f870(f866(x44261),f866(x44261))),f866(x44261)),f259(f866(x44261),f866(x44261))),f324(f145(x44261),x44263))))),f324(f324(f7(f866(x44261),f871(f866(x44261),f866(x44261)),f871(f866(x44261),f870(f866(x44261),f866(x44261)))),f324(f324(f8(f871(f866(x44261),f870(f866(x44261),f866(x44261))),f871(f871(f866(x44261),f866(x44261)),f871(f866(x44261),f870(f866(x44261),f866(x44261)))),f866(x44261)),f8(f866(x44261),f870(f866(x44261),f866(x44261)),f866(x44261))),f259(f866(x44261),f866(x44261)))),f324(f145(x44261),x44263)))),f161(x44261,x44262,x44264)),f161(x44261,x44262,f324(f324(f145(x44261),x44263),x44264))) % 181.55/181.53 [4431]E(f324(f136(f871(x44311,f869(x44312)),f870(x44311,x44312),f324(f7(f870(x44311,x44312),f871(x44311,f869(x44312)),f871(x44311,f869(x44312))),f324(f263(x44311,x44312,f871(f871(x44311,f869(x44312)),f871(x44311,f869(x44312)))),f324(f324(f7(x44311,f871(x44312,f869(x44312)),f871(x44312,f871(f871(x44311,f869(x44312)),f871(x44311,f869(x44312))))),f324(f324(f8(f871(f869(x44312),f871(f871(x44311,f869(x44312)),f871(x44311,f869(x44312)))),f871(f871(x44312,f869(x44312)),f871(x44312,f871(f871(x44311,f869(x44312)),f871(x44311,f869(x44312))))),x44311),f8(f869(x44312),f871(f871(x44311,f869(x44312)),f871(x44311,f869(x44312))),x44312)),f324(f324(f8(f871(f871(x44311,f869(x44312)),f871(f869(x44312),f871(x44311,f869(x44312)))),f871(f869(x44312),f871(f871(x44311,f869(x44312)),f871(x44311,f869(x44312)))),x44311),f7(f871(x44311,f869(x44312)),f869(x44312),f871(x44311,f869(x44312)))),f324(f7(f871(x44311,f869(x44312)),x44311,f871(f869(x44312),f871(x44311,f869(x44312)))),f72(x44311,f869(x44312)))))),f233(x44312)))),x44313),f324(f163(f870(x44311,x44312)),x44314)),f180(x44311,x44312,x44313,f324(f173(x44311,x44312),x44314))) % 181.55/181.53 [3527]E(f324(f192(f864(x35271)),f324(f324(f324(f93(x35271),x35272),x35273),x35274)),f2(a865)) % 181.55/181.53 [3644]E(f324(f324(f170(x36441),x36442),f324(f324(f170(x36441),x36443),x36444)),f324(f324(f170(x36441),f324(f324(f189(a865),x36442),x36443)),x36444)) % 181.55/181.53 [3645]E(f324(f324(f132(x36451),x36452),f324(f324(f132(x36451),x36453),x36454)),f324(f324(f132(x36451),f324(f324(f81(a865),x36452),x36453)),x36454)) % 181.55/181.53 [3657]E(f324(f324(f124(x36571),f324(f324(f145(x36571),x36572),x36573)),x36574),f324(f324(f145(x36571),x36572),f324(f324(f124(x36571),x36573),x36574))) % 181.55/181.53 [3658]E(f324(f324(f124(x36581),f324(f324(f124(x36581),x36582),x36583)),x36584),f324(f324(f124(x36581),x36582),f324(f324(f124(x36581),x36583),x36584))) % 181.55/181.53 [3738]E(f324(f324(f159(x37381),f324(f324(f145(x37381),x37382),x37383)),x37384),f186(x37381,x37382,f324(f159(x37381),x37383),x37384)) % 181.55/181.53 [3747]E(f324(f324(f184(x37471,x37471),x37472),f324(f324(f184(x37471,x37471),x37473),x37474)),f324(f324(f184(x37471,x37471),f324(f324(f82(a865),x37473),x37472)),x37474)) % 181.55/181.53 [3776]E(f324(f324(f113(f871(x37761,a859)),x37762),f324(f324(f302(x37761),x37763),x37764)),f324(f324(f302(x37761),x37763),f324(f324(f113(f871(x37761,a859)),x37762),x37764))) % 181.55/181.53 [3791]E(f324(f324(f324(f184(x37911,x37911),x37912),x37913),f324(x37913,x37914)),f324(x37913,f324(f324(f324(f184(x37911,x37911),x37912),x37913),x37914))) % 181.55/181.53 [3799]E(f324(f324(f281(x37991,x37992,x37993),f191(f871(f870(x37991,x37992),a859))),x37994),f191(f871(f870(x37991,x37993),a859))) % 181.55/181.53 [3815]E(f324(f324(f113(f871(x38151,a859)),f324(f324(f302(x38151),x38152),x38153)),x38154),f324(f324(f302(x38151),x38152),f324(f324(f113(f871(x38151,a859)),x38153),x38154))) % 181.55/181.53 [3833]E(f180(x38331,x38332,f324(f173(x38331,x38332),x38333),f324(f173(x38331,x38332),x38334)),f324(f173(x38331,x38332),f324(f324(f124(f870(x38331,x38332)),x38334),x38333))) % 181.55/181.53 [3834]E(f324(f37(f870(x38341,x38342)),f324(f324(f261(x38341,x38342),x38343),f324(f16(f871(x38342,a859),x38341),x38344))),f324(f324(f82(a865),f324(f37(x38341),x38343)),f324(f37(x38342),x38344))) % 181.55/181.53 [3840]E(f324(f324(f104(f871(x38401,a859)),f324(f324(f302(x38401),x38402),x38403)),f324(f324(f302(x38401),x38402),x38404)),f324(f324(f302(x38401),x38402),f324(f324(f104(f871(x38401,a859)),x38403),x38404))) % 181.55/181.53 [3855]E(f324(f324(f104(f871(x38551,a859)),x38552),f324(f324(f104(f871(x38551,a859)),x38553),x38554)),f324(f324(f104(f871(x38551,a859)),x38553),f324(f324(f104(f871(x38551,a859)),x38552),x38554))) % 181.55/181.53 [3856]E(f324(f324(f113(f871(x38561,a859)),x38562),f324(f324(f113(f871(x38561,a859)),x38563),x38564)),f324(f324(f113(f871(x38561,a859)),x38563),f324(f324(f113(f871(x38561,a859)),x38562),x38564))) % 181.55/181.53 [3865]E(f64(x38651,x38652,f324(f324(f8(x38652,f871(x38652,x38652),x38651),x38653),x38654)),f324(f65(x38652,x38651,x38653),x38654)) % 181.55/181.53 [3875]E(f175(x38751,f324(f324(f148(f866(x38752),f866(x38751)),f324(f148(x38752,x38751),x38753)),x38754)),f324(f324(f148(f866(x38752),f866(x38751)),f324(f148(x38752,x38751),x38753)),f175(x38752,x38754))) % 181.55/181.53 [3892]E(f324(f136(f866(x38921),f866(x38921),f124(x38921),f116(x38921)),f324(f324(f148(x38922,f866(x38921)),x38923),x38924)),f158(x38922,x38921,x38923,x38924)) % 181.55/181.53 [3895]E(f183(x38951,x38952,x38953,f324(f80(f871(x38951,a859)),f324(f324(f302(x38951),x38954),f191(f871(x38951,a859))))),f324(f324(f324(f72(x38951,f869(x38952)),x38953),x38954),f203(x38952))) % 181.55/181.53 [3938]E(f324(f324(f324(f72(x39381,f869(x39382)),f324(f173(x39381,x39382),x39383)),f324(f258(x39381,x39382),x39384)),f324(f233(x39382),f324(f262(x39381,x39382),x39384))),f324(f173(x39381,x39382),f324(f324(f145(f870(x39381,x39382)),x39384),x39383))) % 181.55/181.53 [3957]E(f324(f73(x39571,x39571,x39571,f324(f324(f184(x39571,x39571),x39572),x39573)),f324(f324(f184(x39571,x39571),x39574),x39573)),f324(f324(f184(x39571,x39571),f324(f324(f81(a865),x39572),x39574)),x39573)) % 181.55/181.53 [3982]E(f324(f324(f113(f871(x39821,a859)),f324(f324(f22(f871(x39821,a859)),x39822),x39823)),f324(f324(f22(f871(x39821,a859)),x39822),x39824)),f324(f324(f22(f871(x39821,a859)),x39822),f324(f324(f104(f871(x39821,a859)),x39823),x39824))) % 181.55/181.53 [3983]E(f324(f324(f104(f871(x39831,a859)),f324(f324(f22(f871(x39831,a859)),x39832),x39833)),f324(f324(f22(f871(x39831,a859)),x39832),x39834)),f324(f324(f22(f871(x39831,a859)),x39832),f324(f324(f113(f871(x39831,a859)),x39833),x39834))) % 181.55/181.53 [3984]E(f324(f324(f22(f871(x39841,a859)),f324(f324(f104(f871(x39841,a859)),x39842),x39843)),f324(f324(f104(f871(x39841,a859)),x39842),x39844)),f324(f324(f104(f871(x39841,a859)),x39842),f324(f324(f22(f871(x39841,a859)),x39843),x39844))) % 181.55/181.53 [3985]E(f324(f324(f113(f871(x39851,a859)),f324(f324(f104(f871(x39851,a859)),x39852),x39853)),f324(f324(f104(f871(x39851,a859)),x39852),x39854)),f324(f324(f104(f871(x39851,a859)),x39852),f324(f324(f113(f871(x39851,a859)),x39853),x39854))) % 181.55/181.53 [3986]E(f324(f324(f104(f871(x39861,a859)),f324(f324(f113(f871(x39861,a859)),x39862),x39863)),f324(f324(f113(f871(x39861,a859)),x39862),x39864)),f324(f324(f113(f871(x39861,a859)),x39862),f324(f324(f104(f871(x39861,a859)),x39863),x39864))) % 181.55/181.53 [3992]E(f324(f37(f870(x39921,x39922)),f324(f324(f261(x39921,x39922),f324(f324(f302(x39921),x39923),f191(f871(x39921,a859)))),f324(f16(f871(x39922,a859),x39921),x39924))),f324(f37(x39922),x39924)) % 181.55/181.53 [4028]E(f324(f324(f42(x40281,f871(x40282,a859)),x40283),f324(f324(f8(f871(x40282,a859),f871(x40282,a859),x40281),f80(f871(x40282,a859))),x40284)),f324(f80(f871(x40282,a859)),f324(f324(f41(x40281,f871(x40282,a859)),x40283),x40284))) % 181.55/181.53 [4029]E(f324(f324(f41(x40291,f871(x40292,a859)),x40293),f324(f324(f8(f871(x40292,a859),f871(x40292,a859),x40291),f80(f871(x40292,a859))),x40294)),f324(f80(f871(x40292,a859)),f324(f324(f42(x40291,f871(x40292,a859)),x40293),x40294))) % 181.55/181.53 [4043]E(f324(f324(f281(x40431,x40431,x40431),f324(f324(f184(f870(x40431,x40431),a859),x40432),x40433)),f324(f324(f184(f870(x40431,x40431),a859),x40434),x40433)),f324(f324(f184(f870(x40431,x40431),a859),f324(f324(f81(a865),x40432),x40434)),x40433)) % 181.55/181.53 [4074]E(f324(f324(f42(x40741,f871(f871(x40742,a859),a859)),x40743),f324(f324(f8(f871(x40742,a859),f871(f871(x40742,a859),a859),x40741),f301(x40742)),x40744)),f324(f301(x40742),f324(f324(f42(x40741,f871(x40742,a859)),x40743),x40744))) % 181.55/181.53 [4103]E(f324(f324(f41(f871(x41031,a859),f871(x41032,a859)),x41033),f324(f324(f7(f871(x41031,a859),f871(x41031,f871(x41032,a859)),f871(x41032,a859)),f41(x41031,f871(x41032,a859))),x41034)),f324(f324(f41(x41031,f871(x41032,a859)),f39(f871(x41031,a859),x41033)),x41034)) % 181.55/181.53 [4104]E(f324(f324(f42(f871(x41041,a859),f871(x41042,a859)),x41043),f324(f324(f7(f871(x41041,a859),f871(x41041,f871(x41042,a859)),f871(x41042,a859)),f42(x41041,f871(x41042,a859))),x41044)),f324(f324(f42(x41041,f871(x41042,a859)),f39(f871(x41041,a859),x41043)),x41044)) % 181.55/181.53 [4109]E(f324(f324(f148(x41091,x41092),x41093),f324(f136(f866(x41091),f866(x41091),f124(x41091),f116(x41091)),x41094)),f324(f136(f866(x41092),f866(x41092),f124(x41092),f116(x41092)),f324(f324(f148(f866(x41091),f866(x41092)),f324(f148(x41091,x41092),x41093)),x41094))) % 181.55/181.53 [4112]E(f186(f866(x41121),f116(x41121),f324(f324(f8(f866(x41121),f866(x41121),a865),f324(f145(x41121),x41122)),f324(f324(f7(a865,f866(x41121),f866(x41121)),f170(x41121)),x41123)),x41124),f324(f324(f170(x41121),x41124),f324(f324(f145(x41121),x41122),x41123))) % 181.55/181.53 [4155]P1(f324(f324(f238(f871(x41551,a859)),f324(f303(x41552,x41551,x41553),f324(f304(x41552,x41551,x41553),x41554))),x41554)) % 181.55/181.53 [4159]E(f324(f303(f870(x41591,x41592),f870(x41592,x41591),f324(f263(x41591,x41592,f870(x41592,x41591)),f324(f7(x41592,x41591,f870(x41592,x41591)),f259(x41592,x41591)))),f324(f324(f261(x41591,x41592),x41593),f324(f16(f871(x41592,a859),x41591),x41594))),f324(f324(f261(x41592,x41591),x41594),f324(f16(f871(x41591,a859),x41592),x41593))) % 181.55/181.53 [4168]E(f324(f324(f41(x41681,f871(x41682,a859)),x41683),f324(f324(f8(f871(x41681,a859),f871(x41682,a859),x41681),f304(x41682,x41681,x41684)),f324(f324(f7(x41681,f871(x41681,a859),f871(x41681,a859)),f302(x41681)),f191(f871(x41681,a859))))),f324(f304(x41682,x41681,x41684),x41683)) % 181.55/181.53 [4169]E(f324(f324(f41(x41691,f871(x41692,a859)),x41693),f324(f324(f8(f871(x41691,a859),f871(x41692,a859),x41691),f278(x41691,x41692,x41694)),f324(f324(f7(x41691,f871(x41691,a859),f871(x41691,a859)),f302(x41691)),f191(f871(x41691,a859))))),f324(f278(x41691,x41692,x41694),x41693)) % 181.55/181.53 [4262]E(f324(f324(f113(f871(x42621,a859)),f324(f324(f113(f871(x42621,a859)),f324(f324(f104(f871(x42621,a859)),x42622),x42623)),f324(f324(f104(f871(x42621,a859)),x42623),x42624))),f324(f324(f104(f871(x42621,a859)),x42624),x42622)),f324(f324(f104(f871(x42621,a859)),f324(f324(f104(f871(x42621,a859)),f324(f324(f113(f871(x42621,a859)),x42622),x42623)),f324(f324(f113(f871(x42621,a859)),x42623),x42624))),f324(f324(f113(f871(x42621,a859)),x42624),x42622))) % 181.55/181.53 [4324]E(f324(f136(f866(x43241),f866(x43241),f124(x43241),f116(x43241)),f324(f324(f148(x43242,f866(x43241)),f324(f324(f7(x43242,f866(x43241),f866(x43241)),f324(f324(f8(x43241,f871(f866(x43241),f866(x43241)),x43242),f145(x43241)),x43243)),f116(x43241))),x43244)),f324(f324(f148(x43242,x43241),x43243),x43244)) % 181.55/181.53 [4335]E(f324(f324(f87(a1,x43351),f324(f106(a1),f324(f324(f81(a1),x43352),a100))),f324(f324(f18(a1,x43351,x43351),f324(f324(f7(a1,x43351,f871(x43351,x43351)),f324(f324(f8(a859,f871(x43351,f871(x43351,x43351)),a1),f99(x43351)),a196)),x43353)),f324(f324(f8(a865,x43351,a1),x43354),a107))),f186(x43351,x43353,x43354,f324(f106(a865),x43352))) % 181.55/181.53 [4551]~P1(f324(f324(f191(f871(x45511,f871(x45512,a859))),x45513),x45514)) % 181.55/181.53 [3802]E(f324(f324(f159(x38021),f324(f324(f124(x38021),x38022),x38023)),f324(f324(f81(a865),f324(f192(f866(x38021)),x38022)),x38024)),f324(f324(f159(x38021),x38023),x38024)) % 181.55/181.53 [3808]E(f324(f324(f132(x38081),x38082),f324(f324(f170(x38081),f324(f324(f81(a865),x38083),x38082)),x38084)),f324(f324(f170(x38081),x38083),f324(f324(f132(x38081),x38082),x38084))) % 181.55/181.53 [3908]E(f324(f324(f113(f871(x39081,a859)),f324(f255(x39082,x39081),x39083)),f324(f255(x39082,x39081),x39084)),f324(f255(x39082,x39081),f324(f324(f113(f871(f870(x39082,x39081),a859)),x39083),x39084))) % 181.55/181.53 [3909]E(f324(f324(f113(f871(x39091,a859)),f324(f257(x39091,x39092),x39093)),f324(f257(x39091,x39092),x39094)),f324(f257(x39091,x39092),f324(f324(f113(f871(f870(x39091,x39092),a859)),x39093),x39094))) % 181.55/181.53 [3914]E(f324(f324(f22(f871(x39141,a859)),f324(f324(f104(f871(x39141,a859)),x39142),x39143)),x39144),f324(f324(f104(f871(x39141,a859)),x39142),f324(f324(f22(f871(x39141,a859)),x39143),x39144))) % 181.55/181.53 [3915]E(f324(f324(f104(f871(x39151,a859)),f324(f324(f104(f871(x39151,a859)),x39152),x39153)),x39154),f324(f324(f104(f871(x39151,a859)),x39152),f324(f324(f104(f871(x39151,a859)),x39153),x39154))) % 181.55/181.53 [3916]E(f324(f324(f113(f871(x39161,a859)),f324(f324(f113(f871(x39161,a859)),x39162),x39163)),x39164),f324(f324(f113(f871(x39161,a859)),x39162),f324(f324(f113(f871(x39161,a859)),x39163),x39164))) % 181.55/181.53 [3959]E(f324(f324(f104(f871(f870(x39591,x39592),a859)),f324(f279(x39592,x39591),x39593)),f324(f279(x39592,x39591),x39594)),f324(f279(x39592,x39591),f324(f324(f104(f871(f870(x39592,x39591),a859)),x39593),x39594))) % 181.55/181.53 [3960]E(f324(f324(f113(f871(f870(x39601,x39602),a859)),f324(f279(x39602,x39601),x39603)),f324(f279(x39602,x39601),x39604)),f324(f279(x39602,x39601),f324(f324(f113(f871(f870(x39602,x39601),a859)),x39603),x39604))) % 181.55/181.53 [3974]E(f324(f324(f104(f871(x39741,f871(x39742,a859))),f248(x39742,x39741,x39743)),f248(x39742,x39741,x39744)),f248(x39742,x39741,f324(f324(f104(f871(x39742,f871(x39741,a859))),x39743),x39744))) % 181.55/181.53 [3975]E(f324(f324(f113(f871(x39751,f871(x39752,a859))),f248(x39752,x39751,x39753)),f248(x39752,x39751,x39754)),f248(x39752,x39751,f324(f324(f113(f871(x39752,f871(x39751,a859))),x39753),x39754))) % 181.55/181.53 [4032]E(f324(f324(f113(f871(x40321,a859)),f324(f324(f22(f871(x40321,a859)),x40322),x40323)),f324(f324(f22(f871(x40321,a859)),x40324),x40323)),f324(f324(f22(f871(x40321,a859)),f324(f324(f113(f871(x40321,a859)),x40322),x40324)),x40323)) % 181.55/181.53 [4033]E(f324(f324(f22(f871(x40331,a859)),f324(f324(f104(f871(x40331,a859)),x40332),x40333)),f324(f324(f104(f871(x40331,a859)),x40334),x40333)),f324(f324(f104(f871(x40331,a859)),f324(f324(f22(f871(x40331,a859)),x40332),x40334)),x40333)) % 181.55/181.53 [4034]E(f324(f324(f113(f871(x40341,a859)),f324(f324(f104(f871(x40341,a859)),x40342),x40343)),f324(f324(f104(f871(x40341,a859)),x40344),x40343)),f324(f324(f104(f871(x40341,a859)),f324(f324(f113(f871(x40341,a859)),x40342),x40344)),x40343)) % 181.55/181.53 [4035]E(f324(f324(f104(f871(x40351,a859)),f324(f324(f113(f871(x40351,a859)),x40352),x40353)),f324(f324(f113(f871(x40351,a859)),x40354),x40353)),f324(f324(f113(f871(x40351,a859)),f324(f324(f104(f871(x40351,a859)),x40352),x40354)),x40353)) % 181.55/181.53 [4036]E(f324(f324(f22(f871(x40361,a859)),f324(f324(f104(f871(x40361,a859)),x40362),x40363)),f324(f324(f104(f871(x40361,a859)),x40364),x40363)),f324(f324(f22(f871(x40361,a859)),f324(f324(f104(f871(x40361,a859)),x40362),x40363)),x40364)) % 181.55/181.53 [4046]E(f324(f324(f22(f871(x40461,a859)),f324(f324(f22(f871(x40461,a859)),x40462),f324(f324(f302(x40461),x40463),f191(f871(x40461,a859))))),x40464),f324(f324(f22(f871(x40461,a859)),x40462),f324(f324(f302(x40461),x40463),x40464))) % 181.55/181.53 [4100]E(f324(f324(f113(f871(x41001,a859)),f324(f324(f302(x41001),x41002),f324(f324(f302(x41001),x41003),f191(f871(x41001,a859))))),f324(f277(x41001),x41004)),f324(f277(x41001),f324(f324(f302(f870(x41001,x41001)),f324(f324(f259(x41001,x41001),x41002),x41003)),x41004))) % 181.55/181.53 [4130]E(f324(f324(f41(a865,f871(x41301,a859)),f324(f293(a865),x41302)),f324(f324(f8(a865,f871(x41301,a859),a865),x41303),f324(f324(f7(a865,a865,a865),f81(a865)),x41304))),f324(f324(f41(a865,f871(x41301,a859)),f295(a865,x41304,f324(f324(f81(a865),x41302),x41304))),x41303)) % 181.55/181.53 [4131]E(f169(x41311,f324(f278(x41311,x41311,x41312),f324(f324(f302(x41311),x41313),f191(f871(x41311,a859)))),f324(f278(f866(x41311),f866(x41311),f152(x41311,x41312)),f324(f324(f302(f866(x41311)),x41314),f191(f871(f866(x41311),a859))))),f324(f278(f866(x41311),f866(x41311),f152(x41311,x41312)),f324(f324(f302(f866(x41311)),f324(f324(f145(x41311),x41313),x41314)),f191(f871(f866(x41311),a859))))) % 181.55/181.53 [4195]E(f324(f173(x41951,x41952),f324(f324(f148(x41951,f870(x41951,x41952)),f324(f324(f18(x41951,x41952,f870(x41951,x41952)),f259(x41951,x41952)),x41953)),x41954)),f183(x41951,x41952,f324(f73(x41952,f869(x41952),x41951,f233(x41952)),x41953),f324(f167(x41951),x41954))) % 181.55/181.53 [4201]E(f324(f244(x42011),f324(f324(f7(x42011,f871(x42012,a859),a859),f324(f324(f8(x42012,f871(f871(x42012,a859),a859),x42011),f326(x42012)),x42013)),x42014)),f324(f304(x42011,x42012,x42013),x42014)) % 181.55/181.53 [4295]E(f324(f244(x42951),f324(f324(f7(x42951,f871(f870(x42952,x42951),a859),a859),f324(f324(f8(f870(x42952,x42951),f871(f871(f870(x42952,x42951),a859),a859),x42951),f326(f870(x42952,x42951))),f324(f259(x42952,x42951),x42953))),x42954)),f324(f278(x42952,x42951,x42954),f324(f324(f302(x42952),x42953),f191(f871(x42952,a859))))) % 181.55/181.53 [4309]E(f324(f324(f148(f870(x43091,a865),x43091),f258(x43091,a865)),f324(f130(f870(x43091,a865),f324(f324(f8(a865,a859,f870(x43091,a865)),x43092),f324(f324(f8(a865,a865,f870(x43091,a865)),a115),f262(x43091,a865)))),f324(f324(f177(x43091,a865),x43093),x43094))),f324(f324(f148(f870(x43091,a865),x43091),f258(x43091,a865)),f324(f130(f870(x43091,a865),f324(f324(f8(a865,a859,f870(x43091,a865)),x43092),f262(x43091,a865))),f324(f324(f177(x43091,a865),x43093),f324(f324(f148(a865,a865),a115),x43094))))) % 181.55/181.53 [4316]P1(f324(f324(f238(f871(f871(x43161,a859),a859)),f324(f324(f41(x43162,f871(f871(x43161,a859),a859)),x43163),f324(f324(f8(f871(x43161,a859),f871(f871(x43161,a859),a859),x43162),f301(x43161)),x43164))),f324(f301(x43161),f324(f324(f41(x43162,f871(x43161,a859)),x43163),x43164)))) % 181.55/181.53 [4359]E(f324(f324(f87(a1,x43591),f324(f106(a1),f324(f324(f81(a1),x43592),a100))),f324(f324(f18(a1,x43591,x43591),f324(f324(f7(a1,x43591,f871(x43591,x43591)),f324(f324(f8(a859,f871(x43591,f871(x43591,x43591)),a1),f99(x43591)),a196)),x43593)),f324(f324(f18(a1,x43591,x43591),f324(f324(f8(a865,f871(x43591,x43591),a1),x43594),a107)),f324(f324(f8(a865,x43591,a1),f185(x43591,x43593,x43594)),a107)))),f324(f185(x43591,x43593,x43594),f324(f106(a865),x43592))) % 181.55/181.53 [4362]E(f324(f324(f148(x43621,x43622),f324(f73(f869(x43622),x43622,x43621,f237(x43622)),x43623)),f324(f130(x43621,f324(f324(f8(a859,a859,x43621),a319),f324(f324(f7(x43621,f869(x43622),a859),f324(f324(f8(f869(x43622),f871(f869(x43622),a859),x43621),a321),x43623)),f203(x43622)))),x43624)),f157(x43621,x43622,x43623,x43624)) % 181.55/181.53 [4385]E(f324(f244(f870(x43851,x43852)),f324(f263(x43851,x43852,a859),f324(f324(f7(x43851,f871(x43852,a859),f871(x43852,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x43852,a859),f871(x43852,a859)),x43851),f8(a859,a859,x43852)),f324(f324(f8(a859,f871(a859,a859),x43851),a322),f324(f324(f7(x43851,f871(x43851,a859),a859),f326(x43851)),x43853)))),f324(f324(f7(x43852,f871(x43852,a859),a859),f326(x43852)),x43854)))),f227(x43851,x43852,x43853,x43854)) % 181.55/181.53 [4419]E(f324(f324(f41(x44191,f871(f870(x44191,x44192),a859)),x44193),f324(f324(f18(x44191,f871(x44192,f871(f870(x44191,x44192),a859)),f871(f870(x44191,x44192),a859)),f324(f324(f8(f871(x44192,a859),f871(f871(x44192,f871(f870(x44191,x44192),a859)),f871(f870(x44191,x44192),a859)),x44191),f41(x44192,f871(f870(x44191,x44192),a859))),x44194)),f324(f324(f7(x44191,f871(f870(x44191,x44192),a859),f871(x44192,f871(f870(x44191,x44192),a859))),f324(f324(f8(f871(x44192,f871(f871(f870(x44191,x44192),a859),f871(f870(x44191,x44192),a859))),f871(f871(f870(x44191,x44192),a859),f871(x44192,f871(f870(x44191,x44192),a859))),x44191),f7(x44192,f871(f870(x44191,x44192),a859),f871(f870(x44191,x44192),a859))),f324(f324(f8(f871(x44192,f870(x44191,x44192)),f871(x44192,f871(f871(f870(x44191,x44192),a859),f871(f870(x44191,x44192),a859))),x44191),f324(f8(f870(x44191,x44192),f871(f871(f870(x44191,x44192),a859),f871(f870(x44191,x44192),a859)),x44192),f302(f870(x44191,x44192)))),f259(x44191,x44192)))),f191(f871(f870(x44191,x44192),a859))))),f324(f324(f261(x44191,x44192),x44193),x44194)) % 181.55/181.53 [3969]E(f324(f324(f124(x39691),f324(f324(f170(x39691),x39692),x39693)),f324(f324(f170(x39691),f324(f324(f22(a865),x39692),f324(f192(f866(x39691)),x39693))),x39694)),f324(f324(f170(x39691),x39692),f324(f324(f124(x39691),x39693),x39694))) % 181.55/181.53 [3970]E(f324(f324(f124(x39701),f324(f324(f132(x39701),x39702),x39703)),f324(f324(f132(x39701),f324(f324(f22(a865),x39702),f324(f192(f866(x39701)),x39703))),x39704)),f324(f324(f132(x39701),x39702),f324(f324(f124(x39701),x39703),x39704))) % 181.55/181.53 [4022]E(f324(f324(f81(a865),f324(f324(f82(a865),x40221),x40222)),f324(f324(f81(a865),f324(f324(f82(a865),x40223),x40222)),x40224)),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f81(a865),x40221),x40223)),x40222)),x40224)) % 181.55/181.53 [4173]E(f91(x41731,f324(f324(f7(x41731,x41732,a859),f324(f324(f8(x41732,f871(x41732,a859),x41731),a321),x41733)),x41734)),f324(f94(x41731,x41732,f247(f871(x41731,a859)),x41733),x41734)) % 181.55/181.53 [4226]P1(f324(f324(f238(f871(x42261,a859)),f324(f324(f22(f871(x42261,a859)),f324(f255(x42262,x42261),x42263)),f324(f255(x42262,x42261),x42264))),f324(f255(x42262,x42261),f324(f324(f22(f871(f870(x42262,x42261),a859)),x42263),x42264)))) % 181.55/181.53 [4227]P1(f324(f324(f238(f871(x42271,a859)),f324(f324(f22(f871(x42271,a859)),f324(f257(x42271,x42272),x42273)),f324(f257(x42271,x42272),x42274))),f324(f257(x42271,x42272),f324(f324(f22(f871(f870(x42271,x42272),a859)),x42273),x42274)))) % 181.55/181.53 [4337]E(f324(f324(f81(a1),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x43371),x43372)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x43373),x43374)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),f324(f324(f81(a865),x43371),x43373)),f324(f324(f81(a865),x43372),x43374))),f191(f871(f870(a865,a865),a859)))))) % 181.55/181.53 [4380]E(f324(f324(f82(a1),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x43801),x43802)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x43803),x43804)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),f324(f324(f81(a865),f324(f324(f82(a865),x43801),x43803)),f324(f324(f82(a865),x43802),x43804))),f324(f324(f81(a865),f324(f324(f82(a865),x43801),x43804)),f324(f324(f82(a865),x43802),x43803)))),f191(f871(f870(a865,a865),a859)))))) % 181.55/181.53 [4400]E(f324(f244(x44001),f324(f324(f8(f871(x44002,a859),a859,x44001),f89(x44002)),f324(f324(f8(f871(x44002,a859),f871(x44002,a859),x44001),f324(f18(x44002,a859,a859),f324(f324(f8(a859,f871(a859,a859),x44002),a327),f324(f324(f7(x44002,f871(x44002,a859),a859),f326(x44002)),x44003)))),f324(f324(f7(x44001,f871(x44002,f871(x44001,a859)),f871(x44002,a859)),f324(f324(f8(f871(f871(x44001,a859),a859),f871(f871(x44002,f871(x44001,a859)),f871(x44002,a859)),x44001),f8(f871(x44001,a859),a859,x44002)),f326(x44001))),x44004)))),f324(f324(f42(x44002,f871(x44001,a859)),x44003),x44004)) % 181.55/181.53 [4435]E(f324(f324(f281(x44351,x44351,x44351),f324(f324(f302(f870(x44351,x44351)),f324(f324(f259(x44351,x44351),x44352),x44353)),x44354)),f300(x44351,f324(f324(f302(f870(x44351,x44351)),f324(f324(f259(x44351,x44351),x44352),x44353)),x44354))),f324(f324(f113(f871(f870(x44351,x44351),a859)),f324(f324(f281(x44351,x44351,x44351),x44354),f300(x44351,x44354))),f324(f244(f870(x44351,x44351)),f324(f263(x44351,x44351,a859),f324(f324(f7(x44351,f871(x44351,a859),f871(x44351,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x44351,a859),f871(x44351,a859)),x44351),f8(a859,a859,x44351)),f324(f324(f8(a859,f871(a859,a859),x44351),a322),f324(f324(f7(x44351,f871(f870(x44351,x44351),a859),a859),f324(f324(f8(f870(x44351,x44351),f871(f871(f870(x44351,x44351),a859),a859),x44351),f326(f870(x44351,x44351))),f324(f324(f7(x44351,x44351,f870(x44351,x44351)),f259(x44351,x44351)),x44352))),f300(x44351,x44354))))),f324(f324(f7(x44351,f871(f870(x44351,x44351),a859),a859),f324(f324(f8(f870(x44351,x44351),f871(f871(f870(x44351,x44351),a859),a859),x44351),f326(f870(x44351,x44351))),f324(f259(x44351,x44351),x44353))),f300(x44351,x44354))))))) % 181.55/181.53 [4228]E(f324(f130(x42281,f324(f324(f18(x42281,a859,a859),f324(f324(f8(a859,f871(a859,a859),x42281),a322),x42282)),x42283)),x42284),f324(f130(x42281,x42283),f324(f130(x42281,x42282),x42284))) % 181.55/181.53 [4331]E(f324(f324(f124(x43311),f324(f324(f324(f99(f866(x43311)),f324(f324(f326(a865),f2(a865)),x43312)),f324(f324(f145(x43311),x43313),f116(x43311))),f116(x43311))),f171(x43311,x43314,f324(f244(a865),f324(f324(f7(a865,f871(a865,a859),a859),f324(f324(f8(a865,f871(f871(a865,a859),a859),a865),f326(a865)),a115)),x43312)))),f171(x43311,f324(f324(f145(x43311),x43313),x43314),x43312)) % 181.55/181.53 [4429]E(f324(f244(f870(x44291,x44292)),f324(f324(f8(f871(a865,a859),a859,f870(x44291,x44292)),f88(a865)),f324(f324(f7(f870(x44291,x44292),f871(a865,a859),f871(a865,a859)),f324(f324(f8(f871(a865,f871(a859,a859)),f871(f871(a865,a859),f871(a865,a859)),f870(x44291,x44292)),f18(a865,a859,a859)),f324(f324(f8(f871(a865,a859),f871(a865,f871(a859,a859)),f870(x44291,x44292)),f324(f8(a859,f871(a859,a859),a865),a322)),f324(f324(f7(f870(x44291,x44292),f871(a865,f870(x44291,x44292)),f871(a865,a859)),f324(f324(f8(f871(f870(x44291,x44292),a859),f871(f871(a865,f870(x44291,x44292)),f871(a865,a859)),f870(x44291,x44292)),f8(f870(x44291,x44292),a859,a865)),a321)),f324(f324(f18(a865,x44292,f870(x44291,x44292)),f324(f324(f8(x44291,f871(x44292,f870(x44291,x44292)),a865),f259(x44291,x44292)),f324(f159(x44291),x44293))),f324(f159(x44292),x44294)))))),f324(f324(f7(a865,a865,a859),f239(a865)),f324(f324(f189(a865),f324(f192(f866(x44291)),x44293)),f324(f192(f866(x44292)),x44294)))))),f324(f167(f870(x44291,x44292)),f324(f324(f177(x44291,x44292),x44293),x44294))) % 181.55/181.53 [4350]E(f324(f244(f870(x43501,x43502)),f324(f263(x43501,x43502,a859),f324(f324(f7(x43501,f871(x43502,a859),f871(x43502,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x43502,a859),f871(x43502,a859)),x43501),f8(a859,a859,x43502)),f324(f324(f8(a859,f871(a859,a859),x43501),a322),x43503))),x43504))),f324(f324(f261(x43501,x43502),f324(f244(x43501),x43503)),f324(f16(f871(x43502,a859),x43501),f324(f244(x43502),x43504)))) % 181.55/181.53 [4353]E(f324(f244(f870(x43531,x43532)),f324(f263(x43531,x43532,a859),f324(f324(f18(x43531,f871(x43532,a859),f871(x43532,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x43532,a859),f871(x43532,a859)),x43531),f8(a859,a859,x43532)),f324(f324(f8(a859,f871(a859,a859),x43531),a322),x43533))),x43534))),f324(f324(f261(x43531,x43532),f324(f244(x43531),x43533)),f324(f324(f8(f871(x43532,a859),f871(x43532,a859),x43531),f244(x43532)),x43534))) % 181.55/181.53 [4369]E(f324(f244(x43691),f324(f324(f8(f871(x43692,a859),a859,x43691),f89(x43692)),f324(f324(f8(f871(x43692,a859),f871(x43692,a859),x43691),f324(f18(x43692,a859,a859),f324(f324(f8(a859,f871(a859,a859),x43692),a327),f324(f324(f7(x43692,f871(x43692,a859),a859),f326(x43692)),x43693)))),x43694))),f324(f324(f42(x43692,f871(x43691,a859)),x43693),f324(f324(f8(f871(x43691,a859),f871(x43691,a859),x43692),f244(x43691)),f324(f7(x43691,x43692,a859),x43694)))) % 181.55/181.53 [4413]E(f324(f324(f148(f870(x44131,a865),x44131),f258(x44131,a865)),f324(f130(f870(x44131,a865),f324(f324(f7(f870(x44131,a865),f871(a865,a859),a859),f324(f324(f8(a865,f871(f871(a865,a859),a859),f870(x44131,a865)),f326(a865)),f262(x44131,a865))),x44132)),f324(f324(f177(x44131,a865),x44133),f133(a865,f324(f294(a865,x44134),f324(f324(f81(a865),x44134),f324(f192(f866(x44131)),x44133))))))),f324(f324(f148(f870(x44131,a865),x44131),f258(x44131,a865)),f324(f130(f870(x44131,a865),f324(f324(f7(f870(x44131,a865),f871(a865,a859),a859),f324(f324(f8(a865,f871(f871(a865,a859),a859),f870(x44131,a865)),f326(a865)),f324(f324(f7(f870(x44131,a865),a865,a865),f324(f324(f8(a865,f871(a865,a865),f870(x44131,a865)),f81(a865)),f262(x44131,a865))),x44134))),x44132)),f324(f324(f177(x44131,a865),x44133),f133(a865,f324(f294(a865,f2(a865)),f324(f192(f866(x44131)),x44133))))))) % 181.55/181.53 [4414]E(f324(a115,f324(f324(f190(a865),f324(f192(f866(x44141)),x44142)),f324(f136(a865,f866(x44143),f324(f7(f866(x44143),a865,a865),f324(f324(f8(a865,f871(a865,a865),f866(x44143)),f190(a865)),f324(f324(f7(f866(x44143),a865,a865),f324(f324(f8(a865,f871(a865,a865),f866(x44143)),f22(a865)),f192(f866(x44143)))),f324(a115,f2(a865))))),f2(a865)),f324(f163(f866(x44143)),f324(f130(f866(x44143),f324(f324(f8(a859,a859,f866(x44143)),a319),f324(f324(f7(f866(x44143),f866(x44143),a859),a321),f116(x44143)))),x44144))))),f324(f324(f190(a865),f324(a115,f324(f192(f866(x44141)),x44142))),f324(f136(a865,f866(x44143),f324(f7(f866(x44143),a865,a865),f324(f324(f8(a865,f871(a865,a865),f866(x44143)),f190(a865)),f192(f866(x44143)))),f2(a865)),f324(f163(f866(x44143)),x44144)))) % 181.55/181.53 [4368]E(f324(f324(f124(x43681),f171(x43681,x43682,x43683)),f171(x43681,x43684,f324(f244(a865),f324(f324(f7(a865,f871(a865,a859),a859),f324(f324(f8(a865,f871(f871(a865,a859),a859),a865),f326(a865)),f324(f324(f7(a865,a865,a865),f81(a865)),f324(f192(f866(x43681)),x43682)))),x43683)))),f171(x43681,f324(f324(f124(x43681),x43682),x43684),x43683)) % 181.55/181.53 [4421]E(f324(f324(f145(f866(x44211)),f324(f324(f145(x44211),x44212),f324(f136(f866(x44211),f866(x44211),f124(x44211),f116(x44211)),f324(f324(f148(f866(x44211),f866(x44211)),f150(f866(x44211),x44211,f116(x44211),f324(f324(f8(f866(x44211),f871(f866(x44211),f866(x44211)),x44211),f16(f866(x44211),f866(x44211))),f324(f324(f7(x44211,f866(x44211),f866(x44211)),f145(x44211)),f116(x44211))))),x44213)))),f175(x44211,f324(f324(f145(f866(x44211)),x44214),f324(f136(f866(f866(x44211)),f866(f866(x44211)),f124(f866(x44211)),f116(f866(x44211))),f324(f324(f148(f866(x44211),f866(f866(x44211))),f150(f866(f866(x44211)),x44211,f116(f866(x44211)),f324(f16(f871(f866(x44211),f866(f866(x44211))),x44211),f324(f324(f7(f866(x44211),f866(f866(x44211)),f866(f866(x44211))),f145(f866(x44211))),f116(f866(x44211)))))),x44213))))),f175(x44211,f324(f324(f145(f866(x44211)),f324(f324(f145(x44211),x44212),x44214)),x44213))) % 181.55/181.53 [4430]E(f324(f244(f870(x44301,x44301)),f324(f263(x44301,x44301,a859),f324(f324(f7(x44301,f871(f870(x44302,x44302),a859),f871(x44301,a859)),f324(f324(f8(f871(x44301,f871(f871(f870(x44302,x44302),a859),a859)),f871(f871(f870(x44302,x44302),a859),f871(x44301,a859)),x44301),f7(x44301,f871(f870(x44302,x44302),a859),a859)),f324(f324(f8(f871(x44301,f870(x44302,x44302)),f871(x44301,f871(f871(f870(x44302,x44302),a859),a859)),x44301),f324(f8(f870(x44302,x44302),f871(f871(f870(x44302,x44302),a859),a859),x44301),f326(f870(x44302,x44302)))),f324(f324(f7(x44301,f871(x44301,x44302),f871(x44301,f870(x44302,x44302))),f324(f324(f8(f871(x44302,f870(x44302,x44302)),f871(f871(x44301,x44302),f871(x44301,f870(x44302,x44302))),x44301),f8(x44302,f870(x44302,x44302),x44301)),f324(f324(f8(x44302,f871(x44302,f870(x44302,x44302)),x44301),f259(x44302,x44302)),x44303))),x44303)))),x44304))),f324(f324(f280(x44302,x44301),x44304),x44303)) % 181.55/181.53 [4118]E(f76(x41181,x41182,x41183,x41184,x41185),f76(x41181,x41182,x41184,x41183,x41185)) % 181.55/181.53 [4496]~E(f33(x44961,x44962),f30(x44963,x44964,x44965)) % 181.55/181.53 [4497]~E(f33(x44971,x44972),f29(x44973,x44974,x44975)) % 181.55/181.53 [4498]~E(f26(x44981,x44982),f30(x44983,x44984,x44985)) % 181.55/181.53 [4499]~E(f26(x44991,x44992),f29(x44993,x44994,x44995)) % 181.55/181.53 [4500]~E(f32(x45001,x45002),f30(x45003,x45004,x45005)) % 181.55/181.53 [4501]~E(f32(x45011,x45012),f29(x45013,x45014,x45015)) % 181.55/181.53 [4502]~E(f30(x45021,x45022,x45023),f33(x45024,x45025)) % 181.55/181.53 [4503]~E(f30(x45031,x45032,x45033),f26(x45034,x45035)) % 181.55/181.53 [4504]~E(f30(x45041,x45042,x45043),f32(x45044,x45045)) % 181.55/181.53 [4505]~E(f29(x45051,x45052,x45053),f33(x45054,x45055)) % 181.55/181.53 [4506]~E(f29(x45061,x45062,x45063),f26(x45064,x45065)) % 181.55/181.53 [4507]~E(f29(x45071,x45072,x45073),f32(x45074,x45075)) % 181.55/181.53 [3906]E(f324(f180(x39061,x39062,x39063,x39064),x39065),f324(f235(f869(x39062),x39062,f324(x39063,x39065),f233(x39062)),f324(x39064,x39065))) % 181.55/181.53 [3997]E(f180(x39971,x39972,f180(x39971,x39972,x39973,x39974),x39975),f180(x39971,x39972,x39973,f180(x39971,x39972,x39974,x39975))) % 181.55/181.53 [4157]E(f324(f324(f324(f72(x41571,x41572),f324(f324(f324(f72(x41571,x41572),x41573),x41574),f324(x41573,x41575))),x41575),f324(x41573,x41574)),f76(x41571,x41572,x41574,x41575,x41573)) % 181.55/181.53 [4170]E(f76(x41701,x41702,x41703,x41704,f76(x41701,x41702,x41703,x41704,x41705)),x41705) % 181.55/181.53 [4174]E(f260(x41741,x41742,x41743,f248(x41742,x41741,x41744),f248(x41743,x41742,x41745)),f248(x41743,x41741,f260(x41743,x41742,x41741,x41745,x41744))) % 181.55/181.53 [4181]E(f324(f324(f113(f871(x41811,a859)),f324(f167(x41811),f324(f324(f170(x41811),f324(f192(f866(x41812)),x41813)),x41814))),f179(x41811,x41812,x41815)),f179(x41811,x41812,f182(x41811,x41812,x41815,x41814,x41813))) % 181.55/181.53 [3733]E(f324(f324(f263(x37331,x37332,x37333),x37334),x37335),f324(f324(x37334,f324(f258(x37331,x37332),x37335)),f324(f262(x37331,x37332),x37335))) % 181.55/181.53 [3759]E(f324(f235(x37591,x37592,x37593,x37594),f324(f233(x37592),x37595)),f324(x37594,x37595)) % 181.55/181.53 [3768]E(f324(f324(f324(f65(x37681,x37682,x37683),x37684),x37685),f191(f871(x37682,a859))),x37685) % 181.55/181.53 [3939]E(f236(x39391,x39392,x39393,x39394,f324(f233(x39392),x39395)),f324(x39394,x39395)) % 181.55/181.53 [4052]E(f324(f73(f869(x40521),f869(x40522),f869(x40523),f324(f204(x40521,x40522),x40524)),f324(f204(x40523,x40521),x40525)),f324(f204(x40523,x40522),f324(f73(x40521,x40522,x40523,x40524),x40525))) % 181.55/181.53 [4054]E(f324(f73(f866(x40541),f866(x40542),f866(x40543),f324(f148(x40541,x40542),x40544)),f324(f148(x40543,x40541),x40545)),f324(f148(x40543,x40542),f324(f73(x40541,x40542,x40543,x40544),x40545))) % 181.55/181.53 [4110]E(f324(f235(x41101,f870(x41102,f867(x41102)),x41103,f324(f263(x41102,f867(x41102),x41101),x41104)),f324(f127(x41102),x41105)),f129(x41101,x41102,x41103,x41104,x41105)) % 181.55/181.53 [4134]E(f86(x41341,f66(x41342,x41341,x41343,x41344,x41345)),f324(f324(f64(x41342,x41341,x41343),x41344),x41345)) % 181.55/181.53 [4171]E(f324(f324(f81(a865),f324(f324(f81(a865),f324(x41711,f324(f258(x41712,x41713),x41714))),f324(x41715,f324(f262(x41712,x41713),x41714)))),f324(a115,f2(a865))),f267(x41712,x41713,x41711,x41715,x41714)) % 181.55/181.53 [4364]E(f157(x43641,x43642,f324(f324(f7(x43641,f869(x43642),f869(x43642)),f324(f324(f18(x43641,f869(x43642),f871(f869(x43642),f869(x43642))),f324(f324(f8(a859,f871(f869(x43642),f871(f869(x43642),f869(x43642))),x43641),f99(f869(x43642))),x43643)),f324(f324(f8(x43642,f869(x43642),x43641),f233(x43642)),x43644))),f203(x43642)),x43645),f324(f324(f148(x43641,x43642),x43644),f324(f130(x43641,x43643),x43645))) % 181.55/181.53 [4543]~E(f324(f324(f324(f72(x45431,f869(x45432)),x45433),x45434),f324(f233(x45432),x45435)),f324(f16(f869(x45432),x45431),f203(x45432))) % 181.55/181.53 [3669]E(f324(f324(f170(x36691),x36692),f324(f324(f148(x36693,x36691),x36694),x36695)),f324(f324(f148(x36693,x36691),x36694),f324(f324(f170(x36693),x36692),x36695))) % 181.55/181.53 [3670]E(f324(f324(f132(x36701),x36702),f324(f324(f148(x36703,x36701),x36704),x36705)),f324(f324(f148(x36703,x36701),x36704),f324(f324(f132(x36703),x36702),x36705))) % 181.55/181.53 [3702]E(f324(f324(f148(x37021,x37022),x37023),f324(f324(f145(x37021),x37024),x37025)),f324(f324(f145(x37022),f324(x37023,x37024)),f324(f324(f148(x37021,x37022),x37023),x37025))) % 181.55/181.53 [3763]E(f324(f303(x37631,x37632,x37633),f324(f324(f302(x37631),x37634),x37635)),f324(f324(f302(x37632),f324(x37633,x37634)),f324(f303(x37631,x37632,x37633),x37635))) % 181.55/181.53 [3792]E(f168(x37921,f324(f324(f145(x37921),x37922),x37923),f324(f324(f145(x37921),x37924),x37925)),f324(f324(f145(x37921),x37922),f324(f324(f145(x37921),x37924),f168(x37921,x37923,x37925)))) % 181.55/181.53 [3828]E(f324(f324(f177(x38281,x38282),f324(f324(f170(x38281),x38283),x38284)),f324(f324(f170(x38282),x38283),x38285)),f324(f324(f170(f870(x38281,x38282)),x38283),f324(f324(f177(x38281,x38282),x38284),x38285))) % 181.55/181.53 [3829]E(f324(f324(f177(x38291,x38292),f324(f324(f132(x38291),x38293),x38294)),f324(f324(f132(x38292),x38293),x38295)),f324(f324(f132(f870(x38291,x38292)),x38293),f324(f324(f177(x38291,x38292),x38294),x38295))) % 181.55/181.53 [3839]E(f324(f324(f153(x38391,f324(f324(f145(x38391),x38392),x38393)),f324(a115,x38394)),x38395),f324(f324(f145(x38391),x38392),f324(f324(f153(x38391,x38393),x38394),x38395))) % 181.55/181.53 [3842]E(f324(f235(f869(x38421),x38422,f203(x38421),x38423),f324(f324(f16(f869(x38422),x38424),f203(x38422)),x38425)),f203(x38421)) % 181.55/181.53 [3844]E(f324(f324(f124(x38441),f324(f324(f148(x38442,x38441),x38443),x38444)),f324(f324(f148(x38442,x38441),x38443),x38445)),f324(f324(f148(x38442,x38441),x38443),f324(f324(f124(x38442),x38444),x38445))) % 181.55/181.53 [3848]E(f324(f324(x38481,x38482),f324(f324(f250(x38483,x38484,x38481),x38482),x38485)),f324(f324(f250(x38483,x38484,x38481),x38482),f324(a115,x38485))) % 181.55/181.53 [3878]E(f158(x38781,x38782,x38783,f324(f324(f145(x38781),x38784),x38785)),f324(f324(f124(x38782),f324(x38783,x38784)),f158(x38781,x38782,x38783,x38785))) % 181.55/181.53 [3890]E(f324(f324(f281(x38901,x38902,x38903),f324(f279(x38902,x38901),x38904)),f324(f279(x38903,x38902),x38905)),f324(f279(x38903,x38901),f324(f324(f281(x38903,x38902,x38901),x38905),x38904))) % 181.55/181.53 [3924]E(f324(f324(f324(f184(f866(x39241),f866(x39241)),x39242),f162(x39241)),f324(f324(f148(x39243,x39241),x39244),x39245)),f324(f324(f148(x39243,x39241),x39244),f324(f324(f324(f184(f866(x39243),f866(x39243)),x39242),f162(x39243)),x39245))) % 181.55/181.53 [3925]E(f324(f324(f265(x39251,x39252,x39251,x39253),f324(f259(x39252,x39251),x39254)),x39255),f324(x39255,x39254)) % 181.55/181.53 [3953]E(f149(x39531,x39532,f324(f324(f148(x39533,x39531),x39534),x39535)),f149(x39533,f324(f73(x39531,a865,x39533,x39532),x39534),x39535)) % 181.55/181.53 [4020]E(f324(f324(f73(f869(x40201),f869(x40202),x40203,f324(f204(x40201,x40202),x40204)),f324(f16(f869(x40201),x40203),f203(x40201))),x40205),f203(x40202)) % 181.55/181.53 [4021]E(f172(f870(x40211,x40212),f324(f73(x40212,a859,f870(x40211,x40212),x40213),f262(x40211,x40212)),f324(f324(f177(x40211,x40212),x40214),x40215)),f324(f324(f177(x40211,x40212),x40214),f172(x40212,x40213,x40215))) % 181.55/181.53 [4026]E(f324(f303(x40261,x40262,f324(f324(f8(x40263,x40262,x40261),x40264),x40265)),f247(f871(x40261,a859))),f324(f303(x40263,x40262,x40264),f324(f303(x40261,x40263,x40265),f247(f871(x40261,a859))))) % 181.55/181.53 [4039]E(f172(f870(x40391,x40392),f324(f73(x40391,a859,f870(x40391,x40392),x40393),f258(x40391,x40392)),f324(f324(f177(x40391,x40392),x40394),x40395)),f324(f324(f177(x40391,x40392),f172(x40391,x40393,x40394)),x40395)) % 181.55/181.53 [4058]E(f324(f324(f113(f871(x40581,a859)),f324(f304(x40581,x40582,x40583),f324(f324(f302(x40582),x40584),f191(f871(x40582,a859))))),f324(f304(x40581,x40582,x40583),x40585)),f324(f304(x40581,x40582,x40583),f324(f324(f302(x40582),x40584),x40585))) % 181.55/181.53 [4117]E(f324(f324(f124(f870(x41171,x41172)),f324(f324(f148(x41172,f870(x41171,x41172)),f324(f259(x41171,x41172),x41173)),x41174)),f59(x41171,x41172,x41175,x41174)),f59(x41171,x41172,f324(f324(f145(x41171),x41173),x41175),x41174)) % 181.55/181.53 [4119]E(f324(f324(f148(x41191,x41192),x41193),f172(x41191,f324(f73(x41192,a859,x41191,x41194),x41193),x41195)),f172(x41192,x41194,f324(f324(f148(x41191,x41192),x41193),x41195))) % 181.55/181.53 [4125]E(f324(f136(x41251,x41252,f324(f7(x41252,x41251,x41251),f324(f7(x41251,x41252,x41251),x41253)),x41254),f324(f163(x41252),f324(f163(x41252),x41255))),f324(f136(x41251,x41252,x41253,x41254),x41255)) % 181.55/181.53 [4126]E(f324(f324(f324(f72(x41261,f869(x41262)),f183(x41261,x41262,x41263,x41264)),x41265),f324(x41263,x41265)),f183(x41261,x41262,x41263,f324(f324(f302(x41261),x41265),x41264))) % 181.55/181.53 [4198]E(f324(f235(f866(x41981),x41981,f157(x41982,x41981,x41983,x41984),f324(f324(f7(x41981,f866(x41981),f866(x41981)),f145(x41981)),f157(x41982,x41981,x41983,x41984))),f324(x41983,x41985)),f157(x41982,x41981,x41983,f324(f324(f145(x41982),x41985),x41984))) % 181.55/181.53 [4236]P1(f324(f324(f238(f871(x42361,a859)),f324(f303(x42362,x42361,x42363),f324(f324(f104(f871(x42362,a859)),x42364),x42365))),f324(f324(f104(f871(x42361,a859)),f324(f303(x42362,x42361,x42363),x42364)),f324(f303(x42362,x42361,x42363),x42365)))) % 181.55/181.53 [4237]P1(f324(f324(f238(f871(x42371,a859)),f324(f278(x42372,x42371,x42373),f324(f324(f104(f871(x42372,a859)),x42374),x42375))),f324(f324(f104(f871(x42371,a859)),f324(f278(x42372,x42371,x42373),x42374)),f324(f278(x42372,x42371,x42373),x42375)))) % 181.55/181.53 [4338]E(f324(f262(x43381,x43382),f324(f264(x43383,x43381,x43382,x43382,x43384,f34(x43382)),x43385)),f324(f262(x43383,x43382),x43385)) % 181.55/181.53 [4339]E(f324(f258(x43391,x43392),f324(f264(x43391,x43391,x43393,x43392,f34(x43391),x43394),x43395)),f324(f258(x43391,x43393),x43395)) % 181.55/181.53 [4425]P26(x44251,x44252,f324(f324(f302(f864(x44251)),f324(f324(f324(f93(x44251),f324(f324(f7(x44251,f871(a860,a860),f871(a860,a859)),f324(f324(f8(f871(a860,a859),f871(f871(a860,a860),f871(a860,a859)),x44251),f8(a860,a859,a860)),x44253)),f324(f324(f18(a860,a865,a860),f324(f324(f7(a860,a863,f871(a865,a860)),a199),x44254)),x44255))),f26(x44254,x44255)),x44253)),f191(f871(f864(x44251),a859)))) % 181.55/181.53 [4427]E(f324(f136(f871(x44271,f869(x44272)),f870(x44271,x44272),f324(f324(f8(f871(x44271,f871(x44272,f871(x44271,f869(x44272)))),f871(f870(x44271,x44272),f871(x44271,f869(x44272))),f871(x44271,f869(x44272))),f263(x44271,x44272,f871(x44271,f869(x44272)))),f324(f324(f7(f871(x44271,f869(x44272)),f871(x44272,f869(x44272)),f871(x44271,f871(x44272,f871(x44271,f869(x44272))))),f324(f324(f8(f871(x44271,f871(f871(x44272,f869(x44272)),f871(x44272,f871(x44271,f869(x44272))))),f871(f871(x44272,f869(x44272)),f871(x44271,f871(x44272,f871(x44271,f869(x44272))))),f871(x44271,f869(x44272))),f7(x44271,f871(x44272,f869(x44272)),f871(x44272,f871(x44271,f869(x44272))))),f324(f324(f8(f871(x44271,f871(f869(x44272),f871(x44271,f869(x44272)))),f871(x44271,f871(f871(x44272,f869(x44272)),f871(x44272,f871(x44271,f869(x44272))))),f871(x44271,f869(x44272))),f324(f8(f871(f869(x44272),f871(x44271,f869(x44272))),f871(f871(x44272,f869(x44272)),f871(x44272,f871(x44271,f869(x44272)))),x44271),f8(f869(x44272),f871(x44271,f869(x44272)),x44272))),f72(x44271,f869(x44272))))),f233(x44272))),x44273),f324(f324(f177(x44271,x44272),x44274),x44275)),f182(x44271,x44272,x44273,x44274,x44275)) % 181.55/181.53 [3515]E(f324(f324(f324(f324(f207(x35151),x35152),x35153),x35154),x35155),f195(x35151,x35152)) % 181.55/181.53 [3516]E(f324(f324(f324(f324(f213(x35161),x35162),x35163),x35164),x35165),f208(x35161,x35162)) % 181.55/181.53 [3560]E(f96(x35601,x35602,f324(f324(f324(f93(x35601),x35603),x35604),x35605)),f2(a865)) % 181.55/181.53 [3653]E(f324(f324(f324(f324(f72(x36531,x36532),x36533),x36534),x36535),x36534),x36535) % 181.55/181.53 [3879]E(f324(f324(f41(x38791,f871(x38792,a859)),f324(f324(f302(x38791),x38793),x38794)),x38795),f324(f324(f113(f871(x38792,a859)),f324(x38795,x38793)),f324(f324(f41(x38791,f871(x38792,a859)),x38794),x38795))) % 181.55/181.53 [3880]E(f324(f324(f42(x38801,f871(x38802,a859)),f324(f324(f302(x38801),x38803),x38804)),x38805),f324(f324(f104(f871(x38802,a859)),f324(x38805,x38803)),f324(f324(f42(x38801,f871(x38802,a859)),x38804),x38805))) % 181.55/181.53 [3946]E(f324(f324(f113(f871(x39461,a859)),f324(f303(x39462,x39461,x39463),x39464)),f324(f303(x39462,x39461,x39463),x39465)),f324(f303(x39462,x39461,x39463),f324(f324(f113(f871(x39462,a859)),x39464),x39465))) % 181.55/181.53 [3947]E(f324(f324(f22(f871(x39471,a859)),f324(f304(x39471,x39472,x39473),x39474)),f324(f304(x39471,x39472,x39473),x39475)),f324(f304(x39471,x39472,x39473),f324(f324(f22(f871(x39472,a859)),x39474),x39475))) % 181.55/181.53 [3948]E(f324(f324(f104(f871(x39481,a859)),f324(f304(x39481,x39482,x39483),x39484)),f324(f304(x39481,x39482,x39483),x39485)),f324(f304(x39481,x39482,x39483),f324(f324(f104(f871(x39482,a859)),x39484),x39485))) % 181.55/181.53 [3949]E(f324(f324(f113(f871(x39491,a859)),f324(f304(x39491,x39492,x39493),x39494)),f324(f304(x39491,x39492,x39493),x39495)),f324(f304(x39491,x39492,x39493),f324(f324(f113(f871(x39492,a859)),x39494),x39495))) % 181.55/181.53 [3950]E(f324(f324(f113(f871(x39501,a859)),f324(f278(x39502,x39501,x39503),x39504)),f324(f278(x39502,x39501,x39503),x39505)),f324(f278(x39502,x39501,x39503),f324(f324(f113(f871(x39502,a859)),x39504),x39505))) % 181.55/181.53 [3952]E(f183(x39521,x39522,f183(x39521,x39522,x39523,x39524),x39525),f183(x39521,x39522,x39523,f324(f324(f104(f871(x39521,a859)),x39524),x39525))) % 181.55/181.53 [3955]E(f119(x39551,x39552,f324(x39553,x39554),f324(f324(f7(x39551,a102,f867(x39552)),x39555),x39554)),f324(f201(x39551,x39552,x39553,x39555),x39554)) % 181.55/181.53 [4016]E(f324(f324(f153(x40161,f324(f324(f124(x40161),x40162),f324(f324(f145(x40161),x40163),x40164))),f324(f192(f866(x40161)),x40162)),x40165),f324(f324(f124(x40161),x40162),f324(f324(f145(x40161),x40165),x40164))) % 181.55/181.53 [4024]E(f324(f324(f42(x40241,f871(x40242,a859)),x40243),f324(f324(f8(f871(x40242,a859),f871(x40242,a859),x40241),f324(f302(x40242),x40244)),x40245)),f324(f324(f302(x40242),x40244),f324(f324(f42(x40241,f871(x40242,a859)),x40243),x40245))) % 181.55/181.53 [4092]E(f183(x40921,x40922,f324(f324(f324(f72(x40921,f869(x40922)),x40923),x40924),f324(f233(x40922),x40925)),f324(f80(f871(x40921,a859)),f324(f324(f302(x40921),x40924),f191(f871(x40921,a859))))),f183(x40921,x40922,x40923,f324(f80(f871(x40921,a859)),f324(f324(f302(x40921),x40924),f191(f871(x40921,a859)))))) % 181.55/181.53 [4185]E(f324(f324(f148(x41851,x41852),x41853),f324(f130(x41851,f324(f73(x41852,a859,x41851,x41854),x41853)),x41855)),f324(f130(x41852,x41854),f324(f324(f148(x41851,x41852),x41853),x41855))) % 181.55/181.53 [4191]E(f324(f192(f866(x41911)),f324(f130(x41911,x41912),f324(f324(f148(x41913,x41911),x41914),x41915))),f324(f192(f866(x41913)),f324(f130(x41913,f324(f73(x41911,a859,x41913,x41912),x41914)),x41915))) % 181.55/181.53 [4330]E(f324(f324(f113(f871(x43301,a859)),f324(f324(f22(f871(x43301,a859)),f179(x43301,x43302,x43303)),f324(f244(x43301),f324(f324(f7(x43301,f871(x43301,a859),a859),f326(x43301)),f324(f324(f22(f871(x43301,a859)),x43304),f179(x43301,x43302,x43305)))))),f324(f244(x43301),f324(f324(f7(x43301,f871(x43301,a859),a859),f326(x43301)),f324(f324(f104(f871(x43301,a859)),x43304),f179(x43301,x43302,x43305))))),f179(x43301,x43302,f77(x43301,f869(x43302),x43303,x43305,x43304))) % 181.55/181.53 [4405]E(f324(f150(f866(f870(x44051,x44052)),x44052,f116(f870(x44051,x44052)),f324(f324(f7(x44052,f871(f866(x44052),f866(f870(x44051,x44052))),f871(f866(x44052),f866(f870(x44051,x44052)))),f324(f324(f8(f871(f866(f870(x44051,x44052)),f866(f870(x44051,x44052))),f871(f871(f866(x44052),f866(f870(x44051,x44052))),f871(f866(x44052),f866(f870(x44051,x44052)))),x44052),f8(f866(f870(x44051,x44052)),f866(f870(x44051,x44052)),f866(x44052))),f324(f324(f8(f870(x44051,x44052),f871(f866(f870(x44051,x44052)),f866(f870(x44051,x44052))),x44052),f145(f870(x44051,x44052))),f324(f259(x44051,x44052),x44053)))),f324(f177(x44051,x44052),x44054))),x44055),f324(f324(f177(x44051,x44052),f324(f324(f145(x44051),x44053),x44054)),x44055)) % 181.55/181.53 [3873]E(f324(f324(f153(x38731,f324(f324(f153(x38731,x38732),x38733),x38734)),x38733),x38735),f324(f324(f153(x38731,x38732),x38733),x38735)) % 181.55/181.53 [3927]E(f324(f255(x39271,x39272),f324(f324(f302(f870(x39271,x39272)),f324(f324(f259(x39271,x39272),x39273),x39274)),x39275)),f324(f324(f302(x39272),x39274),f324(f255(x39271,x39272),x39275))) % 181.55/181.53 [3928]E(f324(f257(x39281,x39282),f324(f324(f302(f870(x39281,x39282)),f324(f324(f259(x39281,x39282),x39283),x39284)),x39285)),f324(f324(f302(x39281),x39283),f324(f257(x39281,x39282),x39285))) % 181.55/181.53 [3979]E(f122(x39791,x39792,f324(x39793,x39794),f324(f324(f7(x39791,a102,f867(f869(x39792))),x39795),x39794)),f324(f198(x39791,x39792,x39793,x39795),x39794)) % 181.55/181.53 [4009]E(f324(f324(f22(f871(f870(x40091,x40092),a859)),f324(f324(f261(x40091,x40092),x40093),x40094)),f324(f324(f261(x40091,x40092),x40095),x40094)),f324(f324(f261(x40091,x40092),f324(f324(f22(f871(x40091,a859)),x40093),x40095)),x40094)) % 181.55/181.53 [4010]E(f324(f324(f104(f871(f870(x40101,x40102),a859)),f324(f324(f261(x40101,x40102),x40103),x40104)),f324(f324(f261(x40101,x40102),x40105),x40104)),f324(f324(f261(x40101,x40102),f324(f324(f104(f871(x40101,a859)),x40103),x40105)),x40104)) % 181.55/181.53 [4011]E(f324(f324(f113(f871(f870(x40111,x40112),a859)),f324(f324(f261(x40111,x40112),x40113),x40114)),f324(f324(f261(x40111,x40112),x40115),x40114)),f324(f324(f261(x40111,x40112),f324(f324(f113(f871(x40111,a859)),x40113),x40115)),x40114)) % 181.55/181.53 [4070]E(f324(f324(f113(f871(x40701,a859)),f324(f324(f41(x40702,f871(x40701,a859)),x40703),x40704)),f324(f324(f41(x40702,f871(x40701,a859)),x40705),x40704)),f324(f324(f41(x40702,f871(x40701,a859)),f324(f324(f113(f871(x40702,a859)),x40703),x40705)),x40704)) % 181.55/181.53 [4071]E(f324(f324(f104(f871(x40711,a859)),f324(f324(f42(x40712,f871(x40711,a859)),x40713),x40714)),f324(f324(f42(x40712,f871(x40711,a859)),x40715),x40714)),f324(f324(f42(x40712,f871(x40711,a859)),f324(f324(f113(f871(x40712,a859)),x40713),x40715)),x40714)) % 181.55/181.53 [4085]E(f324(f324(f41(x40851,f871(x40852,a859)),x40853),f324(f324(f8(f871(x40852,a859),f871(x40852,a859),x40851),f324(f22(f871(x40852,a859)),x40854)),x40855)),f324(f324(f22(f871(x40852,a859)),x40854),f324(f324(f42(x40851,f871(x40852,a859)),x40853),x40855))) % 181.55/181.53 [4086]E(f324(f324(f41(x40861,f871(x40862,a859)),x40863),f324(f324(f8(f871(x40862,a859),f871(x40862,a859),x40861),f324(f104(f871(x40862,a859)),x40864)),x40865)),f324(f324(f104(f871(x40862,a859)),x40864),f324(f324(f41(x40861,f871(x40862,a859)),x40863),x40865))) % 181.55/181.53 [4087]E(f324(f324(f42(x40871,f871(x40872,a859)),x40873),f324(f324(f8(f871(x40872,a859),f871(x40872,a859),x40871),f324(f113(f871(x40872,a859)),x40874)),x40875)),f324(f324(f113(f871(x40872,a859)),x40874),f324(f324(f42(x40871,f871(x40872,a859)),x40873),x40875))) % 181.55/181.53 [4124]E(f180(x41241,x41242,x41243,f324(f173(x41241,x41242),f324(f163(f870(x41241,x41242)),f324(f324(f177(x41241,x41242),x41244),x41245)))),f182(x41241,x41242,x41243,x41244,x41245)) % 181.55/181.53 [4146]E(f186(f866(x41461),f324(f324(f145(x41461),x41462),x41463),f324(f324(f8(f866(x41461),f866(x41461),a865),f324(f145(x41461),x41464)),f324(f324(f7(a865,x41461,f866(x41461)),f153(x41461,x41463)),x41462)),x41465),f324(f324(f153(x41461,f324(f324(f145(x41461),x41464),x41463)),x41465),x41462)) % 181.55/181.53 [4150]E(f324(f324(f41(x41501,f871(f870(x41502,x41503),a859)),x41504),f324(f324(f8(f871(f870(x41503,x41502),a859),f871(f870(x41502,x41503),a859),x41501),f279(x41503,x41502)),x41505)),f324(f279(x41503,x41502),f324(f324(f41(x41501,f871(f870(x41503,x41502),a859)),x41504),x41505))) % 181.55/181.53 [4151]E(f324(f324(f42(x41511,f871(f870(x41512,x41513),a859)),x41514),f324(f324(f8(f871(f870(x41513,x41512),a859),f871(f870(x41512,x41513),a859),x41511),f279(x41513,x41512)),x41515)),f324(f279(x41513,x41512),f324(f324(f42(x41511,f871(f870(x41513,x41512),a859)),x41514),x41515))) % 181.55/181.53 [4210]E(f179(x42101,x42102,f324(f324(f18(x42101,f869(x42103),f869(x42102)),f324(f324(f8(f871(x42103,x42102),f871(f869(x42103),f869(x42102)),x42101),f204(x42103,x42102)),x42104)),x42105)),f179(x42101,x42103,x42105)) % 181.55/181.53 [4261]P1(f324(f324(f238(f871(x42611,a859)),f324(f324(f22(f871(x42611,a859)),f324(f303(x42612,x42611,x42613),x42614)),f324(f303(x42612,x42611,x42613),x42615))),f324(f303(x42612,x42611,x42613),f324(f324(f22(f871(x42612,a859)),x42614),x42615)))) % 181.55/181.53 [4409]E(f324(f150(f866(f870(x44091,x44092)),x44091,f116(f870(x44091,x44092)),f324(f324(f7(x44091,f871(f866(x44091),f866(f870(x44091,x44092))),f871(f866(x44091),f866(f870(x44091,x44092)))),f324(f324(f8(f871(f866(f870(x44091,x44092)),f866(f870(x44091,x44092))),f871(f871(f866(x44091),f866(f870(x44091,x44092))),f871(f866(x44091),f866(f870(x44091,x44092)))),x44091),f8(f866(f870(x44091,x44092)),f866(f870(x44091,x44092)),f866(x44091))),f324(f324(f8(f870(x44091,x44092),f871(f866(f870(x44091,x44092)),f866(f870(x44091,x44092))),x44091),f145(f870(x44091,x44092))),f324(f324(f7(x44091,x44092,f870(x44091,x44092)),f259(x44091,x44092)),x44093)))),f324(f324(f7(f866(x44091),f866(x44092),f866(f870(x44091,x44092))),f177(x44091,x44092)),x44094))),x44095),f324(f324(f177(x44091,x44092),x44095),f324(f324(f145(x44092),x44093),x44094))) % 181.55/181.53 [4111]E(f324(f324(f113(f871(x41111,a859)),f324(f278(x41112,x41111,x41113),x41114)),f324(f278(x41112,x41111,x41115),x41114)),f324(f278(x41112,x41111,f324(f324(f113(f871(f870(x41112,x41111),a859)),x41113),x41115)),x41114)) % 181.55/181.53 [4153]E(f324(f324(f124(f870(x41531,x41532)),f324(f324(f177(x41531,x41532),x41533),f324(f324(f170(x41532),f324(f192(f866(x41531)),x41533)),x41534))),f324(f324(f177(x41531,x41532),x41535),f324(f324(f132(x41532),f324(f192(f866(x41531)),x41533)),x41534))),f324(f324(f177(x41531,x41532),f324(f324(f124(x41531),x41533),x41535)),x41534)) % 181.55/181.53 [4264]E(f324(f324(f261(x42641,x42642),x42643),f324(f324(f18(x42641,f871(x42642,a859),f871(x42642,a859)),f324(f324(f8(f871(x42642,a859),f871(f871(x42642,a859),f871(x42642,a859)),x42641),f22(f871(x42642,a859))),x42644)),x42645)),f324(f324(f22(f871(f870(x42641,x42642),a859)),f324(f324(f261(x42641,x42642),x42643),x42644)),f324(f324(f261(x42641,x42642),x42643),x42645))) % 181.55/181.53 [4265]E(f324(f324(f261(x42651,x42652),x42653),f324(f324(f18(x42651,f871(x42652,a859),f871(x42652,a859)),f324(f324(f8(f871(x42652,a859),f871(f871(x42652,a859),f871(x42652,a859)),x42651),f104(f871(x42652,a859))),x42654)),x42655)),f324(f324(f104(f871(f870(x42651,x42652),a859)),f324(f324(f261(x42651,x42652),x42653),x42654)),f324(f324(f261(x42651,x42652),x42653),x42655))) % 181.55/181.53 [4266]E(f324(f324(f261(x42661,x42662),x42663),f324(f324(f18(x42661,f871(x42662,a859),f871(x42662,a859)),f324(f324(f8(f871(x42662,a859),f871(f871(x42662,a859),f871(x42662,a859)),x42661),f113(f871(x42662,a859))),x42664)),x42665)),f324(f324(f113(f871(f870(x42661,x42662),a859)),f324(f324(f261(x42661,x42662),x42663),x42664)),f324(f324(f261(x42661,x42662),x42663),x42665))) % 181.55/181.53 [4270]E(f324(f324(f41(x42701,f871(x42702,a859)),x42703),f324(f324(f7(x42701,f871(x42702,a859),f871(x42702,a859)),f324(f324(f8(f871(x42702,a859),f871(f871(x42702,a859),f871(x42702,a859)),x42701),f22(f871(x42702,a859))),x42704)),x42705)),f324(f324(f22(f871(x42702,a859)),f324(f324(f41(x42701,f871(x42702,a859)),x42703),x42704)),x42705)) % 181.55/181.53 [4271]E(f324(f324(f41(x42711,f871(x42712,a859)),x42713),f324(f324(f7(x42711,f871(x42712,a859),f871(x42712,a859)),f324(f324(f8(f871(x42712,a859),f871(f871(x42712,a859),f871(x42712,a859)),x42711),f104(f871(x42712,a859))),x42714)),x42715)),f324(f324(f104(f871(x42712,a859)),f324(f324(f41(x42711,f871(x42712,a859)),x42713),x42714)),x42715)) % 181.55/181.53 [4272]E(f324(f324(f42(x42721,f871(x42722,a859)),x42723),f324(f324(f7(x42721,f871(x42722,a859),f871(x42722,a859)),f324(f324(f8(f871(x42722,a859),f871(f871(x42722,a859),f871(x42722,a859)),x42721),f113(f871(x42722,a859))),x42724)),x42725)),f324(f324(f113(f871(x42722,a859)),f324(f324(f42(x42721,f871(x42722,a859)),x42723),x42724)),x42725)) % 181.55/181.53 [4276]E(f324(f324(f41(x42761,f871(x42762,a859)),x42763),f324(f324(f18(x42761,f871(x42762,a859),f871(x42762,a859)),f324(f324(f8(f871(x42762,a859),f871(f871(x42762,a859),f871(x42762,a859)),x42761),f113(f871(x42762,a859))),x42764)),x42765)),f324(f324(f113(f871(x42762,a859)),f324(f324(f41(x42761,f871(x42762,a859)),x42763),x42764)),f324(f324(f41(x42761,f871(x42762,a859)),x42763),x42765))) % 181.55/181.53 [4277]E(f324(f324(f42(x42771,f871(x42772,a859)),x42773),f324(f324(f18(x42771,f871(x42772,a859),f871(x42772,a859)),f324(f324(f8(f871(x42772,a859),f871(f871(x42772,a859),f871(x42772,a859)),x42771),f104(f871(x42772,a859))),x42774)),x42775)),f324(f324(f104(f871(x42772,a859)),f324(f324(f42(x42771,f871(x42772,a859)),x42773),x42774)),f324(f324(f42(x42771,f871(x42772,a859)),x42773),x42775))) % 181.55/181.53 [4291]E(f324(f324(f41(x42911,f871(x42912,a859)),x42913),f324(f324(f18(x42911,f871(x42912,a859),f871(x42912,a859)),f324(f324(f8(f871(x42912,a859),f871(f871(x42912,a859),f871(x42912,a859)),x42911),f113(f871(x42912,a859))),x42914)),x42915)),f324(f324(f113(f871(x42912,a859)),f39(f871(x42912,a859),f324(f303(x42911,f871(x42912,a859),x42914),x42913))),f39(f871(x42912,a859),f324(f303(x42911,f871(x42912,a859),x42915),x42913)))) % 181.55/181.53 [4292]E(f324(f324(f42(x42921,f871(x42922,a859)),x42923),f324(f324(f18(x42921,f871(x42922,a859),f871(x42922,a859)),f324(f324(f8(f871(x42922,a859),f871(f871(x42922,a859),f871(x42922,a859)),x42921),f104(f871(x42922,a859))),x42924)),x42925)),f324(f324(f104(f871(x42922,a859)),f40(f871(x42922,a859),f324(f303(x42921,f871(x42922,a859),x42924),x42923))),f40(f871(x42922,a859),f324(f303(x42921,f871(x42922,a859),x42925),x42923)))) % 181.55/181.53 [4326]E(f324(f324(f132(x43261),f324(f192(f866(x43261)),f172(x43261,x43262,f324(f324(f148(x43263,x43261),x43264),x43265)))),f324(f324(f148(x43263,x43261),x43264),x43265)),f324(f324(f148(x43263,x43261),x43264),f324(f324(f132(x43263),f324(f192(f866(x43263)),f172(x43263,f324(f73(x43261,a859,x43263,x43262),x43264),x43265))),x43265))) % 181.55/181.53 [4199]E(f324(f324(f124(f870(x41991,x41992)),f324(f324(f177(x41991,x41992),f324(f324(f170(x41991),f324(f192(f866(x41992)),x41993)),x41994)),x41993)),f324(f324(f177(x41991,x41992),f324(f324(f132(x41991),f324(f192(f866(x41992)),x41993)),x41994)),x41995)),f324(f324(f177(x41991,x41992),x41994),f324(f324(f124(x41992),x41993),x41995))) % 181.55/181.53 [4317]E(f86(x43171,f324(f324(f18(x43171,a859,a859),f324(f324(f8(a859,f871(a859,a859),x43171),a322),f324(f324(f7(x43171,f871(x43171,a859),a859),f326(x43171)),x43172))),f324(f324(f7(x43171,x43173,a859),f324(f324(f8(x43173,f871(x43173,a859),x43171),a321),x43174)),x43175))),f324(f78(x43171,x43173,x43172,x43174),x43175)) % 181.55/181.53 [4318]E(f91(x43181,f324(f324(f18(x43181,a859,a859),f324(f324(f8(a859,f871(a859,a859),x43181),a322),f324(f324(f7(x43181,f871(x43181,a859),a859),f326(x43181)),x43182))),f324(f324(f7(x43181,x43183,a859),f324(f324(f8(x43183,f871(x43183,a859),x43181),a321),x43184)),x43185))),f324(f94(x43181,x43183,x43182,x43184),x43185)) % 181.55/181.53 [4370]E(f324(f324(f87(a1,x43701),f324(f106(a1),f324(f324(f81(a1),x43702),a100))),f324(f324(f18(a1,x43701,x43701),f324(f324(f7(a1,x43701,f871(x43701,x43701)),f324(f324(f8(a859,f871(x43701,f871(x43701,x43701)),a1),f99(x43701)),a196)),f186(x43701,x43703,x43704,x43705))),f324(f324(f8(a865,x43701,a1),x43704),f324(f324(f7(a1,a865,a865),f324(f324(f8(a865,f871(a865,a865),a1),f81(a865)),a107)),x43705)))),f186(x43701,x43703,x43704,f324(f324(f81(a865),f324(f106(a865),x43702)),x43705))) % 181.55/181.53 [4406]E(f324(f173(x44061,x44062),f324(f324(f148(f870(x44061,x44063),f870(x44061,x44062)),f324(f263(x44061,x44063,f870(x44061,x44062)),f324(f324(f7(x44061,f871(x44063,x44062),f871(x44063,f870(x44061,x44062))),f324(f324(f8(f871(x44062,f870(x44061,x44062)),f871(f871(x44063,x44062),f871(x44063,f870(x44061,x44062))),x44061),f8(x44062,f870(x44061,x44062),x44063)),f259(x44061,x44062))),x44064))),x44065)),f324(f73(f869(x44063),f869(x44062),x44061,f324(f204(x44063,x44062),x44064)),f324(f173(x44061,x44063),x44065))) % 181.55/181.53 [4363]E(f179(x43631,x43632,f324(f324(f18(x43631,f869(x43632),f869(x43632)),f324(f324(f18(x43631,f869(x43632),f871(f869(x43632),f869(x43632))),f324(f324(f8(a859,f871(f869(x43632),f871(f869(x43632),f869(x43632))),x43631),f99(f869(x43632))),x43633)),x43634)),x43635)),f324(f324(f113(f871(x43631,a859)),f324(f324(f104(f871(x43631,a859)),f179(x43631,x43632,x43634)),f324(f244(x43631),x43633))),f324(f324(f104(f871(x43631,a859)),f179(x43631,x43632,x43635)),f324(f244(x43631),f324(f324(f8(a859,a859,x43631),a319),x43633))))) % 181.55/181.53 [4404]E(f324(f324(f87(a1,x44041),f324(f106(a1),f324(f324(f81(a1),x44042),a100))),f324(f324(f18(a1,x44041,x44041),f324(f324(f7(a1,x44041,f871(x44041,x44041)),f324(f324(f8(a859,f871(x44041,f871(x44041,x44041)),a1),f99(x44041)),a196)),f324(f185(x44041,x44043,x44044),x44045))),f324(f324(f18(a1,x44041,x44041),f324(f324(f8(a865,f871(x44041,x44041),a1),x44044),f324(f324(f7(a1,a865,a865),f324(f324(f8(a865,f871(a865,a865),a1),f81(a865)),a107)),x44045))),f324(f324(f8(a865,x44041,a1),f185(x44041,x44043,x44044)),f324(f324(f7(a1,a865,a865),f324(f324(f8(a865,f871(a865,a865),a1),f81(a865)),a107)),x44045))))),f324(f185(x44041,x44043,x44044),f324(f324(f81(a865),f324(f106(a865),x44042)),x44045))) % 181.55/181.53 [4440]E(f324(f244(f870(x44401,x44402)),f324(f263(x44401,x44402,a859),f324(f324(f8(f871(x44402,f871(x44403,a859)),f871(x44402,a859),x44401),f324(f8(f871(x44403,a859),a859,x44402),f88(x44403))),f324(f324(f7(x44401,f871(x44402,f871(x44403,a859)),f871(x44402,f871(x44403,a859))),f324(f324(f8(f871(f871(x44403,a859),f871(x44403,a859)),f871(f871(x44402,f871(x44403,a859)),f871(x44402,f871(x44403,a859))),x44401),f8(f871(x44403,a859),f871(x44403,a859),x44402)),f324(f324(f8(f871(x44403,f871(a859,a859)),f871(f871(x44403,a859),f871(x44403,a859)),x44401),f18(x44403,a859,a859)),f324(f324(f8(f871(x44403,a859),f871(x44403,f871(a859,a859)),x44401),f324(f8(a859,f871(a859,a859),x44403),a322)),f324(f324(f7(x44401,f871(f870(x44401,x44403),a859),f871(x44403,a859)),f324(f324(f8(f871(x44403,f871(f871(f870(x44401,x44403),a859),a859)),f871(f871(f870(x44401,x44403),a859),f871(x44403,a859)),x44401),f7(x44403,f871(f870(x44401,x44403),a859),a859)),f324(f324(f8(f871(x44403,f870(x44401,x44403)),f871(x44403,f871(f871(f870(x44401,x44403),a859),a859)),x44401),f324(f8(f870(x44401,x44403),f871(f871(f870(x44401,x44403),a859),a859),x44403),f326(f870(x44401,x44403)))),f259(x44401,x44403)))),x44404))))),f324(f324(f7(x44402,f871(f870(x44403,x44402),a859),f871(x44403,a859)),f324(f324(f8(f871(x44403,f871(f871(f870(x44403,x44402),a859),a859)),f871(f871(f870(x44403,x44402),a859),f871(x44403,a859)),x44402),f7(x44403,f871(f870(x44403,x44402),a859),a859)),f324(f324(f8(f871(x44403,f870(x44403,x44402)),f871(x44403,f871(f871(f870(x44403,x44402),a859),a859)),x44402),f324(f8(f870(x44403,x44402),f871(f871(f870(x44403,x44402),a859),a859),x44403),f326(f870(x44403,x44402)))),f324(f7(x44403,x44402,f870(x44403,x44402)),f259(x44403,x44402))))),x44405))))),f324(f324(f281(x44401,x44403,x44402),x44404),x44405)) % 181.55/181.53 [4528]~E(f29(x45281,x45282,x45283),f30(x45284,x45285,x45286)) % 181.55/181.53 [3964]E(f129(x39641,x39642,x39643,x39644,f125(x39642,x39645,x39646)),f324(f324(x39644,x39645),x39646)) % 181.55/181.53 [4183]E(f182(x41831,x41832,f180(x41831,x41832,x41833,x41834),x41835,x41836),f180(x41831,x41832,x41833,f182(x41831,x41832,x41834,x41835,x41836))) % 181.55/181.53 [4307]E(f324(f73(f870(x43071,x43072),x43072,f870(x43073,x43074),f262(x43071,x43072)),f264(x43073,x43071,x43074,x43072,x43075,x43076)),f324(f73(x43074,x43072,f870(x43073,x43074),x43076),f262(x43073,x43074))) % 181.55/181.53 [4308]E(f324(f73(f870(x43081,x43082),x43081,f870(x43083,x43084),f258(x43081,x43082)),f264(x43083,x43081,x43084,x43082,x43085,x43086)),f324(f73(x43083,x43081,f870(x43083,x43084),x43085),f258(x43083,x43084))) % 181.55/181.53 [3901]E(f324(f324(f73(x39011,x39012,x39013,x39014),x39015),x39016),f324(x39014,f324(x39015,x39016))) % 181.55/181.53 [3700]E(f324(f324(f263(x37001,x37002,x37003),x37004),f324(f324(f259(x37001,x37002),x37005),x37006)),f324(f324(x37004,x37005),x37006)) % 181.55/181.53 [3760]E(f324(f324(f324(f8(x37601,x37602,x37603),x37604),x37605),x37606),f324(x37604,f324(x37605,x37606))) % 181.55/181.53 [3761]E(f324(f324(f324(f7(x37611,x37612,x37613),x37614),x37615),x37616),f324(f324(x37614,x37616),x37615)) % 181.55/181.53 [3778]E(f324(f324(f324(f18(x37781,x37782,x37783),x37784),x37785),x37786),f324(f324(x37784,x37786),f324(x37785,x37786))) % 181.55/181.53 [3800]E(f324(f150(x38001,x38002,x38003,x38004),f324(f324(f145(x38002),x38005),x38006)),f324(f324(x38004,x38005),x38006)) % 181.55/181.53 [3905]E(f324(f324(f145(f870(x39051,x39052)),f324(f324(f259(x39051,x39052),x39053),x39054)),f324(f324(f177(x39051,x39052),x39055),x39056)),f324(f324(f177(x39051,x39052),f324(f324(f145(x39051),x39053),x39055)),f324(f324(f145(x39052),x39054),x39056))) % 181.55/181.53 [3907]E(f324(f324(f148(x39071,x39072),x39073),f324(f324(f153(x39071,x39074),x39075),x39076)),f324(f324(f153(x39072,f324(f324(f148(x39071,x39072),x39073),x39074)),x39075),f324(x39073,x39076))) % 181.55/181.53 [3951]E(f324(f136(x39511,x39512,x39513,x39514),f324(f324(f145(x39512),x39515),x39516)),f324(f136(x39511,x39512,x39513,f324(f324(x39513,x39514),x39515)),x39516)) % 181.55/181.53 [3980]E(f266(x39801,x39802,x39803,x39804,f324(f324(f259(x39801,x39802),x39805),x39806)),f324(f324(x39804,x39805),x39806)) % 181.55/181.53 [4063]E(f324(f324(f41(x40631,f871(x40632,a859)),x40633),f324(f73(x40634,f871(x40632,a859),x40631,x40635),x40636)),f324(f324(f41(x40634,f871(x40632,a859)),f324(f303(x40631,x40634,x40636),x40633)),x40635)) % 181.55/181.53 [4114]E(f324(f324(f148(x41141,x41142),x41143),f324(f324(f148(x41144,x41141),x41145),x41146)),f324(f324(f148(x41144,x41142),f324(f73(x41141,x41142,x41144,x41143),x41145)),x41146)) % 181.55/181.53 [4116]E(f324(f324(f204(x41161,x41162),x41163),f324(f324(f204(x41164,x41161),x41165),x41166)),f324(f324(f204(x41164,x41162),f324(f73(x41161,x41162,x41164,x41163),x41165)),x41166)) % 181.55/181.53 [4122]E(f324(f303(x41221,x41222,f324(f73(x41223,x41222,x41221,x41224),x41225)),x41226),f324(f303(x41223,x41222,x41224),f324(f303(x41221,x41223,x41225),x41226))) % 181.55/181.53 [4123]E(f324(f304(x41231,x41232,f324(f73(x41233,x41232,x41231,x41234),x41235)),x41236),f324(f304(x41231,x41233,x41235),f324(f304(x41233,x41232,x41234),x41236))) % 181.55/181.53 [4152]E(f180(x41521,x41522,x41523,f324(f324(f324(f72(x41521,f869(x41522)),x41524),x41525),f324(f233(x41522),x41526))),f324(f324(f324(f72(x41521,f869(x41522)),f180(x41521,x41522,x41523,x41524)),x41525),f324(f233(x41522),x41526))) % 181.55/181.53 [4154]E(f324(f136(x41541,x41542,x41543,f324(f136(x41541,x41542,x41543,x41544),x41545)),x41546),f324(f136(x41541,x41542,x41543,x41544),f324(f324(f124(x41542),x41545),x41546))) % 181.55/181.53 [4297]E(f324(f264(x42971,x42971,x42972,x42973,f34(x42971),x42974),f324(f324(f259(x42971,x42972),x42975),x42976)),f324(f324(f259(x42971,x42973),x42975),f324(x42974,x42976))) % 181.55/181.53 [4298]E(f324(f264(x42981,x42982,x42983,x42983,x42984,f34(x42983)),f324(f324(f259(x42981,x42983),x42985),x42986)),f324(f324(f259(x42982,x42983),f324(x42984,x42985)),x42986)) % 181.55/181.53 [4388]E(f324(f324(f148(f870(x43881,x43882),f870(x43881,x43883)),f324(f263(x43881,x43882,f870(x43881,x43883)),f324(f324(f7(x43881,f871(x43882,x43883),f871(x43882,f870(x43881,x43883))),f324(f324(f8(f871(x43883,f870(x43881,x43883)),f871(f871(x43882,x43883),f871(x43882,f870(x43881,x43883))),x43881),f8(x43883,f870(x43881,x43883),x43882)),f259(x43881,x43883))),x43884))),f324(f324(f177(x43881,x43882),x43885),x43886)),f324(f324(f177(x43881,x43883),x43885),f324(f324(f148(x43882,x43883),x43884),x43886))) % 181.55/181.53 [3765]E(f97(x37651,x37652,x37653,f324(f324(f324(f93(x37651),x37654),x37655),x37656)),f324(f324(f324(x37653,x37654),x37655),x37656)) % 181.55/181.53 [3766]E(f98(x37661,x37662,x37663,f324(f324(f324(f93(x37661),x37664),x37665),x37666)),f324(f324(f324(x37663,x37664),x37665),x37666)) % 181.55/181.53 [3963]E(f324(f324(f73(x39631,x39632,x39633,f324(f16(x39632,x39631),x39634)),x39635),x39636),x39634) % 181.55/181.53 [3999]E(f324(f303(x39991,x39992,x39993),f324(f303(x39994,x39991,x39995),x39996)),f324(f303(x39994,x39992,f324(f324(f8(x39991,x39992,x39994),x39993),x39995)),x39996)) % 181.55/181.53 [4005]E(f324(f324(f41(x40051,f871(x40052,a859)),f324(f303(x40053,x40051,x40054),x40055)),x40056),f324(f324(f41(x40053,f871(x40052,a859)),x40055),f324(f324(f8(x40051,f871(x40052,a859),x40053),x40056),x40054))) % 181.55/181.53 [4006]E(f324(f324(f42(x40061,f871(x40062,a859)),f324(f303(x40063,x40061,x40064),x40065)),x40066),f324(f324(f42(x40063,f871(x40062,a859)),x40065),f324(f324(f8(x40061,f871(x40062,a859),x40063),x40066),x40064))) % 181.55/181.53 [4007]E(f324(f324(f41(x40071,f871(x40072,a859)),x40073),f324(f324(f8(x40074,f871(x40072,a859),x40071),x40075),x40076)),f324(f324(f41(x40074,f871(x40072,a859)),f324(f303(x40071,x40074,x40076),x40073)),x40075)) % 181.55/181.53 [4008]E(f324(f324(f42(x40081,f871(x40082,a859)),x40083),f324(f324(f8(x40084,f871(x40082,a859),x40081),x40085),x40086)),f324(f324(f42(x40084,f871(x40082,a859)),f324(f303(x40081,x40084,x40086),x40083)),x40085)) % 181.55/181.53 [4065]E(f324(f324(f41(x40651,f871(x40652,a859)),x40653),f324(f324(f8(f871(x40654,a859),f871(x40652,a859),x40651),f303(x40654,x40652,x40655)),x40656)),f324(f303(x40654,x40652,x40655),f324(f324(f41(x40651,f871(x40654,a859)),x40653),x40656))) % 181.55/181.53 [4066]E(f324(f324(f41(x40661,f871(x40662,a859)),x40663),f324(f324(f8(f871(x40664,a859),f871(x40662,a859),x40661),f304(x40662,x40664,x40665)),x40666)),f324(f304(x40662,x40664,x40665),f324(f324(f41(x40661,f871(x40664,a859)),x40663),x40666))) % 181.55/181.53 [4067]E(f324(f324(f42(x40671,f871(x40672,a859)),x40673),f324(f324(f8(f871(x40674,a859),f871(x40672,a859),x40671),f304(x40672,x40674,x40675)),x40676)),f324(f304(x40672,x40674,x40675),f324(f324(f42(x40671,f871(x40674,a859)),x40673),x40676))) % 181.55/181.53 [4068]E(f324(f324(f41(x40681,f871(x40682,a859)),x40683),f324(f324(f8(f871(x40684,a859),f871(x40682,a859),x40681),f278(x40684,x40682,x40685)),x40686)),f324(f278(x40684,x40682,x40685),f324(f324(f41(x40681,f871(x40684,a859)),x40683),x40686))) % 181.55/181.53 [4161]E(f324(f136(x41611,x41612,f324(f7(x41612,x41611,x41611),x41613),x41614),f324(f163(x41612),f324(f324(f145(x41612),x41615),x41616))),f324(f324(x41613,x41615),f324(f136(x41611,x41612,f324(f7(x41612,x41611,x41611),x41613),x41614),f324(f163(x41612),x41616)))) % 181.55/181.53 [4223]E(f324(f324(f18(f870(x42231,x42232),x42232,x42233),f324(f324(f8(x42234,f871(x42232,x42233),f870(x42231,x42232)),x42235),f324(f324(f8(x42231,x42234,f870(x42231,x42232)),x42236),f258(x42231,x42232)))),f262(x42231,x42232)),f324(f263(x42231,x42232,x42233),f324(f324(f8(x42234,f871(x42232,x42233),x42231),x42235),x42236))) % 181.55/181.53 [4230]E(f324(f136(x42301,x42302,f324(f7(x42302,x42301,x42301),x42303),f324(f136(x42301,x42302,f324(f7(x42302,x42301,x42301),x42303),x42304),f324(f163(x42302),x42305))),f324(f163(x42302),x42306)),f324(f136(x42301,x42302,f324(f7(x42302,x42301,x42301),x42303),x42304),f324(f163(x42302),f324(f324(f124(x42302),x42306),x42305)))) % 181.55/181.53 [4232]E(f324(f324(f148(f870(x42321,x42322),f870(x42323,x42322)),f324(f263(x42321,x42322,f870(x42323,x42322)),f324(f324(f8(x42323,f871(x42322,f870(x42323,x42322)),x42321),f259(x42323,x42322)),x42324))),f324(f324(f177(x42321,x42322),x42325),x42326)),f324(f324(f177(x42323,x42322),f324(f324(f148(x42321,x42323),x42324),x42325)),x42326)) % 181.55/181.53 [4280]P1(f324(f324(f238(f871(x42801,a859)),f324(f278(x42802,x42801,x42803),f324(f324(f42(x42804,f871(x42802,a859)),x42805),x42806))),f324(f324(f42(x42804,f871(x42801,a859)),x42805),f324(f324(f8(f871(x42802,a859),f871(x42801,a859),x42804),f278(x42802,x42801,x42803)),x42806)))) % 181.55/181.53 [4078]E(f324(f324(f177(x40781,x40782),f324(f324(f153(x40781,x40783),x40784),f324(f258(x40781,x40782),x40785))),f324(f324(f153(x40782,x40786),x40784),f324(f262(x40781,x40782),x40785))),f324(f324(f153(f870(x40781,x40782),f324(f324(f177(x40781,x40782),x40783),x40786)),x40784),x40785)) % 181.55/181.53 [4141]E(f324(f324(f113(f871(f870(x41411,x41412),a859)),f324(f324(f281(x41411,x41413,x41412),x41414),x41415)),f324(f324(f281(x41411,x41413,x41412),x41414),x41416)),f324(f324(f281(x41411,x41413,x41412),x41414),f324(f324(f113(f871(f870(x41413,x41412),a859)),x41415),x41416))) % 181.55/181.53 [4243]E(f324(f324(f302(f870(x42431,x42432)),f324(f324(f259(x42431,x42432),x42433),x42434)),f324(f324(f113(f871(f870(x42431,x42432),a859)),f324(f324(f261(x42431,x42432),x42435),f324(f16(f871(x42432,a859),x42431),f324(f324(f302(x42432),x42434),x42436)))),f324(f324(f261(x42431,x42432),f324(f324(f302(x42431),x42433),x42435)),f324(f16(f871(x42432,a859),x42431),x42436)))),f324(f324(f261(x42431,x42432),f324(f324(f302(x42431),x42433),x42435)),f324(f16(f871(x42432,a859),x42431),f324(f324(f302(x42432),x42434),x42436)))) % 181.55/181.53 [4321]E(f324(f324(f104(f871(x43211,a859)),f324(f304(x43211,x43212,f324(f73(f870(x43212,x43213),x43212,x43211,f258(x43212,x43213)),x43214)),x43215)),f324(f304(x43211,x43213,f324(f73(f870(x43212,x43213),x43213,x43211,f262(x43212,x43213)),x43214)),x43216)),f324(f304(x43211,f870(x43212,x43213),x43214),f324(f324(f261(x43212,x43213),x43215),f324(f16(f871(x43213,a859),x43212),x43216)))) % 181.55/181.53 [4062]E(f324(f324(f324(f72(x40621,x40622),f324(f324(f324(f72(x40621,x40622),x40623),x40624),x40625)),x40624),x40626),f324(f324(f324(f72(x40621,x40622),x40623),x40624),x40626)) % 181.55/181.53 [4167]E(f324(f324(f113(f871(f870(x41671,x41672),a859)),f324(f324(f281(x41671,x41673,x41672),x41674),x41675)),f324(f324(f281(x41671,x41673,x41672),x41676),x41675)),f324(f324(f281(x41671,x41673,x41672),f324(f324(f113(f871(f870(x41671,x41673),a859)),x41674),x41676)),x41675)) % 181.55/181.53 [4305]E(f324(f324(f41(x43051,f871(x43052,a859)),x43053),f324(f324(f7(x43051,f871(x43054,f871(x43052,a859)),f871(x43052,a859)),f324(f324(f8(f871(x43054,a859),f871(f871(x43054,f871(x43052,a859)),f871(x43052,a859)),x43051),f41(x43054,f871(x43052,a859))),x43055)),x43056)),f324(f324(f41(x43054,f871(x43052,a859)),f324(f324(f41(x43051,f871(x43054,a859)),x43053),x43055)),x43056)) % 181.55/181.53 [4306]E(f324(f324(f42(x43061,f871(x43062,a859)),x43063),f324(f324(f7(x43061,f871(x43064,f871(x43062,a859)),f871(x43062,a859)),f324(f324(f8(f871(x43064,a859),f871(f871(x43064,f871(x43062,a859)),f871(x43062,a859)),x43061),f42(x43064,f871(x43062,a859))),x43065)),x43066)),f324(f324(f42(x43064,f871(x43062,a859)),f324(f324(f41(x43061,f871(x43064,a859)),x43063),x43065)),x43066)) % 181.55/181.53 [4358]E(f324(f263(x43581,x43582,f870(x43583,x43584)),f324(f324(f7(x43581,f871(x43582,x43584),f871(x43582,f870(x43583,x43584))),f324(f324(f8(f871(x43584,f870(x43583,x43584)),f871(f871(x43582,x43584),f871(x43582,f870(x43583,x43584))),x43581),f8(x43584,f870(x43583,x43584),x43582)),f324(f324(f8(x43583,f871(x43584,f870(x43583,x43584)),x43581),f259(x43583,x43584)),x43585))),x43586)),f264(x43581,x43583,x43582,x43584,x43585,x43586)) % 181.55/181.53 [4279]E(f324(f324(f324(f72(x42791,f869(x42792)),f183(x42791,x42792,x42793,f324(f324(f22(f871(x42791,a859)),x42794),f324(f324(f302(x42791),x42795),f191(f871(x42791,a859)))))),x42795),x42796),f324(f324(f324(f72(x42791,f869(x42792)),f183(x42791,x42792,x42793,x42794)),x42795),x42796)) % 181.55/181.53 [4383]E(f324(f303(x43831,x43832,f324(f324(f18(x43831,x43832,x43832),f324(f324(f18(x43831,x43832,f871(x43832,x43832)),f324(f324(f8(a859,f871(x43832,f871(x43832,x43832)),x43831),f99(x43832)),x43833)),x43834)),x43835)),x43836),f324(f324(f113(f871(x43832,a859)),f324(f303(x43831,x43832,x43834),f324(f324(f104(f871(x43831,a859)),x43836),f324(f244(x43831),x43833)))),f324(f303(x43831,x43832,x43835),f324(f324(f104(f871(x43831,a859)),x43836),f324(f244(x43831),f324(f324(f8(a859,a859,x43831),a319),x43833)))))) % 181.55/181.53 [4394]E(f324(f303(x43941,f870(x43942,x43943),f324(f324(f18(x43941,x43943,f870(x43942,x43943)),f324(f324(f8(x43942,f871(x43943,f870(x43942,x43943)),x43941),f259(x43942,x43943)),x43944)),x43945)),x43946),f324(f324(f261(x43942,x43943),f324(f303(x43941,x43942,x43944),x43946)),f324(f324(f8(f871(x43941,a859),f871(x43943,a859),x43942),f303(x43941,x43943,x43945)),f324(f324(f7(x43942,f871(x43941,a859),f871(x43941,a859)),f324(f324(f8(f871(x43941,a859),f871(f871(x43941,a859),f871(x43941,a859)),x43942),f104(f871(x43941,a859))),f324(f324(f8(f871(x43942,a859),f871(x43941,a859),x43942),f304(x43941,x43942,x43944)),f324(f324(f7(x43942,f871(x43942,a859),f871(x43942,a859)),f302(x43942)),f191(f871(x43942,a859)))))),x43946)))) % 181.55/181.53 [4200]E(f324(f73(x42001,x42002,x42003,x42004),f76(x42003,x42001,x42005,x42006,x42007)),f76(x42003,x42002,x42005,x42006,f324(f73(x42001,x42002,x42003,x42004),x42007))) % 181.55/181.53 [4340]E(f324(f262(x43401,x43402),f324(f264(x43403,x43401,x43404,x43402,x43405,x43406),x43407)),f324(x43406,f324(f262(x43403,x43404),x43407))) % 181.55/181.53 [4341]E(f324(f258(x43411,x43412),f324(f264(x43413,x43411,x43414,x43412,x43415,x43416),x43417)),f324(x43415,f324(f258(x43413,x43414),x43417))) % 181.55/181.53 [4040]E(f324(f324(f177(x40401,x40402),f324(f324(f153(x40401,x40403),x40404),x40405)),f324(f324(f153(x40402,x40406),x40404),x40407)),f324(f324(f153(f870(x40401,x40402),f324(f324(f177(x40401,x40402),x40403),x40406)),x40404),f324(f324(f259(x40401,x40402),x40405),x40407))) % 181.55/181.53 [4108]E(f324(f324(f324(f265(x41081,x41082,x41083,x41084),x41085),x41086),x41087),f324(f324(f263(x41082,x41083,x41084),x41086),f324(x41085,x41087))) % 181.55/181.53 [4121]E(f324(f324(f324(f265(x41211,x41212,x41213,x41214),x41215),x41216),x41217),f324(f324(x41216,f324(f258(x41212,x41213),f324(x41215,x41217))),f324(f262(x41212,x41213),f324(x41215,x41217)))) % 181.55/181.53 [4156]E(f182(x41561,x41562,f324(f324(f324(f72(x41561,f869(x41562)),x41563),x41564),f324(f233(x41562),x41565)),x41566,x41567),f182(x41561,x41562,x41563,f324(f324(f145(x41561),x41564),x41566),f324(f324(f145(x41562),x41565),x41567))) % 181.55/181.53 [4177]E(f324(f73(x41771,x41772,x41773,x41774),f324(f73(x41775,x41771,x41773,x41776),x41777)),f324(f73(x41775,x41772,x41773,f324(f73(x41771,x41772,x41775,x41774),x41776)),x41777)) % 181.55/181.53 [4239]E(f324(f73(f869(x42391),f869(x42392),x42393,f324(f204(x42391,x42392),x42394)),f324(f324(f324(f72(x42393,f869(x42391)),x42395),x42396),f324(f233(x42391),x42397))),f324(f324(f324(f72(x42393,f869(x42392)),f324(f73(f869(x42391),f869(x42392),x42393,f324(f204(x42391,x42392),x42394)),x42395)),x42396),f324(f233(x42392),f324(x42394,x42397)))) % 181.55/181.53 [4365]E(f324(f264(x43651,x43652,x43653,x43653,x43654,f34(x43653)),f324(f264(x43651,x43651,x43655,x43653,f34(x43651),x43656),x43657)),f324(f324(f259(x43652,x43653),f324(x43654,f324(f258(x43651,x43655),x43657))),f324(x43656,f324(f262(x43651,x43655),x43657)))) % 181.55/181.53 [4366]E(f324(f264(x43661,x43661,x43662,x43663,f34(x43661),x43664),f324(f264(x43665,x43661,x43662,x43662,x43666,f34(x43662)),x43667)),f324(f324(f259(x43661,x43663),f324(x43666,f324(f258(x43665,x43662),x43667))),f324(x43664,f324(f262(x43665,x43662),x43667)))) % 181.55/181.53 [4381]E(f324(f264(x43811,x43812,x43813,x43813,x43814,f34(x43813)),f324(f264(x43815,x43811,x43813,x43813,x43816,f34(x43813)),x43817)),f324(f264(x43815,x43812,x43813,x43813,f324(f73(x43811,x43812,x43815,x43814),x43816),f34(x43813)),x43817)) % 181.55/181.53 [4382]E(f324(f264(x43821,x43821,x43822,x43823,f34(x43821),x43824),f324(f264(x43821,x43821,x43825,x43822,f34(x43821),x43826),x43827)),f324(f264(x43821,x43821,x43825,x43823,f34(x43821),f324(f73(x43822,x43823,x43825,x43824),x43826)),x43827)) % 181.55/181.53 [4391]E(f324(f264(x43911,x43912,x43913,x43913,x43914,f34(x43913)),f324(f264(x43911,x43911,x43915,x43913,f34(x43911),x43916),x43917)),f324(f264(x43912,x43912,x43915,x43913,f34(x43912),x43916),f324(f264(x43911,x43912,x43915,x43915,x43914,f34(x43915)),x43917))) % 181.55/181.53 [4075]E(f324(f324(f281(x40751,x40752,x40753),f324(f324(f281(x40751,x40754,x40752),x40755),x40756)),x40757),f324(f324(f281(x40751,x40754,x40753),x40755),f324(f324(f281(x40754,x40752,x40753),x40756),x40757))) % 181.55/181.53 [4147]E(f324(f324(f263(x41471,x41472,x41473),f324(f73(x41474,f871(x41472,x41473),x41471,x41475),x41476)),x41477),f324(f324(x41475,f324(x41476,f324(f258(x41471,x41472),x41477))),f324(f262(x41471,x41472),x41477))) % 181.55/181.53 [4203]E(f324(f73(x42031,x42032,x42033,x42034),f324(f324(f324(f72(x42033,x42031),x42035),x42036),x42037)),f324(f324(f324(f72(x42033,x42032),f324(f73(x42031,x42032,x42033,x42034),x42035)),x42036),f324(x42034,x42037))) % 181.55/181.53 [4235]E(f324(f136(x42351,x42352,f324(f7(x42352,x42351,x42351),x42353),x42354),f324(f163(x42352),f324(f324(f148(x42355,x42352),x42356),x42357))),f324(f136(x42351,x42355,f324(f7(x42355,x42351,x42351),f324(f73(x42352,f871(x42351,x42351),x42355,x42353),x42356)),x42354),f324(f163(x42355),x42357))) % 181.55/181.53 [4178]E(f324(f324(f41(x41781,f871(f870(x41782,x41783),a859)),x41784),f324(f324(f8(f871(f870(x41785,x41783),a859),f871(f870(x41782,x41783),a859),x41781),f324(f281(x41782,x41785,x41783),x41786)),x41787)),f324(f324(f281(x41782,x41785,x41783),x41786),f324(f324(f41(x41781,f871(f870(x41785,x41783),a859)),x41784),x41787))) % 181.55/181.53 [4327]E(f324(f324(f41(x43271,f871(f870(x43272,x43273),a859)),x43274),f324(f324(f7(x43271,f871(f870(x43275,x43273),a859),f871(f870(x43272,x43273),a859)),f324(f324(f8(f871(f870(x43272,x43275),a859),f871(f871(f870(x43275,x43273),a859),f871(f870(x43272,x43273),a859)),x43271),f281(x43272,x43275,x43273)),x43276)),x43277)),f324(f324(f281(x43272,x43275,x43273),f324(f324(f41(x43271,f871(f870(x43272,x43275),a859)),x43274),x43276)),x43277)) % 181.55/181.53 [4328]E(f324(f136(x43281,x43282,f324(f324(f7(x43281,f871(x43282,x43283),f871(x43282,x43281)),f324(f324(f8(f871(x43283,x43281),f871(f871(x43282,x43283),f871(x43282,x43281)),x43281),f8(x43283,x43281,x43282)),x43284)),x43285),x43286),x43287),f324(f136(x43281,x43283,x43284,x43286),f324(f324(f148(x43282,x43283),x43285),x43287))) % 181.55/181.53 [4392]E(f324(f324(f41(x43921,f871(x43922,a859)),x43923),f324(f324(f8(f871(x43924,f871(x43922,a859)),f871(x43922,a859),x43921),f324(f41(x43924,f871(x43922,a859)),x43925)),f324(f324(f7(x43921,f871(x43924,f871(x43922,a859)),f871(x43924,f871(x43922,a859))),f324(f324(f8(f871(f871(x43922,a859),f871(x43922,a859)),f871(f871(x43924,f871(x43922,a859)),f871(x43924,f871(x43922,a859))),x43921),f8(f871(x43922,a859),f871(x43922,a859),x43924)),f324(f324(f8(f871(x43922,a859),f871(f871(x43922,a859),f871(x43922,a859)),x43921),f104(f871(x43922,a859))),x43926))),x43927))),f324(f324(f104(f871(x43922,a859)),f324(f324(f41(x43921,f871(x43922,a859)),x43923),x43926)),f324(f324(f41(x43924,f871(x43922,a859)),x43925),x43927))) % 181.55/181.53 [4393]E(f324(f324(f42(x43931,f871(x43932,a859)),x43933),f324(f324(f8(f871(x43934,f871(x43932,a859)),f871(x43932,a859),x43931),f324(f42(x43934,f871(x43932,a859)),x43935)),f324(f324(f7(x43931,f871(x43934,f871(x43932,a859)),f871(x43934,f871(x43932,a859))),f324(f324(f8(f871(f871(x43932,a859),f871(x43932,a859)),f871(f871(x43934,f871(x43932,a859)),f871(x43934,f871(x43932,a859))),x43931),f8(f871(x43932,a859),f871(x43932,a859),x43934)),f324(f324(f8(f871(x43932,a859),f871(f871(x43932,a859),f871(x43932,a859)),x43931),f113(f871(x43932,a859))),x43936))),x43937))),f324(f324(f113(f871(x43932,a859)),f324(f324(f42(x43931,f871(x43932,a859)),x43933),x43936)),f324(f324(f42(x43934,f871(x43932,a859)),x43935),x43937))) % 181.55/181.53 [4386]E(f201(x43861,x43862,f324(f324(f324(x43863,x43864),x43865),x43866),f324(f324(f7(x43861,f870(a102,a102),f871(a102,f867(x43862))),f324(f324(f7(x43861,a102,f871(f870(a102,a102),f871(a102,f867(x43862)))),f324(f324(f7(x43861,a102,f871(a102,f871(f870(a102,a102),f871(a102,f867(x43862))))),x43867),x43864)),x43865)),x43866)),f324(f324(f324(f214(x43861,x43862,x43863,x43867),x43864),x43865),x43866)) % 181.55/181.53 [4399]E(f202(x43991,x43992,f324(f324(f324(x43993,x43994),x43995),x43996),f324(f324(f7(x43991,f870(a102,a102),f871(a102,f867(x43992))),f324(f324(f7(x43991,a102,f871(f870(a102,a102),f871(a102,f867(x43992)))),f324(f324(f7(x43991,a102,f871(a102,f871(f870(a102,a102),f871(a102,f867(x43992))))),x43997),x43994)),x43995)),x43996)),f216(x43991,x43992,x43993,x43997,x43994,x43995,x43996)) % 181.55/181.53 [4390]E(f198(x43901,x43902,f324(f324(f324(x43903,x43904),x43905),x43906),f324(f324(f7(x43901,f870(a102,a102),f871(a102,f867(f869(x43902)))),f324(f324(f7(x43901,a102,f871(f870(a102,a102),f871(a102,f867(f869(x43902))))),f324(f324(f7(x43901,a102,f871(a102,f871(f870(a102,a102),f871(a102,f867(f869(x43902)))))),x43907),x43904)),x43905)),x43906)),f324(f324(f324(f210(x43901,x43902,x43903,x43907),x43904),x43905),x43906)) % 181.55/181.53 [4401]E(f200(x44011,x44012,f324(f324(f324(x44013,x44014),x44015),x44016),f324(f324(f7(x44011,f870(a102,a102),f871(a102,f867(f869(x44012)))),f324(f324(f7(x44011,a102,f871(f870(a102,a102),f871(a102,f867(f869(x44012))))),f324(f324(f7(x44011,a102,f871(a102,f871(f870(a102,a102),f871(a102,f867(f869(x44012)))))),x44017),x44014)),x44015)),x44016)),f212(x44011,x44012,x44013,x44017,x44014,x44015,x44016)) % 181.55/181.53 [4299]E(f324(f264(x42991,x42992,x42993,x42994,x42995,x42996),f324(f324(f259(x42991,x42993),x42997),x42998)),f324(f324(f259(x42992,x42994),f324(x42995,x42997)),f324(x42996,x42998))) % 181.55/181.53 [4403]E(f324(f324(f148(f870(x44031,x44032),f870(x44033,x44034)),f324(f263(x44031,x44032,f870(x44033,x44034)),f324(f324(f7(x44031,f871(x44032,x44034),f871(x44032,f870(x44033,x44034))),f324(f324(f8(f871(x44034,f870(x44033,x44034)),f871(f871(x44032,x44034),f871(x44032,f870(x44033,x44034))),x44031),f8(x44034,f870(x44033,x44034),x44032)),f324(f324(f8(x44033,f871(x44034,f870(x44033,x44034)),x44031),f259(x44033,x44034)),x44035))),x44036))),f324(f324(f177(x44031,x44032),x44037),x44038)),f324(f324(f177(x44033,x44034),f324(f324(f148(x44031,x44033),x44035),x44037)),f324(f324(f148(x44032,x44034),x44036),x44038))) % 181.55/181.53 [4407]E(f324(f324(f148(f870(x44071,x44072),x44073),f324(f263(x44071,x44072,x44073),f324(f324(f8(f871(x44072,f870(x44071,x44074)),f871(x44072,x44073),x44071),f324(f8(f870(x44071,x44074),x44073,x44072),x44075)),f324(f324(f7(x44071,f871(x44072,x44074),f871(x44072,f870(x44071,x44074))),f324(f324(f8(f871(x44074,f870(x44071,x44074)),f871(f871(x44072,x44074),f871(x44072,f870(x44071,x44074))),x44071),f8(x44074,f870(x44071,x44074),x44072)),f259(x44071,x44074))),x44076)))),f324(f324(f177(x44071,x44072),x44077),x44078)),f324(f324(f148(f870(x44071,x44074),x44073),x44075),f324(f324(f177(x44071,x44074),x44077),f324(f324(f148(x44072,x44074),x44076),x44078)))) % 181.55/181.53 [4332]E(f324(f324(f148(f870(x43321,x43322),x43323),f324(f263(x43321,x43322,x43323),f324(f324(f8(f871(x43322,f870(x43324,x43322)),f871(x43322,x43323),x43321),f324(f8(f870(x43324,x43322),x43323,x43322),x43325)),f324(f324(f8(x43324,f871(x43322,f870(x43324,x43322)),x43321),f259(x43324,x43322)),x43326)))),f324(f324(f177(x43321,x43322),x43327),x43328)),f324(f324(f148(f870(x43324,x43322),x43323),x43325),f324(f324(f177(x43324,x43322),f324(f324(f148(x43321,x43324),x43326),x43327)),x43328))) % 181.55/181.53 [4290]E(f324(f324(f263(x42901,x42902,x42903),f324(f324(f8(f871(x42902,f870(x42904,x42905)),f871(x42902,x42903),x42901),f324(f8(f870(x42904,x42905),x42903,x42902),f324(f263(x42904,x42905,x42903),x42906))),x42907)),x42908),f324(f324(f263(x42904,x42905,x42903),x42906),f324(f324(f263(x42901,x42902,f870(x42904,x42905)),x42907),x42908))) % 181.55/181.53 [4408]E(f324(f324(f41(f870(x44081,x44082),f871(f870(x44083,x44084),a859)),f324(f324(f261(x44081,x44082),x44085),f324(f16(f871(x44082,a859),x44081),x44086))),f324(f263(x44081,x44082,f871(f870(x44083,x44084),a859)),f324(f324(f7(x44081,f871(x44082,f871(x44083,f871(x44084,a859))),f871(x44082,f871(f870(x44083,x44084),a859))),f324(f324(f8(f871(f871(x44083,f871(x44084,a859)),f871(f870(x44083,x44084),a859)),f871(f871(x44082,f871(x44083,f871(x44084,a859))),f871(x44082,f871(f870(x44083,x44084),a859))),x44081),f8(f871(x44083,f871(x44084,a859)),f871(f870(x44083,x44084),a859),x44082)),f324(f324(f8(f871(x44083,a859),f871(f871(x44083,f871(x44084,a859)),f871(f870(x44083,x44084),a859)),x44081),f261(x44083,x44084)),x44087))),f324(f324(f8(f871(x44084,a859),f871(x44083,f871(x44084,a859)),x44082),f16(f871(x44084,a859),x44083)),x44088)))),f324(f324(f261(x44083,x44084),f324(f324(f41(x44081,f871(x44083,a859)),x44085),x44087)),f324(f16(f871(x44084,a859),x44083),f324(f324(f41(x44082,f871(x44084,a859)),x44086),x44088)))) % 181.55/181.53 [4346]E(f324(f324(f265(x43461,x43462,x43463,x43464),f324(f324(f265(x43461,x43465,x43466,f870(x43462,x43463)),x43467),x43468)),x43469),f324(f324(f265(x43461,x43465,x43466,x43464),x43467),f324(f324(f7(x43465,f871(x43462,f871(x43463,x43464)),f871(x43466,x43464)),f324(f324(f8(f871(x43466,f870(x43462,x43463)),f871(f871(x43462,f871(x43463,x43464)),f871(x43466,x43464)),x43465),f265(x43466,x43462,x43463,x43464)),x43468)),x43469))) % 181.55/181.53 [4378]E(f324(f73(f870(x43781,x43782),f870(x43783,x43784),f870(x43785,x43786),f264(x43781,x43783,x43782,x43784,x43787,x43788)),f264(x43785,x43781,x43786,x43782,x43789,x437810)),f264(x43785,x43783,x43786,x43784,f324(f73(x43781,x43783,x43785,x43787),x43789),f324(f73(x43782,x43784,x43786,x43788),x437810))) % 181.55/181.53 [4384]E(f324(f264(x43841,x43842,x43843,x43844,x43845,x43846),f324(f264(x43847,x43841,x43848,x43843,x43849,x438410),x438411)),f324(f264(x43847,x43842,x43848,x43844,f324(f73(x43841,x43842,x43847,x43845),x43849),f324(f73(x43843,x43844,x43848,x43846),x438410)),x438411)) % 181.55/181.53 [4564]~P91(x45641)+E(f92(x45641),a321) % 181.55/181.53 [4565]~P58(x45651)+P58(f869(x45651)) % 181.55/181.53 [4566]~P61(x45661)+P61(f869(x45661)) % 181.55/181.53 [4569]~P139(x45691)+~E(f79(x45691),f2(x45691)) % 181.55/181.53 [4571]~E(x45711,f2(a102))+E(f324(a20,x45711),f2(a1)) % 181.55/181.53 [4572]~E(x45721,f2(a1))+E(f83(a1,x45721),f2(a1)) % 181.55/181.53 [4578]~P141(x45781)+P32(x45781,f2(x45781)) % 181.55/181.53 [4580]~P105(x45801)+P16(x45801,f116(x45801)) % 181.55/181.53 [4589]P1(x45891)+P1(f324(a319,x45891)) % 181.55/181.53 [4632]~P141(x46321)+~P32(x46321,f79(x46321)) % 181.55/181.53 [4680]~P1(x46801)+~P1(f324(a319,x46801)) % 181.55/181.53 [4703]E(f324(a107,x47031),f2(a865))+~P1(f324(a196,x47031)) % 181.55/181.53 [4767]~P99(x47671)+P17(x47671,x47671,f104(x47671)) % 181.55/181.53 [4768]~P100(x47681)+P17(x47681,x47681,f113(x47681)) % 181.55/181.53 [4769]~P93(x47691)+P17(x47691,x47691,f82(x47691)) % 181.55/181.53 [4770]~P105(x47701)+P17(x47701,x47701,f189(x47701)) % 181.55/181.53 [4771]~P105(x47711)+P17(x47711,x47711,f190(x47711)) % 181.55/181.53 [4772]~P66(x47721)+P18(x47721,x47721,f82(x47721)) % 181.55/181.53 [4575]~E(x45751,f2(a865))+E(f324(f103(a1),x45751),f2(a1)) % 181.55/181.53 [4582]~P92(x45821)+E(f324(f106(x45821),a84),f2(x45821)) % 181.55/181.53 [4585]~E(f543(x45851),f2(a865))+E(f324(f160(a865),x45851),f2(a865)) % 181.55/181.53 [4586]~P104(x45861)+E(f240(x45861,f238(x45861)),f189(x45861)) % 181.55/181.53 [4587]~P104(x45871)+E(f241(x45871,f238(x45871)),f190(x45871)) % 181.55/181.53 [4588]~P86(x45881)+E(f83(x45881,f2(x45881)),f2(x45881)) % 181.55/181.53 [4597]~P135(x45971)+E(f324(f105(x45971),f79(a1)),f79(x45971)) % 181.55/181.53 [4598]~P135(x45981)+E(f324(f105(x45981),f2(a1)),f2(x45981)) % 181.55/181.53 [4599]~P141(x45991)+E(f324(f103(x45991),f79(a865)),f79(x45991)) % 181.55/181.53 [4600]~P141(x46001)+E(f324(f103(x46001),f2(a865)),f2(x46001)) % 181.55/181.53 [4601]E(x46011,f2(a865))+~E(f324(f103(a1),x46011),f2(a1)) % 181.55/181.53 [4626]~P79(x46261)+E(f324(f80(x46261),f191(x46261)),f247(x46261)) % 181.55/181.53 [4627]~P79(x46271)+E(f324(f80(x46271),f247(x46271)),f191(x46271)) % 181.55/181.53 [4628]~P4(x46281)+E(f324(f80(x46281),f2(x46281)),f2(x46281)) % 181.55/181.53 [4629]~P117(x46291)+E(f324(f75(x46291),f79(x46291)),f79(x46291)) % 181.55/181.53 [4630]~P83(x46301)+E(f324(f75(x46301),f2(x46301)),f2(x46301)) % 181.55/181.53 [4631]~P78(x46311)+E(f324(f160(x46311),f116(x46311)),f2(x46311)) % 181.55/181.53 [4652]~P38(x46521)+P40(f324(f167(a1),x46521)) % 181.55/181.53 [4685]~P92(x46851)+E(f324(f80(x46851),f79(x46851)),f324(f106(x46851),a100)) % 181.55/181.53 [4702]~P92(x47021)+P32(x47021,f324(f106(x47021),a84)) % 181.55/181.53 [4719]~P61(x47191)+E(f324(f167(x47191),f55(x47191)),f247(f871(x47191,a859))) % 181.55/181.53 [4729]P38(x47291)+~P40(f324(f167(a1),x47291)) % 181.55/181.53 [4730]~P61(x47301)+P1(f324(f131(x47301),f55(x47301))) % 181.55/181.53 [4773]E(f324(f103(a1),f324(a107,x47731)),x47731)+P1(f324(a196,x47731)) % 181.55/181.53 [4841]~P110(x48411)+E(f250(x48411,f79(x48411),f82(x48411)),f249(x48411)) % 181.55/181.53 [4871]~P92(x48711)+~P32(x48711,f324(f106(x48711),a100)) % 181.55/181.53 [5010]E(f324(f75(a1),x50101),x50101)+P1(f324(f324(f239(a1),x50101),f2(a1))) % 181.55/181.53 [5028]~E(f324(a107,x50281),f2(a865))+P1(f324(f324(f238(a1),x50281),f2(a1))) % 181.55/181.53 [5087]~P1(f324(a196,x50871))+P1(f324(f324(f239(a1),x50871),f2(a1))) % 181.55/181.53 [5127]~P135(x51271)+P1(f324(f324(f326(x51271),f79(x51271)),f112(x51271))) % 181.55/181.53 [5128]~P141(x51281)+P1(f324(f324(f326(x51281),f79(x51281)),f187(x51281))) % 181.55/181.53 [5129]~P135(x51291)+P1(f324(f324(f326(x51291),f2(x51291)),f112(x51291))) % 181.55/181.53 [5130]~P141(x51301)+P1(f324(f324(f326(x51301),f2(x51301)),f187(x51301))) % 181.55/181.53 [5131]~P120(x51311)+P1(f324(f324(f238(x51311),f2(x51311)),f79(x51311))) % 181.55/181.53 [5132]~P120(x51321)+P1(f324(f324(f239(x51321),f2(x51321)),f79(x51321))) % 181.55/181.53 [5181]E(x51811,f2(a865))+~P1(f324(f324(f238(a865),x51811),f2(a865))) % 181.55/181.53 [5223]E(f324(a107,x52231),f2(a865))+~P1(f324(f324(f238(a1),x52231),f2(a1))) % 181.55/181.53 [5283]P1(f324(a196,x52831))+~P1(f324(f324(f239(a1),x52831),f2(a1))) % 181.55/181.53 [5288]~P105(x52881)+P18(x52881,f866(x52881),f142(x52881,x52881,f5(x52881))) % 181.55/181.53 [5305]P40(x53051)+~P1(f324(f324(f238(a1),f2(a1)),f410(x53051))) % 181.55/181.53 [5311]E(f324(f75(a1),x53111),f324(f80(a1),x53111))+~P1(f324(f324(f239(a1),x53111),f2(a1))) % 181.55/181.53 [5483]~P120(x54831)+~P1(f324(f324(f238(x54831),f79(x54831)),f2(x54831))) % 181.55/181.53 [5484]~P120(x54841)+~P1(f324(f324(f239(x54841),f79(x54841)),f2(x54841))) % 181.55/181.53 [5494]~E(x54941,f2(a865))+P1(f324(f324(f238(a1),f324(f103(a1),x54941)),f2(a1))) % 181.55/181.53 [5495]~E(x54951,f2(a1))+P1(f324(f324(f239(a1),f324(f75(a1),x54951)),f79(a1))) % 181.55/181.53 [5613]~P78(x56131)+E(f136(x56131,x56131,f81(x56131),f2(x56131)),f160(x56131)) % 181.55/181.53 [5783]~P101(x57831)+P27(a865,x57831,f103(x57831),f247(f871(a865,a859))) % 181.55/181.53 [5972]E(x59721,f2(a865))+~P1(f324(f324(f238(a1),f324(f103(a1),x59721)),f2(a1))) % 181.55/181.53 [5973]E(x59731,f2(a1))+~P1(f324(f324(f239(a1),f324(f75(a1),x59731)),f79(a1))) % 181.55/181.53 [6759]~P1(f324(f324(f239(a1),x67591),f2(a1)))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x67591),x67591)),f2(a1))) % 181.55/181.53 [7300]P1(f324(f324(f239(a1),x73001),f2(a1)))+~P1(f324(f324(f239(a1),f324(f324(f81(a1),x73001),x73001)),f2(a1))) % 181.55/181.53 [7849]E(x78491,f324(a3,f2(a865)))+P1(f324(f324(f239(a865),f324(f324(f22(a865),f324(a19,x78491)),f324(a115,f2(a865)))),f324(a19,x78491))) % 181.55/181.53 [8616]~P1(f324(f324(f239(a1),x86161),f2(a1)))+P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x86161),x86161)),a100)),f2(a1))) % 181.55/181.53 [8713]~P1(f324(f324(f239(a1),x87131),f2(a1)))+P1(f324(f324(f239(a1),f324(f324(f81(a1),f324(f324(f81(a1),f79(a1)),x87131)),x87131)),f2(a1))) % 181.55/181.53 [9034]P1(f324(f324(f239(a1),x90341),f2(a1)))+~P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90341),x90341)),a100)),f2(a1))) % 181.55/181.53 [9096]P1(f324(f324(f239(a1),x90961),f2(a1)))+~P1(f324(f324(f239(a1),f324(f324(f81(a1),f324(f324(f81(a1),f79(a1)),x90961)),x90961)),f2(a1))) % 181.55/181.53 [4673]~E(a84,x46731)+E(f324(f324(f81(a1),x46731),x46731),a84) % 181.55/181.53 [4674]~E(x46741,a84)+E(f324(f324(f81(a1),x46741),x46741),a84) % 181.55/181.53 [4688]E(x46881,f2(a1))+E(f324(f324(f38(a1),x46881),x46881),f79(a1)) % 181.55/181.53 [4818]E(x48181,a84)+~E(f324(f324(f81(a1),x48181),x48181),a84) % 181.55/181.53 [4819]E(a84,x48191)+~E(f324(f324(f81(a1),x48191),x48191),a84) % 181.55/181.53 [4831]~P6(x48311)+E(f40(x48311,f191(f871(x48311,a859))),f247(x48311)) % 181.55/181.53 [4832]~P6(x48321)+E(f40(x48321,f247(f871(x48321,a859))),f191(x48321)) % 181.55/181.53 [4833]~P6(x48331)+E(f39(x48331,f191(f871(x48331,a859))),f191(x48331)) % 181.55/181.53 [4834]~P6(x48341)+E(f39(x48341,f247(f871(x48341,a859))),f247(x48341)) % 181.55/181.53 [4835]~P105(x48351)+E(f133(x48351,f191(f871(x48351,a859))),f116(x48351)) % 181.55/181.53 [4969]E(x49691,f2(a865))+P1(f324(f324(f239(a865),f2(a865)),x49691)) % 181.55/181.53 [4988]~P7(x49881)+P1(f324(f324(f238(a1),f2(a1)),x49881)) % 181.55/181.53 [5019]~E(f324(f106(a865),x50191),f2(a865))+P1(f324(f324(f238(a1),x50191),a84)) % 181.55/181.53 [5024]P40(x50241)+P1(f324(f324(f326(a1),f410(x50241)),x50241)) % 181.55/181.53 [5025]E(x50251,f324(a3,f2(a865)))+P1(f324(f324(f238(a102),f79(a102)),x50251)) % 181.55/181.53 [5062]P1(f324(a196,x50621))+P1(f324(f324(f238(a1),f2(a1)),x50621)) % 181.55/181.53 [5109]E(f324(f103(a1),f324(a107,x51091)),f2(a1))+P1(f324(f324(f238(a1),f2(a1)),x51091)) % 181.55/181.53 [5168]E(f324(f103(a1),f324(f106(a865),x51681)),f324(f106(a1),x51681))+P1(f324(a196,f324(f106(a1),x51681))) % 181.55/181.53 [5187]E(f324(f106(a865),x51871),f2(a865))+~P1(f324(a196,f324(f106(a1),x51871))) % 181.55/181.53 [5188]E(f324(f106(a865),x51881),f2(a865))+~P1(f324(f324(f238(a1),x51881),a84)) % 181.55/181.53 [5220]P7(x52201)+~P1(f324(f324(f238(a1),f2(a1)),x52201)) % 181.55/181.53 [5291]E(f324(a115,f331(x52911)),x52911)+~P1(f324(f324(f239(a865),f2(a865)),x52911)) % 181.55/181.53 [5299]E(f324(a115,f324(f106(a865),x52991)),f79(a865))+~P1(f324(a196,f324(f106(a1),x52991))) % 181.55/181.53 [5307]E(f324(f103(a1),f424(x53071)),x53071)+~P1(f324(f324(f239(a1),f2(a1)),x53071)) % 181.55/181.53 [5314]~E(x53141,f324(a3,f2(a865)))+~P1(f324(f324(f238(a102),f79(a102)),x53141)) % 181.55/181.53 [5321]E(f324(f103(a1),f324(f106(a865),x53211)),f2(a1))+~P1(f324(a196,f324(f106(a1),x53211))) % 181.55/181.53 [5347]E(f324(f160(a865),x53471),f2(a865))+P1(f324(f324(f326(a865),f543(x53471)),f324(f167(a865),x53471))) % 181.55/181.53 [5368]E(f324(f103(a1),f324(a107,x53681)),x53681)+~P1(f324(f324(f238(a1),f2(a1)),x53681)) % 181.55/181.53 [5377]~P1(f324(a196,x53771))+~P1(f324(f324(f238(a1),f2(a1)),x53771)) % 181.55/181.53 [5476]E(f324(f324(f81(a865),f79(a865)),f324(f106(a865),x54761)),f79(a865))+~P1(f324(f324(f239(a1),x54761),a84)) % 181.55/181.53 [5534]E(x55341,f2(a865))+~P1(f324(f324(f239(a865),x55341),f324(a115,f2(a865)))) % 181.55/181.53 [5572]E(f324(f324(f22(a865),f324(f106(a865),x55721)),f79(a865)),f2(a865))+~P1(f324(f324(f238(a1),x55721),a84)) % 181.55/181.53 [5573]E(f324(f324(f81(a865),f324(f106(a865),x55731)),f79(a865)),f79(a865))+~P1(f324(f324(f239(a1),x55731),a84)) % 181.55/181.53 [5583]~P40(x55831)+E(f324(f37(a865),f324(f303(a1,a865,a107),x55831)),f324(f37(a1),x55831)) % 181.55/181.53 [5614]~P105(x56141)+E(f240(x56141,f324(f7(x56141,x56141,a859),f238(x56141))),f190(x56141)) % 181.55/181.53 [5615]~P105(x56151)+E(f241(x56151,f324(f7(x56151,x56151,a859),f238(x56151))),f189(x56151)) % 181.55/181.53 [5625]E(f44(a865,f324(a115,f2(a865)),f324(f106(a865),x56251)),f324(a115,f2(a865)))+~P1(f324(a196,f324(f106(a1),x56251))) % 181.55/181.53 [5634]~P1(f324(f324(f239(a1),f2(a1)),x56341))+P1(f324(f324(f238(a1),f79(a1)),x56341)) % 181.55/181.53 [5635]P1(f324(f324(f239(a1),f2(a1)),x56351))+~P1(f324(f324(f238(a1),f79(a1)),x56351)) % 181.55/181.53 [5646]E(f324(a115,f324(f324(f22(a865),x56461),f79(a865))),x56461)+~P1(f324(f324(f239(a865),f2(a865)),x56461)) % 181.55/181.53 [5702]P1(f324(f324(f239(a865),f2(a865)),f424(x57021)))+~P1(f324(f324(f239(a1),f2(a1)),x57021)) % 181.55/181.53 [5761]E(f44(a1,f324(f106(a1),a100),x57611),f324(f324(f22(a1),x57611),f79(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x57611)) % 181.55/181.53 [5795]~P1(f324(f324(f239(a1),a84),x57951))+P1(f324(f324(f239(a865),f2(a865)),f324(f106(a865),x57951))) % 181.55/181.53 [5845]P1(f324(f324(f239(a865),f2(a865)),f324(a107,x58451)))+~P1(f324(f324(f239(a1),f2(a1)),x58451)) % 181.55/181.53 [5894]~P1(f324(f324(f239(a865),f2(a865)),x58941))+P1(f324(f324(f239(a1),f2(a1)),f324(f103(a1),x58941))) % 181.55/181.53 [5929]~P1(f324(f324(f239(a865),f2(a865)),f324(a107,x59291)))+P1(f324(f324(f239(a1),f2(a1)),x59291)) % 181.55/181.53 [5943]~P40(x59431)+E(f324(f303(a865,a1,f103(a1)),f324(f303(a1,a865,a107),x59431)),x59431) % 181.55/181.53 [5953]P1(f324(f324(f239(a1),a84),x59531))+~P1(f324(f324(f239(a865),f2(a865)),f324(f106(a865),x59531))) % 181.55/181.53 [6001]~P61(x60011)+E(f324(f324(f145(f869(x60011)),f203(x60011)),f324(f324(f148(x60011,f869(x60011)),f233(x60011)),f55(x60011))),f55(f869(x60011))) % 181.55/181.53 [6012]P1(f324(f324(f239(a865),f2(a865)),x60121))+~P1(f324(f324(f239(a1),f2(a1)),f324(f103(a1),x60121))) % 181.55/181.53 [6120]E(f324(f303(a865,a1,f103(a1)),f324(f245(a865),f324(a107,x61201))),f324(f294(a1,f2(a1)),x61201))+~P1(f324(f324(f238(a1),f2(a1)),x61201)) % 181.55/181.53 [6134]~P120(x61341)+P1(f324(f324(f239(x61341),f2(x61341)),f324(f324(f81(x61341),f79(x61341)),f79(x61341)))) % 181.55/181.53 [6185]P1(f324(f324(f239(a865),f324(a115,f2(a865))),f324(a107,x61851)))+~P1(f324(f324(f239(a1),f79(a1)),x61851)) % 181.55/181.53 [6279]E(x62791,f2(a1))+P1(f324(f48(f2(a1),x62791),f324(f324(f259(a1,a1),f2(a1)),f2(a1)))) % 181.55/181.53 [6444]~P1(f324(f324(f239(a865),f324(a115,f2(a865))),f324(a107,x64441)))+P1(f324(f324(f239(a1),f79(a1)),x64441)) % 181.55/181.53 [6869]~P111(x68691)+P39(x68691,f324(f244(f870(x68691,x68691)),f324(f263(x68691,x68691,a859),f239(x68691)))) % 181.55/181.53 [5521]E(f324(f106(a865),f324(f324(f22(a1),x55211),a100)),f324(a115,f324(f106(a865),x55211)))+P1(f324(a196,f324(f106(a1),x55211))) % 181.55/181.53 [5537]~P38(x55371)+E(f324(f324(f148(a865,a1),f103(a1)),f324(f324(f148(a1,a865),a107),x55371)),x55371) % 181.55/181.53 [5652]E(f324(f80(a1),f324(f103(a1),f324(a115,f425(x56521)))),x56521)+~P1(f324(f324(f239(a1),x56521),f2(a1))) % 181.55/181.53 [5662]E(f324(f324(f81(a865),f79(a865)),f324(f106(a865),x56621)),f324(f106(a865),f324(f324(f22(a1),x56621),a100)))+P1(f324(f324(f239(a1),x56621),a84)) % 181.55/181.53 [5704]E(f324(f324(f38(a1),f324(f106(a1),a100)),x57041),f324(f106(a1),a100))+~P1(f324(f324(f239(a1),f2(a1)),x57041)) % 181.55/181.53 [5791]E(f324(f324(f22(a865),f324(f106(a865),x57911)),f79(a865)),f324(f106(a865),f324(f324(f81(a1),x57911),a100)))+P1(f324(f324(f238(a1),x57911),a84)) % 181.55/181.53 [5792]E(f324(f324(f81(a865),f324(f106(a865),x57921)),f79(a865)),f324(f106(a865),f324(f324(f22(a1),x57921),a100)))+P1(f324(f324(f239(a1),x57921),a84)) % 181.55/181.53 [5833]E(f324(a107,f324(f324(f81(a1),f79(a1)),x58331)),f324(a115,f324(a107,x58331)))+~P1(f324(f324(f238(a1),f2(a1)),x58331)) % 181.55/181.53 [5867]E(f324(a115,f324(f324(f22(a865),x58671),f324(a115,f2(a865)))),x58671)+~P1(f324(f324(f239(a865),f2(a865)),x58671)) % 181.55/181.53 [6071]E(f44(a865,f324(a115,f2(a865)),f324(f106(a865),x60711)),f324(a107,f44(a1,f79(a1),f324(f106(a1),x60711))))+P1(f324(a196,f324(f106(a1),x60711))) % 181.55/181.53 [6110]~P1(f324(f324(f238(a1),a84),x61101))+P1(f324(f324(f238(a1),a84),f324(f324(f81(a1),x61101),x61101))) % 181.55/181.53 [6111]~P1(f324(f324(f239(a1),a100),x61111))+P1(f324(f324(f238(a1),a100),f324(f324(f81(a1),x61111),x61111))) % 181.55/181.53 [6112]~P1(f324(f324(f239(a1),a84),x61121))+P1(f324(f324(f239(a1),a84),f324(f324(f81(a1),x61121),x61121))) % 181.55/181.53 [6113]~P1(f324(f324(f239(a1),a100),x61131))+P1(f324(f324(f239(a1),a100),f324(f324(f81(a1),x61131),x61131))) % 181.55/181.53 [6114]~P1(f324(f324(f92(a1),a84),x61141))+P1(f324(f324(f92(a1),a84),f324(f324(f81(a1),x61141),x61141))) % 181.55/181.53 [6292]~P1(f324(f61(x62921),f247(f871(x62921,a859))))+P1(f324(f61(f869(x62921)),f247(f871(f869(x62921),a859)))) % 181.55/181.53 [6378]~P1(f324(f324(f238(a1),f2(a1)),x63781))+P1(f324(f324(f239(a1),f2(a1)),f324(f324(f81(a1),f79(a1)),x63781))) % 181.55/181.53 [6385]E(f324(f258(a1,a1),f46(f79(a1),f324(f106(a1),x63851))),f324(f324(f38(a1),f79(a1)),f324(f106(a1),x63851)))+~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x63851))) % 181.55/181.53 [6405]E(f324(f262(a1,a1),f46(f79(a1),f324(f106(a1),x64051))),f44(a1,f79(a1),f324(f106(a1),x64051)))+~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x64051))) % 181.55/181.53 [6416]P1(f324(f61(x64161),f247(f871(x64161,a859))))+~P1(f324(f61(f869(x64161)),f247(f871(f869(x64161),a859)))) % 181.55/181.53 [6445]P1(f324(f324(f238(a1),a84),x64451))+~P1(f324(f324(f238(a1),a84),f324(f324(f81(a1),x64451),x64451))) % 181.55/181.53 [6446]P1(f324(f324(f239(a1),a84),x64461))+~P1(f324(f324(f239(a1),a84),f324(f324(f81(a1),x64461),x64461))) % 181.55/181.53 [6447]P1(f324(f324(f239(a1),a100),x64471))+~P1(f324(f324(f238(a1),a100),f324(f324(f81(a1),x64471),x64471))) % 181.55/181.53 [6448]P1(f324(f324(f239(a1),a100),x64481))+~P1(f324(f324(f239(a1),a100),f324(f324(f81(a1),x64481),x64481))) % 181.55/181.53 [6449]P1(f324(f324(f92(a1),a84),x64491))+~P1(f324(f324(f92(a1),a84),f324(f324(f81(a1),x64491),x64491))) % 181.55/181.53 [6763]~P1(f324(f61(x67631),f247(f871(x67631,a859))))+P1(f324(f324(f239(a865),f2(a865)),f324(f37(x67631),f247(f871(x67631,a859))))) % 181.55/181.53 [7342]P1(f324(f61(a865),x73421))+~P1(f324(f61(a1),f324(f303(a865,a1,f103(a1)),x73421))) % 181.55/181.53 [5451]~E(a100,x54511)+E(f324(f324(f22(a1),f324(f324(f81(a1),x54511),x54511)),a100),a100) % 181.55/181.53 [5452]~E(x54521,a100)+E(f324(f324(f22(a1),f324(f324(f81(a1),x54521),x54521)),a100),a100) % 181.55/181.53 [5948]E(x59481,a100)+~E(f324(f324(f22(a1),f324(f324(f81(a1),x59481),x59481)),a100),a100) % 181.55/181.53 [5949]E(a100,x59491)+~E(f324(f324(f22(a1),f324(f324(f81(a1),x59491),x59491)),a100),a100) % 181.55/181.53 [6346]~E(f324(f106(a865),x63461),f2(a865))+P1(f324(a196,f324(f106(a1),f324(f324(f81(a1),x63461),a100)))) % 181.55/181.53 [6690]~P1(f324(a196,f324(f106(a1),x66901)))+P1(f324(a196,f324(f106(a1),f324(f324(f81(a1),x66901),x66901)))) % 181.55/181.53 [6691]~P1(f324(f324(f238(a1),x66911),a84))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x66911),x66911)),a84)) % 181.55/181.53 [6692]~P1(f324(f324(f238(a1),x66921),a100))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x66921),x66921)),a100)) % 181.55/181.53 [6693]~P1(f324(f324(f239(a1),x66931),a84))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x66931),x66931)),a84)) % 181.55/181.53 [6694]~P1(f324(f324(f238(a1),x66941),a100))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x66941),x66941)),a100)) % 181.55/181.53 [6695]~P1(f324(f324(f92(a1),x66951),a84))+P1(f324(f324(f92(a1),f324(f324(f81(a1),x66951),x66951)),a84)) % 181.55/181.53 [7013]E(f324(f106(a865),x70131),f2(a865))+~P1(f324(a196,f324(f106(a1),f324(f324(f81(a1),x70131),a100)))) % 181.55/181.53 [7251]~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x72511)))+P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),f324(f324(f81(a1),x72511),x72511)))) % 181.55/181.53 [7252]P1(f324(a196,f324(f106(a1),x72521)))+~P1(f324(a196,f324(f106(a1),f324(f324(f81(a1),x72521),x72521)))) % 181.55/181.53 [7253]P1(f324(f324(f238(a1),x72531),a84))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),x72531),x72531)),a84)) % 181.55/181.53 [7254]P1(f324(f324(f238(a1),x72541),a100))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),x72541),x72541)),a100)) % 181.55/181.53 [7255]P1(f324(f324(f238(a1),x72551),a100))+~P1(f324(f324(f239(a1),f324(f324(f81(a1),x72551),x72551)),a100)) % 181.55/181.53 [7256]P1(f324(f324(f239(a1),x72561),a84))+~P1(f324(f324(f239(a1),f324(f324(f81(a1),x72561),x72561)),a84)) % 181.55/181.53 [7257]P1(f324(f324(f92(a1),x72571),a84))+~P1(f324(f324(f92(a1),f324(f324(f81(a1),x72571),x72571)),a84)) % 181.55/181.53 [7621]E(f324(a110,f536(x76211)),x76211)+~P1(f324(f324(f326(f871(f870(a865,a865),a859)),x76211),a101)) % 181.55/181.53 [6265]~P92(x62651)+E(f324(f106(x62651),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f79(x62651)) % 181.55/181.53 [6742]~P1(f324(a196,f324(f106(a1),x67421)))+E(f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),x67421),x67421)),a100)),f2(a865)) % 181.55/181.53 [7792]~P1(f324(f324(f239(a1),f324(f106(a1),x77921)),f2(a1)))+E(f324(f258(a1,a1),f324(a50,f49(f324(f80(a1),f79(a1)),f324(f80(a1),f324(f106(a1),x77921))))),f324(f324(f38(a1),f79(a1)),f324(f106(a1),x77921))) % 181.55/181.53 [7806]~P1(f324(f324(f239(a1),f324(f106(a1),x78061)),f2(a1)))+E(f324(f262(a1,a1),f324(a50,f49(f324(f80(a1),f79(a1)),f324(f80(a1),f324(f106(a1),x78061))))),f44(a1,f79(a1),f324(f106(a1),x78061))) % 181.55/181.53 [7855]~P1(f324(f324(f238(a1),a84),x78551))+P1(f324(f324(f238(a1),a84),f324(f324(f22(a1),f324(f324(f81(a1),x78551),x78551)),a100))) % 181.55/181.53 [7856]~P1(f324(f324(f238(a1),a100),x78561))+P1(f324(f324(f238(a1),a100),f324(f324(f22(a1),f324(f324(f81(a1),x78561),x78561)),a100))) % 181.55/181.53 [7857]~P1(f324(f324(f238(a1),a84),x78571))+P1(f324(f324(f239(a1),a84),f324(f324(f22(a1),f324(f324(f81(a1),x78571),x78571)),a100))) % 181.55/181.53 [7858]~P1(f324(f324(f239(a1),a100),x78581))+P1(f324(f324(f239(a1),a100),f324(f324(f22(a1),f324(f324(f81(a1),x78581),x78581)),a100))) % 181.55/181.53 [7859]~P1(f324(f324(f92(a1),a100),x78591))+P1(f324(f324(f92(a1),a100),f324(f324(f22(a1),f324(f324(f81(a1),x78591),x78591)),a100))) % 181.55/181.53 [8161]~P92(x81611)+~P32(x81611,f324(f106(x81611),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))) % 181.55/181.53 [8344]P1(f324(f324(f238(a1),a84),x83441))+~P1(f324(f324(f238(a1),a84),f324(f324(f22(a1),f324(f324(f81(a1),x83441),x83441)),a100))) % 181.55/181.53 [8345]P1(f324(f324(f238(a1),a84),x83451))+~P1(f324(f324(f239(a1),a84),f324(f324(f22(a1),f324(f324(f81(a1),x83451),x83451)),a100))) % 181.55/181.53 [8346]P1(f324(f324(f238(a1),a100),x83461))+~P1(f324(f324(f238(a1),a100),f324(f324(f22(a1),f324(f324(f81(a1),x83461),x83461)),a100))) % 181.55/181.53 [8347]P1(f324(f324(f239(a1),a100),x83471))+~P1(f324(f324(f239(a1),a100),f324(f324(f22(a1),f324(f324(f81(a1),x83471),x83471)),a100))) % 181.55/181.53 [8348]P1(f324(f324(f92(a1),a100),x83481))+~P1(f324(f324(f92(a1),a100),f324(f324(f22(a1),f324(f324(f81(a1),x83481),x83481)),a100))) % 181.55/181.53 [8663]E(f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),x86631),x86631)),a100)),f324(f324(f87(a865,a865),f324(f106(a865),x86631)),f324(f324(f8(a865,a865,a865),a115),f324(f324(f18(a865,a865,a865),f81(a865)),f5(a865)))))+P1(f324(a196,f324(f106(a1),x86631))) % 181.55/181.53 [9520]E(x95201,f191(f871(f870(a865,a865),a859)))+P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),x95201),f191(f871(f870(a865,a865),a859)))),a68)) % 181.55/181.53 [8589]~P1(f324(a196,f324(f106(a1),x85891)))+P1(f324(a196,f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),x85891),x85891)),a100)))) % 181.55/181.53 [8590]~P1(f324(f324(f239(a1),x85901),a84))+P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),x85901),x85901)),a100)),a84)) % 181.55/181.53 [8591]~P1(f324(f324(f238(a1),x85911),a100))+P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),x85911),x85911)),a100)),a100)) % 181.55/181.53 [8592]~P1(f324(f324(f239(a1),x85921),a84))+P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x85921),x85921)),a100)),a84)) % 181.55/181.53 [8593]~P1(f324(f324(f239(a1),x85931),a100))+P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x85931),x85931)),a100)),a100)) % 181.55/181.53 [8594]~P1(f324(f324(f92(a1),x85941),a100))+P1(f324(f324(f92(a1),f324(f324(f22(a1),f324(f324(f81(a1),x85941),x85941)),a100)),a100)) % 181.55/181.53 [8704]~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x87041)))+P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),x87041),x87041)),a100)))) % 181.55/181.53 [8865]~P92(x88651)+E(f324(f324(f81(x88651),f79(x88651)),f79(x88651)),f324(f106(x88651),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))) % 181.55/181.53 [9017]P1(f324(a196,f324(f106(a1),x90171)))+~P1(f324(a196,f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90171),x90171)),a100)))) % 181.55/181.53 [9018]P1(f324(f324(f238(a1),x90181),a100))+~P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90181),x90181)),a100)),a100)) % 181.55/181.53 [9019]P1(f324(f324(f239(a1),x90191),a84))+~P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90191),x90191)),a100)),a84)) % 181.55/181.53 [9020]P1(f324(f324(f239(a1),x90201),a84))+~P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90201),x90201)),a100)),a84)) % 181.55/181.53 [9021]P1(f324(f324(f239(a1),x90211),a100))+~P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90211),x90211)),a100)),a100)) % 181.55/181.53 [9022]P1(f324(f324(f92(a1),x90221),a100))+~P1(f324(f324(f92(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90221),x90221)),a100)),a100)) % 181.55/181.53 [9567]~P1(f324(f61(f870(a865,a865)),x95671))+P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),f191(f871(f870(a865,a865),a859))),x95671)),a69)) % 181.55/181.53 [9343]~P141(x93431)+E(f324(f324(f249(x93431),f79(x93431)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f79(x93431)) % 181.55/181.53 [9344]~P141(x93441)+E(f324(f324(f249(x93441),f2(x93441)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f2(x93441)) % 181.55/181.53 [9798]~P1(f324(f324(f239(a865),f79(a865)),x97981))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f38(a865),x97981),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.53 [9808]~P1(f324(f324(f239(a865),f2(a865)),x98081))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f38(a865),f324(f324(f81(a865),x98081),f79(a865))),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.53 [9849]~E(f44(a865,x98491,f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f79(a865))+P1(f324(f324(f239(a865),f2(a865)),f44(a865,x98491,f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.53 [9869]E(f44(a865,x98691,f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f79(a865))+~P1(f324(f324(f239(a865),f2(a865)),f44(a865,x98691,f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.53 [4605]~P39(x46051,x46052)+P55(x46051,x46052) % 181.55/181.53 [4606]~P45(x46061,x46062)+P55(x46061,x46062) % 181.55/181.53 [4567]~E(x45671,x45672)+E(f271(x45671,x45672),f79(a102)) % 181.55/181.53 [4570]E(f221(x45701,x45702),x45701)+~E(x45702,f2(a865)) % 181.55/181.53 [4577]~E(x45772,f116(x45771))+E(f146(x45771,x45772),f116(x45771)) % 181.55/181.53 [4596]~E(f146(x45962,x45961),f116(x45962))+E(x45961,f116(x45962)) % 181.55/181.53 [4610]~P2(x46102)+P2(f871(x46101,x46102)) % 181.55/181.53 [4611]~P3(x46112)+P3(f871(x46111,x46112)) % 181.55/181.53 [4612]~P103(x46122)+P103(f871(x46121,x46122)) % 181.55/181.53 [4613]~P107(x46132)+P107(f871(x46131,x46132)) % 181.55/181.53 [4614]~P104(x46142)+P104(f871(x46141,x46142)) % 181.55/181.53 [4615]~P106(x46152)+P106(f871(x46151,x46152)) % 181.55/181.53 [4616]~P79(x46162)+P79(f871(x46161,x46162)) % 181.55/181.53 [4617]~P80(x46172)+P80(f871(x46171,x46172)) % 181.55/181.53 [4618]~P6(x46182)+P6(f871(x46181,x46182)) % 181.55/181.53 [4619]~P94(x46192)+P94(f871(x46191,x46192)) % 181.55/181.53 [4620]~P94(x46202)+P99(f871(x46201,x46202)) % 181.55/181.53 [4621]~P96(x46212)+P95(f871(x46211,x46212)) % 181.55/181.53 [4622]~P96(x46222)+P97(f871(x46221,x46222)) % 181.55/181.53 [4623]~P94(x46232)+P100(f871(x46231,x46232)) % 181.55/181.53 [4624]~P98(x46242)+P98(f871(x46241,x46242)) % 181.55/181.53 [4625]~P96(x46252)+P96(f871(x46251,x46252)) % 181.55/181.53 [4637]E(x46371,x46372)+~E(f324(a25,x46371),f324(a25,x46372)) % 181.55/181.53 [4639]E(x46391,x46392)+~E(f324(a115,x46391),f324(a115,x46392)) % 181.55/181.53 [4640]E(x46401,x46402)+~E(f324(a110,x46401),f324(a110,x46402)) % 181.55/181.53 [4641]E(x46411,x46412)+~E(f324(a3,x46411),f324(a3,x46412)) % 181.55/181.53 [4643]E(x46431,x46432)+~E(f324(a19,x46431),f324(a19,x46432)) % 181.55/181.53 [4746]~P59(x47461)+E(f44(x47461,x47462,x47462),f2(x47461)) % 181.55/181.53 [4780]~P39(x47801,x47802)+P39(f866(x47801),f140(x47801,x47802)) % 181.55/181.53 [4781]~P39(x47811,x47812)+P39(f866(x47811),f139(x47811,x47812)) % 181.55/181.53 [4876]~P39(x48761,x48762)+P39(f871(x48761,a859),f315(x48761,x48762)) % 181.55/181.53 [4877]~P39(x48771,x48772)+P39(f871(x48771,a859),f317(x48771,x48772)) % 181.55/181.53 [4994]~P7(x49941)+P40(f295(a1,x49941,x49942)) % 181.55/181.53 [5090]~P39(x50901,x50902)+P57(x50901,f67(x50901,x50901,x50902)) % 181.55/181.53 [5577]~P75(x55771)+P27(x55771,x55771,f80(x55771),x55772) % 181.55/181.53 [4591]~E(x45912,f116(x45911))+E(f324(f162(x45911),x45912),f116(x45911)) % 181.55/181.53 [4592]~E(x45922,f116(x45921))+E(f324(f163(x45921),x45922),f116(x45921)) % 181.55/181.53 [4647]E(x46471,f324(a107,x46472))+~E(f324(f103(a1),x46471),x46472) % 181.55/181.53 [4650]E(x46501,f116(x46502))+~E(f324(f162(x46502),x46501),f116(x46502)) % 181.55/181.53 [4651]E(x46511,f116(x46512))+~E(f324(f163(x46512),x46511),f116(x46512)) % 181.55/181.53 [4670]~P92(x46701)+E(f324(f106(x46701),x46702),f324(f105(x46701),x46702)) % 181.55/181.53 [4677]~E(x46772,f203(x46771))+E(f232(x46771,x46772),f191(f871(x46771,a859))) % 181.55/181.53 [4679]~P58(x46791)+P1(f324(f61(x46791),x46792)) % 181.55/181.53 [4686]E(x46861,f203(x46862))+E(f324(f233(x46862),f666(x46862,x46861)),x46861) % 181.55/181.53 [4687]E(x46871,f203(x46872))+E(f324(f233(x46872),f823(x46872,x46871)),x46871) % 181.55/181.53 [4689]~E(f667(x46892,x46891),f116(x46891))+E(f175(x46891,x46892),f116(f866(x46891))) % 181.55/181.53 [4698]~E(x46982,f116(x46981))+E(f324(f167(x46981),x46982),f191(f871(x46981,a859))) % 181.55/181.53 [4699]~E(x46992,f116(x46991))+E(f191(f871(x46991,a859)),f324(f167(x46991),x46992)) % 181.55/181.53 [4701]E(x47011,x47012)+~E(f324(f103(a1),x47011),f324(f103(a1),x47012)) % 181.55/181.53 [4704]E(f219(x47041,x47042),f2(a865))+P1(f324(f61(x47041),x47042)) % 181.55/181.53 [4724]~P117(x47241)+E(f83(x47241,f83(x47241,x47242)),f83(x47241,x47242)) % 181.55/181.53 [4737]~P77(x47371)+E(f324(f324(f249(x47371),x47372),f79(a865)),x47372) % 181.55/181.53 [4738]~P112(x47381)+E(f324(f324(f249(x47381),x47382),f79(a865)),x47382) % 181.55/181.53 [4740]E(x47401,x47402)+E(f271(x47401,x47402),f324(f324(f81(a102),x47402),f79(a102))) % 181.55/181.53 [4743]E(f324(f37(x47431),x47432),f2(a865))+P1(f324(f61(x47431),x47432)) % 181.55/181.53 [4747]~E(f146(x47471,x47472),x47472)+P1(f324(f131(x47471),x47472)) % 181.55/181.53 [4750]~P4(x47501)+E(f324(f324(f22(x47501),x47502),f2(x47501)),x47502) % 181.55/181.53 [4751]~P97(x47511)+E(f324(f324(f104(x47511),x47512),f247(x47511)),x47512) % 181.55/181.53 [4752]~P95(x47521)+E(f324(f324(f113(x47521),x47522),f191(x47521)),x47522) % 181.55/181.53 [4753]~P77(x47531)+E(f324(f324(f82(x47531),x47532),f79(x47531)),x47532) % 181.55/181.53 [4754]~P68(x47541)+E(f324(f324(f82(x47541),x47542),f79(x47541)),x47542) % 181.55/181.53 [4755]~P112(x47551)+E(f324(f324(f82(x47551),x47552),f79(x47551)),x47552) % 181.55/181.53 [4756]~P112(x47561)+E(f324(f324(f81(x47561),x47562),f2(x47561)),x47562) % 181.55/181.53 [4757]~P72(x47571)+E(f324(f324(f81(x47571),x47572),f2(x47571)),x47572) % 181.55/181.53 [4758]~P78(x47581)+E(f324(f324(f81(x47581),x47582),f2(x47581)),x47582) % 181.55/181.53 [4759]~P59(x47591)+E(f324(f324(f38(x47591),x47592),f79(x47591)),x47592) % 181.55/181.53 [4760]~P114(x47601)+E(f324(f324(f282(x47601),x47602),f79(x47601)),x47602) % 181.55/181.53 [4761]~P112(x47611)+E(f324(f324(f249(x47611),x47612),f2(a865)),f79(x47611)) % 181.55/181.53 [4762]~P110(x47621)+E(f324(f324(f249(x47621),x47622),f2(a865)),f79(x47621)) % 181.55/181.53 [4763]~E(x47632,f191(f871(x47631,a859)))+E(f324(f37(x47631),x47632),f2(a865)) % 181.55/181.53 [4774]~P59(x47741)+E(f44(x47741,x47742,f2(x47741)),x47742) % 181.55/181.53 [4782]~P95(x47821)+E(f324(f324(f104(x47821),x47822),f191(x47821)),f191(x47821)) % 181.55/181.53 [4783]~P97(x47831)+E(f324(f324(f113(x47831),x47832),f247(x47831)),f247(x47831)) % 181.55/181.53 [4784]~P112(x47841)+E(f324(f324(f82(x47841),x47842),f2(x47841)),f2(x47841)) % 181.55/181.53 [4785]~P125(x47851)+E(f324(f324(f82(x47851),x47852),f2(x47851)),f2(x47851)) % 181.55/181.53 [4786]~P59(x47861)+E(f324(f324(f38(x47861),x47862),f2(x47861)),f2(x47861)) % 181.55/181.53 [4787]~P115(x47871)+E(f324(f324(f282(x47871),x47872),f2(x47871)),f2(x47871)) % 181.55/181.53 [4788]E(x47881,f203(x47882))+~E(f232(x47882,x47881),f191(f871(x47882,a859))) % 181.55/181.53 [4790]~P59(x47901)+E(f44(x47901,x47902,f79(x47901)),f2(x47901)) % 181.55/181.53 [4791]~P59(x47911)+E(f44(x47911,f2(x47911),x47912),f2(x47911)) % 181.55/181.53 [4820]E(x48201,f2(a865))+E(f54(x48202,x48201,f116(x48202)),f116(f866(x48202))) % 181.55/181.53 [4843]P39(x48431,x48432)+~E(f544(x48432,x48431),f191(f871(x48431,a859))) % 181.55/181.53 [4844]E(x48441,f116(x48442))+~E(f324(f167(x48442),x48441),f191(f871(x48442,a859))) % 181.55/181.53 [4845]E(x48451,f116(x48452))+~E(f191(f871(x48452,a859)),f324(f167(x48452),x48451)) % 181.55/181.53 [4848]~E(x48481,x48482)+P1(f324(f324(a321,x48481),x48482)) % 181.55/181.53 [4858]P1(x48581)+P1(f324(f324(a327,x48581),x48582)) % 181.55/181.53 [4859]E(x48591,f116(x48592))+E(f324(f324(f159(x48592),x48591),f2(a865)),f324(f135(x48592),x48591)) % 181.55/181.53 [4862]E(f146(x48621,x48622),x48622)+~P1(f324(f131(x48621),x48622)) % 181.55/181.53 [4867]~P1(x48672)+P1(f324(f324(a327,x48671),x48672)) % 181.55/181.53 [4868]~P1(x48682)+P1(f324(f324(a323,x48681),x48682)) % 181.55/181.53 [4869]~P1(x48691)+P1(f324(f324(a323,x48691),x48692)) % 181.55/181.53 [4879]~E(f668(x48792,x48791),f680(x48792,x48791))+P1(f324(f131(x48791),x48792)) % 181.55/181.53 [4886]E(f324(f244(x48861),x48862),f191(f871(x48861,a859)))+P1(f324(x48862,f567(x48862))) % 181.55/181.53 [4887]E(f191(f871(x48871,a859)),f324(f244(x48871),x48872))+P1(f324(x48872,f583(x48872))) % 181.55/181.53 [4951]~P117(x49511)+E(f324(f324(f82(x49511),x49512),f83(x49511,x49512)),f324(f75(x49511),x49512)) % 181.55/181.53 [4962]~E(x49621,f2(a1))+E(f45(x49621,x49622),f324(f324(f259(a1,a1),f2(a1)),f2(a1))) % 181.55/181.53 [4993]~P55(x49931,x49932)+P55(x49931,f324(f279(x49931,x49931),x49932)) % 181.55/181.53 [5015]E(x50151,x50152)+~P1(f324(f324(a321,x50151),x50152)) % 181.55/181.53 [5026]P1(x50261)+~P1(f324(f324(a322,x50262),x50261)) % 181.55/181.53 [5027]P1(x50271)+~P1(f324(f324(a322,x50271),x50272)) % 181.55/181.53 [5031]~P107(x50311)+P1(f324(f324(f238(x50311),x50312),f247(x50311))) % 181.55/181.53 [5035]E(x50351,x50352)+~E(f324(x50351,f423(x50352,x50351)),f324(x50352,f423(x50352,x50351))) % 181.55/181.53 [5064]E(x50641,f2(a865))+E(f221(x50641,f44(a865,x50642,x50641)),f221(x50642,x50641)) % 181.55/181.53 [5069]~P105(x50691)+P16(x50691,f324(f324(f145(x50691),x50692),f116(x50691))) % 181.55/181.53 [5071]E(x50711,f2(a1))+P1(f324(f48(x50712,x50711),f45(x50712,x50711))) % 181.55/181.53 [5088]~E(x50881,x50882)+P1(f324(f324(f239(a865),x50881),f324(a115,x50882))) % 181.55/181.53 [5098]~E(x50981,f2(a865))+P1(f324(f324(f239(a865),x50981),f324(a115,x50982))) % 181.55/181.53 [5108]P1(f324(x51081,x51082))+P1(f324(f324(f238(a1),f2(a1)),f405(x51081))) % 181.55/181.53 [5172]P55(x51721,x51722)+~P55(x51721,f324(f279(x51721,x51721),x51722)) % 181.55/181.53 [5174]~E(f44(a865,x51742,x51741),f2(a865))+E(f324(f324(f82(a865),x51741),f374(x51741,x51742)),x51742) % 181.55/181.53 [5175]~E(f44(a1,x51752,x51751),f2(a1))+E(f324(f324(f82(a1),x51751),f375(x51751,x51752)),x51752) % 181.55/181.53 [5199]~P1(f324(x51991,x51992))+P1(f324(f324(f238(a1),f2(a1)),f373(x51991))) % 181.55/181.53 [5211]E(f324(f324(f22(a865),f324(a107,x52111)),f324(a107,x52112)),f324(a107,x52111))+~P1(f324(a196,x52112)) % 181.55/181.53 [5240]E(f272(x52401,x52402),f79(a102))+~P1(f324(f324(f238(a102),x52401),f79(a102))) % 181.55/181.53 [5333]E(f324(f324(f159(x53331),x53332),f668(x53332,x53331)),f324(f324(f159(x53331),x53332),f680(x53332,x53331)))+P1(f324(f131(x53331),x53332)) % 181.55/181.53 [5378]~P1(f324(x53781,f91(x53782,x53781)))+P1(f324(x53781,f568(x53782,x53781))) % 181.55/181.53 [5441]P57(x54411,x54412)+~P1(f324(f312(x54411,x54412),f486(x54412,x54411))) % 181.55/181.53 [5584]~E(f324(a115,f44(a865,x55841,x55842)),x55842)+E(f44(a865,f324(a115,x55841),x55842),f2(a865)) % 181.55/181.53 [5641]P39(x56411,x56412)+P1(f324(f324(f326(x56411),f602(x56412,x56411)),f603(x56412,x56411))) % 181.55/181.53 [5648]~P92(x56481)+P1(f324(f324(f326(x56481),f324(f106(x56481),x56482)),f112(x56481))) % 181.55/181.53 [5649]~P135(x56491)+P1(f324(f324(f326(x56491),f324(f105(x56491),x56492)),f112(x56491))) % 181.55/181.53 [5650]~P135(x56501)+P1(f324(f324(f326(x56501),f324(f103(x56501),x56502)),f112(x56501))) % 181.55/181.53 [5651]~P141(x56511)+P1(f324(f324(f326(x56511),f324(f103(x56511),x56512)),f187(x56511))) % 181.55/181.53 [5794]E(f324(a115,f44(a865,x57941,x57942)),x57942)+E(f44(a865,f324(a115,x57941),x57942),f324(a115,f44(a865,x57941,x57942))) % 181.55/181.53 [6197]P39(x61971,x61972)+~P1(f324(f324(f326(x61971),f487(x61972,x61971)),f313(x61971,x61972))) % 181.55/181.53 [6231]~P120(x62311)+~P1(f324(f324(f239(x62311),f324(f103(x62311),x62312)),f2(x62311))) % 181.55/181.53 [6232]~P83(x62321)+~P1(f324(f324(f239(x62321),f324(f75(x62321),x62322)),f2(x62321))) % 181.55/181.53 [6319]P1(f324(f324(f239(a1),x63191),f44(a1,x63192,x63191)))+~P1(f324(f324(f239(a1),x63191),f2(a1))) % 181.55/181.53 [6418]E(f324(f324(f302(a865),f324(a115,x64181)),f295(a865,x64182,x64181)),f295(a865,x64182,f324(a115,x64181)))+~P1(f324(f324(f238(a865),x64182),f324(a115,x64181))) % 181.55/181.53 [6506]~P105(x65061)+P16(x65061,f144(x65061,x65061,f5(x65061),x65062)) % 181.55/181.53 [6634]E(f324(f162(x66341),x66342),x66342)+~P1(f324(f324(f238(a865),f324(f192(f866(x66341)),x66342)),f79(a865))) % 181.55/181.53 [6654]~P83(x66541)+P1(f324(f324(f238(x66541),f324(f80(x66541),f324(f75(x66541),x66542))),f2(x66541))) % 181.55/181.53 [6687]~P39(x66871,x66872)+P39(x66871,f324(f324(f281(x66871,x66871,x66871),x66872),f300(x66871,x66872))) % 181.55/181.53 [6907]~P1(f324(f324(f239(a1),x69072),f2(a1)))+P1(f324(f324(f238(a1),f44(a1,x69071,x69072)),f2(a1))) % 181.55/181.53 [7296]~P141(x72961)+E(f193(x72961,f324(f324(f7(x72961,x72961,x72961),f81(x72961)),f79(x72961)),x72962,f2(x72961)),f324(f103(x72961),x72962)) % 181.55/181.53 [7325]~P122(x73251)+~P1(f324(f324(f239(x73251),f324(f324(f82(x73251),x73252),x73252)),f2(x73251))) % 181.55/181.53 [9959]~P117(x99591)+~P1(f324(f324(f239(x99591),f324(f324(f249(x99591),x99592),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f2(x99591))) % 181.55/181.53 [4648]~E(x46482,f116(x46481))+E(f324(f192(f866(x46481)),x46482),f2(a865)) % 181.55/181.53 [4690]~E(x46901,f2(a865))+E(f324(f324(f81(a865),x46901),x46902),x46902) % 181.55/181.53 [4691]~E(x46912,f2(a865))+E(f324(f324(f82(a865),x46911),x46912),f2(a865)) % 181.55/181.53 [4693]~E(x46931,f2(a865))+E(f324(f324(f82(a865),x46931),x46932),f2(a865)) % 181.55/181.53 [4694]~E(x46942,f2(a865))+E(f324(f324(f249(a865),x46941),x46942),f79(a865)) % 181.55/181.53 [4695]~E(x46952,f2(a1))+E(f324(f324(f38(a1),x46951),x46952),f2(a1)) % 181.55/181.53 [4705]E(x47051,f116(x47052))+~E(f324(f192(f866(x47052)),x47051),f2(a865)) % 181.55/181.53 [4706]~P94(x47061)+E(f324(f324(f104(x47061),x47062),x47062),x47062) % 181.55/181.53 [4708]~P99(x47081)+E(f324(f324(f104(x47081),x47082),x47082),x47082) % 181.55/181.53 [4709]~P94(x47091)+E(f324(f324(f113(x47091),x47092),x47092),x47092) % 181.55/181.53 [4711]~P100(x47111)+E(f324(f324(f113(x47111),x47112),x47112),x47112) % 181.55/181.53 [4713]~P93(x47131)+E(f324(f324(f82(x47131),x47132),x47132),x47132) % 181.55/181.53 [4715]~P105(x47151)+E(f324(f324(f189(x47151),x47152),x47152),x47152) % 181.55/181.53 [4717]~P105(x47171)+E(f324(f324(f190(x47171),x47172),x47172),x47172) % 181.55/181.53 [4736]~P4(x47361)+E(f324(f324(f22(x47361),x47362),x47362),f2(x47361)) % 181.55/181.53 [4748]~P79(x47481)+E(f324(f80(x47481),f324(f80(x47481),x47482)),x47482) % 181.55/181.53 [4749]~P4(x47491)+E(f324(f80(x47491),f324(f80(x47491),x47492)),x47492) % 181.55/181.53 [4766]~E(x47662,f2(a865))+E(f324(f324(f249(a865),x47661),x47662),f324(a115,f2(a865))) % 181.55/181.53 [4799]~P97(x47991)+E(f324(f324(f104(x47991),f247(x47991)),x47992),x47992) % 181.55/181.53 [4800]~P95(x48001)+E(f324(f324(f113(x48001),f191(x48001)),x48002),x48002) % 181.55/181.53 [4801]~P77(x48011)+E(f324(f324(f82(x48011),f79(x48011)),x48012),x48012) % 181.55/181.53 [4802]~P68(x48021)+E(f324(f324(f82(x48021),f79(x48021)),x48022),x48022) % 181.55/181.53 [4803]~P112(x48031)+E(f324(f324(f82(x48031),f79(x48031)),x48032),x48032) % 181.55/181.53 [4804]~P112(x48041)+E(f324(f324(f81(x48041),f2(x48041)),x48042),x48042) % 181.55/181.53 [4805]~P72(x48051)+E(f324(f324(f81(x48051),f2(x48051)),x48052),x48052) % 181.55/181.53 [4806]~P78(x48061)+E(f324(f324(f81(x48061),f2(x48061)),x48062),x48062) % 181.55/181.53 [4824]~P95(x48241)+E(f324(f324(f104(x48241),f191(x48241)),x48242),f191(x48241)) % 181.55/181.53 [4825]~P97(x48251)+E(f324(f324(f113(x48251),f247(x48251)),x48252),f247(x48251)) % 181.55/181.53 [4826]~P112(x48261)+E(f324(f324(f82(x48261),f2(x48261)),x48262),f2(x48261)) % 181.55/181.53 [4827]~P125(x48271)+E(f324(f324(f82(x48271),f2(x48271)),x48272),f2(x48271)) % 181.55/181.53 [4828]~P77(x48281)+E(f324(f324(f249(x48281),f79(x48281)),x48282),f79(x48281)) % 181.55/181.53 [4829]~P59(x48291)+E(f324(f324(f38(x48291),f2(x48291)),x48292),f2(x48291)) % 181.55/181.53 [4830]~P114(x48301)+E(f324(f324(f282(x48301),f2(x48301)),x48302),f2(x48301)) % 181.55/181.53 [4838]E(x48381,f116(x48382))+E(f138(x48382,f324(f163(x48382),x48381)),f324(f135(x48382),x48381)) % 181.55/181.53 [4839]E(x48391,f116(x48392))+E(f324(f135(x48392),f324(f163(x48392),x48391)),f138(x48392,x48391)) % 181.55/181.53 [4840]E(x48401,f2(a865))+~E(f324(f324(f81(a865),x48402),x48401),x48402) % 181.55/181.53 [4846]~P92(x48461)+E(f324(f105(x48461),f324(f106(a1),x48462)),f324(f106(x48461),x48462)) % 181.55/181.53 [4847]~P135(x48471)+E(f324(f105(x48471),f324(f103(a1),x48472)),f324(f103(x48471),x48472)) % 181.55/181.53 [4854]E(x48541,f79(a865))+~E(f324(f324(f82(a865),x48542),x48541),f79(a865)) % 181.55/181.53 [4855]E(x48551,f79(a865))+~E(f324(f324(f82(a865),x48551),x48552),f79(a865)) % 181.55/181.53 [4856]E(x48561,f2(a865))+~E(f324(f324(f81(a865),x48562),x48561),f2(a865)) % 181.55/181.53 [4857]E(x48571,f2(a865))+~E(f324(f324(f81(a865),x48571),x48572),f2(a865)) % 181.55/181.53 [4872]~P83(x48721)+E(f324(f75(x48721),f324(f80(x48721),x48722)),f324(f75(x48721),x48722)) % 181.55/181.53 [4873]~P117(x48731)+E(f324(f75(x48731),f324(f103(x48731),x48732)),f324(f103(x48731),x48732)) % 181.55/181.53 [4874]~P83(x48741)+E(f324(f75(x48741),f324(f75(x48741),x48742)),f324(f75(x48741),x48742)) % 181.55/181.53 [4875]~P72(x48751)+E(f324(f160(x48751),f324(f163(x48751),x48752)),f324(f160(x48751),x48752)) % 181.55/181.53 [4880]~E(x48801,f324(a115,f2(a865)))+E(f324(f324(f249(a865),x48801),x48802),f324(a115,f2(a865))) % 181.55/181.53 [4889]~P4(x48891)+E(f324(f324(f22(x48891),f2(x48891)),x48892),f324(f80(x48891),x48892)) % 181.55/181.53 [4890]~E(x48902,f2(a865))+E(f133(a865,f324(f294(a865,x48901),x48902)),f116(a865)) % 181.55/181.53 [4899]~P92(x48991)+E(f324(f324(f81(x48991),x48992),f324(f106(x48991),a84)),x48992) % 181.55/181.53 [4900]E(x49001,f2(a1))+E(f46(f324(f75(a1),x49002),f324(f75(a1),x49001)),f52(x49002,x49001)) % 181.55/181.53 [4914]~E(x49141,x49142)+P1(f324(f324(f238(a865),x49141),x49142)) % 181.55/181.53 [4921]~E(x49211,f2(a102))+E(f324(f324(f81(a865),f324(a19,x49211)),x49212),x49212) % 181.55/181.53 [4931]~P7(x49311)+P7(f324(f324(f249(a1),x49311),x49312)) % 181.55/181.53 [4932]~P79(x49321)+E(f324(f324(f104(x49321),x49322),f324(f80(x49321),x49322)),f191(x49321)) % 181.55/181.53 [4933]~P79(x49331)+E(f324(f324(f113(x49331),x49332),f324(f80(x49331),x49332)),f247(x49331)) % 181.55/181.53 [4934]~P4(x49341)+E(f324(f324(f81(x49341),x49342),f324(f80(x49341),x49342)),f2(x49341)) % 181.55/181.53 [4959]E(x49591,f2(a865))+~E(f324(f80(a1),f324(f103(a1),x49592)),f324(f103(a1),x49591)) % 181.55/181.53 [4960]E(x49601,f2(a865))+~E(f324(f80(a1),f324(f103(a1),x49601)),f324(f103(a1),x49602)) % 181.55/181.53 [4970]E(f197(x49701,x49702),f2(a1))+P1(f324(f324(f238(a1),x49702),x49701)) % 181.55/181.53 [4971]E(f174(x49711,x49712),f116(a1))+P1(f324(f324(f238(a1),x49711),x49712)) % 181.55/181.53 [4984]E(x49841,f324(a115,f2(a865)))+~E(f324(f324(f82(a865),x49842),x49841),f324(a115,f2(a865))) % 181.55/181.53 [4985]E(x49851,f324(a115,f2(a865)))+~E(f324(f324(f82(a865),x49851),x49852),f324(a115,f2(a865))) % 181.55/181.53 [4986]~P103(x49861)+P1(f324(f324(f238(x49861),x49862),x49862)) % 181.55/181.53 [4987]~P91(x49871)+P1(f324(f324(f92(x49871),x49872),x49872)) % 181.55/181.53 [4990]~P92(x49901)+E(f324(f324(f82(x49901),x49902),f324(f106(x49901),a100)),f324(f80(x49901),x49902)) % 181.55/181.53 [5008]~P92(x50081)+E(f324(f80(x50081),f324(f106(x50081),x50082)),f324(f106(x50081),f324(f80(a1),x50082))) % 181.55/181.53 [5009]~P135(x50091)+E(f324(f80(x50091),f324(f105(x50091),x50092)),f324(f105(x50091),f324(f80(a1),x50092))) % 181.55/181.53 [5036]~E(x50361,f324(a115,x50362))+P1(f324(f324(f239(a865),f2(a865)),x50361)) % 181.55/181.53 [5053]~P105(x50531)+E(f324(f80(f871(x50531,a859)),f324(f245(x50531),x50532)),f324(f246(x50531),x50532)) % 181.55/181.53 [5054]~P105(x50541)+E(f324(f80(f871(x50541,a859)),f324(f293(x50541),x50542)),f324(f296(x50541),x50542)) % 181.55/181.53 [5055]~P105(x50551)+E(f324(f80(f871(x50551,a859)),f324(f296(x50551),x50552)),f324(f293(x50551),x50552)) % 181.55/181.53 [5056]~P105(x50561)+E(f324(f80(f871(x50561,a859)),f324(f246(x50561),x50562)),f324(f245(x50561),x50562)) % 181.55/181.53 [5063]~E(f324(f103(a1),x50632),x50631)+P1(f324(f324(f238(a1),f2(a1)),x50631)) % 181.55/181.53 [5070]~E(x50702,f2(a1))+E(f52(x50701,x50702),f324(f324(f259(a1,a1),f2(a1)),f324(f75(a1),x50701))) % 181.55/181.53 [5072]~P2(x50721)+P1(f324(f324(f238(x50721),f191(x50721)),x50722)) % 181.55/181.53 [5103]E(x51031,x51032)+~E(f324(f324(f81(a1),x51031),x51031),f324(f324(f81(a1),x51032),x51032)) % 181.55/181.53 [5107]~P1(f324(x51071,x51072))+P1(f324(x51071,f324(a107,f373(x51071)))) % 181.55/181.53 [5133]~P117(x51331)+E(f324(f324(f82(x51331),f83(x51331,x51332)),f324(f75(x51331),x51332)),x51332) % 181.55/181.53 [5140]~E(x51402,f2(a865))+E(f86(f870(a865,a865),f47(x51401,x51402)),f324(f324(f259(a865,a865),f2(a865)),x51401)) % 181.55/181.53 [5145]~E(x51451,x51452)+~P1(f324(f324(f239(a865),x51451),x51452)) % 181.55/181.53 [5146]~E(x51461,x51462)+~P1(f324(f324(f239(a1),x51461),x51462)) % 181.55/181.53 [5149]~P141(x51491)+E(f324(f324(f81(x51491),f79(x51491)),f324(f103(x51491),x51492)),f324(f103(x51491),f324(a115,x51492))) % 181.55/181.53 [5153]~E(x51531,f2(a865))+~P1(f324(f324(f239(a865),x51532),x51531)) % 181.55/181.53 [5169]E(f146(x51691,x51692),x51692)+~E(f324(f192(f866(x51691)),f146(x51691,x51692)),f324(f192(f866(x51691)),x51692)) % 181.55/181.53 [5170]E(f324(f37(x51701),f324(f167(x51701),x51702)),f324(f192(f866(x51701)),x51702))+~P1(f324(f131(x51701),x51702)) % 181.55/181.53 [5179]~P1(f324(x51791,f411(x51791)))+P1(f324(x51791,f324(f103(a1),x51792))) % 181.55/181.53 [5190]E(f272(x51901,x51902),f79(a102))+~P1(f324(f324(f239(a102),x51902),x51901)) % 181.55/181.53 [5191]E(f174(x51911,x51912),f116(a1))+~P1(f324(f324(f239(a1),x51912),x51911)) % 181.55/181.53 [5192]~P106(x51921)+E(f295(x51921,x51922,x51922),f324(f324(f302(x51921),x51922),f191(f871(x51921,a859)))) % 181.55/181.53 [5214]~E(f324(f324(f22(a865),x52141),x52142),f2(a865))+P1(f324(f324(f238(a865),x52141),x52142)) % 181.55/181.53 [5215]~E(f324(f324(f22(a1),x52151),x52152),f2(a1))+P1(f324(f324(f92(a1),x52151),x52152)) % 181.55/181.53 [5237]~E(x52372,f2(a865))+E(f54(x52371,x52372,f116(x52371)),f324(f324(f145(f866(x52371)),f116(x52371)),f116(f866(x52371)))) % 181.55/181.53 [5241]~P103(x52411)+~P1(f324(f324(f239(x52411),x52412),x52412)) % 181.55/181.53 [5244]~E(f44(a1,x52441,x52442),f2(a1))+E(f44(a1,x52441,f324(f80(a1),x52442)),f2(a1)) % 181.55/181.53 [5246]~E(f44(a1,x52461,x52462),f2(a1))+E(f44(a1,f324(f80(a1),x52461),x52462),f2(a1)) % 181.55/181.53 [5254]E(f324(f294(a865,x52541),f324(a115,x52542)),f191(f871(a865,a859)))+P1(f324(f324(f238(a865),x52541),x52542)) % 181.55/181.53 [5274]E(f133(a865,f324(f294(a865,x52741),x52742)),f116(a865))+P1(f324(f324(f239(a865),x52741),x52742)) % 181.55/181.53 [5279]~E(f324(f37(x52791),f324(f167(x52791),x52792)),f324(f192(f866(x52791)),x52792))+P1(f324(f131(x52791),x52792)) % 181.55/181.53 [5284]~P1(f324(f131(x52841),x52842))+P1(f324(f131(x52841),f324(f162(x52841),x52842))) % 181.55/181.53 [5285]~P1(f324(f131(x52851),x52852))+P1(f324(f131(x52851),f324(f166(x52851),x52852))) % 181.55/181.53 [5286]~P1(f324(f131(x52861),x52862))+P1(f324(f131(x52861),f324(f163(x52861),x52862))) % 181.55/181.53 [5293]P1(f324(x52931,x52932))+~P1(f324(x52931,f324(a107,f405(x52931)))) % 181.55/181.53 [5294]P1(f324(f324(f238(a865),x52942),x52941))+P1(f324(f324(f238(a865),x52941),x52942)) % 181.55/181.53 [5295]P1(f324(f324(f238(a1),x52952),x52951))+P1(f324(f324(f238(a1),x52951),x52952)) % 181.55/181.53 [5297]~P83(x52971)+P1(f324(f324(f238(x52971),x52972),f324(f75(x52971),x52972))) % 181.55/181.53 [5300]P1(f324(x53001,f415(x53001)))+~P1(f324(x53001,f324(f103(a1),x53002))) % 181.55/181.53 [5325]E(f324(f324(f22(a865),x53251),x53252),f2(a865))+~P1(f324(f324(f238(a865),x53251),x53252)) % 181.55/181.53 [5326]E(f324(f324(f22(a1),x53261),x53262),f2(a1))+~P1(f324(f324(f92(a1),x53261),x53262)) % 181.55/181.53 [5327]E(f324(f324(f38(a865),x53271),x53272),f2(a865))+~P1(f324(f324(f239(a865),x53271),x53272)) % 181.55/181.53 [5345]E(f44(a865,x53451,x53452),x53451)+~P1(f324(f324(f239(a865),x53451),x53452)) % 181.55/181.53 [5354]E(f44(a1,x53541,f324(f80(a1),x53542)),f283(x53541,x53542))+P1(f324(f324(f238(a1),f2(a1)),x53542)) % 181.55/181.53 [5366]E(f324(f324(f22(a1),x53661),x53662),f197(x53661,x53662))+~P1(f324(f324(f238(a1),x53662),x53661)) % 181.55/181.53 [5385]P1(f324(f324(f238(a1),f2(a1)),f411(x53851)))+P1(f324(x53851,f324(f103(a1),x53852))) % 181.55/181.53 [5397]~P61(x53971)+P1(f324(f324(f326(x53971),x53972),f324(f167(x53971),f55(x53971)))) % 181.55/181.53 [5399]~P120(x53991)+P1(f324(f324(f238(x53991),f2(x53991)),f324(f103(x53991),x53992))) % 181.55/181.53 [5400]~P83(x54001)+P1(f324(f324(f238(x54001),f2(x54001)),f324(f75(x54001),x54002))) % 181.55/181.53 [5427]E(f324(f324(f81(a865),x54271),f332(x54272,x54271)),x54272)+~P1(f324(f324(f238(a865),x54271),x54272)) % 181.55/181.53 [5442]E(f295(a1,x54421,x54422),f191(f871(a1,a859)))+~P1(f324(f324(f239(a1),x54422),x54421)) % 181.55/181.53 [5445]~P117(x54451)+E(f324(f324(f82(x54451),f324(f75(x54451),x54452)),f324(f75(x54451),x54452)),f324(f324(f82(x54451),x54452),x54452)) % 181.55/181.53 [5450]E(f133(a865,f324(f294(a865,x54501),f324(a115,x54502))),f116(a865))+P1(f324(f324(f238(a865),x54501),x54502)) % 181.55/181.53 [5454]E(f324(f324(f38(a1),x54541),x54542),f284(x54541,x54542))+~P1(f324(f324(f238(a1),f2(a1)),x54542)) % 181.55/181.53 [5474]P1(f324(f131(x54741),x54742))+~P1(f324(f131(x54741),f324(f162(x54741),x54742))) % 181.55/181.53 [5475]P1(f324(f131(x54751),x54752))+~P1(f324(f131(x54751),f324(f163(x54751),x54752))) % 181.55/181.53 [5496]P1(f324(f61(a865),x54961))+P1(f324(f324(f326(a865),f824(x54961,x54962)),x54961)) % 181.55/181.53 [5497]P1(f324(f61(a865),x54971))+P1(f324(f324(f326(a865),f840(x54971,x54972)),x54971)) % 181.55/181.53 [5498]P1(f324(f324(f239(a865),x54982),f324(a115,x54981)))+P1(f324(f324(f239(a865),x54981),x54982)) % 181.55/181.53 [5499]E(f44(a1,x54991,x54992),f283(x54991,x54992))+~P1(f324(f324(f238(a1),f2(a1)),x54992)) % 181.55/181.53 [5502]E(f133(a865,f324(f294(a865,x55021),x55022)),f116(a865))+~P1(f324(f324(f238(a865),x55022),x55021)) % 181.55/181.53 [5503]~P75(x55031)+E(f324(f303(x55031,x55031,f80(x55031)),f324(f245(x55031),x55032)),f324(f296(x55031),f324(f80(x55031),x55032))) % 181.55/181.53 [5504]~P75(x55041)+E(f324(f303(x55041,x55041,f80(x55041)),f324(f293(x55041),x55042)),f324(f246(x55041),f324(f80(x55041),x55042))) % 181.55/181.53 [5505]~P75(x55051)+E(f324(f303(x55051,x55051,f80(x55051)),f324(f296(x55051),x55052)),f324(f245(x55051),f324(f80(x55051),x55052))) % 181.55/181.53 [5506]~P75(x55061)+E(f324(f303(x55061,x55061,f80(x55061)),f324(f246(x55061),x55062)),f324(f293(x55061),f324(f80(x55061),x55062))) % 181.55/181.53 [5517]E(x55171,f191(f871(x55172,a859)))+P1(f324(f324(f326(x55172),f601(x55171,x55172)),x55171)) % 181.55/181.53 [5518]E(x55181,f191(f871(x55182,a859)))+P1(f324(f324(f326(x55182),f545(x55181,x55182)),x55181)) % 181.55/181.53 [5529]~P1(f324(f324(f239(a865),x55291),x55292))+P1(f324(f324(f238(a865),x55291),x55292)) % 181.55/181.53 [5530]~P1(f324(f324(f239(a1),x55301),x55302))+P1(f324(f324(f238(a1),x55301),x55302)) % 181.55/181.53 [5546]E(f46(x55461,x55462),f324(f324(f259(a1,a1),f2(a1)),x55461))+~P1(f324(f324(f239(a1),x55461),x55462)) % 181.55/181.53 [5547]E(f220(f324(f80(a1),x55471),f324(f80(a1),x55472)),f220(x55471,x55472))+~P1(f324(f324(f239(a1),x55472),f2(a1))) % 181.55/181.53 [5558]E(x55581,x55582)+~E(f324(a3,f324(a115,f324(a19,x55581))),f324(a3,f324(a115,f324(a19,x55582)))) % 181.55/181.53 [5563]E(f46(x55631,x55632),f324(f324(f259(a1,a1),f2(a1)),x55631))+~P1(f324(f324(f238(a1),x55632),f2(a1))) % 181.55/181.53 [5590]E(f44(a865,f324(f106(a865),x55901),f324(f106(a865),x55902)),f2(a865))+~P1(f324(a196,f324(f106(a1),x55901))) % 181.55/181.53 [5605]P1(f324(f324(f238(a1),f2(a1)),f415(x56051)))+~P1(f324(x56051,f324(f103(a1),x56052))) % 181.55/181.53 [5639]P40(f295(a1,x56391,x56392))+~P1(f324(f324(f238(a1),f2(a1)),x56391)) % 181.55/181.53 [5644]~P1(f324(f61(x56441),x56442))+P1(f324(f61(f871(x56441,a859)),f324(f301(x56441),x56442))) % 181.55/181.53 [5657]E(f324(f324(f81(a1),x56571),f324(f103(a1),f418(x56572,x56571))),x56572)+~P1(f324(f324(f238(a1),x56571),x56572)) % 181.55/181.53 [5665]P1(f324(f324(f238(a865),x56651),x56652))+P1(f324(f324(f238(a865),f324(a115,x56652)),x56651)) % 181.55/181.53 [5708]E(f324(f324(f38(a865),f324(f106(a865),x57081)),f324(f106(a865),x57082)),f2(a865))+~P1(f324(a196,f324(f106(a1),x57081))) % 181.55/181.53 [5709]E(f324(f324(f82(a865),f324(f106(a865),x57091)),f324(f106(a865),x57092)),f2(a865))+~P1(f324(f324(f239(a1),x57091),a84)) % 181.55/181.53 [5711]P1(f324(f324(f238(a865),x57111),f324(a115,x57112)))+~P1(f324(f324(f238(a865),x57111),x57112)) % 181.55/181.53 [5713]P1(f324(f324(f239(a865),x57131),f324(a115,x57132)))+~P1(f324(f324(f238(a865),x57131),x57132)) % 181.55/181.53 [5715]P1(f324(f324(f239(a865),x57151),f324(a115,x57152)))+~P1(f324(f324(f239(a865),x57151),x57152)) % 181.55/181.53 [5718]~E(x57181,x57182)+P1(f324(f324(f239(a1),x57181),f324(f324(f81(a1),x57182),f79(a1)))) % 181.55/181.53 [5721]E(f44(a1,x57211,x57212),f2(a1))+E(f324(f324(f22(a1),x57212),f44(a1,x57211,x57212)),f44(a1,f324(f80(a1),x57211),x57212)) % 181.55/181.53 [5730]E(x57301,f116(x57302))+P1(f324(f324(f326(x57302),f138(x57302,x57301)),f324(f167(x57302),x57301))) % 181.55/181.53 [5742]E(f86(f870(a865,a865),f47(x57421,x57422)),f324(f324(f259(a865,a865),f2(a865)),x57421))+~P1(f324(f324(f239(a865),x57421),x57422)) % 181.55/181.53 [5775]E(f324(f324(f22(a865),f324(f106(a865),x57751)),f324(f106(a865),x57752)),f324(f106(a865),x57751))+~P1(f324(f324(f239(a1),x57752),a84)) % 181.55/181.53 [5776]E(f324(f324(f81(a865),f324(f106(a865),x57761)),f324(f106(a865),x57762)),f324(f106(a865),x57762))+~P1(f324(f324(f239(a1),x57761),a84)) % 181.55/181.53 [5781]E(f324(a115,f324(f324(f81(a865),x57811),f334(x57812,x57811))),x57812)+~P1(f324(f324(f239(a865),x57811),x57812)) % 181.55/181.53 [5804]P1(f324(x58041,x58042))+~P1(f324(x58041,f324(a90,f546(x58042,x58041)))) % 181.55/181.53 [5812]~P1(f324(f324(f239(a865),x58121),f324(a115,x58122)))+P1(f324(f324(f238(a865),x58121),x58122)) % 181.55/181.53 [5858]E(f324(f324(f302(a865),x58581),f324(f294(a865,x58582),x58581)),f324(f294(a865,x58582),f324(a115,x58581)))+~P1(f324(f324(f238(a865),x58582),x58581)) % 181.55/181.53 [5860]E(x58601,f116(x58602))+E(f324(f324(f124(x58602),f117(x58602,x58601)),f324(f324(f145(x58602),f138(x58602,x58601)),f116(x58602))),x58601) % 181.55/181.53 [5874]P1(f324(f61(x58741),x58742))+~P1(f324(f324(f239(a865),f2(a865)),f324(f37(x58741),x58742))) % 181.55/181.53 [5876]~E(x58761,f191(f871(x58762,a859)))+~P1(f324(f324(f239(a865),f2(a865)),f324(f37(x58762),x58761))) % 181.55/181.53 [5888]~P1(f324(f324(f239(a865),x58881),x58882))+P1(f324(f324(f238(a865),f324(a115,x58881)),x58882)) % 181.55/181.53 [5895]~P105(x58951)+E(f144(x58951,x58951,f5(x58951),f146(x58951,x58952)),f133(x58951,f324(f167(x58951),x58952))) % 181.55/181.53 [5898]E(x58981,f116(x58982))+P1(f324(f324(f326(x58982),f324(f135(x58982),x58981)),f324(f167(x58982),x58981))) % 181.55/181.53 [5904]~P120(x59041)+P1(f324(f324(f239(x59041),x59042),f324(f324(f81(x59041),x59042),f79(x59041)))) % 181.55/181.53 [5906]~P83(x59061)+P1(f324(f324(f238(x59061),f324(f80(x59061),x59062)),f324(f75(x59061),x59062))) % 181.55/181.53 [5936]P1(f324(f61(a865),x59361))+~P1(f324(f324(f238(a865),f840(x59361,x59362)),x59362)) % 181.55/181.53 [5937]P1(f324(f61(a865),x59371))+~P1(f324(f324(f239(a865),f824(x59371,x59372)),x59372)) % 181.55/181.53 [5940]~P1(f324(f61(f870(x59401,x59401)),x59402))+P1(f324(f61(x59401),f324(f277(x59401),x59402))) % 181.55/181.53 [5993]~P1(f324(f324(f239(a865),x59932),f324(a115,x59931)))+~P1(f324(f324(f239(a865),x59931),x59932)) % 181.55/181.53 [5994]~P106(x59941)+E(f324(f324(f104(f871(x59941,a859)),f324(f293(x59941),x59942)),f324(f246(x59941),x59942)),f324(f324(f302(x59941),x59942),f191(f871(x59941,a859)))) % 181.55/181.53 [6007]P1(f324(f61(x60071),x60072))+~P1(f324(f61(f871(x60071,a859)),f324(f301(x60071),x60072))) % 181.55/181.53 [6030]P1(f324(f324(f238(a865),f324(a115,x60301)),f324(a115,x60302)))+~P1(f324(f324(f238(a865),x60301),x60302)) % 181.55/181.53 [6031]P1(f324(f324(f238(a865),f324(a19,x60311)),f324(a19,x60312)))+~P1(f324(f324(f238(a102),x60311),x60312)) % 181.55/181.53 [6032]P1(f324(f324(f238(a102),f324(a3,x60321)),f324(a3,x60322)))+~P1(f324(f324(f238(a865),x60321),x60322)) % 181.55/181.53 [6034]P1(f324(f324(f239(a865),f324(a115,x60341)),f324(a115,x60342)))+~P1(f324(f324(f239(a865),x60341),x60342)) % 181.55/181.53 [6035]P1(f324(f324(f239(a865),f324(a19,x60351)),f324(a19,x60352)))+~P1(f324(f324(f239(a102),x60351),x60352)) % 181.55/181.53 [6036]P1(f324(f324(f239(a102),f324(a3,x60361)),f324(a3,x60362)))+~P1(f324(f324(f239(a865),x60361),x60362)) % 181.55/181.53 [6039]E(x60391,x60392)+~E(f324(f303(a865,a1,f103(a1)),x60391),f324(f303(a865,a1,f103(a1)),x60392)) % 181.55/181.53 [6055]P1(f324(f324(f238(a865),x60551),x60552))+~P1(f324(f324(f238(a865),f324(a115,x60551)),x60552)) % 181.55/181.53 [6058]P1(f324(f324(f239(a865),x60581),x60582))+~P1(f324(f324(f238(a865),f324(a115,x60581)),x60582)) % 181.55/181.53 [6059]P1(f324(f324(f239(a865),x60591),x60592))+~P1(f324(f324(f239(a865),f324(a115,x60591)),x60592)) % 181.55/181.53 [6074]E(f44(a1,x60741,x60742),f2(a1))+E(f324(f324(f22(a1),f44(a1,x60741,x60742)),x60742),f44(a1,x60741,f324(f80(a1),x60742))) % 181.55/181.53 [6137]E(f324(f37(f871(x61371,a859)),f324(f301(x61371),x61372)),f324(f324(f249(a865),f324(a115,f324(a115,f2(a865)))),f324(f37(x61371),x61372)))+~P1(f324(f61(x61371),x61372)) % 181.55/181.53 [6140]E(x61401,f116(x61402))+E(f324(f324(f159(x61402),x61401),f324(f324(f22(a865),f324(f192(f866(x61402)),x61401)),f79(a865))),f138(x61402,x61401)) % 181.55/181.53 [6165]E(x61651,f116(x61652))+E(f324(f324(f124(x61652),f324(f166(x61652),x61651)),f324(f324(f145(x61652),f324(f135(x61652),x61651)),f116(x61652))),f324(f162(x61652),x61651)) % 181.55/181.53 [6194]~P1(f324(f61(x61941),f39(f871(x61941,a859),x61942)))+P1(f324(f61(f871(x61941,a859)),x61942)) % 181.55/181.53 [6216]P1(f324(f324(f238(a865),f324(f106(a865),x62161)),f324(f106(a865),x62162)))+~P1(f324(f324(f238(a1),x62161),a84)) % 181.55/181.53 [6233]~P1(f324(f324(f239(a1),x62331),x62332))+P1(f324(f324(f238(a1),x62331),f324(f324(f22(a1),x62332),f79(a1)))) % 181.55/181.53 [6234]~P1(f324(f324(f238(a1),x62341),x62342))+P1(f324(f324(f239(a1),x62341),f324(f324(f81(a1),x62342),f79(a1)))) % 181.55/181.53 [6235]~P1(f324(f324(f239(a1),x62351),x62352))+P1(f324(f324(f239(a1),x62351),f324(f324(f81(a1),x62352),f79(a1)))) % 181.55/181.53 [6237]~P1(f324(f324(f238(a1),x62371),x62372))+P1(f324(f324(f238(a865),f324(f106(a865),x62371)),f324(f106(a865),x62372))) % 181.55/181.53 [6238]~P1(f324(f324(f238(a1),x62381),x62382))+P1(f324(f324(f238(a1),f324(f106(a1),x62381)),f324(f106(a1),x62382))) % 181.55/181.53 [6240]~P1(f324(f324(f238(a865),x62401),x62402))+P1(f324(f324(f238(a1),f324(f103(a1),x62401)),f324(f103(a1),x62402))) % 181.55/181.53 [6241]~P1(f324(f324(f239(a1),x62411),x62412))+P1(f324(f324(f239(a1),f324(f106(a1),x62411)),f324(f106(a1),x62412))) % 181.55/181.53 [6243]~P1(f324(f324(f239(a865),x62431),x62432))+P1(f324(f324(f239(a1),f324(f103(a1),x62431)),f324(f103(a1),x62432))) % 181.55/181.53 [6244]~P1(f324(f324(f92(a1),x62441),x62442))+P1(f324(f324(f92(a1),f324(f106(a1),x62441)),f324(f106(a1),x62442))) % 181.55/181.53 [6262]~P1(f324(f324(f238(a865),x62621),x62622))+~P1(f324(f324(f238(a865),f324(a115,x62622)),x62621)) % 181.55/181.53 [6304]~P1(f324(f324(f238(a865),f324(a115,x63041)),f324(a115,x63042)))+P1(f324(f324(f238(a865),x63041),x63042)) % 181.55/181.53 [6305]~P1(f324(f324(f238(a102),f324(a3,x63051)),f324(a3,x63052)))+P1(f324(f324(f238(a865),x63051),x63052)) % 181.55/181.53 [6306]~P1(f324(f324(f238(a865),f324(a19,x63061)),f324(a19,x63062)))+P1(f324(f324(f238(a102),x63061),x63062)) % 181.55/181.53 [6308]~P1(f324(f324(f239(a865),f324(a115,x63081)),f324(a115,x63082)))+P1(f324(f324(f239(a865),x63081),x63082)) % 181.55/181.53 [6309]~P1(f324(f324(f239(a102),f324(a3,x63091)),f324(a3,x63092)))+P1(f324(f324(f239(a865),x63091),x63092)) % 181.55/181.53 [6310]~P1(f324(f324(f239(a865),f324(a107,x63101)),f324(a107,x63102)))+P1(f324(f324(f239(a1),x63101),x63102)) % 181.55/181.53 [6311]~P1(f324(f324(f239(a865),f324(a19,x63111)),f324(a19,x63112)))+P1(f324(f324(f239(a102),x63111),x63112)) % 181.55/181.53 [6352]~P1(f324(f324(f239(a865),f324(a107,x63522)),f324(a107,x63521)))+P1(f324(f324(f239(a1),f2(a1)),x63521)) % 181.55/181.53 [6384]P1(f324(f324(f238(a1),f2(a1)),f44(a1,x63841,x63842)))+~P1(f324(f324(f239(a1),f2(a1)),x63842)) % 181.55/181.53 [6541]P39(x65411,x65412)+~E(f324(f324(f281(x65411,x65411,x65411),x65412),x65412),f191(f871(f870(x65411,x65411),a859))) % 181.55/181.53 [6553]~P39(x65531,x65532)+P39(x65531,f324(f324(f281(x65531,x65531,x65531),x65532),x65532)) % 181.55/181.53 [6564]P1(f324(f324(f238(a1),x65641),x65642))+~P1(f324(f324(f239(a1),x65641),f324(f324(f81(a1),x65642),f79(a1)))) % 181.55/181.53 [6565]P1(f324(f324(f239(a1),x65651),x65652))+~P1(f324(f324(f238(a1),x65651),f324(f324(f22(a1),x65652),f79(a1)))) % 181.55/181.53 [6568]P1(f324(f324(f238(a865),x65681),x65682))+~P1(f324(f324(f238(a1),f324(f103(a1),x65681)),f324(f103(a1),x65682))) % 181.55/181.53 [6569]P1(f324(f324(f238(a1),x65691),x65692))+~P1(f324(f324(f238(a1),f324(f106(a1),x65691)),f324(f106(a1),x65692))) % 181.55/181.53 [6571]P1(f324(f324(f239(a865),x65711),x65712))+~P1(f324(f324(f239(a1),f324(f103(a1),x65711)),f324(f103(a1),x65712))) % 181.55/181.53 [6572]P1(f324(f324(f239(a1),x65721),x65722))+~P1(f324(f324(f239(a865),f324(f106(a865),x65721)),f324(f106(a865),x65722))) % 181.55/181.53 [6573]P1(f324(f324(f239(a1),x65731),x65732))+~P1(f324(f324(f239(a1),f324(f106(a1),x65731)),f324(f106(a1),x65732))) % 181.55/181.53 [6574]P1(f324(f324(f92(a1),x65741),x65742))+~P1(f324(f324(f92(a1),f324(f106(a1),x65741)),f324(f106(a1),x65742))) % 181.55/181.53 [6667]~E(f718(x66672,x66671),f116(x66671))+E(f324(f136(f866(x66671),f866(x66671),f124(x66671),f116(x66671)),x66672),f116(x66671)) % 181.55/181.53 [6668]~E(f721(x66682,x66681),f116(x66681))+E(f324(f136(f866(x66681),f866(x66681),f124(x66681),f116(x66681)),x66682),f116(x66681)) % 181.55/181.53 [6675]~P6(x66751)+E(f324(f136(x66751,x66751,f104(x66751),f247(x66751)),x66752),f40(x66751,f324(f167(x66751),x66752))) % 181.55/181.53 [6676]~P6(x66761)+E(f324(f136(x66761,x66761,f113(x66761),f191(x66761)),x66762),f39(x66761,f324(f167(x66761),x66762))) % 181.55/181.53 [6688]E(x66881,f2(a102))+E(f324(f324(f81(a865),f324(a19,f324(f324(f22(a102),x66881),f79(a102)))),f324(a115,x66882)),f324(f324(f81(a865),f324(a19,x66881)),x66882)) % 181.55/181.53 [6738]P1(f324(f324(f239(a1),f324(f324(f22(a1),x67381),x67382)),f2(a1)))+~P1(f324(f324(f239(a1),x67381),x67382)) % 181.55/181.53 [6765]~P105(x67651)+E(f324(f324(f113(f871(x67651,a859)),f324(f324(f302(x67651),x67652),f191(f871(x67651,a859)))),f324(f296(x67651),x67652)),f324(f246(x67651),x67652)) % 181.55/181.53 [6840]~P57(x68401,x68402)+P39(x68401,f324(f244(f870(x68401,x68401)),f324(f263(x68401,x68401,a859),x68402))) % 181.55/181.53 [6841]~P57(x68411,x68412)+P55(x68411,f324(f244(f870(x68411,x68411)),f324(f263(x68411,x68411,a859),x68412))) % 181.55/181.53 [6842]E(x68421,f191(f871(x68422,a859)))+~P1(f324(f324(f238(f871(x68422,a859)),x68421),f191(f871(x68422,a859)))) % 181.55/181.53 [6923]~P1(f324(f324(f239(a865),f2(a865)),x69232))+P1(f324(f324(f238(a865),f44(a865,x69231,x69232)),x69232)) % 181.55/181.53 [6924]~P1(f324(f324(f238(a1),f2(a1)),x69241))+P1(f324(f324(f238(a1),f44(a1,x69241,x69242)),x69241)) % 181.55/181.53 [6925]~P1(f324(f324(f239(a865),f2(a865)),x69252))+P1(f324(f324(f239(a865),f44(a865,x69251,x69252)),x69252)) % 181.55/181.53 [6927]~P1(f324(f324(f239(a1),f2(a1)),x69272))+P1(f324(f324(f239(a1),f44(a1,x69271,x69272)),x69272)) % 181.55/181.53 [7002]~P106(x70021)+E(f324(f324(f22(f871(x70021,a859)),f324(f324(f302(x70021),x70022),f191(f871(x70021,a859)))),f324(f245(x70021),x70022)),f324(f324(f302(x70021),x70022),f191(f871(x70021,a859)))) % 181.55/181.53 [7075]~P50(x70751,x70752)+P41(x70751,f247(f871(x70751,a859)),f324(f244(f870(x70751,x70751)),f324(f263(x70751,x70751,a859),x70752))) % 181.55/181.53 [7076]P1(f324(x70761,x70762))+P1(f324(f324(f326(f871(f870(a865,a865),a859)),f546(x70762,x70761)),a101)) % 181.55/181.53 [7120]E(f324(f324(f124(a865),f133(a865,f324(f294(a865,x71201),x71202))),f324(f324(f145(a865),x71202),f116(a865))),f133(a865,f324(f294(a865,x71201),f324(a115,x71202))))+~P1(f324(f324(f238(a865),x71201),x71202)) % 181.55/181.53 [7261]E(x72611,f2(a865))+~E(f324(f136(a865,a865,f81(a865),x72611),x72612),f2(a865)) % 181.55/181.53 [7286]~P1(f324(f324(f239(a1),f324(f324(f22(a1),x72861),x72862)),f2(a1)))+P1(f324(f324(f239(a1),x72861),x72862)) % 181.55/181.53 [7316]P39(x73161,x73162)+~P39(x73161,f324(f324(f281(x73161,x73161,x73161),x73162),x73162)) % 181.55/181.53 [7345]~P1(f324(f324(f238(a865),f324(a115,x73451)),x73452))+P1(f186(a859,a242,f324(f238(a865),x73451),x73452)) % 181.55/181.53 [7502]P27(a865,a865,f324(f324(f7(a865,a865,a865),f22(a865)),x75021),x75022)+P1(f324(f324(f326(a865),f555(x75021,x75022)),x75022)) % 181.55/181.53 [7558]E(f324(f324(f324(f65(a865,x75581,f81(a865)),f324(f16(a865,x75581),f79(a865))),f2(a865)),x75582),f324(f37(x75581),x75582))+~P1(f324(f61(x75581),x75582)) % 181.55/181.53 [7600]P27(a865,a865,f324(f324(f7(a865,a865,a865),f22(a865)),x76001),x76002)+~P1(f324(f324(f238(a865),x76001),f555(x76001,x76002))) % 181.55/181.53 [7656]P39(x76561,x76562)+P1(f324(f324(f238(f871(x76561,a859)),f544(x76562,x76561)),f324(f278(x76561,x76561,x76562),f544(x76562,x76561)))) % 181.55/181.53 [7661]P57(x76611,x76612)+~P39(x76611,f324(f244(f870(x76611,x76611)),f324(f263(x76611,x76611,a859),x76612))) % 181.55/181.53 [7725]P1(f324(f324(f238(a865),f324(a115,x77251)),x77252))+~P1(f186(a859,a242,f324(f238(a865),x77251),x77252)) % 181.55/181.53 [7779]P1(f324(f324(f326(f870(a865,a865)),f324(f324(f259(a865,a865),x77791),x77792)),f300(a865,a314)))+~P1(f324(f324(f238(a865),x77791),x77792)) % 181.55/181.53 [7881]P50(x78811,x78812)+~P41(x78811,f247(f871(x78811,a859)),f324(f244(f870(x78811,x78811)),f324(f263(x78811,x78811,a859),x78812))) % 181.55/181.53 [7935]~P1(f324(f131(x79351),x79352))+P1(f324(f131(f871(x79351,a859)),f324(f324(f148(f866(x79351),f871(x79351,a859)),f167(x79351)),f53(x79351,x79352)))) % 181.55/181.53 [8137]~P39(x81371,f324(f279(x81371,x81371),x81372))+P39(x81371,f324(f279(x81371,x81371),f324(f324(f281(x81371,x81371,x81371),x81372),f300(x81371,x81372)))) % 181.55/181.53 [8235]P28(x82351,a865,f570(x82352,x82351),x82352,f324(f294(a865,f2(a865)),f324(f37(x82351),x82352)))+~P1(f324(f61(x82351),x82352)) % 181.55/181.53 [8236]P28(a865,x82361,f557(x82362,x82361),f324(f294(a865,f2(a865)),f324(f37(x82361),x82362)),x82362)+~P1(f324(f61(x82361),x82362)) % 181.55/181.53 [8253]P28(a865,x82531,f556(x82532,x82531),f295(a865,f79(a865),f324(f37(x82531),x82532)),x82532)+~P1(f324(f61(x82531),x82532)) % 181.55/181.53 [8262]P1(f324(f61(f870(x82621,x82621)),f324(f324(f281(x82621,x82621,x82621),x82622),f300(x82621,x82622))))+~P1(f324(f61(f870(x82621,x82621)),x82622)) % 181.55/181.53 [8294]E(x82941,f2(a1))+P1(f324(f48(x82942,x82941),f324(f324(f259(a1,a1),f324(f324(f38(a1),x82942),x82941)),f44(a1,x82942,x82941)))) % 181.55/181.53 [8308]~P1(f324(f324(f326(f870(a865,a865)),f324(f324(f259(a865,a865),x83081),x83082)),f300(a865,a314)))+P1(f324(f324(f238(a865),x83081),x83082)) % 181.55/181.53 [8323]~P78(x83231)+E(f324(f136(x83231,x83231,f324(f7(x83231,x83231,x83231),f81(x83231)),f2(x83231)),f324(f163(x83231),x83232)),f324(f136(x83231,x83231,f81(x83231),f2(x83231)),x83232)) % 181.55/181.53 [8488]~P105(x84881)+E(f324(f136(f866(x84881),x84881,f324(f7(x84881,f866(x84881),f866(x84881)),f142(x84881,x84881,f5(x84881))),f116(x84881)),x84882),f144(x84881,x84881,f5(x84881),x84882)) % 181.55/181.53 [8601]~P55(x86011,f324(f244(f870(x86011,x86011)),f324(f263(x86011,x86011,a859),x86012)))+P55(x86011,f324(f244(f870(x86011,x86011)),f324(f263(x86011,x86011,a859),f248(x86011,x86011,x86012)))) % 181.55/181.53 [8615]P1(f324(f324(f326(f870(a865,a865)),f324(f324(f259(a865,a865),x86151),x86152)),f324(f324(f281(a865,a865,a865),a314),f300(a865,a314))))+~P1(f324(f324(f239(a865),x86151),x86152)) % 181.55/181.53 [8661]~P1(f324(f61(f870(x86611,x86611)),f324(f324(f281(x86611,x86611,x86611),x86612),f300(x86611,x86612))))+P1(f324(f61(f870(x86611,x86611)),x86612)) % 181.55/181.53 [8720]~P55(x87201,f324(f244(f870(x87201,x87201)),f324(f263(x87201,x87201,a859),f248(x87201,x87201,x87202))))+P55(x87201,f324(f244(f870(x87201,x87201)),f324(f263(x87201,x87201,a859),x87202))) % 181.55/181.53 [8916]P55(x89161,x89162)+P1(f324(f324(f326(f870(x89161,x89161)),f324(f324(f259(x89161,x89161),f588(x89162,x89161)),f588(x89162,x89161))),f324(f324(f281(x89161,x89161,x89161),x89162),f300(x89161,x89162)))) % 181.55/181.53 [8917]P55(x89171,x89172)+P1(f324(f324(f326(f870(x89171,x89171)),f324(f324(f259(x89171,x89171),f599(x89172,x89171)),f599(x89172,x89171))),f324(f324(f281(x89171,x89171,x89171),x89172),f300(x89171,x89172)))) % 181.55/181.53 [9037]~P1(f324(f324(f326(f870(a865,a865)),f324(f324(f259(a865,a865),x90371),x90372)),f324(f324(f281(a865,a865,a865),a314),f300(a865,a314))))+P1(f324(f324(f239(a865),x90371),x90372)) % 181.55/181.53 [5049]~P92(x50491)+E(f324(f324(f81(x50491),f324(f106(x50491),a84)),x50492),x50492) % 181.55/181.53 [5077]~P79(x50771)+E(f324(f324(f104(x50771),f324(f80(x50771),x50772)),x50772),f191(x50771)) % 181.55/181.53 [5078]~P79(x50781)+E(f324(f324(f113(x50781),f324(f80(x50781),x50782)),x50782),f247(x50781)) % 181.55/181.53 [5079]~P4(x50791)+E(f324(f324(f81(x50791),f324(f80(x50791),x50792)),x50792),f2(x50791)) % 181.55/181.53 [5080]~P5(x50801)+E(f324(f324(f81(x50801),f324(f80(x50801),x50802)),x50802),f2(x50801)) % 181.55/181.53 [5111]~P92(x51111)+E(f324(f324(f82(x51111),f324(f106(x51111),a100)),x51112),f324(f80(x51111),x51112)) % 181.55/181.53 [5268]~P109(x52681)+E(f324(f324(f82(x52681),f324(f80(x52681),f79(x52681))),x52682),f324(f80(x52681),x52682)) % 181.55/181.53 [5310]E(f324(f75(a1),x53101),f79(a1))+~E(f324(f75(a1),f324(f324(f82(a1),x53101),x53102)),f79(a1)) % 181.55/181.53 [5402]~P92(x54021)+E(f324(f324(f81(x54021),f79(x54021)),f324(f106(x54021),x54022)),f324(f106(x54021),f324(f324(f22(a1),x54022),a100))) % 181.55/181.53 [5455]~P94(x54551)+E(f13(x54551,f324(f324(f302(x54551),x54552),f191(f871(x54551,a859)))),x54552) % 181.55/181.53 [5456]~P94(x54561)+E(f10(x54561,f324(f324(f302(x54561),x54562),f191(f871(x54561,a859)))),x54562) % 181.55/181.53 [5457]~P105(x54571)+E(f14(x54571,f324(f324(f302(x54571),x54572),f191(f871(x54571,a859)))),x54572) % 181.55/181.53 [5458]~P105(x54581)+E(f15(x54581,f324(f324(f302(x54581),x54582),f191(f871(x54581,a859)))),x54582) % 181.55/181.53 [5459]~P6(x54591)+E(f40(x54591,f324(f324(f302(x54591),x54592),f191(f871(x54591,a859)))),x54592) % 181.55/181.53 [5460]~P6(x54601)+E(f39(x54601,f324(f324(f302(x54601),x54602),f191(f871(x54601,a859)))),x54602) % 181.55/181.53 [5482]E(f324(f324(f81(a865),x54821),f324(f324(f22(a865),x54822),x54821)),x54822)+P1(f324(f324(f239(a865),x54822),x54821)) % 181.55/181.53 [5512]E(x55121,f116(x55122))+P1(f324(f324(f239(a865),f2(a865)),f324(f192(f866(x55122)),x55121))) % 181.55/181.53 [5636]~P105(x56361)+E(f11(x56361,f190(x56361),f324(f324(f302(x56361),x56362),f191(f871(x56361,a859)))),x56362) % 181.55/181.53 [5637]~P105(x56371)+E(f12(x56371,f189(x56371),f324(f324(f302(x56371),x56372),f191(f871(x56371,a859)))),x56372) % 181.55/181.53 [5698]E(f324(f324(f22(a865),x56981),f324(f324(f22(a865),x56981),x56982)),x56982)+~P1(f324(f324(f238(a865),x56982),x56981)) % 181.55/181.53 [5699]E(f324(f324(f81(a865),x56991),f324(f324(f22(a865),x56992),x56991)),x56992)+~P1(f324(f324(f238(a865),x56991),x56992)) % 181.55/181.53 [5720]E(f44(a865,f324(f324(f22(a865),x57201),x57202),x57202),f44(a865,x57201,x57202))+P1(f324(f324(f239(a865),x57201),x57202)) % 181.55/181.53 [5731]E(f324(f80(a1),f324(f324(f38(a1),x57311),f324(f80(a1),x57312))),f284(x57311,x57312))+P1(f324(f324(f238(a1),f2(a1)),x57312)) % 181.55/181.53 [5733]~E(x57332,f2(a865))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f249(a865),x57331),x57332))) % 181.55/181.53 [5784]~P92(x57841)+E(f324(f324(f81(x57841),f324(f80(x57841),f79(x57841))),f324(f106(x57841),x57842)),f324(f106(x57841),f324(f324(f81(a1),x57842),a100))) % 181.55/181.53 [5785]E(f324(f324(f249(a865),f324(f106(a865),x57851)),x57852),f324(f324(f249(a865),f2(a865)),x57852))+~P1(f324(a196,f324(f106(a1),x57851))) % 181.55/181.53 [5880]E(f324(f135(a865),f133(a865,f324(f294(a865,x58801),x58802))),x58801)+~P1(f324(f324(f239(a865),x58801),x58802)) % 181.55/181.53 [5899]E(f324(f324(f82(a865),f324(f106(a865),x58991)),f324(f106(a865),x58992)),f324(f106(a865),f324(f324(f82(a1),x58991),x58992)))+P1(f324(f324(f239(a1),x58991),a84)) % 181.55/181.53 [5905]~P122(x59051)+P1(f324(f324(f238(x59051),f2(x59051)),f324(f324(f82(x59051),x59052),x59052))) % 181.55/181.53 [5917]E(f324(f324(f22(a865),f324(a115,x59171)),x59172),f324(a115,f324(f324(f22(a865),x59171),x59172)))+~P1(f324(f324(f238(a865),x59172),x59171)) % 181.55/181.53 [5920]E(f44(a865,f324(f324(f22(a865),x59201),x59202),x59202),f44(a865,x59201,x59202))+~P1(f324(f324(f238(a865),x59202),x59201)) % 181.55/181.53 [5968]E(f324(f324(f249(a865),f324(a107,x59681)),x59682),f324(a107,f324(f324(f249(a1),x59681),x59682)))+~P1(f324(f324(f238(a1),f2(a1)),x59681)) % 181.55/181.53 [5984]P1(f324(f131(x59841),x59842))+P1(f324(f324(f239(a865),f668(x59842,x59841)),f324(f192(f866(x59841)),x59842))) % 181.55/181.53 [5985]P1(f324(f131(x59851),x59852))+P1(f324(f324(f239(a865),f680(x59852,x59851)),f324(f192(f866(x59851)),x59852))) % 181.55/181.53 [6000]~E(x60001,f116(x60002))+~P1(f324(f324(f239(a865),f2(a865)),f324(f192(f866(x60002)),x60001))) % 181.55/181.53 [6014]E(f138(a865,f133(a865,f324(f294(a865,x60141),x60142))),f324(f324(f22(a865),x60142),f79(a865)))+~P1(f324(f324(f239(a865),x60141),x60142)) % 181.55/181.53 [6017]E(f324(f324(f81(a1),x60171),f324(f103(a1),f324(a115,f420(x60172,x60171)))),x60172)+~P1(f324(f324(f239(a1),x60171),x60172)) % 181.55/181.53 [6024]E(x60241,f2(a865))+E(f324(f324(f82(a865),x60242),f324(f324(f249(a865),x60242),f324(f324(f22(a865),x60241),f79(a865)))),f324(f324(f249(a865),x60242),x60241)) % 181.55/181.53 [6049]E(f324(f324(f82(a865),f324(a107,x60491)),f324(a107,x60492)),f324(a107,f324(f324(f82(a1),x60491),x60492)))+~P1(f324(f324(f238(a1),f2(a1)),x60491)) % 181.55/181.53 [6050]E(f324(f324(f38(a865),f324(a107,x60501)),f324(a107,x60502)),f324(a107,f324(f324(f38(a1),x60501),x60502)))+~P1(f324(f324(f238(a1),f2(a1)),x60501)) % 181.55/181.53 [6064]~P112(x60641)+E(f324(f324(f81(x60641),x60642),x60642),f324(f324(f82(x60641),f324(f324(f81(x60641),f79(x60641)),f79(x60641))),x60642)) % 181.55/181.53 [6081]E(f324(f324(f22(a1),f324(f103(a1),x60811)),f324(f103(a1),x60812)),f324(f103(a1),f324(f324(f22(a865),x60811),x60812)))+~P1(f324(f324(f238(a865),x60812),x60811)) % 181.55/181.53 [6083]E(f324(f324(f259(a1,a1),f324(f106(a1),a100)),f324(f324(f81(a1),x60831),x60832)),f49(x60831,x60832))+~P1(f324(f324(f238(a1),x60832),f2(a1))) % 181.55/181.53 [6117]E(f175(x61171,x61172),f116(f866(x61171)))+P1(f324(f324(f326(f866(x61171)),f667(x61172,x61171)),f324(f167(f866(x61171)),x61172))) % 181.55/181.53 [6200]E(f324(f324(f145(a1),x62001),f174(f324(f324(f81(a1),x62001),f79(a1)),x62002)),f174(x62001,x62002))+~P1(f324(f324(f238(a1),x62001),x62002)) % 181.55/181.53 [6236]~P1(f324(f324(f239(a865),x62362),x62361))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f22(a865),x62361),x62362))) % 181.55/181.53 [6267]~P1(f324(f324(f239(a865),x62671),f324(a107,x62672)))+P1(f324(f324(f239(a1),f324(f103(a1),x62671)),x62672)) % 181.55/181.53 [6296]~P105(x62961)+E(f324(f324(f113(f871(x62961,a859)),f324(f245(x62961),x62962)),f324(f324(f302(x62961),x62962),f191(f871(x62961,a859)))),f324(f293(x62961),x62962)) % 181.55/181.53 [6297]~P1(f324(f324(f238(a1),f2(a1)),x62971))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f249(a1),x62971),x62972))) % 181.55/181.53 [6300]~P1(f324(f324(f239(a865),f2(a865)),x63001))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f249(a865),x63001),x63002))) % 181.55/181.53 [6328]~E(f324(x63281,f2(a865)),f2(a865))+E(f324(f324(f6(a865,a865),x63281),f295(a865,f324(a115,f2(a865)),x63282)),f324(f324(f6(a865,a865),x63281),f295(a865,f2(a865),x63282))) % 181.55/181.53 [6392]~P92(x63921)+E(f324(f324(f82(x63921),f324(f324(f81(x63921),f79(x63921)),f79(x63921))),f324(f106(x63921),x63922)),f324(f106(x63921),f324(f324(f81(a1),x63922),x63922))) % 181.55/181.53 [6407]E(f324(f324(f302(a1),x64071),f295(a1,f324(f324(f81(a1),x64071),f79(a1)),x64072)),f295(a1,x64071,x64072))+P1(f324(f324(f239(a1),x64072),x64071)) % 181.55/181.53 [6408]P1(f324(f324(f239(a865),x64081),f324(a107,x64082)))+~P1(f324(f324(f239(a1),f324(f103(a1),x64081)),x64082)) % 181.55/181.53 [6509]E(f324(a107,f324(f324(f38(a1),f324(f106(a1),x65091)),f324(f106(a1),x65092))),f324(f324(f38(a865),f324(f106(a865),x65091)),f324(f106(a865),x65092)))+P1(f324(a196,f324(f106(a1),x65091))) % 181.55/181.53 [6566]P1(f324(f324(f239(a865),x65661),x65662))+~P1(f324(f324(f239(a865),f2(a865)),f324(f324(f22(a865),x65662),x65661))) % 181.55/181.53 [6610]P1(f324(f324(f239(a865),f2(a865)),x66101))+~P1(f324(f324(f239(a865),f2(a865)),f324(f324(f82(a865),x66102),x66101))) % 181.55/181.53 [6611]P1(f324(f324(f239(a865),f2(a865)),x66111))+~P1(f324(f324(f239(a865),f2(a865)),f324(f324(f82(a865),x66111),x66112))) % 181.55/181.53 [6628]~P1(f324(f324(f238(a1),x66281),f2(a1)))+E(f324(f324(f82(a865),f324(a107,f324(f80(a1),x66281))),f324(a107,f324(f80(a1),x66282))),f324(a107,f324(f324(f82(a1),x66281),x66282))) % 181.55/181.53 [6686]~E(x66862,f191(f871(x66861,a859)))+P1(f324(f324(f238(f871(x66861,a859)),x66862),f324(f80(f871(x66861,a859)),x66862))) % 181.55/181.53 [6749]~P92(x67491)+E(f324(f324(f81(x67491),f324(f324(f81(x67491),f2(x67491)),f324(f106(x67491),x67492))),f324(f106(x67491),x67492)),f324(f106(x67491),f324(f324(f81(a1),x67492),x67492))) % 181.55/181.53 [6805]~P1(f324(f324(f239(a1),x68051),x68052))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x68051),f79(a1))),x68052)) % 181.55/181.53 [6870]E(x68701,f2(a865))+~P1(f324(f324(f238(a1),f324(f103(a1),x68702)),f324(f80(a1),f324(f103(a1),x68701)))) % 181.55/181.53 [6871]E(x68711,f2(a865))+~P1(f324(f324(f238(a1),f324(f103(a1),x68711)),f324(f80(a1),f324(f103(a1),x68712)))) % 181.55/181.53 [6973]E(f324(f324(f259(a1,a1),f324(f106(a1),a100)),f324(f324(f81(a1),x69731),x69732)),f49(x69731,x69732))+~P1(f324(f324(f238(a1),f2(a1)),f324(f324(f81(a1),x69731),x69732))) % 181.55/181.53 [7015]~P29(x70151,x70152)+P39(x70151,f324(f258(f871(f870(x70151,x70151),a859),f871(f870(x70151,x70151),a859)),x70152)) % 181.55/181.53 [7033]~P1(f324(f324(f238(a865),f324(a115,f2(a865))),x70331))+P1(f324(f324(f238(a865),f324(a115,f2(a865))),f324(f324(f249(a865),x70331),x70332))) % 181.55/181.53 [7202]~P1(f324(f324(f238(a1),x72021),x72022))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x72021),x72021)),f324(f324(f81(a1),x72022),x72022))) % 181.55/181.53 [7207]~P1(f324(f324(f239(a1),x72071),x72072))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x72071),x72071)),f324(f324(f81(a1),x72072),x72072))) % 181.55/181.53 [7208]~P1(f324(f324(f92(a1),x72081),x72082))+P1(f324(f324(f92(a1),f324(f324(f81(a1),x72081),x72081)),f324(f324(f81(a1),x72082),x72082))) % 181.55/181.53 [7263]~P1(f324(f324(f239(a865),f2(a865)),x72631))+P1(f324(f324(f239(a865),f324(f324(f22(a865),x72631),f324(a115,x72632))),x72631)) % 181.55/181.53 [7298]P1(f324(f324(f238(a865),f324(a115,f2(a865))),x72981))+~P1(f324(f324(f238(a865),f324(a115,f2(a865))),f324(f324(f82(a865),x72982),x72981))) % 181.55/181.53 [7299]P1(f324(f324(f238(a865),f324(a115,f2(a865))),x72991))+~P1(f324(f324(f238(a865),f324(a115,f2(a865))),f324(f324(f82(a865),x72991),x72992))) % 181.55/181.53 [7303]P1(f324(f324(f238(a865),f324(f324(f159(a865),x73031),x73032)),f324(f160(a865),x73031)))+~P1(f324(f324(f239(a865),x73032),f324(f192(f866(a865)),x73031))) % 181.55/181.53 [7344]P1(f324(f324(f239(a1),x73441),x73442))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),x73441),f79(a1))),x73442)) % 181.55/181.53 [7388]P1(f324(f61(x73881),f247(f871(x73881,a859))))+~P1(f324(f61(f871(x73882,x73881)),f247(f871(f871(x73882,x73881),a859)))) % 181.55/181.53 [7389]P1(f324(f61(x73891),f247(f871(x73891,a859))))+~P1(f324(f61(f872(x73892,x73891)),f247(f871(f872(x73892,x73891),a859)))) % 181.55/181.53 [7390]P1(f324(f61(x73901),f247(f871(x73901,a859))))+~P1(f324(f61(f872(x73901,x73902)),f247(f871(f872(x73901,x73902),a859)))) % 181.55/181.53 [7432]E(x74321,f191(f871(x74322,a859)))+~P1(f324(f324(f238(f871(x74322,a859)),x74321),f324(f80(f871(x74322,a859)),x74321))) % 181.55/181.53 [7568]E(f324(f136(f866(x75681),f866(x75681),f124(x75681),f116(x75681)),x75682),f116(x75681))+P1(f324(f324(f326(f866(x75681)),f718(x75682,x75681)),f324(f167(f866(x75681)),x75682))) % 181.55/181.53 [7569]E(f324(f136(f866(x75691),f866(x75691),f124(x75691),f116(x75691)),x75692),f116(x75691))+P1(f324(f324(f326(f866(x75691)),f721(x75692,x75691)),f324(f167(f866(x75691)),x75692))) % 181.55/181.53 [7798]P1(f324(f324(f238(a1),x77981),x77982))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),x77981),x77981)),f324(f324(f81(a1),x77982),x77982))) % 181.55/181.53 [7803]P1(f324(f324(f239(a1),x78031),x78032))+~P1(f324(f324(f239(a1),f324(f324(f81(a1),x78031),x78031)),f324(f324(f81(a1),x78032),x78032))) % 181.55/181.53 [7804]P1(f324(f324(f92(a1),x78041),x78042))+~P1(f324(f324(f92(a1),f324(f324(f81(a1),x78041),x78041)),f324(f324(f81(a1),x78042),x78042))) % 181.55/181.53 [7901]~P112(x79011)+E(f324(f324(f82(x79011),f324(f324(f81(x79011),f79(x79011)),f79(x79011))),f324(f324(f6(a865,x79011),f103(x79011)),f295(a865,f79(a865),x79012))),f324(f324(f82(x79011),f324(f103(x79011),x79012)),f324(f324(f81(x79011),f324(f103(x79011),x79012)),f79(x79011)))) % 181.55/181.53 [7949]P1(f324(f324(f326(a865),x79491),x79492))+~P1(f324(f324(f326(a1),f324(f103(a1),x79491)),f324(f303(a865,a1,f103(a1)),x79492))) % 181.55/181.53 [8108]~P1(f324(f61(x81081),x81082))+E(f324(f303(a865,x81081,f843(x81082,x81081)),f324(f244(a865),f324(f324(f7(a865,a865,a859),f239(a865)),f844(x81082,x81081)))),x81082) % 181.55/181.53 [8392]P43(x83921,x83922)+P1(f324(f324(f326(f870(x83921,x83921)),f324(f324(f259(x83921,x83921),f808(x83922,x83921)),f808(x83922,x83921))),x83922)) % 181.55/181.53 [8532]~P92(x85321)+E(f324(f324(f22(x85321),f79(x85321)),f324(f106(x85321),x85322)),f324(f106(x85321),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f80(a1),x85322)))) % 181.55/181.53 [8658]~P1(f324(f324(f239(f871(a865,a859)),x86581),x86582))+P1(f324(f324(f239(f871(a1,a859)),f324(f303(a865,a1,f103(a1)),x86581)),f324(f303(a865,a1,f103(a1)),x86582))) % 181.55/181.53 [8692]~P1(f324(f324(f239(a1),x86921),x86922))+P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),x86921),x86921)),a100)),f324(f324(f81(a1),x86922),x86922))) % 181.55/181.53 [8694]~P1(f324(f324(f239(a1),x86941),x86942))+P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x86941),x86941)),a100)),f324(f324(f81(a1),x86942),x86942))) % 181.55/181.53 [8768]~P1(f324(f324(f326(a865),x87681),f324(f167(a865),x87682)))+P1(f324(f324(f238(a865),x87681),f324(f136(a865,a865,f81(a865),f2(a865)),x87682))) % 181.55/181.53 [8861]P47(x88611,x88612)+~P1(f324(f324(f326(f870(x88611,x88611)),f324(f324(f259(x88611,x88611),f787(x88612,x88611)),f787(x88612,x88611))),x88612)) % 181.55/181.53 [8998]~P1(f324(f324(f238(f871(a1,a859)),f324(f303(a865,a1,f103(a1)),x89981)),f324(f303(a865,a1,f103(a1)),x89982)))+P1(f324(f324(f238(f871(a865,a859)),x89981),x89982)) % 181.55/181.53 [8999]~P1(f324(f324(f239(f871(a1,a859)),f324(f303(a865,a1,f103(a1)),x89991)),f324(f303(a865,a1,f103(a1)),x89992)))+P1(f324(f324(f239(f871(a865,a859)),x89991),x89992)) % 181.55/181.53 [9083]P1(f324(f324(f239(a1),x90831),x90832))+~P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90831),x90831)),a100)),f324(f324(f81(a1),x90832),x90832))) % 181.55/181.53 [9085]P1(f324(f324(f239(a1),x90851),x90852))+~P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x90851),x90851)),a100)),f324(f324(f81(a1),x90852),x90852))) % 181.55/181.53 [9999]~P1(f324(f61(x99991),x99992))+E(f324(f192(f866(x99991)),f91(f866(x99991),f324(f324(f18(f866(x99991),a859,a859),f324(f324(f8(a859,f871(a859,a859),f866(x99991)),a322),f324(f324(f7(f866(x99991),f871(x99991,a859),a859),f324(f324(f8(f871(x99991,a859),f871(f871(x99991,a859),a859),f866(x99991)),a321),f167(x99991))),x99992))),f131(x99991)))),f219(x99991,x99992)) % 181.55/181.53 [6013]E(f324(f324(f81(a865),f324(f324(f22(a865),x60131),x60132)),x60132),x60131)+~P1(f324(f324(f238(a865),x60132),x60131)) % 181.55/181.53 [6077]E(f324(f324(f38(a865),f324(f324(f82(a865),x60771),x60772)),x60772),x60771)+~P1(f324(f324(f239(a865),f2(a865)),x60772)) % 181.55/181.53 [6078]E(f324(f324(f38(a865),f324(f324(f82(a865),x60781),x60782)),x60781),x60782)+~P1(f324(f324(f239(a865),f2(a865)),x60781)) % 181.55/181.53 [6082]~P72(x60821)+E(f324(f324(f6(a865,x60821),f324(f159(x60821),x60822)),f324(f294(a865,f2(a865)),f324(f192(f866(x60821)),x60822))),f324(f160(x60821),x60822)) % 181.55/181.53 [6192]E(f44(a865,f324(a115,f324(f324(f82(a865),x61921),x61922)),x61921),f79(a865))+~P1(f324(f324(f239(a865),f79(a865)),x61921)) % 181.55/181.53 [6198]E(f324(a115,f324(f324(f81(a865),f324(f106(a865),x61981)),x61982)),f324(f324(f81(a865),f79(a865)),x61982))+~P1(f324(a196,f324(f106(a1),x61981))) % 181.55/181.53 [6225]E(f324(a107,f324(f324(f249(a1),f324(f106(a1),x62251)),x62252)),f324(f324(f249(a865),f324(f106(a865),x62251)),x62252))+P1(f324(a196,f324(f106(a1),x62251))) % 181.55/181.53 [6461]E(f324(f324(f22(a865),x64611),f324(f106(a865),f324(f324(f81(a1),x64612),a100))),f324(f324(f22(a865),f324(a115,x64611)),f324(f106(a865),x64612)))+~P1(f324(f324(f239(a1),a84),x64612)) % 181.55/181.53 [6540]E(x65401,f2(a865))+E(f324(a115,f324(f324(f81(a865),f324(f324(f22(a865),x65401),f79(a865))),x65402)),f324(f324(f81(a865),x65401),x65402)) % 181.55/181.53 [6580]E(x65801,f2(a1))+P1(f324(f324(f239(a1),f2(a1)),f324(f324(f249(a1),f324(f75(a1),x65801)),x65802))) % 181.55/181.53 [6595]~E(x65952,f2(a865))+P1(f324(f324(f239(a1),f2(a1)),f324(f324(f249(a1),f324(f75(a1),x65951)),x65952))) % 181.55/181.53 [6632]E(x66321,f2(a865))+E(f324(f324(f81(a865),x66322),f324(f324(f82(a865),f324(f324(f22(a865),x66321),f79(a865))),x66322)),f324(f324(f82(a865),x66321),x66322)) % 181.55/181.53 [6680]~P1(f324(f324(f238(a1),x66801),x66802))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x66801),a100)),x66802)) % 181.55/181.53 [6808]E(f324(f324(f145(a865),x68081),f133(a865,f324(f294(a865,f324(a115,x68081)),x68082))),f133(a865,f324(f294(a865,x68081),x68082)))+~P1(f324(f324(f239(a865),x68081),x68082)) % 181.55/181.53 [7006]E(x70061,x70062)+~E(f324(f324(f22(a1),f324(f324(f81(a1),x70061),x70061)),a100),f324(f324(f22(a1),f324(f324(f81(a1),x70062),x70062)),a100)) % 181.55/181.53 [7009]E(x70091,f116(x70092))+E(f268(x70092,f324(f324(f148(x70092,f870(a102,x70092)),f324(f259(a102,x70092),f79(a102))),x70091)),f275(x70092,x70091)) % 181.55/181.53 [7232]P1(f324(f324(f238(a1),x72321),x72322))+~P1(f324(f324(f239(a1),f324(f324(f81(a1),x72321),a100)),x72322)) % 181.55/181.53 [7705]~P1(f324(f324(f239(a865),x77051),x77052))+P1(f324(f324(f326(f870(a865,a865)),f324(f324(f259(a865,a865),x77051),x77052)),a243)) % 181.55/181.53 [7926]~P1(f324(f324(f239(a102),f2(a102)),x79261))+P1(f324(f324(f239(a102),f324(f258(a102,f870(a102,a102)),f324(f269(x79261),x79262))),x79261)) % 181.55/181.53 [8239]~P83(x82391)+P1(f324(f324(f238(x82391),f324(f75(x82391),f324(f160(x82391),x82392))),f324(f160(x82391),f324(f324(f148(x82391,x82391),f75(x82391)),x82392)))) % 181.55/181.53 [8264]P1(f324(f324(f239(a865),x82641),x82642))+~P1(f324(f324(f326(f870(a865,a865)),f324(f324(f259(a865,a865),x82641),x82642)),a243)) % 181.55/181.53 [8412]E(f324(f324(f259(x84121,x84121),f608(x84122,x84121)),f608(x84122,x84121)),x84122)+~P1(f324(f324(f326(f870(x84121,x84121)),x84122),f300(x84121,f191(f871(f870(x84121,x84121),a859))))) % 181.55/181.53 [8454]E(f324(f294(a865,x84541),f324(f324(f81(a865),x84541),f324(f37(a865),x84542))),x84542)+~P1(f324(f324(f238(f871(a865,a859)),x84542),f324(f294(a865,x84541),f324(f324(f81(a865),x84541),f324(f37(a865),x84542))))) % 181.55/181.53 [8807]E(f324(f324(f38(a1),f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),x88071),x88071)),a100))),f324(f106(a1),f324(f324(f81(a1),x88072),x88072))),f324(f324(f38(a1),f324(f106(a1),x88071)),f324(f106(a1),x88072)))+~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x88072))) % 181.55/181.53 [8927]E(f172(f866(x89271),f324(f324(f8(a859,a859,f866(x89271)),a319),f324(f324(f7(f866(x89271),f866(x89271),a859),a321),f116(x89271))),x89272),f175(x89271,f175(x89271,x89272)))+~P16(a865,f324(f163(a865),f324(f324(f148(f866(x89271),a865),f192(f866(x89271))),x89272))) % 181.55/181.53 [8930]E(f324(f324(f38(a1),f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),x89301),x89301)),a100))),f324(f106(a1),f324(f324(f81(a1),x89302),x89302))),f324(f324(f38(a1),f324(f324(f81(a1),f324(f106(a1),x89301)),f79(a1))),f324(f106(a1),x89302)))+P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x89302))) % 181.55/181.53 [9778]P1(f324(a196,x97782))+E(f324(f324(f87(a1,a865),f324(f324(f22(a1),x97781),x97782)),f324(f324(f18(a1,a865,a865),f324(f324(f7(a1,a865,f871(a865,a865)),f324(f324(f8(a859,f871(a865,f871(a865,a865)),a1),f99(a865)),a196)),f2(a865))),a107)),f324(f324(f22(a865),f324(a107,x97781)),f324(a107,x97782))) % 181.55/181.53 [9787]E(f324(f324(f87(a1,a865),f324(f106(a1),f324(f324(f81(a1),x97871),f324(f80(a1),x97872)))),f324(f324(f18(a1,a865,a865),f324(f324(f7(a1,a865,f871(a865,a865)),f324(f324(f8(a859,f871(a865,f871(a865,a865)),a1),f99(a865)),a196)),f2(a865))),a107)),f324(f324(f22(a865),f324(f106(a865),x97871)),f324(f106(a865),x97872)))+P1(f324(f324(f239(a1),x97872),a84)) % 181.55/181.53 [9788]~P29(x97881,x97882)+P1(f324(f324(f238(f871(f870(x97881,x97881),a859)),f324(f324(f281(x97881,x97881,x97881),f324(f258(f871(f870(x97881,x97881),a859),f871(f870(x97881,x97881),a859)),x97882)),f324(f262(f871(f870(x97881,x97881),a859),f871(f870(x97881,x97881),a859)),x97882))),f324(f258(f871(f870(x97881,x97881),a859),f871(f870(x97881,x97881),a859)),x97882))) % 181.55/181.53 [9850]~E(f324(f37(a865),f324(f244(a865),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),f324(f324(f7(a865,f871(a865,a859),a859),f326(a865)),x98501))),f324(f324(f7(a865,a865,a859),f239(a865)),f324(a115,x98502))))),f2(a865))+~P1(f324(f324(f326(a865),f2(a865)),x98501)) % 181.55/181.53 [9907]E(f44(a1,f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),x99071),x99071)),a100)),f324(f106(a1),f324(f324(f81(a1),x99072),x99072))),f324(f324(f81(a1),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f44(a1,f324(f106(a1),x99071),f324(f106(a1),x99072)))),f79(a1)))+~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x99072))) % 181.55/181.53 [9916]E(f44(a1,f324(f106(a1),f324(f324(f22(a1),f324(f324(f81(a1),x99161),x99161)),a100)),f324(f106(a1),f324(f324(f81(a1),x99162),x99162))),f324(f324(f22(a1),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f44(a1,f324(f324(f81(a1),f324(f106(a1),x99161)),f79(a1)),f324(f106(a1),x99162)))),f79(a1)))+P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x99162))) % 181.55/181.53 [9968]~P6(x99681)+E(f39(x99681,f324(f244(x99681),f324(f324(f8(f871(x99681,a859),a859,x99681),f89(x99681)),f324(f324(f8(f871(x99681,a859),f871(x99681,a859),x99681),f324(f18(x99681,a859,a859),f324(f324(f8(a859,f871(a859,a859),x99681),a327),f324(f324(f7(x99681,f871(x99681,a859),a859),f326(x99681)),x99682)))),f238(x99681))))),f40(x99681,x99682)) % 181.55/181.53 [9992]~P39(x99921,x99922)+P57(x99921,f324(f324(f7(x99921,f871(f870(x99921,x99921),a859),f871(x99921,a859)),f324(f324(f8(f871(x99921,f871(f871(f870(x99921,x99921),a859),a859)),f871(f871(f870(x99921,x99921),a859),f871(x99921,a859)),x99921),f7(x99921,f871(f870(x99921,x99921),a859),a859)),f324(f324(f8(f871(x99921,f870(x99921,x99921)),f871(x99921,f871(f871(f870(x99921,x99921),a859),a859)),x99921),f324(f8(f870(x99921,x99921),f871(f871(f870(x99921,x99921),a859),a859),x99921),f326(f870(x99921,x99921)))),f259(x99921,x99921)))),x99922)) % 181.55/181.53 [9993]~P9(x99931,f247(f871(x99931,a859)),x99932)+P8(x99931,f324(f324(f7(x99931,f871(f870(x99931,x99931),a859),f871(x99931,a859)),f324(f324(f8(f871(x99931,f871(f871(f870(x99931,x99931),a859),a859)),f871(f871(f870(x99931,x99931),a859),f871(x99931,a859)),x99931),f7(x99931,f871(f870(x99931,x99931),a859),a859)),f324(f324(f8(f871(x99931,f870(x99931,x99931)),f871(x99931,f871(f871(f870(x99931,x99931),a859),a859)),x99931),f324(f8(f870(x99931,x99931),f871(f871(f870(x99931,x99931),a859),a859),x99931),f326(f870(x99931,x99931)))),f259(x99931,x99931)))),x99932)) % 181.55/181.53 [10030]P39(x100301,x100302)+~P57(x100301,f324(f324(f7(x100301,f871(f870(x100301,x100301),a859),f871(x100301,a859)),f324(f324(f8(f871(x100301,f871(f871(f870(x100301,x100301),a859),a859)),f871(f871(f870(x100301,x100301),a859),f871(x100301,a859)),x100301),f7(x100301,f871(f870(x100301,x100301),a859),a859)),f324(f324(f8(f871(x100301,f870(x100301,x100301)),f871(x100301,f871(f871(f870(x100301,x100301),a859),a859)),x100301),f324(f8(f870(x100301,x100301),f871(f871(f870(x100301,x100301),a859),a859),x100301),f326(f870(x100301,x100301)))),f259(x100301,x100301)))),x100302)) % 181.55/181.53 [10031]P9(x100311,f247(f871(x100311,a859)),x100312)+~P8(x100311,f324(f324(f7(x100311,f871(f870(x100311,x100311),a859),f871(x100311,a859)),f324(f324(f8(f871(x100311,f871(f871(f870(x100311,x100311),a859),a859)),f871(f871(f870(x100311,x100311),a859),f871(x100311,a859)),x100311),f7(x100311,f871(f870(x100311,x100311),a859),a859)),f324(f324(f8(f871(x100311,f870(x100311,x100311)),f871(x100311,f871(f871(f870(x100311,x100311),a859),a859)),x100311),f324(f8(f870(x100311,x100311),f871(f871(f870(x100311,x100311),a859),a859),x100311),f326(f870(x100311,x100311)))),f259(x100311,x100311)))),x100312)) % 181.55/181.53 [7183]E(f324(f324(f81(a865),f324(f106(a865),f324(f324(f22(a1),x71831),a100))),x71832),f324(a115,f324(f324(f81(a865),f324(f106(a865),x71831)),x71832)))+P1(f324(a196,f324(f106(a1),x71831))) % 181.55/181.53 [7625]~P92(x76251)+E(f324(f324(f81(x76251),f324(f324(f81(x76251),f79(x76251)),f324(f106(x76251),x76252))),f324(f106(x76251),x76252)),f324(f106(x76251),f324(f324(f22(a1),f324(f324(f81(a1),x76252),x76252)),a100))) % 181.55/181.53 [8266]~P1(f324(f324(f238(a1),x82661),x82662))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x82661),x82661)),f324(f324(f22(a1),f324(f324(f81(a1),x82662),x82662)),a100))) % 181.55/181.53 [8268]~P1(f324(f324(f238(a1),x82681),x82682))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x82681),x82681)),f324(f324(f22(a1),f324(f324(f81(a1),x82682),x82682)),a100))) % 181.55/181.53 [8696]P1(f324(f324(f238(a1),x86961),x86962))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),x86961),x86961)),f324(f324(f22(a1),f324(f324(f81(a1),x86962),x86962)),a100))) % 181.55/181.53 [8698]P1(f324(f324(f238(a1),x86981),x86982))+~P1(f324(f324(f239(a1),f324(f324(f81(a1),x86981),x86981)),f324(f324(f22(a1),f324(f324(f81(a1),x86982),x86982)),a100))) % 181.55/181.53 [8986]~P1(f324(f324(f238(a1),x89861),x89862))+P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),x89861),x89861)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),x89862),x89862)),a100))) % 181.55/181.53 [8988]~P1(f324(f324(f239(a1),x89881),x89882))+P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x89881),x89881)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),x89882),x89882)),a100))) % 181.55/181.53 [8989]~P1(f324(f324(f92(a1),x89891),x89892))+P1(f324(f324(f92(a1),f324(f324(f22(a1),f324(f324(f81(a1),x89891),x89891)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),x89892),x89892)),a100))) % 181.55/181.53 [9254]P1(f324(f324(f238(a1),x92541),x92542))+~P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),x92541),x92541)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),x92542),x92542)),a100))) % 181.55/181.53 [9256]P1(f324(f324(f239(a1),x92561),x92562))+~P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),x92561),x92561)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),x92562),x92562)),a100))) % 181.55/181.53 [9257]P1(f324(f324(f92(a1),x92571),x92572))+~P1(f324(f324(f92(a1),f324(f324(f22(a1),f324(f324(f81(a1),x92571),x92571)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),x92572),x92572)),a100))) % 181.55/181.53 [9290]~P1(f324(f61(x92901),x92902))+P1(f324(f61(f871(x92901,a859)),f324(f244(f871(x92901,a859)),f324(f324(f7(f871(x92901,a859),f871(x92901,a859),a859),f238(f871(x92901,a859))),x92902)))) % 181.55/181.53 [9338]~E(f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),x93381),f191(f871(f870(a865,a865),a859)))),f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),x93382),f191(f871(f870(a865,a865),a859)))))+P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),x93381),x93382)),a111)) % 181.55/181.53 [9428]E(f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),x94281),f191(f871(f870(a865,a865),a859)))),f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),x94282),f191(f871(f870(a865,a865),a859)))))+~P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),x94281),x94282)),a111)) % 181.55/181.53 [9464]P1(f324(f324(f238(a1),f2(a1)),f652(x94641,x94642)))+E(f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),x94641)),f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),x94642))) % 181.55/181.53 [9978]~P6(x99781)+E(f40(x99781,f324(f244(x99781),f324(f324(f8(f871(x99781,a859),a859,x99781),f89(x99781)),f324(f324(f8(f871(x99781,a859),f871(x99781,a859),x99781),f324(f18(x99781,a859,a859),f324(f324(f8(a859,f871(a859,a859),x99781),a327),f324(f324(f7(x99781,f871(x99781,a859),a859),f326(x99781)),x99782)))),f324(f7(x99781,x99781,a859),f238(x99781)))))),f39(x99781,x99782)) % 181.55/181.53 [9998]P1(f324(f324(f326(a865),f2(a865)),x99981))+E(f324(f37(a865),f324(f244(a865),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),f324(f324(f7(a865,f871(a865,a859),a859),f324(f324(f8(a865,f871(f871(a865,a859),a859),a865),f326(a865)),a115)),x99981))),f324(f324(f7(a865,a865,a859),f239(a865)),x99982)))),f324(f37(a865),f324(f244(a865),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),f324(f324(f7(a865,f871(a865,a859),a859),f326(a865)),x99981))),f324(f324(f7(a865,a865,a859),f239(a865)),f324(a115,x99982)))))) % 181.55/181.53 [7496]~P92(x74961)+E(f324(f324(f82(x74961),x74962),f324(f106(x74961),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),x74962) % 181.55/181.53 [7749]~P92(x77491)+E(f324(f324(f81(x77491),f324(f106(x77491),x77492)),f79(x77491)),f324(f106(x77491),f324(f324(f81(a1),x77492),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))) % 181.55/181.53 [7899]P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x78992)))+E(f324(f324(f249(a1),x78991),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),x78992),x78992)),a100))),f79(a1)) % 181.55/181.53 [9316]~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x93162)))+E(f324(f324(f249(a1),x93161),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),x93162),x93162)),a100))),f324(f324(f87(a1,a1),f324(f324(f249(a1),x93161),f324(f106(a865),x93162))),f324(f324(f18(a1,a1,a1),f324(f324(f8(a1,f871(a1,a1),a1),f82(a1)),f324(f82(a1),x93161))),f5(a1)))) % 181.55/181.53 [9693]~P1(f324(f324(f238(a865),f799(x96932,x96931)),f324(x96931,f799(x96932,x96931))))+P1(f324(f61(a865),f324(f244(a865),f324(f324(f7(a865,a865,a859),f324(f324(f8(a865,f871(a865,a859),a865),f238(a865)),x96931)),x96932)))) % 181.55/181.53 [9840]~P1(f324(f324(f238(a865),f324(f106(a865),x98401)),f324(a115,x98402)))+P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x98401),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f7(a1,a865,a859),f324(f324(f8(a865,f871(a865,a859),a1),f238(a865)),a107)),x98402)))) % 181.55/181.53 [9841]~P1(f324(f324(f239(a865),f324(f106(a865),x98411)),f324(a115,x98412)))+P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x98411),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f7(a1,a865,a859),f324(f324(f8(a865,f871(a865,a859),a1),f239(a865)),a107)),x98412)))) % 181.55/181.53 [9891]P1(f324(f324(f238(a865),f324(f106(a865),x98911)),f324(a115,x98912)))+~P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x98911),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f7(a1,a865,a859),f324(f324(f8(a865,f871(a865,a859),a1),f238(a865)),a107)),x98912)))) % 181.55/181.53 [9892]P1(f324(f324(f239(a865),f324(f106(a865),x98921)),f324(a115,x98922)))+~P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x98921),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f7(a1,a865,a859),f324(f324(f8(a865,f871(a865,a859),a1),f239(a865)),a107)),x98922)))) % 181.55/181.53 [9922]~P1(f324(f324(f238(a865),f324(a115,x99222)),f324(f106(a865),x99221)))+P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x99221),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f8(a865,a859,a1),f324(f238(a865),x99222)),a107))))) % 181.55/181.53 [9923]~P1(f324(f324(f239(a865),f324(a115,x99232)),f324(f106(a865),x99231)))+P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x99231),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f8(a865,a859,a1),f324(f239(a865),x99232)),a107))))) % 181.55/181.53 [9966]P1(f324(f324(f238(a865),f324(a115,x99661)),f324(f106(a865),x99662)))+~P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x99662),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f8(a865,a859,a1),f324(f238(a865),x99661)),a107))))) % 181.55/181.53 [9967]P1(f324(f324(f239(a865),f324(a115,x99671)),f324(f106(a865),x99672)))+~P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x99672),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f8(a865,a859,a1),f324(f239(a865),x99671)),a107))))) % 181.55/181.53 [10037]~P1(f324(f324(f326(a865),f2(a865)),x100371))+E(f324(a115,f324(f37(a865),f324(f244(a865),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),f324(f324(f7(a865,f871(a865,a859),a859),f324(f324(f8(a865,f871(f871(a865,a859),a859),a865),f326(a865)),a115)),x100371))),f324(f324(f7(a865,a865,a859),f239(a865)),x100372))))),f324(f37(a865),f324(f244(a865),f324(f324(f18(a865,a859,a859),f324(f324(f8(a859,f871(a859,a859),a865),a322),f324(f324(f7(a865,f871(a865,a859),a859),f326(a865)),x100371))),f324(f324(f7(a865,a865,a859),f239(a865)),f324(a115,x100372)))))) % 181.55/181.53 [8437]~P92(x84371)+E(f324(f324(f82(x84371),f324(f106(x84371),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),x84372),x84372) % 181.55/181.53 [8497]~P92(x84971)+E(f324(f324(f81(x84971),f79(x84971)),f324(f106(x84971),x84972)),f324(f106(x84971),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),x84972))) % 181.55/181.53 [8560]~P92(x85601)+E(f324(f324(f22(x85601),f324(f106(x85601),x85602)),f79(x85601)),f324(f106(x85601),f324(f324(f81(a1),x85602),f324(f80(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.53 [8716]~P1(f324(f324(f239(a865),f324(f106(a865),a84)),x87162))+E(f324(f324(f22(a865),x87161),f324(f324(f22(a865),x87162),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f22(a865),f324(a115,x87161)),x87162)) % 181.55/181.53 [9354]~P112(x93541)+E(f324(f324(f82(x93541),x93542),x93542),f324(f324(f249(x93541),x93542),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.53 [9355]~P77(x93551)+E(f324(f324(f249(x93551),x93552),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f82(x93551),x93552),x93552)) % 181.55/181.53 [9357]~P92(x93571)+E(f324(f324(f82(x93571),x93572),f324(f106(x93571),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f81(x93571),x93572),x93572)) % 181.55/181.53 [9609]~P135(x96091)+E(f324(f324(f249(x96091),f324(f80(x96091),x96092)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f249(x96091),x96092),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.53 [9610]~P117(x96101)+E(f324(f324(f249(x96101),f324(f75(x96101),x96102)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f249(x96101),x96102),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.53 [9606]~P92(x96061)+E(f324(f324(f82(x96061),f324(f106(x96061),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x96062),f324(f324(f81(x96061),x96062),x96062)) % 181.55/181.53 [9733]~P117(x97331)+E(f324(f75(x97331),f324(f324(f249(x97331),x97332),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x97331),x97332),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.53 [9795]~P117(x97951)+P1(f324(f324(f238(x97951),f2(x97951)),f324(f324(f249(x97951),x97952),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.53 [9957]~E(f324(a115,x99572),f324(f106(a865),x99571))+P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x99571),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f7(a1,a865,a859),f324(f324(f8(a865,f871(a865,a859),a1),a321),a107)),x99572))))) % 181.55/181.53 [9958]~E(f324(f106(a865),x99581),f324(a115,x99582))+P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x99581),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f7(a1,a865,a859),f324(f324(f8(a865,f871(a865,a859),a1),a321),a107)),x99582))))) % 181.55/181.53 [10001]E(f324(a115,x100011),f324(f106(a865),x100012))+~P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x100012),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f7(a1,a865,a859),f324(f324(f8(a865,f871(a865,a859),a1),a321),a107)),x100011))))) % 181.55/181.53 [10002]E(f324(f106(a865),x100021),f324(a115,x100022))+~P1(f324(f324(f87(a1,a859),f324(f106(a1),f324(f324(f81(a1),x100021),a100))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a327),f324(f324(f8(a859,a859,a1),a319),a196))),f324(f324(f7(a1,a865,a859),f324(f324(f8(a865,f871(a865,a859),a1),a321),a107)),x100022))))) % 181.55/181.53 [9793]~P92(x97931)+E(f324(f324(f249(x97931),f324(f106(x97931),a100)),f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x97932)),f79(x97931)) % 181.55/181.53 [9794]~P135(x97941)+E(f324(f324(f249(x97941),f324(f80(x97941),f79(x97941))),f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x97942)),f79(x97941)) % 181.55/181.53 [9797]~P77(x97971)+E(f324(f324(f249(x97971),x97972),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),a100))),f324(f324(f82(x97971),f324(f324(f82(x97971),x97972),x97972)),x97972)) % 181.55/181.53 [9981]~P1(f324(f324(f238(a1),f2(a1)),x99812))+E(f44(a1,f324(f324(f81(a1),f79(a1)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x99811)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x99812)),f324(f324(f81(a1),f79(a1)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f44(a1,x99811,x99812)))) % 181.55/181.53 [10004]~P1(f324(f324(f238(a1),f2(a1)),x100042))+E(f324(f324(f38(a1),f324(f324(f81(a1),f79(a1)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100041))),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100042)),f324(f324(f38(a1),x100041),x100042)) % 181.55/181.53 [10006]~P1(f324(f324(f238(a1),x100062),f2(a1)))+E(f324(f324(f38(a1),f324(f324(f81(a1),f79(a1)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100061))),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100062)),f324(f324(f38(a1),f324(f324(f81(a1),x100061),f79(a1))),x100062)) % 181.55/181.53 [10007]~P1(f324(f324(f238(a1),x100072),f2(a1)))+E(f44(a1,f324(f324(f81(a1),f79(a1)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100071)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100072)),f324(f324(f22(a1),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f44(a1,f324(f324(f81(a1),x100071),f79(a1)),x100072))),f79(a1))) % 181.55/181.53 [9882]~P92(x98821)+E(f324(f324(f249(x98821),f324(f106(x98821),a100)),f324(a115,f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98822))),f324(f106(x98821),a100)) % 181.55/181.53 [9884]~P135(x98841)+E(f324(f324(f249(x98841),f324(f80(x98841),f79(x98841))),f324(a115,f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98842))),f324(f80(x98841),f79(x98841))) % 181.55/181.53 [7964]~E(x79642,x79643)+P36(x79641,x79641,a321,x79642,x79643) % 181.55/181.53 [8511]E(x85111,x85112)+~P36(x85113,x85113,a321,x85111,x85112) % 181.55/181.53 [5089]~P39(x50891,x50893)+P39(x50891,f318(x50891,x50892,x50893)) % 181.55/181.53 [5249]P30(x52491,x52492,x52493)+~P30(x52491,f324(a115,x52492),x52493) % 181.55/181.53 [5334]~P9(x53341,x53342,x53343)+P9(f866(x53341),f155(x53341,x53342),f152(x53341,x53343)) % 181.55/181.53 [5335]~P41(x53351,x53352,x53353)+P41(f866(x53351),f155(x53351,x53352),f152(x53351,x53353)) % 181.55/181.53 [5447]P53(x54471,x54472,x54473)+~E(f594(x54473,x54472,x54471),f595(x54473,x54472,x54471)) % 181.55/181.53 [5448]P52(x54481,x54482,x54483)+~E(f597(x54483,x54482,x54481),f598(x54483,x54482,x54481)) % 181.55/181.53 [6367]P31(x63671,x63672,x63673)+~P30(x63671,f551(x63673,x63672,x63671),f552(x63673,x63672,x63671)) % 181.55/181.53 [7970]~E(x79702,x79703)+P28(x79701,x79701,f34(x79701),x79702,x79703) % 181.55/181.53 [8519]E(x85191,x85192)+~P28(x85193,x85193,f34(x85193),x85191,x85192) % 181.55/181.53 [4645]~E(x46451,f203(x46452))+~E(x46451,f324(f233(x46452),x46453)) % 181.55/181.53 [4696]~E(f324(f163(x46962),x46961),x46963)+E(x46961,f324(f163(x46962),x46963)) % 181.55/181.53 [4697]~E(x46972,f324(f163(x46971),x46973))+E(f324(f163(x46971),x46972),x46973) % 181.55/181.53 [4744]E(x47441,x47442)+~E(f324(f233(x47443),x47441),f324(f233(x47443),x47442)) % 181.55/181.53 [4745]E(x47451,x47452)+~E(f324(f163(x47453),x47451),f324(f163(x47453),x47452)) % 181.55/181.53 [4947]~P8(x49473,x49471)+P1(f324(f324(x49471,x49472),x49472)) % 181.55/181.53 [4948]~P50(x49483,x49481)+P1(f324(f324(x49481,x49482),x49482)) % 181.55/181.53 [4950]~P57(x49501,x49502)+P1(f324(f312(x49501,x49502),x49503)) % 181.55/181.53 [5011]~P39(x50111,x50112)+P39(f866(x50111),f324(f137(x50111,x50112),x50113)) % 181.55/181.53 [5016]~P1(f324(x50162,x50163))+~E(f324(f244(x50161),x50162),f191(f871(x50161,a859))) % 181.55/181.53 [5017]~P1(f324(x50172,x50173))+~E(f191(f871(x50171,a859)),f324(f244(x50171),x50172)) % 181.55/181.53 [5046]~P1(f324(x50461,x50463))+P1(f324(x50461,f91(x50462,x50461))) % 181.55/181.53 [5161]~E(x51612,x51613)+P1(f324(f324(f326(x51611),x51612),f324(a321,x51613))) % 181.55/181.53 [5216]E(f324(f163(x52161),x52162),f324(f324(f145(x52161),x52163),f116(x52161)))+~E(x52162,f324(f324(f145(x52161),x52163),f116(x52161))) % 181.55/181.53 [5217]~E(x52173,f324(f324(f145(x52171),x52172),f116(x52171)))+E(f324(f324(f145(x52171),x52172),f116(x52171)),f324(f163(x52171),x52173)) % 181.55/181.53 [5242]~E(x52423,f324(f16(f869(x52422),x52421),f203(x52422)))+E(f179(x52421,x52422,x52423),f191(f871(x52421,a859))) % 181.55/181.53 [5263]~P35(x52631,x52632,x52633)+P35(x52631,x52632,f324(f163(x52631),x52633)) % 181.55/181.53 [5264]~P33(x52641,x52642,x52643)+P33(x52641,x52642,f324(f163(x52641),x52643)) % 181.55/181.53 [5267]E(f324(f37(x52671),f330(x52672,x52673,x52671)),x52672)+~E(f324(f37(x52671),x52673),f324(a115,x52672)) % 181.55/181.53 [5273]~P39(x52731,x52733)+P1(f324(f324(f326(x52731),x52732),f313(x52731,x52733))) % 181.55/181.53 [5276]~E(f324(f163(x52762),x52761),f324(f324(f145(x52762),x52763),f116(x52762)))+E(x52761,f324(f324(f145(x52762),x52763),f116(x52762))) % 181.55/181.53 [5277]~E(f324(f324(f145(x52772),x52773),f116(x52772)),f324(f163(x52772),x52771))+E(x52771,f324(f324(f145(x52772),x52773),f116(x52772))) % 181.55/181.53 [5292]E(x52921,f324(f16(f869(x52922),x52923),f203(x52922)))+~E(f179(x52923,x52922,x52921),f191(f871(x52923,a859))) % 181.55/181.53 [5298]E(f86(f870(a865,a865),f47(x52981,x52982)),x52983)+~P1(f324(f47(x52981,x52982),x52983)) % 181.55/181.53 [5306]~E(x53063,f324(f233(x53061),x53062))+P1(f324(f324(f326(x53061),x53062),f232(x53061,x53063))) % 181.55/181.53 [5338]P35(x53381,x53382,x53383)+~P35(x53381,x53382,f324(f163(x53381),x53383)) % 181.55/181.53 [5339]P33(x53391,x53392,x53393)+~P33(x53391,x53392,f324(f163(x53391),x53393)) % 181.55/181.53 [5401]~E(x54012,f116(x54011))+P1(f324(f324(f326(f866(x54011)),x54012),f155(x54011,x54013))) % 181.55/181.53 [5408]~P41(x54081,x54082,x54083)+P41(x54081,x54082,f324(f279(x54081,x54081),x54083)) % 181.55/181.53 [5409]~P53(x54091,x54092,x54093)+P53(x54091,x54092,f324(f279(x54091,x54091),x54093)) % 181.55/181.53 [5428]~P59(x54281)+E(f44(x54281,f44(x54281,x54282,x54283),x54283),f44(x54281,x54282,x54283)) % 181.55/181.53 [5523]E(x55231,x55232)+~P1(f324(f324(f326(x55233),x55231),f324(a321,x55232))) % 181.55/181.53 [5568]~P141(x55681)+E(f193(x55681,x55682,f2(a865),x55683),x55683) % 181.55/181.53 [5588]P41(x55881,x55882,x55883)+~P41(x55881,x55882,f324(f279(x55881,x55881),x55883)) % 181.55/181.53 [5589]P53(x55891,x55892,x55893)+~P53(x55891,x55892,f324(f279(x55891,x55891),x55893)) % 181.55/181.53 [5593]~P105(x55932)+E(f144(x55931,x55932,x55933,f116(x55931)),f116(x55931)) % 181.55/181.53 [5606]E(f164(x56061,x56062,f146(x56061,x56063)),f146(x56061,f164(x56061,x56062,x56063)))+~P1(f324(f131(x56061),x56063)) % 181.55/181.53 [5612]E(x56121,f324(f233(x56122),x56123))+~P1(f324(f324(f326(x56122),x56123),f232(x56122,x56121))) % 181.55/181.53 [5707]E(f324(f130(x57071,x57072),x57073),f116(x57071))+P1(f324(x57072,f681(x57073,x57072,x57071))) % 181.55/181.53 [5850]~P1(f324(f131(x58501),x58502))+P1(f324(f131(x58501),f171(x58501,x58502,x58503))) % 181.55/181.53 [5851]~P1(f324(f131(x58511),x58513))+P1(f324(f131(x58511),f164(x58511,x58512,x58513))) % 181.55/181.53 [5852]~P1(f324(f131(x58521),x58523))+P1(f324(f131(x58521),f172(x58521,x58522,x58523))) % 181.55/181.53 [5853]~P1(f324(f131(x58531),x58533))+P1(f324(f131(x58531),f134(x58531,x58532,x58533))) % 181.55/181.53 [5854]~P143(x58541,x58543,x58542)+P1(f324(x58541,f44(a1,x58542,x58543))) % 181.55/181.53 [5871]~P35(x58713,x58711,x58712)+P1(f324(x58711,f764(x58712,x58711,x58713))) % 181.55/181.53 [5872]~P37(x58723,x58721,x58722)+P1(f324(x58721,f791(x58722,x58721,x58723))) % 181.55/181.53 [5893]E(f324(f130(x58931,x58932),x58933),f172(x58931,x58932,x58933))+P1(f324(x58932,f738(x58933,x58932,x58931))) % 181.55/181.53 [5932]~P1(f324(f131(x59321),x59323))+P1(f324(f131(f866(x59321)),f54(x59321,x59322,x59323))) % 181.55/181.53 [5963]~P106(x59631)+E(f324(f324(f104(f871(x59631,a859)),f324(f245(x59631),x59632)),f295(x59631,x59632,x59633)),f191(f871(x59631,a859))) % 181.55/181.53 [5964]~P106(x59641)+E(f324(f324(f104(f871(x59641,a859)),f324(f293(x59641),x59642)),f298(x59641,x59642,x59643)),f191(f871(x59641,a859))) % 181.55/181.53 [5965]~P106(x59651)+E(f324(f324(f104(f871(x59651,a859)),f324(f293(x59651),x59652)),f297(x59651,x59652,x59653)),f191(f871(x59651,a859))) % 181.55/181.53 [6188]E(f324(f130(x61881,x61882),x61883),x61883)+~P1(f324(x61882,f682(x61883,x61882,x61881))) % 181.55/181.53 [6190]E(f324(f324(f302(x61901),f371(x61902,x61903,x61901)),f330(x61902,x61903,x61901)),x61903)+~E(f324(f37(x61901),x61903),f324(a115,x61902)) % 181.55/181.53 [6205]P143(x62051,x62052,x62053)+~P1(f324(x62051,f44(a1,x62053,x62052))) % 181.55/181.53 [6252]P33(x62521,x62522,x62523)+~P1(f324(x62522,f778(x62523,x62522,x62521))) % 181.55/181.53 [6253]P33(x62531,x62532,x62533)+~P1(f324(x62532,f788(x62532,x62533,x62531))) % 181.55/181.53 [6254]P33(x62541,x62542,x62543)+~P1(f324(x62542,f789(x62543,x62542,x62541))) % 181.55/181.53 [6256]E(f172(x62561,x62562,x62563),x62563)+~P1(f324(x62562,f739(x62563,x62562,x62561))) % 181.55/181.53 [6335]~P1(f324(x63352,f534(x63353,x63352,x63351)))+P1(f324(f252(x63351,x63352),x63353)) % 181.55/181.53 [6336]~P1(f324(x63362,f743(x63363,x63362,x63361)))+P1(f324(f154(x63361,x63362),x63363)) % 181.55/181.53 [6581]~P1(f324(f312(x65811,x65812),f391(x65813,x65812,x65811)))+P1(f324(f312(x65811,x65812),x65813)) % 181.55/181.53 [6582]~P1(f324(f312(x65821,x65822),f396(x65823,x65822,x65821)))+P1(f324(f312(x65821,x65822),x65823)) % 181.55/181.53 [7184]~P59(x71841)+E(f324(f324(f81(x71841),f324(f324(f82(x71841),x71842),f324(f324(f38(x71841),x71843),x71842))),f44(x71841,x71843,x71842)),x71843) % 181.55/181.53 [7648]E(f324(f324(f259(x76481,x76481),f827(x76482,x76483,x76481)),f827(x76482,x76483,x76481)),x76483)+~P1(f324(f324(f326(f870(x76481,x76481)),x76483),f256(x76481,x76482))) % 181.55/181.53 [7757]~P1(f324(f324(f326(x77571),f511(x77573,x77572,x77571)),f313(x77571,x77573)))+P1(f324(f324(f326(x77571),x77572),f313(x77571,x77573))) % 181.55/181.53 [7758]~P1(f324(f324(f326(x77581),f569(x77583,x77582,x77581)),f313(x77581,x77583)))+P1(f324(f324(f326(x77581),x77582),f313(x77581,x77583))) % 181.55/181.53 [7759]~P1(f324(f324(f326(x77591),f572(x77593,x77592,x77591)),f313(x77591,x77593)))+P1(f324(f324(f326(x77591),x77592),f313(x77591,x77593))) % 181.55/181.53 [7945]~P59(x79451)+E(f324(f324(f81(x79451),f324(f324(f82(x79451),f324(f324(f38(x79451),x79452),x79453)),x79453)),f44(x79451,x79452,x79453)),x79452) % 181.55/181.53 [7992]~E(f324(f37(x79921),x79922),f324(a115,x79923))+~P1(f324(f324(f326(x79921),f371(x79923,x79922,x79921)),f330(x79923,x79922,x79921))) % 181.55/181.53 [8617]P1(f324(f324(f238(f871(f870(x86171,x86171),a859)),f300(x86171,x86172)),f300(x86171,x86173)))+~P1(f324(f324(f238(f871(f870(x86171,x86171),a859)),x86172),f300(x86171,x86173))) % 181.55/181.53 [8896]E(x88961,f116(x88962))+~P1(f324(f324(f326(f870(f866(x88962),f866(x88962))),f324(f324(f259(f866(x88962),f866(x88962)),x88961),f116(x88962))),f152(x88962,x88963))) % 181.55/181.53 [8921]E(x89211,f116(x89212))+~P1(f324(f324(f326(f870(f866(x89212),f866(x89212))),f324(f324(f259(f866(x89212),f866(x89212)),f116(x89212)),x89211)),f152(x89212,x89213))) % 181.55/181.53 [9048]E(f324(f324(f145(x90481),f705(x90482,x90483,x90481)),f706(x90482,x90483,x90481)),x90483)+~P1(f324(f324(f326(f870(f866(x90481),f866(x90481))),f324(f324(f259(f866(x90481),f866(x90481)),f116(x90481)),x90483)),f141(x90481,x90482))) % 181.55/181.53 [9283]~P122(x92831)+~P1(f324(f324(f239(x92831),f324(f324(f81(x92831),f324(f324(f82(x92831),x92832),x92832)),f324(f324(f82(x92831),x92833),x92833))),f2(x92831))) % 181.55/181.53 [9333]P1(f324(f61(x93331),x93332))+~P1(f324(f324(f326(f870(f871(x93331,a859),f871(x93331,a859))),f324(f324(f259(f871(x93331,a859),f871(x93331,a859)),x93333),x93332)),f299(x93331))) % 181.55/181.53 [9632]~P48(x96321,x96322,x96323)+P1(f324(f324(f238(a1),f324(f324(f73(f870(a1,a1),a1,x96321,f258(a1,a1)),f217(x96321)),f228(x96321,x96322,f225(x96321,x96323)))),f2(a1))) % 181.55/181.53 [9633]~P49(x96331,x96332,x96333)+P1(f324(f324(f239(a1),f324(f324(f73(f870(a1,a1),a1,x96331,f258(a1,a1)),f217(x96331)),f228(x96331,x96332,f225(x96331,x96333)))),f2(a1))) % 181.55/181.53 [9761]P49(x97611,x97612,x97613)+~P1(f324(f324(f239(a1),f324(f324(f73(f870(a1,a1),a1,x97611,f258(a1,a1)),f217(x97611)),f228(x97611,x97612,f225(x97611,x97613)))),f2(a1))) % 181.55/181.53 [9762]P48(x97621,x97622,x97623)+~P1(f324(f324(f238(a1),f324(f324(f73(f870(a1,a1),a1,x97621,f258(a1,a1)),f217(x97621)),f228(x97621,x97622,f225(x97621,x97623)))),f2(a1))) % 181.55/181.53 [10082]~P117(x100821)+~P1(f324(f324(f239(x100821),f324(f324(f81(x100821),f324(f324(f249(x100821),x100822),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100821),x100823),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))),f2(x100821))) % 181.55/181.53 [4727]~E(x47273,f116(x47271))+E(f324(f324(f124(x47271),x47272),x47273),x47272) % 181.55/181.53 [4728]~E(x47282,f116(x47281))+E(f324(f324(f124(x47281),x47282),x47283),x47283) % 181.55/181.53 [4735]~E(x47352,f2(a865))+E(f324(f324(f170(x47351),x47352),x47353),f116(x47351)) % 181.55/181.53 [4739]~E(x47393,f116(x47391))+E(f324(f324(f170(x47391),x47392),x47393),f116(x47391)) % 181.55/181.53 [4779]~E(x47791,x47793)+E(x47791,f324(f324(f124(x47792),f116(x47792)),x47793)) % 181.55/181.53 [4865]~P2(x48652)+E(f324(f191(f871(x48651,x48652)),x48653),f191(x48652)) % 181.55/181.53 [4866]~P107(x48662)+E(f324(f247(f871(x48661,x48662)),x48663),f247(x48662)) % 181.55/181.53 [4884]E(x48841,f116(x48842))+~E(f324(f324(f124(x48842),x48843),x48841),x48843) % 181.55/181.53 [4885]E(x48851,f116(x48852))+~E(f324(f324(f124(x48852),x48851),x48853),x48853) % 181.55/181.53 [4893]E(x48931,f116(x48932))+~E(f324(f324(f124(x48932),x48933),x48931),f116(x48932)) % 181.55/181.53 [4894]E(x48941,f116(x48942))+~E(f324(f324(f124(x48942),x48941),x48943),f116(x48942)) % 181.55/181.53 [4917]~E(x49172,f2(a865))+E(f324(f324(f82(a865),x49171),x49172),f324(f324(f82(a865),x49173),x49172)) % 181.55/181.53 [4919]~E(x49191,f2(a865))+E(f324(f324(f82(a865),x49191),x49192),f324(f324(f82(a865),x49191),x49193)) % 181.55/181.53 [4972]~P94(x49721)+E(f324(f324(f104(x49721),x49722),x49723),f324(f324(f104(x49721),x49723),x49722)) % 181.55/181.53 [4974]~P99(x49741)+E(f324(f324(f104(x49741),x49742),x49743),f324(f324(f104(x49741),x49743),x49742)) % 181.55/181.53 [4975]~P94(x49751)+E(f324(f324(f113(x49751),x49752),x49753),f324(f324(f113(x49751),x49753),x49752)) % 181.55/181.53 [4977]~P100(x49771)+E(f324(f324(f113(x49771),x49772),x49773),f324(f324(f113(x49771),x49773),x49772)) % 181.55/181.53 [4978]~P112(x49781)+E(f324(f324(f82(x49781),x49782),x49783),f324(f324(f82(x49781),x49783),x49782)) % 181.55/181.53 [4979]~P112(x49791)+E(f324(f324(f81(x49791),x49792),x49793),f324(f324(f81(x49791),x49793),x49792)) % 181.55/181.53 [4981]~P105(x49811)+E(f324(f324(f189(x49811),x49812),x49813),f324(f324(f189(x49811),x49813),x49812)) % 181.55/181.53 [4983]~P105(x49831)+E(f324(f324(f190(x49831),x49832),x49833),f324(f324(f190(x49831),x49833),x49832)) % 181.55/181.53 [5041]E(f44(a865,x50411,x50412),f2(a865))+~E(x50411,f324(f324(f82(a865),x50412),x50413)) % 181.55/181.53 [5042]E(f44(a1,x50421,x50422),f2(a1))+~E(x50421,f324(f324(f82(a1),x50422),x50423)) % 181.55/181.53 [5101]E(x51011,x51012)+~E(f324(f324(f81(a865),x51013),x51011),f324(f324(f81(a865),x51013),x51012)) % 181.55/181.53 [5102]E(x51021,x51022)+~E(f324(f324(f81(a865),x51021),x51023),f324(f324(f81(a865),x51022),x51023)) % 181.55/181.53 [5112]~P79(x51121)+E(f324(f324(f104(x51121),x51122),f324(f80(x51121),x51123)),f324(f324(f22(x51121),x51122),x51123)) % 181.55/181.53 [5113]~P4(x51131)+E(f324(f324(f81(x51131),x51132),f324(f80(x51131),x51133)),f324(f324(f22(x51131),x51132),x51133)) % 181.55/181.53 [5114]~P5(x51141)+E(f324(f324(f81(x51141),x51142),f324(f80(x51141),x51143)),f324(f324(f22(x51141),x51142),x51143)) % 181.55/181.53 [5115]~P109(x51151)+E(f324(f324(f81(x51151),x51152),f324(f80(x51151),x51153)),f324(f324(f22(x51151),x51152),x51153)) % 181.55/181.53 [5116]~P4(x51161)+E(f324(f324(f22(x51161),x51162),f324(f80(x51161),x51163)),f324(f324(f81(x51161),x51162),x51163)) % 181.55/181.53 [5154]~P1(f324(x51543,x51542))+P1(f324(f324(f326(x51541),x51542),x51543)) % 181.55/181.53 [5156]~P68(x51562)+E(f324(f324(f9(x51561,x51562),x51563),f191(f871(x51561,a859))),f79(x51562)) % 181.55/181.53 [5158]~P72(x51582)+E(f324(f324(f6(x51581,x51582),x51583),f191(f871(x51581,a859))),f2(x51582)) % 181.55/181.53 [5204]~E(x52042,f324(f324(f81(a865),x52041),x52043))+P1(f324(f324(f238(a865),x52041),x52042)) % 181.55/181.53 [5207]~E(x52072,f191(f871(x52071,a859)))+E(f324(f324(f60(x52071),x52072),x52073),f191(f871(f871(x52071,a859),a859))) % 181.55/181.53 [5208]~E(x52082,f191(f871(x52081,a859)))+E(f191(f871(f871(x52081,a859),a859)),f324(f324(f60(x52081),x52082),x52083)) % 181.55/181.53 [5281]~E(f324(f255(x52812,x52813),x52811),f191(f871(x52813,a859)))+E(x52811,f191(f871(f870(x52812,x52813),a859))) % 181.55/181.53 [5282]~E(f324(f257(x52822,x52823),x52821),f191(f871(x52822,a859)))+E(x52821,f191(f871(f870(x52822,x52823),a859))) % 181.55/181.53 [5312]E(f324(f255(x53121,x53122),x53123),f191(f871(x53122,a859)))+~E(x53123,f191(f871(f870(x53121,x53122),a859))) % 181.55/181.53 [5313]E(f324(f257(x53131,x53132),x53133),f191(f871(x53131,a859)))+~E(x53133,f191(f871(f870(x53131,x53132),a859))) % 181.55/181.53 [5316]E(f274(x53161,x53162,x53163),f324(f324(f22(a102),x53162),x53163))+P1(f324(f324(f239(a102),x53162),x53163)) % 181.55/181.53 [5332]P1(f324(x53321,x53322))+~P1(f324(f324(f326(x53323),x53322),x53321)) % 181.55/181.53 [5371]E(x53711,x53712)+~E(f324(f80(f871(x53713,a859)),x53711),f324(f80(f871(x53713,a859)),x53712)) % 181.55/181.53 [5376]E(f306(x53761,x53762,x53763),f203(f866(a320)))+~P1(f324(f324(f239(a1),x53762),x53763)) % 181.55/181.53 [5381]~E(x53811,f191(f871(x53812,a859)))+~P1(f324(f324(f326(x53812),x53813),x53811)) % 181.55/181.53 [5410]~E(x54102,f324(f324(f81(a1),x54101),f324(f103(a1),x54103)))+P1(f324(f324(f238(a1),x54101),x54102)) % 181.55/181.53 [5426]E(f324(f324(f302(x54261),x54262),x54263),x54263)+~P1(f324(f324(f326(x54261),x54262),x54263)) % 181.55/181.53 [5437]E(x54371,f191(f871(x54372,a859)))+~E(f324(f324(f60(x54372),x54371),x54373),f191(f871(f871(x54372,a859),a859))) % 181.55/181.53 [5438]E(x54381,f191(f871(x54382,a859)))+~E(f191(f871(f871(x54382,a859),a859)),f324(f324(f60(x54382),x54381),x54383)) % 181.55/181.53 [5444]~P116(x54441)+E(f324(f324(f82(x54441),f324(f80(x54441),x54442)),f324(f80(x54441),x54443)),f324(f324(f82(x54441),x54442),x54443)) % 181.55/181.53 [5446]~P62(x54461)+E(f324(f324(f282(x54461),f324(f80(x54461),x54462)),f324(f80(x54461),x54463)),f324(f324(f282(x54461),x54462),x54463)) % 181.55/181.53 [5478]~P1(f324(x54783,x54782))+P1(f324(f324(f326(x54781),x54782),f324(f244(x54781),x54783))) % 181.55/181.53 [5516]E(f164(x55161,x55162,x55163),x55163)+P1(f324(f324(f326(x55161),x55162),f324(f167(x55161),x55163))) % 181.55/181.53 [5597]~P1(f324(f131(x55971),x55973))+P1(f324(f131(x55971),f324(f130(x55971,x55972),x55973))) % 181.55/181.53 [5642]~P59(x56421)+E(f324(f324(f38(x56421),f44(x56421,x56422,x56423)),x56423),f2(x56421)) % 181.55/181.53 [5661]E(f171(x56611,f324(f324(f145(x56611),x56612),f116(x56611)),x56613),f116(x56611))+P1(f324(f324(f326(a865),f2(a865)),x56613)) % 181.55/181.53 [5667]E(x56671,f2(a865))+E(f324(f166(x56672),f165(x56672,x56671,x56673)),f165(x56672,f324(f324(f22(a865),x56671),f79(a865)),x56673)) % 181.55/181.53 [5717]E(f324(f324(f145(x57171),x57172),x57173),f134(x57171,x57172,x57173))+P1(f324(f324(f326(x57171),x57172),f324(f167(x57171),x57173))) % 181.55/181.53 [5726]E(x57261,x57262)+~E(f324(f324(f82(a865),f324(a115,x57263)),x57261),f324(f324(f82(a865),f324(a115,x57263)),x57262)) % 181.55/181.53 [5727]~E(x57272,f324(f324(f81(a1),x57271),f324(f103(a1),f324(a115,x57273))))+P1(f324(f324(f239(a1),x57271),x57272)) % 181.55/181.53 [5832]~E(x58323,f116(x58321))+E(f324(f324(f324(f184(f866(x58321),f866(x58321)),x58322),f162(x58321)),x58323),f116(x58321)) % 181.55/181.53 [5836]P1(f324(x58361,x58362))+~P1(f324(f324(f326(x58363),x58362),f324(f244(x58363),x58361))) % 181.55/181.53 [5866]E(x58661,x58662)+~E(f324(f324(f302(x58663),x58661),f191(f871(x58663,a859))),f324(f324(f302(x58663),x58662),f191(f871(x58663,a859)))) % 181.55/181.53 [5877]~P106(x58771)+E(f324(f324(f104(f871(x58771,a859)),f324(f245(x58771),x58772)),f324(f294(x58771,x58772),x58773)),f191(f871(x58771,a859))) % 181.55/181.53 [5919]E(f134(x59191,x59192,x59193),x59193)+~P1(f324(f324(f326(x59191),x59192),f324(f167(x59191),x59193))) % 181.55/181.53 [5939]~P75(x59391)+E(f324(f303(x59391,x59391,f80(x59391)),f324(f294(x59391,x59392),x59393)),f297(x59391,f324(f80(x59391),x59393),f324(f80(x59391),x59392))) % 181.55/181.53 [5947]E(f324(f192(f866(x59471)),f164(x59471,x59472,x59473)),f324(f192(f866(x59471)),x59473))+P1(f324(f324(f326(x59471),x59472),f324(f167(x59471),x59473))) % 181.55/181.53 [5999]~P106(x59991)+E(f324(f324(f104(f871(x59991,a859)),f324(f294(x59991,x59992),x59993)),f324(f246(x59991),x59993)),f191(f871(x59991,a859))) % 181.55/181.53 [6022]~P75(x60221)+E(f324(f303(x60221,x60221,f80(x60221)),f298(x60221,x60222,x60223)),f298(x60221,f324(f80(x60221),x60223),f324(f80(x60221),x60222))) % 181.55/181.53 [6023]~P75(x60231)+E(f324(f303(x60231,x60231,f80(x60231)),f295(x60231,x60232,x60233)),f295(x60231,f324(f80(x60231),x60233),f324(f80(x60231),x60232))) % 181.55/181.53 [6079]E(f171(x60791,f324(f324(f145(x60791),x60792),f116(x60791)),x60793),f324(f324(f145(x60791),x60792),f116(x60791)))+~P1(f324(f324(f326(a865),f2(a865)),x60793)) % 181.55/181.53 [6086]~P75(x60861)+E(f324(f303(x60861,x60861,f80(x60861)),f297(x60861,x60862,x60863)),f324(f294(x60861,f324(f80(x60861),x60863)),f324(f80(x60861),x60862))) % 181.55/181.53 [6106]~P60(x61061)+E(f44(x61061,f324(f80(x61061),f44(x61061,x61062,x61063)),x61063),f44(x61061,f324(f80(x61061),x61062),x61063)) % 181.55/181.53 [6203]~P1(f324(f61(f870(x62032,x62031)),x62033))+P1(f324(f61(x62031),f324(f255(x62032,x62031),x62033))) % 181.55/181.53 [6204]~P1(f324(f61(f870(x62041,x62042)),x62043))+P1(f324(f61(x62041),f324(f257(x62041,x62042),x62043))) % 181.55/181.53 [6209]~P106(x62091)+E(f324(f324(f104(f871(x62091,a859)),f298(x62091,x62092,x62093)),f324(f246(x62091),x62093)),f191(f871(x62091,a859))) % 181.55/181.53 [6210]~P106(x62101)+E(f324(f324(f104(f871(x62101,a859)),f297(x62101,x62102,x62103)),f324(f296(x62101),x62103)),f191(f871(x62101,a859))) % 181.55/181.53 [6211]~P106(x62111)+E(f324(f324(f104(f871(x62111,a859)),f295(x62111,x62112,x62113)),f324(f296(x62111),x62113)),f191(f871(x62111,a859))) % 181.55/181.53 [6277]E(f324(f324(f159(x62771),x62772),f683(x62772,x62773,x62771)),x62773)+~P1(f324(f324(f326(x62771),x62773),f324(f167(x62771),x62772))) % 181.55/181.53 [6417]E(x64171,f116(x64172))+~E(f324(f324(f324(f184(f866(x64172),f866(x64172)),x64173),f162(x64172)),x64171),f116(x64172)) % 181.55/181.53 [6519]~P1(f324(f61(f870(x65192,x65191)),x65193))+P1(f324(f61(f870(x65191,x65192)),f324(f279(x65192,x65191),x65193))) % 181.55/181.53 [6669]P53(x66691,x66692,x66693)+P1(f324(f324(f326(x66691),f595(x66693,x66692,x66691)),x66692)) % 181.55/181.53 [6670]P53(x66701,x66702,x66703)+P1(f324(f324(f326(x66701),f594(x66703,x66702,x66701)),x66702)) % 181.55/181.53 [6682]P1(f324(f312(x66821,x66822),x66823))+P1(f324(f324(x66822,f391(x66823,x66822,x66821)),x66823)) % 181.55/181.53 [6683]P1(f324(f312(x66831,x66832),x66833))+P1(f324(f324(x66832,f396(x66833,x66832,x66831)),x66833)) % 181.55/181.53 [6714]E(f324(f192(f866(x67141)),f164(x67141,x67142,x67143)),f324(f324(f22(a865),f324(f192(f866(x67141)),x67143)),f79(a865)))+~P1(f324(f324(f326(x67141),x67142),f324(f167(x67141),x67143))) % 181.55/181.53 [6754]P1(f324(f252(x67541,x67542),x67543))+P1(f324(f324(f326(x67541),f534(x67543,x67542,x67541)),x67543)) % 181.55/181.53 [6764]~P1(f324(f61(f870(x67642,x67641)),f324(f279(x67641,x67642),x67643)))+P1(f324(f61(f870(x67641,x67642)),x67643)) % 181.55/181.53 [6820]~P1(f324(f324(f326(x68201),x68202),f324(f167(x68201),f117(x68201,x68203))))+P1(f324(f324(f326(x68201),x68202),f324(f167(x68201),x68203))) % 181.55/181.53 [6825]P31(x68251,x68252,x68253)+P1(f324(f324(f326(f864(x68251)),f552(x68253,x68252,x68251)),x68253)) % 181.55/181.53 [6853]E(f324(f130(x68531,x68532),x68533),x68533)+P1(f324(f324(f326(x68531),f682(x68533,x68532,x68531)),f324(f167(x68531),x68533))) % 181.55/181.53 [6868]E(f324(f130(x68681,x68682),x68683),f116(x68681))+P1(f324(f324(f326(x68681),f681(x68683,x68682,x68681)),f324(f167(x68681),x68683))) % 181.55/181.53 [6891]P33(x68911,x68912,x68913)+P1(f324(f324(f326(x68911),f778(x68913,x68912,x68911)),f324(f167(x68911),x68913))) % 181.55/181.53 [6892]P33(x68921,x68922,x68923)+P1(f324(f324(f326(x68921),f789(x68923,x68922,x68921)),f324(f167(x68921),x68923))) % 181.55/181.53 [6893]P33(x68931,x68932,x68933)+P1(f324(f324(f326(x68931),f788(x68932,x68933,x68931)),f324(f167(x68931),x68933))) % 181.55/181.53 [6896]E(f172(x68961,x68962,x68963),x68963)+P1(f324(f324(f326(x68961),f739(x68963,x68962,x68961)),f324(f167(x68961),x68963))) % 181.55/181.53 [6974]P1(f324(f154(x69741,x69742),x69743))+P1(f324(f324(f326(x69741),f743(x69743,x69742,x69741)),f324(f167(x69741),x69743))) % 181.55/181.53 [6983]~P35(x69831,x69833,x69832)+P1(f324(f324(f326(x69831),f764(x69832,x69833,x69831)),f324(f167(x69831),x69832))) % 181.55/181.53 [6984]~P37(x69841,x69843,x69842)+P1(f324(f324(f326(x69841),f791(x69842,x69843,x69841)),f324(f167(x69841),x69842))) % 181.55/181.53 [7019]P1(f324(f324(f326(x70191),x70192),f649(x70193,x70192,x70191)))+~P1(f324(f324(f326(x70191),x70192),f39(f871(x70191,a859),x70193))) % 181.55/181.53 [7020]~P72(x70201)+E(f324(f324(f81(x70201),f324(f324(f6(a865,x70201),x70202),f324(f245(a865),x70203))),f324(x70202,x70203)),f324(f324(f6(a865,x70201),x70202),f324(f245(a865),f324(a115,x70203)))) % 181.55/181.53 [7109]~P35(x71092,x71091,x71093)+P1(f324(x71091,f324(f324(f159(x71092),x71093),f777(x71093,x71091,x71092)))) % 181.55/181.53 [7121]~P1(f324(f324(f326(x71211),x71212),f639(x71212,x71213,x71211)))+P1(f324(f324(f326(x71211),x71212),f40(f871(x71211,a859),x71213))) % 181.55/181.53 [7151]~P72(x71511)+E(f324(f324(f81(x71511),f324(f324(f6(a865,x71511),x71512),f324(f293(a865),x71513))),f324(x71512,f324(a115,x71513))),f324(f324(f6(a865,x71511),x71512),f324(f293(a865),f324(a115,x71513)))) % 181.55/181.53 [7284]P1(f324(f324(f326(f866(x72841)),x72842),f155(x72841,x72843)))+P1(f324(f324(f326(x72841),f685(x72843,x72842,x72841)),f324(f167(x72841),x72842))) % 181.55/181.53 [7301]~P1(f324(f324(f326(f866(x73011)),x73012),f155(x73011,f313(x73011,x73013))))+P1(f324(f324(f326(f866(x73011)),x73012),f313(f866(x73011),f151(x73011,x73013)))) % 181.55/181.53 [7326]~P1(f324(f324(f326(f866(x73261)),x73262),f313(f866(x73261),f151(x73261,x73263))))+P1(f324(f324(f326(f866(x73261)),x73262),f155(x73261,f313(x73261,x73263)))) % 181.55/181.53 [7362]E(f324(f324(f324(f184(f866(x73621),f866(x73621)),x73622),f162(x73621)),x73623),x73623)+~P1(f324(f324(f238(a865),f324(f192(f866(x73621)),x73623)),f79(a865))) % 181.55/181.53 [7397]E(f324(f324(f124(x73971),f780(x73972,x73973,x73971)),f324(f324(f145(x73971),x73973),f785(x73972,x73973,x73971))),x73972)+~P1(f324(f324(f326(x73971),x73973),f324(f167(x73971),x73972))) % 181.55/181.53 [7398]E(f324(f324(f124(x73981),f781(x73982,x73983,x73981)),f324(f324(f145(x73981),x73983),f782(x73982,x73983,x73981))),x73982)+~P1(f324(f324(f326(x73981),x73983),f324(f167(x73981),x73982))) % 181.55/181.53 [7399]E(f324(f324(f124(x73991),f783(x73992,x73993,x73991)),f324(f324(f145(x73991),x73993),f784(x73992,x73993,x73991))),x73992)+~P1(f324(f324(f326(x73991),x73993),f324(f167(x73991),x73992))) % 181.55/181.53 [7423]~P27(x74231,x74232,x74233,f247(f871(x74231,a859)))+P27(f866(x74231),f866(x74232),f324(f148(x74231,x74232),x74233),f247(f871(f866(x74231),a859))) % 181.55/181.53 [7571]E(x75711,f324(f324(f81(a865),f324(f324(f82(a865),f324(f258(a865,a865),x75712)),x75713)),f324(f262(a865,a865),x75712)))+~P1(f324(f47(x75711,x75713),x75712)) % 181.55/181.53 [7579]P27(x75791,x75792,x75793,f247(f871(x75791,a859)))+~P27(f866(x75791),f866(x75792),f324(f148(x75791,x75792),x75793),f247(f871(f866(x75791),a859))) % 181.55/181.53 [7620]P1(f324(f324(f326(f871(x76201,a859)),f639(x76202,x76203,x76201)),x76203))+P1(f324(f324(f326(x76201),x76202),f40(f871(x76201,a859),x76203))) % 181.55/181.53 [7708]P1(f324(f324(f326(f866(x77081)),x77082),f155(x77081,x77083)))+~P1(f324(f324(f326(x77081),f685(x77083,x77082,x77081)),x77083)) % 181.55/181.53 [7808]P33(x78081,x78082,x78083)+~P1(f324(x78082,f324(f324(f159(x78081),x78083),f779(x78083,x78082,x78081)))) % 181.55/181.53 [7832]E(x78321,x78322)+~E(f324(f324(f7(x78323,f871(x78323,a859),a859),f326(x78323)),x78321),f324(f324(f7(x78323,f871(x78323,a859),a859),f326(x78323)),x78322)) % 181.55/181.53 [7840]~P1(f324(f324(f326(f870(x78401,x78401)),x78403),f256(x78401,x78402)))+P1(f324(f324(f326(x78401),f827(x78402,x78403,x78401)),x78402)) % 181.55/181.53 [7842]~P1(f324(f324(f326(x78421),x78423),f39(f871(x78421,a859),x78422)))+P1(f324(f324(f326(f871(x78421,a859)),f649(x78422,x78423,x78421)),x78422)) % 181.55/181.53 [7965]P27(x79651,x79652,f94(x79652,x79651,f247(f871(x79652,a859)),x79653),f247(f871(x79651,a859)))+~E(f324(f303(x79652,x79651,x79653),f247(f871(x79652,a859))),f247(f871(x79651,a859))) % 181.55/181.53 [8019]~P1(f324(f324(f326(x80191),x80192),f324(f167(x80191),f781(x80193,x80192,x80191))))+~P1(f324(f324(f326(x80191),x80192),f324(f167(x80191),x80193))) % 181.55/181.53 [8020]~P1(f324(f324(f326(x80201),x80202),f324(f167(x80201),f784(x80203,x80202,x80201))))+~P1(f324(f324(f326(x80201),x80202),f324(f167(x80201),x80203))) % 181.55/181.53 [8107]E(f324(f235(f869(f866(a320)),f866(a320),f306(x81071,x81072,f324(f324(f81(a1),x81073),f79(a1))),f233(f866(a320))),f324(x81071,x81073)),f306(x81071,x81072,x81073))+P1(f324(f324(f239(a1),x81072),x81073)) % 181.55/181.53 [8210]E(x82101,f116(x82102))+P1(f324(f324(f326(x82102),f324(f258(x82102,f870(a102,a102)),f324(f275(x82102,x82101),x82103))),f324(f167(x82102),x82101))) % 181.55/181.53 [8313]~P67(x83131)+E(f324(f136(x83131,x83131,f324(f7(x83131,x83131,x83131),f81(x83131)),x83132),f324(f163(x83131),x83133)),f324(f136(x83131,x83131,f81(x83131),x83132),x83133)) % 181.55/181.53 [8498]~P27(x84982,x84981,x84983,f247(f871(x84982,a859)))+E(f324(f303(x84981,x84982,f94(x84982,x84981,f247(f871(x84982,a859)),x84983)),f247(f871(x84981,a859))),f247(f871(x84982,a859))) % 181.55/181.53 [8813]~P105(x88131)+E(f324(f167(x88131),f143(x88131,x88131,f5(x88131),x88132,x88133)),f324(f324(f302(x88131),x88132),f324(f167(x88131),x88133))) % 181.55/181.53 [8823]~E(f324(x88233,f324(f94(x88231,x88232,f247(f871(x88231,a859)),x88233),f526(x88233,x88232,x88231))),f526(x88233,x88232,x88231))+E(f324(f303(x88231,x88232,x88233),f247(f871(x88231,a859))),f247(f871(x88232,a859))) % 181.55/181.53 [8825]P1(f324(f324(f239(a865),f2(a865)),f590(x88251,x88252,x88253)))+~P1(f324(f324(f326(f870(x88253,x88253)),x88252),f324(f324(f281(x88253,x88253,x88253),x88251),f300(x88253,x88251)))) % 181.55/181.53 [9107]~P55(x91071,x91072)+~P1(f324(f324(f326(f870(x91071,x91071)),f324(f324(f259(x91071,x91071),x91073),x91073)),f324(f324(f281(x91071,x91071,x91071),x91072),f300(x91071,x91072)))) % 181.55/181.53 [9237]~E(f324(f324(f104(f871(f870(x92371,x92371),a859)),f324(f279(x92371,x92371),x92372)),f300(x92371,x92372)),f191(f871(f870(x92371,x92371),a859)))+~P1(f324(f324(f326(f870(x92371,x92371)),f324(f324(f259(x92371,x92371),x92373),x92373)),f324(f324(f281(x92371,x92371,x92371),x92372),f300(x92371,x92372)))) % 181.55/181.53 [9422]~P1(f324(f61(x94221),x94222))+P1(f324(f324(f238(a865),f324(f37(x94221),f324(f324(f22(f871(x94221,a859)),x94222),f324(f324(f302(x94221),x94223),f191(f871(x94221,a859)))))),f324(f37(x94221),x94222))) % 181.55/181.53 [5030]~E(x50303,f116(x50301))+E(f138(x50301,f324(f324(f145(x50301),x50302),x50303)),x50302) % 181.55/181.53 [5038]~E(x50383,f116(x50381))+E(f117(x50381,f324(f324(f145(x50381),x50382),x50383)),f116(x50381)) % 181.55/181.53 [5066]E(x50661,f116(x50662))+E(f138(x50662,f324(f324(f145(x50662),x50663),x50661)),f138(x50662,x50661)) % 181.55/181.53 [5068]E(x50681,f116(x50682))+E(f138(x50682,f324(f324(f124(x50682),x50683),x50681)),f138(x50682,x50681)) % 181.55/181.53 [5074]~E(x50743,f116(x50741))+E(f138(x50741,f324(f324(f124(x50741),x50742),x50743)),f138(x50741,x50742)) % 181.55/181.53 [5075]~E(x50753,f116(x50751))+E(f117(x50751,f324(f324(f124(x50751),x50752),x50753)),f117(x50751,x50752)) % 181.55/181.53 [5106]E(x51061,f116(x51062))+E(f324(f135(x51062),f324(f324(f124(x51062),x51061),x51063)),f324(f135(x51062),x51061)) % 181.55/181.53 [5134]~E(x51342,f116(x51341))+E(f324(f135(x51341),f324(f324(f124(x51341),x51342),x51343)),f324(f135(x51341),x51343)) % 181.55/181.53 [5182]~P94(x51821)+E(f324(f324(f104(x51821),x51822),f324(f324(f113(x51821),x51822),x51823)),x51822) % 181.55/181.53 [5183]~P94(x51831)+E(f324(f324(f113(x51831),x51832),f324(f324(f104(x51831),x51832),x51833)),x51832) % 181.55/181.53 [5184]~P105(x51841)+E(f324(f324(f189(x51841),x51842),f324(f324(f190(x51841),x51842),x51843)),x51842) % 181.55/181.53 [5185]~P105(x51851)+E(f324(f324(f190(x51851),x51852),f324(f324(f189(x51851),x51852),x51853)),x51852) % 181.55/181.53 [5202]~P59(x52021)+E(f44(x52021,f324(f324(f82(x52021),x52022),x52023),x52023),f2(x52021)) % 181.55/181.53 [5203]~P59(x52031)+E(f44(x52031,f324(f324(f82(x52031),x52032),x52033),x52032),f2(x52031)) % 181.55/181.53 [5275]~P5(x52751)+E(f324(f80(x52751),f324(f324(f22(x52751),x52752),x52753)),f324(f324(f22(x52751),x52753),x52752)) % 181.55/181.53 [5336]E(x53361,f116(x53362))+E(f117(x53362,f324(f324(f145(x53362),x53363),x53361)),f324(f324(f145(x53362),x53363),f117(x53362,x53361))) % 181.55/181.53 [5337]E(x53371,f116(x53372))+E(f117(x53372,f324(f324(f124(x53372),x53373),x53371)),f324(f324(f124(x53372),x53373),f117(x53372,x53371))) % 181.55/181.53 [5340]~P6(x53401)+E(f40(x53401,f324(f324(f302(x53401),x53402),x53403)),f324(f324(f104(x53401),x53402),f40(x53401,x53403))) % 181.55/181.53 [5341]~P6(x53411)+E(f39(x53411,f324(f324(f302(x53411),x53412),x53413)),f324(f324(f113(x53411),x53412),f39(x53411,x53413))) % 181.55/181.53 [5386]~P94(x53861)+E(f324(f324(f104(x53861),x53862),f324(f324(f104(x53861),x53862),x53863)),f324(f324(f104(x53861),x53862),x53863)) % 181.55/181.53 [5388]~P99(x53881)+E(f324(f324(f104(x53881),x53882),f324(f324(f104(x53881),x53882),x53883)),f324(f324(f104(x53881),x53882),x53883)) % 181.55/181.53 [5389]~P94(x53891)+E(f324(f324(f113(x53891),x53892),f324(f324(f113(x53891),x53892),x53893)),f324(f324(f113(x53891),x53892),x53893)) % 181.55/181.53 [5391]~P100(x53911)+E(f324(f324(f113(x53911),x53912),f324(f324(f113(x53911),x53912),x53913)),f324(f324(f113(x53911),x53912),x53913)) % 181.55/181.53 [5392]~P93(x53921)+E(f324(f324(f82(x53921),x53922),f324(f324(f82(x53921),x53922),x53923)),f324(f324(f82(x53921),x53922),x53923)) % 181.55/181.53 [5394]~P105(x53941)+E(f324(f324(f189(x53941),x53942),f324(f324(f189(x53941),x53942),x53943)),f324(f324(f189(x53941),x53942),x53943)) % 181.55/181.53 [5396]~P105(x53961)+E(f324(f324(f190(x53961),x53962),f324(f324(f190(x53961),x53962),x53963)),f324(f324(f190(x53961),x53962),x53963)) % 181.55/181.53 [5404]~P59(x54041)+E(f44(x54041,f324(f324(f81(x54041),x54042),x54043),x54043),f44(x54041,x54042,x54043)) % 181.55/181.53 [5405]~P59(x54051)+E(f44(x54051,f324(f324(f81(x54051),x54052),x54053),x54052),f44(x54051,x54053,x54052)) % 181.55/181.53 [5411]~P116(x54111)+E(f324(f324(f82(x54111),x54112),f324(f80(x54111),x54113)),f324(f80(x54111),f324(f324(f82(x54111),x54112),x54113))) % 181.55/181.53 [5412]~P62(x54121)+E(f324(f324(f282(x54121),x54122),f324(f80(x54121),x54123)),f324(f80(x54121),f324(f324(f282(x54121),x54122),x54123))) % 181.55/181.53 [5413]~P78(x54131)+E(f324(f324(f81(x54131),x54132),f324(f160(x54131),x54133)),f324(f160(x54131),f324(f324(f145(x54131),x54132),x54133))) % 181.55/181.53 [5443]~P116(x54431)+E(f324(f324(f82(x54431),f324(f80(x54431),x54432)),x54433),f324(f324(f82(x54431),x54432),f324(f80(x54431),x54433))) % 181.55/181.53 [5449]~P9(x54491,x54492,x54493)+E(f39(f871(x54491,a859),f324(f324(f60(x54491),x54492),x54493)),x54492) % 181.55/181.53 [5508]~P110(x55081)+E(f324(f324(f82(x55081),x55082),f324(f324(f249(x55081),x55082),x55083)),f324(f324(f249(x55081),x55082),f324(a115,x55083))) % 181.55/181.53 [5509]~P112(x55091)+E(f324(f324(f82(x55091),x55092),f324(f324(f249(x55091),x55092),x55093)),f324(f324(f249(x55091),x55092),f324(a115,x55093))) % 181.55/181.53 [5519]~P4(x55191)+E(f324(f324(f81(x55191),f324(f80(x55191),x55192)),f324(f324(f81(x55191),x55192),x55193)),x55193) % 181.55/181.53 [5542]~P135(x55421)+E(f324(f324(f249(x55421),f324(f105(x55421),x55422)),x55423),f324(f105(x55421),f324(f324(f249(a1),x55422),x55423))) % 181.55/181.53 [5543]~P141(x55431)+E(f324(f324(f249(x55431),f324(f103(x55431),x55432)),x55433),f324(f103(x55431),f324(f324(f249(a865),x55432),x55433))) % 181.55/181.53 [5548]~P83(x55481)+E(f324(f75(x55481),f324(f324(f22(x55481),x55482),x55483)),f324(f75(x55481),f324(f324(f22(x55481),x55483),x55482))) % 181.55/181.53 [5550]~P117(x55501)+E(f324(f324(f82(x55501),f83(x55501,x55502)),f83(x55501,x55503)),f83(x55501,f324(f324(f82(x55501),x55502),x55503))) % 181.55/181.53 [5554]E(x55541,f116(x55542))+E(f324(f324(f124(x55542),f324(f166(x55542),x55541)),x55543),f324(f166(x55542),f324(f324(f124(x55542),x55541),x55543))) % 181.55/181.53 [5559]~E(x55592,f324(a115,f324(f324(f81(a865),x55591),x55593)))+P1(f324(f324(f239(a865),x55591),x55592)) % 181.55/181.53 [5560]~P116(x55601)+E(f324(f324(f82(x55601),f324(f80(x55601),x55602)),x55603),f324(f80(x55601),f324(f324(f82(x55601),x55602),x55603))) % 181.55/181.53 [5561]~P114(x55611)+E(f324(f324(f282(x55611),f324(f80(x55611),x55612)),x55613),f324(f80(x55611),f324(f324(f282(x55611),x55612),x55613))) % 181.55/181.53 [5562]~P117(x55621)+E(f324(f324(f249(x55621),f324(f75(x55621),x55622)),x55623),f324(f75(x55621),f324(f324(f249(x55621),x55622),x55623))) % 181.55/181.53 [5660]E(f812(x56601,x56602,x56603),f813(x56601,x56602,x56603))+E(f324(f324(f104(f871(x56603,a859)),x56602),x56601),f191(f871(x56603,a859))) % 181.55/181.53 [5675]~P68(x56752)+E(f324(f324(f9(x56751,x56752),f324(f16(x56752,x56751),f79(x56752))),x56753),f79(x56752)) % 181.55/181.53 [5676]~P72(x56762)+E(f324(f324(f6(x56761,x56762),f324(f16(x56762,x56761),f2(x56762))),x56763),f2(x56762)) % 181.55/181.53 [5678]~P92(x56781)+E(f324(f324(f22(x56781),f324(f106(x56781),x56782)),f324(f106(x56781),x56783)),f324(f106(x56781),f324(f324(f22(a1),x56782),x56783))) % 181.55/181.53 [5681]~P135(x56811)+E(f324(f324(f22(x56811),f324(f105(x56811),x56812)),f324(f105(x56811),x56813)),f324(f105(x56811),f324(f324(f22(a1),x56812),x56813))) % 181.55/181.53 [5682]~P135(x56821)+E(f324(f324(f82(x56821),f324(f105(x56821),x56822)),f324(f105(x56821),x56823)),f324(f105(x56821),f324(f324(f82(a1),x56822),x56823))) % 181.55/181.53 [5683]~P135(x56831)+E(f324(f324(f81(x56831),f324(f105(x56831),x56832)),f324(f105(x56831),x56833)),f324(f105(x56831),f324(f324(f81(a1),x56832),x56833))) % 181.55/181.53 [5684]~P141(x56841)+E(f324(f324(f82(x56841),f324(f103(x56841),x56842)),f324(f103(x56841),x56843)),f324(f103(x56841),f324(f324(f82(a865),x56842),x56843))) % 181.55/181.53 [5685]~P141(x56851)+E(f324(f324(f81(x56851),f324(f103(x56851),x56852)),f324(f103(x56851),x56853)),f324(f103(x56851),f324(f324(f81(a865),x56852),x56853))) % 181.55/181.53 [5686]~P92(x56861)+E(f324(f324(f82(x56861),f324(f106(x56861),x56862)),f324(f106(x56861),x56863)),f324(f106(x56861),f324(f324(f82(a1),x56862),x56863))) % 181.55/181.53 [5687]~P92(x56871)+E(f324(f324(f81(x56871),f324(f106(x56871),x56872)),f324(f106(x56871),x56873)),f324(f106(x56871),f324(f324(f81(a1),x56872),x56873))) % 181.55/181.53 [5734]~E(x57343,x57342)+P1(f324(f324(f238(f871(x57341,a859)),x57342),x57343)) % 181.55/181.53 [5740]~E(x57402,x57403)+P1(f324(f324(f238(f871(x57401,a859)),x57402),x57403)) % 181.55/181.53 [5745]~P79(x57451)+E(f324(f324(f113(x57451),f324(f80(x57451),x57452)),f324(f80(x57451),x57453)),f324(f80(x57451),f324(f324(f104(x57451),x57452),x57453))) % 181.55/181.53 [5746]~P79(x57461)+E(f324(f324(f104(x57461),f324(f80(x57461),x57462)),f324(f80(x57461),x57463)),f324(f80(x57461),f324(f324(f113(x57461),x57462),x57463))) % 181.55/181.53 [5747]~P4(x57471)+E(f324(f324(f81(x57471),f324(f80(x57471),x57472)),f324(f80(x57471),x57473)),f324(f80(x57471),f324(f324(f81(x57471),x57473),x57472))) % 181.55/181.53 [5748]~P5(x57481)+E(f324(f324(f81(x57481),f324(f80(x57481),x57482)),f324(f80(x57481),x57483)),f324(f80(x57481),f324(f324(f81(x57481),x57482),x57483))) % 181.55/181.53 [5749]~P74(x57491)+E(f324(f324(f190(x57491),f324(f80(x57491),x57492)),f324(f80(x57491),x57493)),f324(f80(x57491),f324(f324(f189(x57491),x57492),x57493))) % 181.55/181.53 [5750]~P74(x57501)+E(f324(f324(f189(x57501),f324(f80(x57501),x57502)),f324(f80(x57501),x57503)),f324(f80(x57501),f324(f324(f190(x57501),x57502),x57503))) % 181.55/181.53 [5751]~P117(x57511)+E(f324(f324(f82(x57511),f324(f75(x57511),x57512)),f324(f75(x57511),x57513)),f324(f75(x57511),f324(f324(f82(x57511),x57512),x57513))) % 181.55/181.53 [5752]~P64(x57521)+E(f324(f324(f282(x57521),f324(f75(x57521),x57522)),f324(f75(x57521),x57523)),f324(f75(x57521),f324(f324(f282(x57521),x57522),x57523))) % 181.55/181.53 [5753]~P78(x57531)+E(f324(f324(f81(x57531),f324(f160(x57531),x57532)),f324(f160(x57531),x57533)),f324(f160(x57531),f324(f324(f124(x57531),x57532),x57533))) % 181.55/181.53 [5754]E(x57541,f191(f871(x57542,a859)))+~E(f324(f324(f113(f871(x57542,a859)),x57543),x57541),f191(f871(x57542,a859))) % 181.55/181.53 [5755]E(x57551,f191(f871(x57552,a859)))+~E(f324(f324(f113(f871(x57552,a859)),x57551),x57553),f191(f871(x57552,a859))) % 181.55/181.53 [5756]~P144(x57561,x57563,x57562)+P1(f324(x57561,f324(f324(f38(a1),x57562),x57563))) % 181.55/181.53 [5806]~P1(f324(f61(x58061),x58063))+P1(f324(f61(x58061),f324(f324(f302(x58061),x58062),x58063))) % 181.55/181.53 [5807]~P1(f324(f131(x58071),x58073))+P1(f324(f131(x58071),f324(f324(f170(x58071),x58072),x58073))) % 181.55/181.53 [5808]~P1(f324(f131(x58081),x58083))+P1(f324(f131(x58081),f324(f324(f132(x58081),x58082),x58083))) % 181.55/181.53 [5837]~P94(x58371)+P1(f324(f324(f238(x58371),x58372),f324(f324(f113(x58371),x58373),x58372))) % 181.55/181.53 [5838]~P100(x58381)+P1(f324(f324(f238(x58381),x58382),f324(f324(f113(x58381),x58383),x58382))) % 181.55/181.53 [5839]~P94(x58391)+P1(f324(f324(f238(x58391),x58392),f324(f324(f113(x58391),x58392),x58393))) % 181.55/181.53 [5840]~P100(x58401)+P1(f324(f324(f238(x58401),x58402),f324(f324(f113(x58401),x58402),x58403))) % 181.55/181.53 [5841]~P105(x58411)+P1(f324(f324(f238(x58411),x58412),f324(f324(f190(x58411),x58413),x58412))) % 181.55/181.53 [5842]~P105(x58421)+P1(f324(f324(f238(x58421),x58422),f324(f324(f190(x58421),x58422),x58423))) % 181.55/181.53 [5856]~E(x58561,f2(a865))+E(f324(f324(f38(a865),f324(f324(f82(a865),x58561),x58562)),f324(f324(f82(a865),x58561),x58563)),f2(a865)) % 181.55/181.53 [5934]~P92(x59341)+E(f324(f324(f22(x59341),f324(f106(x59341),x59342)),f324(f106(x59341),x59343)),f324(f106(x59341),f324(f324(f81(a1),x59342),f324(f80(a1),x59343)))) % 181.55/181.53 [5986]E(x59861,f2(a865))+E(f324(f324(f38(a865),f324(f324(f82(a865),x59861),x59862)),f324(f324(f82(a865),x59861),x59863)),f324(f324(f38(a865),x59862),x59863)) % 181.55/181.53 [6020]E(f146(x60201,f324(f324(f145(x60201),x60202),x60203)),f324(f324(f145(x60201),x60202),f146(x60201,x60203)))+P1(f324(f324(f326(x60201),x60202),f324(f167(x60201),x60203))) % 181.55/181.53 [6053]P144(x60531,x60532,x60533)+~P1(f324(x60531,f324(f324(f38(a1),x60533),x60532))) % 181.55/181.53 [6122]E(x61221,f116(x61222))+E(f324(f324(f145(x61222),f324(f135(x61222),x61221)),f324(f324(f170(x61222),x61223),f324(f166(x61222),x61221))),f324(f324(f170(x61222),f324(a115,x61223)),x61221)) % 181.55/181.53 [6128]E(f324(f324(f22(f871(x61281,a859)),x61282),x61283),x61282)+~E(f324(f324(f104(f871(x61281,a859)),x61282),x61283),f191(f871(x61281,a859))) % 181.55/181.53 [6141]E(f146(x61411,f324(f324(f145(x61411),x61412),x61413)),f146(x61411,x61413))+~P1(f324(f324(f326(x61411),x61412),f324(f167(x61411),x61413))) % 181.55/181.53 [6173]~P1(f324(f324(f238(a865),x61731),x61733))+P1(f324(f324(f238(a865),x61731),f324(f324(f81(a865),x61732),x61733))) % 181.55/181.53 [6175]~P1(f324(f324(f238(a865),x61751),x61752))+P1(f324(f324(f238(a865),x61751),f324(f324(f81(a865),x61752),x61753))) % 181.55/181.53 [6177]~P1(f324(f324(f239(a865),x61771),x61773))+P1(f324(f324(f239(a865),x61771),f324(f324(f81(a865),x61772),x61773))) % 181.55/181.53 [6179]~P1(f324(f324(f239(a865),x61791),x61792))+P1(f324(f324(f239(a865),x61791),f324(f324(f81(a865),x61792),x61793))) % 181.55/181.53 [6217]P1(f324(f61(x62171),x62172))+~P1(f324(f61(x62171),f324(f324(f302(x62171),x62173),x62172))) % 181.55/181.53 [6218]P1(f324(f131(x62181),x62182))+~P1(f324(f131(x62181),f324(f324(f145(x62181),x62183),x62182))) % 181.55/181.53 [6219]P1(f324(f131(x62191),x62192))+~P1(f324(f131(x62191),f324(f324(f124(x62191),x62193),x62192))) % 181.55/181.53 [6220]P1(f324(f131(x62201),x62202))+~P1(f324(f131(x62201),f324(f324(f124(x62201),x62202),x62203))) % 181.55/181.53 [6266]~P112(x62661)+E(f324(f324(f81(x62661),x62662),f324(f324(f82(x62661),x62663),x62662)),f324(f324(f82(x62661),f324(f324(f81(x62661),x62663),f79(x62661))),x62662)) % 181.55/181.53 [6312]~E(x63121,x63122)+~P1(f324(f324(f239(f871(x63123,a859)),x63121),x63122)) % 181.55/181.53 [6358]P1(f324(f324(f326(x63581),x63582),x63583))+P1(f324(f324(f326(x63581),x63582),f324(f80(f871(x63581,a859)),x63583))) % 181.55/181.53 [6364]E(f138(x63641,f324(f324(f132(x63641),x63642),x63643)),f138(x63641,x63643))+~P1(f324(f324(f239(a865),x63642),f324(f192(f866(x63641)),x63643))) % 181.55/181.53 [6365]E(f324(f324(f170(x63651),x63652),f117(x63651,x63653)),f324(f324(f170(x63651),x63652),x63653))+~P1(f324(f324(f239(a865),x63652),f324(f192(f866(x63651)),x63653))) % 181.55/181.53 [6419]E(f324(f324(f324(f184(f866(x64191),f866(x64191)),x64192),f162(x64191)),x64193),x64193)+~E(f44(a865,x64192,f324(f192(f866(x64191)),x64193)),f2(a865)) % 181.55/181.53 [6426]~P9(x64261,x64263,x64262)+E(f324(f324(f281(x64261,x64261,x64261),f324(f279(x64261,x64261),x64262)),x64262),x64262) % 181.55/181.53 [6468]~E(f324(f324(f113(f871(x64681,a859)),x64682),x64683),x64683)+P1(f324(f324(f238(f871(x64681,a859)),x64682),x64683)) % 181.55/181.53 [6473]~P52(x64731,x64731,x64733)+P52(x64731,x64731,f324(f324(f184(f870(x64731,x64731),a859),x64732),x64733)) % 181.55/181.53 [6476]~P1(f324(f324(f326(x64761),x64763),f324(f167(x64761),x64762)))+P1(f324(f324(f239(a865),f2(a865)),f324(f192(f866(x64761)),x64762))) % 181.55/181.53 [6502]~P83(x65021)+E(f324(f75(x65021),f324(f324(f81(x65021),f324(f75(x65021),x65022)),f324(f75(x65021),x65023))),f324(f324(f81(x65021),f324(f75(x65021),x65022)),f324(f75(x65021),x65023))) % 181.55/181.53 [6512]E(f324(f324(f38(a865),f324(f324(f82(a865),x65121),x65122)),f324(f324(f82(a865),x65121),x65123)),f324(f324(f38(a865),x65122),x65123))+~P1(f324(f324(f239(a865),f2(a865)),x65121)) % 181.55/181.53 [6648]~P1(f324(f61(x66481),x66483))+E(f324(f324(f64(x66481,f871(x66481,a859),f302(x66481)),x66482),x66483),f324(f324(f113(f871(x66481,a859)),x66483),x66482)) % 181.55/181.53 [6707]E(f324(f324(f104(f871(x67071,a859)),x67072),x67073),x67073)+~P1(f324(f324(f238(f871(x67071,a859)),x67073),x67072)) % 181.55/181.53 [6708]E(f324(f324(f104(f871(x67081,a859)),x67082),x67083),x67082)+~P1(f324(f324(f238(f871(x67081,a859)),x67082),x67083)) % 181.55/181.53 [6709]E(f324(f324(f113(f871(x67091,a859)),x67092),x67093),x67092)+~P1(f324(f324(f238(f871(x67091,a859)),x67093),x67092)) % 181.55/181.53 [6711]E(f324(f324(f113(f871(x67111,a859)),x67112),x67113),x67113)+~P1(f324(f324(f238(f871(x67111,a859)),x67112),x67113)) % 181.55/181.53 [6762]~P1(f324(f131(x67621),x67622))+E(f324(f324(f22(f871(x67621,a859)),f324(f167(x67621),x67622)),f324(f324(f302(x67621),x67623),f191(f871(x67621,a859)))),f324(f167(x67621),f164(x67621,x67623,x67622))) % 181.55/181.53 [6815]P39(x68151,x68152)+~P39(x68151,f324(f324(f184(f870(x68151,x68151),a859),x68153),x68152)) % 181.55/181.53 [6879]P1(f324(f48(x68791,x68792),f324(a50,x68793)))+~P1(f324(f48(f324(f80(a1),x68791),f324(f80(a1),x68792)),x68793)) % 181.55/181.53 [6884]E(f324(f324(f22(f871(x68841,a859)),f324(f324(f302(x68841),x68842),x68843)),f324(f324(f302(x68841),x68842),f191(f871(x68841,a859)))),x68843)+P1(f324(f324(f326(x68841),x68842),x68843)) % 181.55/181.53 [6905]E(f324(f324(f104(f871(x69051,a859)),f324(f167(x69051),x69052)),f324(f167(x69051),x69053)),f191(f871(x69051,a859)))+~P1(f324(f131(x69051),f324(f324(f124(x69051),x69052),x69053))) % 181.55/181.53 [6921]~P1(f324(f324(f326(x69211),x69212),f324(f167(x69211),x69213)))+~P1(f324(f131(x69211),f324(f324(f145(x69211),x69212),x69213))) % 181.55/181.53 [6990]P33(x69901,x69902,x69903)+P1(f324(f324(f239(a865),f779(x69903,x69902,x69901)),f324(f192(f866(x69901)),x69903))) % 181.55/181.53 [7000]E(f324(f324(f104(f871(x70001,a859)),x70002),x70003),f191(f871(x70001,a859)))+P1(f324(f324(f326(x70001),f812(x70003,x70002,x70001)),x70002)) % 181.55/181.53 [7001]E(f324(f324(f104(f871(x70011,a859)),x70012),x70013),f191(f871(x70011,a859)))+P1(f324(f324(f326(x70011),f813(x70013,x70012,x70011)),x70013)) % 181.55/181.53 [7005]E(f117(x70051,f324(f324(f170(x70051),x70052),x70053)),f324(f324(f170(x70051),f324(f324(f22(a865),x70052),f79(a865))),x70053))+~P1(f324(f324(f238(a865),x70052),f324(f192(f866(x70051)),x70053))) % 181.55/181.53 [7064]~P35(x70643,x70642,x70641)+P1(f324(f324(f239(a865),f777(x70641,x70642,x70643)),f324(f192(f866(x70643)),x70641))) % 181.55/181.53 [7082]P1(f324(f324(f239(a865),f2(a865)),x70821))+P1(f324(f324(f238(a865),f324(f324(f82(a865),x70822),x70821)),f324(f324(f82(a865),x70823),x70821))) % 181.55/181.53 [7083]P1(f324(f324(f239(a865),f2(a865)),x70831))+P1(f324(f324(f238(a865),f324(f324(f82(a865),x70831),x70832)),f324(f324(f82(a865),x70831),x70833))) % 181.55/181.53 [7086]~P1(f324(f324(f326(x70861),x70862),x70863))+~P1(f324(f324(f326(x70861),x70862),f324(f80(f871(x70861,a859)),x70863))) % 181.55/181.53 [7093]~P1(f324(f324(f239(f871(x70931,a859)),x70932),x70933))+P1(f324(f324(f238(f871(x70931,a859)),x70932),x70933)) % 181.55/181.53 [7191]~P1(f324(f324(f238(a865),x71913),x71912))+P1(f324(f324(f238(a865),f324(f324(f22(a865),x71911),x71912)),f324(f324(f22(a865),x71911),x71913))) % 181.55/181.53 [7192]~P1(f324(f324(f238(a865),x71921),x71923))+P1(f324(f324(f238(a865),f324(f324(f22(a865),x71921),x71922)),f324(f324(f22(a865),x71923),x71922))) % 181.55/181.53 [7194]~P1(f324(f324(f238(a865),x71942),x71943))+P1(f324(f324(f238(a865),f324(f324(f82(a865),x71941),x71942)),f324(f324(f82(a865),x71941),x71943))) % 181.55/181.53 [7196]~P1(f324(f324(f238(a865),x71961),x71963))+P1(f324(f324(f238(a865),f324(f324(f82(a865),x71961),x71962)),f324(f324(f82(a865),x71963),x71962))) % 181.55/181.53 [7197]~P1(f324(f324(f238(a865),x71972),x71973))+P1(f324(f324(f238(a865),f324(f324(f81(a865),x71971),x71972)),f324(f324(f81(a865),x71971),x71973))) % 181.55/181.53 [7198]~P1(f324(f324(f238(a865),x71981),x71983))+P1(f324(f324(f238(a865),f324(f324(f81(a865),x71981),x71982)),f324(f324(f81(a865),x71983),x71982))) % 181.55/181.53 [7199]~P1(f324(f324(f238(a865),x71991),x71993))+P1(f324(f324(f238(a865),f324(f324(f38(a865),x71991),x71992)),f324(f324(f38(a865),x71993),x71992))) % 181.55/181.53 [7200]~P1(f324(f324(f238(a1),x72002),x72003))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x72001),x72002)),f324(f324(f81(a1),x72001),x72003))) % 181.55/181.53 [7203]~P1(f324(f324(f239(a865),x72032),x72033))+P1(f324(f324(f239(a865),f324(f324(f81(a865),x72031),x72032)),f324(f324(f81(a865),x72031),x72033))) % 181.55/181.53 [7204]~P1(f324(f324(f239(a865),x72041),x72043))+P1(f324(f324(f239(a865),f324(f324(f81(a865),x72041),x72042)),f324(f324(f81(a865),x72043),x72042))) % 181.55/181.53 [7205]~P1(f324(f324(f239(a1),x72051),x72053))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x72051),x72052)),f324(f324(f81(a1),x72053),x72052))) % 181.55/181.53 [7283]E(x72831,x72832)+~P1(f324(f324(f326(x72833),x72831),f324(f324(f302(x72833),x72832),f191(f871(x72833,a859))))) % 181.55/181.53 [7285]~E(f324(f324(f104(f871(x72851,a859)),x72852),x72853),f191(f871(x72851,a859)))+P1(f324(f324(f238(f871(x72851,a859)),x72852),f324(f80(f871(x72851,a859)),x72853))) % 181.55/181.53 [7292]P1(f324(f324(f326(f871(x72921,a859)),x72922),f324(f301(x72921),x72923)))+~P1(f324(f324(f238(f871(x72921,a859)),x72922),x72923)) % 181.55/181.53 [7297]P1(f324(f324(f326(x72971),f607(x72972,x72973,x72971)),x72973))+P1(f324(f324(f238(f871(x72971,a859)),x72973),x72972)) % 181.55/181.53 [7346]E(f324(f324(f145(x73461),f324(f324(f159(x73461),x73462),x73463)),f324(f324(f132(x73461),f324(a115,x73463)),x73462)),f324(f324(f132(x73461),x73463),x73462))+~P1(f324(f324(f239(a865),x73463),f324(f192(f866(x73461)),x73462))) % 181.55/181.53 [7373]P1(f324(f324(f326(f870(x73731,x73731)),x73732),f300(x73731,x73733)))+~P1(f324(f324(f326(f870(x73731,x73731)),x73732),x73733)) % 181.55/181.53 [7383]~P1(f324(f324(f326(f871(x73831,a859)),x73832),f324(f301(x73831),x73833)))+P1(f324(f324(f238(f871(x73831,a859)),x73832),x73833)) % 181.55/181.53 [7429]P1(f324(f324(f238(f871(x74291,a859)),x74292),f39(f871(x74291,a859),x74293)))+~P1(f324(f324(f326(f871(x74291,a859)),x74292),x74293)) % 181.55/181.53 [7454]~P135(x74541)+E(f324(f324(f82(x74541),f324(f324(f249(x74541),f324(f80(x74541),f79(x74541))),x74542)),f324(f324(f249(x74541),x74543),x74542)),f324(f324(f249(x74541),f324(f80(x74541),x74543)),x74542)) % 181.55/181.53 [7475]E(f324(f324(f159(x74751),x74752),f324(f324(f22(a865),f324(f192(f866(x74751)),x74752)),f324(a115,x74753))),f324(f324(f159(x74751),f324(f163(x74751),x74752)),x74753))+~P1(f324(f324(f239(a865),x74753),f324(f192(f866(x74751)),x74752))) % 181.55/181.53 [7492]~E(f324(f324(f104(f871(x74921,a859)),f622(x74923,x74922,x74921)),x74923),f191(f871(x74921,a859)))+E(f324(f324(f104(f871(x74921,a859)),f39(f871(x74921,a859),x74922)),x74923),f191(f871(x74921,a859))) % 181.55/181.53 [7553]~P1(f324(f324(f326(x75533),x75532),f324(f167(x75533),x75531)))+P1(f324(f324(f239(a865),f683(x75531,x75532,x75533)),f324(f192(f866(x75533)),x75531))) % 181.55/181.53 [7561]P1(f324(f324(f326(x75611),f324(f324(f159(x75611),x75612),x75613)),f324(f167(x75611),x75612)))+~P1(f324(f324(f239(a865),x75613),f324(f192(f866(x75611)),x75612))) % 181.55/181.53 [7659]~P1(f324(x76592,f741(x76593,x76592,x76591)))+E(f324(f324(f132(x76591),f324(f192(f866(x76591)),f172(x76591,x76592,x76593))),x76593),f116(x76591)) % 181.55/181.53 [7669]P1(f324(f324(f238(f871(f866(x76691),a859)),f155(x76691,x76692)),f155(x76691,x76693)))+~P1(f324(f324(f238(f871(x76691,a859)),x76692),x76693)) % 181.55/181.53 [7670]P1(f324(f324(f238(f871(f866(x76701),a859)),f154(x76701,x76702)),f154(x76701,x76703)))+~P1(f324(f324(f238(f871(x76701,a859)),x76702),x76703)) % 181.55/181.53 [7696]E(f324(f324(f104(f871(x76961,a859)),f39(f871(x76961,a859),x76962)),x76963),f191(f871(x76961,a859)))+P1(f324(f324(f326(f871(x76961,a859)),f622(x76963,x76962,x76961)),x76962)) % 181.55/181.53 [7699]~P1(f324(f324(f326(f871(x76991,a859)),x76993),x76992))+P1(f324(f324(f238(f871(x76991,a859)),f40(f871(x76991,a859),x76992)),x76993)) % 181.55/181.53 [7701]E(f324(f324(f104(f871(x77011,a859)),x77012),x77013),f191(f871(x77011,a859)))+~P1(f324(f324(f238(f871(x77011,a859)),x77012),f324(f80(f871(x77011,a859)),x77013))) % 181.55/181.53 [7745]E(f324(f324(f22(a865),f324(f324(f81(a865),f324(f160(a865),x77451)),x77452)),f324(f324(f159(a865),x77451),x77453)),f324(f160(a865),f324(f324(f153(a865,x77451),x77453),x77452)))+~P1(f324(f324(f239(a865),x77453),f324(f192(f866(a865)),x77451))) % 181.55/181.53 [7796]P1(f324(f324(f238(a865),x77961),x77962))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),x77963),x77961)),f324(f324(f81(a865),x77963),x77962))) % 181.55/181.53 [7799]P1(f324(f324(f239(a865),x77991),x77992))+~P1(f324(f324(f239(a865),f324(f324(f81(a865),x77993),x77991)),f324(f324(f81(a865),x77993),x77992))) % 181.55/181.53 [7800]P1(f324(f324(f239(a865),x78001),x78002))+~P1(f324(f324(f239(a865),f324(f324(f82(a865),x78003),x78001)),f324(f324(f82(a865),x78003),x78002))) % 181.55/181.53 [7801]P1(f324(f324(f239(a865),x78011),x78012))+~P1(f324(f324(f239(a865),f324(f324(f82(a865),x78011),x78013)),f324(f324(f82(a865),x78012),x78013))) % 181.55/181.53 [7830]P1(f324(f324(f239(a865),f2(a865)),x78301))+~P1(f324(f324(f239(a865),f324(f324(f82(a865),x78302),x78301)),f324(f324(f82(a865),x78303),x78301))) % 181.55/181.53 [7831]P1(f324(f324(f239(a865),f2(a865)),x78311))+~P1(f324(f324(f239(a865),f324(f324(f82(a865),x78311),x78312)),f324(f324(f82(a865),x78311),x78313))) % 181.55/181.53 [7872]~P1(f324(f324(f326(x78721),f607(x78723,x78722,x78721)),x78723))+P1(f324(f324(f238(f871(x78721,a859)),x78722),x78723)) % 181.55/181.53 [7908]E(f251(x79081,x79082,x79083),x79082)+~P1(f324(f324(f238(f871(x79081,a859)),x79083),f324(f324(f302(x79081),x79082),f191(f871(x79081,a859))))) % 181.55/181.53 [7958]~P1(f324(f131(x79581),x79583))+E(f324(f130(x79581,f324(f324(f8(a859,a859,x79581),a319),f324(a321,x79582))),x79583),f164(x79581,x79582,x79583)) % 181.55/181.53 [7983]E(f324(f324(f132(x79831),f324(f192(f866(x79831)),f172(x79831,x79832,x79833))),x79833),f116(x79831))+P1(f324(f324(f326(x79831),f741(x79833,x79832,x79831)),f324(f167(x79831),x79833))) % 181.55/181.53 [7987]E(f324(f324(f124(x79871),f324(f324(f170(x79871),x79872),x79873)),f324(f324(f145(x79871),f324(f324(f159(x79871),x79873),x79872)),f116(x79871))),f324(f324(f170(x79871),f324(a115,x79872)),x79873))+~P1(f324(f324(f239(a865),x79872),f324(f192(f866(x79871)),x79873))) % 181.55/181.53 [8048]E(f324(f130(x80481,f324(f324(f8(a859,a859,x80481),a319),f324(a321,x80482))),x80483),x80483)+P1(f324(f324(f326(x80481),x80482),f324(f167(x80481),x80483))) % 181.55/181.53 [8055]P1(f324(f324(f238(f871(f871(x80551,a859),a859)),f252(x80551,x80552)),f252(x80551,x80553)))+~P1(f324(f324(f238(f871(x80551,a859)),x80552),x80553)) % 181.55/181.53 [8098]~P1(f324(f131(x80981),x80983))+P1(f324(f131(x80981),f324(f324(f324(f184(f866(x80981),f866(x80981)),x80982),f162(x80981)),x80983))) % 181.55/181.53 [8104]~P1(f324(f324(f239(a865),x81042),x81043))+P1(f324(f324(f239(a865),f324(f324(f82(a865),f324(a115,x81041)),x81042)),f324(f324(f82(a865),f324(a115,x81041)),x81043))) % 181.55/181.53 [8126]P1(f324(f324(f238(f871(f871(x81261,a859),a859)),f324(f301(x81261),x81262)),f324(f301(x81261),x81263)))+~P1(f324(f324(f238(f871(x81261,a859)),x81262),x81263)) % 181.55/181.53 [8195]~E(f324(f303(x81951,x81952,x81953),f247(f871(x81951,a859))),f247(f871(x81952,a859)))+E(f324(f73(x81951,x81952,x81952,x81953),f94(x81951,x81952,f247(f871(x81951,a859)),x81953)),f34(x81952)) % 181.55/181.53 [8293]~P1(f324(f324(f238(f871(x82931,a859)),x82933),x82932))+P1(f324(f324(f238(f871(x82931,a859)),f324(f80(f871(x82931,a859)),x82932)),f324(f80(f871(x82931,a859)),x82933))) % 181.55/181.53 [8326]E(f324(f303(a865,a865,f324(f324(f7(a865,a865,a865),f22(a865)),x83261)),f324(f294(a865,x83262),x83263)),f324(f294(a865,f324(f324(f22(a865),x83262),x83261)),f324(f324(f22(a865),x83263),x83261)))+~P1(f324(f324(f239(a865),x83261),x83263)) % 181.55/181.53 [8352]~P78(x83521)+E(f324(f324(f81(x83521),x83522),f324(f136(x83521,x83521,f81(x83521),f2(x83521)),x83523)),f324(f136(x83521,x83521,f81(x83521),x83522),x83523)) % 181.55/181.53 [8424]~P83(x84241)+P1(f324(f324(f238(x84241),f324(f75(x84241),f324(f324(f22(x84241),x84242),x84243))),f324(f324(f81(x84241),f324(f75(x84241),x84242)),f324(f75(x84241),x84243)))) % 181.55/181.53 [8425]~P83(x84251)+P1(f324(f324(f238(x84251),f324(f75(x84251),f324(f324(f81(x84251),x84252),x84253))),f324(f324(f81(x84251),f324(f75(x84251),x84252)),f324(f75(x84251),x84253)))) % 181.55/181.53 [8435]E(f324(f324(f81(a1),f324(f324(f82(a1),x84351),f44(a1,f324(f324(f38(a1),x84352),x84351),x84353))),f44(a1,x84352,x84351)),f44(a1,x84352,f324(f324(f82(a1),x84351),x84353)))+~P1(f324(f324(f239(a1),f2(a1)),x84353)) % 181.55/181.53 [8441]E(f324(f324(f124(x84411),f324(f324(f170(x84411),x84412),x84413)),f324(f324(f145(x84411),f324(f135(x84411),f324(f324(f132(x84411),x84412),x84413))),f116(x84411))),f324(f324(f170(x84411),f324(a115,x84412)),x84413))+~P1(f324(f324(f239(a865),x84412),f324(f192(f866(x84411)),x84413))) % 181.55/181.53 [8461]E(f324(f270(x84611,f324(f324(f148(x84611,f870(a102,x84611)),f324(f259(a102,x84611),f79(a102))),x84612)),f324(a3,x84613)),f324(f324(f159(x84611),x84612),x84613))+~P1(f324(f324(f239(a865),x84613),f324(f192(f866(x84611)),x84612))) % 181.55/181.53 [8529]P1(f324(f324(f326(f870(x85291,x85291)),x85292),f324(f324(f281(x85291,x85291,x85291),x85293),f300(x85291,x85293))))+~P1(f324(f324(f326(f870(x85291,x85291)),x85292),x85293)) % 181.55/181.53 [8540]E(f324(f303(x85401,x85402,x85403),f247(f871(x85401,a859))),f247(f871(x85402,a859)))+~E(f324(f73(x85401,x85402,x85402,x85403),f94(x85401,x85402,f247(f871(x85401,a859)),x85403)),f34(x85402)) % 181.55/181.53 [8550]P1(f324(f324(f238(a865),x85501),x85502))+~P1(f324(f324(f238(a865),f324(f324(f82(a865),f324(a115,x85503)),x85501)),f324(f324(f82(a865),f324(a115,x85503)),x85502))) % 181.55/181.53 [8565]P1(f324(f324(f238(f871(x85651,a859)),x85652),x85653))+~P1(f324(f324(f238(f871(x85651,a859)),f324(f80(f871(x85651,a859)),x85653)),f324(f80(f871(x85651,a859)),x85652))) % 181.55/181.53 [8588]P1(f324(f131(x85881),x85882))+~P1(f324(f131(x85881),f324(f324(f324(f184(f866(x85881),f866(x85881)),x85883),f162(x85881)),x85882))) % 181.55/181.53 [8653]E(f324(f303(f870(x86531,x86532),x86532,f262(x86531,x86532)),f324(f167(f870(x86531,x86532)),x86533)),f181(x86531,x86532,f324(f173(x86531,x86532),x86533)))+~P1(f324(f131(x86531),f324(f324(f148(f870(x86531,x86532),x86531),f258(x86531,x86532)),x86533))) % 181.55/181.53 [8662]E(f324(f278(x86621,x86621,f300(x86621,x86622)),x86623),x86623)+~P1(f324(f324(f238(f871(x86621,a859)),f324(f278(x86621,x86621,x86622),x86623)),x86623)) % 181.55/181.53 [8710]~P105(x87101)+P16(x87101,f324(f130(x87101,f324(f324(f7(x87101,x87101,a859),a321),f324(x87102,x87103))),x87103)) % 181.55/181.53 [8718]~P1(f324(f324(f238(a865),x87181),x87182))+P1(f324(f324(f238(a865),x87181),f324(f136(a865,a865,f81(a865),x87182),x87183))) % 181.55/181.53 [8797]~P1(f324(f324(f326(f870(x87971,x87971)),x87972),f300(x87971,x87973)))+P1(f324(f324(f326(f870(x87971,x87971)),x87972),f324(f324(f184(f870(x87971,x87971),a859),f587(x87973,x87972,x87971)),x87973))) % 181.55/181.53 [8885]~P78(x88851)+E(f324(f324(f81(x88851),x88852),f324(f136(x88851,x88851,f324(f7(x88851,x88851,x88851),f81(x88851)),f2(x88851)),f324(f163(x88851),x88853))),f324(f136(x88851,x88851,f81(x88851),x88852),x88853)) % 181.55/181.53 [9002]~P28(x90022,x90021,x90023,f247(f871(x90022,a859)),f247(f871(x90021,a859)))+E(f94(x90021,x90022,f247(f871(x90021,a859)),f94(x90022,x90021,f247(f871(x90022,a859)),x90023)),x90023) % 181.55/181.53 [9158]P52(x91581,x91582,x91583)+P1(f324(f324(f326(f870(x91581,x91582)),f324(f324(f259(x91581,x91582),f600(x91583,x91582,x91581)),f598(x91583,x91582,x91581))),x91583)) % 181.55/181.53 [9159]P52(x91591,x91592,x91593)+P1(f324(f324(f326(f870(x91591,x91592)),f324(f324(f259(x91591,x91592),f600(x91593,x91592,x91591)),f597(x91593,x91592,x91591))),x91593)) % 181.55/181.53 [9224]~P1(f324(f324(f326(f870(x92241,x92241)),x92242),f324(f324(f281(x92241,x92241,x92241),x92243),f300(x92241,x92243))))+P1(f324(f324(f326(f870(x92241,x92241)),x92242),f324(f324(f184(f870(x92241,x92241),a859),f590(x92243,x92242,x92241)),x92243))) % 181.55/181.53 [9225]~P1(f324(x92251,f324(f324(f159(x92252),x92253),f324(f192(f866(x92252)),f172(x92252,x92251,x92253)))))+~P1(f324(f324(f239(a865),f324(f192(f866(x92252)),f172(x92252,x92251,x92253))),f324(f192(f866(x92252)),x92253))) % 181.55/181.53 [9314]~P1(f324(f324(f238(f871(x93141,a859)),x93142),x93143))+P1(f324(f324(f238(f871(x93141,a859)),f324(f324(f7(x93141,f871(x93141,a859),a859),f326(x93141)),x93142)),f324(f324(f7(x93141,f871(x93141,a859),a859),f326(x93141)),x93143))) % 181.55/181.53 [9370]~P1(f324(f324(f326(f870(f871(x93701,a859),f871(x93701,a859))),f324(f324(f259(f871(x93701,a859),f871(x93701,a859)),x93702),x93703)),f299(x93701)))+P1(f324(f324(f239(f871(x93701,a859)),x93702),x93703)) % 181.55/181.53 [9393]P53(x93931,x93932,x93933)+~P1(f324(f324(f326(f870(x93931,x93931)),f324(f324(f259(x93931,x93931),f595(x93933,x93932,x93931)),f594(x93933,x93932,x93931))),x93933)) % 181.55/181.53 [9394]P53(x93941,x93942,x93943)+~P1(f324(f324(f326(f870(x93941,x93941)),f324(f324(f259(x93941,x93941),f594(x93943,x93942,x93941)),f595(x93943,x93942,x93941))),x93943)) % 181.55/181.53 [9435]~P1(f324(f324(f326(f870(f866(x94351),f866(x94351))),f324(f324(f259(f866(x94351),f866(x94351)),x94352),x94352)),f141(x94351,x94353)))+P1(f324(f324(f326(f870(x94351,x94351)),f324(f324(f259(x94351,x94351),f710(x94352,x94353,x94351)),f710(x94352,x94353,x94351))),x94353)) % 181.55/181.53 [9487]P1(f324(f324(f238(f871(x94871,a859)),x94872),x94873))+~P1(f324(f324(f238(f871(x94871,a859)),f324(f324(f7(x94871,f871(x94871,a859),a859),f326(x94871)),x94872)),f324(f324(f7(x94871,f871(x94871,a859),a859),f326(x94871)),x94873))) % 181.55/181.53 [9571]E(f324(f324(f22(a865),f324(f324(f6(a865,a865),x95711),f324(f245(a865),x95712))),f324(f324(f6(a865,a865),x95713),f324(f245(a865),x95712))),f324(f324(f6(a865,a865),f324(f324(f18(a865,a865,a865),f324(f324(f8(a865,f871(a865,a865),a865),f22(a865)),x95711)),x95713)),f324(f245(a865),x95712)))+~P1(f324(f324(f238(a865),f324(x95713,f502(x95712,x95711,x95713))),f324(x95711,f502(x95712,x95711,x95713)))) % 181.55/181.53 [9876]E(f324(f244(f870(x98761,x98762)),f324(f263(x98761,x98762,a859),f324(f324(f7(x98761,f871(x98762,f869(x98762)),f871(x98762,a859)),f324(f324(f8(f871(f869(x98762),a859),f871(f871(x98762,f869(x98762)),f871(x98762,a859)),x98761),f8(f869(x98762),a859,x98762)),f324(f324(f8(f869(x98762),f871(f869(x98762),a859),x98761),a321),f324(f173(x98761,x98762),x98763)))),f233(x98762)))),f324(f167(f870(x98761,x98762)),x98763))+~P1(f324(f131(x98761),f324(f324(f148(f870(x98761,x98762),x98761),f258(x98761,x98762)),x98763))) % 181.55/181.53 [5594]~P4(x55941)+E(f324(f324(f22(x55941),f324(f324(f81(x55941),x55942),x55943)),x55943),x55942) % 181.55/181.53 [5595]~P4(x55951)+E(f324(f324(f81(x55951),f324(f324(f22(x55951),x55952),x55953)),x55953),x55952) % 181.55/181.53 [5814]~P4(x58141)+E(f324(f324(f81(x58141),x58142),f324(f324(f81(x58141),f324(f80(x58141),x58142)),x58143)),x58143) % 181.55/181.53 [5896]~P77(x58961)+E(f324(f324(f82(x58961),f324(f324(f249(x58961),x58962),x58963)),x58962),f324(f324(f249(x58961),x58962),f324(a115,x58963))) % 181.55/181.53 [5897]~P112(x58971)+E(f324(f324(f82(x58971),f324(f324(f249(x58971),x58972),x58973)),x58972),f324(f324(f249(x58971),x58972),f324(a115,x58973))) % 181.55/181.53 [6103]~P117(x61031)+E(f324(f75(x61031),f324(f324(f249(x61031),f324(f80(x61031),x61032)),x61033)),f324(f75(x61031),f324(f324(f249(x61031),x61032),x61033))) % 181.55/181.53 [6153]~P77(x61531)+E(f324(f324(f82(x61531),f324(f324(f249(x61531),x61532),x61533)),x61532),f324(f324(f82(x61531),x61532),f324(f324(f249(x61531),x61532),x61533))) % 181.55/181.53 [6208]E(f324(f324(f22(a102),f324(f324(f81(a102),x62081),x62082)),x62083),f274(x62081,x62082,x62083))+~P1(f324(f324(f239(a102),x62082),x62083)) % 181.55/181.53 [6229]~E(f324(f324(f132(x62291),x62293),x62292),f116(x62291))+P1(f324(f324(f238(a865),f324(f192(f866(x62291)),x62292)),x62293)) % 181.55/181.53 [6363]E(f324(f324(f82(a865),f324(f106(a865),x63631)),f324(f324(f82(a865),f324(f106(a865),x63632)),x63633)),f2(a865))+~P1(f324(f324(f239(a1),x63631),a84)) % 181.55/181.53 [6379]~P62(x63791)+E(f324(f324(f249(x63791),f324(f324(f282(x63791),f79(x63791)),x63792)),x63793),f324(f324(f282(x63791),f79(x63791)),f324(f324(f249(x63791),x63792),x63793))) % 181.55/181.53 [6455]E(f324(f324(f22(a865),f324(f324(f81(a865),x64551),x64552)),x64553),f324(f324(f22(a865),x64551),f324(f324(f22(a865),x64553),x64552)))+~P1(f324(f324(f238(a865),x64552),x64553)) % 181.55/181.53 [6457]E(f324(f324(f22(a865),f324(f324(f81(a865),x64571),x64572)),x64573),f324(f324(f81(a865),x64571),f324(f324(f22(a865),x64572),x64573)))+~P1(f324(f324(f238(a865),x64573),x64572)) % 181.55/181.53 [6493]~P94(x64931)+P1(f324(f324(f238(x64931),f324(f324(f104(x64931),x64932),x64933)),x64933)) % 181.55/181.53 [6494]~P99(x64941)+P1(f324(f324(f238(x64941),f324(f324(f104(x64941),x64942),x64943)),x64943)) % 181.55/181.53 [6495]~P94(x64951)+P1(f324(f324(f238(x64951),f324(f324(f104(x64951),x64952),x64953)),x64952)) % 181.55/181.53 [6496]~P99(x64961)+P1(f324(f324(f238(x64961),f324(f324(f104(x64961),x64962),x64963)),x64962)) % 181.55/181.53 [6497]~P105(x64971)+P1(f324(f324(f238(x64971),f324(f324(f189(x64971),x64972),x64973)),x64973)) % 181.55/181.53 [6498]~P105(x64981)+P1(f324(f324(f238(x64981),f324(f324(f189(x64981),x64982),x64983)),x64982)) % 181.55/181.53 [6511]E(f324(f324(f38(a1),f324(f324(f38(a1),x65111),x65112)),x65113),f324(f324(f38(a1),x65111),f324(f324(f82(a1),x65112),x65113)))+~P1(f324(f324(f239(a1),f2(a1)),x65113)) % 181.55/181.53 [6562]~P112(x65621)+E(f324(f324(f81(x65621),f324(f324(f82(x65621),x65622),x65623)),x65623),f324(f324(f82(x65621),f324(f324(f81(x65621),x65622),f79(x65621))),x65623)) % 181.55/181.53 [6563]~P92(x65631)+E(f324(f324(f82(x65631),f324(f80(x65631),f324(f106(x65631),x65632))),x65633),f324(f324(f82(x65631),f324(f106(x65631),f324(f80(a1),x65632))),x65633)) % 181.55/181.53 [6635]~P78(x66351)+E(f324(f160(x66351),f324(f324(f148(x66352,x66351),f324(f16(x66351,x66352),f2(x66351))),x66353)),f2(x66351)) % 181.55/181.53 [6651]E(f324(f324(f81(a865),f324(f106(a865),x66511)),f324(f324(f81(a865),f324(f106(a865),x66512)),x66513)),f324(f324(f81(a865),f324(f106(a865),x66512)),x66513))+~P1(f324(a196,f324(f106(a1),x66511))) % 181.55/181.53 [6665]~P6(x66651)+E(f40(x66651,f324(f324(f302(x66651),x66652),f324(f324(f302(x66651),x66653),f191(f871(x66651,a859))))),f324(f324(f104(x66651),x66652),x66653)) % 181.55/181.53 [6666]~P6(x66661)+E(f39(x66661,f324(f324(f302(x66661),x66662),f324(f324(f302(x66661),x66663),f191(f871(x66661,a859))))),f324(f324(f113(x66661),x66662),x66663)) % 181.55/181.53 [6689]E(f324(f324(f170(x66891),x66892),x66893),x66893)+~P1(f324(f324(f238(a865),f324(f192(f866(x66891)),x66893)),x66892)) % 181.55/181.53 [6702]E(f324(f324(f132(x67021),x67022),x67023),f116(x67021))+~P1(f324(f324(f238(a865),f324(f192(f866(x67021)),x67023)),x67022)) % 181.55/181.53 [6713]E(f324(f324(f81(a865),f324(f324(f22(a865),x67131),x67132)),x67133),f324(f324(f22(a865),f324(f324(f81(a865),x67131),x67133)),x67132))+~P1(f324(f324(f238(a865),x67132),x67131)) % 181.55/181.53 [6727]~P1(f324(f324(f239(a865),x67271),x67273))+P1(f324(f324(f239(a865),f324(f324(f22(a865),x67271),x67272)),x67273)) % 181.55/181.53 [6755]~P105(x67551)+E(f164(x67551,x67552,f324(f324(f142(x67551,x67551,f5(x67551)),x67552),x67553)),x67553) % 181.55/181.53 [6843]E(f324(f324(f22(a865),f324(f324(f81(a865),x68431),x68432)),f324(a115,x68433)),f324(f324(f22(a865),x68431),f324(a115,f324(f324(f22(a865),x68433),x68432))))+~P1(f324(f324(f238(a865),x68432),x68433)) % 181.55/181.53 [6844]~P117(x68441)+P1(f324(f324(f238(x68441),f2(x68441)),f324(f324(f249(x68441),f324(f75(x68441),x68442)),x68443))) % 181.55/181.53 [6889]P26(x68891,x68892,x68893)+~P1(f324(f324(f238(f871(f864(x68891),a859)),x68893),x68892)) % 181.55/181.53 [6932]~P1(f324(f61(x69321),x69322))+P1(f324(f61(x69321),f324(f324(f22(f871(x69321,a859)),x69322),x69323))) % 181.55/181.53 [6933]~P1(f324(f61(x69331),x69333))+P1(f324(f61(x69331),f324(f324(f104(f871(x69331,a859)),x69332),x69333))) % 181.55/181.53 [6934]~P1(f324(f61(x69341),x69342))+P1(f324(f61(x69341),f324(f324(f104(f871(x69341,a859)),x69342),x69343))) % 181.55/181.53 [7072]~P39(x70721,x70723)+P39(x70721,f324(f324(f104(f871(f870(x70721,x70721),a859)),x70722),x70723)) % 181.55/181.53 [7073]~P39(x70731,x70732)+P39(x70731,f324(f324(f104(f871(f870(x70731,x70731),a859)),x70732),x70733)) % 181.55/181.53 [7187]~P94(x71871)+E(f13(x71871,f324(f167(x71871),f324(f324(f145(x71871),x71872),x71873))),f324(f136(x71871,x71871,f113(x71871),x71872),x71873)) % 181.55/181.53 [7188]~P94(x71881)+E(f10(x71881,f324(f167(x71881),f324(f324(f145(x71881),x71882),x71883))),f324(f136(x71881,x71881,f104(x71881),x71882),x71883)) % 181.55/181.53 [7189]~P105(x71891)+E(f14(x71891,f324(f167(x71891),f324(f324(f145(x71891),x71892),x71893))),f324(f136(x71891,x71891,f190(x71891),x71892),x71893)) % 181.55/181.53 [7190]~P105(x71901)+E(f15(x71901,f324(f167(x71901),f324(f324(f145(x71901),x71902),x71903))),f324(f136(x71901,x71901,f189(x71901),x71902),x71903)) % 181.55/181.53 [7250]~P1(f324(f61(x72501),x72502))+P1(f324(f324(f238(a865),f324(f37(x72501),x72502)),f324(f37(x72501),f324(f324(f302(x72501),x72503),x72502)))) % 181.55/181.53 [7258]E(f324(f324(f113(f871(a865,a859)),f324(f294(a865,x72581),x72582)),f324(f294(a865,x72582),f324(f324(f81(a865),x72582),x72583))),f324(f294(a865,x72581),f324(f324(f81(a865),x72582),x72583)))+~P1(f324(f324(f238(a865),x72581),x72582)) % 181.55/181.53 [7268]P1(f324(f324(f238(a865),x72681),x72682))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),x72683),x72681)),x72682)) % 181.55/181.53 [7269]P1(f324(f324(f238(a865),x72691),x72692))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),x72691),x72693)),x72692)) % 181.55/181.53 [7270]P1(f324(f324(f239(a865),x72701),x72702))+~P1(f324(f324(f239(a865),f324(f324(f81(a865),x72701),x72703)),x72702)) % 181.55/181.53 [7310]~P105(x73101)+E(f11(x73101,f190(x73101),f324(f167(x73101),f324(f324(f145(x73101),x73102),x73103))),f324(f136(x73101,x73101,f190(x73101),x73102),x73103)) % 181.55/181.53 [7311]~P105(x73111)+E(f12(x73111,f189(x73111),f324(f167(x73111),f324(f324(f145(x73111),x73112),x73113))),f324(f136(x73111,x73111,f189(x73111),x73112),x73113)) % 181.55/181.53 [7315]~E(x73152,f191(f871(f870(x73151,x73151),a859)))+P1(f324(f324(f238(f871(f870(x73151,x73151),a859)),x73152),x73153)) % 181.55/181.53 [7424]E(f324(f324(f113(f871(x74241,a859)),x74242),f324(f324(f22(f871(x74241,a859)),x74243),x74242)),x74243)+~P1(f324(f324(f238(f871(x74241,a859)),x74242),x74243)) % 181.55/181.53 [7425]~P1(f324(f324(f238(a865),x74251),f324(f324(f81(a865),x74253),x74252)))+P1(f324(f324(f238(a865),f324(f324(f22(a865),x74251),x74252)),x74253)) % 181.55/181.53 [7426]~P1(f324(f324(f239(a865),x74261),f324(f324(f22(a865),x74263),x74262)))+P1(f324(f324(f239(a865),f324(f324(f81(a865),x74261),x74262)),x74263)) % 181.55/181.53 [7482]E(x74821,f116(x74822))+E(f324(f135(x74822),f324(f324(f324(f184(f866(x74822),f866(x74822)),x74823),f162(x74822)),x74821)),f324(f324(f159(x74822),x74821),f44(a865,x74823,f324(f192(f866(x74822)),x74821)))) % 181.55/181.53 [7491]E(f324(f324(f302(x74911),x74912),f324(f324(f22(f871(x74911,a859)),x74913),f324(f324(f302(x74911),x74912),f191(f871(x74911,a859))))),x74913)+~P1(f324(f324(f326(x74911),x74912),x74913)) % 181.55/181.53 [7650]P1(f324(f324(f238(a865),x76501),f324(f324(f81(a865),x76502),x76503)))+~P1(f324(f324(f238(a865),f324(f324(f22(a865),x76501),x76503)),x76502)) % 181.55/181.53 [7651]P1(f324(f324(f239(a865),x76511),f324(f324(f22(a865),x76512),x76513)))+~P1(f324(f324(f239(a865),f324(f324(f81(a865),x76511),x76513)),x76512)) % 181.55/181.53 [7673]P1(f324(f61(x76731),x76732))+~P1(f324(f61(x76731),f324(f324(f113(f871(x76731,a859)),x76733),x76732))) % 181.55/181.53 [7674]P1(f324(f61(x76741),x76742))+~P1(f324(f61(x76741),f324(f324(f113(f871(x76741,a859)),x76742),x76743))) % 181.55/181.53 [7744]~P47(x77441,x77443)+P1(f324(f324(f326(f870(x77441,x77441)),f324(f324(f259(x77441,x77441),x77442),x77442)),x77443)) % 181.55/181.53 [7882]E(f324(f324(f159(a865),f133(a865,f324(f294(a865,x78821),x78822))),x78823),f324(f324(f81(a865),x78821),x78823))+~P1(f324(f324(f239(a865),f324(f324(f81(a865),x78821),x78823)),x78822)) % 181.55/181.53 [7947]E(f324(f324(f170(a865),x79471),f133(a865,f324(f294(a865,x79472),x79473))),f133(a865,f324(f294(a865,x79472),f324(f324(f81(a865),x79472),x79471))))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),x79472),x79471)),x79473)) % 181.55/181.53 [8002]~P92(x80021)+E(f324(f324(f249(x80021),x80022),f324(f106(a865),f324(f324(f81(a1),x80023),x80023))),f324(f324(f87(x80021,x80021),f324(f324(f249(x80021),x80022),f324(f106(a865),x80023))),f324(f324(f18(x80021,x80021,x80021),f82(x80021)),f5(x80021)))) % 181.55/181.53 [8272]E(f324(f324(f124(x82721),f324(f324(f170(x82721),x82722),x82723)),f324(f324(f145(x82721),f324(f324(f159(x82721),x82723),x82722)),f324(f324(f132(x82721),f324(a115,x82722)),x82723))),x82723)+~P1(f324(f324(f239(a865),x82722),f324(f192(f866(x82721)),x82723))) % 181.55/181.53 [8279]P1(f324(f324(f238(f871(x82791,a859)),f312(x82791,x82792)),f312(x82791,x82793)))+~P1(f324(f324(f238(f871(x82791,f871(x82791,a859))),x82793),x82792)) % 181.55/181.53 [8281]~P53(x82811,x82812,x82813)+P53(x82811,x82812,f324(f324(f22(f871(f870(x82811,x82811),a859)),x82813),f300(x82811,f191(f871(f870(x82811,x82811),a859))))) % 181.55/181.53 [8301]P1(f324(f324(f238(f871(x83011,a859)),f313(x83011,x83012)),f313(x83011,x83013)))+~P1(f324(f324(f238(f871(f870(x83011,x83011),a859)),x83013),x83012)) % 181.55/181.53 [8307]~P1(f324(f324(f239(f871(x83071,a859)),x83073),x83072))+P1(f324(f324(f326(x83071),f489(x83072,x83073,x83071)),f324(f324(f22(f871(x83071,a859)),x83072),x83073))) % 181.55/181.53 [8309]~P122(x83091)+P1(f324(f324(f238(x83091),f2(x83091)),f324(f324(f81(x83091),f324(f324(f82(x83091),x83092),x83092)),f324(f324(f82(x83091),x83093),x83093)))) % 181.55/181.53 [8341]P1(f324(f324(f238(f871(x83411,a859)),f324(f277(x83411),x83412)),f324(f277(x83411),x83413)))+~P1(f324(f324(f238(f871(f870(x83411,x83411),a859)),x83412),x83413)) % 181.55/181.53 [8370]~P43(x83701,x83702)+~P1(f324(f324(f326(f870(x83701,x83701)),f324(f324(f259(x83701,x83701),x83703),x83703)),x83702)) % 181.55/181.53 [8372]~P39(x83721,x83722)+~P1(f324(f324(f326(f870(x83721,x83721)),f324(f324(f259(x83721,x83721),x83723),x83723)),x83722)) % 181.55/181.53 [8426]P1(f324(f324(f238(f871(x84261,a859)),f40(f871(x84261,a859),x84262)),f40(f871(x84261,a859),x84263)))+~P1(f324(f324(f238(f871(f871(x84261,a859),a859)),x84263),x84262)) % 181.55/181.53 [8427]P1(f324(f324(f238(f871(x84271,a859)),f39(f871(x84271,a859),x84272)),f39(f871(x84271,a859),x84273)))+~P1(f324(f324(f238(f871(f871(x84271,a859),a859)),x84272),x84273)) % 181.55/181.53 [8480]~P9(x84801,x84803,x84802)+P1(f324(f324(f238(f871(f870(x84801,x84801),a859)),x84802),f324(f324(f261(x84801,x84801),x84803),f324(f16(f871(x84801,a859),x84801),x84803)))) % 181.55/181.53 [8481]~P41(x84811,x84813,x84812)+P1(f324(f324(f238(f871(f870(x84811,x84811),a859)),x84812),f324(f324(f261(x84811,x84811),x84813),f324(f16(f871(x84811,a859),x84811),x84813)))) % 181.55/181.53 [8530]~P83(x85301)+P1(f324(f324(f238(x85301),f324(f324(f22(x85301),f324(f75(x85301),x85302)),f324(f75(x85301),x85303))),f324(f75(x85301),f324(f324(f22(x85301),x85303),x85302)))) % 181.55/181.53 [8531]~P83(x85311)+P1(f324(f324(f238(x85311),f324(f324(f22(x85311),f324(f75(x85311),x85312)),f324(f75(x85311),x85313))),f324(f75(x85311),f324(f324(f22(x85311),x85312),x85313)))) % 181.55/181.53 [8563]P1(f324(f324(f238(f871(f870(x85631,x85631),a859)),f300(x85631,x85632)),f300(x85631,x85633)))+~P1(f324(f324(f238(f871(f870(x85631,x85631),a859)),x85632),x85633)) % 181.55/181.53 [8675]~P27(x86752,x86751,x86753,f247(f871(x86752,a859)))+E(f324(f73(x86751,x86752,x86752,f94(x86752,x86751,f247(f871(x86752,a859)),x86753)),x86753),f34(x86752)) % 181.55/181.53 [8736]P53(x87361,x87362,x87363)+~P53(x87361,x87362,f324(f324(f22(f871(f870(x87361,x87361),a859)),x87363),f300(x87361,f191(f871(f870(x87361,x87361),a859))))) % 181.55/181.53 [8756]P1(f324(f324(f238(f871(f870(f866(x87561),f866(x87561)),a859)),f151(x87561,x87562)),f151(x87561,x87563)))+~P1(f324(f324(f238(f871(f870(x87561,x87561),a859)),x87562),x87563)) % 181.55/181.53 [8757]P1(f324(f324(f238(f871(f870(f866(x87571),f866(x87571)),a859)),f152(x87571,x87572)),f152(x87571,x87573)))+~P1(f324(f324(f238(f871(f870(x87571,x87571),a859)),x87572),x87573)) % 181.55/181.53 [8776]~P41(x87761,x87763,x87762)+P1(f324(f324(f238(f871(f870(x87761,x87761),a859)),x87762),f324(f324(f281(x87761,x87761,x87761),f324(f279(x87761,x87761),x87762)),x87762))) % 181.55/181.53 [8826]~P1(f324(f131(x88261),x88262))+E(f324(f130(x88261,f324(f324(f7(x88261,f871(x88261,a859),a859),f326(x88261)),f324(f167(x88261),f171(x88261,x88262,x88263)))),x88262),f171(x88261,x88262,x88263)) % 181.55/181.53 [8883]E(x88831,x88832)+~P1(f324(f324(f326(f870(x88833,x88833)),f324(f324(f259(x88833,x88833),x88831),x88832)),f300(x88833,f191(f871(f870(x88833,x88833),a859))))) % 181.55/181.53 [8964]P1(f324(f324(f326(x89641),x89642),f313(x89641,x89643)))+P1(f324(f324(f326(f870(x89641,x89641)),f324(f324(f259(x89641,x89641),f511(x89643,x89642,x89641)),x89642)),x89643)) % 181.55/181.53 [8965]P1(f324(f324(f326(x89651),x89652),f313(x89651,x89653)))+P1(f324(f324(f326(f870(x89651,x89651)),f324(f324(f259(x89651,x89651),f569(x89653,x89652,x89651)),x89652)),x89653)) % 181.55/181.53 [8966]P1(f324(f324(f326(x89661),x89662),f313(x89661,x89663)))+P1(f324(f324(f326(f870(x89661,x89661)),f324(f324(f259(x89661,x89661),f572(x89663,x89662,x89661)),x89662)),x89663)) % 181.55/181.53 [9003]P27(x90031,x90032,x90033,f247(f871(x90031,a859)))+~E(f324(f73(x90032,x90031,x90031,f94(x90031,x90032,f247(f871(x90031,a859)),x90033)),x90033),f34(x90031)) % 181.55/181.53 [9057]~P1(f324(f324(f326(f866(x90571)),x90573),f155(x90571,x90572)))+P1(f324(f154(x90571,f324(f324(f7(x90571,f871(x90571,a859),a859),f326(x90571)),x90572)),x90573)) % 181.55/181.53 [9078]P1(f324(x90783,x90782))+E(f324(f244(x90781),f324(f324(f18(x90781,a859,a859),f324(f324(f8(a859,f871(a859,a859),x90781),a322),f324(a321,x90782))),x90783)),f191(f871(x90781,a859))) % 181.55/181.53 [9098]~P83(x90981)+P1(f324(f324(f238(x90981),f324(f75(x90981),f324(f324(f22(x90981),f324(f75(x90981),x90982)),f324(f75(x90981),x90983)))),f324(f75(x90981),f324(f324(f22(x90981),x90982),x90983)))) % 181.55/181.53 [9112]~P1(f324(x91123,x91122))+E(f324(f244(x91121),f324(f324(f18(x91121,a859,a859),f324(f324(f8(a859,f871(a859,a859),x91121),a322),f324(a321,x91122))),x91123)),f324(f324(f302(x91121),x91122),f191(f871(x91121,a859)))) % 181.55/181.53 [9120]~P1(f324(f324(f326(f871(x91201,a859)),x91203),f324(f301(x91201),x91202)))+P1(f324(f252(x91201,f324(f324(f7(x91201,f871(x91201,a859),a859),f326(x91201)),x91202)),x91203)) % 181.55/181.53 [9157]P39(x91571,x91572)+P1(f324(f324(f326(f870(x91571,x91571)),f324(f324(f259(x91571,x91571),f324(f522(x91572,x91571),f324(a115,x91573))),f324(f522(x91572,x91571),x91573))),x91572)) % 181.55/181.53 [9292]P1(f324(f324(f326(f866(x92921)),x92922),f155(x92921,x92923)))+~P1(f324(f154(x92921,f324(f324(f7(x92921,f871(x92921,a859),a859),f326(x92921)),x92923)),x92922)) % 181.55/181.53 [9306]P1(f324(f324(f326(f871(x93061,a859)),x93062),f324(f301(x93061),x93063)))+~P1(f324(f252(x93061,f324(f324(f7(x93061,f871(x93061,a859),a859),f326(x93061)),x93063)),x93062)) % 181.55/181.53 [9364]P1(f324(f324(f326(x93641),f324(f270(x93641,x93642),x93643)),f324(f167(x93641),f324(f324(f148(f870(a102,x93641),x93641),f262(a102,x93641)),x93642))))+~P1(f324(f324(f239(a102),x93643),f324(f160(a102),f324(f324(f148(f870(a102,x93641),a102),f258(a102,x93641)),x93642)))) % 181.55/181.53 [9415]P1(f324(f324(f238(f871(f870(f866(x94151),f866(x94151)),a859)),f152(x94151,x94152)),f324(f324(f261(f866(x94151),f866(x94151)),f155(x94151,x94153)),f324(f16(f871(f866(x94151),a859),f866(x94151)),f155(x94151,x94153)))))+~P1(f324(f324(f238(f871(f870(x94151,x94151),a859)),x94152),f324(f324(f261(x94151,x94151),x94153),f324(f16(f871(x94151,a859),x94151),x94153)))) % 181.55/181.53 [9438]P1(f324(f324(f326(x94381),f324(f258(x94381,f870(a102,a102)),f324(f268(x94381,x94382),x94383))),f324(f167(x94381),f324(f324(f148(f870(a102,x94381),x94381),f262(a102,x94381)),x94382))))+~P1(f324(f324(f239(a102),f2(a102)),f324(f160(a102),f324(f324(f148(f870(a102,x94381),a102),f258(a102,x94381)),x94382)))) % 181.55/181.54 [9454]~P1(f324(f324(f238(f871(f870(x94541,x94541),a859)),x94542),f324(f324(f261(x94541,x94541),x94543),f324(f16(f871(x94541,a859),x94541),x94543))))+P1(f324(f324(f238(f871(f870(x94541,x94541),a859)),f324(f324(f281(x94541,x94541,x94541),x94542),f300(x94541,x94542))),f324(f324(f261(x94541,x94541),x94543),f324(f16(f871(x94541,a859),x94541),x94543)))) % 181.55/181.54 [9764]~P39(x97641,x97642)+~P1(f324(f324(f326(f870(x97641,x97641)),f324(f324(f259(x97641,x97641),f324(x97643,f324(a115,f523(x97642,x97641,x97643)))),f324(x97643,f523(x97642,x97641,x97643)))),x97642)) % 181.55/181.54 [9765]~P39(x97651,x97652)+~P1(f324(f324(f326(f870(x97651,x97651)),f324(f324(f259(x97651,x97651),f324(x97653,f324(a115,f581(x97653,x97652,x97651)))),f324(x97653,f581(x97653,x97652,x97651)))),x97652)) % 181.55/181.54 [10015]P1(f324(f324(f238(f871(f870(f871(x100151,a859),f871(x100151,a859)),a859)),f324(f324(f281(f871(x100151,a859),f871(x100151,a859),f871(x100151,a859)),f315(x100151,x100152)),f324(f324(f113(f871(f870(f871(x100151,a859),f871(x100151,a859)),a859)),f315(x100151,x100153)),f324(f324(f302(f870(f871(x100151,a859),f871(x100151,a859))),f324(f324(f259(f871(x100151,a859),f871(x100151,a859)),f191(f871(x100151,a859))),f191(f871(x100151,a859)))),f191(f871(f870(f871(x100151,a859),f871(x100151,a859)),a859)))))),f315(x100151,x100152)))+~P1(f324(f324(f238(f871(f870(x100151,x100151),a859)),f324(f324(f281(x100151,x100151,x100151),x100152),x100153)),x100152)) % 181.55/181.54 [10016]P1(f324(f324(f238(f871(f870(f871(x100161,a859),f871(x100161,a859)),a859)),f324(f324(f281(f871(x100161,a859),f871(x100161,a859),f871(x100161,a859)),f317(x100161,x100162)),f324(f324(f113(f871(f870(f871(x100161,a859),f871(x100161,a859)),a859)),f317(x100161,x100163)),f324(f324(f302(f870(f871(x100161,a859),f871(x100161,a859))),f324(f324(f259(f871(x100161,a859),f871(x100161,a859)),f191(f871(x100161,a859))),f191(f871(x100161,a859)))),f191(f871(f870(f871(x100161,a859),f871(x100161,a859)),a859)))))),f317(x100161,x100162)))+~P1(f324(f324(f238(f871(f870(x100161,x100161),a859)),f324(f324(f281(x100161,x100161,x100161),x100162),x100163)),x100162)) % 181.55/181.54 [7186]~P1(f324(f324(f238(a865),x71862),x71861))+E(f324(f324(f22(a865),f324(a115,f324(f324(f22(a865),x71861),x71862))),x71863),f324(f324(f22(a865),f324(a115,x71861)),f324(f324(f81(a865),x71862),x71863))) % 181.55/181.54 [7225]~P59(x72251)+E(f324(f324(f81(x72251),f44(x72251,x72252,x72253)),f324(f324(f82(x72251),f324(f324(f38(x72251),x72252),x72253)),x72253)),x72252) % 181.55/181.54 [7430]E(f324(f324(f82(a865),f324(f106(a865),x74301)),f324(f324(f82(a865),f324(f106(a865),x74302)),x74303)),f324(f324(f82(a865),f324(f106(a865),f324(f324(f82(a1),x74301),x74302))),x74303))+P1(f324(f324(f239(a1),x74301),a84)) % 181.55/181.54 [7891]~P1(f324(f324(f238(a865),x78913),x78912))+P1(f324(f324(f238(a865),x78911),f324(f324(f22(a865),f324(f324(f81(a865),x78912),x78911)),x78913))) % 181.55/181.54 [8088]~P1(f324(f324(f238(a865),x80881),x80882))+E(f324(f324(f124(a865),f133(a865,f324(f294(a865,x80881),x80882))),f133(a865,f324(f294(a865,x80882),f324(f324(f81(a865),x80882),x80883)))),f133(a865,f324(f294(a865,x80881),f324(f324(f81(a865),x80882),x80883)))) % 181.55/181.54 [8349]~P1(f324(f61(x83491),x83492))+E(f324(a115,f324(f37(x83491),f324(f324(f22(f871(x83491,a859)),x83492),f324(f324(f302(x83491),x83493),f191(f871(x83491,a859)))))),f324(f37(x83491),f324(f324(f302(x83491),x83493),x83492))) % 181.55/181.54 [8389]~P1(f324(f61(x83891),x83892))+E(f324(f324(f81(a865),f79(a865)),f324(f37(x83891),f324(f324(f22(f871(x83891,a859)),x83892),f324(f324(f302(x83891),x83893),f191(f871(x83891,a859)))))),f324(f37(x83891),f324(f324(f302(x83891),x83893),x83892))) % 181.55/181.54 [8572]E(f324(f324(f22(a865),f324(f37(x85721),x85722)),f324(f37(x85721),f324(f324(f104(f871(x85721,a859)),x85722),x85723))),f324(f37(x85721),f324(f324(f22(f871(x85721,a859)),x85722),x85723)))+~P1(f324(f61(x85721),f324(f324(f104(f871(x85721,a859)),x85722),x85723))) % 181.55/181.54 [8821]~P7(f324(x88212,f427(x88212,x88213,x88211)))+E(f324(f103(a1),f324(f324(f9(x88211,a865),f324(f324(f8(a1,a865,x88211),a107),x88212)),x88213)),f324(f324(f9(x88211,a1),x88212),x88213)) % 181.55/181.54 [8822]~P7(f324(x88222,f483(x88222,x88223,x88221)))+E(f324(f103(a1),f324(f324(f6(x88221,a865),f324(f324(f8(a1,a865,x88221),a107),x88222)),x88223)),f324(f324(f6(x88221,a1),x88222),x88223)) % 181.55/181.54 [8868]~P1(f324(f61(x88681),x88683))+P1(f324(f324(f238(a865),f324(f324(f22(a865),f324(f37(x88681),x88682)),f324(f37(x88681),x88683))),f324(f37(x88681),f324(f324(f22(f871(x88681,a859)),x88682),x88683)))) % 181.55/181.54 [8891]P1(f324(f324(f326(x88911),f427(x88912,x88913,x88911)),x88913))+E(f324(f103(a1),f324(f324(f9(x88911,a865),f324(f324(f8(a1,a865,x88911),a107),x88912)),x88913)),f324(f324(f9(x88911,a1),x88912),x88913)) % 181.55/181.54 [8892]P1(f324(f324(f326(x88921),f483(x88922,x88923,x88921)),x88923))+E(f324(f103(a1),f324(f324(f6(x88921,a865),f324(f324(f8(a1,a865,x88921),a107),x88922)),x88923)),f324(f324(f6(x88921,a1),x88922),x88923)) % 181.55/181.54 [8956]E(f86(x89561,f324(f324(f7(x89561,f871(x89561,a859),a859),f326(x89561)),f324(f324(f22(f871(x89561,a859)),x89562),f324(f324(f302(x89561),x89563),f191(f871(x89561,a859)))))),f251(x89561,x89563,x89562))+P1(f324(f324(f238(f871(x89561,a859)),x89562),f324(f324(f302(x89561),x89563),f191(f871(x89561,a859))))) % 181.55/181.54 [9307]E(f324(f324(f148(f866(x93071),x93071),f324(f324(f7(f866(x93071),a865,x93071),f159(x93071)),x93072)),f324(f130(f866(x93071),f324(f324(f8(a865,a859,f866(x93071)),f324(f239(a865),x93072)),f192(f866(x93071)))),x93073)),f324(f324(f159(f866(x93071)),f175(x93071,x93073)),x93072))+~P1(f324(f324(f239(a865),x93072),f324(f192(f866(f866(x93071))),f175(x93071,x93073)))) % 181.55/181.54 [9383]E(f324(f130(x93831,x93832),x93833),f172(x93831,x93832,x93833))+P1(f324(f324(f326(x93831),f738(x93833,x93832,x93831)),f324(f167(x93831),f324(f324(f132(x93831),f324(f192(f866(x93831)),f172(x93831,x93832,x93833))),x93833)))) % 181.55/181.54 [9529]E(f324(f324(f132(x95291),f324(f192(f866(x95291)),f172(x95291,x95292,x95293))),x95293),f116(x95291))+~P1(f324(x95292,f324(f135(x95291),f324(f324(f132(x95291),f324(f192(f866(x95291)),f172(x95291,x95292,x95293))),x95293)))) % 181.55/181.54 [9624]~P1(f324(f324(f326(f870(x96241,x96241)),x96242),f300(x96241,x96243)))+P1(f324(f324(f326(f870(x96241,x96241)),x96242),f324(f324(f41(a865,f871(f870(x96241,x96241),a859)),f247(f871(a865,a859))),f324(f324(f7(a865,f871(f870(x96241,x96241),a859),f871(f870(x96241,x96241),a859)),f184(f870(x96241,x96241),a859)),x96243)))) % 181.55/181.54 [9683]~P1(f324(f324(f238(f871(x96831,a859)),f324(f324(f41(a865,f871(x96831,a859)),f324(f294(a865,f2(a865)),f476(x96833,x96832,x96831))),x96832)),x96833))+P1(f324(f324(f238(f871(x96831,a859)),f324(f324(f41(a865,f871(x96831,a859)),f247(f871(a865,a859))),x96832)),x96833)) % 181.55/181.54 [9740]~P1(f324(f324(f239(a1),f2(a1)),x97403))+P1(f324(f324(f239(a1),x97401),f324(f324(f81(a1),x97402),f324(f324(f82(a1),f324(f324(f81(a1),f324(f75(a1),f324(f324(f22(a1),x97402),x97401))),f79(a1))),x97403)))) % 181.55/181.54 [9751]~P39(x97511,f324(f324(f113(f871(f870(x97511,x97511),a859)),x97512),x97513))+P39(x97511,f324(f324(f113(f871(f870(x97511,x97511),a859)),f324(f324(f113(f871(f870(x97511,x97511),a859)),f324(f324(f281(x97511,x97511,x97511),x97512),x97512)),f324(f324(f281(x97511,x97511,x97511),x97513),x97512))),x97513)) % 181.55/181.54 [9832]P39(x98321,f324(f324(f113(f871(f870(x98321,x98321),a859)),x98322),x98323))+~P39(x98321,f324(f324(f113(f871(f870(x98321,x98321),a859)),f324(f324(f113(f871(f870(x98321,x98321),a859)),f324(f324(f281(x98321,x98321,x98321),x98322),x98322)),f324(f324(f281(x98321,x98321,x98321),x98323),x98322))),x98323)) % 181.55/181.54 [9386]~P135(x93861)+E(f324(f105(x93861),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x93862),x93863)),f191(f871(f870(a865,a865),a859)))))),f324(f324(f22(x93861),f324(f103(x93861),x93862)),f324(f103(x93861),x93863))) % 181.55/181.54 [9472]P1(f324(x94723,x94722))+E(f324(f244(x94721),f324(f324(f18(x94721,a859,a859),f324(f324(f8(a859,f871(a859,a859),x94721),a322),f324(f324(f7(x94721,x94721,a859),a321),x94722))),x94723)),f191(f871(x94721,a859))) % 181.55/181.54 [9474]~P1(f324(x94743,x94742))+E(f324(f244(x94741),f324(f324(f18(x94741,a859,a859),f324(f324(f8(a859,f871(a859,a859),x94741),a322),f324(f324(f7(x94741,x94741,a859),a321),x94742))),x94743)),f324(f324(f302(x94741),x94742),f191(f871(x94741,a859)))) % 181.55/181.54 [9719]E(x97191,x97192)+P1(f324(f324(f248(x97193,x97193,f324(f324(f8(f871(x97193,a859),f871(x97193,a859),x97193),f324(f8(a859,a859,x97193),a319)),a321)),x97191),x97192)) % 181.55/181.54 [9810]~E(x98101,x98102)+~P1(f324(f324(f248(x98103,x98103,f324(f324(f8(f871(x98103,a859),f871(x98103,a859),x98103),f324(f8(a859,a859,x98103),a319)),a321)),x98101),x98102)) % 181.55/181.54 [9824]~P1(f324(f61(x98241),x98243))+E(f324(f324(f64(x98241,f871(x98241,a859),f324(f324(f8(f871(x98241,a859),f871(f871(x98241,a859),f871(x98241,a859)),x98241),f324(f7(f871(x98241,a859),f871(x98241,a859),f871(x98241,a859)),f22(f871(x98241,a859)))),f324(f324(f7(x98241,f871(x98241,a859),f871(x98241,a859)),f302(x98241)),f191(f871(x98241,a859))))),x98242),x98243),f324(f324(f22(f871(x98241,a859)),x98242),x98243)) % 181.55/181.54 [9855]~P1(f324(f324(f239(a1),f2(a1)),x98553))+P1(f324(f324(f239(a1),f324(f324(f22(a1),x98551),f324(f324(f82(a1),f324(f324(f81(a1),f324(f75(a1),f324(f324(f22(a1),x98551),x98552))),f79(a1))),x98553))),x98552)) % 181.55/181.54 [10078]~P1(f324(f324(f326(x100781),x100783),f313(x100781,x100782)))+P1(f324(f312(x100781,f324(f324(f7(x100781,f871(f870(x100781,x100781),a859),f871(x100781,a859)),f324(f324(f8(f871(x100781,f871(f871(f870(x100781,x100781),a859),a859)),f871(f871(f870(x100781,x100781),a859),f871(x100781,a859)),x100781),f7(x100781,f871(f870(x100781,x100781),a859),a859)),f324(f324(f8(f871(x100781,f870(x100781,x100781)),f871(x100781,f871(f871(f870(x100781,x100781),a859),a859)),x100781),f324(f8(f870(x100781,x100781),f871(f871(f870(x100781,x100781),a859),a859),x100781),f326(f870(x100781,x100781)))),f259(x100781,x100781)))),x100782)),x100783)) % 181.55/181.54 [10091]P1(f324(f324(f326(x100911),x100912),f313(x100911,x100913)))+~P1(f324(f312(x100911,f324(f324(f7(x100911,f871(f870(x100911,x100911),a859),f871(x100911,a859)),f324(f324(f8(f871(x100911,f871(f871(f870(x100911,x100911),a859),a859)),f871(f871(f870(x100911,x100911),a859),f871(x100911,a859)),x100911),f7(x100911,f871(f870(x100911,x100911),a859),a859)),f324(f324(f8(f871(x100911,f870(x100911,x100911)),f871(x100911,f871(f871(f870(x100911,x100911),a859),a859)),x100911),f324(f8(f870(x100911,x100911),f871(f871(f870(x100911,x100911),a859),a859),x100911),f326(f870(x100911,x100911)))),f259(x100911,x100911)))),x100913)),x100912)) % 181.55/181.54 [9681]~P1(f324(f61(x96811),f324(f244(x96811),x96813)))+P1(f324(f61(x96811),f324(f244(x96811),f324(f324(f18(x96811,a859,a859),f324(f324(f8(a859,f871(a859,a859),x96811),a322),x96812)),x96813)))) % 181.55/181.54 [9682]~P1(f324(f61(x96821),f324(f244(x96821),x96822)))+P1(f324(f61(x96821),f324(f244(x96821),f324(f324(f18(x96821,a859,a859),f324(f324(f8(a859,f871(a859,a859),x96821),a322),x96822)),x96823)))) % 181.55/181.54 [9785]P1(f324(f61(x97851),f324(f244(x97851),x97852)))+~P1(f324(f61(x97851),f324(f244(x97851),f324(f324(f18(x97851,a859,a859),f324(f324(f8(a859,f871(a859,a859),x97851),a323),x97853)),x97852)))) % 181.55/181.54 [9786]P1(f324(f61(x97861),f324(f244(x97861),x97862)))+~P1(f324(f61(x97861),f324(f244(x97861),f324(f324(f18(x97861,a859,a859),f324(f324(f8(a859,f871(a859,a859),x97861),a323),x97862)),x97863)))) % 181.55/181.54 [10063]~P1(f324(f61(x100631),x100632))+P1(f324(f61(f866(x100631)),f324(f244(f866(x100631)),f324(f324(f18(f866(x100631),a859,a859),f324(f324(f8(a859,f871(a859,a859),f866(x100631)),a322),f324(f324(f7(f866(x100631),f871(x100631,a859),a859),f324(f324(f8(f871(x100631,a859),f871(f871(x100631,a859),a859),f866(x100631)),f238(f871(x100631,a859))),f167(x100631))),x100632))),f324(f324(f7(f866(x100631),a865,a859),f324(f324(f8(a865,f871(a865,a859),f866(x100631)),a321),f192(f866(x100631)))),x100633))))) % 181.55/181.54 [10064]~P1(f324(f61(x100641),x100642))+P1(f324(f61(f866(x100641)),f324(f244(f866(x100641)),f324(f324(f18(f866(x100641),a859,a859),f324(f324(f8(a859,f871(a859,a859),f866(x100641)),a322),f324(f324(f7(f866(x100641),f871(x100641,a859),a859),f324(f324(f8(f871(x100641,a859),f871(f871(x100641,a859),a859),f866(x100641)),f238(f871(x100641,a859))),f167(x100641))),x100642))),f324(f324(f7(f866(x100641),a865,a859),f324(f324(f8(a865,f871(a865,a859),f866(x100641)),f238(a865)),f192(f866(x100641)))),x100643))))) % 181.55/181.54 [9799]~P112(x97991)+E(f324(f324(f249(x97991),x97992),f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x97993)),f324(f324(f82(x97991),f324(f324(f249(x97991),x97992),x97993)),f324(f324(f249(x97991),x97992),x97993))) % 181.55/181.54 [9836]~P77(x98361)+E(f324(f324(f249(x98361),f324(f324(f249(x98361),x98362),x98363)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f249(x98361),x98362),f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98363))) % 181.55/181.54 [9883]~P135(x98831)+E(f324(f324(f249(x98831),f324(f80(x98831),x98832)),f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98833)),f324(f324(f249(x98831),x98832),f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98833))) % 181.55/181.54 [10022]~P117(x100221)+P1(f324(f324(f238(x100221),f2(x100221)),f324(f324(f81(x100221),f324(f324(f249(x100221),x100222),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100221),x100223),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))))) % 181.55/181.54 [9893]~P112(x98931)+E(f324(f324(f249(x98931),x98932),f324(a115,f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98933))),f324(f324(f82(x98931),x98932),f324(f324(f82(x98931),f324(f324(f249(x98931),x98932),x98933)),f324(f324(f249(x98931),x98932),x98933)))) % 181.55/181.54 [9942]~P77(x99421)+E(f324(f324(f82(x99421),x99422),f324(f324(f249(x99421),f324(f324(f249(x99421),x99422),x99423)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x99421),x99422),f324(a115,f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x99423)))) % 181.55/181.54 [9980]~P117(x99801)+P1(f324(f324(f238(x99801),f2(x99801)),f324(f324(f249(x99801),x99802),f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x99803)))) % 181.55/181.54 [10044]~P92(x100441)+E(f324(f324(f22(x100441),f324(f324(f81(x100441),f324(f324(f249(x100441),x100442),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100441),x100443),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))),f324(f324(f82(x100441),f324(f324(f82(x100441),f324(f106(x100441),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100442)),x100443)),f324(f324(f249(x100441),f324(f324(f22(x100441),x100442),x100443)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.54 [10045]~P92(x100451)+E(f324(f324(f81(x100451),f324(f324(f81(x100451),f324(f324(f249(x100451),x100452),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100451),x100453),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))),f324(f324(f82(x100451),f324(f324(f82(x100451),f324(f106(x100451),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100452)),x100453)),f324(f324(f249(x100451),f324(f324(f81(x100451),x100452),x100453)),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.54 [4664]E(x46641,x46642)+~E(f33(x46643,x46641),f33(x46644,x46642)) % 181.55/181.54 [4665]E(x46651,x46652)+~E(f33(x46651,x46653),f33(x46652,x46654)) % 181.55/181.54 [4666]E(x46661,x46662)+~E(f26(x46663,x46661),f26(x46664,x46662)) % 181.55/181.54 [4667]E(x46671,x46672)+~E(f26(x46671,x46673),f26(x46672,x46674)) % 181.55/181.54 [4668]E(x46681,x46682)+~E(f32(x46683,x46681),f32(x46684,x46682)) % 181.55/181.54 [4669]E(x46691,x46692)+~E(f32(x46691,x46693),f32(x46692,x46694)) % 181.55/181.54 [7690]P27(x76901,x76902,x76903,x76904)+~E(f388(x76904,x76903,x76902,x76901),f397(x76904,x76903,x76902,x76901)) % 181.55/181.54 [7981]P36(x79811,x79812,x79813,x79814,f116(x79812))+~E(x79814,f116(x79811)) % 181.55/181.54 [7982]P36(x79821,x79822,x79823,f116(x79821),x79824)+~E(x79824,f116(x79822)) % 181.55/181.54 [8194]~P27(x81941,f869(x81942),x81944,f179(x81941,x81942,x81944))+P27(x81941,f869(x81942),f180(x81941,x81942,x81943,x81944),f179(x81941,x81942,x81944)) % 181.55/181.54 [8403]~P27(x84031,f869(x84032),f180(x84031,x84032,x84034,x84033),f179(x84031,x84032,x84033))+P27(x84031,f869(x84032),x84033,f179(x84031,x84032,x84033)) % 181.55/181.54 [8520]~P36(x85202,x85203,x85204,x85201,f116(x85203))+E(x85201,f116(x85202)) % 181.55/181.54 [8521]~P36(x85213,x85212,x85214,f116(x85213),x85211)+E(x85211,f116(x85212)) % 181.55/181.54 [5034]~P19(x50343,x50341,x50344)+E(f324(f324(x50341,x50342),x50342),x50342) % 181.55/181.54 [5309]~E(x53094,f191(f871(x53091,a859)))+E(f324(f303(x53091,x53092,x53093),x53094),f191(f871(x53092,a859))) % 181.55/181.54 [5575]~E(f324(f303(x55752,x55753,x55754),x55751),f191(f871(x55753,a859)))+E(x55751,f191(f871(x55752,a859))) % 181.55/181.54 [5857]~P105(x58572)+E(f324(f324(f142(x58571,x58572,x58573),x58574),f116(x58571)),f324(f324(f145(x58571),x58574),f116(x58571))) % 181.55/181.54 [5892]E(f324(x58921,x58922),f203(x58923))+P1(f324(f324(f326(x58924),x58922),f179(x58924,x58923,x58921))) % 181.55/181.54 [6202]~E(x62021,f191(f871(x62022,a859)))+~P1(f324(f62(x62022,x62023,x62021),x62024)) % 181.55/181.54 [6223]~P56(x62231,x62233,x62234,x62232)+P1(f324(f61(x62231),x62232)) % 181.55/181.54 [6224]~P56(x62241,x62243,x62242,x62244)+P1(f324(f61(x62241),x62242)) % 181.55/181.54 [6230]~P56(x62302,x62303,x62304,x62301)+~E(x62301,f191(f871(x62302,a859))) % 181.55/181.54 [6261]~P106(x62611)+E(f324(f324(f104(f871(x62611,a859)),f324(f294(x62611,x62612),x62613)),f295(x62611,x62613,x62614)),f191(f871(x62611,a859))) % 181.55/181.54 [6288]~P1(f324(f324(x62883,x62884),x62882))+P1(f324(f324(f326(x62881),x62882),f285(x62881,x62883,x62884))) % 181.55/181.54 [6289]~P1(f324(f324(x62893,x62894),x62892))+P1(f324(f324(f326(x62891),x62892),f286(x62891,x62893,x62894))) % 181.55/181.54 [6290]~P1(f324(f324(x62903,x62902),x62904))+P1(f324(f324(f326(x62901),x62902),f287(x62901,x62903,x62904))) % 181.55/181.54 [6291]~P1(f324(f324(x62913,x62912),x62914))+P1(f324(f324(f326(x62911),x62912),f290(x62911,x62913,x62914))) % 181.55/181.54 [6354]~P51(x63544,x63541,x63542,x63543)+P1(f324(f324(x63541,x63542),x63543)) % 181.55/181.54 [6430]~P106(x64301)+E(f324(f324(f104(f871(x64301,a859)),f298(x64301,x64302,x64303)),f295(x64301,x64303,x64304)),f191(f871(x64301,a859))) % 181.55/181.54 [6431]~P106(x64311)+E(f324(f324(f104(f871(x64311,a859)),f297(x64311,x64312,x64313)),f298(x64311,x64313,x64314)),f191(f871(x64311,a859))) % 181.55/181.54 [6432]~P106(x64321)+E(f324(f324(f104(f871(x64321,a859)),f297(x64321,x64322,x64323)),f297(x64321,x64323,x64324)),f191(f871(x64321,a859))) % 181.55/181.54 [6433]~P106(x64331)+E(f324(f324(f104(f871(x64331,a859)),f295(x64331,x64332,x64333)),f298(x64331,x64333,x64334)),f191(f871(x64331,a859))) % 181.55/181.54 [6434]~P106(x64341)+E(f324(f324(f104(f871(x64341,a859)),f295(x64341,x64342,x64343)),f297(x64341,x64343,x64344)),f191(f871(x64341,a859))) % 181.55/181.54 [6471]P1(f324(f324(x64711,x64712),f535(x64712,x64711)))+~P1(f324(f253(x64713,x64714,x64711),x64712)) % 181.55/181.54 [6475]~P51(x64751,x64752,x64753,x64754)+~P1(f324(f324(x64752,x64754),x64753)) % 181.55/181.54 [6520]~E(f324(x65201,x65202),f203(x65203))+~P1(f324(f324(f326(x65204),x65202),f179(x65204,x65203,x65201))) % 181.55/181.54 [6549]~P105(x65492)+E(f324(f167(x65491),f144(x65491,x65492,x65493,x65494)),f324(f167(x65491),x65494)) % 181.55/181.54 [6600]~P141(x66001)+E(f193(x66001,x66002,f324(a115,x66003),x66004),f193(x66001,x66002,x66003,f324(x66002,x66004))) % 181.55/181.54 [6660]~P1(f324(f324(f326(x66604),x66603),f285(x66604,x66601,x66602)))+P1(f324(f324(x66601,x66602),x66603)) % 181.55/181.54 [6661]~P1(f324(f324(f326(x66614),x66613),f286(x66614,x66611,x66612)))+P1(f324(f324(x66611,x66612),x66613)) % 181.55/181.54 [6662]~P1(f324(f324(f326(x66624),x66622),f287(x66624,x66621,x66623)))+P1(f324(f324(x66621,x66622),x66623)) % 181.55/181.54 [6663]~P1(f324(f324(f326(x66634),x66632),f290(x66634,x66631,x66633)))+P1(f324(f324(x66631,x66632),x66633)) % 181.55/181.54 [6740]E(f324(f37(f872(x67401,x67402)),f311(x67401,x67402,x67403,x67404)),f2(a865))+P1(f324(f61(x67402),x67404)) % 181.55/181.54 [6741]E(f324(f37(f872(x67411,x67412)),f311(x67411,x67412,x67413,x67414)),f2(a865))+P1(f324(f61(x67411),x67413)) % 181.55/181.54 [6940]~P17(x69404,x69401,x69402)+E(f324(f73(x69401,x69401,x69401,f324(x69402,x69403)),f324(x69402,x69403)),f324(x69402,x69403)) % 181.55/181.54 [7809]~E(x78092,x78093)+P1(f324(f324(f326(f870(x78091,x78091)),f324(f324(f259(x78091,x78091),x78092),x78093)),f300(x78091,x78094))) % 181.55/181.54 [7838]~P27(x78381,x78382,x78383,f247(f871(x78381,a859)))+E(f324(f78(x78381,x78382,f247(f871(x78381,a859)),x78383),f324(x78383,x78384)),x78384) % 181.55/181.54 [7839]~P27(x78391,x78392,x78393,f247(f871(x78391,a859)))+E(f324(f94(x78391,x78392,f247(f871(x78391,a859)),x78393),f324(x78393,x78394)),x78394) % 181.55/181.54 [7930]~P1(f324(f324(f326(f866(x79301)),f324(f324(f145(x79301),x79304),x79302)),f155(x79301,x79303)))+P1(f324(f324(f326(f866(x79301)),x79302),f155(x79301,x79303))) % 181.55/181.54 [7931]~P1(f324(f324(f326(f866(x79311)),f324(f324(f124(x79311),x79314),x79312)),f155(x79311,x79313)))+P1(f324(f324(f326(f866(x79311)),x79312),f155(x79311,x79313))) % 181.55/181.54 [7932]~P1(f324(f324(f326(f866(x79321)),f324(f324(f124(x79321),x79322),x79324)),f155(x79321,x79323)))+P1(f324(f324(f326(f866(x79321)),x79322),f155(x79321,x79323))) % 181.55/181.54 [7943]~P105(x79431)+P16(x79431,f324(f324(f148(x79432,x79431),x79433),f144(x79432,x79431,x79433,x79434))) % 181.55/181.54 [8042]P27(x80424,x80423,x80421,x80422)+E(f324(x80421,f388(x80422,x80421,x80423,x80424)),f324(x80421,f397(x80422,x80421,x80423,x80424))) % 181.55/181.54 [8054]E(f180(x80541,x80542,x80543,x80544),f180(x80541,x80542,x80544,x80543))+~E(f324(f324(f104(f871(x80541,a859)),f179(x80541,x80542,x80543)),f179(x80541,x80542,x80544)),f191(f871(x80541,a859))) % 181.55/181.54 [8157]~P27(x81572,x81571,x81574,x81573)+P27(x81571,x81572,f78(x81572,x81571,x81573,x81574),f324(f303(x81572,x81571,x81574),x81573)) % 181.55/181.54 [8299]P39(f870(x82992,x82994),f276(x82992,x82994,x82991,x82993))+P1(f324(x82991,f521(x82992,x82993,x82994,x82991))) % 181.55/181.54 [8410]E(x84101,x84102)+~P1(f324(f324(f326(f870(x84103,x84103)),f324(f324(f259(x84103,x84103),x84101),x84102)),f256(x84103,x84104))) % 181.55/181.54 [8472]~P1(f324(f61(f872(x84723,x84721)),f311(x84723,x84721,x84724,x84722)))+P1(f324(f61(x84721),x84722)) % 181.55/181.54 [8473]~P1(f324(f61(f872(x84731,x84733)),f311(x84731,x84733,x84732,x84734)))+P1(f324(f61(x84731),x84732)) % 181.55/181.54 [8482]~P27(x84821,x84822,x84823,x84824)+P28(x84821,x84822,x84823,x84824,f324(f303(x84821,x84822,x84823),x84824)) % 181.55/181.54 [8573]~P28(x85732,x85733,x85734,x85731,f191(f871(x85733,a859)))+E(x85731,f191(f871(x85732,a859))) % 181.55/181.54 [8574]~P28(x85743,x85742,x85744,f191(f871(x85743,a859)),x85741)+E(x85741,f191(f871(x85742,a859))) % 181.55/181.54 [8667]P39(f870(x86671,x86672),f276(x86671,x86672,x86673,x86674))+~P39(x86672,f324(x86674,f521(x86671,x86674,x86672,x86673))) % 181.55/181.54 [9229]E(f324(f324(f153(x92291,x92292),f689(x92293,x92294,x92292,x92291)),f690(x92293,x92294,x92292,x92291)),x92294)+~P1(f324(f324(f326(f870(f866(x92291),f866(x92291))),f324(f324(f259(f866(x92291),f866(x92291)),x92292),x92294)),f151(x92291,x92293))) % 181.55/181.54 [9234]~P1(f324(f324(f326(f870(f866(x92341),f866(x92341))),f324(f324(f259(f866(x92341),f866(x92341)),x92342),x92343)),f139(x92341,x92344)))+P1(f324(f324(f326(f870(f866(x92341),f866(x92341))),f324(f324(f259(f866(x92341),f866(x92341)),x92342),x92343)),f141(x92341,x92344))) % 181.55/181.54 [9341]P1(f324(f61(x93411),x93412))+~P1(f324(f324(f326(f870(f871(x93411,a859),f871(x93411,a859))),f324(f324(f259(f871(x93411,a859),f871(x93411,a859)),x93413),x93412)),f315(x93411,x93414))) % 181.55/181.54 [9342]P1(f324(f61(x93421),x93422))+~P1(f324(f324(f326(f870(f871(x93421,a859),f871(x93421,a859))),f324(f324(f259(f871(x93421,a859),f871(x93421,a859)),x93422),x93423)),f315(x93421,x93424))) % 181.55/181.54 [9345]~E(x93451,f191(f871(x93452,a859)))+~P1(f324(f324(f326(f870(f871(x93452,a859),f871(x93452,a859))),f324(f324(f259(f871(x93452,a859),f871(x93452,a859)),x93453),x93451)),f315(x93452,x93454))) % 181.55/181.54 [9991]P14(x99911,x99912,x99913,x99914)+~P1(f324(f324(f263(x99911,x99911,a859),f324(f324(f7(x99911,f871(x99911,x99912),f871(x99911,a859)),f324(f324(f8(f871(x99912,a859),f871(f871(x99911,x99912),f871(x99911,a859)),x99911),f8(x99912,a859,x99911)),f324(f324(f8(x99912,f871(x99912,a859),x99911),a321),x99914))),x99914)),f542(x99914,x99913,x99912,x99911))) % 181.55/181.54 [4938]~E(x49384,f116(x49381))+E(f324(f324(f148(x49381,x49382),x49383),x49384),f116(x49382)) % 181.55/181.54 [4939]~E(x49394,f203(x49391))+E(f324(f324(f204(x49391,x49392),x49393),x49394),f203(x49392)) % 181.55/181.54 [4940]~E(x49402,f116(x49401))+E(f324(f324(f153(x49401,x49402),x49403),x49404),f116(x49401)) % 181.55/181.54 [5163]E(x51631,f203(x51632))+~E(f324(f324(f204(x51632,x51633),x51634),x51631),f203(x51633)) % 181.55/181.54 [5164]E(x51641,f116(x51642))+~E(f324(f324(f148(x51642,x51643),x51644),x51641),f116(x51643)) % 181.55/181.54 [5165]E(x51651,f116(x51652))+~E(f324(f324(f153(x51652,x51651),x51653),x51654),f116(x51652)) % 181.55/181.54 [5194]E(x51941,x51942)+~E(f324(f324(f124(x51943),x51944),x51941),f324(f324(f124(x51943),x51944),x51942)) % 181.55/181.54 [5195]E(x51951,x51952)+~E(f324(f324(f124(x51953),x51951),x51954),f324(f324(f124(x51953),x51952),x51954)) % 181.55/181.54 [5346]P1(f324(x53463,x53462))+E(f164(x53461,x53462,f324(f130(x53461,x53463),x53464)),f324(f130(x53461,x53463),x53464)) % 181.55/181.54 [5349]~P1(f324(x53492,x53493))+P35(x53491,x53492,f324(f324(f145(x53491),x53493),x53494)) % 181.55/181.54 [5358]E(x53581,x53582)+~E(f133(a865,f324(f294(a865,x53581),x53583)),f324(f324(f145(a865),x53582),x53584)) % 181.55/181.54 [5406]~P29(x54062,x54063)+P29(x54061,f324(f324(f74(x54062,x54061),x54063),x54064)) % 181.55/181.54 [5407]~P39(x54072,x54073)+P39(x54071,f324(f324(f280(x54072,x54071),x54073),x54074)) % 181.55/181.54 [5531]~P35(x55311,x55312,x55314)+P35(x55311,x55312,f324(f324(f145(x55311),x55313),x55314)) % 181.55/181.54 [5532]~P35(x55321,x55322,x55324)+P35(x55321,x55322,f324(f324(f124(x55321),x55323),x55324)) % 181.55/181.54 [5533]~P35(x55331,x55332,x55333)+P35(x55331,x55332,f324(f324(f124(x55331),x55333),x55334)) % 181.55/181.54 [5618]~E(x56181,f116(x56182))+~E(f324(f324(f124(x56182),x56183),f324(f324(f145(x56182),x56184),f116(x56182))),x56181) % 181.55/181.54 [5643]~P33(x56433,x56431,f324(f324(f145(x56433),x56432),x56434))+P1(f324(x56431,x56432)) % 181.55/181.54 [5653]E(f138(x56531,x56532),x56533)+~E(f324(f324(f124(x56531),x56534),f324(f324(f145(x56531),x56533),f116(x56531))),x56532) % 181.55/181.54 [5654]E(f117(x56541,x56542),x56543)+~E(f324(f324(f124(x56541),x56543),f324(f324(f145(x56541),x56544),f116(x56541))),x56542) % 181.55/181.54 [5762]~E(f133(a865,f324(f294(a865,x57621),x57622)),f324(f324(f145(a865),x57623),x57624))+P1(f324(f324(f239(a865),x57621),x57622)) % 181.55/181.54 [5770]P33(x57701,x57702,x57703)+~P33(x57701,x57702,f324(f324(f145(x57701),x57704),x57703)) % 181.55/181.54 [5771]P33(x57711,x57712,x57713)+~P33(x57711,x57712,f324(f324(f124(x57711),x57714),x57713)) % 181.55/181.54 [5772]P33(x57721,x57722,x57723)+~P33(x57721,x57722,f324(f324(f124(x57721),x57723),x57724)) % 181.55/181.54 [5954]E(x59541,f324(f324(f124(x59542),f324(f163(x59542),x59543)),f324(f324(f145(x59542),x59544),f116(x59542))))+~E(f324(f163(x59542),x59541),f324(f324(f145(x59542),x59544),x59543)) % 181.55/181.54 [6124]~P106(x61241)+E(f324(f324(f104(f871(x61241,a859)),f324(f294(x61241,x61242),x61243)),f324(f294(x61241,x61243),x61244)),f191(f871(x61241,a859))) % 181.55/181.54 [6160]~P72(x61601)+E(f324(f160(x61601),f324(f324(f148(a1,x61601),x61602),f174(x61603,x61604))),f324(f324(f6(a1,x61601),x61602),f324(f167(a1),f174(x61603,x61604)))) % 181.55/181.54 [6161]~P72(x61611)+E(f324(f324(f6(a1,x61611),x61612),f324(f167(a1),f174(x61613,x61614))),f324(f160(x61611),f324(f324(f148(a1,x61611),x61612),f174(x61613,x61614)))) % 181.55/181.54 [6301]~E(x63012,f324(f324(f124(x63011),f324(f163(x63011),x63014)),f324(f324(f145(x63011),x63013),f116(x63011))))+E(f324(f163(x63011),x63012),f324(f324(f145(x63011),x63013),x63014)) % 181.55/181.54 [6316]~P21(x63162,x63163,x63164,x63161)+E(f324(x63161,f191(f871(x63162,a859))),f34(x63163)) % 181.55/181.54 [6343]~P106(x63431)+E(f324(f324(f104(f871(x63431,a859)),f298(x63431,x63432,x63433)),f324(f294(x63431,x63433),x63434)),f191(f871(x63431,a859))) % 181.55/181.54 [6550]E(x65501,f191(f871(x65502,a859)))+~E(f311(x65503,x65502,x65504,x65501),f191(f871(f872(x65503,x65502),a859))) % 181.55/181.54 [6551]E(x65511,f191(f871(x65512,a859)))+~E(f311(x65512,x65513,x65511,x65514),f191(f871(f872(x65512,x65513),a859))) % 181.55/181.54 [6619]~P105(x66192)+E(f324(f192(f866(x66191)),f144(x66191,x66192,x66193,x66194)),f324(f192(f866(x66191)),x66194)) % 181.55/181.54 [6631]~P1(f324(f254(x66313,x66314,x66311),x66312))+P1(f324(f324(x66311,f518(x66312,x66311)),x66312)) % 181.55/181.54 [6671]~P1(f324(f61(x66712),x66714))+P1(f324(f61(x66711),f324(f303(x66712,x66711,x66713),x66714))) % 181.55/181.54 [6901]~P27(x69012,x69011,x69013,x69014)+E(f324(f37(x69011),f324(f303(x69012,x69011,x69013),x69014)),f324(f37(x69012),x69014)) % 181.55/181.54 [6920]E(f324(f303(x69201,x69202,x69203),f324(f304(x69201,x69202,x69203),x69204)),x69204)+~E(f324(f303(x69201,x69202,x69203),f247(f871(x69201,a859))),f247(f871(x69202,a859))) % 181.55/181.54 [7324]~P27(x73241,x73242,x73243,f247(f871(x73241,a859)))+E(f324(f304(x73241,x73242,x73243),f324(f303(x73241,x73242,x73243),x73244)),x73244) % 181.55/181.54 [7653]P1(f324(x76531,x76532))+~P1(f324(f324(f326(x76533),x76532),f324(f167(x76533),f172(x76533,x76531,x76534)))) % 181.55/181.54 [7754]~P1(f324(f324(f326(f866(x77541)),f324(f324(f145(x77541),x77542),x77544)),f155(x77541,x77543)))+P1(f324(f324(f326(x77541),x77542),x77543)) % 181.55/181.54 [7888]~P1(f324(f324(f326(x78881),x78882),f324(f167(x78881),f171(x78881,x78883,x78884))))+P1(f324(f324(f326(x78881),x78882),f324(f167(x78881),x78883))) % 181.55/181.54 [7889]~P1(f324(f324(f326(x78891),x78892),f324(f167(x78891),f164(x78891,x78894,x78893))))+P1(f324(f324(f326(x78891),x78892),f324(f167(x78891),x78893))) % 181.55/181.54 [7890]~P1(f324(f324(f326(x78901),x78902),f324(f167(x78901),f172(x78901,x78904,x78903))))+P1(f324(f324(f326(x78901),x78902),f324(f167(x78901),x78903))) % 181.55/181.54 [7900]E(f324(f192(f866(x79001)),x79002),x79003)+~P1(f324(f324(f326(f866(x79001)),x79002),f324(f167(f866(x79001)),f54(x79001,x79003,x79004)))) % 181.55/181.54 [7993]P1(f324(x79933,x79932))+E(f324(f130(x79931,f324(f324(f8(a859,a859,x79931),a319),f324(a321,x79932))),f324(f130(x79931,x79933),x79934)),f324(f130(x79931,x79933),x79934)) % 181.55/181.54 [8105]E(f324(f324(f159(x81051),f172(x81051,x81052,x81053)),x81054),f324(f324(f159(x81051),x81053),x81054))+~P1(f324(f324(f239(a865),x81054),f324(f192(f866(x81051)),f172(x81051,x81052,x81053)))) % 181.55/181.54 [8192]~P72(x81921)+E(f324(f324(f6(a865,x81921),f324(f324(f8(a865,x81921,a865),x81922),a115)),f324(f294(a865,x81923),x81924)),f324(f324(f6(a865,x81921),x81922),f324(f294(a865,f324(a115,x81923)),f324(a115,x81924)))) % 181.55/181.54 [8203]~P72(x82031)+E(f324(f324(f6(a865,x82031),f324(f324(f8(a865,x82031,a865),x82032),a115)),f295(a865,x82033,x82034)),f324(f324(f6(a865,x82031),x82032),f295(a865,f324(a115,x82033),f324(a115,x82034)))) % 181.55/181.54 [8334]~P27(x83341,x83343,x83344,f247(f871(x83341,a859)))+P27(x83341,f871(x83342,x83343),f324(f324(f8(x83343,f871(x83342,x83343),x83341),f16(x83343,x83342)),x83344),f247(f871(x83341,a859))) % 181.55/181.54 [8415]~P27(x84152,x84151,x84154,x84153)+E(f324(f303(x84151,x84152,f78(x84152,x84151,x84153,x84154)),f324(f303(x84152,x84151,x84154),x84153)),x84153) % 181.55/181.54 [8474]~P1(f324(f324(f326(f870(x84741,x84741)),f324(f324(f259(x84741,x84741),x84742),x84744)),f256(x84741,x84743)))+P1(f324(f324(f326(x84741),x84742),x84743)) % 181.55/181.54 [8568]E(f324(f324(f324(f72(x85681,f869(x85682)),f324(f16(f869(x85682),x85681),f203(x85682))),x85683),f324(f233(x85682),f815(x85683,x85684,x85682,x85681))),x85684)+~E(f179(x85681,x85682,x85684),f324(f324(f302(x85681),x85683),f191(f871(x85681,a859)))) % 181.55/181.54 [8598]~P27(x85982,x85981,x85983,f247(f871(x85982,a859)))+E(f324(f303(x85981,x85982,f94(x85982,x85981,f247(f871(x85982,a859)),x85983)),f324(f303(x85982,x85981,x85983),x85984)),x85984) % 181.55/181.54 [8673]~P28(x86731,x86732,x86733,x86734,f247(f871(x86732,a859)))+E(f324(f303(x86731,x86732,x86733),f247(f871(x86731,a859))),f247(f871(x86732,a859))) % 181.55/181.54 [8706]~E(f324(f324(f6(x87061,a865),x87064),x87063),f324(a115,x87062))+P1(f324(f324(f326(x87061),f561(x87062,x87063,x87064,x87061)),x87063)) % 181.55/181.54 [8728]~E(f324(f324(f6(x87284,a865),x87281),x87283),f324(a115,x87282))+P1(f324(f324(f239(a865),f2(a865)),f324(x87281,f561(x87282,x87283,x87281,x87284)))) % 181.55/181.54 [8739]~P1(f324(f61(x87392),x87394))+P1(f324(f324(f238(a865),f324(f37(x87391),f324(f303(x87392,x87391,x87393),x87394))),f324(f37(x87392),x87394))) % 181.55/181.54 [8740]E(f324(f324(f259(x87401,x87402),f653(x87403,x87404,x87402,x87401)),f654(x87403,x87404,x87402,x87401)),x87404)+~P1(f324(f324(f326(f870(x87401,x87402)),x87404),f324(f279(x87402,x87401),x87403))) % 181.55/181.54 [8748]P27(x87481,x87482,x87483,x87484)+P1(f324(f324(f326(x87481),f388(x87484,x87483,x87482,x87481)),x87484)) % 181.55/181.54 [8749]P27(x87491,x87492,x87493,x87494)+P1(f324(f324(f326(x87491),f397(x87494,x87493,x87492,x87491)),x87494)) % 181.55/181.54 [8812]P14(x88121,x88122,x88123,x88124)+P1(f324(f324(f326(f870(x88121,x88121)),f542(x88124,x88123,x88122,x88121)),x88123)) % 181.55/181.54 [8872]P1(f324(x88721,x88722))+~P1(f324(x88721,f324(f324(f259(x88723,x88724),f403(x88724,x88723,x88721)),f404(x88724,x88723,x88721)))) % 181.55/181.54 [8886]E(f324(f192(f866(x88861)),x88862),f324(f192(f866(x88861)),x88863))+~P1(f324(f324(f326(f870(f866(x88861),f866(x88861))),f324(f324(f259(f866(x88861),f866(x88861)),x88862),x88863)),f139(x88861,x88864))) % 181.55/181.54 [8887]E(f324(f192(f866(x88871)),x88872),f324(f192(f866(x88871)),x88873))+~P1(f324(f324(f326(f870(f866(x88871),f866(x88871))),f324(f324(f259(f866(x88871),f866(x88871)),x88872),x88873)),f151(x88871,x88874))) % 181.55/181.54 [8890]E(f324(f192(f866(x88901)),x88902),f324(f192(f866(x88901)),x88903))+~P1(f324(f324(f326(f870(f866(x88901),f866(x88901))),f324(f324(f259(f866(x88901),f866(x88901)),x88902),x88903)),f152(x88901,x88904))) % 181.55/181.54 [8960]P1(f324(f324(f238(a865),f149(x89601,x89602,x89603)),f149(x89601,x89604,x89603)))+P1(f324(f324(f326(x89601),f713(x89604,x89602,x89603,x89601)),f324(f167(x89601),x89603))) % 181.55/181.54 [8963]E(f324(f192(f866(x89631)),x89632),f324(f192(f866(x89631)),x89633))+~P1(f324(f324(f326(f870(f866(x89631),f866(x89631))),f324(f324(f259(f866(x89631),f866(x89631)),x89632),x89633)),f300(f866(x89631),f151(x89631,x89634)))) % 181.55/181.54 [9201]~P27(x92011,x92012,x92013,x92014)+~P1(f324(f324(f239(a865),f324(f37(x92012),f324(f303(x92011,x92012,x92013),x92014))),f324(f37(x92011),x92014))) % 181.55/181.54 [9245]~P1(f324(f324(f326(f870(f866(x92451),f866(x92451))),f324(f324(f259(f866(x92451),f866(x92451)),x92452),x92453)),f151(x92451,x92454)))+P1(f324(f324(f326(f870(f866(x92451),f866(x92451))),f324(f324(f259(f866(x92451),f866(x92451)),x92452),x92453)),f152(x92451,f300(x92451,x92454)))) % 181.55/181.54 [9249]~P1(f324(f324(f326(f870(f866(x92491),f866(x92491))),f324(f324(f259(f866(x92491),f866(x92491)),x92492),x92493)),f152(x92491,x92494)))+P1(f324(f324(f326(f870(f866(x92491),f866(x92491))),f324(f324(f259(f866(x92491),f866(x92491)),x92492),x92493)),f300(f866(x92491),f151(x92491,x92494)))) % 181.55/181.54 [9266]P1(f324(f324(f326(f870(x92661,x92661)),f324(f324(f259(x92661,x92661),x92662),x92663)),f300(x92661,x92664)))+~P1(f324(f324(f326(f870(x92661,x92661)),f324(f324(f259(x92661,x92661),x92662),x92663)),f324(f324(f281(x92661,x92661,x92661),x92664),f300(x92661,x92664)))) % 181.55/181.54 [9455]E(f324(f324(f124(x94551),f697(x94552,x94553,x94554,x94551)),f324(f324(f145(x94551),f698(x94552,x94553,x94554,x94551)),f701(x94552,x94553,x94554,x94551))),x94554)+~P1(f324(f324(f326(f870(f866(x94551),f866(x94551))),f324(f324(f259(f866(x94551),f866(x94551)),x94554),x94553)),f151(x94551,x94552))) % 181.55/181.54 [9456]E(f324(f324(f124(x94561),f697(x94562,x94563,x94564,x94561)),f324(f324(f145(x94561),f700(x94562,x94563,x94564,x94561)),f701(x94562,x94563,x94564,x94561))),x94563)+~P1(f324(f324(f326(f870(f866(x94561),f866(x94561))),f324(f324(f259(f866(x94561),f866(x94561)),x94564),x94563)),f151(x94561,x94562))) % 181.55/181.54 [9536]P1(f324(f324(f326(f870(x95361,x95361)),f324(f324(f259(x95361,x95361),x95362),f614(x95363,x95364,x95362,x95361))),f300(x95361,x95363)))+~P1(f324(f324(f326(f870(x95361,x95361)),f324(f324(f259(x95361,x95361),x95362),x95364)),f324(f324(f281(x95361,x95361,x95361),x95363),f300(x95361,x95363)))) % 181.55/181.54 [9607]P1(f324(f324(f238(a865),f149(x96071,x96072,x96073)),f149(x96071,x96074,x96073)))+~P1(f324(f324(f239(a865),f324(x96072,f713(x96074,x96072,x96073,x96071))),f324(x96074,f713(x96074,x96072,x96073,x96071)))) % 181.55/181.54 [9677]P1(f324(f324(f326(f870(x96771,x96771)),f324(f324(f259(x96771,x96771),f613(x96772,x96773,x96774,x96771)),x96773)),f300(x96771,x96772)))+~P1(f324(f324(f326(f870(x96771,x96771)),f324(f324(f259(x96771,x96771),x96774),x96773)),f324(f324(f281(x96771,x96771,x96771),x96772),f300(x96771,x96772)))) % 181.55/181.54 [5178]~E(x51782,x51783)+E(f164(x51781,x51782,f324(f324(f145(x51781),x51783),x51784)),x51784) % 181.55/181.54 [5301]P1(f324(x53012,x53013))+E(f172(x53011,x53012,f324(f324(f145(x53011),x53013),x53014)),f116(x53011)) % 181.55/181.54 [5370]~P80(x53702)+E(f324(f324(f80(f871(x53701,x53702)),x53703),x53704),f324(f80(x53702),f324(x53703,x53704))) % 181.55/181.54 [5382]~E(x53822,f2(a865))+E(f324(f324(f132(x53821),x53822),f324(f324(f145(x53821),x53823),x53824)),f324(f324(f145(x53821),x53823),x53824)) % 181.55/181.54 [5383]P1(f324(x53832,x53833))+E(f324(f130(x53831,x53832),f324(f324(f145(x53831),x53833),x53834)),f324(f130(x53831,x53832),x53834)) % 181.55/181.54 [5514]~E(x55142,x55144)+P1(f324(f324(f324(f302(x55141),x55142),x55143),x55144)) % 181.55/181.54 [5522]E(x55221,f116(x55222))+E(f138(x55223,f324(f324(f148(x55222,x55223),x55224),x55221)),f324(x55224,f138(x55222,x55221))) % 181.55/181.54 [5536]~E(x55361,f63(x55362,x55364))+E(f324(x55361,f324(f324(f302(x55362),x55363),f191(f871(x55362,a859)))),x55363) % 181.55/181.54 [5570]E(x55701,f116(x55702))+E(f324(f135(x55703),f324(f324(f148(x55702,x55703),x55704),x55701)),f324(x55704,f324(f135(x55702),x55701))) % 181.55/181.54 [5673]~P1(f324(x56733,x56734))+P1(f324(f324(f324(f302(x56731),x56732),x56733),x56734)) % 181.55/181.54 [5787]~P20(x57872,x57874,x57871)+E(f324(x57871,f324(f324(f302(x57872),x57873),f191(f871(x57872,a859)))),x57873) % 181.55/181.54 [5811]~E(x58112,x58113)+P1(f324(f324(f326(x58111),x58112),f324(f324(f302(x58111),x58113),x58114))) % 181.55/181.54 [5815]~P94(x58151)+E(f324(f324(f104(x58151),x58152),f324(f324(f104(x58151),x58153),x58154)),f324(f324(f104(x58151),x58153),f324(f324(f104(x58151),x58152),x58154))) % 181.55/181.54 [5817]~P99(x58171)+E(f324(f324(f104(x58171),x58172),f324(f324(f104(x58171),x58173),x58174)),f324(f324(f104(x58171),x58173),f324(f324(f104(x58171),x58172),x58174))) % 181.55/181.54 [5818]~P94(x58181)+E(f324(f324(f113(x58181),x58182),f324(f324(f113(x58181),x58183),x58184)),f324(f324(f113(x58181),x58183),f324(f324(f113(x58181),x58182),x58184))) % 181.55/181.54 [5820]~P100(x58201)+E(f324(f324(f113(x58201),x58202),f324(f324(f113(x58201),x58203),x58204)),f324(f324(f113(x58201),x58203),f324(f324(f113(x58201),x58202),x58204))) % 181.55/181.54 [5821]~P112(x58211)+E(f324(f324(f82(x58211),x58212),f324(f324(f82(x58211),x58213),x58214)),f324(f324(f82(x58211),x58213),f324(f324(f82(x58211),x58212),x58214))) % 181.55/181.54 [5822]~P112(x58221)+E(f324(f324(f81(x58221),x58222),f324(f324(f81(x58221),x58223),x58224)),f324(f324(f81(x58221),x58223),f324(f324(f81(x58221),x58222),x58224))) % 181.55/181.54 [5824]~P105(x58241)+E(f324(f324(f189(x58241),x58242),f324(f324(f189(x58241),x58243),x58244)),f324(f324(f189(x58241),x58243),f324(f324(f189(x58241),x58242),x58244))) % 181.55/181.54 [5826]~P105(x58261)+E(f324(f324(f190(x58261),x58262),f324(f324(f190(x58261),x58263),x58264)),f324(f324(f190(x58261),x58263),f324(f324(f190(x58261),x58262),x58264))) % 181.55/181.54 [5831]E(x58311,x58312)+E(f164(x58313,x58311,f324(f324(f145(x58313),x58312),x58314)),f324(f324(f145(x58313),x58312),f164(x58313,x58311,x58314))) % 181.55/181.54 [5844]~P1(f324(x58442,x58443))+E(f324(f130(x58441,x58442),f324(f324(f145(x58441),x58443),x58444)),f324(f324(f145(x58441),x58443),f324(f130(x58441,x58442),x58444))) % 181.55/181.54 [5974]~P1(f324(x59742,x59743))+E(f172(x59741,x59742,f324(f324(f145(x59741),x59743),x59744)),f324(f324(f145(x59741),x59743),f172(x59741,x59742,x59744))) % 181.55/181.54 [6037]E(x60371,f191(f871(x60372,a859)))+E(f324(f324(f41(x60372,f871(x60373,a859)),x60371),f324(f16(f871(x60373,a859),x60372),x60374)),x60374) % 181.55/181.54 [6038]E(x60381,f191(f871(x60382,a859)))+E(f324(f324(f42(x60382,f871(x60383,a859)),x60381),f324(f16(f871(x60383,a859),x60382),x60384)),x60384) % 181.55/181.54 [6047]~E(x60474,f191(f871(x60472,a859)))+E(f324(f324(f261(x60471,x60472),x60473),f324(f16(f871(x60472,a859),x60471),x60474)),f191(f871(f870(x60471,x60472),a859))) % 181.55/181.54 [6048]~E(x60483,f191(f871(x60481,a859)))+E(f324(f324(f261(x60481,x60482),x60483),f324(f16(f871(x60482,a859),x60481),x60484)),f191(f871(f870(x60481,x60482),a859))) % 181.55/181.54 [6094]E(x60941,f2(a865))+E(f324(f324(f132(x60942),x60941),f324(f324(f145(x60942),x60943),x60944)),f324(f324(f132(x60942),f324(f324(f22(a865),x60941),f79(a865))),x60944)) % 181.55/181.54 [6118]E(x61181,f191(f871(x61182,a859)))+E(f324(f303(x61182,x61183,f324(f16(x61183,x61182),x61184)),x61181),f324(f324(f302(x61183),x61184),f191(f871(x61183,a859)))) % 181.55/181.54 [6121]E(f324(f304(x61211,x61212,f324(f16(x61212,x61211),x61213)),x61214),f191(f871(x61211,a859)))+P1(f324(f324(f326(x61212),x61213),x61214)) % 181.55/181.54 [6186]~E(x61863,f191(f871(x61861,a859)))+E(f324(f324(f41(x61861,f871(x61862,a859)),x61863),f324(f16(f871(x61862,a859),x61861),x61864)),f191(f871(x61862,a859))) % 181.55/181.54 [6187]~E(x61873,f191(f871(x61871,a859)))+E(f324(f324(f42(x61871,f871(x61872,a859)),x61873),f324(f16(f871(x61872,a859),x61871),x61874)),f247(f871(x61872,a859))) % 181.55/181.54 [6189]~P59(x61891)+E(f44(x61891,f324(f324(f82(x61891),x61892),x61893),f324(f324(f82(x61891),x61892),x61894)),f324(f324(f82(x61891),x61892),f44(x61891,x61893,x61894))) % 181.55/181.54 [6353]E(f324(f304(x63531,x63532,f324(f16(x63532,x63531),x63533)),x63534),f247(f871(x63531,a859)))+~P1(f324(f324(f326(x63532),x63533),x63534)) % 181.55/181.54 [6377]~P1(f324(f324(f326(x63771),x63772),x63774))+P1(f324(f324(f326(x63771),x63772),f324(f324(f302(x63771),x63773),x63774))) % 181.55/181.54 [6382]P1(f324(x63821,x63822))+~P1(f324(f154(x63823,x63821),f324(f324(f145(x63823),x63822),x63824))) % 181.55/181.54 [6391]~E(x63913,f324(f324(f22(a865),f324(f192(f866(x63911)),x63912)),f79(a865)))+E(f117(x63911,f324(f324(f153(x63911,x63912),x63913),x63914)),f117(x63911,x63912)) % 181.55/181.54 [6409]~P105(x64091)+E(f324(f324(f104(f871(x64091,a859)),f324(f293(x64091),x64092)),f295(x64091,x64093,x64094)),f295(x64091,x64093,f324(f324(f189(x64091),x64092),x64094))) % 181.55/181.54 [6410]~P105(x64101)+E(f324(f324(f104(f871(x64101,a859)),f324(f246(x64101),x64102)),f295(x64101,x64103,x64104)),f295(x64101,f324(f324(f190(x64101),x64102),x64103),x64104)) % 181.55/181.54 [6425]E(f324(f324(f104(f871(x64251,a859)),x64252),f324(f324(f302(x64251),x64253),x64254)),f324(f324(f104(f871(x64251,a859)),x64252),x64254))+P1(f324(f324(f326(x64251),x64253),x64252)) % 181.55/181.54 [6437]E(f164(x64371,x64372,f324(f324(f124(x64371),x64373),x64374)),f324(f324(f124(x64371),x64373),f164(x64371,x64372,x64374)))+P1(f324(f324(f326(x64371),x64372),f324(f167(x64371),x64373))) % 181.55/181.54 [6441]~P77(x64411)+E(f324(f324(f82(x64411),f324(f324(f249(x64411),x64412),x64413)),f324(f324(f249(x64411),x64412),x64414)),f324(f324(f249(x64411),x64412),f324(f324(f81(a865),x64413),x64414))) % 181.55/181.54 [6442]~P112(x64421)+E(f324(f324(f82(x64421),f324(f324(f249(x64421),x64422),x64423)),f324(f324(f249(x64421),x64422),x64424)),f324(f324(f249(x64421),x64422),f324(f324(f81(a865),x64423),x64424))) % 181.55/181.54 [6479]~P98(x64791)+E(f324(f324(f113(x64791),f324(f324(f104(x64791),x64792),x64793)),f324(f324(f104(x64791),x64792),x64794)),f324(f324(f104(x64791),x64792),f324(f324(f113(x64791),x64793),x64794))) % 181.55/181.54 [6480]~P98(x64801)+E(f324(f324(f104(x64801),f324(f324(f113(x64801),x64802),x64803)),f324(f324(f113(x64801),x64802),x64804)),f324(f324(f113(x64801),x64802),f324(f324(f104(x64801),x64803),x64804))) % 181.55/181.54 [6481]~P112(x64811)+E(f324(f324(f81(x64811),f324(f324(f82(x64811),x64812),x64813)),f324(f324(f82(x64811),x64812),x64814)),f324(f324(f82(x64811),x64812),f324(f324(f81(x64811),x64813),x64814))) % 181.55/181.54 [6482]~P105(x64821)+E(f324(f324(f190(x64821),f324(f324(f189(x64821),x64822),x64823)),f324(f324(f189(x64821),x64822),x64824)),f324(f324(f189(x64821),x64822),f324(f324(f190(x64821),x64823),x64824))) % 181.55/181.54 [6483]~P105(x64831)+E(f324(f324(f189(x64831),f324(f324(f190(x64831),x64832),x64833)),f324(f324(f190(x64831),x64832),x64834)),f324(f324(f190(x64831),x64832),f324(f324(f189(x64831),x64833),x64834))) % 181.55/181.54 [6514]~P59(x65141)+E(f44(x65141,f324(f324(f82(x65141),x65142),x65143),f324(f324(f82(x65141),x65144),x65143)),f324(f324(f82(x65141),f44(x65141,x65142,x65144)),x65143)) % 181.55/181.54 [6517]~E(f324(f192(f866(x65171)),x65173),f324(f192(f866(x65172)),x65174))+E(f324(f324(f148(f870(x65171,x65172),x65172),f262(x65171,x65172)),f324(f324(f177(x65171,x65172),x65173),x65174)),x65174) % 181.55/181.54 [6518]~E(f324(f192(f866(x65181)),x65183),f324(f192(f866(x65182)),x65184))+E(f324(f324(f148(f870(x65181,x65182),x65181),f258(x65181,x65182)),f324(f324(f177(x65181,x65182),x65183),x65184)),x65183) % 181.55/181.54 [6524]P1(f324(f154(x65241,x65242),x65243))+~P1(f324(f154(x65241,x65242),f324(f324(f145(x65241),x65244),x65243))) % 181.55/181.54 [6525]P1(f324(f154(x65251,x65252),x65253))+~P1(f324(f154(x65251,x65252),f324(f324(f124(x65251),x65254),x65253))) % 181.55/181.54 [6526]P1(f324(f154(x65261,x65262),x65263))+~P1(f324(f154(x65261,x65262),f324(f324(f124(x65261),x65263),x65264))) % 181.55/181.54 [6531]~P60(x65311)+E(f44(x65311,f324(f324(f22(x65311),x65312),f44(x65311,x65313,x65314)),x65314),f44(x65311,f324(f324(f22(x65311),x65312),x65313),x65314)) % 181.55/181.54 [6532]~P59(x65321)+E(f44(x65321,f324(f324(f82(x65321),x65322),f44(x65321,x65323,x65324)),x65324),f44(x65321,f324(f324(f82(x65321),x65322),x65323),x65324)) % 181.55/181.54 [6534]~P59(x65341)+E(f44(x65341,f324(f324(f81(x65341),x65342),f44(x65341,x65343,x65344)),x65344),f44(x65341,f324(f324(f81(x65341),x65342),x65343),x65344)) % 181.55/181.54 [6613]~P105(x66131)+E(f324(f324(f104(f871(x66131,a859)),f295(x66131,x66132,x66133)),f324(f293(x66131),x66134)),f295(x66131,x66132,f324(f324(f189(x66131),x66133),x66134))) % 181.55/181.54 [6614]~P105(x66141)+E(f324(f324(f104(f871(x66141,a859)),f295(x66141,x66142,x66143)),f324(f246(x66141),x66144)),f295(x66141,f324(f324(f190(x66141),x66142),x66144),x66143)) % 181.55/181.54 [6617]~E(f324(f192(f866(x66171)),x66173),f324(f192(f866(x66172)),x66174))+E(f324(f324(f177(x66171,x66172),f324(f163(x66171),x66173)),f324(f163(x66172),x66174)),f324(f163(f870(x66171,x66172)),f324(f324(f177(x66171,x66172),x66173),x66174))) % 181.55/181.54 [6627]E(x66271,f324(f324(f22(a865),f324(f192(f866(x66272)),x66273)),f79(a865)))+E(f117(x66272,f324(f324(f153(x66272,x66273),x66271),x66274)),f324(f324(f153(x66272,f117(x66272,x66273)),x66271),x66274)) % 181.55/181.54 [6642]~P1(f324(f131(x66422),x66424))+P1(f324(f131(f870(x66421,x66422)),f324(f324(f177(x66421,x66422),x66423),x66424))) % 181.55/181.54 [6643]~P1(f324(f131(x66431),x66433))+P1(f324(f131(f870(x66431,x66432)),f324(f324(f177(x66431,x66432),x66433),x66434))) % 181.55/181.54 [6904]E(f324(f324(f38(a865),x69041),x69042),x69043)+~P1(f324(f47(x69041,x69042),f324(f324(f259(a865,a865),x69043),x69044))) % 181.55/181.54 [6928]E(f44(a865,x69281,x69282),x69283)+~P1(f324(f47(x69281,x69282),f324(f324(f259(a865,a865),x69284),x69283))) % 181.55/181.54 [6931]P1(f324(f131(x69311),x69312))+~P1(f324(f131(x69313),f324(f324(f148(x69311,x69313),x69314),x69312))) % 181.55/181.54 [7014]E(f164(x70141,x70142,f324(f324(f124(x70141),x70143),x70144)),f324(f324(f124(x70141),f164(x70141,x70142,x70143)),x70144))+~P1(f324(f324(f326(x70141),x70142),f324(f167(x70141),x70143))) % 181.55/181.54 [7104]~P60(x71041)+E(f44(x71041,f324(f324(f22(x71041),f44(x71041,x71042,x71043)),x71044),x71043),f44(x71041,f324(f324(f22(x71041),x71042),x71044),x71043)) % 181.55/181.54 [7107]~P59(x71071)+E(f44(x71071,f324(f324(f82(x71071),f44(x71071,x71072,x71073)),x71074),x71073),f44(x71071,f324(f324(f82(x71071),x71072),x71074),x71073)) % 181.55/181.54 [7108]~P59(x71081)+E(f44(x71081,f324(f324(f81(x71081),f44(x71081,x71082,x71083)),x71084),x71083),f44(x71081,f324(f324(f81(x71081),x71082),x71084),x71083)) % 181.55/181.54 [7294]~E(x72941,f324(f324(f145(x72942),x72943),x72944))+~P1(f324(f324(f238(a865),f324(f192(f866(x72942)),x72941)),f324(f192(f866(x72942)),x72944))) % 181.55/181.54 [7370]~E(f324(f173(x73701,x73702),x73703),f324(f173(x73701,x73702),x73704))+E(f324(f303(f870(x73701,x73702),x73701,f258(x73701,x73702)),f324(f167(f870(x73701,x73702)),x73703)),f324(f303(f870(x73701,x73702),x73701,f258(x73701,x73702)),f324(f167(f870(x73701,x73702)),x73704))) % 181.55/181.54 [7503]P27(x75031,x75032,x75033,f324(f167(x75031),x75034))+~P1(f324(f131(x75032),f324(f324(f148(x75031,x75032),x75033),x75034))) % 181.55/181.54 [7577]~P1(f324(f324(f238(f871(x75771,a859)),x75772),x75774))+P1(f324(f324(f238(f871(x75771,a859)),x75772),f324(f324(f302(x75771),x75773),x75774))) % 181.55/181.54 [7610]~P60(x76101)+E(f44(x76101,f324(f324(f22(x76101),f44(x76101,x76102,x76103)),f44(x76101,x76104,x76103)),x76103),f44(x76101,f324(f324(f22(x76101),x76102),x76104),x76103)) % 181.55/181.54 [7611]~P59(x76111)+E(f44(x76111,f324(f324(f82(x76111),f44(x76111,x76112,x76113)),f44(x76111,x76114,x76113)),x76113),f44(x76111,f324(f324(f82(x76111),x76112),x76114),x76113)) % 181.55/181.54 [7612]~P59(x76121)+E(f44(x76121,f324(f324(f81(x76121),f44(x76121,x76122,x76123)),f44(x76121,x76124,x76123)),x76123),f44(x76121,f324(f324(f81(x76121),x76122),x76124),x76123)) % 181.55/181.54 [7712]~E(f324(x77124,f719(x77124,x77123,x77121,x77122)),f191(f871(x77122,a859)))+E(f324(f324(f41(x77121,f871(x77122,a859)),x77123),x77124),f191(f871(x77122,a859))) % 181.55/181.54 [7713]~E(f324(x77134,f623(x77134,x77133,x77131,x77132)),f247(f871(x77132,a859)))+E(f324(f324(f42(x77131,f871(x77132,a859)),x77133),x77134),f247(f871(x77132,a859))) % 181.55/181.54 [7714]~E(f324(x77144,f704(x77144,x77143,x77142,x77141)),f191(f871(x77142,a859)))+E(f324(f324(f41(x77141,f871(x77142,a859)),x77143),x77144),f191(f871(x77142,a859))) % 181.55/181.54 [7715]~E(f324(x77154,f624(x77154,x77153,x77152,x77151)),f247(f871(x77152,a859)))+E(f324(f324(f42(x77151,f871(x77152,a859)),x77153),x77154),f247(f871(x77152,a859))) % 181.55/181.54 [8106]P1(f324(x81061,x81062))+~P1(f324(f324(f326(x81063),x81062),f324(f324(f104(f871(x81063,a859)),x81064),f324(f244(x81063),x81061)))) % 181.55/181.54 [8145]~P1(f324(f324(f238(f871(x81451,a859)),x81453),x81454))+P1(f324(f324(f238(f871(x81451,a859)),f324(f324(f302(x81451),x81452),x81453)),f324(f324(f302(x81451),x81452),x81454))) % 181.55/181.54 [8156]E(f324(x81561,f482(x81561,x81562,x81563)),x81563)+~P1(f324(f324(f326(x81564),x81563),f324(f303(x81562,x81564,x81561),f247(f871(x81562,a859))))) % 181.55/181.54 [8327]P1(f324(x83272,x83273))+E(f324(f324(f132(x83271),f324(f192(f866(x83271)),f172(x83271,x83272,f324(f324(f145(x83271),x83273),x83274)))),f324(f324(f145(x83271),x83273),x83274)),f324(f324(f145(x83271),x83273),x83274)) % 181.55/181.54 [8429]~P1(f324(f324(f239(a865),f324(x84294,x84292)),f324(x84294,x84293)))+P1(f324(f324(f326(f870(x84291,x84291)),f324(f324(f259(x84291,x84291),x84292),x84293)),f324(f324(f280(a865,x84291),a243),x84294))) % 181.55/181.54 [8523]~P1(f324(x85232,f767(x85234,x85232,x85233,x85231)))+E(f172(x85231,x85232,f324(f324(f124(x85231),x85233),x85234)),f324(f324(f124(x85231),x85233),f172(x85231,x85232,x85234))) % 181.55/181.54 [8602]P27(f866(x86021),f866(x86022),f324(f148(x86021,x86022),x86023),x86024)+~P27(x86021,x86022,x86023,f39(f871(x86021,a859),f324(f303(f866(x86021),f871(x86021,a859),f167(x86021)),x86024))) % 181.55/181.54 [8677]~P1(f324(x86772,x86773))+E(f324(f324(f132(x86771),f324(f192(f866(x86771)),f172(x86771,x86772,f324(f324(f145(x86771),x86773),x86774)))),f324(f324(f145(x86771),x86773),x86774)),f324(f324(f132(x86771),f324(f192(f866(x86771)),f172(x86771,x86772,x86774))),x86774)) % 181.55/181.54 [8719]~E(x87192,x87193)+E(f324(f130(x87191,f324(f324(f8(a859,a859,x87191),a319),f324(a321,x87192))),f324(f324(f145(x87191),x87193),x87194)),f324(f130(x87191,f324(f324(f8(a859,a859,x87191),a319),f324(a321,x87192))),x87194)) % 181.55/181.54 [8729]E(f324(f324(f41(x87291,f871(x87292,a859)),x87293),x87294),f191(f871(x87292,a859)))+P1(f324(f324(f326(x87291),f719(x87294,x87293,x87291,x87292)),x87293)) % 181.55/181.54 [8730]E(f324(f324(f42(x87301,f871(x87302,a859)),x87303),x87304),f247(f871(x87302,a859)))+P1(f324(f324(f326(x87301),f623(x87304,x87303,x87301,x87302)),x87303)) % 181.55/181.54 [8731]E(f324(f324(f41(x87311,f871(x87312,a859)),x87313),x87314),f191(f871(x87312,a859)))+P1(f324(f324(f326(x87311),f704(x87314,x87313,x87312,x87311)),x87313)) % 181.55/181.54 [8732]E(f324(f324(f42(x87321,f871(x87322,a859)),x87323),x87324),f247(f871(x87322,a859)))+P1(f324(f324(f326(x87321),f624(x87324,x87323,x87322,x87321)),x87323)) % 181.55/181.54 [8770]P1(f324(f324(f239(a865),f324(x87701,x87702)),f324(x87701,x87703)))+~P1(f324(f324(f326(f870(x87704,x87704)),f324(f324(f259(x87704,x87704),x87702),x87703)),f324(f324(f280(a865,x87704),a243),x87701))) % 181.55/181.54 [8791]E(f172(x87911,x87912,f324(f324(f124(x87911),x87913),x87914)),f324(f324(f124(x87911),x87913),f172(x87911,x87912,x87914)))+P1(f324(f324(f326(x87911),f767(x87914,x87912,x87913,x87911)),f324(f167(x87911),x87913))) % 181.55/181.54 [8847]~P28(x88471,x88472,x88473,f247(f871(x88471,a859)),f247(f871(x88472,a859)))+E(f324(f303(x88471,x88472,x88473),f324(f80(f871(x88471,a859)),x88474)),f324(f80(f871(x88472,a859)),f324(f303(x88471,x88472,x88473),x88474))) % 181.55/181.54 [8949]P1(f324(f324(f326(x89491),f609(x89492,x89493,x89494,x89491)),x89493))+~P1(f324(f324(f326(f871(x89491,a859)),x89494),f324(f324(f60(x89491),x89493),x89492))) % 181.55/181.54 [8952]E(x89521,x89522)+~P1(f324(f324(f326(f870(x89523,x89523)),f324(f324(f259(x89523,x89523),x89521),x89522)),f324(f324(f184(f870(x89523,x89523),a859),f2(a865)),x89524))) % 181.55/181.54 [9036]E(f324(f278(x90361,x90361,x90362),f324(f324(f302(x90361),f609(x90362,x90363,x90364,x90361)),f191(f871(x90361,a859)))),x90364)+~P1(f324(f324(f326(f871(x90361,a859)),x90364),f324(f324(f60(x90361),x90363),x90362))) % 181.55/181.54 [9041]~P1(f324(f324(f326(f870(x90411,x90411)),f324(f324(f259(x90411,x90411),x90413),x90412)),f300(x90411,x90414)))+P1(f324(f324(f326(f870(x90411,x90411)),f324(f324(f259(x90411,x90411),x90412),x90413)),f300(x90411,f324(f279(x90411,x90411),x90414)))) % 181.55/181.54 [9053]~P59(x90531)+E(f324(f324(f81(x90531),f324(f324(f81(x90531),f324(f324(f82(x90531),x90532),f324(f324(f38(x90531),x90533),x90532))),f44(x90531,x90533,x90532))),x90534),f324(f324(f81(x90531),x90533),x90534)) % 181.55/181.54 [9063]~P1(f324(f324(f326(x90631),x90633),x90634))+P1(f324(f324(f326(f871(x90631,a859)),f324(f278(x90631,x90631,x90632),f324(f324(f302(x90631),x90633),f191(f871(x90631,a859))))),f324(f324(f60(x90631),x90634),x90632))) % 181.55/181.54 [9074]P1(f324(f324(f326(f870(x90741,x90741)),f324(f324(f259(x90741,x90741),x90742),x90743)),f300(x90741,x90744)))+~P1(f324(f324(f326(f870(x90741,x90741)),f324(f324(f259(x90741,x90741),x90743),x90742)),f300(x90741,f324(f279(x90741,x90741),x90744)))) % 181.55/181.54 [9164]E(f324(f324(f153(x91641,f324(f163(x91641),x91642)),f324(f324(f22(a865),f324(f324(f22(a865),f324(f192(f866(x91641)),x91642)),x91643)),f79(a865))),x91644),f324(f163(x91641),f324(f324(f153(x91641,x91642),x91643),x91644)))+~P1(f324(f324(f239(a865),x91643),f324(f192(f866(x91641)),x91642))) % 181.55/181.54 [9167]~P1(f324(x91672,f759(x91674,x91672,x91673,x91671)))+E(f324(f324(f132(x91671),f324(f192(f866(x91671)),f172(x91671,x91672,f324(f324(f124(x91671),x91673),x91674)))),f324(f324(f124(x91671),x91673),x91674)),f324(f324(f132(x91671),f324(f192(f866(x91671)),f172(x91671,x91672,x91674))),x91674)) % 181.55/181.54 [9209]~P27(x92092,x92091,x92093,f247(f871(x92092,a859)))+P1(f324(f324(f238(f871(x92091,a859)),f324(f303(x92092,x92091,x92093),f324(f80(f871(x92092,a859)),x92094))),f324(f80(f871(x92091,a859)),f324(f303(x92092,x92091,x92093),x92094)))) % 181.55/181.54 [9220]~P6(x92201)+E(f324(f136(x92201,x92202,f324(f7(x92202,x92201,x92201),f324(f324(f8(x92201,f871(x92201,x92201),x92202),f113(x92201)),x92203)),f191(x92201)),x92204),f324(f324(f41(x92202,x92201),f324(f167(x92202),x92204)),x92203)) % 181.55/181.54 [9221]~P6(x92211)+E(f324(f136(x92211,x92212,f324(f7(x92212,x92211,x92211),f324(f324(f8(x92211,f871(x92211,x92211),x92212),f104(x92211)),x92213)),f247(x92211)),x92214),f324(f324(f42(x92212,x92211),f324(f167(x92212),x92214)),x92213)) % 181.55/181.54 [9231]E(f324(f324(f132(x92311),f324(f192(f866(x92311)),f172(x92311,x92312,f324(f324(f124(x92311),x92313),x92314)))),f324(f324(f124(x92311),x92313),x92314)),f324(f324(f132(x92311),f324(f192(f866(x92311)),f172(x92311,x92312,x92314))),x92314))+P1(f324(f324(f326(x92311),f759(x92314,x92312,x92313,x92311)),f324(f167(x92311),x92313))) % 181.55/181.54 [9301]~P1(f324(f324(f326(f870(f866(x93014),f866(x93014))),f324(f324(f259(f866(x93014),f866(x93014)),x93013),x93012)),f151(x93014,x93011)))+P1(f324(f324(f239(a865),f689(x93011,x93012,x93013,x93014)),f324(f192(f866(x93014)),x93013))) % 181.55/181.54 [9302]~P59(x93021)+E(f324(f324(f81(x93021),f324(f324(f81(x93021),f324(f324(f82(x93021),f324(f324(f38(x93021),x93022),x93023)),x93023)),f44(x93021,x93022,x93023))),x93024),f324(f324(f81(x93021),x93022),x93024)) % 181.55/181.54 [9329]~P1(f324(f324(f326(f870(f866(x93291),f866(x93291))),f324(f324(f259(f866(x93291),f866(x93291)),x93292),x93293)),f324(f279(f866(x93291),f866(x93291)),f151(x93291,x93294))))+P1(f324(f324(f326(f870(f866(x93291),f866(x93291))),f324(f324(f259(f866(x93291),f866(x93291)),x93292),x93293)),f151(x93291,f324(f279(x93291,x93291),x93294)))) % 181.55/181.54 [9330]P1(f324(f324(f326(f870(f866(x93301),f866(x93301))),f324(f324(f259(f866(x93301),f866(x93301)),x93302),x93303)),f324(f279(f866(x93301),f866(x93301)),f151(x93301,x93304))))+~P1(f324(f324(f326(f870(f866(x93301),f866(x93301))),f324(f324(f259(f866(x93301),f866(x93301)),x93302),x93303)),f151(x93301,f324(f279(x93301,x93301),x93304)))) % 181.55/181.54 [9368]~P1(f324(f324(f326(x93681),x93683),f324(f257(x93681,x93682),x93684)))+P1(f324(f324(f326(f870(x93681,x93682)),f324(f324(f259(x93681,x93682),x93683),f532(x93684,x93682,x93683,x93681))),x93684)) % 181.55/181.54 [9369]~P1(f324(f324(f326(x93691),x93693),f324(f257(x93691,x93692),x93694)))+P1(f324(f324(f326(f870(x93691,x93692)),f324(f324(f259(x93691,x93692),x93693),f533(x93694,x93692,x93693,x93691))),x93694)) % 181.55/181.54 [9482]~P1(f324(f61(f869(x94821)),f324(f303(x94822,f869(x94821),x94823),f247(f871(x94822,a859)))))+P1(f324(f61(f869(x94821)),f324(f303(x94822,f869(x94821),f180(x94822,x94821,x94823,f324(f173(x94822,x94821),x94824))),f247(f871(x94822,a859))))) % 181.55/181.54 [9531]~P1(f324(f324(f326(f870(x95311,x95311)),f324(f324(f259(x95311,x95311),x95312),x95314)),f324(f324(f281(x95311,x95311,x95311),x95313),f300(x95311,x95313))))+P1(f324(f324(f326(f870(x95311,x95311)),f324(f324(f259(x95311,x95311),x95312),f613(x95313,x95314,x95312,x95311))),x95313)) % 181.55/181.54 [9704]~P1(f324(f324(f326(f870(x97042,x97041)),x97044),f324(f279(x97041,x97042),x97043)))+P1(f324(f324(f326(f870(x97041,x97042)),f324(f324(f259(x97041,x97042),f654(x97043,x97044,x97041,x97042)),f653(x97043,x97044,x97041,x97042))),x97043)) % 181.55/181.54 [9732]~P1(f324(f324(f326(f870(f866(x97321),f866(x97321))),f324(f324(f259(f866(x97321),f866(x97321)),x97324),x97323)),f151(x97321,x97322)))+P1(f324(f324(f326(f870(x97321,x97321)),f324(f324(f259(x97321,x97321),f698(x97322,x97323,x97324,x97321)),f700(x97322,x97323,x97324,x97321))),x97322)) % 181.55/181.54 [9826]~P1(f324(f324(f326(f870(f866(x98261),f866(x98261))),f324(f324(f259(f866(x98261),f866(x98261)),x98262),x98264)),f151(x98261,x98263)))+P1(f324(f324(f326(f870(x98261,x98261)),f324(f324(f259(x98261,x98261),f324(f324(f159(x98261),x98262),f689(x98263,x98264,x98262,x98261))),f690(x98263,x98264,x98262,x98261))),x98263)) % 181.55/181.54 [9847]~P1(f324(f61(x98472),x98474))+E(f324(f324(f324(f65(f871(x98471,a859),x98472,f113(f871(x98471,a859))),f324(f324(f7(x98472,f871(x98471,a859),f871(x98471,a859)),f324(f324(f8(x98471,f871(f871(x98471,a859),f871(x98471,a859)),x98472),f302(x98471)),x98473)),f191(f871(x98471,a859)))),f191(f871(x98471,a859))),x98474),f324(f303(x98472,x98471,x98473),x98474)) % 181.55/181.54 [9943]~P27(x99431,x99432,x99433,f247(f871(x99431,a859)))+P1(f324(f324(f238(f871(x99431,a859)),f324(f304(x99431,x99432,x99433),f324(f324(f302(x99432),x99434),f191(f871(x99432,a859))))),f324(f324(f302(x99431),f86(x99431,f324(f324(f7(x99431,x99432,a859),f324(f324(f8(x99432,f871(x99432,a859),x99431),a321),x99433)),x99434))),f191(f871(x99431,a859))))) % 181.55/181.54 [5579]~E(f324(f324(f124(x55791),x55792),x55794),x55793)+E(f324(f324(f170(x55791),f324(f192(f866(x55791)),x55792)),x55793),x55792) % 181.55/181.54 [5580]~E(f324(f324(f124(x55802),x55803),x55801),x55804)+E(x55801,f324(f324(f132(x55802),f324(f192(f866(x55802)),x55803)),x55804)) % 181.55/181.54 [5591]~E(x55914,f2(a865))+E(f324(f324(f159(x55911),f324(f324(f145(x55911),x55912),x55913)),x55914),x55912) % 181.55/181.54 [6107]~P112(x61071)+E(f324(f324(f249(x61071),f324(f324(f249(x61071),x61072),x61073)),x61074),f324(f324(f249(x61071),x61072),f324(f324(f82(a865),x61073),x61074))) % 181.55/181.54 [6108]~P77(x61081)+E(f324(f324(f249(x61081),f324(f324(f249(x61081),x61082),x61083)),x61084),f324(f324(f249(x61081),x61082),f324(f324(f82(a865),x61083),x61084))) % 181.55/181.54 [6119]E(x61191,f2(a865))+E(f324(f324(f159(x61192),f324(f324(f145(x61192),x61193),x61194)),x61191),f324(f324(f159(x61192),x61194),f324(f324(f22(a865),x61191),f79(a865)))) % 181.55/181.54 [6143]~P114(x61431)+E(f324(f324(f282(x61431),f324(f324(f82(x61431),x61432),x61433)),x61434),f324(f324(f82(x61431),x61432),f324(f324(f282(x61431),x61433),x61434))) % 181.55/181.54 [6145]~P94(x61451)+E(f324(f324(f104(x61451),f324(f324(f104(x61451),x61452),x61453)),x61454),f324(f324(f104(x61451),x61452),f324(f324(f104(x61451),x61453),x61454))) % 181.55/181.54 [6147]~P99(x61471)+E(f324(f324(f104(x61471),f324(f324(f104(x61471),x61472),x61473)),x61474),f324(f324(f104(x61471),x61472),f324(f324(f104(x61471),x61473),x61474))) % 181.55/181.54 [6148]~P94(x61481)+E(f324(f324(f113(x61481),f324(f324(f113(x61481),x61482),x61483)),x61484),f324(f324(f113(x61481),x61482),f324(f324(f113(x61481),x61483),x61484))) % 181.55/181.54 [6150]~P100(x61501)+E(f324(f324(f113(x61501),f324(f324(f113(x61501),x61502),x61503)),x61504),f324(f324(f113(x61501),x61502),f324(f324(f113(x61501),x61503),x61504))) % 181.55/181.54 [6151]~P66(x61511)+E(f324(f324(f82(x61511),f324(f324(f82(x61511),x61512),x61513)),x61514),f324(f324(f82(x61511),x61512),f324(f324(f82(x61511),x61513),x61514))) % 181.55/181.54 [6152]~P112(x61521)+E(f324(f324(f82(x61521),f324(f324(f82(x61521),x61522),x61523)),x61524),f324(f324(f82(x61521),x61522),f324(f324(f82(x61521),x61523),x61524))) % 181.55/181.54 [6154]~P112(x61541)+E(f324(f324(f81(x61541),f324(f324(f81(x61541),x61542),x61543)),x61544),f324(f324(f81(x61541),x61542),f324(f324(f81(x61541),x61543),x61544))) % 181.55/181.54 [6155]~P67(x61551)+E(f324(f324(f81(x61551),f324(f324(f81(x61551),x61552),x61553)),x61554),f324(f324(f81(x61551),x61552),f324(f324(f81(x61551),x61553),x61554))) % 181.55/181.54 [6157]~P105(x61571)+E(f324(f324(f189(x61571),f324(f324(f189(x61571),x61572),x61573)),x61574),f324(f324(f189(x61571),x61572),f324(f324(f189(x61571),x61573),x61574))) % 181.55/181.54 [6159]~P105(x61591)+E(f324(f324(f190(x61591),f324(f324(f190(x61591),x61592),x61593)),x61594),f324(f324(f190(x61591),x61592),f324(f324(f190(x61591),x61593),x61594))) % 181.55/181.54 [6170]~P59(x61701)+E(f44(x61701,f324(f324(f81(x61701),x61702),f324(f324(f82(x61701),x61703),x61704)),x61704),f44(x61701,x61702,x61704)) % 181.55/181.54 [6171]~P59(x61711)+E(f44(x61711,f324(f324(f81(x61711),x61712),f324(f324(f82(x61711),x61713),x61714)),x61713),f44(x61711,x61712,x61713)) % 181.55/181.54 [6302]E(f324(f324(f159(x63021),f324(f324(f170(x63021),x63022),x63023)),x63024),f324(f324(f159(x63021),x63023),x63024))+~P1(f324(f324(f239(a865),x63024),x63022)) % 181.55/181.54 [6477]~P112(x64771)+E(f324(f324(f82(x64771),f324(f324(f82(x64771),x64772),x64773)),x64774),f324(f324(f82(x64771),f324(f324(f82(x64771),x64772),x64774)),x64773)) % 181.55/181.54 [6478]~P112(x64781)+E(f324(f324(f81(x64781),f324(f324(f81(x64781),x64782),x64783)),x64784),f324(f324(f81(x64781),f324(f324(f81(x64781),x64782),x64784)),x64783)) % 181.55/181.54 [6537]~P141(x65372)+E(f324(f324(f6(x65371,x65372),f324(f16(x65372,x65371),x65373)),x65374),f324(f324(f82(x65372),f324(f103(x65372),f324(f37(x65371),x65374))),x65373)) % 181.55/181.54 [6705]E(f324(f324(f104(f871(x67051,a859)),f324(f324(f302(x67051),x67052),x67053)),x67054),f324(f324(f104(f871(x67051,a859)),x67053),x67054))+P1(f324(f324(f326(x67051),x67052),x67054)) % 181.55/181.54 [6774]~P75(x67741)+E(f324(f324(f189(x67741),f324(f324(f22(x67741),x67742),x67743)),f324(f324(f22(x67741),x67744),x67743)),f324(f324(f22(x67741),f324(f324(f189(x67741),x67742),x67744)),x67743)) % 181.55/181.54 [6775]~P75(x67751)+E(f324(f324(f190(x67751),f324(f324(f22(x67751),x67752),x67753)),f324(f324(f22(x67751),x67754),x67753)),f324(f324(f22(x67751),f324(f324(f190(x67751),x67752),x67754)),x67753)) % 181.55/181.54 [6776]~P98(x67761)+E(f324(f324(f113(x67761),f324(f324(f104(x67761),x67762),x67763)),f324(f324(f104(x67761),x67764),x67763)),f324(f324(f104(x67761),f324(f324(f113(x67761),x67762),x67764)),x67763)) % 181.55/181.54 [6777]~P98(x67771)+E(f324(f324(f104(x67771),f324(f324(f113(x67771),x67772),x67773)),f324(f324(f113(x67771),x67774),x67773)),f324(f324(f113(x67771),f324(f324(f104(x67771),x67772),x67774)),x67773)) % 181.55/181.54 [6779]~P113(x67791)+E(f324(f324(f81(x67791),f324(f324(f82(x67791),x67792),x67793)),f324(f324(f82(x67791),x67794),x67793)),f324(f324(f82(x67791),f324(f324(f81(x67791),x67792),x67794)),x67793)) % 181.55/181.54 [6780]~P81(x67801)+E(f324(f324(f189(x67801),f324(f324(f81(x67801),x67802),x67803)),f324(f324(f81(x67801),x67804),x67803)),f324(f324(f81(x67801),f324(f324(f189(x67801),x67802),x67804)),x67803)) % 181.55/181.54 [6781]~P81(x67811)+E(f324(f324(f190(x67811),f324(f324(f81(x67811),x67812),x67813)),f324(f324(f81(x67811),x67814),x67813)),f324(f324(f81(x67811),f324(f324(f190(x67811),x67812),x67814)),x67813)) % 181.55/181.54 [6782]~P105(x67821)+E(f324(f324(f190(x67821),f324(f324(f189(x67821),x67822),x67823)),f324(f324(f189(x67821),x67824),x67823)),f324(f324(f189(x67821),f324(f324(f190(x67821),x67822),x67824)),x67823)) % 181.55/181.54 [6783]~P105(x67831)+E(f324(f324(f189(x67831),f324(f324(f190(x67831),x67832),x67833)),f324(f324(f190(x67831),x67834),x67833)),f324(f324(f190(x67831),f324(f324(f189(x67831),x67832),x67834)),x67833)) % 181.55/181.54 [6784]~P68(x67841)+E(f324(f324(f82(x67841),f324(f324(f249(x67841),x67842),x67843)),f324(f324(f249(x67841),x67844),x67843)),f324(f324(f249(x67841),f324(f324(f82(x67841),x67842),x67844)),x67843)) % 181.55/181.54 [6785]~P112(x67851)+E(f324(f324(f82(x67851),f324(f324(f249(x67851),x67852),x67853)),f324(f324(f249(x67851),x67854),x67853)),f324(f324(f249(x67851),f324(f324(f82(x67851),x67852),x67854)),x67853)) % 181.55/181.54 [6786]~P62(x67861)+E(f324(f324(f282(x67861),f324(f324(f249(x67861),x67862),x67863)),f324(f324(f249(x67861),x67864),x67863)),f324(f324(f249(x67861),f324(f324(f282(x67861),x67862),x67864)),x67863)) % 181.55/181.54 [6787]~P114(x67871)+E(f324(f324(f22(x67871),f324(f324(f282(x67871),x67872),x67873)),f324(f324(f282(x67871),x67874),x67873)),f324(f324(f282(x67871),f324(f324(f22(x67871),x67872),x67874)),x67873)) % 181.55/181.54 [6788]~P114(x67881)+E(f324(f324(f81(x67881),f324(f324(f282(x67881),x67882),x67883)),f324(f324(f282(x67881),x67884),x67883)),f324(f324(f282(x67881),f324(f324(f81(x67881),x67882),x67884)),x67883)) % 181.55/181.54 [6789]~P112(x67891)+E(f324(f324(f81(x67891),f324(f324(f82(x67891),x67892),x67893)),f324(f324(f82(x67891),x67894),x67893)),f324(f324(f82(x67891),f324(f324(f81(x67891),x67892),x67894)),x67893)) % 181.55/181.54 [6821]E(f324(f324(f153(x68211,x68212),x68213),x68214),x68212)+~P1(f324(f324(f238(a865),f324(f192(f866(x68211)),x68212)),x68213)) % 181.55/181.54 [6846]~P1(f324(x68463,x68464))+P1(f324(f324(f324(f113(f871(x68461,a859)),x68462),x68463),x68464)) % 181.55/181.54 [6848]~P1(f324(x68482,x68484))+P1(f324(f324(f324(f113(f871(x68481,a859)),x68482),x68483),x68484)) % 181.55/181.54 [6867]E(f324(f324(f159(x68671),f324(f324(f124(x68671),x68672),x68673)),x68674),f324(f324(f159(x68671),x68672),x68674))+~P1(f324(f324(f239(a865),x68674),f324(f192(f866(x68671)),x68672))) % 181.55/181.54 [6877]E(f324(f324(f22(f871(x68771,a859)),f324(f324(f302(x68771),x68772),x68773)),x68774),f324(f324(f22(f871(x68771,a859)),x68773),x68774))+~P1(f324(f324(f326(x68771),x68772),x68774)) % 181.55/181.54 [6918]~E(f133(a865,f324(f294(a865,x69181),x69182)),f324(f324(f145(a865),x69184),x69183))+E(f133(a865,f324(f294(a865,f324(f324(f81(a865),x69181),f79(a865))),x69182)),x69183) % 181.55/181.54 [6988]E(x69881,f2(a865))+E(f324(f324(f145(x69882),x69883),f324(f324(f170(x69882),f324(f324(f22(a865),x69881),f79(a865))),x69884)),f324(f324(f170(x69882),x69881),f324(f324(f145(x69882),x69883),x69884))) % 181.55/181.54 [7088]E(f324(f324(f159(x70881),x70882),f324(f324(f22(a865),x70883),f324(f192(f866(x70881)),x70884))),f324(f324(f159(x70881),f324(f324(f124(x70881),x70884),x70882)),x70883))+P1(f324(f324(f239(a865),x70883),f324(f192(f866(x70881)),x70884))) % 181.55/181.54 [7117]E(f324(f324(f104(f871(x71171,a859)),x71172),f324(f324(f302(x71171),x71173),x71174)),f324(f324(f302(x71171),x71173),f324(f324(f104(f871(x71171,a859)),x71172),x71174)))+~P1(f324(f324(f326(x71171),x71173),x71172)) % 181.55/181.54 [7152]E(f324(f324(f159(x71521),f324(f324(f153(x71521,x71522),x71523),x71524)),x71523),x71524)+~P1(f324(f324(f239(a865),x71523),f324(f192(f866(x71521)),x71522))) % 181.55/181.54 [7173]E(x71731,f191(f871(x71732,a859)))+E(f324(f303(f870(x71733,x71732),x71733,f258(x71733,x71732)),f324(f324(f261(x71733,x71732),x71734),f324(f16(f871(x71732,a859),x71733),x71731))),x71734) % 181.55/181.54 [7174]E(x71741,f191(f871(x71742,a859)))+E(f324(f303(f870(x71742,x71743),x71743,f262(x71742,x71743)),f324(f324(f261(x71742,x71743),x71741),f324(f16(f871(x71743,a859),x71742),x71744))),x71744) % 181.55/181.54 [7241]E(f324(f324(f22(f871(x72411,a859)),f324(f324(f302(x72411),x72412),x72413)),x72414),f324(f324(f302(x72411),x72412),f324(f324(f22(f871(x72411,a859)),x72413),x72414)))+P1(f324(f324(f326(x72411),x72412),x72414)) % 181.55/181.54 [7278]~E(x72784,f191(f871(x72782,a859)))+E(f324(f303(f870(x72781,x72782),x72781,f258(x72781,x72782)),f324(f324(f261(x72781,x72782),x72783),f324(f16(f871(x72782,a859),x72781),x72784))),f191(f871(x72781,a859))) % 181.55/181.54 [7279]~E(x72793,f191(f871(x72791,a859)))+E(f324(f303(f870(x72791,x72792),x72792,f262(x72791,x72792)),f324(f324(f261(x72791,x72792),x72793),f324(f16(f871(x72792,a859),x72791),x72794))),f191(f871(x72792,a859))) % 181.55/181.54 [7335]~P1(f324(f324(f326(x73351),x73352),x73354))+P1(f324(f324(f326(x73351),x73352),f324(f324(f113(f871(x73351,a859)),x73353),x73354))) % 181.55/181.54 [7338]~P1(f324(f324(f326(x73381),x73382),x73383))+P1(f324(f324(f326(x73381),x73382),f324(f324(f113(f871(x73381,a859)),x73383),x73384))) % 181.55/181.54 [7357]E(f324(f324(f104(f871(x73571,a859)),f324(f324(f302(x73571),x73572),x73573)),x73574),f324(f324(f302(x73571),x73572),f324(f324(f104(f871(x73571,a859)),x73573),x73574)))+~P1(f324(f324(f326(x73571),x73572),x73574)) % 181.55/181.54 [7632]P1(f324(x76321,x76322))+~P1(f324(f324(f324(f104(f871(x76323,a859)),x76324),x76321),x76322)) % 181.55/181.54 [7633]P1(f324(x76331,x76332))+~P1(f324(f324(f324(f104(f871(x76333,a859)),x76331),x76334),x76332)) % 181.55/181.54 [7636]E(f324(f324(f6(x76361,a865),x76362),f324(f324(f22(f871(x76361,a859)),x76363),f324(f324(f302(x76361),x76364),f191(f871(x76361,a859))))),f324(f324(f6(x76361,a865),x76362),x76363))+P1(f324(f324(f326(x76361),x76364),x76363)) % 181.55/181.54 [7641]~P72(x76411)+E(f324(f160(x76411),f324(f324(f148(a865,x76411),x76412),f133(a865,f324(f294(a865,x76413),x76414)))),f324(f324(f6(a865,x76411),x76412),f324(f167(a865),f133(a865,f324(f294(a865,x76413),x76414))))) % 181.55/181.54 [7642]~P72(x76421)+E(f324(f324(f6(a865,x76421),x76422),f324(f167(a865),f133(a865,f324(f294(a865,x76423),x76424)))),f324(f160(x76421),f324(f324(f148(a865,x76421),x76422),f133(a865,f324(f294(a865,x76423),x76424))))) % 181.55/181.54 [7747]~E(x77473,x77474)+P1(f324(f62(x77471,x77472,f324(f324(f302(x77471),x77473),f191(f871(x77471,a859)))),x77474)) % 181.55/181.54 [7847]P1(f324(f324(f326(x78471),x78472),f324(f167(x78471),x78473)))+~P1(f324(f324(f326(x78471),x78472),f324(f167(x78471),f324(f324(f170(x78471),x78474),x78473)))) % 181.55/181.54 [7848]P1(f324(f324(f326(x78481),x78482),f324(f167(x78481),x78483)))+~P1(f324(f324(f326(x78481),x78482),f324(f167(x78481),f324(f324(f132(x78481),x78484),x78483)))) % 181.55/181.54 [7920]P1(f324(f324(f326(x79201),x79202),x79203))+~P1(f324(f324(f326(x79201),x79202),f324(f324(f22(f871(x79201,a859)),x79203),x79204))) % 181.55/181.54 [7922]P1(f324(f324(f326(x79221),x79222),x79223))+~P1(f324(f324(f326(x79221),x79222),f324(f324(f104(f871(x79221,a859)),x79224),x79223))) % 181.55/181.54 [7925]P1(f324(f324(f326(x79251),x79252),x79253))+~P1(f324(f324(f326(x79251),x79252),f324(f324(f104(f871(x79251,a859)),x79253),x79254))) % 181.55/181.54 [7940]E(f324(f324(f124(x79401),f324(f324(f170(x79401),x79402),x79403)),f324(f324(f145(x79401),x79404),f324(f324(f132(x79401),f324(a115,x79402)),x79403))),f324(f324(f153(x79401,x79403),x79402),x79404))+~P1(f324(f324(f239(a865),x79402),f324(f192(f866(x79401)),x79403))) % 181.55/181.54 [7963]P1(f324(f324(f326(x79631),x79632),x79633))+~P1(f324(f324(f238(f871(x79631,a859)),f324(f324(f302(x79631),x79632),x79634)),x79633)) % 181.55/181.54 [7998]~P1(f324(f324(f326(x79981),x79982),x79983))+~P1(f324(f324(f326(x79981),x79982),f324(f324(f22(f871(x79981,a859)),x79984),x79983))) % 181.55/181.54 [8030]~P1(f324(f324(f239(a865),x80304),f324(f192(f866(x80301)),x80303)))+P1(f324(f324(f326(x80301),x80302),f324(f167(x80301),f324(f324(f153(x80301,x80303),x80304),x80302)))) % 181.55/181.54 [8083]E(f324(f324(f159(x80831),f324(f324(f132(x80831),x80832),x80833)),x80834),f324(f324(f159(x80831),x80833),f324(f324(f81(a865),x80832),x80834)))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),x80832),x80834)),f324(f192(f866(x80831)),x80833))) % 181.55/181.54 [8093]~P135(x80932)+E(f324(f324(f6(x80931,x80932),f324(f324(f8(a1,x80932,x80931),f105(x80932)),x80933)),x80934),f324(f105(x80932),f324(f324(f6(x80931,a1),x80933),x80934))) % 181.55/181.54 [8094]~P141(x80942)+E(f324(f324(f6(x80941,x80942),f324(f324(f8(a865,x80942,x80941),f103(x80942)),x80943)),x80944),f324(f103(x80942),f324(f324(f6(x80941,a865),x80943),x80944))) % 181.55/181.54 [8147]~P65(x81472)+E(f324(f324(f9(x81471,x81472),f324(f324(f8(x81472,x81472,x81471),f75(x81472)),x81473)),x81474),f324(f75(x81472),f324(f324(f9(x81471,x81472),x81473),x81474))) % 181.55/181.54 [8148]~P5(x81482)+E(f324(f324(f6(x81481,x81482),f324(f324(f8(x81482,x81482,x81481),f80(x81482)),x81483)),x81484),f324(f80(x81482),f324(f324(f6(x81481,x81482),x81483),x81484))) % 181.55/181.54 [8150]E(f324(f324(f6(x81501,a865),x81502),f324(f324(f22(f871(x81501,a859)),x81503),f324(f324(f302(x81501),x81504),f191(f871(x81501,a859))))),f324(f324(f22(a865),f324(f324(f6(x81501,a865),x81502),x81503)),f324(x81502,x81504)))+~P1(f324(f324(f326(x81501),x81504),x81503)) % 181.55/181.54 [8171]P1(f324(f324(f238(f871(x81711,a859)),x81712),x81713))+~P1(f324(f324(f238(f871(x81711,a859)),f324(f324(f302(x81711),x81714),x81712)),x81713)) % 181.55/181.54 [8297]~E(f324(f303(x82972,x82973,x82971),f247(f871(x82972,a859))),f247(f871(x82973,a859)))+E(f324(x82971,f324(f94(x82972,x82973,f247(f871(x82972,a859)),x82971),x82974)),x82974) % 181.55/181.54 [8379]E(f324(f324(f173(x83791,x83792),x83793),x83794),f203(x83792))+P1(f324(f324(f326(x83791),x83794),f324(f303(f870(x83791,x83792),x83791,f258(x83791,x83792)),f324(f167(f870(x83791,x83792)),x83793)))) % 181.55/181.54 [8380]P39(x83801,x83802)+~P39(x83801,f324(f324(f302(f870(x83801,x83801)),f324(f324(f259(x83801,x83801),x83803),x83804)),x83802)) % 181.55/181.54 [8381]P55(x83811,x83812)+~P55(x83811,f324(f324(f302(f870(x83811,x83811)),f324(f324(f259(x83811,x83811),x83813),x83814)),x83812)) % 181.55/181.54 [8386]~P105(x83861)+E(f324(f324(f142(x83861,x83861,f5(x83861)),x83862),f324(f324(f142(x83861,x83861,f5(x83861)),x83863),x83864)),f324(f324(f142(x83861,x83861,f5(x83861)),x83863),f324(f324(f142(x83861,x83861,f5(x83861)),x83862),x83864))) % 181.55/181.54 [8396]E(x83961,x83962)+~P1(f324(f62(x83963,x83964,f324(f324(f302(x83963),x83961),f191(f871(x83963,a859)))),x83962)) % 181.55/181.54 [8406]E(f324(f324(f124(x84061),f324(f324(f170(x84061),x84062),x84063)),f324(f324(f170(x84061),x84064),f324(f324(f132(x84061),x84062),x84063))),f324(f324(f170(x84061),f324(f324(f81(a865),x84062),x84064)),x84063))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),x84062),x84064)),f324(f192(f866(x84061)),x84063))) % 181.55/181.54 [8444]P1(f324(f61(x84441),x84442))+~E(x84442,f324(f303(a865,x84441,x84443),f324(f244(a865),f324(f324(f7(a865,a865,a859),f239(a865)),x84444)))) % 181.55/181.54 [8464]~P87(x84641)+E(f324(f136(x84641,x84641,f81(x84641),f324(f324(f81(x84641),x84642),x84643)),x84644),f324(f324(f81(x84641),x84642),f324(f136(x84641,x84641,f81(x84641),x84643),x84644))) % 181.55/181.54 [8499]P1(f324(f324(f238(f871(x84991,a859)),f324(f257(x84991,x84992),x84993)),f324(f257(x84991,x84992),x84994)))+~P1(f324(f324(f238(f871(f870(x84991,x84992),a859)),x84993),x84994)) % 181.55/181.54 [8512]~P1(f324(f324(f238(a865),x85122),x85124))+P1(f324(f324(f238(f871(x85121,a859)),f324(f167(x85121),f324(f324(f170(x85121),x85122),x85123))),f324(f167(x85121),f324(f324(f170(x85121),x85124),x85123)))) % 181.55/181.54 [8513]~P1(f324(f324(f238(a865),x85134),x85132))+P1(f324(f324(f238(f871(x85131,a859)),f324(f167(x85131),f324(f324(f132(x85131),x85132),x85133))),f324(f167(x85131),f324(f324(f132(x85131),x85134),x85133)))) % 181.55/181.54 [8570]~P1(f324(f61(x85701),f324(f324(f22(f871(x85701,a859)),x85702),x85704)))+P1(f324(f61(x85701),f324(f324(f22(f871(x85701,a859)),x85702),f324(f324(f302(x85701),x85703),x85704)))) % 181.55/181.54 [8613]P1(f324(f324(f326(f870(x86131,x86131)),x86132),f300(x86131,x86133)))+~P1(f324(f324(f326(f870(x86131,x86131)),x86132),f324(f324(f184(f870(x86131,x86131),a859),x86134),x86133))) % 181.55/181.54 [8699]~P1(f324(f61(x86991),f324(f324(f22(f871(x86991,a859)),x86992),f324(f324(f302(x86991),x86994),x86993))))+P1(f324(f61(x86991),f324(f324(f22(f871(x86991,a859)),x86992),x86993))) % 181.55/181.54 [8851]~E(f324(f324(f173(x88511,x88512),x88513),x88514),f203(x88512))+~P1(f324(f324(f326(x88511),x88514),f324(f303(f870(x88511,x88512),x88511,f258(x88511,x88512)),f324(f167(f870(x88511,x88512)),x88513)))) % 181.55/181.54 [8909]~P94(x89091)+P1(f324(f324(f238(x89091),f324(f324(f113(x89091),x89092),f324(f324(f104(x89091),x89093),x89094))),f324(f324(f104(x89091),f324(f324(f113(x89091),x89092),x89093)),f324(f324(f113(x89091),x89092),x89094)))) % 181.55/181.54 [8910]~P105(x89101)+P1(f324(f324(f238(x89101),f324(f324(f190(x89101),x89102),f324(f324(f189(x89101),x89103),x89104))),f324(f324(f189(x89101),f324(f324(f190(x89101),x89102),x89103)),f324(f324(f190(x89101),x89102),x89104)))) % 181.55/181.54 [9059]E(x90591,x90592)+~P1(f324(f324(f326(f870(x90593,x90593)),f324(f324(f259(x90593,x90593),x90591),x90592)),f324(f167(f870(x90593,x90593)),f324(f324(f177(x90593,x90593),x90594),x90594)))) % 181.55/181.54 [9089]~P1(f324(f324(f326(f870(x90891,x90891)),f324(f324(f259(x90891,x90891),x90893),x90892)),f300(x90891,x90894)))+~P39(x90891,f324(f324(f302(f870(x90891,x90891)),f324(f324(f259(x90891,x90891),x90892),x90893)),x90894)) % 181.55/181.54 [9090]~P1(f324(f324(f326(f870(x90901,x90901)),f324(f324(f259(x90901,x90901),x90903),x90902)),f300(x90901,x90904)))+~P55(x90901,f324(f324(f302(f870(x90901,x90901)),f324(f324(f259(x90901,x90901),x90902),x90903)),x90904)) % 181.55/181.54 [9097]E(x90971,x90972)+E(f324(f130(x90973,f324(f324(f8(a859,a859,x90973),a319),f324(a321,x90971))),f324(f324(f145(x90973),x90972),x90974)),f324(f324(f145(x90973),x90972),f324(f130(x90973,f324(f324(f8(a859,a859,x90973),a319),f324(a321,x90971))),x90974))) % 181.55/181.54 [9127]~P28(x91272,x91271,x91273,f247(f871(x91272,a859)),f247(f871(x91271,a859)))+E(f324(f303(x91271,x91272,f94(x91272,x91271,f247(f871(x91272,a859)),x91273)),x91274),f324(f304(x91272,x91271,x91273),x91274)) % 181.55/181.54 [9146]~P94(x91461)+P1(f324(f324(f238(x91461),f324(f324(f113(x91461),f324(f324(f104(x91461),x91462),x91463)),f324(f324(f104(x91461),x91462),x91464))),f324(f324(f104(x91461),x91462),f324(f324(f113(x91461),x91463),x91464)))) % 181.55/181.54 [9147]~P105(x91471)+P1(f324(f324(f238(x91471),f324(f324(f190(x91471),f324(f324(f189(x91471),x91472),x91473)),f324(f324(f189(x91471),x91472),x91474))),f324(f324(f189(x91471),x91472),f324(f324(f190(x91471),x91473),x91474)))) % 181.55/181.54 [9203]~P28(x92032,x92031,x92034,f247(f871(x92032,a859)),f247(f871(x92031,a859)))+E(f324(f244(x92031),f324(f324(f8(x92032,a859,x92031),x92033),f94(x92032,x92031,f247(f871(x92032,a859)),x92034))),f324(f303(x92032,x92031,x92034),f324(f244(x92032),x92033))) % 181.55/181.54 [9216]~E(f324(f303(x92162,x92161,x92163),f247(f871(x92162,a859))),f247(f871(x92161,a859)))+P1(f324(f324(f238(f871(x92161,a859)),f324(f80(f871(x92161,a859)),f324(f303(x92162,x92161,x92163),x92164))),f324(f303(x92162,x92161,x92163),f324(f80(f871(x92162,a859)),x92164)))) % 181.55/181.54 [9546]P1(f324(f324(f326(f870(x95461,x95461)),f324(f324(f259(x95461,x95461),x95462),x95463)),f324(f279(x95461,x95461),f324(f324(f281(x95461,x95461,x95461),x95464),f300(x95461,x95464)))))+~P1(f324(f324(f326(f870(x95461,x95461)),f324(f324(f259(x95461,x95461),x95462),x95463)),f324(f324(f281(x95461,x95461,x95461),f324(f279(x95461,x95461),x95464)),f300(x95461,f324(f279(x95461,x95461),x95464))))) % 181.55/181.54 [9547]~P1(f324(f324(f326(f870(x95471,x95471)),f324(f324(f259(x95471,x95471),x95472),x95473)),f324(f279(x95471,x95471),f324(f324(f281(x95471,x95471,x95471),x95474),f300(x95471,x95474)))))+P1(f324(f324(f326(f870(x95471,x95471)),f324(f324(f259(x95471,x95471),x95472),x95473)),f324(f324(f281(x95471,x95471,x95471),f324(f279(x95471,x95471),x95474)),f300(x95471,f324(f279(x95471,x95471),x95474))))) % 181.55/181.54 [9568]~P1(f324(f324(f326(x95682),x95684),f324(f255(x95681,x95682),x95683)))+P1(f324(f324(f326(f870(x95681,x95682)),f324(f324(f259(x95681,x95682),f528(x95683,x95681,x95684,x95682)),x95684)),x95683)) % 181.55/181.54 [9569]~P1(f324(f324(f326(x95692),x95694),f324(f255(x95691,x95692),x95693)))+P1(f324(f324(f326(f870(x95691,x95692)),f324(f324(f259(x95691,x95692),f531(x95693,x95691,x95694,x95692)),x95694)),x95693)) % 181.55/181.54 [9595]~P1(f324(f324(f326(x95951),x95954),f324(f324(f104(f871(x95951,a859)),x95952),x95953)))+P1(f324(f324(f324(f104(f871(x95951,a859)),f324(f324(f7(x95951,f871(x95951,a859),a859),f326(x95951)),x95952)),f324(f324(f7(x95951,f871(x95951,a859),a859),f326(x95951)),x95953)),x95954)) % 181.55/181.54 [9596]~P1(f324(f324(f326(x95961),x95964),f324(f324(f113(f871(x95961,a859)),x95962),x95963)))+P1(f324(f324(f324(f113(f871(x95961,a859)),f324(f324(f7(x95961,f871(x95961,a859),a859),f326(x95961)),x95962)),f324(f324(f7(x95961,f871(x95961,a859),a859),f326(x95961)),x95963)),x95964)) % 181.55/181.54 [9675]~P1(f324(f324(f326(f870(x96751,x96751)),f324(f324(f259(x96751,x96751),x96754),x96753)),f324(f324(f281(x96751,x96751,x96751),x96752),f300(x96751,x96752))))+P1(f324(f324(f326(f870(x96751,x96751)),f324(f324(f259(x96751,x96751),f614(x96752,x96753,x96754,x96751)),x96753)),x96752)) % 181.55/181.54 [9720]P1(f324(f324(f326(x97201),x97202),f324(f324(f104(f871(x97201,a859)),x97203),x97204)))+~P1(f324(f324(f324(f104(f871(x97201,a859)),f324(f324(f7(x97201,f871(x97201,a859),a859),f326(x97201)),x97203)),f324(f324(f7(x97201,f871(x97201,a859),a859),f326(x97201)),x97204)),x97202)) % 181.55/181.54 [9721]P1(f324(f324(f326(x97211),x97212),f324(f324(f113(f871(x97211,a859)),x97213),x97214)))+~P1(f324(f324(f324(f113(f871(x97211,a859)),f324(f324(f7(x97211,f871(x97211,a859),a859),f326(x97211)),x97213)),f324(f324(f7(x97211,f871(x97211,a859),a859),f326(x97211)),x97214)),x97212)) % 181.55/181.54 [9996]P34(x99961,f324(f324(f7(x99961,f871(f870(x99961,x99961),a859),f871(x99961,a859)),f324(f324(f8(f871(x99961,f871(f871(f870(x99961,x99961),a859),a859)),f871(f871(f870(x99961,x99961),a859),f871(x99961,a859)),x99961),f7(x99961,f871(f870(x99961,x99961),a859),a859)),f324(f324(f8(f871(x99961,f870(x99961,x99961)),f871(x99961,f871(f871(f870(x99961,x99961),a859),a859)),x99961),f324(f8(f870(x99961,x99961),f871(f871(f870(x99961,x99961),a859),a859),x99961),f326(f870(x99961,x99961)))),f259(x99961,x99961)))),x99962),x99963,x99964)+~P1(f324(f324(f326(f870(f866(x99961),f866(x99961))),f324(f324(f259(f866(x99961),f866(x99961)),x99963),x99964)),f152(x99961,x99962))) % 181.55/181.54 [10000]P56(x100001,f324(f324(f7(x100001,f871(f870(x100001,x100001),a859),f871(x100001,a859)),f324(f324(f8(f871(x100001,f871(f871(f870(x100001,x100001),a859),a859)),f871(f871(f870(x100001,x100001),a859),f871(x100001,a859)),x100001),f7(x100001,f871(f870(x100001,x100001),a859),a859)),f324(f324(f8(f871(x100001,f870(x100001,x100001)),f871(x100001,f871(f871(f870(x100001,x100001),a859),a859)),x100001),f324(f8(f870(x100001,x100001),f871(f871(f870(x100001,x100001),a859),a859),x100001),f326(f870(x100001,x100001)))),f259(x100001,x100001)))),x100002),x100003,x100004)+~P1(f324(f324(f326(f870(f871(x100001,a859),f871(x100001,a859))),f324(f324(f259(f871(x100001,a859),f871(x100001,a859)),x100003),x100004)),f315(x100001,x100002))) % 181.55/181.54 [10029]E(x100291,x100292)+~E(f324(f324(f7(x100293,f871(f870(x100293,x100294),a859),f871(x100294,a859)),f324(f324(f8(f871(x100294,f871(f871(f870(x100293,x100294),a859),a859)),f871(f871(f870(x100293,x100294),a859),f871(x100294,a859)),x100293),f7(x100294,f871(f870(x100293,x100294),a859),a859)),f324(f324(f8(f871(x100294,f870(x100293,x100294)),f871(x100294,f871(f871(f870(x100293,x100294),a859),a859)),x100293),f324(f8(f870(x100293,x100294),f871(f871(f870(x100293,x100294),a859),a859),x100294),f326(f870(x100293,x100294)))),f259(x100293,x100294)))),x100291),f324(f324(f7(x100293,f871(f870(x100293,x100294),a859),f871(x100294,a859)),f324(f324(f8(f871(x100294,f871(f871(f870(x100293,x100294),a859),a859)),f871(f871(f870(x100293,x100294),a859),f871(x100294,a859)),x100293),f7(x100294,f871(f870(x100293,x100294),a859),a859)),f324(f324(f8(f871(x100294,f870(x100293,x100294)),f871(x100294,f871(f871(f870(x100293,x100294),a859),a859)),x100293),f324(f8(f870(x100293,x100294),f871(f871(f870(x100293,x100294),a859),a859),x100294),f326(f870(x100293,x100294)))),f259(x100293,x100294)))),x100292)) % 181.55/181.54 [10032]~P34(x100321,f324(f324(f7(x100321,f871(f870(x100321,x100321),a859),f871(x100321,a859)),f324(f324(f8(f871(x100321,f871(f871(f870(x100321,x100321),a859),a859)),f871(f871(f870(x100321,x100321),a859),f871(x100321,a859)),x100321),f7(x100321,f871(f870(x100321,x100321),a859),a859)),f324(f324(f8(f871(x100321,f870(x100321,x100321)),f871(x100321,f871(f871(f870(x100321,x100321),a859),a859)),x100321),f324(f8(f870(x100321,x100321),f871(f871(f870(x100321,x100321),a859),a859),x100321),f326(f870(x100321,x100321)))),f259(x100321,x100321)))),x100324),x100322,x100323)+P1(f324(f324(f326(f870(f866(x100321),f866(x100321))),f324(f324(f259(f866(x100321),f866(x100321)),x100322),x100323)),f152(x100321,x100324))) % 181.55/181.54 [10033]~P56(x100331,f324(f324(f7(x100331,f871(f870(x100331,x100331),a859),f871(x100331,a859)),f324(f324(f8(f871(x100331,f871(f871(f870(x100331,x100331),a859),a859)),f871(f871(f870(x100331,x100331),a859),f871(x100331,a859)),x100331),f7(x100331,f871(f870(x100331,x100331),a859),a859)),f324(f324(f8(f871(x100331,f870(x100331,x100331)),f871(x100331,f871(f871(f870(x100331,x100331),a859),a859)),x100331),f324(f8(f870(x100331,x100331),f871(f871(f870(x100331,x100331),a859),a859),x100331),f326(f870(x100331,x100331)))),f259(x100331,x100331)))),x100334),x100332,x100333)+P1(f324(f324(f326(f870(f871(x100331,a859),f871(x100331,a859))),f324(f324(f259(f871(x100331,a859),f871(x100331,a859)),x100332),x100333)),f315(x100331,x100334))) % 181.55/181.54 [7408]~P92(x74081)+E(f324(f324(f82(x74081),f324(f106(x74081),x74082)),f324(f324(f82(x74081),f324(f106(x74081),x74083)),x74084)),f324(f324(f82(x74081),f324(f106(x74081),f324(f324(f82(a1),x74082),x74083))),x74084)) % 181.55/181.54 [7409]~P92(x74091)+E(f324(f324(f81(x74091),f324(f106(x74091),x74092)),f324(f324(f22(x74091),f324(f106(x74091),x74093)),x74094)),f324(f324(f22(x74091),f324(f106(x74091),f324(f324(f81(a1),x74092),x74093))),x74094)) % 181.55/181.54 [7410]~P92(x74101)+E(f324(f324(f81(x74101),f324(f106(x74101),x74102)),f324(f324(f81(x74101),f324(f106(x74101),x74103)),x74104)),f324(f324(f81(x74101),f324(f106(x74101),f324(f324(f81(a1),x74102),x74103))),x74104)) % 181.55/181.54 [7455]~P141(x74551)+E(f324(f160(x74551),f324(f324(f148(x74552,x74551),f324(f16(x74551,x74552),x74553)),x74554)),f324(f324(f82(x74551),f324(f103(x74551),f324(f192(f866(x74552)),x74554))),x74553)) % 181.55/181.54 [7686]E(f324(f270(x76861,f324(f324(f145(f870(a102,x76861)),x76862),x76863)),x76864),f324(f262(a102,x76861),x76862))+~P1(f324(f324(f239(a102),x76864),f324(f258(a102,x76861),x76862))) % 181.55/181.54 [7726]~P92(x77261)+E(f324(f324(f81(x77261),f324(f106(x77261),x77262)),f324(f324(f22(x77261),x77263),f324(f106(x77261),x77264))),f324(f324(f81(x77261),f324(f106(x77261),f324(f324(f81(a1),x77262),f324(f80(a1),x77264)))),x77263)) % 181.55/181.54 [7860]E(f324(f270(x78601,x78602),f324(f324(f22(a102),x78603),f324(f258(a102,x78601),x78604))),f324(f270(x78601,f324(f324(f145(f870(a102,x78601)),x78604),x78602)),x78603))+P1(f324(f324(f239(a102),x78603),f324(f258(a102,x78601),x78604))) % 181.55/181.54 [8303]~P1(f324(f324(f326(x83031),x83032),f324(f167(x83031),f117(x83031,x83034))))+P1(f324(f324(f326(x83031),x83032),f324(f167(x83031),f117(x83031,f324(f324(f124(x83031),x83033),x83034))))) % 181.55/181.54 [8304]~P1(f324(f324(f326(x83041),x83042),f324(f167(x83041),f117(x83041,x83043))))+P1(f324(f324(f326(x83041),x83042),f324(f167(x83041),f117(x83041,f324(f324(f124(x83041),x83043),x83044))))) % 181.55/181.54 [8322]E(f324(f324(f113(f871(x83221,a859)),f324(f324(f104(f871(x83221,a859)),x83222),x83223)),x83224),f324(f324(f104(f871(x83221,a859)),x83222),f324(f324(f113(f871(x83221,a859)),x83223),x83224)))+~P1(f324(f324(f238(f871(x83221,a859)),x83224),x83222)) % 181.55/181.54 [8627]~E(f324(f324(f113(f871(x86271,a859)),f324(f324(f104(f871(x86271,a859)),x86273),x86274)),x86272),f324(f324(f104(f871(x86271,a859)),x86273),f324(f324(f113(f871(x86271,a859)),x86274),x86272)))+P1(f324(f324(f238(f871(x86271,a859)),x86272),x86273)) % 181.55/181.54 [8915]~P1(f324(f324(f238(f871(x89151,a859)),x89152),f324(f324(f113(f871(x89151,a859)),x89153),x89154)))+P1(f324(f324(f238(f871(x89151,a859)),f324(f324(f22(f871(x89151,a859)),x89152),x89153)),x89154)) % 181.55/181.54 [9033]~E(f324(f303(x90331,x90332,x90333),f247(f871(x90331,a859))),f247(f871(x90332,a859)))+E(f324(f303(x90331,x90332,x90333),f324(f303(x90332,x90331,f94(x90331,x90332,f247(f871(x90331,a859)),x90333)),x90334)),x90334) % 181.55/181.54 [9038]P1(f324(f324(f238(f871(x90381,a859)),x90382),f324(f324(f113(f871(x90381,a859)),x90383),x90384)))+~P1(f324(f324(f238(f871(x90381,a859)),f324(f324(f22(f871(x90381,a859)),x90382),x90383)),x90384)) % 181.55/181.54 [9123]~P83(x91231)+E(f324(f75(x91231),f324(f324(f6(x91232,x91231),f324(f324(f8(x91231,x91231,x91232),f75(x91231)),x91233)),x91234)),f324(f324(f6(x91232,x91231),f324(f324(f8(x91231,x91231,x91232),f75(x91231)),x91233)),x91234)) % 181.55/181.54 [9291]~P83(x92911)+P1(f324(f324(f238(x92911),f2(x92911)),f324(f324(f6(x92912,x92911),f324(f324(f8(x92911,x92911,x92912),f75(x92911)),x92913)),x92914))) % 181.55/181.54 [9296]~P5(x92961)+E(f324(f160(x92961),f324(f324(f148(x92962,x92961),f324(f73(x92961,x92961,x92962,f80(x92961)),x92963)),x92964)),f324(f80(x92961),f324(f160(x92961),f324(f324(f148(x92962,x92961),x92963),x92964)))) % 181.55/181.54 [9437]~P83(x94371)+P1(f324(f324(f238(x94371),f324(f75(x94371),f324(f324(f6(x94372,x94371),x94373),x94374))),f324(f324(f6(x94372,x94371),f324(f324(f8(x94371,x94371,x94372),f75(x94371)),x94373)),x94374))) % 181.55/181.54 [9466]~E(f324(f324(f81(a865),x94661),x94664),f324(f324(f81(a865),x94663),x94662))+P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),f324(f324(f259(a865,a865),x94661),x94662)),f324(f324(f259(a865,a865),x94663),x94664))),a111)) % 181.55/181.54 [9467]~P1(f324(f324(f239(a865),x94671),x94673))+P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),f324(f324(f259(a865,a865),x94671),x94672)),f324(f324(f259(a865,a865),x94673),x94674))),a35)) % 181.55/181.54 [9468]~P1(f324(f324(f239(a865),x94681),x94683))+P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),f324(f324(f259(a865,a865),x94681),x94682)),f324(f324(f259(a865,a865),x94683),x94684))),a70)) % 181.55/181.54 [9620]E(f324(f324(f81(a865),x96201),x96202),f324(f324(f81(a865),x96203),x96204))+~P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),f324(f324(f259(a865,a865),x96201),x96204)),f324(f324(f259(a865,a865),x96203),x96202))),a111)) % 181.55/181.54 [9649]E(f324(f324(f159(x96491),f324(f324(f132(x96491),f324(f192(f866(x96491)),f172(x96491,x96492,x96493))),x96493)),x96494),f324(f324(f159(x96491),x96493),f324(f324(f81(a865),x96494),f324(f192(f866(x96491)),f172(x96491,x96492,x96493)))))+~P1(f324(f324(f239(a865),x96494),f324(f192(f866(x96491)),f324(f324(f132(x96491),f324(f192(f866(x96491)),f172(x96491,x96492,x96493))),x96493)))) % 181.55/181.54 [9666]~P1(f324(f324(f326(x96662),x96664),f324(f324(f41(x96661,f871(x96662,a859)),f247(f871(x96661,a859))),x96663)))+P1(f324(f324(f324(f41(x96661,f871(x96662,a859)),f247(f871(x96661,a859))),f324(f324(f8(f871(x96662,a859),f871(x96662,a859),x96661),f324(f7(x96662,f871(x96662,a859),a859),f326(x96662))),x96663)),x96664)) % 181.55/181.54 [9667]~P1(f324(f324(f326(x96672),x96674),f324(f324(f42(x96671,f871(x96672,a859)),f247(f871(x96671,a859))),x96673)))+P1(f324(f324(f324(f42(x96671,f871(x96672,a859)),f247(f871(x96671,a859))),f324(f324(f8(f871(x96672,a859),f871(x96672,a859),x96671),f324(f7(x96672,f871(x96672,a859),a859),f326(x96672))),x96673)),x96674)) % 181.55/181.54 [9747]~P1(f324(f48(x97471,x97472),f324(f324(f259(a1,a1),x97474),x97473)))+P1(f324(f48(f324(f80(a1),x97471),x97472),f324(f324(f259(a1,a1),f324(f324(f324(f99(a1),f324(f324(a321,x97473),f2(a1))),f324(f80(a1),x97474)),f324(f324(f22(a1),f324(f80(a1),x97474)),f79(a1)))),f324(f324(f324(f99(a1),f324(f324(a321,x97473),f2(a1))),f2(a1)),f324(f324(f22(a1),x97472),x97473))))) % 181.55/181.54 [9756]P1(f324(f324(f326(x97561),x97562),f324(f324(f41(x97563,f871(x97561,a859)),f247(f871(x97563,a859))),x97564)))+~P1(f324(f324(f324(f41(x97563,f871(x97561,a859)),f247(f871(x97563,a859))),f324(f324(f8(f871(x97561,a859),f871(x97561,a859),x97563),f324(f7(x97561,f871(x97561,a859),a859),f326(x97561))),x97564)),x97562)) % 181.55/181.54 [9757]P1(f324(f324(f326(x97571),x97572),f324(f324(f42(x97573,f871(x97571,a859)),f247(f871(x97573,a859))),x97574)))+~P1(f324(f324(f324(f42(x97573,f871(x97571,a859)),f247(f871(x97573,a859))),f324(f324(f8(f871(x97571,a859),f871(x97571,a859),x97573),f324(f7(x97571,f871(x97571,a859),a859),f326(x97571))),x97574)),x97572)) % 181.55/181.54 [9769]E(f324(f324(f41(a865,f871(x97691,a859)),f247(f871(a865,a859))),x97692),f324(f324(f41(a865,f871(x97691,a859)),f247(f871(a865,a859))),x97693))+~E(f324(f324(f41(a865,f871(x97691,a859)),f324(f294(a865,f2(a865)),f477(x97692,x97694,x97693,x97691))),x97693),f324(f324(f41(a865,f871(x97691,a859)),f324(f294(a865,f2(a865)),f324(f324(f81(a865),f477(x97692,x97694,x97693,x97691)),x97694))),x97692)) % 181.55/181.54 [10089]~P1(f324(f324(f238(f871(f870(x100891,x100892),a859)),x100893),x100894))+P1(f324(f324(f238(f871(x100891,f871(x100892,a859))),f324(f324(f7(x100891,f871(f870(x100891,x100892),a859),f871(x100892,a859)),f324(f324(f8(f871(x100892,f871(f871(f870(x100891,x100892),a859),a859)),f871(f871(f870(x100891,x100892),a859),f871(x100892,a859)),x100891),f7(x100892,f871(f870(x100891,x100892),a859),a859)),f324(f324(f8(f871(x100892,f870(x100891,x100892)),f871(x100892,f871(f871(f870(x100891,x100892),a859),a859)),x100891),f324(f8(f870(x100891,x100892),f871(f871(f870(x100891,x100892),a859),a859),x100892),f326(f870(x100891,x100892)))),f259(x100891,x100892)))),x100893)),f324(f324(f7(x100891,f871(f870(x100891,x100892),a859),f871(x100892,a859)),f324(f324(f8(f871(x100892,f871(f871(f870(x100891,x100892),a859),a859)),f871(f871(f870(x100891,x100892),a859),f871(x100892,a859)),x100891),f7(x100892,f871(f870(x100891,x100892),a859),a859)),f324(f324(f8(f871(x100892,f870(x100891,x100892)),f871(x100892,f871(f871(f870(x100891,x100892),a859),a859)),x100891),f324(f8(f870(x100891,x100892),f871(f871(f870(x100891,x100892),a859),a859),x100892),f326(f870(x100891,x100892)))),f259(x100891,x100892)))),x100894))) % 181.55/181.54 [10105]P1(f324(f324(f238(f871(f870(x101051,x101052),a859)),x101053),x101054))+~P1(f324(f324(f238(f871(x101051,f871(x101052,a859))),f324(f324(f7(x101051,f871(f870(x101051,x101052),a859),f871(x101052,a859)),f324(f324(f8(f871(x101052,f871(f871(f870(x101051,x101052),a859),a859)),f871(f871(f870(x101051,x101052),a859),f871(x101052,a859)),x101051),f7(x101052,f871(f870(x101051,x101052),a859),a859)),f324(f324(f8(f871(x101052,f870(x101051,x101052)),f871(x101052,f871(f871(f870(x101051,x101052),a859),a859)),x101051),f324(f8(f870(x101051,x101052),f871(f871(f870(x101051,x101052),a859),a859),x101052),f326(f870(x101051,x101052)))),f259(x101051,x101052)))),x101053)),f324(f324(f7(x101051,f871(f870(x101051,x101052),a859),f871(x101052,a859)),f324(f324(f8(f871(x101052,f871(f871(f870(x101051,x101052),a859),a859)),f871(f871(f870(x101051,x101052),a859),f871(x101052,a859)),x101051),f7(x101052,f871(f870(x101051,x101052),a859),a859)),f324(f324(f8(f871(x101052,f870(x101051,x101052)),f871(x101052,f871(f871(f870(x101051,x101052),a859),a859)),x101051),f324(f8(f870(x101051,x101052),f871(f871(f870(x101051,x101052),a859),a859),x101052),f326(f870(x101051,x101052)))),f259(x101051,x101052)))),x101054))) % 181.55/181.54 [9170]~P1(f324(f324(f326(f870(x91701,x91701)),x91702),f300(x91701,x91704)))+P1(f324(f324(f326(f870(x91701,x91701)),x91702),f300(x91701,f324(f324(f113(f871(f870(x91701,x91701),a859)),x91703),x91704)))) % 181.55/181.54 [9171]~P1(f324(f324(f326(f870(x91711,x91711)),x91712),f300(x91711,x91713)))+P1(f324(f324(f326(f870(x91711,x91711)),x91712),f300(x91711,f324(f324(f113(f871(f870(x91711,x91711),a859)),x91713),x91714)))) % 181.55/181.54 [9537]~E(f324(f167(x95371),x95374),f179(x95371,x95372,x95373))+E(f324(f173(x95371,x95372),f324(f324(f148(x95371,f870(x95371,x95372)),f324(f324(f18(x95371,x95372,f870(x95371,x95372)),f259(x95371,x95372)),f324(f324(f8(f869(x95372),x95372,x95371),f237(x95372)),x95373))),x95374)),x95373) % 181.55/181.54 [9862]~P1(f324(f324(f238(a865),f324(f324(f81(a865),x98621),x98624)),f324(f324(f81(a865),x98623),x98622)))+P1(f324(f324(f238(a1),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x98621),x98622)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x98623),x98624)),f191(f871(f870(a865,a865),a859))))))) % 181.55/181.54 [9863]~P1(f324(f324(f239(a865),f324(f324(f81(a865),x98631),x98634)),f324(f324(f81(a865),x98633),x98632)))+P1(f324(f324(f239(a1),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x98631),x98632)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x98633),x98634)),f191(f871(f870(a865,a865),a859))))))) % 181.55/181.54 [9940]P1(f324(f324(f238(a865),f324(f324(f81(a865),x99401),x99402)),f324(f324(f81(a865),x99403),x99404)))+~P1(f324(f324(f238(a1),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x99401),x99404)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x99403),x99402)),f191(f871(f870(a865,a865),a859))))))) % 181.55/181.54 [9941]P1(f324(f324(f239(a865),f324(f324(f81(a865),x99411),x99412)),f324(f324(f81(a865),x99413),x99414)))+~P1(f324(f324(f239(a1),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x99411),x99414)),f191(f871(f870(a865,a865),a859)))))),f324(a90,f324(f278(f870(a865,a865),f870(a865,a865),a111),f324(f324(f302(f870(a865,a865)),f324(f324(f259(a865,a865),x99413),x99412)),f191(f871(f870(a865,a865),a859))))))) % 181.55/181.54 [9982]P1(f324(f324(f238(f871(x99821,a859)),f324(f324(f41(a865,f871(x99821,a859)),f247(f871(a865,a859))),x99822)),f324(f324(f41(a865,f871(x99821,a859)),f247(f871(a865,a859))),x99823)))+~P1(f324(f324(f238(f871(x99821,a859)),f324(f324(f41(a865,f871(x99821,a859)),f324(f294(a865,f2(a865)),f466(x99823,x99824,x99822,x99821))),x99822)),f324(f324(f41(a865,f871(x99821,a859)),f324(f294(a865,f2(a865)),f324(f324(f81(a865),f466(x99823,x99824,x99822,x99821)),x99824))),x99823))) % 181.55/181.54 [10079]~P1(f324(f324(f326(x100792),x100794),f324(f255(x100791,x100792),x100793)))+P1(f324(f254(x100791,x100792,f324(f324(f7(x100791,f871(f870(x100791,x100792),a859),f871(x100792,a859)),f324(f324(f8(f871(x100792,f871(f871(f870(x100791,x100792),a859),a859)),f871(f871(f870(x100791,x100792),a859),f871(x100792,a859)),x100791),f7(x100792,f871(f870(x100791,x100792),a859),a859)),f324(f324(f8(f871(x100792,f870(x100791,x100792)),f871(x100792,f871(f871(f870(x100791,x100792),a859),a859)),x100791),f324(f8(f870(x100791,x100792),f871(f871(f870(x100791,x100792),a859),a859),x100792),f326(f870(x100791,x100792)))),f259(x100791,x100792)))),x100793)),x100794)) % 181.55/181.54 [10080]~P1(f324(f324(f326(x100801),x100804),f324(f257(x100801,x100802),x100803)))+P1(f324(f253(x100801,x100802,f324(f324(f7(x100801,f871(f870(x100801,x100802),a859),f871(x100802,a859)),f324(f324(f8(f871(x100802,f871(f871(f870(x100801,x100802),a859),a859)),f871(f871(f870(x100801,x100802),a859),f871(x100802,a859)),x100801),f7(x100802,f871(f870(x100801,x100802),a859),a859)),f324(f324(f8(f871(x100802,f870(x100801,x100802)),f871(x100802,f871(f871(f870(x100801,x100802),a859),a859)),x100801),f324(f8(f870(x100801,x100802),f871(f871(f870(x100801,x100802),a859),a859),x100802),f326(f870(x100801,x100802)))),f259(x100801,x100802)))),x100803)),x100804)) % 181.55/181.54 [10092]P1(f324(f324(f326(x100921),x100922),f324(f255(x100923,x100921),x100924)))+~P1(f324(f254(x100923,x100921,f324(f324(f7(x100923,f871(f870(x100923,x100921),a859),f871(x100921,a859)),f324(f324(f8(f871(x100921,f871(f871(f870(x100923,x100921),a859),a859)),f871(f871(f870(x100923,x100921),a859),f871(x100921,a859)),x100923),f7(x100921,f871(f870(x100923,x100921),a859),a859)),f324(f324(f8(f871(x100921,f870(x100923,x100921)),f871(x100921,f871(f871(f870(x100923,x100921),a859),a859)),x100923),f324(f8(f870(x100923,x100921),f871(f871(f870(x100923,x100921),a859),a859),x100921),f326(f870(x100923,x100921)))),f259(x100923,x100921)))),x100924)),x100922)) % 181.55/181.54 [10093]P1(f324(f324(f326(x100931),x100932),f324(f257(x100931,x100933),x100934)))+~P1(f324(f253(x100931,x100933,f324(f324(f7(x100931,f871(f870(x100931,x100933),a859),f871(x100933,a859)),f324(f324(f8(f871(x100933,f871(f871(f870(x100931,x100933),a859),a859)),f871(f871(f870(x100931,x100933),a859),f871(x100933,a859)),x100931),f7(x100933,f871(f870(x100931,x100933),a859),a859)),f324(f324(f8(f871(x100933,f870(x100931,x100933)),f871(x100933,f871(f871(f870(x100931,x100933),a859),a859)),x100931),f324(f8(f870(x100931,x100933),f871(f871(f870(x100931,x100933),a859),a859),x100933),f326(f870(x100931,x100933)))),f259(x100931,x100933)))),x100934)),x100932)) % 181.55/181.54 [9780]P1(f324(f154(x97801,x97802),x97803))+~P1(f324(f154(x97801,f324(f324(f18(x97801,a859,a859),f324(f324(f8(a859,f871(a859,a859),x97801),a322),x97804)),x97802)),x97803)) % 181.55/181.54 [9781]P1(f324(f154(x97811,x97812),x97813))+~P1(f324(f154(x97811,f324(f324(f18(x97811,a859,a859),f324(f324(f8(a859,f871(a859,a859),x97811),a322),x97812)),x97814)),x97813)) % 181.55/181.54 [9864]~P112(x98641)+E(f324(f324(f82(x98641),f324(f324(f81(x98641),f79(x98641)),f79(x98641))),f324(f324(f6(a865,x98641),f324(f324(f8(x98641,x98641,a865),f324(f81(x98641),x98642)),f324(f324(f7(a865,x98641,x98641),f324(f324(f8(x98641,f871(x98641,x98641),a865),f82(x98641)),f103(x98641))),x98643))),f324(f245(a865),x98644))),f324(f324(f82(x98641),f324(f103(x98641),x98644)),f324(f324(f81(x98641),x98642),f324(f324(f81(x98641),x98642),f324(f324(f82(x98641),f324(f103(x98641),f324(f324(f22(a865),x98644),f79(a865)))),x98643))))) % 181.55/181.54 [10003]P1(f324(x100031,f525(x100032,x100033,x100034,x100031)))+P39(x100032,f324(f244(f870(x100032,x100032)),f324(f263(x100032,x100032,a859),f324(f324(f8(f871(x100032,a859),f871(x100032,a859),x100032),f324(f18(x100032,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100032),a322),x100031))),f324(f324(f7(x100032,f871(x100032,x100032),f871(x100032,a859)),f324(f324(f8(f871(x100032,a859),f871(f871(x100032,x100032),f871(x100032,a859)),x100032),f8(x100032,a859,x100032)),a321)),x100033))))) % 181.55/181.54 [10017]~P1(f324(f324(f239(a865),f324(x100174,f324(x100173,f525(x100171,x100173,x100174,x100172)))),f324(x100174,f525(x100171,x100173,x100174,x100172))))+P39(x100171,f324(f244(f870(x100171,x100171)),f324(f263(x100171,x100171,a859),f324(f324(f8(f871(x100171,a859),f871(x100171,a859),x100171),f324(f18(x100171,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100171),a322),x100172))),f324(f324(f7(x100171,f871(x100171,x100171),f871(x100171,a859)),f324(f324(f8(f871(x100171,a859),f871(f871(x100171,x100171),f871(x100171,a859)),x100171),f8(x100171,a859,x100171)),a321)),x100173))))) % 181.55/181.54 [10117]~P1(f324(f324(f326(f870(x101171,x101171)),f324(f324(f259(x101171,x101171),x101173),x101174)),f324(f324(f113(f871(f870(x101171,x101171),a859)),x101172),f300(x101171,f191(f871(f870(x101171,x101171),a859))))))+P1(f324(f324(f324(f324(f113(f871(x101171,f871(x101171,a859))),f324(f324(f7(x101171,f871(f870(x101171,x101171),a859),f871(x101171,a859)),f324(f324(f8(f871(x101171,f871(f871(f870(x101171,x101171),a859),a859)),f871(f871(f870(x101171,x101171),a859),f871(x101171,a859)),x101171),f7(x101171,f871(f870(x101171,x101171),a859),a859)),f324(f324(f8(f871(x101171,f870(x101171,x101171)),f871(x101171,f871(f871(f870(x101171,x101171),a859),a859)),x101171),f324(f8(f870(x101171,x101171),f871(f871(f870(x101171,x101171),a859),a859),x101171),f326(f870(x101171,x101171)))),f259(x101171,x101171)))),x101172)),a321),x101173),x101174)) % 181.55/181.54 [10126]P1(f324(f324(f326(f870(x101261,x101261)),f324(f324(f259(x101261,x101261),x101262),x101263)),f324(f324(f113(f871(f870(x101261,x101261),a859)),x101264),f300(x101261,f191(f871(f870(x101261,x101261),a859))))))+~P1(f324(f324(f324(f324(f113(f871(x101261,f871(x101261,a859))),f324(f324(f7(x101261,f871(f870(x101261,x101261),a859),f871(x101261,a859)),f324(f324(f8(f871(x101261,f871(f871(f870(x101261,x101261),a859),a859)),f871(f871(f870(x101261,x101261),a859),f871(x101261,a859)),x101261),f7(x101261,f871(f870(x101261,x101261),a859),a859)),f324(f324(f8(f871(x101261,f870(x101261,x101261)),f871(x101261,f871(f871(f870(x101261,x101261),a859),a859)),x101261),f324(f8(f870(x101261,x101261),f871(f871(f870(x101261,x101261),a859),a859),x101261),f326(f870(x101261,x101261)))),f259(x101261,x101261)))),x101264)),a321),x101262),x101263)) % 181.55/181.54 [10076]E(f324(f324(f145(f866(x100761)),f324(f324(f145(x100761),x100762),f324(f136(f866(x100761),f866(x100761),f124(x100761),f116(x100761)),f324(f324(f148(f866(x100761),f866(x100761)),f150(f866(x100761),x100761,f116(x100761),f324(f324(f8(f866(x100761),f871(f866(x100761),f866(x100761)),x100761),f16(f866(x100761),f866(x100761))),f324(f324(f7(x100761,f866(x100761),f866(x100761)),f145(x100761)),f116(x100761))))),x100763)))),f175(x100761,f324(f324(f145(f866(x100761)),x100764),f324(f136(f866(f866(x100761)),f866(f866(x100761)),f124(f866(x100761)),f116(f866(x100761))),f324(f324(f148(f866(x100761),f866(f866(x100761))),f150(f866(f866(x100761)),x100761,f116(f866(x100761)),f324(f16(f871(f866(x100761),f866(f866(x100761))),x100761),f324(f324(f7(f866(x100761),f866(f866(x100761)),f866(f866(x100761))),f145(f866(x100761))),f116(f866(x100761)))))),x100763))))),f175(x100761,f324(f324(f145(f866(x100761)),f324(f324(f145(x100761),x100762),x100764)),x100763)))+~P1(f324(f312(f866(f866(x100761)),f176(x100761)),f324(f324(f145(f866(x100761)),f324(f324(f145(x100761),x100762),x100764)),x100763))) % 181.55/181.54 [10116]~P1(f324(f61(x101162),f324(f244(x101162),x101164)))+P1(f324(f61(x101161),f324(f244(x101161),f324(f324(f8(f871(x101162,a859),a859,x101161),f88(x101162)),f324(f324(f7(x101161,f871(x101162,a859),f871(x101162,a859)),f324(f324(f8(f871(x101162,f871(a859,a859)),f871(f871(x101162,a859),f871(x101162,a859)),x101161),f18(x101162,a859,a859)),f324(f324(f8(f871(x101162,a859),f871(x101162,f871(a859,a859)),x101161),f324(f8(a859,f871(a859,a859),x101162),a322)),f324(f324(f7(x101161,f871(x101162,x101161),f871(x101162,a859)),f324(f324(f8(f871(x101161,a859),f871(f871(x101162,x101161),f871(x101162,a859)),x101161),f8(x101161,a859,x101162)),a321)),x101163)))),x101164))))) % 181.55/181.54 [8665]P27(x86651,x86652,x86653,x86654)+~P28(x86651,x86652,x86653,x86654,x86655) % 181.55/181.54 [5230]E(x52301,x52302)+~E(f125(x52303,x52304,x52301),f125(x52303,x52305,x52302)) % 181.55/181.54 [5231]E(x52311,x52312)+~E(f125(x52313,x52311,x52314),f125(x52313,x52312,x52315)) % 181.55/181.54 [9144]~P28(x91442,x91441,x91444,x91443,x91445)+P28(x91441,x91442,f78(x91442,x91441,x91443,x91444),x91445,x91443) % 181.55/181.54 [9145]~P28(x91452,x91451,x91454,x91453,x91455)+P28(x91451,x91452,f94(x91452,x91451,x91453,x91454),x91455,x91453) % 181.55/181.54 [5604]E(f324(f324(f302(x56041),x56042),f179(x56041,x56043,x56044)),f179(x56041,x56043,x56044))+~E(f324(x56044,x56042),f324(f233(x56043),x56045)) % 181.55/181.54 [6004]P1(f324(f254(x60041,x60042,x60043),x60044))+~P1(f324(f324(x60043,x60045),x60044)) % 181.55/181.54 [6006]P1(f324(f253(x60061,x60062,x60063),x60064))+~P1(f324(f324(x60063,x60064),x60065)) % 181.55/181.54 [6009]~E(f324(x60094,x60092),f324(f233(x60093),x60095))+P1(f324(f324(f326(x60091),x60092),f179(x60091,x60093,x60094))) % 181.55/181.54 [6010]~E(f324(x60104,x60105),f324(f233(x60101),x60102))+P1(f324(f324(f326(x60101),x60102),f181(x60103,x60101,x60104))) % 181.55/181.54 [6466]~E(x64665,f2(a102))+E(f324(f200(x64661,x64662,x64663,x64664),x64665),f126(x64662)) % 181.55/181.54 [6467]~E(x64675,f2(a102))+E(f324(f202(x64671,x64672,x64673,x64674),x64675),f118(x64672)) % 181.55/181.54 [6602]~E(x66023,f2(a102))+E(f324(f273(x66021,x66022,x66023,x66024),x66025),f324(f259(x66021,x66022),x66025)) % 181.55/181.54 [6674]~E(f324(x66744,x66745),f203(x66742))+E(f324(f235(f869(x66741),x66742,f203(x66741),x66743),f324(x66744,x66745)),f203(x66741)) % 181.55/181.54 [7289]E(f324(x72891,x72892),f203(x72893))+~E(f324(f180(x72894,x72893,x72895,x72891),x72892),f203(x72893)) % 181.55/181.54 [7290]E(f324(x72901,x72902),f203(x72903))+~E(f324(f180(x72904,x72903,x72901,x72905),x72902),f203(x72903)) % 181.55/181.54 [7327]E(f324(f180(x73271,x73272,x73273,x73274),x73275),f324(x73273,x73275))+P1(f324(f324(f326(x73271),x73275),f179(x73271,x73272,x73274))) % 181.55/181.54 [7328]E(f324(f180(x73281,x73282,x73283,x73284),x73285),f324(x73284,x73285))+P1(f324(f324(f326(x73281),x73285),f179(x73281,x73282,x73283))) % 181.55/181.54 [7646]~P22(x76464,x76461,x76462,x76465)+E(f324(f73(x76461,x76461,x76461,f324(x76462,x76463)),f324(x76462,x76463)),f324(x76462,x76463)) % 181.55/181.54 [7688]E(f324(f180(x76881,x76882,x76883,x76884),x76885),f324(x76884,x76885))+~P1(f324(f324(f326(x76881),x76885),f179(x76881,x76882,x76884))) % 181.55/181.54 [8031]~P18(x80315,x80311,x80312)+E(f324(f73(x80311,x80311,x80311,f324(x80312,x80313)),f324(x80312,x80314)),f324(f73(x80311,x80311,x80311,f324(x80312,x80314)),f324(x80312,x80313))) % 181.55/181.54 [8362]P1(f324(f324(f326(f870(x83621,x83621)),f324(f324(f259(x83621,x83621),x83622),x83623)),f318(x83621,x83624,x83625)))+~P1(f324(f324(f239(a865),f324(x83624,x83622)),f324(x83624,x83623))) % 181.55/181.54 [8450]~P1(f324(f324(f326(x84504),x84503),f288(x84504,x84501,x84502,x84505)))+P1(f324(f324(x84501,x84502),x84503)) % 181.55/181.54 [8451]~P1(f324(f324(f326(x84514),x84513),f291(x84514,x84511,x84512,x84515)))+P1(f324(f324(x84511,x84512),x84513)) % 181.55/181.54 [8452]~P1(f324(f324(f326(x84524),x84522),f288(x84524,x84521,x84525,x84523)))+P1(f324(f324(x84521,x84522),x84523)) % 181.55/181.54 [8453]~P1(f324(f324(f326(x84534),x84532),f291(x84534,x84531,x84535,x84533)))+P1(f324(f324(x84531,x84532),x84533)) % 181.55/181.54 [8534]~P28(x85341,x85343,x85345,x85342,x85344)+E(f324(f37(x85341),x85342),f324(f37(x85343),x85344)) % 181.55/181.54 [8582]~P28(x85821,x85822,x85823,x85824,x85825)+E(f324(f303(x85821,x85822,x85823),x85824),x85825) % 181.55/181.54 [8603]~P54(x86032,x86031,x86035,x86033,x86034)+E(f324(f303(x86031,x86032,x86033),x86034),f247(f871(x86032,a859))) % 181.55/181.54 [9049]~P36(x90491,x90492,x90493,x90494,x90495)+P36(x90491,x90492,x90493,f324(f163(x90491),x90494),f324(f163(x90492),x90495)) % 181.55/181.54 [9051]~P36(x90511,x90512,x90513,f324(f163(x90511),x90514),x90515)+P36(x90511,x90512,x90513,x90514,f324(f163(x90512),x90515)) % 181.55/181.54 [9052]~P36(x90521,x90522,x90523,x90524,f324(f163(x90522),x90525))+P36(x90521,x90522,x90523,f324(f163(x90521),x90524),x90525) % 181.55/181.54 [9058]P36(x90581,x90582,x90583,x90584,x90585)+~P36(x90581,x90582,x90583,f324(f163(x90581),x90584),f324(f163(x90582),x90585)) % 181.55/181.54 [9400]~P28(x94001,x94002,x94005,f247(f871(x94001,a859)),f247(f871(x94002,a859)))+P28(x94001,x94002,f76(x94001,x94002,x94003,x94004,x94005),f247(f871(x94001,a859)),f247(f871(x94002,a859))) % 181.55/181.54 [9457]P1(f324(f324(f326(f870(f866(x94571),f866(x94571))),f324(f324(f259(f866(x94571),f866(x94571)),f324(f324(f145(x94571),x94572),x94573)),f324(f324(f145(x94571),x94572),x94574))),f151(x94571,x94575)))+~P1(f324(f324(f326(f870(f866(x94571),f866(x94571))),f324(f324(f259(f866(x94571),f866(x94571)),x94573),x94574)),f151(x94571,x94575))) % 181.55/181.54 [9458]P1(f324(f324(f326(f870(f866(x94581),f866(x94581))),f324(f324(f259(f866(x94581),f866(x94581)),f324(f324(f124(x94581),x94582),x94583)),f324(f324(f124(x94581),x94582),x94584))),f141(x94581,x94585)))+~P1(f324(f324(f326(f870(f866(x94581),f866(x94581))),f324(f324(f259(f866(x94581),f866(x94581)),x94583),x94584)),f141(x94581,x94585))) % 181.55/181.54 [9475]~P28(x94751,x94752,f76(x94751,x94752,x94754,x94755,x94753),f247(f871(x94751,a859)),f247(f871(x94752,a859)))+P28(x94751,x94752,x94753,f247(f871(x94751,a859)),f247(f871(x94752,a859))) % 181.55/181.54 [9656]E(f324(f324(f145(x96561),f674(x96562,x96563,x96564,x96565,x96561)),f675(x96562,x96563,x96564,x96565,x96561)),x96565)+~P1(f324(f324(f326(f870(f866(x96561),f866(x96561))),f324(f324(f259(f866(x96561),f866(x96561)),x96565),f324(f324(f145(x96561),x96564),x96563))),f152(x96561,x96562))) % 181.55/181.54 [9678]E(f324(f324(f145(x96781),f676(x96782,x96783,x96784,x96785,x96781)),f677(x96782,x96783,x96784,x96785,x96781)),x96783)+~P1(f324(f324(f326(f870(f866(x96781),f866(x96781))),f324(f324(f259(f866(x96781),f866(x96781)),f324(f324(f145(x96781),x96785),x96784)),x96783)),f152(x96781,x96782))) % 181.55/181.54 [9837]~P1(f324(f324(f326(f870(f866(x98371),f866(x98371))),f324(f324(f259(f866(x98371),f866(x98371)),f324(f324(f145(x98371),x98375),x98372)),x98374)),f152(x98371,x98373)))+P1(f324(f324(f326(f870(f866(x98371),f866(x98371))),f324(f324(f259(f866(x98371),f866(x98371)),x98372),f677(x98373,x98374,x98372,x98375,x98371))),f152(x98371,x98373))) % 181.55/181.54 [9908]~P1(f324(f324(f326(f870(f866(x99081),f866(x99081))),f324(f324(f259(f866(x99081),f866(x99081)),x99085),f324(f324(f145(x99081),x99084),x99083))),f152(x99081,x99082)))+P1(f324(f324(f326(f870(f866(x99081),f866(x99081))),f324(f324(f259(f866(x99081),f866(x99081)),f675(x99082,x99083,x99084,x99085,x99081)),x99083)),f152(x99081,x99082))) % 181.55/181.54 [10071]P1(f324(f324(f326(f870(x100711,x100711)),f324(f324(f259(x100711,x100711),f324(x100712,f324(f324(f81(a865),x100713),x100714))),f324(x100712,x100713))),f300(x100711,x100715)))+~P1(f324(f324(f326(f870(x100711,x100711)),f324(f324(f259(x100711,x100711),f324(x100712,f324(a115,f589(x100714,x100713,x100715,x100712,x100711)))),f324(x100712,f589(x100714,x100713,x100715,x100712,x100711)))),f300(x100711,x100715))) % 181.55/181.54 [5196]E(x51961,x51962)+~E(f324(f324(f145(x51963),x51964),x51961),f324(f324(f145(x51963),x51965),x51962)) % 181.55/181.54 [5197]E(x51971,x51972)+~E(f324(f324(f145(x51973),x51971),x51974),f324(f324(f145(x51973),x51972),x51975)) % 181.55/181.54 [5247]P1(f324(x52471,x52472))+~E(f324(f130(x52473,x52471),x52474),f324(f324(f145(x52473),x52472),x52475)) % 181.55/181.54 [5248]P1(f324(x52481,x52482))+~E(f324(f324(f145(x52483),x52482),x52484),f324(f130(x52483,x52481),x52485)) % 181.55/181.54 [5403]~E(f324(f324(f132(x54031),x54033),x54032),f324(f324(f145(x54031),x54034),x54035))+E(f324(f324(f159(x54031),x54032),x54033),x54034) % 181.55/181.54 [5535]~P17(x55354,x55355,x55351)+E(f324(f324(x55351,x55352),f324(f324(x55351,x55352),x55353)),f324(f324(x55351,x55352),x55353)) % 181.55/181.54 [6061]~E(x60614,f2(a102))+E(f324(f324(f120(x60611,x60612,x60613),x60614),x60615),f324(f324(f259(f866(x60612),x60611),f116(x60612)),x60615)) % 181.55/181.54 [6127]~P105(x61272)+~E(f324(f324(f142(x61271,x61272,x61273),x61274),x61275),f116(x61271)) % 181.55/181.54 [6504]E(x65041,x65042)+~E(f324(f324(f124(x65043),x65044),f324(f324(f145(x65043),x65041),f116(x65043))),f324(f324(f124(x65043),x65045),f324(f324(f145(x65043),x65042),f116(x65043)))) % 181.55/181.54 [6505]E(x65051,x65052)+~E(f324(f324(f124(x65053),x65051),f324(f324(f145(x65053),x65054),f116(x65053))),f324(f324(f124(x65053),x65052),f324(f324(f145(x65053),x65055),f116(x65053)))) % 181.55/181.54 [6757]E(f324(f183(x67571,x67572,x67573,x67574),x67575),f203(x67572))+P1(f324(f324(f326(x67571),x67575),x67574)) % 181.55/181.54 [6819]E(f324(f324(f302(x68191),f324(x68192,x68193)),f324(f303(x68194,x68191,x68192),x68195)),f324(f303(x68194,x68191,x68192),x68195))+~P1(f324(f324(f326(x68194),x68193),x68195)) % 181.55/181.54 [6826]~P1(f324(x68264,f324(x68263,x68265)))+P1(f324(f324(f304(x68261,x68262,x68263),x68264),x68265)) % 181.55/181.54 [6829]~P1(f324(f324(x68293,x68295),x68294))+P1(f324(f324(f248(x68291,x68292,x68293),x68294),x68295)) % 181.55/181.54 [6922]~E(f324(f303(x69221,x69222,x69223),x69224),x69225)+E(f324(f303(f871(x69221,a859),f871(x69222,a859),f303(x69221,x69222,x69223)),f324(f301(x69221),x69224)),f324(f301(x69222),x69225)) % 181.55/181.54 [6951]E(f324(f183(x69511,x69512,x69513,x69514),x69515),f324(x69513,x69515))+~P1(f324(f324(f326(x69511),x69515),x69514)) % 181.55/181.54 [7249]P27(x72491,x72492,x72493,x72494)+~P27(x72491,x72492,x72493,f324(f324(f302(x72491),x72495),x72494)) % 181.55/181.54 [7317]P1(f324(x73171,x73172))+~P1(f324(f324(f95(x73173,x73174,x73171),x73175),x73172)) % 181.55/181.54 [7361]~P1(f324(f324(f326(x73614),x73613),x73615))+P1(f324(f324(f326(x73611),f324(x73612,x73613)),f324(f303(x73614,x73611,x73612),x73615))) % 181.55/181.54 [7384]~P105(x73842)+E(f144(x73841,x73842,x73843,f324(f130(x73841,x73844),x73845)),f324(f130(x73841,x73844),f144(x73841,x73842,x73843,x73845))) % 181.55/181.54 [7417]P1(f324(x74171,f324(x74172,x74173)))+~P1(f324(f324(f304(x74174,x74175,x74172),x74171),x74173)) % 181.55/181.54 [7420]P1(f324(f324(x74201,x74202),x74203))+~P1(f324(f324(f248(x74204,x74205,x74201),x74203),x74202)) % 181.55/181.54 [7421]P1(f324(f324(x74211,x74212),x74213))+~P1(f324(f324(f95(x74214,x74211,x74215),x74212),x74213)) % 181.55/181.54 [7484]~P1(f324(f324(f326(x74843),f324(x74844,x74842)),x74845))+P1(f324(f324(f326(x74841),x74842),f324(f304(x74841,x74843,x74844),x74845))) % 181.55/181.54 [7876]~P1(f324(f324(f326(x78765),x78763),f324(f304(x78765,x78761,x78762),x78764)))+P1(f324(f324(f326(x78761),f324(x78762,x78763)),x78764)) % 181.55/181.54 [8095]~E(x80953,f324(f324(f324(f72(x80951,f869(x80952)),f324(f16(f869(x80952),x80951),f203(x80952))),x80954),f324(f233(x80952),x80955)))+E(f179(x80951,x80952,x80953),f324(f324(f302(x80951),x80954),f191(f871(x80951,a859)))) % 181.55/181.54 [8176]~P18(x81762,x81761,x81763)+E(f324(f136(x81761,x81762,f324(f7(x81762,x81761,x81761),x81763),x81764),f146(x81762,x81765)),f324(f324(f64(x81762,x81761,x81763),x81764),f324(f167(x81762),x81765))) % 181.55/181.54 [8196]E(f324(x81961,f766(x81962,x81961,x81963,x81964)),x81964)+~P1(f324(f324(f326(x81965),x81964),f324(f303(x81963,x81965,x81961),x81962))) % 181.55/181.54 [8197]E(f324(x81971,f854(x81972,x81971,x81973,x81974)),x81974)+~P1(f324(f324(f326(x81975),x81974),f324(f303(x81973,x81975,x81971),x81972))) % 181.55/181.54 [8496]~E(x84962,f324(f324(f145(x84961),x84964),x84965))+P1(f324(f324(f326(f870(f866(x84961),f866(x84961))),f324(f324(f259(f866(x84961),f866(x84961)),f116(x84961)),x84962)),f141(x84961,x84963))) % 181.55/181.54 [8543]E(f324(x85431,f324(f94(x85432,x85433,x85434,x85431),x85435)),x85435)+~P1(f324(f324(f326(x85433),x85435),f324(f303(x85432,x85433,x85431),x85434))) % 181.55/181.54 [8546]P27(x85461,x85462,f94(x85462,x85461,x85463,x85464),x85465)+~P1(f324(f324(f238(f871(x85461,a859)),x85465),f324(f303(x85462,x85461,x85464),x85463))) % 181.55/181.54 [8554]~P36(x85541,x85543,x85545,x85542,x85544)+E(f324(f192(f866(x85541)),x85542),f324(f192(f866(x85543)),x85544)) % 181.55/181.54 [8564]P1(f324(f324(f238(f871(x85641,a859)),f324(f324(f42(x85642,f871(x85641,a859)),x85643),x85644)),f324(x85644,x85645)))+~P1(f324(f324(f326(x85642),x85645),x85643)) % 181.55/181.54 [8619]~P54(x86191,x86192,x86193,x86195,x86194)+E(f324(f303(x86191,x86192,x86193),f247(f871(x86191,a859))),x86194) % 181.55/181.54 [8836]E(f324(f324(f324(f72(x88361,f869(x88362)),f183(x88361,x88362,x88363,x88364)),x88365),f203(x88362)),f183(x88361,x88362,x88363,x88364))+P1(f324(f324(f326(x88361),x88365),x88364)) % 181.55/181.54 [8841]E(f324(f130(x88411,x88412),f768(x88413,x88414,x88415,x88412,x88411)),x88413)+~E(f324(f130(x88411,x88412),x88415),f324(f324(f145(x88411),x88414),x88413)) % 181.55/181.54 [8842]E(f324(f130(x88421,x88422),f769(x88423,x88422,x88424,x88425,x88421)),x88424)+~E(f324(f324(f145(x88421),x88425),x88424),f324(f130(x88421,x88422),x88423)) % 181.55/181.54 [8843]E(f324(x88431,f661(x88432,x88433,x88431,x88434,x88435)),x88432)+~E(f324(f324(f204(x88435,x88434),x88431),x88433),f324(f233(x88434),x88432)) % 181.55/181.54 [8846]E(f324(f233(x88461),f661(x88462,x88463,x88464,x88465,x88461)),x88463)+~E(f324(f324(f204(x88461,x88465),x88464),x88463),f324(f233(x88465),x88462)) % 181.55/181.54 [8936]E(f324(f192(f866(x89361)),x89362),x89363)+~P1(f324(f324(f326(f870(f866(x89361),f866(x89361))),f324(f324(f259(f866(x89361),f866(x89361)),x89364),x89362)),f324(f137(x89361,x89365),x89363))) % 181.55/181.54 [8937]E(f324(f192(f866(x89371)),x89372),x89373)+~P1(f324(f324(f326(f870(f866(x89371),f866(x89371))),f324(f324(f259(f866(x89371),f866(x89371)),x89372),x89374)),f324(f137(x89371,x89375),x89373))) % 181.55/181.54 [9007]P1(f324(f324(f326(x90071),f766(x90072,x90073,x90071,x90074)),x90072))+~P1(f324(f324(f326(x90075),x90074),f324(f303(x90071,x90075,x90073),x90072))) % 181.55/181.54 [9008]P1(f324(f324(f326(x90081),f854(x90082,x90083,x90081,x90084)),x90082))+~P1(f324(f324(f326(x90085),x90084),f324(f303(x90081,x90085,x90083),x90082))) % 181.55/181.54 [9168]E(f324(f303(x91681,x91682,x91683),f429(x91684,x91683,x91681,x91685,x91682)),x91685)+~P1(f324(f324(f238(f871(x91682,a859)),x91685),f324(f303(x91681,x91682,x91683),x91684))) % 181.55/181.54 [9363]~E(f324(f303(x93631,x93632,x93635),f247(f871(x93631,a859))),f247(f871(x93632,a859)))+E(f324(f303(x93631,x93632,f76(x93631,x93632,x93633,x93634,x93635)),f247(f871(x93631,a859))),f247(f871(x93632,a859))) % 181.55/181.54 [9427]E(f324(x94271,f831(x94272,x94271,x94273,x94274,x94275)),f324(f233(x94275),x94274))+~P1(f324(f324(f326(x94275),x94274),f181(x94273,x94275,f183(x94273,x94275,x94271,x94272)))) % 181.55/181.54 [9473]P1(f324(f324(f326(f870(f866(x94731),f866(x94731))),f324(f324(f259(f866(x94731),f866(x94731)),f324(f324(f145(x94731),x94732),x94733)),f324(f324(f145(x94731),x94732),x94734))),f300(f866(x94731),f151(x94731,x94735))))+~P1(f324(f324(f326(f870(f866(x94731),f866(x94731))),f324(f324(f259(f866(x94731),f866(x94731)),x94733),x94734)),f300(f866(x94731),f151(x94731,x94735)))) % 181.55/181.54 [9507]~E(f324(x95073,f664(x95075,x95074,x95073,x95072,x95071)),f324(x95075,f664(x95075,x95074,x95073,x95072,x95071)))+E(f324(f324(f148(x95071,x95072),x95073),x95074),f324(f324(f148(x95071,x95072),x95075),x95074)) % 181.55/181.54 [9519]~E(f324(f303(x95191,x95192,f76(x95191,x95192,x95194,x95195,x95193)),f247(f871(x95191,a859))),f247(f871(x95192,a859)))+E(f324(f303(x95191,x95192,x95193),f247(f871(x95191,a859))),f247(f871(x95192,a859))) % 181.55/181.54 [9586]~E(f324(f130(x95861,x95865),x95864),f324(f324(f145(x95861),x95863),x95862))+E(f324(f324(f124(x95861),f772(x95862,x95863,x95864,x95865,x95861)),f324(f324(f145(x95861),x95863),f768(x95862,x95863,x95864,x95865,x95861))),x95864) % 181.55/181.54 [9587]~E(f324(f324(f145(x95871),x95875),x95874),f324(f130(x95871,x95873),x95872))+E(f324(f324(f124(x95871),f770(x95872,x95873,x95874,x95875,x95871)),f324(f324(f145(x95871),x95875),f769(x95872,x95873,x95874,x95875,x95871))),x95872) % 181.55/181.54 [9591]E(f324(f324(f148(x95911,x95912),x95913),x95914),f324(f324(f148(x95911,x95912),x95915),x95914))+P1(f324(f324(f326(x95911),f664(x95913,x95914,x95915,x95912,x95911)),f324(f167(x95911),x95914))) % 181.55/181.54 [9621]~P1(f324(f324(f326(x96215),x96214),f324(f278(x96211,x96215,x96213),x96212)))+P1(f324(f324(f326(x96211),f774(x96212,x96213,x96211,x96214,x96215)),x96212)) % 181.55/181.54 [9622]~P1(f324(f324(f326(x96225),x96224),f324(f278(x96221,x96225,x96223),x96222)))+P1(f324(f324(f326(x96221),f809(x96222,x96223,x96221,x96224,x96225)),x96222)) % 181.55/181.54 [9650]~P1(f324(f324(f238(f871(x96505,a859)),x96504),f324(f303(x96501,x96505,x96503),x96502)))+P1(f324(f324(f238(f871(x96501,a859)),f429(x96502,x96503,x96501,x96504,x96505)),x96502)) % 181.55/181.54 [9701]~P1(f324(f324(f326(x97015),x97014),f181(x97011,x97015,f183(x97011,x97015,x97013,x97012))))+P1(f324(f324(f326(x97011),f831(x97012,x97013,x97011,x97014,x97015)),x97012)) % 181.55/181.54 [10095]E(x100951,f2(a102))+E(f324(f235(f870(f866(x100952),x100953),f870(x100952,x100953),f324(f324(f259(f866(x100952),x100953),f116(x100952)),x100954),f324(f263(x100952,x100953,f870(f866(x100952),x100953)),f324(f324(f7(x100952,f871(x100953,f870(f866(x100952),x100953)),f871(x100953,f870(f866(x100952),x100953))),f324(f324(f8(f871(f870(f866(x100952),x100953),f870(f866(x100952),x100953)),f871(f871(x100953,f870(f866(x100952),x100953)),f871(x100953,f870(f866(x100952),x100953))),x100952),f8(f870(f866(x100952),x100953),f870(f866(x100952),x100953),x100953)),f324(f324(f8(f871(f866(x100952),f871(x100953,f870(f866(x100952),x100953))),f871(f870(f866(x100952),x100953),f870(f866(x100952),x100953)),x100952),f263(f866(x100952),x100953,f870(f866(x100952),x100953))),f324(f324(f8(f871(f866(x100952),f866(x100952)),f871(f866(x100952),f871(x100953,f870(f866(x100952),x100953))),x100952),f324(f8(f866(x100952),f871(x100953,f870(f866(x100952),x100953)),f866(x100952)),f259(f866(x100952),x100953))),f145(x100952))))),f324(f120(x100953,x100952,x100955),f324(f324(f22(a102),x100951),f79(a102)))))),f324(x100955,x100954)),f324(f324(f120(x100953,x100952,x100955),x100951),x100954)) % 181.55/181.54 [5416]~E(f324(x54163,x54164),x54165)+E(f324(f324(f324(f72(x54161,x54162),x54163),x54164),x54165),x54163) % 181.55/181.54 [5855]E(f324(x58551,x58552),x58553)+~E(f324(f324(f324(f72(x58554,x58555),x58551),x58552),x58553),x58551) % 181.55/181.54 [5944]E(x59441,x59442)+~E(f324(f262(x59443,x59444),f324(f324(f259(x59443,x59444),x59445),x59441)),x59442) % 181.55/181.54 [5945]E(x59451,x59452)+~E(f324(f258(x59453,x59454),f324(f324(f259(x59453,x59454),x59451),x59455)),x59452) % 181.55/181.54 [6201]~E(x62013,f324(f324(f124(x62011),x62014),f324(f324(f145(x62011),x62012),x62015)))+P1(f324(f324(f326(x62011),x62012),f324(f167(x62011),x62013))) % 181.55/181.54 [6589]E(f324(f303(x65891,x65892,f324(f16(x65892,x65891),x65893)),x65894),f324(f324(f302(x65892),x65893),f191(f871(x65892,a859))))+~P1(f324(f324(f326(x65891),x65895),x65894)) % 181.55/181.54 [6659]E(f324(f324(f113(f871(x66591,a859)),f324(f167(x66591),x66592)),f324(f167(x66591),x66593)),f324(f167(x66591),x66594))+~E(f161(x66591,x66595,x66594),f324(f324(f259(f866(x66591),f866(x66591)),x66592),x66593)) % 181.55/181.54 [6761]~P105(x67612)+E(f324(f192(f866(x67611)),f324(f324(f142(x67611,x67612,x67613),x67614),x67615)),f324(a115,f324(f192(f866(x67611)),x67615))) % 181.55/181.54 [6773]~P105(x67732)+E(f324(f167(x67731),f324(f324(f142(x67731,x67732,x67733),x67734),x67735)),f324(f324(f302(x67731),x67734),f324(f167(x67731),x67735))) % 181.55/181.54 [7042]~P112(x70421)+E(f324(f324(f82(x70421),f324(f324(f82(x70421),x70422),x70423)),f324(f324(f82(x70421),x70424),x70425)),f324(f324(f82(x70421),f324(f324(f82(x70421),x70422),x70424)),f324(f324(f82(x70421),x70423),x70425))) % 181.55/181.54 [7043]~P112(x70431)+E(f324(f324(f81(x70431),f324(f324(f81(x70431),x70432),x70433)),f324(f324(f81(x70431),x70434),x70435)),f324(f324(f81(x70431),f324(f324(f81(x70431),x70432),x70434)),f324(f324(f81(x70431),x70433),x70435))) % 181.55/181.54 [7044]~P62(x70441)+E(f324(f324(f282(x70441),f324(f324(f82(x70441),x70442),x70443)),f324(f324(f82(x70441),x70444),x70445)),f324(f324(f82(x70441),f324(f324(f282(x70441),x70442),x70444)),f324(f324(f282(x70441),x70443),x70445))) % 181.55/181.54 [7058]~P105(x70581)+E(f298(x70581,f324(f324(f190(x70581),x70582),x70583),f324(f324(f189(x70581),x70584),x70585)),f324(f324(f104(f871(x70581,a859)),f298(x70581,x70582,x70584)),f298(x70581,x70583,x70585))) % 181.55/181.54 [7059]~P105(x70591)+E(f297(x70591,f324(f324(f190(x70591),x70592),x70593),f324(f324(f189(x70591),x70594),x70595)),f324(f324(f104(f871(x70591,a859)),f297(x70591,x70592,x70594)),f297(x70591,x70593,x70595))) % 181.55/181.54 [7060]~P105(x70601)+E(f295(x70601,f324(f324(f190(x70601),x70602),x70603),f324(f324(f189(x70601),x70604),x70605)),f324(f324(f104(f871(x70601,a859)),f295(x70601,x70602,x70604)),f295(x70601,x70603,x70605))) % 181.55/181.54 [7061]~P105(x70611)+E(f324(f324(f104(f871(x70611,a859)),f324(f294(x70611,x70612),x70613)),f324(f294(x70611,x70614),x70615)),f324(f294(x70611,f324(f324(f190(x70611),x70612),x70614)),f324(f324(f189(x70611),x70613),x70615))) % 181.55/181.54 [7175]~P1(f324(x71751,f400(x71753,x71752,x71751)))+P1(f324(x71751,f324(f324(f259(x71752,x71753),x71754),x71755))) % 181.55/181.54 [7262]~E(f324(x72623,x72624),f203(x72622))+E(f181(x72621,x72622,f324(f324(f324(f72(x72621,f869(x72622)),x72623),x72624),f324(f233(x72622),x72625))),f324(f324(f302(x72622),x72625),f181(x72621,x72622,x72623))) % 181.55/181.54 [7281]~E(x72812,f324(x72814,x72815))+P1(f324(f324(f326(x72811),x72812),f324(f303(x72813,x72811,x72814),f247(f871(x72813,a859))))) % 181.55/181.54 [7339]~E(f324(x73393,x73394),f203(x73392))+E(f324(f324(f22(f871(x73391,a859)),f179(x73391,x73392,x73393)),f324(f324(f302(x73391),x73394),x73395)),f324(f324(f22(f871(x73391,a859)),f179(x73391,x73392,x73393)),x73395)) % 181.55/181.54 [7358]~P17(x73583,x73582,x73584)+P17(x73581,x73582,f324(f324(f8(x73583,f871(x73582,x73582),x73581),x73584),x73585)) % 181.55/181.54 [7359]~P18(x73593,x73592,x73594)+P18(x73591,x73592,f324(f324(f8(x73593,f871(x73592,x73592),x73591),x73594),x73595)) % 181.55/181.54 [7500]~P27(x75001,x75002,x75003,x75004)+P27(x75001,x75002,x75003,f324(f324(f22(f871(x75001,a859)),x75004),x75005)) % 181.55/181.54 [7655]~P1(f324(f324(x76553,x76554),x76555))+P1(f324(f324(f263(x76551,x76552,a859),x76553),f324(f324(f259(x76551,x76552),x76554),x76555))) % 181.55/181.54 [7760]~P1(f324(x77602,x77604))+~E(f324(f324(f132(x77601),f324(f192(f866(x77601)),f172(x77601,x77602,x77603))),x77603),f324(f324(f145(x77601),x77604),x77605)) % 181.55/181.54 [7780]P27(x77801,x77802,x77803,x77804)+~P27(x77801,x77802,x77803,f324(f324(f113(f871(x77801,a859)),x77805),x77804)) % 181.55/181.54 [7781]P27(x77811,x77812,x77813,x77814)+~P27(x77811,x77812,x77813,f324(f324(f113(f871(x77811,a859)),x77814),x77815)) % 181.55/181.54 [7829]~P105(x78292)+E(f324(f324(f142(x78291,x78292,x78293),x78294),f144(x78291,x78292,x78293,x78295)),f144(x78291,x78292,x78293,f324(f324(f145(x78291),x78294),x78295))) % 181.55/181.54 [7991]~P30(x79911,f324(a115,x79912),f324(f324(f324(f93(x79911),x79913),f324(a25,x79914)),x79915))+P30(x79911,x79912,f324(f324(f324(f93(x79911),x79913),f324(f237(a861),f324(a28,x79914))),x79915)) % 181.55/181.54 [8122]P30(x81221,f324(a115,x81222),f324(f324(f324(f93(x81221),x81223),f324(a25,x81224)),x81225))+~P30(x81221,x81222,f324(f324(f324(f93(x81221),x81223),f324(f237(a861),f324(a28,x81224))),x81225)) % 181.55/181.54 [8151]~P17(x81512,x81511,x81513)+E(f324(f136(x81511,x81512,f324(f7(x81512,x81511,x81511),x81513),x81514),x81515),f324(f324(f64(x81512,x81511,x81513),x81514),f324(f167(x81512),x81515))) % 181.55/181.54 [8181]~E(f324(f324(f132(x81811),f324(f192(f866(x81811)),f172(x81811,x81812,x81813))),x81813),f324(f324(f145(x81811),x81814),x81815))+E(f324(f324(f124(x81811),f172(x81811,x81812,x81813)),f324(f324(f145(x81811),x81814),x81815)),x81813) % 181.55/181.54 [8207]P1(f324(f324(x82071,x82072),x82073))+~P1(f324(f324(f263(x82074,x82075,a859),x82071),f324(f324(f259(x82074,x82075),x82072),x82073))) % 181.55/181.54 [8271]~E(f324(f324(f173(x82711,x82712),x82715),x82713),f324(f233(x82712),x82714))+P1(f324(f324(f326(f870(x82711,x82712)),f324(f324(f259(x82711,x82712),x82713),x82714)),f324(f167(f870(x82711,x82712)),x82715))) % 181.55/181.54 [8682]P1(f324(f324(f238(f871(x86821,a859)),f324(f303(x86822,x86821,x86823),x86824)),f324(f303(x86822,x86821,x86823),x86825)))+~P1(f324(f324(f238(f871(x86822,a859)),x86824),x86825)) % 181.55/181.54 [8683]P1(f324(f324(f238(f871(x86831,a859)),f324(f304(x86831,x86832,x86833),x86834)),f324(f304(x86831,x86832,x86833),x86835)))+~P1(f324(f324(f238(f871(x86832,a859)),x86834),x86835)) % 181.55/181.54 [8763]E(x87631,f2(a102))+E(f324(f324(f265(x87632,x87633,x87632,f870(x87633,x87632)),f324(x87634,x87635)),f273(x87633,x87632,f324(f324(f22(a102),x87631),f79(a102)),x87634)),f324(f273(x87633,x87632,x87631,x87634),x87635)) % 181.55/181.54 [9277]E(f324(f233(x92771),f714(x92772,x92773,x92774,x92771,x92775)),f324(f324(f173(x92775,x92771),x92772),x92774))+~P1(f324(f324(f326(f870(x92775,x92771)),f324(f324(f259(x92775,x92771),x92774),x92773)),f324(f167(f870(x92775,x92771)),x92772))) % 181.55/181.54 [9324]~P1(f324(f324(f326(x93242),x93245),f324(f303(x93241,x93242,x93244),x93243)))+P1(f324(f324(f326(x93241),f324(f94(x93241,x93242,x93243,x93244),x93245)),x93243)) % 181.55/181.54 [9417]~P1(f324(f61(x94173),f324(f303(x94172,x94173,x94175),f247(f871(x94172,a859)))))+P1(f324(f61(x94171),f324(f303(x94172,x94171,f324(f324(f8(x94173,x94171,x94172),x94174),x94175)),f247(f871(x94172,a859))))) % 181.55/181.54 [9441]P1(f324(f324(f238(f871(f871(x94411,a859),a859)),f324(f303(f871(x94412,a859),f871(x94411,a859),f303(x94412,x94411,x94413)),f324(f301(x94412),x94414))),f324(f301(x94411),x94415)))+~P1(f324(f324(f238(f871(x94411,a859)),f324(f303(x94412,x94411,x94413),x94414)),x94415)) % 181.55/181.54 [9452]~P1(f324(f61(f869(x94521)),f324(f303(x94522,f869(x94521),x94523),f247(f871(x94522,a859)))))+P1(f324(f61(f869(x94521)),f324(f303(x94522,f869(x94521),f324(f324(f324(f72(x94522,f869(x94521)),x94523),x94524),f324(f233(x94521),x94525))),f247(f871(x94522,a859))))) % 181.55/181.54 [9515]E(x95151,x95152)+~P1(f324(f66(x95153,x95154,x95155,x95151,f191(f871(x95153,a859))),x95152)) % 181.55/181.54 [9532]E(f324(f324(f259(x95321,x95322),f501(x95323,x95324,x95325,x95322,x95321)),f506(x95323,x95324,x95325,x95322,x95321)),x95325)+~P1(f324(f324(f326(f870(x95321,x95322)),x95325),f324(f324(f261(x95321,x95322),x95324),x95323))) % 181.55/181.54 [9626]P1(f324(f324(f326(x96261),f501(x96262,x96263,x96264,x96265,x96261)),x96263))+~P1(f324(f324(f326(f870(x96261,x96265)),x96264),f324(f324(f261(x96261,x96265),x96263),x96262))) % 181.55/181.54 [9634]P1(f324(f324(f326(x96341),f516(x96342,x96343,x96344,x96345,x96341)),x96345))+P1(f324(f324(f238(f871(x96344,a859)),f324(f303(x96341,x96344,x96343),x96345)),x96342)) % 181.55/181.54 [9789]P1(f324(f324(f326(x97891),f506(x97892,x97893,x97894,x97891,x97895)),f324(x97892,f501(x97892,x97893,x97894,x97891,x97895))))+~P1(f324(f324(f326(f870(x97895,x97891)),x97894),f324(f324(f261(x97895,x97891),x97893),x97892))) % 181.55/181.54 [9814]P1(f324(f324(f326(f870(x98141,x98141)),f324(f324(f259(x98141,x98141),x98142),f616(x98143,x98144,x98145,x98142,x98141))),x98143))+~P1(f324(f324(f326(f870(x98141,x98141)),f324(f324(f259(x98141,x98141),x98142),x98145)),f324(f324(f184(f870(x98141,x98141),a859),f324(a115,x98144)),x98143))) % 181.55/181.54 [9815]P1(f324(f324(f326(f870(x98151,x98151)),f324(f324(f259(x98151,x98151),x98152),f617(x98153,x98154,x98155,x98152,x98151))),x98153))+~P1(f324(f324(f326(f870(x98151,x98151)),f324(f324(f259(x98151,x98151),x98152),x98155)),f324(f324(f184(f870(x98151,x98151),a859),f324(a115,x98154)),x98153))) % 181.55/181.54 [9833]~P1(f324(f324(f326(f870(f866(x98331),f866(x98331))),f324(f324(f259(f866(x98331),f866(x98331)),f324(f324(f145(x98331),x98332),x98335)),x98334)),f152(x98331,x98333)))+P1(f324(f324(f326(f870(x98331,x98331)),f324(f324(f259(x98331,x98331),x98332),f676(x98333,x98334,x98335,x98332,x98331))),x98333)) % 181.55/181.54 [9835]~P26(x98351,x98352,f324(f324(f302(f864(x98351)),f324(f324(f324(f93(x98351),f95(x98351,x98353,x98354)),x98355),x98353)),f191(f871(f864(x98351),a859))))+P26(x98351,x98352,f324(f324(f302(f864(x98351)),f324(f324(f324(f93(x98351),x98353),f32(x98354,x98355)),f95(x98351,x98353,f324(f73(a859,a859,a860,a319),x98354)))),f191(f871(f864(x98351),a859)))) % 181.55/181.54 [9856]~P1(f324(f324(f326(x98561),f324(x98563,f516(x98565,x98563,x98561,x98564,x98562))),x98565))+P1(f324(f324(f238(f871(x98561,a859)),f324(f303(x98562,x98561,x98563),x98564)),x98565)) % 181.55/181.54 [6274]P1(f324(x62742,x62744))+E(f172(x62741,x62742,f324(f324(f124(x62741),x62743),f324(f324(f145(x62741),x62744),x62745))),f172(x62741,x62742,x62743)) % 181.55/181.54 [6322]~P3(x63222)+E(f324(f324(f324(f22(f871(x63221,x63222)),x63223),x63224),x63225),f324(f324(f22(x63222),f324(x63223,x63225)),f324(x63224,x63225))) % 181.55/181.54 [6324]~P94(x63242)+E(f324(f324(f324(f104(f871(x63241,x63242)),x63243),x63244),x63245),f324(f324(f104(x63242),f324(x63243,x63245)),f324(x63244,x63245))) % 181.55/181.54 [6326]~P94(x63262)+E(f324(f324(f324(f113(f871(x63261,x63262)),x63263),x63264),x63265),f324(f324(f113(x63262),f324(x63263,x63265)),f324(x63264,x63265))) % 181.55/181.54 [6344]E(x63441,x63442)+E(f324(f324(f159(x63443),f324(f324(f153(x63443,x63444),x63441),x63445)),x63442),f324(f324(f159(x63443),x63444),x63442)) % 181.55/181.54 [6607]~E(x66074,f191(f871(x66073,a859)))+E(f324(f324(f22(f871(x66071,a859)),x66072),f324(f324(f41(x66073,f871(x66071,a859)),x66074),x66075)),x66072) % 181.55/181.54 [6608]~E(x66084,f191(f871(x66083,a859)))+E(f324(f324(f104(f871(x66081,a859)),x66082),f324(f324(f42(x66083,f871(x66081,a859)),x66084),x66085)),x66082) % 181.55/181.54 [6609]~E(x66094,f191(f871(x66093,a859)))+E(f324(f324(f113(f871(x66091,a859)),x66092),f324(f324(f41(x66093,f871(x66091,a859)),x66094),x66095)),x66092) % 181.55/181.54 [6623]~E(x66234,f191(f871(x66233,a859)))+E(f324(f324(f302(x66231),x66232),f324(f324(f41(x66233,f871(x66231,a859)),x66234),x66235)),f324(f324(f302(x66231),x66232),f191(f871(x66231,a859)))) % 181.55/181.54 [7406]E(f324(f324(f159(x74061),f324(f324(f148(x74062,x74061),x74063),x74064)),x74065),f324(x74063,f324(f324(f159(x74062),x74064),x74065)))+~P1(f324(f324(f239(a865),x74065),f324(f192(f866(x74062)),x74064))) % 181.55/181.54 [7472]E(f324(f324(f104(f871(x74721,a859)),f324(x74722,x74723)),f324(f324(f42(x74724,f871(x74721,a859)),x74725),x74722)),f324(f324(f42(x74724,f871(x74721,a859)),x74725),x74722))+~P1(f324(f324(f326(x74724),x74723),x74725)) % 181.55/181.54 [7473]E(f324(f324(f113(f871(x74731,a859)),f324(x74732,x74733)),f324(f324(f41(x74734,f871(x74731,a859)),x74735),x74732)),f324(f324(f41(x74734,f871(x74731,a859)),x74735),x74732))+~P1(f324(f324(f326(x74734),x74733),x74735)) % 181.55/181.54 [8068]~E(x80683,f191(f871(x80681,a859)))+E(f324(f324(f41(x80681,f871(x80682,a859)),x80683),f324(f324(f8(f871(x80682,a859),f871(x80682,a859),x80681),f324(f302(x80682),x80684)),x80685)),f191(f871(x80682,a859))) % 181.55/181.54 [8073]~P1(f324(f324(f326(x80734),x80733),x80735))+P1(f324(f324(f238(f871(x80731,a859)),f324(x80732,x80733)),f324(f324(f41(x80734,f871(x80731,a859)),x80735),x80732))) % 181.55/181.54 [8206]~E(f324(x82064,x82062),x82065)+P1(f324(f324(f326(x82061),x82062),f324(f304(x82061,x82063,x82064),f324(f324(f302(x82063),x82065),f191(f871(x82063,a859)))))) % 181.55/181.54 [8252]~P52(x82521,x82522,f324(f279(x82522,x82521),x82523))+E(f324(f324(f104(f871(x82521,a859)),f324(f278(x82522,x82521,x82523),x82524)),f324(f278(x82522,x82521,x82523),x82525)),f324(f278(x82522,x82521,x82523),f324(f324(f104(f871(x82522,a859)),x82524),x82525))) % 181.55/181.54 [8282]E(x82821,f2(a102))+E(f119(x82822,x82823,f324(x82824,f324(f324(f22(a102),x82821),f79(a102))),f324(f324(f7(x82822,a102,f867(x82823)),x82825),x82821)),f324(f202(x82822,x82823,x82824,x82825),x82821)) % 181.55/181.54 [8369]E(x83691,f191(f871(x83692,a859)))+E(f324(f324(f41(x83692,f871(x83693,a859)),x83691),f324(f324(f8(f871(x83693,a859),f871(x83693,a859),x83692),f324(f302(x83693),x83694)),x83695)),f324(f324(f302(x83693),x83694),f324(f324(f41(x83692,f871(x83693,a859)),x83691),x83695))) % 181.55/181.54 [8416]~P27(x84162,x84161,x84163,f247(f871(x84162,a859)))+E(f324(f324(f22(f871(x84161,a859)),f324(f303(x84162,x84161,x84163),x84164)),f324(f303(x84162,x84161,x84163),x84165)),f324(f303(x84162,x84161,x84163),f324(f324(f22(f871(x84162,a859)),x84164),x84165))) % 181.55/181.54 [8417]~P27(x84172,x84171,x84173,f247(f871(x84172,a859)))+E(f324(f324(f104(f871(x84171,a859)),f324(f303(x84172,x84171,x84173),x84174)),f324(f303(x84172,x84171,x84173),x84175)),f324(f303(x84172,x84171,x84173),f324(f324(f104(f871(x84172,a859)),x84174),x84175))) % 181.55/181.54 [8483]~P1(f324(f324(f67(x84831,x84832,x84835),x84833),x84834))+P1(f324(f324(f326(f870(x84831,x84832)),f324(f324(f259(x84831,x84832),x84833),x84834)),x84835)) % 181.55/181.54 [8516]P1(f324(f324(f326(x85161),x85162),f324(f255(x85163,x85161),x85164)))+~P1(f324(f324(f326(f870(x85163,x85161)),f324(f324(f259(x85163,x85161),x85165),x85162)),x85164)) % 181.55/181.54 [8518]P1(f324(f324(f326(x85181),x85182),f324(f257(x85181,x85183),x85184)))+~P1(f324(f324(f326(f870(x85181,x85183)),f324(f324(f259(x85181,x85183),x85182),x85185)),x85184)) % 181.55/181.54 [8666]P1(f324(f324(f67(x86661,x86662,x86663),x86664),x86665))+~P1(f324(f324(f326(f870(x86661,x86662)),f324(f324(f259(x86661,x86662),x86664),x86665)),x86663)) % 181.55/181.54 [8705]E(f324(x87051,x87052),x87053)+~P1(f324(f324(f326(x87054),x87052),f324(f304(x87054,x87055,x87051),f324(f324(f302(x87055),x87053),f191(f871(x87055,a859)))))) % 181.55/181.54 [8933]P1(f324(f324(f326(f870(x89331,x89332)),f324(f324(f259(x89331,x89332),x89333),x89334)),f324(f279(x89332,x89331),x89335)))+~P1(f324(f324(f326(f870(x89332,x89331)),f324(f324(f259(x89332,x89331),x89334),x89333)),x89335)) % 181.55/181.54 [8951]~P1(f324(f324(x89511,x89515),x89514))+P1(f324(f324(x89511,f324(f262(x89512,x89513),f324(f324(f259(x89512,x89513),x89514),x89515))),f324(f258(x89512,x89513),f324(f324(f259(x89512,x89513),x89514),x89515)))) % 181.55/181.54 [8981]~P1(f324(f324(f326(f870(x89812,x89811)),f324(f324(f259(x89812,x89811),x89814),x89813)),f324(f279(x89811,x89812),x89815)))+P1(f324(f324(f326(f870(x89811,x89812)),f324(f324(f259(x89811,x89812),x89813),x89814)),x89815)) % 181.55/181.54 [9015]~P1(f324(f324(f326(f870(x90153,x90151)),f324(f324(f259(x90153,x90151),x90155),x90152)),x90154))+P1(f324(f324(f326(x90151),x90152),f324(f278(x90153,x90151,x90154),f324(f324(f302(x90153),x90155),f191(f871(x90153,a859)))))) % 181.55/181.54 [9061]P1(f324(f324(f326(f870(x90611,x90612)),f324(f324(f259(x90611,x90612),x90613),x90614)),x90615))+~P1(f324(f324(f326(x90612),x90614),f324(f278(x90611,x90612,x90615),f324(f324(f302(x90611),x90613),f191(f871(x90611,a859)))))) % 181.55/181.54 [9081]E(f324(f324(f324(f72(x90811,f869(x90812)),f183(x90811,x90812,x90813,x90814)),x90815),f203(x90812)),f183(x90811,x90812,x90813,f324(f324(f22(f871(x90811,a859)),x90814),f324(f324(f302(x90811),x90815),f191(f871(x90811,a859))))))+~P1(f324(f324(f326(x90811),x90815),x90814)) % 181.55/181.54 [9154]~P72(x91541)+E(f324(f324(f6(a865,x91541),x91542),f295(a865,f324(f324(f81(a865),x91543),x91544),f324(f324(f81(a865),x91545),x91544))),f324(f324(f6(a865,x91541),f324(f324(f8(a865,x91541,a865),x91542),f324(f324(f7(a865,a865,a865),f81(a865)),x91544))),f295(a865,x91543,x91545))) % 181.55/181.54 [9173]~P72(x91731)+E(f324(f324(f6(a865,x91731),x91732),f324(f294(a865,f324(f324(f81(a865),x91733),x91734)),f324(f324(f81(a865),x91735),x91734))),f324(f324(f6(a865,x91731),f324(f324(f8(a865,x91731,a865),x91732),f324(f324(f7(a865,a865,a865),f81(a865)),x91734))),f324(f294(a865,x91733),x91735))) % 181.55/181.54 [9226]~P27(x92261,x92262,x92263,f247(f871(x92261,a859)))+E(f324(f324(f148(x92261,x92262),x92263),f324(f130(x92261,f324(f324(f8(a859,a859,x92261),a319),f324(a321,x92264))),x92265)),f324(f130(x92262,f324(f324(f8(a859,a859,x92262),a319),f324(a321,f324(x92263,x92264)))),f324(f324(f148(x92261,x92262),x92263),x92265))) % 181.55/181.54 [9242]~P27(x92421,x92422,x92423,f324(f324(f302(x92421),x92424),f324(f167(x92421),x92425)))+E(f324(f324(f148(x92421,x92422),x92423),f324(f130(x92421,f324(f324(f8(a859,a859,x92421),a319),f324(a321,x92424))),x92425)),f324(f130(x92422,f324(f324(f8(a859,a859,x92422),a319),f324(a321,f324(x92423,x92424)))),f324(f324(f148(x92421,x92422),x92423),x92425))) % 181.55/181.54 [9402]P1(f324(f324(f326(f870(f866(x94021),f866(x94021))),f324(f324(f259(f866(x94021),f866(x94021)),f324(f324(f145(x94021),x94022),x94023)),f324(f324(f145(x94021),x94024),x94023))),f151(x94021,x94025)))+~P1(f324(f324(f326(f870(x94021,x94021)),f324(f324(f259(x94021,x94021),x94022),x94024)),x94025)) % 181.55/181.54 [9527]E(f324(f324(f302(x95271),f832(x95272,x95273,x95274,x95275,x95271)),f833(x95272,x95273,x95274,x95275,x95271)),f324(f324(f302(x95271),x95274),x95273))+~P1(f324(f62(x95271,x95275,f324(f324(f302(x95271),x95274),x95273)),x95272)) % 181.55/181.54 [9528]E(f324(f324(f302(x95281),f834(x95282,x95283,x95284,x95285,x95281)),f835(x95282,x95283,x95284,x95285,x95281)),f324(f324(f302(x95281),x95284),x95283))+~P1(f324(f62(x95281,x95285,f324(f324(f302(x95281),x95284),x95283)),x95282)) % 181.55/181.54 [9612]P1(f324(f324(f326(x96121),f626(x96122,x96123,x96124,x96125,x96121)),x96124))+P1(f324(f324(f324(f42(x96121,f871(x96125,a859)),x96124),x96123),x96122)) % 181.55/181.54 [9617]P1(f324(f324(f326(x96171),f627(x96172,x96173,x96171,x96174,x96175)),x96173))+P1(f324(f324(f326(x96175),x96174),f324(f324(f42(x96171,f871(x96175,a859)),x96173),x96172))) % 181.55/181.54 [9625]P1(f324(f324(f326(x96251),f625(x96252,x96253,x96251,x96254,x96255)),x96253))+P1(f324(f324(f238(f871(x96255,a859)),x96254),f324(f324(f42(x96251,f871(x96255,a859)),x96253),x96252))) % 181.55/181.54 [9627]P1(f324(f324(x96271,f631(x96272,x96271,x96273,x96274,x96275)),x96272))+~P1(f324(f324(f324(f41(x96275,f871(x96274,a859)),x96273),x96271),x96272)) % 181.55/181.54 [9631]P1(f324(f324(f326(x96311),f631(x96312,x96313,x96314,x96315,x96311)),x96314))+~P1(f324(f324(f324(f41(x96311,f871(x96315,a859)),x96314),x96313),x96312)) % 181.55/181.54 [9642]P1(f324(f324(f326(x96421),f699(x96422,x96423,x96421,x96424,x96425)),x96423))+~P1(f324(f324(f326(x96425),x96424),f324(f324(f41(x96421,f871(x96425,a859)),x96423),x96422))) % 181.55/181.54 [9648]P1(f324(f324(f326(x96481),x96482),f324(x96483,f699(x96483,x96484,x96485,x96482,x96481))))+~P1(f324(f324(f326(x96481),x96482),f324(f324(f41(x96485,f871(x96481,a859)),x96484),x96483))) % 181.55/181.54 [9741]~P1(f324(f324(x97414,f626(x97415,x97414,x97413,x97412,x97411)),x97415))+P1(f324(f324(f324(f42(x97411,f871(x97412,a859)),x97413),x97414),x97415)) % 181.55/181.54 [9744]~P1(f324(f324(f326(x97441),x97442),f324(x97445,f627(x97445,x97444,x97443,x97442,x97441))))+P1(f324(f324(f326(x97441),x97442),f324(f324(f42(x97443,f871(x97441,a859)),x97444),x97445))) % 181.55/181.54 [9748]~P1(f324(f324(f238(f871(x97481,a859)),x97482),f324(x97485,f625(x97485,x97484,x97483,x97482,x97481))))+P1(f324(f324(f238(f871(x97481,a859)),x97482),f324(f324(f42(x97483,f871(x97481,a859)),x97484),x97485))) % 181.55/181.54 [9818]~P1(f324(f324(f326(x98181),f832(x98185,x98184,x98183,x98182,x98181)),f833(x98185,x98184,x98183,x98182,x98181)))+~P1(f324(f62(x98181,x98182,f324(f324(f302(x98181),x98183),x98184)),x98185)) % 181.55/181.54 [9819]~P1(f324(f324(f326(x98191),f834(x98195,x98194,x98193,x98192,x98191)),f835(x98195,x98194,x98193,x98192,x98191)))+~P1(f324(f62(x98191,x98192,f324(f324(f302(x98191),x98193),x98194)),x98195)) % 181.55/181.54 [9820]~P1(f324(f324(f326(f870(x98201,x98201)),f324(f324(f259(x98201,x98201),x98202),x98205)),f324(f324(f184(f870(x98201,x98201),a859),f324(a115,x98204)),x98203)))+P1(f324(f324(f326(f870(x98201,x98201)),f324(f324(f259(x98201,x98201),x98202),f618(x98203,x98204,x98205,x98202,x98201))),f324(f324(f184(f870(x98201,x98201),a859),x98204),x98203))) % 181.55/181.54 [9827]P1(f324(f66(x98271,x98271,x98272,f832(x98273,x98274,x98275,x98272,x98271),f833(x98273,x98274,x98275,x98272,x98271)),x98273))+~P1(f324(f62(x98271,x98272,f324(f324(f302(x98271),x98275),x98274)),x98273)) % 181.55/181.54 [9828]P1(f324(f66(x98281,x98281,x98282,f834(x98283,x98284,x98285,x98282,x98281),f835(x98283,x98284,x98285,x98282,x98281)),x98283))+~P1(f324(f62(x98281,x98282,f324(f324(f302(x98281),x98285),x98284)),x98283)) % 181.55/181.54 [9839]~P105(x98391)+P16(x98391,f324(f324(f148(x98392,x98391),x98393),f324(f130(x98392,f324(f324(f7(x98392,x98391,a859),f324(f324(f8(x98391,f871(x98391,a859),x98392),a321),x98393)),f324(x98394,x98395))),x98395))) % 181.55/181.54 [9880]~P1(f324(f324(f326(x98802),x98805),f324(f278(x98801,x98802,x98804),x98803)))+P1(f324(f324(f326(f870(x98801,x98802)),f324(f324(f259(x98801,x98802),f774(x98803,x98804,x98801,x98805,x98802)),x98805)),x98804)) % 181.55/181.54 [9881]~P1(f324(f324(f326(x98812),x98815),f324(f278(x98811,x98812,x98814),x98813)))+P1(f324(f324(f326(f870(x98811,x98812)),f324(f324(f259(x98811,x98812),f809(x98813,x98814,x98811,x98815,x98812)),x98815)),x98814)) % 181.55/181.54 [9901]~P1(f324(f324(f326(f870(x99011,x99011)),f324(f324(f259(x99011,x99011),x99015),x99014)),f324(f324(f184(f870(x99011,x99011),a859),f324(a115,x99013)),x99012)))+P1(f324(f324(f326(f870(x99011,x99011)),f324(f324(f259(x99011,x99011),f618(x99012,x99013,x99014,x99015,x99011)),x99014)),x99012)) % 181.55/181.54 [9904]~P1(f324(f324(f326(f870(x99041,x99041)),f324(f324(f259(x99041,x99041),x99045),x99044)),f324(f324(f184(f870(x99041,x99041),a859),f324(a115,x99043)),x99042)))+P1(f324(f324(f326(f870(x99041,x99041)),f324(f324(f259(x99041,x99041),f616(x99042,x99043,x99044,x99045,x99041)),x99044)),f324(f324(f184(f870(x99041,x99041),a859),x99043),x99042))) % 181.55/181.54 [9905]~P1(f324(f324(f326(f870(x99051,x99051)),f324(f324(f259(x99051,x99051),x99055),x99054)),f324(f324(f184(f870(x99051,x99051),a859),f324(a115,x99053)),x99052)))+P1(f324(f324(f326(f870(x99051,x99051)),f324(f324(f259(x99051,x99051),f617(x99052,x99053,x99054,x99055,x99051)),x99054)),f324(f324(f184(f870(x99051,x99051),a859),x99053),x99052))) % 181.55/181.54 [9906]~P1(f324(f324(f326(f870(f866(x99061),f866(x99061))),f324(f324(f259(f866(x99061),f866(x99061)),x99065),f324(f324(f145(x99061),x99064),x99063))),f152(x99061,x99062)))+P1(f324(f324(f326(f870(x99061,x99061)),f324(f324(f259(x99061,x99061),f674(x99062,x99063,x99064,x99065,x99061)),x99064)),x99062)) % 181.55/181.54 [7004]E(x70041,f203(x70042))+E(f179(x70043,x70042,f324(f324(f324(f72(x70043,f869(x70042)),x70044),x70045),x70041)),f324(f324(f302(x70043),x70045),f179(x70043,x70042,x70044))) % 181.55/181.54 [7493]~E(x74933,f191(f871(x74932,a859)))+E(f324(f324(f104(f871(x74931,a859)),f324(f324(f42(x74932,f871(x74931,a859)),x74933),x74934)),x74935),x74935) % 181.55/181.54 [7494]~E(x74943,f191(f871(x74942,a859)))+E(f324(f324(f113(f871(x74941,a859)),f324(f324(f41(x74942,f871(x74941,a859)),x74943),x74944)),x74945),x74945) % 181.55/181.54 [7846]~E(x78465,f203(x78462))+E(f179(x78461,x78462,f324(f324(f324(f72(x78461,f869(x78462)),x78463),x78464),x78465)),f324(f324(f22(f871(x78461,a859)),f179(x78461,x78462,x78463)),f324(f324(f302(x78461),x78464),f191(f871(x78461,a859))))) % 181.55/181.54 [7914]~E(x79143,f191(f871(x79142,a859)))+E(f324(f324(f22(f871(x79141,a859)),f324(f324(f42(x79142,f871(x79141,a859)),x79143),x79144)),x79145),f324(f324(f22(f871(x79141,a859)),f247(f871(x79141,a859))),x79145)) % 181.55/181.54 [8041]E(f324(f324(f153(x80411,f324(f324(f124(x80411),x80412),x80413)),x80414),x80415),f324(f324(f124(x80411),f324(f324(f153(x80411,x80412),x80414),x80415)),x80413))+~P1(f324(f324(f239(a865),x80414),f324(f192(f866(x80411)),x80412))) % 181.55/181.54 [8155]P1(f324(f324(f326(x81551),x81555),f324(f167(x81551),x81553)))+E(f324(f324(f173(x81551,x81552),f324(f324(f177(x81551,x81552),x81553),f324(f324(f148(x81551,x81552),x81554),x81553))),x81555),f203(x81552)) % 181.55/181.54 [8280]~P1(f324(f324(f326(x82801),x82805),f324(f167(x82801),x82803)))+E(f324(f324(f173(x82801,x82802),f324(f324(f177(x82801,x82802),x82803),f324(f324(f148(x82801,x82802),x82804),x82803))),x82805),f324(f233(x82802),f324(x82804,x82805))) % 181.55/181.54 [8321]E(f324(f324(f159(x83211),f324(f324(f148(a865,x83211),x83212),f133(a865,f324(f294(a865,x83213),x83214)))),x83215),f324(x83212,f324(f324(f81(a865),x83213),x83215)))+~P1(f324(f324(f239(a865),x83215),f324(f324(f22(a865),x83214),x83213))) % 181.55/181.54 [8335]E(x83351,f2(a102))+E(f122(x83352,x83353,f324(x83354,f324(f324(f22(a102),x83351),f79(a102))),f324(f324(f7(x83352,a102,f867(f869(x83353))),x83355),x83351)),f324(f200(x83352,x83353,x83354,x83355),x83351)) % 181.55/181.54 [8359]~E(x83593,f191(f871(x83591,a859)))+E(f324(f324(f41(x83591,f871(x83592,a859)),x83593),f324(f324(f8(f871(x83592,a859),f871(x83592,a859),x83591),f324(f113(f871(x83592,a859)),x83594)),x83595)),f191(f871(x83592,a859))) % 181.55/181.54 [8360]~E(x83603,f191(f871(x83601,a859)))+E(f324(f324(f42(x83601,f871(x83602,a859)),x83603),f324(f324(f8(f871(x83602,a859),f871(x83602,a859),x83601),f324(f22(f871(x83602,a859)),x83604)),x83605)),f247(f871(x83602,a859))) % 181.55/181.54 [8361]~E(x83613,f191(f871(x83611,a859)))+E(f324(f324(f42(x83611,f871(x83612,a859)),x83613),f324(f324(f8(f871(x83612,a859),f871(x83612,a859),x83611),f324(f104(f871(x83612,a859)),x83614)),x83615)),f247(f871(x83612,a859))) % 181.55/181.54 [8363]~P140(x83632)+E(f324(f324(f6(x83631,x83632),f324(f324(f8(x83632,x83632,x83631),f324(f82(x83632),x83633)),x83634)),x83635),f324(f324(f82(x83632),x83633),f324(f324(f6(x83631,x83632),x83634),x83635))) % 181.55/181.54 [8649]E(x86491,f191(f871(x86492,a859)))+E(f324(f324(f41(x86492,f871(x86493,a859)),x86491),f324(f324(f8(f871(x86493,a859),f871(x86493,a859),x86492),f324(f113(f871(x86493,a859)),x86494)),x86495)),f324(f324(f113(f871(x86493,a859)),x86494),f324(f324(f41(x86492,f871(x86493,a859)),x86491),x86495))) % 181.55/181.54 [8650]E(x86501,f191(f871(x86502,a859)))+E(f324(f324(f42(x86502,f871(x86503,a859)),x86501),f324(f324(f8(f871(x86503,a859),f871(x86503,a859),x86502),f324(f22(f871(x86503,a859)),x86504)),x86505)),f324(f324(f22(f871(x86503,a859)),x86504),f324(f324(f41(x86502,f871(x86503,a859)),x86501),x86505))) % 181.55/181.54 [8651]E(x86511,f191(f871(x86512,a859)))+E(f324(f324(f42(x86512,f871(x86513,a859)),x86511),f324(f324(f8(f871(x86513,a859),f871(x86513,a859),x86512),f324(f104(f871(x86513,a859)),x86514)),x86515)),f324(f324(f104(f871(x86513,a859)),x86514),f324(f324(f42(x86512,f871(x86513,a859)),x86511),x86515))) % 181.55/181.54 [8856]~P1(f324(f324(f239(a865),f324(x88564,x88562)),f324(x88564,x88563)))+P1(f324(f324(f326(f870(x88561,x88561)),f324(f324(f259(x88561,x88561),x88562),x88563)),f147(x88561,f324(f324(f145(f871(x88561,a865)),x88564),x88565)))) % 181.55/181.54 [9117]~P27(x91172,x91171,x91173,f324(f324(f113(f871(x91172,a859)),x91174),x91175))+E(f324(f324(f104(f871(x91171,a859)),f324(f303(x91172,x91171,x91173),f324(f324(f22(f871(x91172,a859)),x91174),x91175))),f324(f303(x91172,x91171,x91173),f324(f324(f22(f871(x91172,a859)),x91175),x91174))),f191(f871(x91171,a859))) % 181.55/181.54 [9367]~P27(x93673,x93671,x93675,f247(f871(x93673,a859)))+E(f324(f73(x93671,x93672,x93673,f324(f73(x93673,x93672,x93671,x93674),f94(x93673,x93671,f247(f871(x93673,a859)),x93675))),x93675),x93674) % 181.55/181.54 [9397]~P1(f324(f324(f238(f871(x93973,a859)),f324(f278(x93971,x93973,x93974),x93972)),x93975))+P1(f324(f324(f238(f871(x93971,a859)),x93972),f324(f80(f871(x93971,a859)),f324(f278(x93973,x93971,f324(f279(x93971,x93973),x93974)),f324(f80(f871(x93973,a859)),x93975))))) % 181.55/181.54 [9426]~P27(x94261,x94262,x94263,f324(f324(f302(x94261),x94264),x94265))+~P1(f324(f324(f326(x94262),f324(x94263,x94264)),f324(f303(x94261,x94262,x94263),f324(f324(f22(f871(x94261,a859)),x94265),f324(f324(f302(x94261),x94264),f191(f871(x94261,a859))))))) % 181.55/181.54 [9478]P1(f324(f324(f238(f871(x94781,a859)),f324(f278(x94782,x94781,x94783),x94784)),x94785))+~P1(f324(f324(f238(f871(x94782,a859)),x94784),f324(f80(f871(x94782,a859)),f324(f278(x94781,x94782,f324(f279(x94782,x94781),x94783)),f324(f80(f871(x94781,a859)),x94785))))) % 181.55/181.54 [9556]~P83(x95561)+P1(f324(f324(f238(x95561),f324(f75(x95561),f324(f324(f22(x95561),f324(f324(f81(x95561),x95562),x95563)),f324(f324(f81(x95561),x95564),x95565)))),f324(f324(f81(x95561),f324(f75(x95561),f324(f324(f22(x95561),x95562),x95564))),f324(f75(x95561),f324(f324(f22(x95561),x95563),x95565))))) % 181.55/181.54 [9663]P1(f324(f324(f326(x96631),f728(x96632,x96633,x96634,x96631,x96635)),x96634))+P1(f324(f324(f238(f871(x96635,a859)),f324(f324(f41(x96631,f871(x96635,a859)),x96634),x96633)),x96632)) % 181.55/181.54 [9858]~P1(f324(f324(f238(f871(x98581,a859)),f324(x98584,f728(x98585,x98584,x98583,x98582,x98581))),x98585))+P1(f324(f324(f238(f871(x98581,a859)),f324(f324(f41(x98582,f871(x98581,a859)),x98583),x98584)),x98585)) % 181.55/181.54 [8463]E(f324(f324(f124(x84631),x84632),f324(f324(f153(x84631,x84633),f324(f324(f22(a865),x84634),f324(f192(f866(x84631)),x84632))),x84635)),f324(f324(f153(x84631,f324(f324(f124(x84631),x84632),x84633)),x84634),x84635))+P1(f324(f324(f239(a865),x84634),f324(f192(f866(x84631)),x84632))) % 181.55/181.54 [8490]~P137(x84901)+E(f324(f324(f81(x84901),f324(f324(f82(x84901),x84902),x84903)),f324(f324(f81(x84901),f324(f324(f82(x84901),x84904),x84903)),x84905)),f324(f324(f81(x84901),f324(f324(f82(x84901),f324(f324(f81(x84901),x84902),x84904)),x84903)),x84905)) % 181.55/181.54 [9071]~P140(x90711)+E(f324(f160(x90711),f324(f324(f148(x90712,x90711),f324(f324(f8(x90711,x90711,x90712),f324(f82(x90711),x90713)),x90714)),x90715)),f324(f324(f82(x90711),x90713),f324(f160(x90711),f324(f324(f148(x90712,x90711),x90714),x90715)))) % 181.55/181.54 [9241]E(f324(f192(f866(x92411)),f324(f324(f170(x92411),f324(f324(f189(a865),f324(f192(f866(x92411)),x92412)),f324(f192(f866(x92413)),x92414))),x92412)),f324(f192(f866(x92413)),f324(f324(f170(x92413),f324(f324(f189(a865),f324(f192(f866(x92411)),x92412)),f324(f192(f866(x92413)),x92414))),x92414)))+P1(f324(x92415,f324(f324(f177(x92411,x92413),x92412),x92414))) % 181.55/181.54 [9490]~P140(x94902)+E(f324(f324(f6(x94901,x94902),f324(f324(f7(x94901,x94902,x94902),f324(f324(f8(x94902,f871(x94902,x94902),x94901),f82(x94902)),x94903)),x94904)),x94905),f324(f324(f82(x94902),f324(f324(f6(x94901,x94902),x94903),x94905)),x94904)) % 181.55/181.54 [9491]~P63(x94912)+E(f324(f324(f6(x94911,x94912),f324(f324(f7(x94911,x94912,x94912),f324(f324(f8(x94912,f871(x94912,x94912),x94911),f282(x94912)),x94913)),x94914)),x94915),f324(f324(f282(x94912),f324(f324(f6(x94911,x94912),x94913),x94915)),x94914)) % 181.55/181.54 [9498]~P68(x94982)+E(f324(f324(f9(x94981,x94982),f324(f324(f18(x94981,x94982,x94982),f324(f324(f8(x94982,f871(x94982,x94982),x94981),f82(x94982)),x94983)),x94984)),x94985),f324(f324(f82(x94982),f324(f324(f9(x94981,x94982),x94983),x94985)),f324(f324(f9(x94981,x94982),x94984),x94985))) % 181.55/181.54 [9499]~P5(x94992)+E(f324(f324(f6(x94991,x94992),f324(f324(f18(x94991,x94992,x94992),f324(f324(f8(x94992,f871(x94992,x94992),x94991),f22(x94992)),x94993)),x94994)),x94995),f324(f324(f22(x94992),f324(f324(f6(x94991,x94992),x94993),x94995)),f324(f324(f6(x94991,x94992),x94994),x94995))) % 181.55/181.54 [9500]~P72(x95002)+E(f324(f324(f6(x95001,x95002),f324(f324(f18(x95001,x95002,x95002),f324(f324(f8(x95002,f871(x95002,x95002),x95001),f81(x95002)),x95003)),x95004)),x95005),f324(f324(f81(x95002),f324(f324(f6(x95001,x95002),x95003),x95005)),f324(f324(f6(x95001,x95002),x95004),x95005))) % 181.55/181.54 [9540]~E(x95403,f191(f871(x95401,a859)))+E(f324(f324(f41(x95401,f871(x95402,a859)),x95403),f324(f324(f7(x95401,f871(x95402,a859),f871(x95402,a859)),f324(f324(f8(f871(x95402,a859),f871(f871(x95402,a859),f871(x95402,a859)),x95401),f113(f871(x95402,a859))),x95404)),x95405)),f191(f871(x95402,a859))) % 181.55/181.54 [9541]~E(x95413,f191(f871(x95411,a859)))+E(f324(f324(f42(x95411,f871(x95412,a859)),x95413),f324(f324(f7(x95411,f871(x95412,a859),f871(x95412,a859)),f324(f324(f8(f871(x95412,a859),f871(f871(x95412,a859),f871(x95412,a859)),x95411),f22(f871(x95412,a859))),x95414)),x95415)),f247(f871(x95412,a859))) % 181.55/181.54 [9542]~E(x95423,f191(f871(x95421,a859)))+E(f324(f324(f42(x95421,f871(x95422,a859)),x95423),f324(f324(f7(x95421,f871(x95422,a859),f871(x95422,a859)),f324(f324(f8(f871(x95422,a859),f871(f871(x95422,a859),f871(x95422,a859)),x95421),f104(f871(x95422,a859))),x95424)),x95425)),f247(f871(x95422,a859))) % 181.55/181.54 [9564]E(x95641,f191(f871(x95642,a859)))+E(f324(f324(f41(x95642,f871(x95643,a859)),x95641),f324(f324(f7(x95642,f871(x95643,a859),f871(x95643,a859)),f324(f324(f8(f871(x95643,a859),f871(f871(x95643,a859),f871(x95643,a859)),x95642),f113(f871(x95643,a859))),x95644)),x95645)),f324(f324(f113(f871(x95643,a859)),f324(f324(f41(x95642,f871(x95643,a859)),x95641),x95644)),x95645)) % 181.55/181.54 [9565]E(x95651,f191(f871(x95652,a859)))+E(f324(f324(f42(x95652,f871(x95653,a859)),x95651),f324(f324(f7(x95652,f871(x95653,a859),f871(x95653,a859)),f324(f324(f8(f871(x95653,a859),f871(f871(x95653,a859),f871(x95653,a859)),x95652),f22(f871(x95653,a859))),x95654)),x95655)),f324(f324(f22(f871(x95653,a859)),f324(f324(f42(x95652,f871(x95653,a859)),x95651),x95654)),x95655)) % 181.55/181.54 [9566]E(x95661,f191(f871(x95662,a859)))+E(f324(f324(f42(x95662,f871(x95663,a859)),x95661),f324(f324(f7(x95662,f871(x95663,a859),f871(x95663,a859)),f324(f324(f8(f871(x95663,a859),f871(f871(x95663,a859),f871(x95663,a859)),x95662),f104(f871(x95663,a859))),x95664)),x95665)),f324(f324(f104(f871(x95663,a859)),f324(f324(f42(x95662,f871(x95663,a859)),x95661),x95664)),x95665)) % 181.55/181.54 [9124]~P1(f324(f324(f238(a865),x91241),x91244))+E(f324(f324(f22(a865),f324(f324(f81(a865),f324(f324(f82(a865),x91241),x91242)),x91243)),f324(f324(f81(a865),f324(f324(f82(a865),x91244),x91242)),x91245)),f324(f324(f22(a865),x91243),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x91244),x91241)),x91242)),x91245))) % 181.55/181.54 [9723]~P140(x97231)+E(f324(f160(x97231),f324(f324(f148(x97232,x97231),f324(f324(f7(x97232,x97231,x97231),f324(f324(f8(x97231,f871(x97231,x97231),x97232),f82(x97231)),x97233)),x97234)),x97235)),f324(f324(f82(x97231),f324(f160(x97231),f324(f324(f148(x97232,x97231),x97233),x97235))),x97234)) % 181.55/181.54 [9729]~P5(x97291)+E(f324(f160(x97291),f324(f324(f148(x97292,x97291),f324(f324(f18(x97292,x97291,x97291),f324(f324(f8(x97291,f871(x97291,x97291),x97292),f22(x97291)),x97293)),x97294)),x97295)),f324(f324(f22(x97291),f324(f160(x97291),f324(f324(f148(x97292,x97291),x97293),x97295))),f324(f160(x97291),f324(f324(f148(x97292,x97291),x97294),x97295)))) % 181.55/181.54 [9730]~P72(x97301)+E(f324(f160(x97301),f324(f324(f148(x97302,x97301),f324(f324(f18(x97302,x97301,x97301),f324(f324(f8(x97301,f871(x97301,x97301),x97302),f81(x97301)),x97303)),x97304)),x97305)),f324(f324(f81(x97301),f324(f160(x97301),f324(f324(f148(x97302,x97301),x97303),x97305))),f324(f160(x97301),f324(f324(f148(x97302,x97301),x97304),x97305)))) % 181.55/181.54 [9871]P1(f324(x98711,f324(f324(f177(x98712,x98713),x98714),x98715)))+~P1(f324(x98711,f324(f324(f177(x98712,x98713),f324(f324(f170(x98712),f324(f324(f189(a865),f324(f192(f866(x98712)),x98714)),f324(f192(f866(x98713)),x98715))),x98714)),f324(f324(f170(x98713),f324(f324(f189(a865),f324(f192(f866(x98712)),x98714)),f324(f192(f866(x98713)),x98715))),x98715)))) % 181.55/181.54 [10104]~P1(f324(f324(f326(f870(x101042,x101041)),f324(f324(f259(x101042,x101041),x101044),x101045)),f324(f279(x101041,x101042),x101043)))+P1(f324(f324(f248(x101041,x101042,f324(f324(f7(x101041,f871(f870(x101041,x101042),a859),f871(x101042,a859)),f324(f324(f8(f871(x101042,f871(f871(f870(x101041,x101042),a859),a859)),f871(f871(f870(x101041,x101042),a859),f871(x101042,a859)),x101041),f7(x101042,f871(f870(x101041,x101042),a859),a859)),f324(f324(f8(f871(x101042,f870(x101041,x101042)),f871(x101042,f871(f871(f870(x101041,x101042),a859),a859)),x101041),f324(f8(f870(x101041,x101042),f871(f871(f870(x101041,x101042),a859),a859),x101042),f326(f870(x101041,x101042)))),f259(x101041,x101042)))),x101043)),x101044),x101045)) % 181.55/181.54 [10113]P1(f324(f324(f326(f870(x101131,x101132)),f324(f324(f259(x101131,x101132),x101133),x101134)),f324(f279(x101132,x101131),x101135)))+~P1(f324(f324(f248(x101132,x101131,f324(f324(f7(x101132,f871(f870(x101132,x101131),a859),f871(x101131,a859)),f324(f324(f8(f871(x101131,f871(f871(f870(x101132,x101131),a859),a859)),f871(f871(f870(x101132,x101131),a859),f871(x101131,a859)),x101132),f7(x101131,f871(f870(x101132,x101131),a859),a859)),f324(f324(f8(f871(x101131,f870(x101132,x101131)),f871(x101131,f871(f871(f870(x101132,x101131),a859),a859)),x101132),f324(f8(f870(x101132,x101131),f871(f871(f870(x101132,x101131),a859),a859),x101131),f326(f870(x101132,x101131)))),f259(x101132,x101131)))),x101135)),x101133),x101134)) % 181.55/181.54 [9365]~P1(f324(f324(f238(a865),x93654),x93651))+E(f324(f324(f22(a865),f324(f324(f81(a865),f324(f324(f82(a865),x93651),x93652)),x93653)),f324(f324(f81(a865),f324(f324(f82(a865),x93654),x93652)),x93655)),f324(f324(f22(a865),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x93651),x93654)),x93652)),x93653)),x93655)) % 181.55/181.54 [10121]P26(x101211,x101212,f324(f303(a862,f864(x101211),f324(f324(f18(a862,f871(x101211,f871(a860,a859)),f864(x101211)),f324(f324(f18(a862,a861,f871(f871(x101211,f871(a860,a859)),f864(x101211))),f324(f324(f8(f871(x101211,f871(a860,a859)),f871(a861,f871(f871(x101211,f871(a860,a859)),f864(x101211))),a862),f93(x101211)),x101213)),a25)),x101214)),x101215))+~P26(x101211,f324(f324(f113(f871(f864(x101211),a859)),x101212),f324(f303(a862,f864(x101211),f324(f324(f18(a862,f871(x101211,f871(a860,a859)),f864(x101211)),f324(f324(f18(a862,a861,f871(f871(x101211,f871(a860,a859)),f864(x101211))),f324(f324(f8(f871(x101211,f871(a860,a859)),f871(a861,f871(f871(x101211,f871(a860,a859)),f864(x101211))),a862),f93(x101211)),x101213)),a25)),x101214)),x101215)),f324(f303(a862,f864(x101211),f324(f324(f18(a862,f871(x101211,f871(a860,a859)),f864(x101211)),f324(f324(f18(a862,a861,f871(f871(x101211,f871(a860,a859)),f864(x101211))),f324(f324(f8(f871(x101211,f871(a860,a859)),f871(a861,f871(f871(x101211,f871(a860,a859)),f864(x101211))),a862),f93(x101211)),x101213)),f324(f324(f8(f869(a861),a861,a862),f237(a861)),a28))),x101214)),x101215)) % 181.55/181.54 [5224]E(x52241,x52242)+~E(f30(x52243,x52244,x52241),f30(x52245,x52246,x52242)) % 181.55/181.54 [5225]E(x52251,x52252)+~E(f30(x52253,x52251,x52254),f30(x52255,x52252,x52256)) % 181.55/181.54 [5226]E(x52261,x52262)+~E(f30(x52261,x52263,x52264),f30(x52262,x52265,x52266)) % 181.55/181.54 [5227]E(x52271,x52272)+~E(f29(x52273,x52274,x52271),f29(x52275,x52276,x52272)) % 181.55/181.54 [5228]E(x52281,x52282)+~E(f29(x52283,x52281,x52284),f29(x52285,x52282,x52286)) % 181.55/181.54 [5229]E(x52291,x52292)+~E(f29(x52291,x52293,x52294),f29(x52292,x52295,x52296)) % 181.55/181.54 [6650]E(f324(f180(x66501,x66502,x66503,x66504),x66505),f324(f233(x66502),x66506))+~E(f324(x66504,x66505),f324(f233(x66502),x66506)) % 181.55/181.54 [6793]E(f324(f235(f869(x67931),x67932,f203(x67931),x67933),f324(x67934,x67935)),f324(x67933,x67936))+~E(f324(x67934,x67935),f324(f233(x67932),x67936)) % 181.55/181.54 [8306]~P21(x83065,x83061,x83062,x83066)+E(f324(f73(x83061,x83061,x83061,f324(x83062,x83063)),f324(x83062,x83064)),f324(f73(x83061,x83061,x83061,f324(x83062,x83064)),f324(x83062,x83063))) % 181.55/181.54 [8535]~P54(x85354,x85355,x85352,x85351,x85356)+E(f324(x85351,f324(x85352,x85353)),x85353) % 181.55/181.54 [8703]P27(x87031,x87032,x87033,x87034)+~P27(x87031,x87035,f324(f73(x87032,x87035,x87031,x87036),x87033),x87034) % 181.55/181.54 [8790]~P27(x87904,x87902,f324(f73(x87901,x87902,x87904,x87903),x87905),x87906)+P27(x87901,x87902,x87903,f324(f303(x87904,x87901,x87905),x87906)) % 181.55/181.54 [9501]P1(f324(f61(x95011),x95012))+~P1(f324(f66(x95011,x95013,x95014,x95015,x95012),x95016)) % 181.55/181.54 [9510]~P1(f324(f324(f326(x95104),x95103),f289(x95104,x95101,x95105,x95102,x95106)))+P1(f324(f324(x95101,x95102),x95103)) % 181.55/181.54 [9511]~P1(f324(f324(f326(x95114),x95113),f292(x95114,x95115,x95111,x95112,x95116)))+P1(f324(f324(x95111,x95112),x95113)) % 181.55/181.54 [9512]~P1(f324(f324(f326(x95124),x95122),f289(x95124,x95125,x95121,x95126,x95123)))+P1(f324(f324(x95121,x95122),x95123)) % 181.55/181.54 [9513]~P1(f324(f324(f326(x95134),x95132),f292(x95134,x95131,x95135,x95136,x95133)))+P1(f324(f324(x95131,x95132),x95133)) % 181.55/181.54 [5723]E(x57231,x57232)+~E(f324(f324(f259(x57233,x57234),x57235),x57231),f324(f324(f259(x57233,x57234),x57236),x57232)) % 181.55/181.54 [5725]E(x57251,x57252)+~E(f324(f324(f259(x57253,x57254),x57251),x57255),f324(f324(f259(x57253,x57254),x57252),x57256)) % 181.55/181.54 [5849]~P18(x58495,x58496,x58491)+E(f324(f324(x58491,x58492),f324(f324(x58491,x58493),x58494)),f324(f324(x58491,x58493),f324(f324(x58491,x58492),x58494))) % 181.55/181.54 [7243]~P34(x72434,x72431,f324(f324(f145(x72434),x72432),x72435),f324(f324(f145(x72434),x72433),x72436))+P1(f324(f324(x72431,x72432),x72433)) % 181.55/181.54 [7607]P34(x76071,x76072,x76073,x76074)+~P34(x76071,x76072,f324(f324(f145(x76071),x76075),x76073),f324(f324(f145(x76071),x76076),x76074)) % 181.55/181.54 [8640]~P54(x86405,x86401,x86402,x86406,x86404)+P1(f324(f324(f326(x86401),f324(x86402,x86403)),x86404)) % 181.55/181.54 [8818]E(f324(f77(x88181,x88182,x88183,x88184,x88185),x88186),f324(x88183,x88186))+P1(f324(f324(f326(x88181),x88186),x88185)) % 181.55/181.54 [8839]~E(x88393,f324(f324(f145(x88391),x88395),x88396))+P1(f324(f324(f326(f870(f866(x88391),f866(x88391))),f324(f324(f259(f866(x88391),f866(x88391)),x88392),f324(f324(f124(x88391),x88392),x88393))),f141(x88391,x88394))) % 181.55/181.54 [8845]E(f324(f77(x88451,x88452,x88453,x88454,x88455),x88456),f324(x88454,x88456))+~P1(f324(f324(f326(x88451),x88456),x88455)) % 181.55/181.54 [8852]E(f324(f182(x88521,x88522,x88523,x88524,x88525),x88526),f324(x88523,x88526))+P1(f324(f324(f326(x88521),x88526),f324(f167(x88521),x88524))) % 181.55/181.54 [9075]~P36(x90751,x90752,x90753,x90755,x90756)+P36(x90751,x90752,x90753,f324(f324(f170(x90751),x90754),x90755),f324(f324(f170(x90752),x90754),x90756)) % 181.55/181.54 [9076]~P36(x90761,x90762,x90763,x90765,x90766)+P36(x90761,x90762,x90763,f324(f324(f132(x90761),x90764),x90765),f324(f324(f132(x90762),x90764),x90766)) % 181.55/181.54 [9576]~P25(x95764,x95762,x95765,x95763,x95766,x95761)+E(f324(x95761,f191(f871(x95762,a859))),x95763) % 181.55/181.54 [9821]~E(f324(x98214,f324(f258(x98211,x98213),x98215)),f324(x98216,f324(f258(x98211,x98213),x98215)))+E(f324(f264(x98211,x98212,x98213,x98213,x98214,f34(x98213)),x98215),f324(f264(x98211,x98212,x98213,x98213,x98216,f34(x98213)),x98215)) % 181.55/181.54 [9822]~E(f324(x98224,f324(f262(x98221,x98222),x98225)),f324(x98226,f324(f262(x98221,x98222),x98225)))+E(f324(f264(x98221,x98221,x98222,x98223,f34(x98221),x98224),x98225),f324(f264(x98221,x98221,x98222,x98223,f34(x98221),x98226),x98225)) % 181.55/181.54 [9867]~E(f324(f264(x98672,x98676,x98673,x98673,x98671,f34(x98673)),x98674),f324(f264(x98672,x98676,x98673,x98673,x98675,f34(x98673)),x98674))+E(f324(x98671,f324(f258(x98672,x98673),x98674)),f324(x98675,f324(f258(x98672,x98673),x98674))) % 181.55/181.54 [9868]~E(f324(f264(x98682,x98682,x98683,x98686,f34(x98682),x98681),x98684),f324(f264(x98682,x98682,x98683,x98686,f34(x98682),x98685),x98684))+E(f324(x98681,f324(f262(x98682,x98683),x98684)),f324(x98685,f324(f262(x98682,x98683),x98684))) % 181.55/181.54 [8744]P1(f324(f324(f326(x87441),x87442),x87443))+~P1(f324(f324(f326(f870(x87441,x87444)),f324(f324(f259(x87441,x87444),x87442),x87445)),f324(f324(f261(x87441,x87444),x87443),x87446))) % 181.55/181.54 [8760]P1(f324(f324(f326(x87601),x87602),f324(x87603,x87604)))+~P1(f324(f324(f326(f870(x87605,x87601)),f324(f324(f259(x87605,x87601),x87604),x87602)),f324(f324(f261(x87605,x87601),x87606),x87603))) % 181.55/181.54 [8848]~E(f324(f192(f866(x88481)),x88484),f324(f192(f866(x88482)),x88485))+E(f182(x88481,x88482,x88483,x88484,f324(f324(f124(x88482),x88485),x88486)),f182(x88481,x88482,x88483,x88484,x88485)) % 181.55/181.54 [8849]~E(f324(f192(f866(x88491)),x88494),f324(f192(f866(x88492)),x88496))+E(f182(x88491,x88492,x88493,f324(f324(f124(x88491),x88494),x88495),x88496),f182(x88491,x88492,x88493,x88494,x88496)) % 181.55/181.54 [9095]P1(f324(f324(f326(x90951),x90954),f179(x90951,x90952,x90956)))+E(f180(x90951,x90952,f324(f324(f324(f72(x90951,f869(x90952)),x90953),x90954),f324(f233(x90952),x90955)),x90956),f324(f324(f324(f72(x90951,f869(x90952)),f180(x90951,x90952,x90953,x90956)),x90954),f324(f233(x90952),x90955))) % 181.55/181.54 [9194]P1(f324(f324(f326(f870(x91941,x91941)),f324(f324(f259(x91941,x91941),f324(x91942,x91943)),f324(x91942,x91944))),x91945))+~P1(f324(f324(f326(f870(x91946,x91946)),f324(f324(f259(x91946,x91946),x91943),x91944)),f324(f324(f280(x91941,x91946),x91945),x91942))) % 181.55/181.54 [9213]~P1(f324(f324(f326(f870(x92134,x92134)),f324(f324(f259(x92134,x92134),f324(x92136,x92132)),f324(x92136,x92133))),x92135))+P1(f324(f324(f326(f870(x92131,x92131)),f324(f324(f259(x92131,x92131),x92132),x92133)),f324(f324(f280(x92134,x92131),x92135),x92136))) % 181.55/181.54 [9870]E(f324(f324(f259(x98701,x98702),f655(x98703,x98704,x98705,x98706,x98702,x98701)),f656(x98703,x98704,x98705,x98706,x98702,x98701)),x98706)+~P1(f324(f324(f326(f870(x98701,x98702)),x98706),f324(f324(f281(x98701,x98705,x98702),x98704),x98703))) % 181.55/181.54 [10068]~P1(f324(f324(f326(f870(x100681,x100686)),x100685),f324(f324(f281(x100681,x100682,x100686),x100684),x100683)))+P1(f324(f324(f326(f870(x100681,x100682)),f324(f324(f259(x100681,x100682),f655(x100683,x100684,x100682,x100685,x100686,x100681)),f657(x100683,x100684,x100682,x100685,x100686,x100681))),x100684)) % 181.55/181.54 [10069]~P1(f324(f324(f326(f870(x100696,x100692)),x100695),f324(f324(f281(x100696,x100691,x100692),x100694),x100693)))+P1(f324(f324(f326(f870(x100691,x100692)),f324(f324(f259(x100691,x100692),f657(x100693,x100694,x100691,x100695,x100692,x100696)),f656(x100693,x100694,x100691,x100695,x100692,x100696))),x100693)) % 181.55/181.54 [6116]~E(x61166,x61164)+E(f324(f324(f324(f324(f72(x61161,x61162),x61163),x61164),x61165),x61166),x61165) % 181.55/181.54 [6164]E(x61641,x61642)+E(f324(f324(f324(f324(f72(x61643,x61644),x61645),x61642),x61646),x61641),f324(x61645,x61641)) % 181.55/181.54 [7675]~P6(x76752)+E(f324(f324(f41(x76751,x76752),x76753),f324(f324(f7(x76751,x76754,x76752),x76755),x76756)),f324(f324(f324(f41(x76751,f871(x76754,x76752)),x76753),x76755),x76756)) % 181.55/181.54 [7676]~P6(x76762)+E(f324(f324(f42(x76761,x76762),x76763),f324(f324(f7(x76761,x76764,x76762),x76765),x76766)),f324(f324(f324(f42(x76761,f871(x76764,x76762)),x76763),x76765),x76766)) % 181.55/181.54 [8445]E(f324(f324(f41(x84451,f871(x84452,a859)),x84453),f324(f324(f8(f871(x84452,a859),f871(x84452,a859),x84451),f324(f302(x84452),x84454)),x84455)),f324(f324(f302(x84452),x84454),f324(f324(f41(x84451,f871(x84452,a859)),x84453),x84455)))+~P1(f324(f324(f326(x84451),x84456),x84453)) % 181.55/181.54 [8894]~P6(x88942)+E(f324(f324(f41(x88941,x88942),x88943),f324(f324(f8(f871(x88944,x88942),x88942,x88941),f324(f41(x88944,x88942),x88945)),f324(f7(x88944,x88941,x88942),x88946))),f324(f324(f41(x88944,x88942),x88945),f324(f324(f8(f871(x88941,x88942),x88942,x88944),f324(f41(x88941,x88942),x88943)),x88946))) % 181.55/181.54 [8895]~P6(x88952)+E(f324(f324(f42(x88951,x88952),x88953),f324(f324(f8(f871(x88954,x88952),x88952,x88951),f324(f42(x88954,x88952),x88955)),f324(f7(x88954,x88951,x88952),x88956))),f324(f324(f42(x88954,x88952),x88955),f324(f324(f8(f871(x88951,x88952),x88952,x88954),f324(f42(x88951,x88952),x88953)),x88956))) % 181.55/181.54 [9104]P1(f324(f324(f326(x91041),x91042),f324(f167(x91041),x91043)))+~P1(f324(f324(f326(f870(x91044,x91041)),f324(f324(f259(x91044,x91041),x91045),x91042)),f324(f167(f870(x91044,x91041)),f324(f324(f177(x91044,x91041),x91046),x91043)))) % 181.55/181.54 [9105]P1(f324(f324(f326(x91051),x91052),f324(f167(x91051),x91053)))+~P1(f324(f324(f326(f870(x91051,x91054)),f324(f324(f259(x91051,x91054),x91052),x91055)),f324(f167(f870(x91051,x91054)),f324(f324(f177(x91051,x91054),x91053),x91056)))) % 181.55/181.54 [9210]P1(f324(f324(f238(f871(x92101,a859)),f324(f278(x92102,x92101,x92103),x92104)),x92105))+~P1(f324(f324(f238(f871(f870(x92102,x92101),a859)),x92103),f324(f324(f261(x92102,x92101),x92106),f324(f16(f871(x92101,a859),x92102),x92105)))) % 181.55/181.54 [9214]~P28(x92144,x92142,x92145,f247(f871(x92144,a859)),f247(f871(x92142,a859)))+E(f324(f324(f42(x92141,f871(x92142,a859)),x92143),f324(f324(f8(f871(x92144,a859),f871(x92142,a859),x92141),f303(x92144,x92142,x92145)),x92146)),f324(f303(x92144,x92142,x92145),f324(f324(f42(x92141,f871(x92144,a859)),x92143),x92146))) % 181.55/181.54 [9401]P1(f324(f324(f326(f870(f866(x94011),f866(x94011))),f324(f324(f259(f866(x94011),f866(x94011)),f324(f324(f145(x94011),x94012),x94013)),f324(f324(f145(x94011),x94014),x94015))),f141(x94011,x94016)))+~P1(f324(f324(f326(f870(x94011,x94011)),f324(f324(f259(x94011,x94011),x94012),x94014)),x94016)) % 181.55/181.54 [9866]E(f324(f324(f259(x98661,x98662),f564(x98663,x98664,x98665,x98662,x98661,x98666)),f566(x98663,x98664,x98665,x98662,x98661,x98666)),x98666)+P1(f324(f324(f326(x98665),x98664),f324(f324(f263(x98661,x98662,f871(x98665,a859)),x98663),x98666))) % 181.55/181.54 [9872]E(f324(f324(f259(x98721,x98722),f563(x98723,x98724,x98722,x98721,x98725,x98726)),f565(x98723,x98724,x98722,x98721,x98725,x98726)),x98723)+~P1(f324(f324(f326(x98726),x98725),f324(f324(f263(x98721,x98722,f871(x98726,a859)),x98724),x98723))) % 181.55/181.54 [10028]P1(f324(f324(f326(x100281),x100282),f324(f324(x100283,f563(x100284,x100283,x100285,x100286,x100282,x100281)),f565(x100284,x100283,x100285,x100286,x100282,x100281))))+~P1(f324(f324(f326(x100281),x100282),f324(f324(f263(x100286,x100285,f871(x100281,a859)),x100283),x100284))) % 181.55/181.54 [10046]~P1(f324(f324(f326(x100461),x100462),f324(f324(x100465,f564(x100465,x100462,x100461,x100464,x100463,x100466)),f566(x100465,x100462,x100461,x100464,x100463,x100466))))+P1(f324(f324(f326(x100461),x100462),f324(f324(f263(x100463,x100464,f871(x100461,a859)),x100465),x100466))) % 181.55/181.54 [7789]P1(f324(f324(f326(x77891),x77894),x77896))+E(f183(x77891,x77892,f324(f324(f324(f72(x77891,f869(x77892)),x77893),x77894),x77895),x77896),f183(x77891,x77892,x77893,x77896)) % 181.55/181.54 [7869]P1(f324(f324(f326(x78691),x78694),x78696))+E(f324(f303(x78691,x78692,f324(f324(f324(f72(x78691,x78692),x78693),x78694),x78695)),x78696),f324(f303(x78691,x78692,x78693),x78696)) % 181.55/181.54 [7898]P1(f324(f324(f326(x78981),x78984),f324(f167(x78981),x78986)))+E(f324(f324(f148(x78981,x78982),f324(f324(f324(f72(x78981,x78982),x78983),x78984),x78985)),x78986),f324(f324(f148(x78981,x78982),x78983),x78986)) % 181.55/181.54 [8351]E(x83511,x83512)+E(f324(f324(f153(x83513,f324(f324(f153(x83513,x83514),x83511),x83515)),x83512),x83516),f324(f324(f153(x83513,f324(f324(f153(x83513,x83514),x83512),x83516)),x83511),x83515)) % 181.55/181.54 [8900]~P1(f324(f324(f326(x89003),x89006),x89005))+E(f324(f324(f302(x89001),x89002),f324(f303(x89003,x89001,x89004),f324(f324(f22(f871(x89003,a859)),x89005),f324(f324(f302(x89003),x89006),f191(f871(x89003,a859)))))),f324(f303(x89003,x89001,f324(f324(f324(f72(x89003,x89001),x89004),x89006),x89002)),x89005)) % 181.55/181.54 [9685]E(f182(x96851,x96852,x96853,f324(f324(f124(x96851),x96854),f324(f324(f145(x96851),x96855),f116(x96851))),x96856),f324(f324(f324(f72(x96851,f869(x96852)),f182(x96851,x96852,x96853,x96854,x96856)),x96855),f324(f233(x96852),f324(f324(f159(x96852),x96856),f324(f192(f866(x96851)),x96854)))))+~P1(f324(f324(f239(a865),f324(f192(f866(x96851)),x96854)),f324(f192(f866(x96852)),x96856))) % 181.55/181.54 [8684]~E(x86843,x86846)+E(f324(f324(f173(x86841,x86842),f324(f324(f145(f870(x86841,x86842)),f324(f324(f259(x86841,x86842),x86843),x86844)),x86845)),x86846),f324(f233(x86842),x86844)) % 181.55/181.54 [8714]E(x87141,x87142)+E(f324(f324(f173(x87143,x87144),f324(f324(f145(f870(x87143,x87144)),f324(f324(f259(x87143,x87144),x87141),x87145)),x87146)),x87142),f324(f324(f173(x87143,x87144),x87146),x87142)) % 181.55/181.54 [8974]~P1(f324(f324(x89744,x89745),x89746))+P1(f324(f324(f324(f324(f113(f871(x89741,f871(x89742,a859))),x89743),x89744),x89745),x89746)) % 181.55/181.54 [8976]~P1(f324(f324(x89763,x89765),x89766))+P1(f324(f324(f324(f324(f113(f871(x89761,f871(x89762,a859))),x89763),x89764),x89765),x89766)) % 181.55/181.54 [9263]P1(f324(f324(x92631,x92632),x92633))+~P1(f324(f324(f324(f324(f104(f871(x92634,f871(x92635,a859))),x92636),x92631),x92632),x92633)) % 181.55/181.54 [9264]P1(f324(f324(x92641,x92642),x92643))+~P1(f324(f324(f324(f324(f104(f871(x92644,f871(x92645,a859))),x92641),x92646),x92642),x92643)) % 181.55/181.54 [9707]~P68(x97072)+E(f324(f324(f9(x97071,x97072),f324(f324(f7(x97071,f871(x97073,a859),x97072),f324(f324(f8(f871(x97073,x97072),f871(f871(x97073,a859),x97072),x97071),f9(x97073,x97072)),x97074)),x97075)),x97076),f324(f324(f9(f870(x97071,x97073),x97072),f324(f263(x97071,x97073,x97072),x97074)),f324(f324(f261(x97071,x97073),x97076),f324(f16(f871(x97073,a859),x97071),x97075)))) % 181.55/181.54 [9708]~P72(x97082)+E(f324(f324(f6(x97081,x97082),f324(f324(f7(x97081,f871(x97083,a859),x97082),f324(f324(f8(f871(x97083,x97082),f871(f871(x97083,a859),x97082),x97081),f6(x97083,x97082)),x97084)),x97085)),x97086),f324(f324(f6(f870(x97081,x97083),x97082),f324(f263(x97081,x97083,x97082),x97084)),f324(f324(f261(x97081,x97083),x97086),f324(f16(f871(x97083,a859),x97081),x97085)))) % 181.55/181.54 [9848]~P72(x98482)+E(f324(f324(f6(x98481,x98482),f324(f324(f7(x98481,f871(x98483,a859),x98482),f324(f324(f8(f871(x98483,x98482),f871(f871(x98483,a859),x98482),x98481),f6(x98483,x98482)),f324(f7(x98483,x98481,x98482),x98484))),x98485)),x98486),f324(f324(f6(x98483,x98482),f324(f324(f7(x98483,f871(x98481,a859),x98482),f324(f324(f8(f871(x98481,x98482),f871(f871(x98481,a859),x98482),x98483),f6(x98481,x98482)),x98484)),x98486)),x98485)) % 181.55/181.54 [9545]~P1(f324(f324(f326(x95451),x95455),x95454))+E(f324(f324(f324(f72(x95451,f869(x95452)),f183(x95451,x95452,x95453,f324(f324(f22(f871(x95451,a859)),x95454),f324(f324(f302(x95451),x95455),f191(f871(x95451,a859)))))),x95455),x95456),f183(x95451,x95452,f324(f324(f324(f72(x95451,f869(x95452)),x95453),x95455),x95456),x95454)) % 181.55/181.54 [10124]~P1(f324(f324(f326(f870(x101241,x101242)),f324(f324(f259(x101241,x101242),x101245),x101246)),f324(f324(f104(f871(f870(x101241,x101242),a859)),x101243),x101244)))+P1(f324(f324(f324(f324(f104(f871(x101241,f871(x101242,a859))),f324(f324(f7(x101241,f871(f870(x101241,x101242),a859),f871(x101242,a859)),f324(f324(f8(f871(x101242,f871(f871(f870(x101241,x101242),a859),a859)),f871(f871(f870(x101241,x101242),a859),f871(x101242,a859)),x101241),f7(x101242,f871(f870(x101241,x101242),a859),a859)),f324(f324(f8(f871(x101242,f870(x101241,x101242)),f871(x101242,f871(f871(f870(x101241,x101242),a859),a859)),x101241),f324(f8(f870(x101241,x101242),f871(f871(f870(x101241,x101242),a859),a859),x101242),f326(f870(x101241,x101242)))),f259(x101241,x101242)))),x101243)),f324(f324(f7(x101241,f871(f870(x101241,x101242),a859),f871(x101242,a859)),f324(f324(f8(f871(x101242,f871(f871(f870(x101241,x101242),a859),a859)),f871(f871(f870(x101241,x101242),a859),f871(x101242,a859)),x101241),f7(x101242,f871(f870(x101241,x101242),a859),a859)),f324(f324(f8(f871(x101242,f870(x101241,x101242)),f871(x101242,f871(f871(f870(x101241,x101242),a859),a859)),x101241),f324(f8(f870(x101241,x101242),f871(f871(f870(x101241,x101242),a859),a859),x101242),f326(f870(x101241,x101242)))),f259(x101241,x101242)))),x101244)),x101245),x101246)) % 181.55/181.54 [10125]~P1(f324(f324(f326(f870(x101251,x101252)),f324(f324(f259(x101251,x101252),x101255),x101256)),f324(f324(f113(f871(f870(x101251,x101252),a859)),x101253),x101254)))+P1(f324(f324(f324(f324(f113(f871(x101251,f871(x101252,a859))),f324(f324(f7(x101251,f871(f870(x101251,x101252),a859),f871(x101252,a859)),f324(f324(f8(f871(x101252,f871(f871(f870(x101251,x101252),a859),a859)),f871(f871(f870(x101251,x101252),a859),f871(x101252,a859)),x101251),f7(x101252,f871(f870(x101251,x101252),a859),a859)),f324(f324(f8(f871(x101252,f870(x101251,x101252)),f871(x101252,f871(f871(f870(x101251,x101252),a859),a859)),x101251),f324(f8(f870(x101251,x101252),f871(f871(f870(x101251,x101252),a859),a859),x101252),f326(f870(x101251,x101252)))),f259(x101251,x101252)))),x101253)),f324(f324(f7(x101251,f871(f870(x101251,x101252),a859),f871(x101252,a859)),f324(f324(f8(f871(x101252,f871(f871(f870(x101251,x101252),a859),a859)),f871(f871(f870(x101251,x101252),a859),f871(x101252,a859)),x101251),f7(x101252,f871(f870(x101251,x101252),a859),a859)),f324(f324(f8(f871(x101252,f870(x101251,x101252)),f871(x101252,f871(f871(f870(x101251,x101252),a859),a859)),x101251),f324(f8(f870(x101251,x101252),f871(f871(f870(x101251,x101252),a859),a859),x101252),f326(f870(x101251,x101252)))),f259(x101251,x101252)))),x101254)),x101255),x101256)) % 181.55/181.54 [10131]P1(f324(f324(f326(f870(x101311,x101312)),f324(f324(f259(x101311,x101312),x101313),x101314)),f324(f324(f104(f871(f870(x101311,x101312),a859)),x101315),x101316)))+~P1(f324(f324(f324(f324(f104(f871(x101311,f871(x101312,a859))),f324(f324(f7(x101311,f871(f870(x101311,x101312),a859),f871(x101312,a859)),f324(f324(f8(f871(x101312,f871(f871(f870(x101311,x101312),a859),a859)),f871(f871(f870(x101311,x101312),a859),f871(x101312,a859)),x101311),f7(x101312,f871(f870(x101311,x101312),a859),a859)),f324(f324(f8(f871(x101312,f870(x101311,x101312)),f871(x101312,f871(f871(f870(x101311,x101312),a859),a859)),x101311),f324(f8(f870(x101311,x101312),f871(f871(f870(x101311,x101312),a859),a859),x101312),f326(f870(x101311,x101312)))),f259(x101311,x101312)))),x101315)),f324(f324(f7(x101311,f871(f870(x101311,x101312),a859),f871(x101312,a859)),f324(f324(f8(f871(x101312,f871(f871(f870(x101311,x101312),a859),a859)),f871(f871(f870(x101311,x101312),a859),f871(x101312,a859)),x101311),f7(x101312,f871(f870(x101311,x101312),a859),a859)),f324(f324(f8(f871(x101312,f870(x101311,x101312)),f871(x101312,f871(f871(f870(x101311,x101312),a859),a859)),x101311),f324(f8(f870(x101311,x101312),f871(f871(f870(x101311,x101312),a859),a859),x101312),f326(f870(x101311,x101312)))),f259(x101311,x101312)))),x101316)),x101313),x101314)) % 181.55/181.54 [10132]P1(f324(f324(f326(f870(x101321,x101322)),f324(f324(f259(x101321,x101322),x101323),x101324)),f324(f324(f113(f871(f870(x101321,x101322),a859)),x101325),x101326)))+~P1(f324(f324(f324(f324(f113(f871(x101321,f871(x101322,a859))),f324(f324(f7(x101321,f871(f870(x101321,x101322),a859),f871(x101322,a859)),f324(f324(f8(f871(x101322,f871(f871(f870(x101321,x101322),a859),a859)),f871(f871(f870(x101321,x101322),a859),f871(x101322,a859)),x101321),f7(x101322,f871(f870(x101321,x101322),a859),a859)),f324(f324(f8(f871(x101322,f870(x101321,x101322)),f871(x101322,f871(f871(f870(x101321,x101322),a859),a859)),x101321),f324(f8(f870(x101321,x101322),f871(f871(f870(x101321,x101322),a859),a859),x101322),f326(f870(x101321,x101322)))),f259(x101321,x101322)))),x101325)),f324(f324(f7(x101321,f871(f870(x101321,x101322),a859),f871(x101322,a859)),f324(f324(f8(f871(x101322,f871(f871(f870(x101321,x101322),a859),a859)),f871(f871(f870(x101321,x101322),a859),f871(x101322,a859)),x101321),f7(x101322,f871(f870(x101321,x101322),a859),a859)),f324(f324(f8(f871(x101322,f870(x101321,x101322)),f871(x101322,f871(f871(f870(x101321,x101322),a859),a859)),x101321),f324(f8(f870(x101321,x101322),f871(f871(f870(x101321,x101322),a859),a859),x101322),f326(f870(x101321,x101322)))),f259(x101321,x101322)))),x101326)),x101323),x101324)) % 181.55/181.54 [10119]~P1(f324(f324(f326(f870(x101192,x101193)),f324(f324(f259(x101192,x101193),x101195),x101196)),f324(f324(f41(x101191,f871(f870(x101192,x101193),a859)),f247(f871(x101191,a859))),x101194)))+P1(f324(f324(f324(f324(f41(x101191,f871(x101192,f871(x101193,a859))),f247(f871(x101191,a859))),f324(f324(f8(f871(f870(x101192,x101193),a859),f871(x101192,f871(x101193,a859)),x101191),f324(f7(x101192,f871(f870(x101192,x101193),a859),f871(x101193,a859)),f324(f324(f8(f871(x101193,f871(f871(f870(x101192,x101193),a859),a859)),f871(f871(f870(x101192,x101193),a859),f871(x101193,a859)),x101192),f7(x101193,f871(f870(x101192,x101193),a859),a859)),f324(f324(f8(f871(x101193,f870(x101192,x101193)),f871(x101193,f871(f871(f870(x101192,x101193),a859),a859)),x101192),f324(f8(f870(x101192,x101193),f871(f871(f870(x101192,x101193),a859),a859),x101193),f326(f870(x101192,x101193)))),f259(x101192,x101193))))),x101194)),x101195),x101196)) % 181.55/181.54 [10120]~P1(f324(f324(f326(f870(x101202,x101203)),f324(f324(f259(x101202,x101203),x101205),x101206)),f324(f324(f42(x101201,f871(f870(x101202,x101203),a859)),f247(f871(x101201,a859))),x101204)))+P1(f324(f324(f324(f324(f42(x101201,f871(x101202,f871(x101203,a859))),f247(f871(x101201,a859))),f324(f324(f8(f871(f870(x101202,x101203),a859),f871(x101202,f871(x101203,a859)),x101201),f324(f7(x101202,f871(f870(x101202,x101203),a859),f871(x101203,a859)),f324(f324(f8(f871(x101203,f871(f871(f870(x101202,x101203),a859),a859)),f871(f871(f870(x101202,x101203),a859),f871(x101203,a859)),x101202),f7(x101203,f871(f870(x101202,x101203),a859),a859)),f324(f324(f8(f871(x101203,f870(x101202,x101203)),f871(x101203,f871(f871(f870(x101202,x101203),a859),a859)),x101202),f324(f8(f870(x101202,x101203),f871(f871(f870(x101202,x101203),a859),a859),x101203),f326(f870(x101202,x101203)))),f259(x101202,x101203))))),x101204)),x101205),x101206)) % 181.55/181.54 [10128]P1(f324(f324(f326(f870(x101281,x101282)),f324(f324(f259(x101281,x101282),x101283),x101284)),f324(f324(f41(x101285,f871(f870(x101281,x101282),a859)),f247(f871(x101285,a859))),x101286)))+~P1(f324(f324(f324(f324(f41(x101285,f871(x101281,f871(x101282,a859))),f247(f871(x101285,a859))),f324(f324(f8(f871(f870(x101281,x101282),a859),f871(x101281,f871(x101282,a859)),x101285),f324(f7(x101281,f871(f870(x101281,x101282),a859),f871(x101282,a859)),f324(f324(f8(f871(x101282,f871(f871(f870(x101281,x101282),a859),a859)),f871(f871(f870(x101281,x101282),a859),f871(x101282,a859)),x101281),f7(x101282,f871(f870(x101281,x101282),a859),a859)),f324(f324(f8(f871(x101282,f870(x101281,x101282)),f871(x101282,f871(f871(f870(x101281,x101282),a859),a859)),x101281),f324(f8(f870(x101281,x101282),f871(f871(f870(x101281,x101282),a859),a859),x101282),f326(f870(x101281,x101282)))),f259(x101281,x101282))))),x101286)),x101283),x101284)) % 181.55/181.54 [10129]P1(f324(f324(f326(f870(x101291,x101292)),f324(f324(f259(x101291,x101292),x101293),x101294)),f324(f324(f42(x101295,f871(f870(x101291,x101292),a859)),f247(f871(x101295,a859))),x101296)))+~P1(f324(f324(f324(f324(f42(x101295,f871(x101291,f871(x101292,a859))),f247(f871(x101295,a859))),f324(f324(f8(f871(f870(x101291,x101292),a859),f871(x101291,f871(x101292,a859)),x101295),f324(f7(x101291,f871(f870(x101291,x101292),a859),f871(x101292,a859)),f324(f324(f8(f871(x101292,f871(f871(f870(x101291,x101292),a859),a859)),f871(f871(f870(x101291,x101292),a859),f871(x101292,a859)),x101291),f7(x101292,f871(f870(x101291,x101292),a859),a859)),f324(f324(f8(f871(x101292,f870(x101291,x101292)),f871(x101292,f871(f871(f870(x101291,x101292),a859),a859)),x101291),f324(f8(f870(x101291,x101292),f871(f871(f870(x101291,x101292),a859),a859),x101292),f326(f870(x101291,x101292)))),f259(x101291,x101292))))),x101296)),x101293),x101294)) % 181.55/181.54 [7354]E(f324(x73541,f324(x73542,x73543)),f324(x73544,x73543))+~E(f324(f73(x73545,x73546,x73547,x73541),x73542),x73544) % 181.55/181.54 [9575]~P24(x95753,x95754,x95751,x95755,x95756,x95757)+E(f324(f324(x95751,x95752),x95752),x95752) % 181.55/181.54 [9946]~E(f324(f235(f869(x99467),x99461,f203(x99467),x99465),f324(x99464,x99463)),f324(f233(x99467),x99462))+E(f324(f233(x99461),f663(x99462,x99463,x99464,x99465,x99466,x99467,x99461)),f324(x99464,x99463)) % 181.55/181.54 [9947]~E(f324(f235(f869(x99476),x99477,f203(x99476),x99471),f324(x99474,x99473)),f324(f233(x99476),x99472))+E(f324(x99471,f663(x99472,x99473,x99474,x99471,x99475,x99476,x99477)),f324(f233(x99476),x99472)) % 181.55/181.54 [5946]~E(f324(f324(f148(x59461,x59465),x59466),x59462),f324(f324(f148(x59463,x59465),x59467),x59464))+E(f324(f192(f866(x59461)),x59462),f324(f192(f866(x59463)),x59464)) % 181.55/181.54 [7431]E(x74311,x74312)+~E(f324(f324(f324(f72(x74313,f869(x74314)),x74315),x74316),f324(f233(x74314),x74311)),f324(f324(f324(f72(x74313,f869(x74314)),x74317),x74316),f324(f233(x74314),x74312))) % 181.55/181.54 [8383]E(f324(x83831,f324(x83832,x83833)),f324(x83834,x83833))+~E(f324(f73(x83835,x83836,x83837,x83831),x83832),f324(f73(x83836,x83836,x83837,f34(x83836)),x83834)) % 181.55/181.54 [8733]~P36(x87334,x87335,x87331,f324(f324(f145(x87334),x87332),x87336),f324(f324(f145(x87335),x87333),x87337))+P1(f324(f324(x87331,x87332),x87333)) % 181.55/181.54 [9111]P36(x91111,x91112,x91113,x91114,x91115)+~P36(x91111,x91112,x91113,f324(f324(f145(x91111),x91116),x91114),f324(f324(f145(x91112),x91117),x91115)) % 181.55/181.54 [9745]P1(f324(f324(x97451,x97452),f517(x97453,x97452,x97454,x97451)))+~P1(f324(f324(f260(x97455,x97456,x97457,x97451,x97454),x97452),x97453)) % 181.55/181.54 [9766]P1(f324(f324(x97661,f517(x97662,x97663,x97661,x97664)),x97662))+~P1(f324(f324(f260(x97665,x97666,x97667,x97664,x97661),x97663),x97662)) % 181.55/181.54 [5989]E(x59891,x59892)+~E(f324(f324(f324(f93(x59893),x59894),x59895),x59891),f324(f324(f324(f93(x59893),x59896),x59897),x59892)) % 181.55/181.54 [5990]E(x59901,x59902)+~E(f324(f324(f324(f93(x59903),x59904),x59901),x59905),f324(f324(f324(f93(x59903),x59906),x59902),x59907)) % 181.55/181.54 [5991]E(x59911,x59912)+~E(f324(f324(f324(f93(x59913),x59911),x59914),x59915),f324(f324(f324(f93(x59913),x59912),x59916),x59917)) % 181.55/181.54 [8854]~P22(x88546,x88541,x88543,x88547)+E(f324(f73(x88541,x88541,x88542,f324(x88543,x88544)),f324(f73(x88541,x88541,x88542,f324(x88543,x88544)),x88545)),f324(f73(x88541,x88541,x88542,f324(x88543,x88544)),x88545)) % 181.55/181.54 [9217]~P36(x92173,x92172,x92174,f324(f324(f148(x92171,x92173),x92175),x92176),x92177)+P36(x92171,x92172,f324(f324(f8(x92173,f871(x92172,a859),x92171),x92174),x92175),x92176,x92177) % 181.55/181.54 [9238]P36(x92381,x92382,x92383,f324(f324(f148(x92384,x92381),x92385),x92386),x92387)+~P36(x92384,x92382,f324(f324(f8(x92381,f871(x92382,a859),x92384),x92383),x92385),x92386,x92387) % 181.55/181.54 [9665]E(f182(x96651,x96652,f324(f324(f324(f72(x96651,f869(x96652)),x96653),x96654),f324(f233(x96652),x96655)),x96656,x96657),f324(f324(f324(f72(x96651,f869(x96652)),f182(x96651,x96652,x96653,x96656,x96657)),x96654),f324(f233(x96652),x96655)))+P1(f324(f324(f326(x96651),x96654),f324(f167(x96651),x96656))) % 181.55/181.54 [8853]~P1(f324(f324(f326(x88531),x88532),f324(f324(x88535,x88536),x88537)))+P1(f324(f324(f326(x88531),x88532),f324(f324(f263(x88533,x88534,f871(x88531,a859)),x88535),f324(f324(f259(x88533,x88534),x88536),x88537)))) % 181.55/181.54 [9139]P1(f324(f324(f324(x91391,x91392),x91393),x91394))+~P1(f324(f324(f324(f263(x91395,x91396,f871(x91397,a859)),x91391),f324(f324(f259(x91395,x91396),x91392),x91393)),x91394)) % 181.55/181.54 [9278]P1(f324(f324(f326(x92781),f324(f324(x92782,x92783),x92784)),f324(f303(f870(x92785,x92786),x92781,f324(f263(x92785,x92786,x92781),x92782)),x92787)))+~P1(f324(f324(f326(f870(x92785,x92786)),f324(f324(f259(x92785,x92786),x92783),x92784)),x92787)) % 181.55/181.54 [9623]P1(f324(f324(f326(f870(f866(x96231),f866(x96231))),f324(f324(f259(f866(x96231),f866(x96231)),f324(f324(f124(x96231),x96232),f324(f324(f145(x96231),x96233),x96234))),f324(f324(f124(x96231),x96232),f324(f324(f145(x96231),x96235),x96236)))),f141(x96231,x96237)))+~P1(f324(f324(f326(f870(x96231,x96231)),f324(f324(f259(x96231,x96231),x96233),x96235)),x96237)) % 181.55/181.54 [9687]~P36(x96871,x96873,x96874,x96876,f324(f324(f148(x96872,x96873),x96875),x96877))+P36(x96871,x96872,f324(f324(f7(x96871,f871(x96872,x96873),f871(x96872,a859)),f324(f324(f8(f871(x96873,a859),f871(f871(x96872,x96873),f871(x96872,a859)),x96871),f8(x96873,a859,x96872)),x96874)),x96875),x96876,x96877) % 181.55/181.54 [9770]P36(x97701,x97702,x97703,x97704,f324(f324(f148(x97705,x97702),x97706),x97707))+~P36(x97701,x97705,f324(f324(f7(x97701,f871(x97705,x97702),f871(x97705,a859)),f324(f324(f8(f871(x97702,a859),f871(f871(x97705,x97702),f871(x97705,a859)),x97701),f8(x97702,a859,x97705)),x97703)),x97706),x97704,x97707) % 181.55/181.54 [9131]E(x91311,x91312)+E(f324(f324(f324(f72(x91313,x91314),f324(f324(f324(f72(x91313,x91314),x91315),x91311),x91316)),x91312),x91317),f324(f324(f324(f72(x91313,x91314),f324(f324(f324(f72(x91313,x91314),x91315),x91312),x91317)),x91311),x91316)) % 181.55/181.54 [9376]E(f182(x93761,x93762,f324(f324(f324(f72(x93761,f869(x93762)),x93763),x93764),f324(f233(x93762),x93765)),x93766,x93767),f182(x93761,x93762,x93763,x93766,x93767))+~P1(f324(f324(f326(x93761),x93764),f324(f167(x93761),f324(f324(f170(x93761),f324(f192(f866(x93762)),x93767)),x93766)))) % 181.55/181.54 [9698]E(f182(x96981,x96982,f324(f324(f324(f72(x96981,f869(x96982)),x96983),x96984),f324(f233(x96982),x96985)),x96986,x96987),f324(f324(f324(f72(x96981,f869(x96982)),f182(x96981,x96982,x96983,x96986,x96987)),x96984),f324(f233(x96982),x96985)))+P1(f324(f324(f326(x96981),x96984),f324(f167(x96981),f324(f324(f170(x96981),f324(f192(f866(x96982)),x96987)),x96986)))) % 181.55/181.54 [10057]P1(f324(f324(f326(x100571),f628(x100572,x100573,x100574,x100575,x100576,x100577,x100571)),x100575))+P1(f324(f324(f324(f324(f42(x100571,f871(x100577,f871(x100576,a859))),x100575),x100574),x100573),x100572)) % 181.55/181.54 [10058]P1(f324(f324(f326(x100581),f810(x100582,x100583,x100584,x100585,x100586,x100587,x100581)),x100585))+~P1(f324(f324(f324(f324(f41(x100581,f871(x100587,f871(x100586,a859))),x100585),x100584),x100583),x100582)) % 181.55/181.54 [10085]P1(f324(f324(f324(x100851,f810(x100852,x100853,x100851,x100854,x100855,x100856,x100857)),x100853),x100852))+~P1(f324(f324(f324(f324(f41(x100857,f871(x100856,f871(x100855,a859))),x100854),x100851),x100853),x100852)) % 181.55/181.54 [10102]~P1(f324(f324(f324(x101025,f628(x101027,x101026,x101025,x101024,x101023,x101022,x101021)),x101026),x101027))+P1(f324(f324(f324(f324(f42(x101021,f871(x101022,f871(x101023,a859))),x101024),x101025),x101026),x101027)) % 181.55/181.54 [10118]~P1(f324(f324(f326(f870(x101181,x101183)),f324(f324(f259(x101181,x101183),x101186),x101187)),f324(f324(f281(x101181,x101182,x101183),x101184),x101185)))+P1(f324(f324(f260(x101181,x101182,x101183,f324(f324(f7(x101181,f871(f870(x101181,x101182),a859),f871(x101182,a859)),f324(f324(f8(f871(x101182,f871(f871(f870(x101181,x101182),a859),a859)),f871(f871(f870(x101181,x101182),a859),f871(x101182,a859)),x101181),f7(x101182,f871(f870(x101181,x101182),a859),a859)),f324(f324(f8(f871(x101182,f870(x101181,x101182)),f871(x101182,f871(f871(f870(x101181,x101182),a859),a859)),x101181),f324(f8(f870(x101181,x101182),f871(f871(f870(x101181,x101182),a859),a859),x101182),f326(f870(x101181,x101182)))),f259(x101181,x101182)))),x101184),f324(f324(f7(x101182,f871(f870(x101182,x101183),a859),f871(x101183,a859)),f324(f324(f8(f871(x101183,f871(f871(f870(x101182,x101183),a859),a859)),f871(f871(f870(x101182,x101183),a859),f871(x101183,a859)),x101182),f7(x101183,f871(f870(x101182,x101183),a859),a859)),f324(f324(f8(f871(x101183,f870(x101182,x101183)),f871(x101183,f871(f871(f870(x101182,x101183),a859),a859)),x101182),f324(f8(f870(x101182,x101183),f871(f871(f870(x101182,x101183),a859),a859),x101183),f326(f870(x101182,x101183)))),f259(x101182,x101183)))),x101185)),x101186),x101187)) % 181.55/181.54 [10127]P1(f324(f324(f326(f870(x101271,x101272)),f324(f324(f259(x101271,x101272),x101273),x101274)),f324(f324(f281(x101271,x101275,x101272),x101276),x101277)))+~P1(f324(f324(f260(x101271,x101275,x101272,f324(f324(f7(x101271,f871(f870(x101271,x101275),a859),f871(x101275,a859)),f324(f324(f8(f871(x101275,f871(f871(f870(x101271,x101275),a859),a859)),f871(f871(f870(x101271,x101275),a859),f871(x101275,a859)),x101271),f7(x101275,f871(f870(x101271,x101275),a859),a859)),f324(f324(f8(f871(x101275,f870(x101271,x101275)),f871(x101275,f871(f871(f870(x101271,x101275),a859),a859)),x101271),f324(f8(f870(x101271,x101275),f871(f871(f870(x101271,x101275),a859),a859),x101275),f326(f870(x101271,x101275)))),f259(x101271,x101275)))),x101276),f324(f324(f7(x101275,f871(f870(x101275,x101272),a859),f871(x101272,a859)),f324(f324(f8(f871(x101272,f871(f871(f870(x101275,x101272),a859),a859)),f871(f871(f870(x101275,x101272),a859),f871(x101272,a859)),x101275),f7(x101272,f871(f870(x101275,x101272),a859),a859)),f324(f324(f8(f871(x101272,f870(x101275,x101272)),f871(x101272,f871(f871(f870(x101275,x101272),a859),a859)),x101275),f324(f8(f870(x101275,x101272),f871(f871(f870(x101275,x101272),a859),a859),x101272),f326(f870(x101275,x101272)))),f259(x101275,x101272)))),x101277)),x101273),x101274)) % 181.55/181.54 [10067]~P140(x100672)+E(f324(f324(f6(x100671,x100672),f324(f324(f7(x100671,f871(x100673,a859),x100672),f324(f324(f8(f871(x100673,x100672),f871(f871(x100673,a859),x100672),x100671),f6(x100673,x100672)),f324(f324(f7(x100671,f871(x100673,x100672),f871(x100673,x100672)),f324(f324(f8(f871(x100672,x100672),f871(f871(x100673,x100672),f871(x100673,x100672)),x100671),f8(x100672,x100672,x100673)),f324(f324(f8(x100672,f871(x100672,x100672),x100671),f82(x100672)),x100674))),x100675))),x100676)),x100677),f324(f324(f82(x100672),f324(f324(f6(x100671,x100672),x100674),x100677)),f324(f324(f6(x100673,x100672),x100675),x100676))) % 181.55/181.54 [9169]~P21(x91697,x91691,x91693,x91698)+E(f324(f73(x91691,x91691,x91692,f324(x91693,x91694)),f324(f73(x91691,x91691,x91692,f324(x91693,x91695)),x91696)),f324(f73(x91691,x91691,x91692,f324(x91693,x91695)),f324(f73(x91691,x91691,x91692,f324(x91693,x91694)),x91696))) % 181.55/181.54 [10122]E(f324(f324(f259(x101221,x101222),f324(x101223,f509(x101224,x101225,x101223,x101226,x101227,x101228,x101222,x101221))),f324(x101225,f510(x101224,x101225,x101223,x101226,x101227,x101228,x101222,x101221))),x101228)+~P1(f324(f324(f326(f870(x101221,x101222)),x101228),f324(f303(f870(x101227,x101226),f870(x101221,x101222),f264(x101227,x101221,x101226,x101222,x101223,x101225)),x101224))) % 181.55/181.54 [10136]~P1(f324(f324(f326(f870(x101368,x101367)),x101366),f324(f303(f870(x101361,x101362),f870(x101368,x101367),f264(x101361,x101368,x101362,x101367,x101365,x101364)),x101363)))+P1(f324(f324(f326(f870(x101361,x101362)),f324(f324(f259(x101361,x101362),f509(x101363,x101364,x101365,x101362,x101361,x101366,x101367,x101368)),f510(x101363,x101364,x101365,x101362,x101361,x101366,x101367,x101368))),x101363)) % 181.55/181.54 [9613]P1(f324(f324(f326(f870(f870(x96131,x96132),f870(x96131,x96132))),f324(f324(f259(f870(x96131,x96132),f870(x96131,x96132)),f324(f324(f259(x96131,x96132),x96133),x96134)),f324(f324(f259(x96131,x96132),x96135),x96136))),f316(x96131,x96132,x96137,x96138)))+~P1(f324(f324(f326(f870(x96131,x96131)),f324(f324(f259(x96131,x96131),x96133),x96135)),x96137)) % 181.55/181.54 [10112]E(f324(f136(x101121,x101122,f324(f7(x101122,x101121,x101121),x101123),f324(x101124,x101125)),x101126),f324(x101124,f324(f136(x101127,x101122,f324(f7(x101122,x101127,x101127),x101128),x101125),x101126)))+P1(f324(f324(f326(x101122),f758(x101125,x101128,x101124,x101123,x101127,x101121,x101126,x101122)),f324(f167(x101122),x101126))) % 181.55/181.54 [10130]~E(f324(f73(x101301,x101301,x101307,f324(x101303,f758(x101305,x101308,x101304,x101303,x101307,x101301,x101306,x101302))),x101304),f324(f73(x101307,x101301,x101307,x101304),f324(x101308,f758(x101305,x101308,x101304,x101303,x101307,x101301,x101306,x101302))))+E(f324(f136(x101301,x101302,f324(f7(x101302,x101301,x101301),x101303),f324(x101304,x101305)),x101306),f324(x101304,f324(f136(x101307,x101302,f324(f7(x101302,x101307,x101307),x101308),x101305),x101306))) % 181.55/181.54 [8388]E(f324(x83881,f324(x83882,x83883)),f324(x83884,f324(x83885,x83883)))+~E(f324(f73(x83886,x83887,x83888,x83881),x83882),f324(f73(x83889,x83887,x83888,x83884),x83885)) % 181.55/181.54 [9997]P1(f324(f324(f326(f870(x99971,x99972)),f324(f324(f259(x99971,x99972),f324(x99973,x99974)),f324(x99975,x99976))),f324(f303(f870(x99977,x99978),f870(x99971,x99972),f264(x99977,x99971,x99978,x99972,x99973,x99975)),x99979)))+~P1(f324(f324(f326(f870(x99977,x99978)),f324(f324(f259(x99977,x99978),x99974),x99976)),x99979)) % 181.55/181.54 [8678]~E(f324(x86784,f324(x86785,x86786)),f324(x86789,f324(x867810,x867811)))+E(f324(f324(f73(x86781,x86782,x86783,x86784),x86785),x86786),f324(f324(f73(x86787,x86782,x86788,x86789),x867810),x867811)) % 181.55/181.54 [4573]~P105(x45731)+~P99(x45731)+E(f104(x45731),f189(x45731)) % 181.55/181.54 [4574]~P105(x45741)+~P100(x45741)+E(f113(x45741),f190(x45741)) % 181.55/181.54 [4817]~P117(x48171)+~P92(x48171)+E(f324(f75(x48171),f324(f106(x48171),a100)),f79(x48171)) % 181.55/181.54 [5086]E(x50861,f2(a1))+E(f83(a1,x50861),f324(f80(a1),f79(a1)))+P1(f324(f324(f239(a1),f2(a1)),x50861)) % 181.55/181.54 [5287]E(x52871,f2(a1))+E(f83(a1,x52871),f79(a1))+~P1(f324(f324(f239(a1),f2(a1)),x52871)) % 181.55/181.54 [7247]~P40(x72471)+P1(f324(f61(a1),x72471))+~P1(f324(f61(a865),f324(f303(a1,a865,a107),x72471))) % 181.55/181.54 [9574]E(x95741,f191(f871(f870(a865,a865),a859)))+~P1(f324(f61(f870(a865,a865)),x95741))+P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),f191(f871(f870(a865,a865),a859))),x95741)),a36)) % 181.55/181.54 [9746]E(x97461,f2(a865))+E(x97461,f324(a115,f2(a865)))+~P1(f324(f324(f239(a865),x97461),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.54 [10025]E(x100251,f2(a102))+E(f324(f324(f81(a1),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(a20,f324(f324(f38(a102),x100251),f324(f106(a102),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))))),f79(a1)),f324(a20,x100251))+E(f44(a102,x100251,f324(f106(a102),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f2(a102)) % 181.55/181.54 [9877]E(x98771,f2(a102))+~E(f44(a102,x98771,f324(f106(a102),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f2(a102))+E(f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(a20,f324(f324(f38(a102),x98771),f324(f106(a102),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))),f324(a20,x98771)) % 181.55/181.54 [4646]~P55(x46461,x46462)+P45(x46461,x46462)+~P46(a859) % 181.55/181.54 [4583]~P141(x45831)+P32(x45831,x45832)+~E(x45832,f2(x45831)) % 181.55/181.54 [4584]~P105(x45841)+P16(x45841,x45842)+~E(x45842,f116(x45841)) % 181.55/181.54 [4593]~P117(x45931)+~E(x45932,f2(x45931))+E(f83(x45931,x45932),f2(x45931)) % 181.55/181.54 [4594]~P86(x45941)+~E(x45942,f2(x45941))+E(f83(x45941,x45942),f2(x45941)) % 181.55/181.54 [4602]~P141(x46022)+~P32(x46022,x46021)+E(x46021,f2(x46022)) % 181.55/181.54 [4636]~P117(x46362)+~E(f83(x46362,x46361),f2(x46362))+E(x46361,f2(x46362)) % 181.55/181.54 [4653]~P58(x46532)+~P58(x46531)+P58(f871(x46531,x46532)) % 181.55/181.54 [4654]~P58(x46542)+~P58(x46541)+P58(f870(x46541,x46542)) % 181.55/181.54 [4655]~P58(x46552)+~P58(x46551)+P58(f872(x46551,x46552)) % 181.55/181.54 [4656]~P7(x46562)+~P7(x46561)+P7(f197(x46561,x46562)) % 181.55/181.54 [4657]~P142(x46572)+~P142(x46571)+P142(f870(x46571,x46572)) % 181.55/181.54 [4658]~P61(x46582)+~P61(x46581)+P61(f871(x46581,x46582)) % 181.55/181.54 [4659]~P61(x46592)+~P61(x46591)+P61(f870(x46591,x46592)) % 181.55/181.54 [4660]~P61(x46602)+~P61(x46601)+P61(f872(x46601,x46602)) % 181.55/181.54 [4661]~P61(x46611)+~P91(x46612)+P91(f871(x46611,x46612)) % 181.55/181.54 [4789]~P105(x47891)+~P16(x47891,x47892)+P16(x47891,f146(x47891,x47892)) % 181.55/181.54 [5020]~P7(x50202)+~P7(x50201)+P7(f44(a1,x50201,x50202)) % 181.55/181.54 [4604]~P74(x46041)+~E(x46042,f2(x46041))+E(f324(f80(x46041),x46042),x46042) % 181.55/181.54 [4608]~P135(x46081)+~E(x46082,f2(a1))+E(f324(f105(x46081),x46082),f2(x46081)) % 181.55/181.54 [4609]~P89(x46091)+~E(x46092,f2(a1))+E(f324(f105(x46091),x46092),f2(x46091)) % 181.55/181.54 [4633]~P4(x46331)+~E(f2(x46331),x46332)+E(f324(f80(x46331),x46332),f2(x46331)) % 181.55/181.54 [4634]~P4(x46341)+~E(x46342,f2(x46341))+E(f324(f80(x46341),x46342),f2(x46341)) % 181.55/181.54 [4635]~P83(x46351)+~E(x46352,f2(x46351))+E(f324(f75(x46351),x46352),f2(x46351)) % 181.55/181.54 [4663]~P74(x46632)+E(x46631,f2(x46632))+~E(f324(f80(x46632),x46631),x46631) % 181.55/181.54 [4671]E(x46711,f324(a107,x46712))+~E(x46711,f2(a865))+~E(x46712,f324(f103(a1),x46711)) % 181.55/181.54 [4672]E(f324(a107,x46721),x46722)+~E(x46722,f2(a865))+~E(x46721,f324(f103(a1),x46722)) % 181.55/181.54 [4676]~P89(x46762)+E(x46761,f2(a1))+~E(f324(f105(x46762),x46761),f2(x46762)) % 181.55/181.54 [4681]~P4(x46812)+E(x46811,f2(x46812))+~E(f324(f80(x46812),x46811),f2(x46812)) % 181.55/181.54 [4682]~P83(x46822)+E(x46821,f2(x46822))+~E(f324(f75(x46822),x46821),f2(x46822)) % 181.55/181.54 [4683]~P4(x46831)+E(f2(x46831),x46832)+~E(f324(f80(x46831),x46832),f2(x46831)) % 181.55/181.54 [4863]~P105(x48631)+~P16(x48631,x48632)+P16(x48631,f324(f166(x48631),x48632)) % 181.55/181.54 [4888]~P1(x48882)+~P1(x48881)+P1(f324(f324(a322,x48881),x48882)) % 181.55/181.54 [4920]~E(f79(a865),f2(a865))+E(f324(f37(x49201),x49202),f2(a865))+~P1(f324(f61(x49201),x49202)) % 181.55/181.54 [4953]~P110(x49531)+~P140(x49531)+E(f324(f324(f249(x49531),f2(x49531)),f324(a115,x49532)),f2(x49531)) % 181.55/181.54 [4991]~P105(x49911)+P16(x49911,f133(x49911,x49912))+~P1(f324(f61(x49911),x49912)) % 181.55/181.54 [4992]~P105(x49921)+P16(x49921,f747(x49922,x49921))+~P1(f324(f61(x49921),x49922)) % 181.55/181.54 [5012]~P105(x50121)+E(f324(f167(x50121),f133(x50121,x50122)),x50122)+~P1(f324(f61(x50121),x50122)) % 181.55/181.54 [5013]~P105(x50131)+E(f324(f167(x50131),f747(x50132,x50131)),x50132)+~P1(f324(f61(x50131),x50132)) % 181.55/181.54 [5040]P1(x50401)+P1(x50402)+~P1(f324(f324(a323,x50402),x50401)) % 181.55/181.54 [5052]E(x50521,f191(f871(x50522,a859)))+~E(f324(f37(x50522),x50521),f2(a865))+~P1(f324(f61(x50522),x50521)) % 181.55/181.54 [5057]P1(x50571)+~P1(x50572)+~P1(f324(f324(a327,x50572),x50571)) % 181.55/181.54 [5104]~P71(x51041)+E(f324(f75(x51041),x51042),x51042)+P1(f324(f324(f239(x51041),x51042),f2(x51041))) % 181.55/181.54 [5166]~P61(x51662)+~P1(f324(f57(x51662),x51661))+P1(f324(x51661,f716(x51661,x51662))) % 181.55/181.54 [5167]~P61(x51672)+~P1(f324(f57(x51672),x51671))+P1(f324(x51671,f726(x51671,x51672))) % 181.55/181.54 [5200]E(x52001,f116(x52002))+P1(f324(f131(x52002),f117(x52002,x52001)))+~P1(f324(f131(x52002),x52001)) % 181.55/181.54 [5205]~P105(x52051)+~P1(f324(f61(x52051),x52052))+P1(f324(f131(x52051),f133(x52051,x52052))) % 181.55/181.54 [5206]~P105(x52061)+~P1(f324(f61(x52061),x52062))+P1(f324(f131(x52061),f747(x52062,x52061))) % 181.55/181.54 [5212]~P135(x52121)+E(f324(f103(x52121),f324(a107,x52122)),f324(f105(x52121),x52122))+P1(f324(f324(f239(a1),x52122),f2(a1))) % 181.55/181.54 [5239]P8(x52392,x52391)+E(f324(x52391,f790(x52391)),f324(x52391,f811(x52391)))+P1(f324(f324(x52391,f790(x52391)),f811(x52391))) % 181.55/181.54 [5253]E(f324(f103(a1),f414(x52531,x52532)),x52531)+P1(f324(x52532,f324(a107,x52531)))+~P1(f324(x52532,f2(a865))) % 181.55/181.54 [5265]~P61(x52651)+~P1(f324(x52652,f727(x52652,x52651)))+P1(f324(f58(x52651),x52652)) % 181.55/181.54 [5266]~P61(x52661)+~P1(f324(x52662,f729(x52662,x52661)))+P1(f324(f58(x52661),x52662)) % 181.55/181.54 [5280]~P61(x52802)+~P37(x52802,x52801,f55(x52802))+P1(f324(x52801,f762(x52801,x52802))) % 181.55/181.54 [5296]~P117(x52961)+~E(f83(x52961,x52962),f324(f80(x52961),f79(x52961)))+P1(f324(f324(f239(x52961),x52962),f2(x52961))) % 181.55/181.54 [5372]~E(x53722,f2(a1))+E(f220(x53721,x53722),f324(f324(f259(a1,a1),f2(a1)),f79(a1)))+P1(f324(f324(f239(a1),x53722),f2(a1))) % 181.55/181.54 [5373]~E(x53731,f2(a1))+E(f220(x53731,x53732),f324(f324(f259(a1,a1),f2(a1)),f79(a1)))+P1(f324(f324(f239(a1),x53732),f2(a1))) % 181.55/181.54 [5425]E(f324(f103(a1),f414(x54251,x54252)),x54251)+P1(f324(x54252,f324(a107,x54251)))+P1(f324(f324(f239(a1),x54251),f2(a1))) % 181.55/181.54 [5488]~P117(x54881)+E(f83(x54881,x54882),f324(f80(x54881),f79(x54881)))+~P1(f324(f324(f239(x54881),x54882),f2(x54881))) % 181.55/181.54 [5489]~P83(x54891)+E(f324(f75(x54891),x54892),f324(f80(x54891),x54892))+~P1(f324(f324(f238(x54891),x54892),f2(x54891))) % 181.55/181.54 [5490]~P83(x54901)+E(f324(f75(x54901),x54902),f324(f80(x54901),x54902))+~P1(f324(f324(f239(x54901),x54902),f2(x54901))) % 181.55/181.54 [5491]~P71(x54911)+E(f324(f75(x54911),x54912),f324(f80(x54911),x54912))+~P1(f324(f324(f239(x54911),x54912),f2(x54911))) % 181.55/181.54 [5585]~P1(f324(x55851,f414(x55852,x55851)))+P1(f324(x55851,f324(a107,x55852)))+~P1(f324(x55851,f2(a865))) % 181.55/181.54 [5592]E(x55921,f2(a865))+E(f324(a115,f368(x55922,x55921)),x55921)+~P1(f324(f324(f239(a865),x55921),f324(a115,x55922))) % 181.55/181.54 [5596]P8(x55961,x55962)+~E(f324(x55962,f790(x55962)),f324(x55962,f811(x55962)))+~P1(f324(f324(x55962,f790(x55962)),f811(x55962))) % 181.55/181.54 [5616]~P105(x56161)+P16(x56161,x56162)+P1(f324(f324(f238(a865),f730(x56162,x56161)),f731(x56162,x56161))) % 181.55/181.54 [5617]~P105(x56171)+P16(x56171,x56172)+P1(f324(f324(f238(a865),f736(x56172,x56171)),f737(x56172,x56171))) % 181.55/181.54 [5703]~P83(x57031)+~E(x57032,f2(x57031))+P1(f324(f324(f238(x57031),f324(f75(x57031),x57032)),f2(x57031))) % 181.55/181.54 [5782]~P61(x57822)+~P61(x57821)+E(f59(x57821,x57822,f55(x57821),f55(x57822)),f55(f870(x57821,x57822))) % 181.55/181.54 [5786]~P1(f324(x57861,f414(x57862,x57861)))+P1(f324(x57861,f324(a107,x57862)))+P1(f324(f324(f239(a1),x57862),f2(a1))) % 181.55/181.54 [5809]~P1(f324(x58091,f324(a107,x58092)))+P1(f324(x58091,f2(a865)))+~P1(f324(f324(f239(a1),x58092),f2(a1))) % 181.55/181.54 [6136]~P117(x61361)+~P1(f324(f324(f239(x61361),x61362),f2(x61361)))+P1(f324(f324(f239(x61361),f83(x61361,x61362)),f2(x61361))) % 181.55/181.54 [6249]~P117(x62491)+P1(f324(f324(f238(x62491),f324(f105(x62491),x62492)),f2(x62491)))+~P1(f324(f324(f238(a1),x62492),f2(a1))) % 181.55/181.54 [6250]~P117(x62501)+P1(f324(f324(f239(x62501),f324(f105(x62501),x62502)),f2(x62501)))+~P1(f324(f324(f239(a1),x62502),f2(a1))) % 181.55/181.54 [6257]~P83(x62572)+E(x62571,f2(x62572))+~P1(f324(f324(f238(x62572),f324(f75(x62572),x62571)),f2(x62572))) % 181.55/181.54 [6333]~P135(x63331)+~P1(f324(f324(f326(x63331),x63332),f112(x63331)))+P1(f324(f324(f326(x63331),f324(f80(x63331),x63332)),f112(x63331))) % 181.55/181.54 [6366]~P117(x63661)+~P1(f324(f324(f239(x63661),f83(x63661,x63662)),f2(x63661)))+P1(f324(f324(f239(x63661),x63662),f2(x63661))) % 181.55/181.54 [6535]~P117(x65352)+~P1(f324(f324(f238(x65352),f324(f105(x65352),x65351)),f2(x65352)))+P1(f324(f324(f238(a1),x65351),f2(a1))) % 181.55/181.54 [6536]~P117(x65362)+~P1(f324(f324(f239(x65362),f324(f105(x65362),x65361)),f2(x65362)))+P1(f324(f324(f239(a1),x65361),f2(a1))) % 181.55/181.54 [7035]~P74(x70351)+~P1(f324(f324(f238(x70351),x70352),f2(x70351)))+P1(f324(f324(f238(x70351),f324(f324(f81(x70351),x70352),x70352)),f2(x70351))) % 181.55/181.54 [7036]~P117(x70361)+~P1(f324(f324(f239(x70361),x70362),f2(x70361)))+P1(f324(f324(f239(x70361),f324(f324(f81(x70361),x70362),x70362)),f2(x70361))) % 181.55/181.54 [7037]~P74(x70371)+~P1(f324(f324(f239(x70371),x70372),f2(x70371)))+P1(f324(f324(f239(x70371),f324(f324(f81(x70371),x70372),x70372)),f2(x70371))) % 181.55/181.54 [7601]~P74(x76011)+~P1(f324(f324(f238(x76011),f324(f324(f81(x76011),x76012),x76012)),f2(x76011)))+P1(f324(f324(f238(x76011),x76012),f2(x76011))) % 181.55/181.54 [7602]~P117(x76021)+~P1(f324(f324(f239(x76021),f324(f324(f81(x76021),x76022),x76022)),f2(x76021)))+P1(f324(f324(f239(x76021),x76022),f2(x76021))) % 181.55/181.54 [7603]~P74(x76031)+~P1(f324(f324(f239(x76031),f324(f324(f81(x76031),x76032),x76032)),f2(x76031)))+P1(f324(f324(f239(x76031),x76032),f2(x76031))) % 181.55/181.54 [4721]~E(x47212,f79(a865))+~E(x47211,f79(a865))+E(f324(f324(f82(a865),x47211),x47212),f79(a865)) % 181.55/181.54 [4722]~E(x47222,f79(a1))+~E(x47221,f79(a1))+E(f324(f324(f82(a1),x47221),x47222),f79(a1)) % 181.55/181.54 [4723]~E(x47232,f2(a865))+~E(x47231,f2(a865))+E(f324(f324(f81(a865),x47231),x47232),f2(a865)) % 181.55/181.54 [4775]~P59(x47752)+E(x47751,f2(x47752))+E(f324(f324(f38(x47752),x47751),x47751),f79(x47752)) % 181.55/181.54 [4776]~P114(x47762)+E(x47761,f2(x47762))+E(f324(f324(f282(x47762),x47761),x47761),f79(x47762)) % 181.55/181.54 [4777]~P115(x47772)+E(x47771,f2(x47772))+E(f324(f324(f282(x47772),x47771),x47771),f79(x47772)) % 181.55/181.54 [4795]~P134(x47951)+~E(x47952,f79(x47951))+E(f324(f324(f82(x47951),x47952),x47952),f79(x47951)) % 181.55/181.54 [4796]~P74(x47961)+~E(x47962,f2(x47961))+E(f324(f324(f81(x47961),x47962),x47962),f2(x47961)) % 181.55/181.54 [4797]~P115(x47971)+~E(x47972,f2(x47971))+E(f324(f324(f282(x47971),x47972),x47972),f2(x47971)) % 181.55/181.54 [4842]~E(x48422,f2(a865))+~E(x48421,f2(a865))+E(f324(f80(a1),f324(f103(a1),x48421)),f324(f103(a1),x48422)) % 181.55/181.54 [4860]E(x48601,f79(a865))+E(x48602,f2(a865))+~E(f324(f324(f82(a865),x48602),x48601),x48602) % 181.55/181.54 [4870]E(x48701,f2(a865))+E(x48702,f2(a865))+~E(f324(f324(f82(a865),x48702),x48701),f2(a865)) % 181.55/181.54 [4897]~E(x48972,f2(a865))+~E(x48971,f324(a115,f2(a865)))+E(f324(f324(f81(a865),x48971),x48972),f324(a115,f2(a865))) % 181.55/181.54 [4898]~E(x48981,f2(a865))+~E(x48982,f324(a115,f2(a865)))+E(f324(f324(f81(a865),x48981),x48982),f324(a115,f2(a865))) % 181.55/181.54 [4903]E(x49031,f79(a1))+E(x49032,f324(f106(a1),a100))+~E(f324(f324(f82(a1),x49031),x49032),f79(a1)) % 181.55/181.54 [4904]E(x49041,f79(a1))+E(x49042,f324(f106(a1),a100))+~E(f324(f324(f82(a1),x49042),x49041),f79(a1)) % 181.55/181.54 [4905]E(x49051,f79(a1))+E(x49051,f324(f106(a1),a100))+~E(f324(f324(f82(a1),x49052),x49051),f79(a1)) % 181.55/181.54 [4907]E(x49071,f79(a1))+E(x49071,f324(f106(a1),a100))+~E(f324(f324(f82(a1),x49071),x49072),f79(a1)) % 181.55/181.54 [4924]~P74(x49242)+E(x49241,f2(x49242))+~E(f324(f324(f81(x49242),x49241),x49241),f2(x49242)) % 181.55/181.54 [4930]~E(x49301,f324(f106(a1),a100))+~E(x49302,f324(f106(a1),a100))+E(f324(f324(f82(a1),x49301),x49302),f79(a1)) % 181.55/181.54 [4942]E(x49421,f2(a865))+E(x49422,f2(a865))+~E(f324(f324(f81(a865),x49422),x49421),f324(a115,f2(a865))) % 181.55/181.54 [4952]~P62(x49521)+~P92(x49521)+E(f324(f324(f282(x49521),x49522),f324(f106(x49521),a84)),f2(x49521)) % 181.55/181.54 [4958]~P134(x49581)+~E(x49582,f324(f80(x49581),f79(x49581)))+E(f324(f324(f82(x49581),x49582),x49582),f79(x49581)) % 181.55/181.54 [4963]~P7(x49632)+~P7(x49631)+P7(f324(f324(f82(a1),x49631),x49632)) % 181.55/181.54 [4964]~P7(x49642)+~P7(x49641)+P7(f324(f324(f81(a1),x49641),x49642)) % 181.55/181.54 [4965]~P7(x49652)+~P7(x49651)+P7(f324(f324(f38(a1),x49651),x49652)) % 181.55/181.54 [4967]~E(x49672,f2(a1))+E(x49671,f2(a1))+E(f45(x49671,x49672),f324(f324(f259(a1,a1),f2(a1)),x49671)) % 181.55/181.54 [4989]~E(x49892,f324(a115,f2(a865)))+~E(x49891,f324(a115,f2(a865)))+E(f324(f324(f82(a865),x49891),x49892),f324(a115,f2(a865))) % 181.55/181.54 [5004]E(x50041,f2(a865))+E(x50042,f324(a115,f2(a865)))+~E(f324(f324(f249(a865),x50042),x50041),f324(a115,f2(a865))) % 181.55/181.54 [5005]E(x50051,f2(a865))+E(x50051,f324(a115,f2(a865)))+~E(f324(f324(f81(a865),x50052),x50051),f324(a115,f2(a865))) % 181.55/181.54 [5006]E(x50061,f2(a865))+E(x50061,f324(a115,f2(a865)))+~E(f324(f324(f81(a865),x50061),x50062),f324(a115,f2(a865))) % 181.55/181.54 [5014]~P62(x50141)+~P92(x50141)+E(f324(f324(f282(x50141),x50142),f324(f106(x50141),a100)),f324(f80(x50141),x50142)) % 181.55/181.54 [5032]E(x50321,f324(a107,x50322))+~E(x50321,f2(a865))+P1(f324(f324(f238(a1),f2(a1)),x50322)) % 181.55/181.54 [5033]E(f324(a107,x50331),x50332)+~E(x50332,f2(a865))+P1(f324(f324(f238(a1),f2(a1)),x50331)) % 181.55/181.54 [5048]E(x50481,f324(a115,f2(a865)))+E(x50482,f324(a115,f2(a865)))+~E(f324(f324(f81(a865),x50481),x50482),f324(a115,f2(a865))) % 181.55/181.54 [5058]~E(x50581,f324(a107,x50582))+E(x50581,f2(a865))+P1(f324(f324(f238(a1),f2(a1)),x50582)) % 181.55/181.54 [5059]~E(f324(a107,x50592),x50591)+E(x50591,f2(a865))+P1(f324(f324(f238(a1),f2(a1)),x50592)) % 181.55/181.54 [5081]~P94(x50811)+E(f324(f63(x50811,f113(x50811)),x50812),f13(x50811,x50812))+~P1(f324(f61(x50811),x50812)) % 181.55/181.54 [5082]~P94(x50821)+E(f324(f63(x50821,f104(x50821)),x50822),f10(x50821,x50822))+~P1(f324(f61(x50821),x50822)) % 181.55/181.54 [5083]~P105(x50831)+E(f324(f63(x50831,f190(x50831)),x50832),f14(x50831,x50832))+~P1(f324(f61(x50831),x50832)) % 181.55/181.54 [5084]~P105(x50841)+E(f324(f63(x50841,f189(x50841)),x50842),f15(x50841,x50842))+~P1(f324(f61(x50841),x50842)) % 181.55/181.54 [5085]~P61(x50851)+~P1(f324(x50852,f203(x50851)))+P1(f324(f57(f869(x50851)),x50852)) % 181.55/181.54 [5159]~P61(x51592)+P1(f324(x51591,f203(x51592)))+~P1(f324(f58(f869(x51592)),x51591)) % 181.55/181.54 [5160]E(x51601,x51602)+~E(f324(f324(f22(a865),x51602),x51601),f2(a865))+~E(f324(f324(f22(a865),x51601),x51602),f2(a865)) % 181.55/181.54 [5173]P7(x51731)+~P40(x51732)+~P1(f324(f324(f326(a1),x51731),x51732)) % 181.55/181.54 [5201]~P117(x52011)+~E(f83(x52011,x52012),f79(x52011))+P1(f324(f324(f239(x52011),f2(x52011)),x52012)) % 181.55/181.54 [5213]~P92(x52131)+E(f324(f103(x52131),f324(f106(a865),x52132)),f324(f106(x52131),x52132))+P1(f324(a196,f324(f106(a1),x52132))) % 181.55/181.54 [5219]~P45(x52191,x52192)+P46(a859)+P1(f324(f61(f870(x52191,x52191)),x52192)) % 181.55/181.54 [5289]~P105(x52891)+E(f324(f63(x52891,f190(x52891)),x52892),f11(x52891,f190(x52891),x52892))+~P1(f324(f61(x52891),x52892)) % 181.55/181.54 [5290]~P105(x52901)+E(f324(f63(x52901,f189(x52901)),x52902),f12(x52901,f189(x52901),x52902))+~P1(f324(f61(x52901),x52902)) % 181.55/181.54 [5303]E(x53031,x53032)+P1(f324(f324(f239(a865),x53032),x53031))+P1(f324(f324(f239(a865),x53031),x53032)) % 181.55/181.54 [5304]E(x53041,x53042)+P1(f324(f324(f239(a1),x53042),x53041))+P1(f324(f324(f239(a1),x53041),x53042)) % 181.55/181.54 [5359]~P92(x53591)+E(f324(f103(x53591),f324(f106(a865),x53592)),f2(x53591))+~P1(f324(a196,f324(f106(a1),x53592))) % 181.55/181.54 [5362]~E(x53622,f324(a107,x53621))+E(x53621,f324(f103(a1),x53622))+~P1(f324(f324(f238(a1),f2(a1)),x53621)) % 181.55/181.54 [5363]~E(f324(a107,x53631),x53632)+E(x53631,f324(f103(a1),x53632))+~P1(f324(f324(f238(a1),f2(a1)),x53631)) % 181.55/181.54 [5364]~E(x53641,f324(a107,x53642))+E(f324(f103(a1),x53641),x53642)+~P1(f324(f324(f238(a1),f2(a1)),x53642)) % 181.55/181.54 [5374]E(x53741,f324(a107,x53742))+~E(x53742,f324(f103(a1),x53741))+~P1(f324(f324(f238(a1),f2(a1)),x53742)) % 181.55/181.54 [5375]E(f324(a107,x53751),x53752)+~E(x53751,f324(f103(a1),x53752))+~P1(f324(f324(f238(a1),f2(a1)),x53751)) % 181.55/181.54 [5414]~P83(x54142)+E(x54141,f2(x54142))+P1(f324(f324(f239(x54142),f2(x54142)),f324(f75(x54142),x54141))) % 181.55/181.54 [5481]~P117(x54811)+E(f83(x54811,x54812),f79(x54811))+~P1(f324(f324(f239(x54811),f2(x54811)),x54812)) % 181.55/181.54 [5485]~P92(x54851)+E(f324(f103(x54851),f324(f106(a865),x54852)),f2(x54851))+P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x54852))) % 181.55/181.54 [5492]~P83(x54921)+E(f324(f75(x54921),x54922),x54922)+~P1(f324(f324(f238(x54921),f2(x54921)),x54922)) % 181.55/181.54 [5493]~P83(x54931)+E(f324(f75(x54931),x54932),x54932)+~P1(f324(f324(f239(x54931),f2(x54931)),x54932)) % 181.55/181.54 [5500]E(x55001,f2(a865))+~E(f133(a865,f324(f294(a865,x55002),x55001)),f116(a865))+P1(f324(f324(f238(a865),x55001),x55002)) % 181.55/181.54 [5510]~P72(x55101)+E(f324(f324(f6(x55101,x55101),f5(x55101)),f324(f167(x55101),x55102)),f324(f160(x55101),x55102))+~P1(f324(f131(x55101),x55102)) % 181.55/181.54 [5513]~P135(x55131)+E(f324(f103(x55131),f324(a107,x55132)),f324(f105(x55131),x55132))+~P1(f324(f324(f238(a1),f2(a1)),x55132)) % 181.55/181.54 [5540]E(x55401,x55402)+P1(f324(f324(f239(a865),x55401),x55402))+~P1(f324(f324(f238(a865),x55401),x55402)) % 181.55/181.54 [5541]E(x55411,x55412)+P1(f324(f324(f239(a1),x55411),x55412))+~P1(f324(f324(f238(a1),x55411),x55412)) % 181.55/181.54 [5544]E(x55441,f79(a1))+~E(f324(f324(f82(a1),x55442),x55441),f79(a1))+~P1(f324(f324(f239(a1),f2(a1)),x55442)) % 181.55/181.54 [5545]E(x55451,f79(a1))+~E(f324(f324(f82(a1),x55451),x55452),f79(a1))+~P1(f324(f324(f239(a1),f2(a1)),x55451)) % 181.55/181.54 [5582]~P40(x55822)+P1(f324(f324(f238(a1),f2(a1)),x55821))+~P1(f324(f324(f326(a1),x55821),x55822)) % 181.55/181.54 [5601]~P55(x56011,x56012)+P39(x56011,x56012)+~P1(f324(f61(f870(x56011,x56011)),x56012)) % 181.55/181.54 [5603]~P55(x56031,x56032)+P45(x56031,x56032)+~P1(f324(f61(f870(x56031,x56031)),x56032)) % 181.55/181.54 [5647]E(x56471,f191(f871(x56472,a859)))+~P1(f324(f61(x56472),x56471))+P1(f324(f324(f239(a865),f2(a865)),f324(f37(x56472),x56471))) % 181.55/181.54 [5674]~P1(f324(x56741,x56742))+P1(f324(x56741,f2(a865)))+P1(f324(f324(f239(a865),f376(x56742,x56741)),x56742)) % 181.55/181.54 [5697]E(x56971,f2(a865))+~E(f324(f160(a865),x56972),f2(a865))+~P1(f324(f324(f326(a865),x56971),f324(f167(a865),x56972))) % 181.55/181.54 [5763]E(x57631,x57632)+~P1(f324(f324(f238(a865),x57632),x57631))+~P1(f324(f324(f238(a865),x57631),x57632)) % 181.55/181.54 [5764]E(x57641,x57642)+~P1(f324(f324(f238(a1),x57642),x57641))+~P1(f324(f324(f238(a1),x57641),x57642)) % 181.55/181.54 [5765]E(f324(f37(x57651),x57652),f2(a865))+~P1(f324(f61(x57651),x57652))+P1(f324(f324(f326(x57651),f573(x57652,x57651)),x57652)) % 181.55/181.54 [5774]E(f49(x57741,x57742),f45(x57741,x57742))+P1(f324(f324(f238(a1),f2(a1)),x57741))+~P1(f324(f324(f239(a1),f2(a1)),x57742)) % 181.55/181.54 [5798]~P1(f324(x57981,f406(x57981)))+P1(f324(x57981,f324(a107,x57982)))+~P1(f324(f324(f238(a1),f2(a1)),x57982)) % 181.55/181.54 [5800]P1(f324(f324(f238(a865),x58001),f841(x58002)))+~P1(f324(f61(a865),x58002))+~P1(f324(f324(f326(a865),x58001),x58002)) % 181.55/181.54 [5801]P1(f324(f324(f239(a865),x58011),f825(x58012)))+~P1(f324(f61(a865),x58012))+~P1(f324(f324(f326(a865),x58011),x58012)) % 181.55/181.54 [5830]E(x58301,x58302)+~P1(f324(f324(f239(a865),x58301),f324(a115,x58302)))+P1(f324(f324(f239(a865),x58301),x58302)) % 181.55/181.54 [5862]E(x58621,f324(a115,x58622))+~P1(f324(f324(f238(a865),x58621),f324(a115,x58622)))+P1(f324(f324(f238(a865),x58621),x58622)) % 181.55/181.54 [5875]P1(f324(x58751,f407(x58751)))+~P1(f324(x58751,f324(a107,x58752)))+~P1(f324(f324(f238(a1),f2(a1)),x58752)) % 181.55/181.54 [5889]~P1(f324(x58891,x58892))+~P1(f324(f324(f238(a1),f2(a1)),x58892))+P1(f324(x58891,f324(f103(a1),f416(x58891)))) % 181.55/181.54 [5903]~P83(x59032)+~E(x59031,f2(x59032))+~P1(f324(f324(f239(x59032),f2(x59032)),f324(f75(x59032),x59031))) % 181.55/181.54 [5927]~P55(x59271,x59272)+P39(x59271,f324(f279(x59271,x59271),x59272))+~P1(f324(f61(f870(x59271,x59271)),x59272)) % 181.55/181.54 [5935]~P92(x59351)+E(f324(f103(x59351),f324(f106(a865),x59352)),f324(f106(x59351),x59352))+~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x59352))) % 181.55/181.54 [5938]E(f324(a115,x59381),x59382)+~P1(f324(f324(f239(a865),x59381),x59382))+P1(f324(f324(f239(a865),f324(a115,x59381)),x59382)) % 181.55/181.54 [5951]E(f324(f324(f38(a1),x59511),x59512),f2(a1))+~P1(f324(f324(f238(a1),x59511),f2(a1)))+~P1(f324(f324(f239(a1),x59512),x59511)) % 181.55/181.54 [5962]E(f44(a1,x59621,x59622),x59621)+~P1(f324(f324(f238(a1),x59621),f2(a1)))+~P1(f324(f324(f239(a1),x59622),x59621)) % 181.55/181.54 [5975]E(f46(x59751,x59752),f45(x59751,x59752))+~P1(f324(f324(f238(a1),f2(a1)),x59751))+~P1(f324(f324(f238(a1),f2(a1)),x59752)) % 181.55/181.54 [5983]E(f324(f324(f38(a1),x59831),x59832),f2(a1))+~P1(f324(f324(f238(a1),f2(a1)),x59831))+~P1(f324(f324(f239(a1),x59831),x59832)) % 181.55/181.54 [5995]E(f44(a865,f324(f106(a865),x59951),f324(f106(a865),x59952)),f324(f106(a865),x59951))+P1(f324(a196,f324(f106(a1),x59951)))+~P1(f324(a196,f324(f106(a1),x59952))) % 181.55/181.54 [5997]E(f44(a1,x59971,x59972),x59971)+~P1(f324(f324(f238(a1),f2(a1)),x59971))+~P1(f324(f324(f239(a1),x59971),x59972)) % 181.55/181.54 [5998]E(x59981,x59982)+~P1(f324(f324(f239(a865),x59981),f324(a115,x59982)))+~P1(f324(f324(f238(a865),x59982),x59981)) % 181.55/181.54 [6015]~P74(x60151)+~P1(f324(f324(f238(x60151),x60152),f2(x60151)))+P1(f324(f324(f238(x60151),x60152),f324(f80(x60151),x60152))) % 181.55/181.54 [6016]~P117(x60161)+~P1(f324(f324(f239(x60161),x60162),f2(x60161)))+P1(f324(f324(f239(x60161),x60162),f324(f80(x60161),x60162))) % 181.55/181.54 [6025]~P6(x60251)+E(f324(f324(f64(x60251,x60251,f104(x60251)),f247(x60251)),x60252),f40(x60251,x60252))+~P1(f324(f61(x60251),x60252)) % 181.55/181.54 [6026]~P6(x60261)+E(f324(f324(f64(x60261,x60261,f113(x60261)),f191(x60261)),x60262),f39(x60261,x60262))+~P1(f324(f61(x60261),x60262)) % 181.55/181.54 [6040]~P117(x60401)+~P1(f324(f324(f238(a1),f2(a1)),x60402))+P1(f324(f324(f238(x60401),f2(x60401)),f324(f105(x60401),x60402))) % 181.55/181.54 [6041]~P117(x60411)+~P1(f324(f324(f239(a1),f2(a1)),x60412))+P1(f324(f324(f239(x60411),f2(x60411)),f324(f105(x60411),x60412))) % 181.55/181.54 [6042]~P120(x60421)+~P1(f324(f324(f239(a865),f2(a865)),x60422))+P1(f324(f324(f239(x60421),f2(x60421)),f324(f103(x60421),x60422))) % 181.55/181.54 [6045]~P7(x60452)+~P7(x60451)+E(f324(f303(a865,a1,f103(a1)),f295(a865,f324(a107,x60451),f324(a107,x60452))),f295(a1,x60451,x60452)) % 181.55/181.54 [6051]P1(f324(x60511,x60512))+~P1(f324(f324(f238(a1),f2(a1)),x60512))+~P1(f324(x60511,f324(f103(a1),f417(x60511)))) % 181.55/181.54 [6076]E(f324(f324(f81(a865),f324(f106(a865),x60761)),f324(f106(a865),x60762)),f324(f106(a865),x60761))+P1(f324(f324(f239(a1),x60761),a84))+~P1(f324(f324(f239(a1),x60762),a84)) % 181.55/181.54 [6080]~P117(x60801)+P1(f324(f324(f239(x60801),f2(x60801)),f83(x60801,x60802)))+~P1(f324(f324(f239(x60801),f2(x60801)),x60802)) % 181.55/181.54 [6091]~P75(x60911)+~P1(f324(f324(f238(x60911),x60912),f2(x60911)))+P1(f324(f324(f238(x60911),f2(x60911)),f324(f80(x60911),x60912))) % 181.55/181.54 [6092]~P75(x60921)+~P1(f324(f324(f239(x60921),x60922),f2(x60921)))+P1(f324(f324(f239(x60921),f2(x60921)),f324(f80(x60921),x60922))) % 181.55/181.54 [6095]E(x60951,f247(f871(x60952,a859)))+~E(f324(f37(x60952),x60951),f324(f37(x60952),f247(f871(x60952,a859))))+~P1(f324(f61(x60952),f247(f871(x60952,a859)))) % 181.55/181.54 [6129]~P74(x61291)+P1(f324(f324(f238(x61291),x61292),f2(x61291)))+~P1(f324(f324(f238(x61291),x61292),f324(f80(x61291),x61292))) % 181.55/181.54 [6130]~P117(x61301)+P1(f324(f324(f239(x61301),x61302),f2(x61301)))+~P1(f324(f324(f239(x61301),x61302),f324(f80(x61301),x61302))) % 181.55/181.54 [6138]~P92(x61381)+P1(f324(f324(f326(x61381),f324(f106(x61381),x61382)),f187(x61381)))+~P1(f324(f324(f238(a1),a84),x61382)) % 181.55/181.54 [6169]E(x61691,f2(a865))+~P1(f324(f324(f239(a865),x61691),f324(a115,x61692)))+P1(f324(f324(f239(a865),f368(x61692,x61691)),x61692)) % 181.55/181.54 [6191]~P117(x61911)+~P1(f324(f324(f239(x61911),f2(x61911)),f83(x61911,x61912)))+P1(f324(f324(f239(x61911),f2(x61911)),x61912)) % 181.55/181.54 [6193]~E(f324(f106(a865),x61932),f324(f106(a865),x61931))+P1(f324(f324(f238(a1),f324(f106(a1),x61931)),f2(a1)))+~P1(f324(a196,f324(f106(a1),x61932))) % 181.55/181.54 [6222]E(f324(f258(a1,a1),f49(x62221,x62222)),f324(f324(f38(a1),x62221),x62222))+~P1(f324(f324(f239(a1),x62221),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x62222)) % 181.55/181.54 [6255]E(f324(f262(a1,a1),f49(x62551,x62552)),f44(a1,x62551,x62552))+~P1(f324(f324(f239(a1),x62551),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x62552)) % 181.55/181.54 [6258]~P117(x62582)+~P1(f324(f324(f238(x62582),f2(x62582)),f324(f105(x62582),x62581)))+P1(f324(f324(f238(a1),f2(a1)),x62581)) % 181.55/181.54 [6259]~P120(x62592)+~P1(f324(f324(f239(x62592),f2(x62592)),f324(f103(x62592),x62591)))+P1(f324(f324(f239(a865),f2(a865)),x62591)) % 181.55/181.54 [6260]~P117(x62602)+~P1(f324(f324(f239(x62602),f2(x62602)),f324(f105(x62602),x62601)))+P1(f324(f324(f239(a1),f2(a1)),x62601)) % 181.55/181.54 [6263]E(f324(f258(a1,a1),f46(x62631,x62632)),f324(f324(f38(a1),x62631),x62632))+~P1(f324(f324(f238(a1),f2(a1)),x62632))+~P1(f324(f324(f239(a1),f2(a1)),x62631)) % 181.55/181.54 [6278]E(f324(f262(a1,a1),f46(x62781,x62782)),f44(a1,x62781,x62782))+~P1(f324(f324(f238(a1),f2(a1)),x62782))+~P1(f324(f324(f239(a1),f2(a1)),x62781)) % 181.55/181.54 [6293]~P75(x62931)+P1(f324(f324(f238(x62931),x62932),f2(x62931)))+~P1(f324(f324(f238(x62931),f2(x62931)),f324(f80(x62931),x62932))) % 181.55/181.54 [6294]~P75(x62941)+P1(f324(f324(f239(x62941),x62942),f2(x62941)))+~P1(f324(f324(f239(x62941),f2(x62941)),f324(f80(x62941),x62942))) % 181.55/181.54 [6320]P1(f324(f48(x63201,x63202),f49(x63201,x63202)))+~P1(f324(f324(f239(a1),x63201),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x63202)) % 181.55/181.54 [6345]P1(f324(f48(x63451,x63452),f46(x63451,x63452)))+~P1(f324(f324(f238(a1),f2(a1)),x63451))+~P1(f324(f324(f239(a1),f2(a1)),x63452)) % 181.55/181.54 [6389]~P75(x63891)+P1(f324(f324(f238(x63891),f324(f80(x63891),x63892)),f2(x63891)))+~P1(f324(f324(f238(x63891),f2(x63891)),x63892)) % 181.55/181.54 [6390]~P75(x63901)+P1(f324(f324(f239(x63901),f324(f80(x63901),x63902)),f2(x63901)))+~P1(f324(f324(f239(x63901),f2(x63901)),x63902)) % 181.55/181.54 [6406]E(f324(f324(f22(a865),f324(a107,x64061)),f324(a107,x64062)),f324(a107,f197(x64061,x64062)))+~P1(f324(f324(f238(a1),f2(a1)),x64062))+~P1(f324(f324(f238(a1),f2(a1)),x64061)) % 181.55/181.54 [6423]P1(f324(f324(f238(a1),f2(a1)),f197(x64231,x64232)))+~P1(f324(f324(f238(a1),f2(a1)),x64232))+~P1(f324(f324(f238(a1),f2(a1)),x64231)) % 181.55/181.54 [6460]~P1(f324(x64601,x64602))+P1(f324(x64601,f2(a865)))+P1(f324(x64601,f324(f324(f81(a865),f376(x64602,x64601)),f79(a865)))) % 181.55/181.54 [6542]E(f324(f106(a865),x65421),f324(f106(a865),x65422))+~P1(f324(f324(f238(a1),f324(f106(a1),x65422)),f2(a1)))+~P1(f324(a196,f324(f106(a1),x65421))) % 181.55/181.54 [6552]~E(x65521,f2(a865))+~E(f684(x65522,x65521),f2(a865))+E(f324(f136(a865,a865,f81(a865),x65521),x65522),f2(a865)) % 181.55/181.54 [6577]~P1(f324(f61(x65771),f604(x65772,x65771)))+~P1(f324(f61(f871(x65771,a859)),x65772))+P1(f324(f61(x65771),f39(f871(x65771,a859),x65772))) % 181.55/181.54 [6583]E(x65831,x65832)+P1(f324(f324(f239(a1),x65831),x65832))+~P1(f324(f324(f239(a1),x65831),f324(f324(f81(a1),x65832),f79(a1)))) % 181.55/181.54 [6584]P1(f324(f324(f238(a865),f324(a107,x65841)),f324(a107,x65842)))+~P1(f324(f324(f238(a1),f2(a1)),x65842))+~P1(f324(f324(f238(a1),x65841),x65842)) % 181.55/181.54 [6585]P1(f324(f324(f238(a865),f324(a107,x65851)),f324(a107,x65852)))+~P1(f324(f324(f239(a1),f2(a1)),x65851))+~P1(f324(f324(f238(a1),x65851),x65852)) % 181.55/181.54 [6587]P1(f324(f324(f239(a865),f324(a107,x65871)),f324(a107,x65872)))+~P1(f324(f324(f238(a1),f2(a1)),x65871))+~P1(f324(f324(f239(a1),x65871),x65872)) % 181.55/181.54 [6588]P1(f324(f324(f239(a865),f324(a107,x65881)),f324(a107,x65882)))+~P1(f324(f324(f239(a1),f2(a1)),x65882))+~P1(f324(f324(f239(a1),x65881),x65882)) % 181.55/181.54 [6599]E(f44(a865,f324(a107,x65991),f324(a107,x65992)),f324(a107,f44(a1,x65991,x65992)))+~P1(f324(f324(f238(a1),f2(a1)),x65992))+~P1(f324(f324(f238(a1),f2(a1)),x65991)) % 181.55/181.54 [6621]~P75(x66211)+~P1(f324(f324(f238(x66211),f324(f80(x66211),x66212)),f2(x66211)))+P1(f324(f324(f238(x66211),f2(x66211)),x66212)) % 181.55/181.54 [6622]~P75(x66221)+~P1(f324(f324(f239(x66221),f324(f80(x66221),x66222)),f2(x66221)))+P1(f324(f324(f239(x66221),f2(x66221)),x66222)) % 181.55/181.54 [6637]~P1(f324(f324(f239(a1),a84),x66372))+~P1(f324(f324(f239(a1),x66371),x66372))+P1(f324(f324(f239(a865),f324(f106(a865),x66371)),f324(f106(a865),x66372))) % 181.55/181.54 [6728]~P1(f324(f324(f238(a1),f2(a1)),x67281))+P1(f324(f324(f239(a865),f324(a107,x67281)),x67282))+~P1(f324(f324(f239(a1),x67281),f324(f103(a1),x67282))) % 181.55/181.54 [6745]E(x67451,f2(a1))+E(f44(a1,x67452,x67451),f2(a1))+E(f324(f324(f22(a1),f324(f80(a1),f324(f324(f38(a1),x67452),x67451))),f79(a1)),f324(f324(f38(a1),x67452),f324(f80(a1),x67451))) % 181.55/181.54 [6760]~P1(f324(f324(f238(a1),f2(a1)),x67601))+~P1(f324(f324(f239(a865),f324(a107,x67601)),x67602))+P1(f324(f324(f239(a1),x67601),f324(f103(a1),x67602))) % 181.55/181.54 [6795]~P1(f324(f324(f238(a865),f324(a107,x67951)),f324(a107,x67952)))+~P1(f324(f324(f238(a1),f2(a1)),x67952))+P1(f324(f324(f238(a1),x67951),x67952)) % 181.55/181.54 [6796]~P1(f324(f324(f238(a865),f324(a107,x67961)),f324(a107,x67962)))+~P1(f324(f324(f239(a1),f2(a1)),x67961))+P1(f324(f324(f238(a1),x67961),x67962)) % 181.55/181.54 [6824]P1(f324(f324(f238(a1),x68241),x68242))+~P1(f324(f324(f238(a865),f324(f106(a865),x68241)),f324(f106(a865),x68242)))+P1(f324(f324(f238(a1),x68241),a84)) % 181.55/181.54 [6849]P1(f324(f324(f238(a1),f2(a1)),f44(a1,x68491,x68492)))+~P1(f324(f324(f238(a1),f2(a1)),x68492))+~P1(f324(f324(f238(a1),f2(a1)),x68491)) % 181.55/181.54 [6946]P1(f324(f324(f239(a1),a84),x69461))+~P1(f324(f324(f239(a1),x69462),x69461))+~P1(f324(f324(f239(a865),f324(f106(a865),x69462)),f324(f106(a865),x69461))) % 181.55/181.54 [6997]E(f324(f324(f259(a1,a1),f324(f324(f38(a1),x69971),x69972)),f44(a1,x69971,x69972)),f49(x69971,x69972))+~P1(f324(f324(f239(a1),x69971),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x69972)) % 181.55/181.54 [7018]E(f324(f324(f259(a1,a1),f324(f324(f38(a1),x70181),x70182)),f44(a1,x70181,x70182)),f46(x70181,x70182))+~P1(f324(f324(f238(a1),f2(a1)),x70182))+~P1(f324(f324(f238(a1),f2(a1)),x70181)) % 181.55/181.54 [7069]~P93(x70692)+E(x70691,f116(x70692))+E(f324(f136(x70692,x70692,f82(x70692),f324(f135(x70692),x70691)),f324(f166(x70692),x70691)),f324(f63(x70692,f82(x70692)),f324(f167(x70692),x70691))) % 181.55/181.54 [7180]~E(x71801,f2(a865))+E(f324(f136(a865,a865,f81(a865),x71801),x71802),f2(a865))+P1(f324(f324(f326(a865),f684(x71802,x71801)),f324(f167(a865),x71802))) % 181.55/181.54 [7227]~P1(f324(f324(f238(a1),x72271),f2(a1)))+P1(f324(f324(f238(a1),f324(f324(f38(a1),x72271),x72272)),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x72272)) % 181.55/181.54 [7228]~P1(f324(f324(f239(a1),x72282),f2(a1)))+P1(f324(f324(f238(a1),f324(f324(f38(a1),x72281),x72282)),f2(a1)))+~P1(f324(f324(f238(a1),f2(a1)),x72281)) % 181.55/181.54 [7229]~P1(f324(f324(f239(a1),x72292),f2(a1)))+P1(f324(f324(f239(a1),f324(f324(f38(a1),x72291),x72292)),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x72291)) % 181.55/181.54 [7231]~P1(f324(f324(f239(a1),x72311),f2(a1)))+P1(f324(f324(f239(a1),f324(f324(f38(a1),x72311),x72312)),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x72312)) % 181.55/181.54 [7237]P1(f324(f324(f326(f871(x72371,a859)),f604(x72372,x72371)),x72372))+~P1(f324(f61(f871(x72371,a859)),x72372))+P1(f324(f61(x72371),f39(f871(x72371,a859),x72372))) % 181.55/181.54 [7332]P27(x73321,x73321,x73322,f247(f871(x73321,a859)))+~E(f324(f303(x73321,x73321,x73322),f247(f871(x73321,a859))),f247(f871(x73321,a859)))+~P1(f324(f61(x73321),f247(f871(x73321,a859)))) % 181.55/181.54 [7459]~P27(x74591,x74591,x74592,f247(f871(x74591,a859)))+E(f324(f303(x74591,x74591,x74592),f247(f871(x74591,a859))),f247(f871(x74591,a859)))+~P1(f324(f61(x74591),f247(f871(x74591,a859)))) % 181.55/181.54 [7595]E(f324(f324(f38(a1),x75951),x75952),f324(f106(a1),a100))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),x75951),x75952)),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x75951)) % 181.55/181.54 [7652]~P1(f324(f324(f239(a1),x76522),f2(a1)))+~P1(f324(f324(f239(a1),f324(f324(f38(a1),x76521),x76522)),f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x76521)) % 181.55/181.54 [7657]E(f324(f324(f81(a1),x76571),x76572),f44(a1,x76571,x76572))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),x76571),x76572)),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x76571)) % 181.55/181.54 [7660]P1(f324(f324(f239(a1),x76601),f2(a1)))+~P1(f324(f324(f239(a1),f324(f324(f38(a1),x76601),x76602)),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x76602)) % 181.55/181.54 [8044]~P61(x80441)+~P1(f324(f58(f869(x80441)),x80442))+P1(f324(f58(x80441),f324(f324(f8(f869(x80441),a859,x80441),x80442),f233(x80441)))) % 181.55/181.54 [8356]~P105(x83561)+P16(x83561,x83562)+~P1(f324(f324(f238(x83561),f324(f324(f159(x83561),x83562),f730(x83562,x83561))),f324(f324(f159(x83561),x83562),f731(x83562,x83561)))) % 181.55/181.54 [8357]~P105(x83571)+P16(x83571,x83572)+~P1(f324(f324(f238(x83571),f324(f324(f159(x83571),x83572),f736(x83572,x83571))),f324(f324(f159(x83571),x83572),f737(x83572,x83571)))) % 181.55/181.54 [8502]~P61(x85021)+P1(f324(f57(f869(x85021)),x85022))+~P1(f324(f57(x85021),f324(f324(f8(f869(x85021),a859,x85021),x85022),f233(x85021)))) % 181.55/181.54 [9695]~P61(x96951)+~P61(x96952)+E(f324(f324(f148(f866(x96951),f871(x96952,x96951)),f324(f324(f8(f871(x96952,f869(x96951)),f871(x96952,x96951),f866(x96951)),f73(f869(x96951),x96951,x96952,f237(x96951))),f324(f324(f8(f866(f870(x96952,x96951)),f871(x96952,f869(x96951)),f866(x96951)),f173(x96952,x96951)),f324(f177(x96952,x96951),f55(x96952))))),f54(x96951,f324(f192(f866(x96952)),f55(x96952)),f55(x96951))),f55(f871(x96952,x96951))) % 181.55/181.54 [5640]E(x56401,f2(a1))+~E(f44(a1,x56402,x56401),f2(a1))+E(f324(f324(f38(a1),x56402),f324(f80(a1),x56401)),f324(f80(a1),f324(f324(f38(a1),x56402),x56401))) % 181.55/181.54 [5658]~P40(x56582)+~P40(x56581)+P40(f324(f324(f104(f871(a1,a859)),x56581),x56582)) % 181.55/181.54 [5659]~P40(x56592)+~P40(x56591)+P40(f324(f324(f113(f871(a1,a859)),x56591),x56592)) % 181.55/181.54 [5677]~P62(x56771)+~P92(x56771)+E(f324(f80(x56771),f324(f324(f282(x56771),f79(x56771)),x56772)),f324(f324(f282(x56771),f324(f106(x56771),a100)),x56772)) % 181.55/181.54 [5790]E(x57901,f2(a1))+~E(f44(a1,x57902,x57901),f2(a1))+E(f324(f324(f38(a1),f324(f80(a1),x57902)),x57901),f324(f80(a1),f324(f324(f38(a1),x57902),x57901))) % 181.55/181.54 [5921]~P105(x59211)+P16(x59211,x59212)+P1(f324(f324(f239(a865),f731(x59212,x59211)),f324(f192(f866(x59211)),x59212))) % 181.55/181.54 [5922]~P105(x59221)+P16(x59221,x59222)+P1(f324(f324(f239(a865),f737(x59222,x59221)),f324(f192(f866(x59221)),x59222))) % 181.55/181.54 [6072]~P92(x60721)+~E(f324(f106(x60721),x60722),f2(x60721))+P32(x60721,f324(f106(x60721),f324(f324(f81(a1),x60722),f324(f80(a1),a84)))) % 181.55/181.54 [6073]~P92(x60731)+~E(f324(f106(x60731),x60732),f2(x60731))+P32(x60731,f324(f106(x60731),f324(f324(f81(a1),a84),f324(f80(a1),x60732)))) % 181.55/181.54 [6075]E(f324(a50,f46(f324(f80(a1),x60751),f324(f80(a1),x60752))),f45(x60751,x60752))+P1(f324(f324(f238(a1),f2(a1)),x60751))+P1(f324(f324(f239(a1),f2(a1)),x60752)) % 181.55/181.54 [6199]~E(x61992,f2(a865))+~E(x61991,f2(a865))+P1(f324(f324(f238(a1),f324(f103(a1),x61991)),f324(f80(a1),f324(f103(a1),x61992)))) % 181.55/181.54 [6226]E(f324(f324(f81(a865),f324(f106(a865),x62261)),f324(f106(a865),x62262)),f324(f106(a865),f324(f324(f81(a1),x62261),x62262)))+P1(f324(f324(f239(a1),x62261),a84))+P1(f324(f324(f239(a1),x62262),a84)) % 181.55/181.54 [6355]~P74(x63551)+~P1(f324(f324(f238(x63551),f2(x63551)),x63552))+P1(f324(f324(f238(x63551),f324(f80(x63551),x63552)),x63552)) % 181.55/181.54 [6356]~P74(x63561)+~P1(f324(f324(f239(x63561),f2(x63561)),x63562))+P1(f324(f324(f239(x63561),f324(f80(x63561),x63562)),x63562)) % 181.55/181.54 [6528]E(f324(f324(f22(a865),f324(a107,x65281)),f324(a107,x65282)),f324(a107,f324(f324(f22(a1),x65281),x65282)))+~P1(f324(f324(f238(a1),f2(a1)),x65282))+~P1(f324(f324(f238(a1),x65282),x65281)) % 181.55/181.54 [6560]E(f324(a107,f44(a1,f324(f106(a1),x65601),f324(f106(a1),x65602))),f44(a865,f324(f106(a865),x65601),f324(f106(a865),x65602)))+P1(f324(a196,f324(f106(a1),x65601)))+P1(f324(a196,f324(f106(a1),x65602))) % 181.55/181.54 [6578]~P74(x65781)+P1(f324(f324(f238(x65781),f2(x65781)),x65782))+~P1(f324(f324(f238(x65781),f324(f80(x65781),x65782)),x65782)) % 181.55/181.54 [6579]~P74(x65791)+P1(f324(f324(f239(x65791),f2(x65791)),x65792))+~P1(f324(f324(f239(x65791),f324(f80(x65791),x65792)),x65792)) % 181.55/181.54 [6591]~P74(x65911)+~P1(f324(f324(f238(x65911),f2(x65911)),x65912))+P1(f324(f324(f238(x65911),f2(x65911)),f324(f324(f81(x65911),x65912),x65912))) % 181.55/181.54 [6593]~P74(x65931)+~P1(f324(f324(f239(x65931),f2(x65931)),x65932))+P1(f324(f324(f239(x65931),f2(x65931)),f324(f324(f81(x65931),x65932),x65932))) % 181.55/181.54 [6605]E(f324(f324(f81(a865),f324(a107,x66051)),f324(a107,x66052)),f324(a107,f324(f324(f81(a1),x66051),x66052)))+~P1(f324(f324(f238(a1),f2(a1)),x66052))+~P1(f324(f324(f238(a1),f2(a1)),x66051)) % 181.55/181.54 [6616]E(x66161,f2(a865))+P1(f324(f324(f239(a865),f2(a865)),x66162))+~P1(f324(f324(f239(a865),f2(a865)),f324(f324(f249(a865),x66162),x66161))) % 181.55/181.54 [6646]~P92(x66461)+E(f324(f106(x66461),x66462),f2(x66461))+~P32(x66461,f324(f106(x66461),f324(f324(f81(a1),a84),f324(f80(a1),x66462)))) % 181.55/181.54 [6647]~P92(x66471)+E(f324(f106(x66471),x66472),f2(x66471))+~P32(x66471,f324(f106(x66471),f324(f324(f81(a1),x66472),f324(f80(a1),a84)))) % 181.55/181.54 [6706]~P1(f324(f61(x67061),x67062))+~P1(f324(f61(x67061),f247(f871(x67061,a859))))+P1(f324(f61(x67061),f324(f80(f871(x67061,a859)),x67062))) % 181.55/181.54 [6729]~P1(f324(f324(f239(a1),f2(a1)),x67292))+~P1(f324(f324(f238(a1),x67292),x67291))+P1(f324(f324(f239(a1),f2(a1)),f324(f324(f38(a1),x67291),x67292))) % 181.55/181.54 [6730]~P1(f324(f324(f238(a1),x67301),f2(a1)))+~P1(f324(f324(f239(a1),x67302),f2(a1)))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f38(a1),x67301),x67302))) % 181.55/181.54 [6768]~P1(f324(f324(f238(a1),f2(a1)),x67682))+~P1(f324(f324(f238(a1),f2(a1)),x67681))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f82(a1),x67681),x67682))) % 181.55/181.54 [6769]~P1(f324(f324(f238(a1),f2(a1)),x67692))+~P1(f324(f324(f238(a1),f2(a1)),x67691))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f81(a1),x67691),x67692))) % 181.55/181.54 [6770]~P1(f324(f324(f238(a1),f2(a1)),x67702))+~P1(f324(f324(f238(a1),f2(a1)),x67701))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f38(a1),x67701),x67702))) % 181.55/181.54 [6771]~P1(f324(f324(f238(a1),f2(a1)),x67711))+~P1(f324(f324(f239(a1),f2(a1)),x67712))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f38(a1),x67711),x67712))) % 181.55/181.54 [6772]~P1(f324(f324(f239(a865),f2(a865)),x67722))+~P1(f324(f324(f239(a865),f2(a865)),x67721))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f82(a865),x67721),x67722))) % 181.55/181.54 [6837]E(x68371,f2(a1))+E(f44(a1,x68372,x68371),f2(a1))+E(f324(f324(f22(a1),f324(f80(a1),f324(f324(f38(a1),x68372),x68371))),f79(a1)),f324(f324(f38(a1),f324(f80(a1),x68372)),x68371)) % 181.55/181.54 [6890]P1(f324(f324(f239(a865),f2(a865)),x68901))+P1(f324(f324(f239(a865),f2(a865)),x68902))+~P1(f324(f324(f239(a865),f2(a865)),f324(f324(f81(a865),x68902),x68901))) % 181.55/181.54 [6894]~P74(x68941)+P1(f324(f324(f238(x68941),f2(x68941)),x68942))+~P1(f324(f324(f238(x68941),f2(x68941)),f324(f324(f81(x68941),x68942),x68942))) % 181.55/181.54 [6895]~P74(x68951)+P1(f324(f324(f239(x68951),f2(x68951)),x68952))+~P1(f324(f324(f239(x68951),f2(x68951)),f324(f324(f81(x68951),x68952),x68952))) % 181.55/181.54 [6947]~P1(f324(f61(x69471),x69472))+P1(f324(f61(x69471),f247(f871(x69471,a859))))+~P1(f324(f61(x69471),f324(f80(f871(x69471,a859)),x69472))) % 181.55/181.54 [7010]P1(f324(f324(f238(a1),x70101),f2(a1)))+~P1(f324(f324(f239(a1),x70102),f2(a1)))+~P1(f324(f324(f238(a1),f2(a1)),f324(f324(f38(a1),x70101),x70102))) % 181.55/181.54 [7016]~P1(f324(f324(f239(a1),f2(a1)),x70161))+P1(f324(f324(f238(a1),x70161),x70162))+~P1(f324(f324(f239(a1),f2(a1)),f324(f324(f38(a1),x70162),x70161))) % 181.55/181.54 [7017]~P1(f324(f324(f238(a1),f2(a1)),x70172))+P1(f324(f324(f238(a1),x70171),x70172))+~P1(f324(f324(f239(a1),f2(a1)),f324(f324(f38(a1),x70172),x70171))) % 181.55/181.54 [7046]P1(f324(f324(f238(a1),f2(a1)),x70461))+~P1(f324(f324(f239(a1),f2(a1)),x70462))+~P1(f324(f324(f238(a1),f2(a1)),f324(f324(f38(a1),x70461),x70462))) % 181.55/181.54 [7047]P1(f324(f324(f239(a1),f2(a1)),x70471))+~P1(f324(f324(f238(a1),f2(a1)),x70472))+~P1(f324(f324(f239(a1),f2(a1)),f324(f324(f38(a1),x70472),x70471))) % 181.55/181.54 [7489]~P1(f324(f61(x74892),f247(f871(x74892,a859))))+~P1(f324(f61(x74891),f247(f871(x74891,a859))))+P1(f324(f61(f870(x74891,x74892)),f247(f871(f870(x74891,x74892),a859)))) % 181.55/181.54 [7490]~P1(f324(f61(x74902),f247(f871(x74902,a859))))+~P1(f324(f61(x74901),f247(f871(x74901,a859))))+P1(f324(f61(f872(x74901,x74902)),f247(f871(f872(x74901,x74902),a859)))) % 181.55/181.54 [7559]~P1(f324(f324(f239(a865),f324(a115,f2(a865))),x75591))+~P1(f324(f324(f239(a865),f324(a115,f2(a865))),x75592))+P1(f324(f324(f239(a865),x75591),f324(f324(f82(a865),x75592),x75591))) % 181.55/181.54 [7560]~P1(f324(f324(f239(a865),f324(a115,f2(a865))),x75601))+~P1(f324(f324(f239(a865),f324(a115,f2(a865))),x75602))+P1(f324(f324(f239(a865),x75601),f324(f324(f82(a865),x75601),x75602))) % 181.55/181.54 [7594]E(f324(f37(x75941),f247(f871(x75941,a859))),f324(a115,f2(a865)))+P1(f324(f61(x75942),f247(f871(x75942,a859))))+~P1(f324(f61(f871(x75942,x75941)),f247(f871(f871(x75942,x75941),a859)))) % 181.55/181.54 [7716]~P1(f324(f324(f238(a865),f324(a115,f2(a865))),x77161))+~P1(f324(f324(f238(a865),f324(a115,f2(a865))),x77162))+P1(f324(f324(f238(a865),f324(a115,f2(a865))),f324(f324(f82(a865),x77161),x77162))) % 181.55/181.54 [7717]~P1(f324(f324(f239(a865),f324(a115,f2(a865))),x77172))+~P1(f324(f324(f239(a865),f324(a115,f2(a865))),x77171))+P1(f324(f324(f239(a865),f324(a115,f2(a865))),f324(f324(f82(a865),x77171),x77172))) % 181.55/181.54 [8399]E(x83991,f116(x83992))+~P1(f324(f131(x83992),x83991))+E(f172(x83992,f324(f324(f8(a859,a859,x83992),a319),f324(f324(f7(x83992,x83992,a859),a321),f138(x83992,x83991))),x83991),f117(x83992,x83991)) % 181.55/181.54 [8492]~P40(x84922)+~P40(x84921)+E(f324(f303(a865,a1,f103(a1)),f324(f324(f104(f871(a865,a859)),f324(f303(a1,a865,a107),x84921)),f324(f303(a1,a865,a107),x84922))),f324(f324(f104(f871(a1,a859)),x84921),x84922)) % 181.55/181.54 [8493]~P40(x84932)+~P40(x84931)+E(f324(f303(a865,a1,f103(a1)),f324(f324(f113(f871(a865,a859)),f324(f303(a1,a865,a107),x84931)),f324(f303(a1,a865,a107),x84932))),f324(f324(f113(f871(a1,a859)),x84931),x84932)) % 181.55/181.54 [9163]~P92(x91631)+~E(f324(f106(x91631),x91632),f79(x91631))+P32(x91631,f324(f106(x91631),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f80(a1),x91632)))) % 181.55/181.54 [9398]~P92(x93981)+E(f324(f106(x93981),x93982),f79(x93981))+~P32(x93981,f324(f106(x93981),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f80(a1),x93982)))) % 181.55/181.54 [10134]E(x101341,f2(a1))+E(x101342,f2(a1))+E(f324(f264(a1,a1,a1,a1,f34(a1),f324(f82(a1),f83(a1,x101342))),f324(f324(f324(f99(f870(a1,a1)),f324(f324(a321,f83(a1,x101341)),f83(a1,x101342))),f52(x101341,x101342)),f324(f324(f263(a1,a1,f870(a1,a1)),f324(f324(f18(a1,f871(a1,f870(a1,a1)),f871(a1,f870(a1,a1))),f324(f324(f8(f871(a1,f871(f870(a1,a1),f870(a1,a1))),f871(f871(a1,f870(a1,a1)),f871(a1,f870(a1,a1))),a1),f18(a1,f870(a1,a1),f870(a1,a1))),f324(f324(f8(f870(a1,a1),f871(a1,f871(f870(a1,a1),f870(a1,a1))),a1),f324(f7(a1,f870(a1,a1),f871(f870(a1,a1),f870(a1,a1))),f324(f324(f8(a859,f871(f870(a1,a1),f871(f870(a1,a1),f870(a1,a1))),a1),f99(f870(a1,a1))),f324(f324(f7(a1,a1,a859),a321),f2(a1))))),f324(f324(f7(a1,a1,f870(a1,a1)),f324(f324(f8(a1,f871(a1,f870(a1,a1)),a1),f259(a1,a1)),f80(a1))),f2(a1))))),f324(f324(f7(a1,f871(a1,a1),f871(a1,f870(a1,a1))),f324(f324(f8(f871(a1,f870(a1,a1)),f871(f871(a1,a1),f871(a1,f870(a1,a1))),a1),f8(a1,f870(a1,a1),a1)),f324(f324(f8(a1,f871(a1,f870(a1,a1)),a1),f259(a1,a1)),f324(f324(f7(a1,a1,a1),f324(f324(f8(a1,f871(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f324(f22(a1),f324(f75(a1),x101342))))),f52(x101341,x101342)))),f45(x101341,x101342)) % 181.55/181.54 [10135]E(x101351,f2(a1))+E(x101352,f2(a1))+E(f324(f264(a1,a1,a1,a1,f34(a1),f324(f82(a1),f83(a1,x101352))),f324(f324(f324(f99(f870(a1,a1)),f324(f324(a323,f324(f324(a322,f324(f324(f239(a1),f2(a1)),x101352)),f324(f324(f238(a1),f2(a1)),x101351))),f324(f324(a322,f324(f324(f239(a1),x101352),f2(a1))),f324(f324(f239(a1),x101351),f2(a1))))),f52(x101351,x101352)),f324(f324(f263(a1,a1,f870(a1,a1)),f324(f324(f18(a1,f871(a1,f870(a1,a1)),f871(a1,f870(a1,a1))),f324(f324(f8(f871(a1,f871(f870(a1,a1),f870(a1,a1))),f871(f871(a1,f870(a1,a1)),f871(a1,f870(a1,a1))),a1),f18(a1,f870(a1,a1),f870(a1,a1))),f324(f324(f8(f870(a1,a1),f871(a1,f871(f870(a1,a1),f870(a1,a1))),a1),f324(f7(a1,f870(a1,a1),f871(f870(a1,a1),f870(a1,a1))),f324(f324(f8(a859,f871(f870(a1,a1),f871(f870(a1,a1),f870(a1,a1))),a1),f99(f870(a1,a1))),f324(f324(f7(a1,a1,a859),a321),f2(a1))))),f324(f324(f7(a1,a1,f870(a1,a1)),f324(f324(f8(a1,f871(a1,f870(a1,a1)),a1),f259(a1,a1)),f80(a1))),f2(a1))))),f324(f324(f7(a1,f871(a1,a1),f871(a1,f870(a1,a1))),f324(f324(f8(f871(a1,f870(a1,a1)),f871(f871(a1,a1),f871(a1,f870(a1,a1))),a1),f8(a1,f870(a1,a1),a1)),f324(f324(f8(a1,f871(a1,f870(a1,a1)),a1),f259(a1,a1)),f324(f324(f7(a1,a1,a1),f324(f324(f8(a1,f871(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f324(f22(a1),f324(f75(a1),x101352))))),f52(x101351,x101352)))),f45(x101351,x101352)) % 181.55/181.54 [5666]~P117(x56661)+~P92(x56661)+E(f324(f75(x56661),f324(f324(f249(x56661),f324(f106(x56661),a100)),x56662)),f79(x56661)) % 181.55/181.54 [6139]~P135(x61391)+~P1(f324(f324(f239(a1),x61392),f2(a1)))+E(f324(f80(x61391),f324(f103(x61391),f324(a107,f324(f80(a1),x61392)))),f324(f105(x61391),x61392)) % 181.55/181.54 [6338]P1(f324(f324(f238(a102),x63381),f79(a102)))+E(f324(f324(f81(a102),f79(a102)),f272(x63381,f324(f324(f38(a102),x63382),x63381))),f272(x63381,x63382))+P1(f324(f324(f239(a102),x63382),x63381)) % 181.55/181.54 [6935]~P89(x69351)+~P1(f324(f324(f326(x69351),x69352),f112(x69351)))+~E(f324(f324(f81(x69351),f324(f324(f81(x69351),f79(x69351)),x69352)),x69352),f2(x69351)) % 181.55/181.54 [7048]~P1(f324(f324(f238(a1),x70482),f2(a1)))+~P1(f324(f324(f239(a1),x70481),f2(a1)))+E(f324(f258(a1,a1),f324(a50,f46(f324(f80(a1),x70481),f324(f80(a1),x70482)))),f324(f324(f38(a1),x70481),x70482)) % 181.55/181.54 [7065]~P1(f324(f324(f238(a1),x70652),f2(a1)))+~P1(f324(f324(f239(a1),x70651),f2(a1)))+E(f324(f262(a1,a1),f324(a50,f46(f324(f80(a1),x70651),f324(f80(a1),x70652)))),f44(a1,x70651,x70652)) % 181.55/181.54 [7071]~P1(f324(f324(f239(a1),x70712),f2(a1)))+E(f324(f258(a1,a1),f324(a50,f49(f324(f80(a1),x70711),f324(f80(a1),x70712)))),f324(f324(f38(a1),x70711),x70712))+~P1(f324(f324(f239(a1),f2(a1)),x70711)) % 181.55/181.54 [7089]~P1(f324(f324(f239(a1),x70892),f2(a1)))+E(f324(f262(a1,a1),f324(a50,f49(f324(f80(a1),x70891),f324(f80(a1),x70892)))),f44(a1,x70891,x70892))+~P1(f324(f324(f239(a1),f2(a1)),x70891)) % 181.55/181.54 [7141]E(f324(f324(f38(a1),f324(f324(f249(a1),x71411),x71412)),x71411),f324(f324(f249(a1),x71411),f324(f324(f22(a865),x71412),f324(a115,f2(a865)))))+~P1(f324(f324(f239(a865),f2(a865)),x71412))+~P1(f324(f324(f239(a1),f2(a1)),x71411)) % 181.55/181.54 [7234]~P1(f324(f324(f239(a865),f2(a865)),x72341))+~P1(f324(f324(f239(a865),f2(a865)),x72342))+P1(f324(f324(f239(a865),f324(f324(f22(a865),x72341),x72342)),x72341)) % 181.55/181.54 [7235]~P1(f324(f324(f239(a865),f2(a865)),x72351))+~P1(f324(f324(f239(a865),f79(a865)),x72352))+P1(f324(f324(f239(a865),f324(f324(f38(a865),x72351),x72352)),x72351)) % 181.55/181.54 [7236]~P1(f324(f324(f239(a1),f2(a1)),x72361))+~P1(f324(f324(f239(a1),f79(a1)),x72362))+P1(f324(f324(f239(a1),f324(f324(f38(a1),x72361),x72362)),x72361)) % 181.55/181.54 [7381]E(x73811,f2(a865))+~E(x73812,f2(a1))+~P1(f324(f324(f239(a1),f2(a1)),f324(f324(f249(a1),f324(f75(a1),x73812)),x73811))) % 181.55/181.54 [7793]~E(x77932,f116(f866(x77931)))+E(f324(f192(f866(f866(x77931))),f175(x77931,x77932)),f2(a865))+~P16(a865,f324(f163(a865),f324(f324(f148(f866(x77931),a865),f192(f866(x77931))),x77932))) % 181.55/181.54 [8043]P1(f324(x80431,x80432))+~P1(f324(x80431,f324(a110,f538(x80431,x80432))))+~P1(f324(f324(f326(f871(f870(a865,a865),a859)),x80432),a101)) % 181.55/181.54 [8061]E(x80611,f116(f866(x80612)))+E(f324(f192(f866(x80612)),f324(f324(f159(f866(x80612)),x80611),f2(a865))),f324(f192(f866(f866(x80612))),f175(x80612,x80611)))+~P16(a865,f324(f163(a865),f324(f324(f148(f866(x80612),a865),f192(f866(x80612))),x80611))) % 181.55/181.54 [8778]~P1(f324(f61(x87781),f324(f244(x87781),x87782)))+~P1(f324(f61(x87781),f247(f871(x87781,a859))))+P1(f324(f61(x87781),f324(f244(x87781),f324(f324(f8(a859,a859,x87781),a319),x87782)))) % 181.55/181.54 [8840]E(f324(f324(f259(a865,a865),f324(a115,f324(f324(f38(a865),f324(f324(f22(a865),x88401),x88402)),x88402))),f44(a865,f324(f324(f22(a865),x88401),x88402),x88402)),f86(f870(a865,a865),f47(x88401,x88402)))+~P1(f324(f324(f239(a865),f2(a865)),x88402))+~P1(f324(f324(f238(a865),x88402),x88401)) % 181.55/181.54 [9129]~P1(f324(f61(x91291),f324(f244(x91291),x91292)))+P1(f324(f61(x91291),f247(f871(x91291,a859))))+~P1(f324(f61(x91291),f324(f244(x91291),f324(f324(f8(a859,a859,x91291),a319),x91292)))) % 181.55/181.54 [9860]P29(x98601,x98602)+~P39(x98601,f324(f258(f871(f870(x98601,x98601),a859),f871(f870(x98601,x98601),a859)),x98602))+~P1(f324(f324(f238(f871(f870(x98601,x98601),a859)),f324(f324(f281(x98601,x98601,x98601),f324(f258(f871(f870(x98601,x98601),a859),f871(f870(x98601,x98601),a859)),x98602)),f324(f262(f871(f870(x98601,x98601),a859),f871(f870(x98601,x98601),a859)),x98602))),f324(f258(f871(f870(x98601,x98601),a859),f871(f870(x98601,x98601),a859)),x98602))) % 181.55/181.54 [7167]~P1(f324(f324(f239(a865),f2(a865)),x71672))+P1(f324(f324(f239(a865),x71671),x71672))+E(f324(a115,f324(f324(f38(a865),f324(f324(f22(a865),x71671),x71672)),x71672)),f324(f324(f38(a865),x71671),x71672)) % 181.55/181.54 [7302]~P1(f324(f324(f239(a865),f2(a865)),x73022))+~P1(f324(f324(f238(a865),x73022),x73021))+E(f324(a115,f324(f324(f38(a865),f324(f324(f22(a865),x73021),x73022)),x73022)),f324(f324(f38(a865),x73021),x73022)) % 181.55/181.54 [8273]~P92(x82731)+~P89(x82731)+~P32(x82731,f324(f106(x82731),f324(f324(f22(a1),f324(f324(f81(a1),x82732),x82732)),a100))) % 181.55/181.54 [9035]E(x90351,f2(a865))+E(f324(f324(f263(a865,a865,f870(a865,a865)),f324(f324(f8(a865,f871(a865,f870(a865,a865)),a865),f259(a865,a865)),a115)),f86(f870(a865,a865),f47(f324(f324(f22(a865),x90352),x90351),x90351))),f86(f870(a865,a865),f47(x90352,x90351)))+P1(f324(f324(f239(a865),x90352),x90351)) % 181.55/181.54 [9465]P1(f324(x94652,f652(x94652,x94651)))+P1(f324(x94651,f652(x94652,x94651)))+E(f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),x94651)),f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),x94652))) % 181.55/181.54 [9469]~P1(f324(x94692,f652(x94692,x94691)))+~P1(f324(x94691,f652(x94692,x94691)))+E(f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),x94691)),f324(f244(a1),f324(f324(f18(a1,a859,a859),f324(f324(f8(a859,f871(a859,a859),a1),a322),f324(f238(a1),f2(a1)))),x94692))) % 181.55/181.54 [7517]~P63(x75171)+~P92(x75171)+E(f324(f324(f282(x75171),x75172),f324(f106(x75171),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))),x75172) % 181.55/181.54 [9162]~P92(x91621)+~E(f324(f106(x91621),x91622),f79(x91621))+P32(x91621,f324(f106(x91621),f324(f324(f81(a1),x91622),f324(f80(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.54 [9339]~P134(x93391)+~E(x93392,f79(x93391))+E(f324(f324(f249(x93391),x93392),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f79(x93391)) % 181.55/181.54 [9340]~P134(x93401)+~E(x93402,f2(x93401))+E(f324(f324(f249(x93401),x93402),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f2(x93401)) % 181.55/181.54 [9353]~P134(x93531)+~E(x93532,f324(f80(x93531),f79(x93531)))+E(f324(f324(f249(x93531),x93532),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f79(x93531)) % 181.55/181.54 [9399]~P92(x93991)+E(f324(f106(x93991),x93992),f79(x93991))+~P32(x93991,f324(f106(x93991),f324(f324(f81(a1),x93992),f324(f80(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.54 [9796]~P117(x97962)+E(x97961,f2(x97962))+P1(f324(f324(f239(x97962),f2(x97962)),f324(f324(f249(x97962),x97961),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.54 [9859]~P117(x98592)+~E(x98591,f2(x98592))+~P1(f324(f324(f239(x98592),f2(x98592)),f324(f324(f249(x98592),x98591),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.54 [9885]P1(f324(f324(f238(a1),x98851),f2(a1)))+P1(f324(f324(f239(a1),x98852),x98851))+E(f324(f43(x98851),f46(x98852,f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98851))),f46(x98852,x98851)) % 181.55/181.54 [9886]~P1(f324(f324(f239(a1),f2(a1)),x98861))+P1(f324(f324(f239(a1),x98862),x98861))+E(f324(f43(x98861),f46(x98862,f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98861))),f46(x98862,x98861)) % 181.55/181.54 [9887]P1(f324(f324(f238(a1),x98871),f2(a1)))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f81(a1),x98872),x98871)))+E(f324(f43(x98871),f49(x98872,f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98871))),f49(x98872,x98871)) % 181.55/181.54 [9888]~P1(f324(f324(f239(a1),f2(a1)),x98881))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f81(a1),x98882),x98881)))+E(f324(f43(x98881),f49(x98882,f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98881))),f49(x98882,x98881)) % 181.55/181.54 [9889]~P141(x98891)+~P1(f324(f324(f238(a1),f2(a1)),x98892))+E(f324(f103(x98891),f324(a107,f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x98892))),f324(f324(f81(x98891),f324(f103(x98891),f324(a107,x98892))),f324(f103(x98891),f324(a107,x98892)))) % 181.55/181.54 [5021]~P143(x50211,x50213,x50212)+~E(x50213,f2(a1))+P1(f324(x50211,x50212)) % 181.55/181.54 [5138]~P105(x51381)+~P16(x51381,x51383)+P16(x51381,f164(x51381,x51382,x51383)) % 181.55/181.54 [5139]~P105(x51391)+~P16(x51391,x51393)+P16(x51391,f172(x51391,x51392,x51393)) % 181.55/181.54 [4732]~P4(x47322)+~E(x47323,f324(f80(x47322),x47321))+E(x47321,f324(f80(x47322),x47323)) % 181.55/181.54 [4734]~P4(x47341)+~E(f324(f80(x47341),x47343),x47342)+E(f324(f80(x47341),x47342),x47343) % 181.55/181.54 [4807]~P79(x48073)+E(x48071,x48072)+~E(f324(f80(x48073),x48071),f324(f80(x48073),x48072)) % 181.55/181.54 [4808]~P4(x48083)+E(x48081,x48082)+~E(f324(f80(x48083),x48081),f324(f80(x48083),x48082)) % 181.55/181.54 [4809]~P89(x48093)+E(x48091,x48092)+~E(f324(f105(x48093),x48091),f324(f105(x48093),x48092)) % 181.55/181.54 [4810]~P101(x48103)+E(x48101,x48102)+~E(f324(f103(x48103),x48101),f324(f103(x48103),x48102)) % 181.55/181.54 [4811]~P105(x48113)+E(x48111,x48112)+~E(f324(f245(x48113),x48111),f324(f245(x48113),x48112)) % 181.55/181.54 [4812]~P105(x48123)+E(x48121,x48122)+~E(f324(f293(x48123),x48121),f324(f293(x48123),x48122)) % 181.55/181.54 [4813]~P105(x48133)+E(x48131,x48132)+~E(f324(f296(x48133),x48131),f324(f296(x48133),x48132)) % 181.55/181.54 [4814]~P105(x48143)+E(x48141,x48142)+~E(f324(f246(x48143),x48141),f324(f246(x48143),x48142)) % 181.55/181.54 [4911]~P61(x49111)+~P1(f324(x49112,x49113))+P1(f324(f57(x49111),x49112)) % 181.55/181.54 [4944]~P61(x49443)+P1(f324(x49441,x49442))+~P1(f324(f58(x49443),x49441)) % 181.55/181.54 [5039]~P144(x50391,x50392,x50393)+~E(x50392,f2(a1))+P1(f324(x50391,f2(a1))) % 181.55/181.54 [5076]~E(x50761,f2(a865))+E(f330(x50761,x50762,x50763),f191(f871(x50763,a859)))+~E(f324(f37(x50763),x50762),f324(a115,x50761)) % 181.55/181.54 [5218]~E(x52182,f2(a865))+E(f324(f258(a865,a865),x52181),f2(a865))+~P1(f324(f47(x52183,x52182),x52181)) % 181.55/181.54 [5262]P1(f324(x52621,x52622))+~E(x52623,f324(f103(a1),x52622))+~P1(f324(x52621,f324(a107,x52623))) % 181.55/181.54 [5729]~E(x57293,f2(a865))+~P1(f324(x57291,x57292))+P1(f324(x57291,f44(a865,x57292,x57293))) % 181.55/181.54 [5890]~P61(x58903)+~P12(x58903,x58901,x58902)+P1(f324(x58901,f717(x58902,x58901,x58903))) % 181.55/181.54 [6123]~E(x61233,f2(a865))+P1(f324(x61231,x61232))+~P1(f324(x61231,f44(a865,x61232,x61233))) % 181.55/181.54 [6269]~P61(x62691)+P13(x62691,x62692,x62693)+~P1(f324(x62692,f725(x62693,x62692,x62691))) % 181.55/181.54 [6794]E(x67941,f2(a865))+~P1(f324(x67942,f398(x67941,x67943,x67942)))+P1(f324(x67942,f44(a865,x67943,x67941))) % 181.55/181.54 [6900]~P6(x69001)+~P1(f324(f324(f238(x69001),x69002),f606(x69003,x69002,x69001)))+P1(f324(f324(f238(x69001),x69002),f40(x69001,x69003))) % 181.55/181.54 [6902]~P1(f324(x69021,x69022))+~P1(f324(x69021,f398(x69023,x69022,x69021)))+P1(f324(x69021,f44(a865,x69022,x69023))) % 181.55/181.54 [7003]E(x70031,f116(x70032))+E(f324(f324(f145(x70032),f703(x70033,x70031,x70032)),f711(x70033,x70031,x70032)),x70031)+~P1(f324(f324(f326(f866(x70032)),x70031),f155(x70032,x70033))) % 181.55/181.54 [7034]~P135(x70341)+~P1(f324(f324(f326(x70341),x70342),f112(x70341)))+P1(f324(f324(f326(x70341),f324(f324(f249(x70341),x70342),x70343)),f112(x70341))) % 181.55/181.54 [7351]P39(x73511,x73512)+~P1(f324(f324(f326(x73511),x73513),f603(x73512,x73511)))+P1(f324(f324(f326(x73511),f650(x73512,x73511,x73513)),f603(x73512,x73511))) % 181.55/181.54 [7619]E(x76191,f116(x76192))+~P1(f324(f324(f326(f866(x76192)),x76191),f155(x76192,x76193)))+P1(f324(f324(f326(f866(x76192)),f711(x76193,x76191,x76192)),f155(x76192,x76193))) % 181.55/181.54 [7671]E(x76711,f2(a865))+E(f324(f324(f81(a865),f324(f324(f82(a865),x76711),f399(x76711,x76712,x76713))),f398(x76711,x76712,x76713)),x76712)+P1(f324(x76713,f44(a865,x76712,x76711))) % 181.55/181.54 [7711]~P1(f324(x77113,x77112))+E(f324(f324(f81(a865),f324(f324(f82(a865),x77111),f399(x77111,x77112,x77113))),f398(x77111,x77112,x77113)),x77112)+P1(f324(x77113,f44(a865,x77112,x77111))) % 181.55/181.54 [7851]P1(f324(f324(f239(a1),x78511),f392(x78512,x78513,x78511)))+P1(f324(f324(x78513,f324(f324(f38(a1),x78512),x78511)),f44(a1,x78512,x78511)))+~P1(f324(f324(f239(a1),x78511),f2(a1))) % 181.55/181.54 [8121]P1(f324(f324(x81212,f324(f324(f38(a1),x81211),x81213)),f44(a1,x81211,x81213)))+~P1(f324(f324(f239(a1),x81213),f2(a1)))+P1(f324(f324(f238(a1),f392(x81211,x81212,x81213)),f2(a1))) % 181.55/181.54 [8310]E(f324(f324(f81(a1),f324(f324(f82(a1),x83101),f395(x83102,x83103,x83101))),f392(x83102,x83103,x83101)),x83102)+P1(f324(f324(x83103,f324(f324(f38(a1),x83102),x83101)),f44(a1,x83102,x83101)))+~P1(f324(f324(f239(a1),x83101),f2(a1))) % 181.55/181.54 [8541]~P1(f324(f324(x85411,f395(x85412,x85411,x85413)),f392(x85412,x85411,x85413)))+P1(f324(f324(x85411,f324(f324(f38(a1),x85412),x85413)),f44(a1,x85412,x85413)))+~P1(f324(f324(f239(a1),x85413),f2(a1))) % 181.55/181.54 [8788]~P105(x87881)+~P16(x87881,x87883)+P16(x87881,f143(x87881,x87881,f5(x87881),x87882,x87883)) % 181.55/181.54 [9288]~P121(x92882)+E(x92881,f2(x92882))+~P1(f324(f324(f238(x92882),f324(f324(f81(x92882),f324(f324(f82(x92882),x92883),x92883)),f324(f324(f82(x92882),x92881),x92881))),f2(x92882))) % 181.55/181.54 [9289]~P121(x92892)+E(x92891,f2(x92892))+~P1(f324(f324(f238(x92892),f324(f324(f81(x92892),f324(f324(f82(x92892),x92891),x92891)),f324(f324(f82(x92892),x92893),x92893))),f2(x92892))) % 181.55/181.54 [10074]~P117(x100741)+~P1(f324(f324(f239(x100741),x100742),f2(x100741)))+P1(f324(f324(f239(x100741),f324(f324(f249(x100741),x100742),f324(a115,f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100743)))),f2(x100741))) % 181.55/181.54 [10083]~P117(x100832)+E(x100831,f2(x100832))+~P1(f324(f324(f238(x100832),f324(f324(f81(x100832),f324(f324(f249(x100832),x100833),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100832),x100831),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))),f2(x100832))) % 181.55/181.54 [10084]~P117(x100842)+E(x100841,f2(x100842))+~P1(f324(f324(f238(x100842),f324(f324(f81(x100842),f324(f324(f249(x100842),x100841),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100842),x100843),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))),f2(x100842))) % 181.55/181.54 [4764]~E(x47642,x47643)+~P4(x47641)+E(f324(f324(f22(x47641),x47642),x47643),f2(x47641)) % 181.55/181.54 [4765]~E(x47652,x47653)+~P5(x47651)+E(f324(f324(f22(x47651),x47652),x47653),f2(x47651)) % 181.55/181.54 [4778]~P136(x47781)+~E(x47783,f2(x47781))+E(f324(f324(f81(x47781),x47782),x47783),x47782) % 181.55/181.54 [4793]~P138(x47931)+~E(x47933,f2(x47931))+E(f324(f324(f82(x47931),x47932),x47933),f2(x47931)) % 181.55/181.54 [4794]~P138(x47941)+~E(x47942,f2(x47941))+E(f324(f324(f82(x47941),x47942),x47943),f2(x47941)) % 181.55/181.54 [4816]~E(x48163,f116(x48161))+~E(x48162,f116(x48161))+E(f324(f324(f124(x48161),x48162),x48163),f116(x48161)) % 181.55/181.54 [4901]~P136(x49012)+E(x49011,f2(x49012))+~E(f324(f324(f81(x49012),x49013),x49011),x49013) % 181.55/181.54 [4902]~P4(x49021)+~E(x49022,f324(f80(x49021),x49023))+E(f324(f324(f81(x49021),x49022),x49023),f2(x49021)) % 181.55/181.54 [4909]E(x49091,f116(x49092))+E(x49093,f2(a865))+~E(f324(f324(f170(x49092),x49093),x49091),f116(x49092)) % 181.55/181.54 [4915]~P4(x49153)+E(x49151,x49152)+~E(f324(f324(f22(x49153),x49151),x49152),f2(x49153)) % 181.55/181.54 [4916]~P5(x49163)+E(x49161,x49162)+~E(f324(f324(f22(x49163),x49161),x49162),f2(x49163)) % 181.55/181.54 [4925]~P134(x49252)+E(x49251,f2(x49252))+~E(f324(f324(f249(x49252),x49251),x49253),f2(x49252)) % 181.55/181.54 [4926]~P95(x49262)+E(x49261,f191(x49262))+~E(f324(f324(f113(x49262),x49263),x49261),f191(x49262)) % 181.55/181.54 [4927]~P95(x49272)+E(x49271,f191(x49272))+~E(f324(f324(f113(x49272),x49271),x49273),f191(x49272)) % 181.55/181.54 [4928]~P97(x49282)+E(x49281,f247(x49282))+~E(f324(f324(f104(x49282),x49283),x49281),f247(x49282)) % 181.55/181.54 [4929]~P97(x49292)+E(x49291,f247(x49292))+~E(f324(f324(f104(x49292),x49291),x49293),f247(x49292)) % 181.55/181.54 [4995]~P4(x49952)+E(x49951,f324(f80(x49952),x49953))+~E(f324(f324(f81(x49952),x49951),x49953),f2(x49952)) % 181.55/181.54 [4996]~P4(x49961)+E(f324(f80(x49961),x49962),x49963)+~E(f324(f324(f81(x49961),x49962),x49963),f2(x49961)) % 181.55/181.54 [4998]~E(x49982,x49983)+~P103(x49981)+P1(f324(f324(f238(x49981),x49982),x49983)) % 181.55/181.54 [5000]~E(x50002,x50003)+~P106(x50001)+P1(f324(f324(f238(x50001),x50002),x50003)) % 181.55/181.54 [5001]~E(x50012,x50013)+~P91(x50011)+P1(f324(f324(f92(x50011),x50012),x50013)) % 181.55/181.54 [5091]~P108(x50911)+~E(x50912,f324(f80(x50911),x50913))+E(f324(f324(f82(x50911),x50912),x50912),f324(f324(f82(x50911),x50913),x50913)) % 181.55/181.54 [5099]~P105(x50991)+~P16(x50991,x50993)+P16(x50991,f324(f324(f170(x50991),x50992),x50993)) % 181.55/181.54 [5100]~P105(x51001)+~P16(x51001,x51003)+P16(x51001,f324(f324(f132(x51001),x51002),x51003)) % 181.55/181.54 [5136]E(x51361,x51362)+E(x51363,f2(a865))+~E(f324(f324(f82(a865),x51363),x51361),f324(f324(f82(a865),x51363),x51362)) % 181.55/181.54 [5137]E(x51371,x51372)+E(x51373,f2(a865))+~E(f324(f324(f82(a865),x51371),x51373),f324(f324(f82(a865),x51372),x51373)) % 181.55/181.54 [5209]~E(x52092,x52093)+~P106(x52091)+E(f295(x52091,x52092,x52093),f324(f324(f302(x52091),x52092),f191(f871(x52091,a859)))) % 181.55/181.54 [5250]E(x52501,x52502)+~P91(x52503)+~P1(f324(f324(f92(x52503),x52501),x52502)) % 181.55/181.54 [5260]~E(x52601,x52602)+~P105(x52603)+~P1(f324(f324(f239(x52603),x52601),x52602)) % 181.55/181.54 [5261]~E(x52611,x52612)+~P106(x52613)+~P1(f324(f324(f239(x52613),x52611),x52612)) % 181.55/181.54 [5271]~P106(x52711)+E(f324(f294(x52711,x52712),x52713),f191(f871(x52711,a859)))+P1(f324(f324(f239(x52711),x52712),x52713)) % 181.55/181.54 [5317]~P106(x53171)+E(f297(x53171,x53172,x53173),f191(f871(x53171,a859)))+P1(f324(f324(f239(x53171),x53172),x53173)) % 181.55/181.54 [5318]~P106(x53181)+E(f295(x53181,x53182,x53183),f191(f871(x53181,a859)))+P1(f324(f324(f238(x53181),x53182),x53183)) % 181.55/181.54 [5319]~P106(x53191)+E(f191(f871(x53191,a859)),f297(x53191,x53192,x53193))+P1(f324(f324(f239(x53191),x53192),x53193)) % 181.55/181.54 [5320]~P106(x53201)+E(f191(f871(x53201,a859)),f295(x53201,x53202,x53203))+P1(f324(f324(f238(x53201),x53202),x53203)) % 181.55/181.54 [5328]~P99(x53281)+~E(f324(f324(f104(x53281),x53282),x53283),x53282)+P1(f324(f324(f238(x53281),x53282),x53283)) % 181.55/181.54 [5329]~P100(x53291)+~E(f324(f324(f113(x53291),x53292),x53293),x53293)+P1(f324(f324(f238(x53291),x53292),x53293)) % 181.55/181.54 [5330]~P105(x53301)+~E(f324(f324(f189(x53301),x53302),x53303),x53302)+P1(f324(f324(f238(x53301),x53302),x53303)) % 181.55/181.54 [5331]~P105(x53311)+~E(f324(f324(f190(x53311),x53312),x53313),x53313)+P1(f324(f324(f238(x53311),x53312),x53313)) % 181.55/181.54 [5351]~P105(x53511)+P16(x53511,x53512)+~P16(x53511,f324(f324(f145(x53511),x53513),x53512)) % 181.55/181.54 [5352]~P105(x53521)+P16(x53521,x53522)+~P16(x53521,f324(f324(f124(x53521),x53523),x53522)) % 181.55/181.54 [5353]~P105(x53531)+P16(x53531,x53532)+~P16(x53531,f324(f324(f124(x53531),x53532),x53533)) % 181.55/181.54 [5418]~P105(x54181)+P1(f324(f324(f238(x54181),x54183),x54182))+P1(f324(f324(f238(x54181),x54182),x54183)) % 181.55/181.54 [5423]~P105(x54231)+P1(f324(f324(f239(x54231),x54233),x54232))+P1(f324(f324(f238(x54231),x54232),x54233)) % 181.55/181.54 [5461]~P99(x54611)+E(f324(f324(f104(x54611),x54612),x54613),x54613)+~P1(f324(f324(f238(x54611),x54613),x54612)) % 181.55/181.54 [5463]~P99(x54631)+E(f324(f324(f104(x54631),x54632),x54633),x54632)+~P1(f324(f324(f238(x54631),x54632),x54633)) % 181.55/181.54 [5464]~P100(x54641)+E(f324(f324(f113(x54641),x54642),x54643),x54642)+~P1(f324(f324(f238(x54641),x54643),x54642)) % 181.55/181.54 [5466]~P100(x54661)+E(f324(f324(f113(x54661),x54662),x54663),x54663)+~P1(f324(f324(f238(x54661),x54662),x54663)) % 181.55/181.54 [5467]~P105(x54671)+E(f324(f324(f189(x54671),x54672),x54673),x54673)+~P1(f324(f324(f238(x54671),x54673),x54672)) % 181.55/181.54 [5469]~P105(x54691)+E(f324(f324(f189(x54691),x54692),x54693),x54692)+~P1(f324(f324(f238(x54691),x54692),x54693)) % 181.55/181.54 [5470]~P105(x54701)+E(f324(f324(f190(x54701),x54702),x54703),x54702)+~P1(f324(f324(f238(x54701),x54703),x54702)) % 181.55/181.54 [5472]~P105(x54721)+E(f324(f324(f190(x54721),x54722),x54723),x54723)+~P1(f324(f324(f238(x54721),x54722),x54723)) % 181.55/181.54 [5479]~P114(x54792)+E(x54791,f2(x54792))+E(f324(f324(f282(x54792),f324(f80(x54792),x54793)),f324(f80(x54792),x54791)),f324(f324(f282(x54792),x54793),x54791)) % 181.55/181.54 [5524]~P106(x55241)+E(f324(f294(x55241,x55242),x55243),f191(f871(x55241,a859)))+~P1(f324(f324(f238(x55241),x55243),x55242)) % 181.55/181.54 [5555]~P106(x55551)+E(f298(x55551,x55552,x55553),f191(f871(x55551,a859)))+~P1(f324(f324(f238(x55551),x55553),x55552)) % 181.55/181.54 [5556]~P106(x55561)+E(f297(x55561,x55562,x55563),f191(f871(x55561,a859)))+~P1(f324(f324(f238(x55561),x55563),x55562)) % 181.55/181.54 [5557]~P106(x55571)+E(f295(x55571,x55572,x55573),f191(f871(x55571,a859)))+~P1(f324(f324(f239(x55571),x55573),x55572)) % 181.55/181.54 [5608]~E(f324(f324(f22(a865),x56081),x56083),x56082)+E(x56081,f324(f324(f81(a865),x56082),x56083))+~P1(f324(f324(f238(a865),x56083),x56081)) % 181.55/181.54 [5609]~E(x56091,f324(f324(f81(a865),x56093),x56092))+E(f324(f324(f22(a865),x56091),x56092),x56093)+~P1(f324(f324(f238(a865),x56092),x56091)) % 181.55/181.54 [5655]~P1(f324(x56551,x56553))+P1(f324(x56551,f440(x56551,x56552)))+~P1(f324(f324(f238(a865),x56553),x56552)) % 181.55/181.54 [5656]~P1(f324(x56561,x56563))+P1(f324(x56561,f442(x56561,x56562)))+~P1(f324(f324(f239(a865),x56563),x56562)) % 181.55/181.54 [5664]~P106(x56641)+~E(f324(f294(x56641,x56642),x56643),f191(f871(x56641,a859)))+~P1(f324(f324(f239(x56641),x56642),x56643)) % 181.55/181.54 [5669]~P103(x56691)+~P1(f324(f324(f239(x56691),x56692),x56693))+P1(f324(f324(f238(x56691),x56692),x56693)) % 181.55/181.54 [5671]~P106(x56711)+~P1(f324(f324(f239(x56711),x56712),x56713))+P1(f324(f324(f238(x56711),x56712),x56713)) % 181.55/181.54 [5777]~P106(x57771)+~E(f297(x57771,x57772,x57773),f191(f871(x57771,a859)))+~P1(f324(f324(f239(x57771),x57772),x57773)) % 181.55/181.54 [5778]~P106(x57781)+~E(f295(x57781,x57782,x57783),f191(f871(x57781,a859)))+~P1(f324(f324(f238(x57781),x57782),x57783)) % 181.55/181.54 [5779]~P106(x57791)+~E(f191(f871(x57791,a859)),f297(x57791,x57792,x57793))+~P1(f324(f324(f239(x57791),x57792),x57793)) % 181.55/181.54 [5780]~P106(x57801)+~E(f191(f871(x57801,a859)),f295(x57801,x57802,x57803))+~P1(f324(f324(f238(x57801),x57802),x57803)) % 181.55/181.54 [5788]P1(f324(x57881,x57882))+~P1(f324(x57881,f441(x57881,x57883)))+~P1(f324(f324(f238(a865),x57882),x57883)) % 181.55/181.54 [5789]P1(f324(x57891,x57892))+~P1(f324(x57891,f443(x57891,x57893)))+~P1(f324(f324(f239(a865),x57892),x57893)) % 181.55/181.54 [5797]~E(x57971,f324(a115,x57973))+P1(f324(f324(f239(a865),x57971),f324(a115,x57972)))+~P1(f324(f324(f239(a865),x57973),x57972)) % 181.55/181.54 [5813]E(x58131,x58132)+~E(f324(f324(f82(a865),x58133),x58131),f324(f324(f82(a865),x58133),x58132))+~P1(f324(f324(f239(a865),f2(a865)),x58133)) % 181.55/181.54 [5869]E(f324(x58691,f446(x58691,x58692,x58693)),f79(a865))+~E(f324(f324(f6(x58693,a865),x58691),x58692),f79(a865))+~P1(f324(f61(x58693),x58692)) % 181.55/181.54 [5881]~P6(x58811)+P1(f324(f324(f238(x58811),x58812),f39(x58811,x58813)))+~P1(f324(f324(f326(x58811),x58812),x58813)) % 181.55/181.54 [5907]~P103(x59071)+~P1(f324(f324(f239(x59071),x59073),x59072))+~P1(f324(f324(f238(x59071),x59072),x59073)) % 181.55/181.54 [5911]~P103(x59111)+~P1(f324(f324(f239(x59111),x59113),x59112))+~P1(f324(f324(f239(x59111),x59112),x59113)) % 181.55/181.54 [5914]~P105(x59141)+~P1(f324(f324(f239(x59141),x59143),x59142))+~P1(f324(f324(f238(x59141),x59142),x59143)) % 181.55/181.54 [5915]~P105(x59151)+~P1(f324(f324(f239(x59151),x59153),x59152))+~P1(f324(f324(f239(x59151),x59152),x59153)) % 181.55/181.54 [5916]~P106(x59161)+~P1(f324(f324(f239(x59161),x59163),x59162))+~P1(f324(f324(f239(x59161),x59162),x59163)) % 181.55/181.54 [5941]~E(f324(x59412,f380(x59412,x59413,x59411)),f79(a865))+E(f324(f324(f9(x59411,a865),x59412),x59413),f79(a865))+~P1(f324(f61(x59411),x59413)) % 181.55/181.54 [5942]~E(f324(x59422,f447(x59422,x59423,x59421)),f2(a865))+E(f324(f324(f6(x59421,a865),x59422),x59423),f2(a865))+~P1(f324(f61(x59421),x59423)) % 181.55/181.54 [5955]~P104(x59551)+~P1(f324(f324(f239(x59551),x59553),x59552))+P1(f324(f324(f326(x59551),x59552),f324(f296(x59551),x59553))) % 181.55/181.54 [5956]~P104(x59561)+~P1(f324(f324(f238(x59561),x59563),x59562))+P1(f324(f324(f326(x59561),x59562),f324(f246(x59561),x59563))) % 181.55/181.54 [5957]~P104(x59571)+~P1(f324(f324(f239(x59571),x59572),x59573))+P1(f324(f324(f326(x59571),x59572),f324(f245(x59571),x59573))) % 181.55/181.54 [5958]~P104(x59581)+~P1(f324(f324(f238(x59581),x59582),x59583))+P1(f324(f324(f326(x59581),x59582),f324(f293(x59581),x59583))) % 181.55/181.54 [5970]E(f324(x59701,f479(x59701,x59702,x59703)),f324(a115,f2(a865)))+~E(f324(f324(f6(x59703,a865),x59701),x59702),f324(a115,f2(a865)))+~P1(f324(f61(x59703),x59702)) % 181.55/181.54 [6052]~P6(x60521)+~P1(f324(f324(f326(x60521),x60523),x60522))+P1(f324(f324(f238(x60521),f40(x60521,x60522)),x60523)) % 181.55/181.54 [6069]~P1(f324(f324(f238(a865),x60691),x60693))+P1(f324(f324(f238(a865),x60691),x60692))+~P1(f324(f324(f238(a865),x60693),x60692)) % 181.55/181.54 [6070]~P1(f324(f324(f238(a1),x60701),x60703))+P1(f324(f324(f238(a1),x60701),x60702))+~P1(f324(f324(f238(a1),x60703),x60702)) % 181.55/181.54 [6087]~P104(x60871)+~P1(f324(f324(f326(x60871),x60873),f324(f246(x60871),x60872)))+P1(f324(f324(f238(x60871),x60872),x60873)) % 181.55/181.54 [6088]~P104(x60881)+~P1(f324(f324(f326(x60881),x60882),f324(f293(x60881),x60883)))+P1(f324(f324(f238(x60881),x60882),x60883)) % 181.55/181.54 [6089]~P104(x60891)+~P1(f324(f324(f326(x60891),x60893),f324(f296(x60891),x60892)))+P1(f324(f324(f239(x60891),x60892),x60893)) % 181.55/181.54 [6090]~P104(x60901)+~P1(f324(f324(f326(x60901),x60902),f324(f245(x60901),x60903)))+P1(f324(f324(f239(x60901),x60902),x60903)) % 181.55/181.54 [6303]~P64(x63031)+P1(f324(f324(f239(x63031),f2(x63031)),f488(x63033,x63032,x63031)))+P1(f324(f324(f238(x63031),x63032),x63033)) % 181.55/181.54 [6372]~P75(x63721)+~P1(f324(f324(f238(x63721),x63723),f324(f80(x63721),x63722)))+P1(f324(f324(f238(x63721),x63722),f324(f80(x63721),x63723))) % 181.55/181.54 [6374]~P75(x63741)+~P1(f324(f324(f239(x63741),x63743),f324(f80(x63741),x63742)))+P1(f324(f324(f239(x63741),x63742),f324(f80(x63741),x63743))) % 181.55/181.54 [6386]~P1(f324(f324(f239(a865),x63861),x63863))+~P1(f324(f324(f239(a865),x63863),x63862))+P1(f324(f324(f239(a865),f324(a115,x63861)),x63862)) % 181.55/181.54 [6411]~P117(x64111)+P1(f324(f324(f238(x64111),f324(f105(x64111),x64112)),f324(f105(x64111),x64113)))+~P1(f324(f324(f238(a1),x64112),x64113)) % 181.55/181.54 [6412]~P120(x64121)+P1(f324(f324(f238(x64121),f324(f103(x64121),x64122)),f324(f103(x64121),x64123)))+~P1(f324(f324(f238(a865),x64122),x64123)) % 181.55/181.54 [6413]~P117(x64131)+P1(f324(f324(f239(x64131),f324(f105(x64131),x64132)),f324(f105(x64131),x64133)))+~P1(f324(f324(f239(a1),x64132),x64133)) % 181.55/181.54 [6415]~P120(x64151)+P1(f324(f324(f239(x64151),f324(f103(x64151),x64152)),f324(f103(x64151),x64153)))+~P1(f324(f324(f239(a865),x64152),x64153)) % 181.55/181.54 [6421]~P105(x64211)+E(f324(f324(f113(f871(x64211,a859)),f324(f245(x64211),x64212)),f324(f294(x64211,x64212),x64213)),f324(f245(x64211),x64213))+~P1(f324(f324(f238(x64211),x64212),x64213)) % 181.55/181.54 [6451]~P75(x64511)+~P1(f324(f324(f238(x64511),x64513),x64512))+P1(f324(f324(f238(x64511),f324(f80(x64511),x64512)),f324(f80(x64511),x64513))) % 181.55/181.54 [6453]~P79(x64531)+~P1(f324(f324(f238(x64531),x64533),x64532))+P1(f324(f324(f238(x64531),f324(f80(x64531),x64532)),f324(f80(x64531),x64533))) % 181.55/181.54 [6454]~P75(x64541)+~P1(f324(f324(f239(x64541),x64543),x64542))+P1(f324(f324(f239(x64541),f324(f80(x64541),x64542)),f324(f80(x64541),x64543))) % 181.55/181.54 [6487]~P105(x64871)+E(f324(f324(f113(f871(x64871,a859)),f324(f245(x64871),x64872)),f295(x64871,x64872,x64873)),f324(f293(x64871),x64873))+~P1(f324(f324(f238(x64871),x64872),x64873)) % 181.55/181.54 [6488]~P105(x64881)+E(f324(f324(f113(f871(x64881,a859)),f324(f293(x64881),x64882)),f298(x64881,x64882,x64883)),f324(f245(x64881),x64883))+~P1(f324(f324(f239(x64881),x64882),x64883)) % 181.55/181.54 [6489]~P105(x64891)+E(f324(f324(f113(f871(x64891,a859)),f324(f293(x64891),x64892)),f297(x64891,x64892,x64893)),f324(f293(x64891),x64893))+~P1(f324(f324(f238(x64891),x64892),x64893)) % 181.55/181.54 [6523]~P105(x65231)+E(f324(f324(f113(f871(x65231,a859)),f324(f294(x65231,x65232),x65233)),f324(f246(x65231),x65233)),f324(f246(x65231),x65232))+~P1(f324(f324(f238(x65231),x65232),x65233)) % 181.55/181.54 [6677]~P105(x66771)+E(f324(f324(f113(f871(x66771,a859)),f298(x66771,x66772,x66773)),f324(f246(x66771),x66773)),f324(f296(x66771),x66772))+~P1(f324(f324(f239(x66771),x66772),x66773)) % 181.55/181.54 [6678]~P105(x66781)+E(f324(f324(f113(f871(x66781,a859)),f297(x66781,x66782,x66783)),f324(f296(x66781),x66783)),f324(f296(x66781),x66782))+~P1(f324(f324(f238(x66781),x66782),x66783)) % 181.55/181.54 [6679]~P105(x66791)+E(f324(f324(f113(f871(x66791,a859)),f295(x66791,x66792,x66793)),f324(f296(x66791),x66793)),f324(f246(x66791),x66792))+~P1(f324(f324(f238(x66791),x66792),x66793)) % 181.55/181.54 [6697]P1(f324(x66971,x66972))+~P1(f324(f324(f238(a865),x66972),x66973))+P1(f324(f324(f326(a865),f441(x66971,x66973)),f295(a865,f2(a865),x66973))) % 181.55/181.54 [6731]E(x67311,x67312)+~E(f324(f324(f159(x67313),x67311),f669(x67313,x67312,x67311)),f324(f324(f159(x67313),x67312),f669(x67313,x67312,x67311)))+~E(f324(f192(f866(x67313)),x67311),f324(f192(f866(x67313)),x67312)) % 181.55/181.54 [6736]~E(x67363,f324(f324(f38(a865),x67361),x67362))+~P1(f324(f324(f239(a865),f2(a865)),x67362))+P1(f324(f324(f239(a865),x67361),f324(f324(f82(a865),x67362),f324(a115,x67363)))) % 181.55/181.54 [6753]~P1(f324(x67531,x67533))+~P1(f324(f324(f238(a865),x67533),x67532))+P1(f324(f324(f326(a865),f440(x67531,x67532)),f295(a865,f2(a865),x67532))) % 181.55/181.54 [6791]~P1(f324(x67911,x67913))+P1(f324(x67911,f445(x67911,x67912)))+~P1(f324(f324(f326(a865),x67913),f295(a865,f2(a865),x67912))) % 181.55/181.54 [6810]~P120(x68103)+~P1(f324(f324(f238(x68103),f324(f103(x68103),x68101)),f324(f103(x68103),x68102)))+P1(f324(f324(f238(a865),x68101),x68102)) % 181.55/181.54 [6811]~P117(x68113)+~P1(f324(f324(f238(x68113),f324(f105(x68113),x68111)),f324(f105(x68113),x68112)))+P1(f324(f324(f238(a1),x68111),x68112)) % 181.55/181.54 [6813]~P120(x68133)+~P1(f324(f324(f239(x68133),f324(f103(x68133),x68131)),f324(f103(x68133),x68132)))+P1(f324(f324(f239(a865),x68131),x68132)) % 181.55/181.54 [6814]~P117(x68143)+~P1(f324(f324(f239(x68143),f324(f105(x68143),x68141)),f324(f105(x68143),x68142)))+P1(f324(f324(f239(a1),x68141),x68142)) % 181.55/181.54 [6831]~P120(x68311)+~P1(f324(f324(f239(x68311),f79(x68311)),x68312))+P1(f324(f324(f239(x68311),f79(x68311)),f324(f324(f249(x68311),x68312),f324(a115,x68313)))) % 181.55/181.54 [6833]~P75(x68331)+~P1(f324(f324(f238(x68331),f324(f80(x68331),x68333)),f324(f80(x68331),x68332)))+P1(f324(f324(f238(x68331),x68332),x68333)) % 181.55/181.54 [6834]~P79(x68341)+~P1(f324(f324(f238(x68341),f324(f80(x68341),x68343)),f324(f80(x68341),x68342)))+P1(f324(f324(f238(x68341),x68342),x68343)) % 181.55/181.54 [6835]~P75(x68351)+~P1(f324(f324(f239(x68351),f324(f80(x68351),x68353)),f324(f80(x68351),x68352)))+P1(f324(f324(f239(x68351),x68352),x68353)) % 181.55/181.54 [6859]P1(f324(x68591,x68592))+~P1(f324(x68591,f432(x68591,x68593)))+~P1(f324(f324(f326(a865),x68592),f295(a865,f2(a865),x68593))) % 181.55/181.54 [6878]~P64(x68781)+P1(f324(f324(f239(x68781),f488(x68783,x68782,x68781)),f79(x68781)))+P1(f324(f324(f238(x68781),x68782),x68783)) % 181.55/181.54 [6897]~E(f44(a865,x68973,x68972),f44(a865,x68971,x68972))+E(f324(f324(f81(a865),x68971),f324(f324(f82(a865),x68972),f553(x68971,x68972,x68973))),x68973)+~P1(f324(f324(f238(a865),x68971),x68973)) % 181.55/181.54 [6916]E(f324(x69161,f554(x69161,x69162,x69163)),f203(x69162))+~P1(f324(f61(x69163),f179(x69163,x69162,x69161)))+P1(f324(f61(x69163),f247(f871(x69163,a859)))) % 181.55/181.54 [6954]E(f324(f324(f9(x69541,a865),x69542),x69543),f79(a865))+~P1(f324(f61(x69541),x69543))+P1(f324(f324(f326(x69541),f380(x69542,x69543,x69541)),x69543)) % 181.55/181.54 [6955]E(f324(f324(f6(x69551,a865),x69552),x69553),f2(a865))+~P1(f324(f61(x69551),x69553))+P1(f324(f324(f326(x69551),f447(x69552,x69553,x69551)),x69553)) % 181.55/181.54 [6977]~P105(x69771)+~P1(f324(f324(f238(x69771),x69772),x69773))+P1(f324(f324(f238(f871(x69771,a859)),f324(f245(x69771),x69772)),f324(f245(x69771),x69773))) % 181.55/181.54 [6978]~P106(x69781)+~P1(f324(f324(f238(x69781),x69782),x69783))+P1(f324(f324(f238(f871(x69781,a859)),f324(f293(x69781),x69782)),f324(f293(x69781),x69783))) % 181.55/181.54 [6979]~P105(x69791)+~P1(f324(f324(f238(x69791),x69793),x69792))+P1(f324(f324(f238(f871(x69791,a859)),f324(f296(x69791),x69792)),f324(f296(x69791),x69793))) % 181.55/181.54 [6980]~P106(x69801)+~P1(f324(f324(f238(x69801),x69803),x69802))+P1(f324(f324(f238(f871(x69801,a859)),f324(f246(x69801),x69802)),f324(f246(x69801),x69803))) % 181.55/181.54 [6981]~P105(x69811)+~P1(f324(f324(f239(x69811),x69812),x69813))+P1(f324(f324(f239(f871(x69811,a859)),f324(f245(x69811),x69812)),f324(f245(x69811),x69813))) % 181.55/181.54 [6989]~P6(x69891)+P1(f324(f324(f238(x69891),x69892),f40(x69891,x69893)))+P1(f324(f324(f326(x69891),f606(x69893,x69892,x69891)),x69893)) % 181.55/181.54 [6995]~P75(x69951)+P1(f324(f324(f238(x69951),f324(f324(f22(x69951),x69952),x69953)),f2(x69951)))+~P1(f324(f324(f238(x69951),x69952),x69953)) % 181.55/181.54 [6996]~P75(x69961)+P1(f324(f324(f239(x69961),f324(f324(f22(x69961),x69962),x69963)),f2(x69961)))+~P1(f324(f324(f239(x69961),x69962),x69963)) % 181.55/181.54 [7038]P1(f324(x70381,x70382))+P1(f324(f324(f238(a865),f432(x70381,x70383)),x70383))+~P1(f324(f324(f326(a865),x70382),f295(a865,f2(a865),x70383))) % 181.55/181.54 [7078]~E(f324(f324(f6(x70781,a865),x70782),x70783),f79(a865))+~P1(f324(f61(x70781),x70783))+P1(f324(f324(f326(x70781),f446(x70782,x70783,x70781)),x70783)) % 181.55/181.54 [7079]~P1(f324(x70791,x70793))+P1(f324(f324(f238(a865),f445(x70791,x70792)),x70792))+~P1(f324(f324(f326(a865),x70793),f295(a865,f2(a865),x70792))) % 181.55/181.54 [7118]~P6(x71181)+P1(f324(f324(f326(x71181),f629(x71183,x71182,x71181)),x71182))+P1(f324(f324(f238(x71181),f39(x71181,x71182)),x71183)) % 181.55/181.54 [7149]~E(f324(f324(f6(x71491,a865),x71492),x71493),f324(a115,f2(a865)))+~P1(f324(f61(x71491),x71493))+P1(f324(f324(f326(x71491),f479(x71492,x71493,x71491)),x71493)) % 181.55/181.54 [7160]E(x71601,f2(a865))+P1(f324(x71602,f44(a865,x71603,x71601)))+P1(f324(f324(f239(a865),f398(x71601,x71603,x71602)),x71601)) % 181.55/181.54 [7265]~P1(f324(x72651,x72652))+P1(f324(x72651,f44(a865,x72652,x72653)))+P1(f324(f324(f239(a865),f398(x72653,x72652,x72651)),x72653)) % 181.55/181.54 [7385]E(x73851,f116(x73852))+~P1(f324(f324(f326(f866(x73852)),x73851),f155(x73852,x73853)))+P1(f324(f324(f326(x73852),f703(x73853,x73851,x73852)),x73853)) % 181.55/181.54 [7407]~P105(x74071)+E(f324(f324(f113(f871(x74071,a859)),f324(f324(f302(x74071),x74072),f191(f871(x74071,a859)))),f298(x74071,x74072,x74073)),f324(f294(x74071,x74072),x74073))+~P1(f324(f324(f239(x74071),x74072),x74073)) % 181.55/181.54 [7433]~P105(x74331)+E(f324(f324(f113(f871(x74331,a859)),f324(f324(f302(x74331),x74332),f191(f871(x74331,a859)))),f297(x74331,x74332,x74333)),f295(x74331,x74332,x74333))+~P1(f324(f324(f238(x74331),x74332),x74333)) % 181.55/181.54 [7539]~P105(x75391)+P1(f324(f324(f238(x75391),x75392),x75393))+~P1(f324(f324(f238(f871(x75391,a859)),f324(f296(x75391),x75393)),f324(f296(x75391),x75392))) % 181.55/181.54 [7540]~P106(x75401)+P1(f324(f324(f238(x75401),x75402),x75403))+~P1(f324(f324(f238(f871(x75401,a859)),f324(f246(x75401),x75403)),f324(f246(x75401),x75402))) % 181.55/181.54 [7541]~P105(x75411)+P1(f324(f324(f238(x75411),x75412),x75413))+~P1(f324(f324(f238(f871(x75411,a859)),f324(f245(x75411),x75412)),f324(f245(x75411),x75413))) % 181.55/181.54 [7542]~P106(x75421)+P1(f324(f324(f238(x75421),x75422),x75423))+~P1(f324(f324(f238(f871(x75421,a859)),f324(f293(x75421),x75422)),f324(f293(x75421),x75423))) % 181.55/181.54 [7543]~P105(x75431)+P1(f324(f324(f239(x75431),x75432),x75433))+~P1(f324(f324(f239(f871(x75431,a859)),f324(f245(x75431),x75432)),f324(f245(x75431),x75433))) % 181.55/181.54 [7566]~P75(x75661)+~P1(f324(f324(f238(x75661),f324(f324(f22(x75661),x75662),x75663)),f2(x75661)))+P1(f324(f324(f238(x75661),x75662),x75663)) % 181.55/181.54 [7567]~P75(x75671)+~P1(f324(f324(f239(x75671),f324(f324(f22(x75671),x75672),x75673)),f2(x75671)))+P1(f324(f324(f239(x75671),x75672),x75673)) % 181.55/181.54 [7718]E(x77181,f2(a865))+~E(f324(f136(a865,a865,f81(a865),x77182),x77183),f2(a865))+~P1(f324(f324(f326(a865),x77181),f324(f167(a865),x77183))) % 181.55/181.54 [7722]~P6(x77221)+~P1(f324(f324(f238(x77221),f629(x77223,x77222,x77221)),x77223))+P1(f324(f324(f238(x77221),f39(x77221,x77222)),x77223)) % 181.55/181.54 [7879]P1(f324(f324(f238(a1),f2(a1)),f393(x78791,x78792,x78793)))+P1(f324(f324(x78792,f324(f324(f38(a1),x78791),x78793)),f44(a1,x78791,x78793)))+~P1(f324(f324(f239(a1),f2(a1)),x78793)) % 181.55/181.54 [7966]E(x79661,x79662)+~E(f324(f192(f866(x79663)),x79661),f324(f192(f866(x79663)),x79662))+~P1(f324(f324(f263(x79663,x79663,a859),a321),f670(x79663,x79661,x79662))) % 181.55/181.54 [8034]~P39(x80342,x80343)+E(x80341,f191(f871(x80342,a859)))+~P1(f324(f324(f238(f871(x80342,a859)),x80341),f324(f278(x80342,x80342,x80343),x80341))) % 181.55/181.54 [8102]P41(x81021,x81022,x81023)+P1(f324(f324(f326(x81021),f540(x81023,x81022,x81021)),x81022))+P1(f324(f324(f326(f870(x81021,x81021)),f541(x81023,x81022,x81021)),x81023)) % 181.55/181.54 [8125]P1(f324(f324(x81252,f324(f324(f38(a1),x81251),x81253)),f44(a1,x81251,x81253)))+~P1(f324(f324(f239(a1),f2(a1)),x81253))+P1(f324(f324(f239(a1),f393(x81251,x81252,x81253)),x81253)) % 181.55/181.54 [8149]E(f324(f303(a865,a865,f324(f324(f7(a865,a865,a865),f22(a865)),x81491)),f324(f294(a865,x81492),x81493)),f191(f871(a865,a859)))+P1(f324(f324(f239(a865),x81491),x81493))+P1(f324(f324(f239(a865),x81492),x81493)) % 181.55/181.54 [8259]E(f324(f303(a865,a865,f324(f324(f7(a865,a865,a865),f22(a865)),x82591)),f324(f294(a865,x82592),x82593)),f324(f324(f302(a865),f2(a865)),f191(f871(a865,a859))))+P1(f324(f324(f239(a865),x82591),x82593))+~P1(f324(f324(f239(a865),x82592),x82593)) % 181.55/181.54 [8276]~P105(x82761)+E(f143(x82761,x82761,f5(x82761),x82762,x82763),x82763)+~P1(f324(f324(f326(x82761),x82762),f324(f167(x82761),x82763))) % 181.55/181.54 [8291]P27(x82911,x82911,x82912,x82913)+~P1(f324(f61(x82911),x82913))+~P1(f324(f324(f238(f871(x82911,a859)),x82913),f324(f303(x82911,x82911,x82912),x82913))) % 181.55/181.54 [8317]E(f324(f324(f81(a1),f324(f324(f82(a1),x83171),f394(x83172,x83173,x83171))),f393(x83172,x83173,x83171)),x83172)+P1(f324(f324(x83173,f324(f324(f38(a1),x83172),x83171)),f44(a1,x83172,x83171)))+~P1(f324(f324(f239(a1),f2(a1)),x83171)) % 181.55/181.54 [8549]~P1(f324(f324(x85491,f394(x85492,x85491,x85493)),f393(x85492,x85491,x85493)))+P1(f324(f324(x85491,f324(f324(f38(a1),x85492),x85493)),f44(a1,x85492,x85493)))+~P1(f324(f324(f239(a1),f2(a1)),x85493)) % 181.55/181.54 [9433]~P1(f324(f61(x94331),x94332))+~P1(f324(f324(f326(x94331),x94333),x94332))+P1(f324(f324(f239(a865),f324(f37(x94331),f324(f324(f22(f871(x94331,a859)),x94332),f324(f324(f302(x94331),x94333),f191(f871(x94331,a859)))))),f324(f37(x94331),x94332))) % 181.55/181.54 [10034]P41(x100341,x100342,x100343)+~P1(f324(f324(f263(x100341,x100341,a859),f324(f324(f7(x100341,f871(x100341,a859),f871(x100341,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x100341,a859),f871(x100341,a859)),x100341),f8(a859,a859,x100341)),f324(f324(f8(a859,f871(a859,a859),x100341),a322),f324(f324(f7(x100341,f871(x100341,a859),a859),f326(x100341)),x100342)))),f324(f324(f7(x100341,f871(x100341,a859),a859),f326(x100341)),x100342))),f541(x100343,x100342,x100341)))+P1(f324(f324(f326(x100341),f540(x100343,x100342,x100341)),x100342)) % 181.55/181.54 [5440]~P114(x54402)+E(x54401,f2(x54402))+E(f324(f324(f282(x54402),x54403),f324(f80(x54402),x54401)),f324(f80(x54402),f324(f324(f282(x54402),x54403),x54401))) % 181.55/181.54 [5571]~E(x55713,f191(f871(x55711,a859)))+~E(x55712,f191(f871(x55711,a859)))+E(f324(f324(f113(f871(x55711,a859)),x55712),x55713),f191(f871(x55711,a859))) % 181.55/181.54 [5629]~E(x56293,f2(a865))+~P1(f324(x56291,f2(a865)))+P1(f324(x56291,f324(f324(f38(a865),x56292),x56293))) % 181.55/181.54 [5769]~P65(x57692)+E(x57691,f2(x57692))+E(f324(f324(f282(x57692),f324(f75(x57692),x57693)),f324(f75(x57692),x57691)),f324(f75(x57692),f324(f324(f282(x57692),x57693),x57691))) % 181.55/181.54 [5931]~P1(f324(f61(x59311),x59313))+E(f324(f37(x59311),f324(f324(f302(x59311),x59312),x59313)),f324(a115,f324(f37(x59311),x59313)))+P1(f324(f324(f326(x59311),x59312),x59313)) % 181.55/181.54 [6002]~E(x60022,f2(a865))+P1(f324(x60021,f2(a865)))+~P1(f324(x60021,f324(f324(f38(a865),x60023),x60022))) % 181.55/181.54 [6021]~P1(f324(f61(x60211),x60213))+E(f324(f37(x60211),f324(f324(f302(x60211),x60212),x60213)),f324(f37(x60211),x60213))+~P1(f324(f324(f326(x60211),x60212),x60213)) % 181.55/181.54 [6054]~P1(f324(f61(x60541),x60543))+E(f324(f37(x60541),f324(f324(f302(x60541),x60542),x60543)),f324(f324(f81(a865),f79(a865)),f324(f37(x60541),x60543)))+P1(f324(f324(f326(x60541),x60542),x60543)) % 181.55/181.54 [6167]E(f324(f324(f81(a865),x61671),f369(x61671,x61672,x61673)),x61672)+~P1(f324(x61673,f2(a865)))+P1(f324(x61673,f324(f324(f22(a865),x61672),x61671))) % 181.55/181.54 [6168]E(f324(f324(f81(a865),x61681),f370(x61681,x61682,x61683)),x61682)+~P1(f324(x61683,f2(a865)))+P1(f324(x61683,f324(f324(f22(a865),x61682),x61681))) % 181.55/181.54 [6214]~P6(x62141)+~P1(f324(f61(x62141),x62143))+E(f324(f324(f64(x62141,x62141,f104(x62141)),x62142),x62143),f324(f324(f104(x62141),x62142),f40(x62141,x62143))) % 181.55/181.54 [6215]~P6(x62151)+~P1(f324(f61(x62151),x62153))+E(f324(f324(f64(x62151,x62151,f113(x62151)),x62152),x62153),f324(f324(f113(x62151),x62152),f39(x62151,x62153))) % 181.55/181.54 [6221]~P92(x62211)+~E(f324(f106(x62211),x62212),f324(f106(x62211),x62213))+P32(x62211,f324(f106(x62211),f324(f324(f81(a1),x62212),f324(f80(a1),x62213)))) % 181.55/181.54 [6228]~P135(x62281)+E(f324(f324(f22(x62281),f324(f103(x62281),x62282)),f324(f103(x62281),x62283)),f324(f103(x62281),f324(f324(f22(a865),x62282),x62283)))+~P1(f324(f324(f238(a865),x62283),x62282)) % 181.55/181.54 [6313]E(f324(f324(f81(a865),x63131),f369(x63131,x63132,x63133)),x63132)+P1(f324(f324(f239(a865),x63132),x63131))+P1(f324(x63133,f324(f324(f22(a865),x63132),x63131))) % 181.55/181.54 [6314]E(f324(f324(f81(a865),x63141),f370(x63141,x63142,x63143)),x63142)+P1(f324(f324(f239(a865),x63142),x63141))+P1(f324(x63143,f324(f324(f22(a865),x63142),x63141))) % 181.55/181.54 [6330]~P117(x63301)+E(f324(f324(f82(x63301),f324(f75(x63301),x63302)),x63303),f324(f75(x63301),f324(f324(f82(x63301),x63302),x63303)))+~P1(f324(f324(f238(x63301),f2(x63301)),x63303)) % 181.55/181.54 [6331]~P64(x63311)+E(f324(f324(f282(x63311),f324(f75(x63311),x63312)),x63313),f324(f75(x63311),f324(f324(f282(x63311),x63312),x63313)))+~P1(f324(f324(f239(x63311),f2(x63311)),x63313)) % 181.55/181.54 [6339]~P94(x63391)+~P1(f324(f61(x63391),x63393))+E(f324(f324(f64(x63391,x63391,f113(x63391)),x63392),x63393),f13(x63391,f324(f324(f302(x63391),x63392),x63393))) % 181.55/181.54 [6340]~P94(x63401)+~P1(f324(f61(x63401),x63403))+E(f324(f324(f64(x63401,x63401,f104(x63401)),x63402),x63403),f10(x63401,f324(f324(f302(x63401),x63402),x63403))) % 181.55/181.54 [6341]~P105(x63411)+~P1(f324(f61(x63411),x63413))+E(f324(f324(f64(x63411,x63411,f190(x63411)),x63412),x63413),f14(x63411,f324(f324(f302(x63411),x63412),x63413))) % 181.55/181.54 [6342]~P105(x63421)+~P1(f324(f61(x63421),x63423))+E(f324(f324(f64(x63421,x63421,f189(x63421)),x63422),x63423),f15(x63421,f324(f324(f302(x63421),x63422),x63423))) % 181.55/181.54 [6388]E(x63881,f116(x63882))+~E(f175(x63882,x63883),f116(f866(x63882)))+~P1(f324(f324(f326(f866(x63882)),x63881),f324(f167(f866(x63882)),x63883))) % 181.55/181.54 [6429]~P1(f324(f131(x64291),x64293))+P1(f324(f324(f326(x64291),x64292),f324(f167(x64291),x64293)))+P1(f324(f131(x64291),f324(f324(f145(x64291),x64292),x64293))) % 181.55/181.54 [6440]~P93(x64401)+~P1(f324(f61(x64401),x64403))+E(f324(f63(x64401,f82(x64401)),f324(f324(f302(x64401),x64402),x64403)),f324(f324(f64(x64401,x64401,f82(x64401)),x64402),x64403)) % 181.55/181.54 [6462]~P105(x64621)+~P1(f324(f61(x64621),x64623))+E(f11(x64621,f190(x64621),f324(f324(f302(x64621),x64622),x64623)),f324(f324(f64(x64621,x64621,f190(x64621)),x64622),x64623)) % 181.55/181.54 [6463]~P105(x64631)+~P1(f324(f61(x64631),x64633))+E(f12(x64631,f189(x64631),f324(f324(f302(x64631),x64632),x64633)),f324(f324(f64(x64631,x64631,f189(x64631)),x64632),x64633)) % 181.55/181.54 [6465]P1(f324(x64651,f2(a865)))+~P1(f324(f324(f239(a865),x64652),x64653))+~P1(f324(x64651,f324(f324(f22(a865),x64652),x64653))) % 181.55/181.54 [6485]~P83(x64851)+P1(f324(f324(f238(x64851),x64852),x64853))+~P1(f324(f324(f238(x64851),f324(f75(x64851),x64852)),x64853)) % 181.55/181.54 [6486]~P117(x64861)+P1(f324(f324(f239(x64861),x64862),x64863))+~P1(f324(f324(f239(x64861),f324(f75(x64861),x64862)),x64863)) % 181.55/181.54 [6503]E(x65031,f116(x65032))+E(f324(f135(x65032),f324(f324(f132(x65032),x65033),x65031)),f324(f324(f159(x65032),x65031),x65033))+~P1(f324(f324(f239(a865),x65033),f324(f192(f866(x65032)),x65031))) % 181.55/181.54 [6554]~P1(f324(x65541,x65543))+P1(f324(x65541,f448(x65541,x65542)))+~P1(f324(f324(f326(a865),x65543),f324(f294(a865,f2(a865)),x65542))) % 181.55/181.54 [6575]P1(f324(x65751,x65752))+~P1(f324(f324(f239(a865),x65752),x65753))+P1(f324(f324(f326(a865),f443(x65751,x65753)),f324(f294(a865,f2(a865)),x65753))) % 181.55/181.54 [6590]~P120(x65901)+~P1(f324(f324(f238(x65901),f79(x65901)),x65902))+P1(f324(f324(f238(x65901),f79(x65901)),f324(f324(f249(x65901),x65902),x65903))) % 181.55/181.54 [6592]~P120(x65921)+~P1(f324(f324(f238(x65921),f2(x65921)),x65922))+P1(f324(f324(f238(x65921),f2(x65921)),f324(f324(f249(x65921),x65922),x65923))) % 181.55/181.54 [6594]~P120(x65941)+~P1(f324(f324(f239(x65941),f2(x65941)),x65942))+P1(f324(f324(f239(x65941),f2(x65941)),f324(f324(f249(x65941),x65942),x65943))) % 181.55/181.54 [6618]~P1(f324(x66181,x66183))+~P1(f324(f324(f239(a865),x66183),x66182))+P1(f324(f324(f326(a865),f442(x66181,x66182)),f324(f294(a865,f2(a865)),x66182))) % 181.55/181.54 [6625]P1(f324(f61(x66251),x66252))+~P1(f324(f61(x66251),x66253))+~P1(f324(f324(f238(f871(x66251,a859)),x66252),x66253)) % 181.55/181.54 [6633]P1(f324(x66331,x66332))+~P1(f324(x66331,f444(x66331,x66333)))+~P1(f324(f324(f326(a865),x66332),f324(f294(a865,f2(a865)),x66333))) % 181.55/181.54 [6644]E(x66441,f2(a865))+P1(f324(x66442,f382(x66441,x66443,x66442)))+~P1(f324(x66442,f324(f324(f38(a865),x66443),x66441))) % 181.55/181.54 [6652]~P121(x66522)+E(x66521,f2(x66522))+~E(f324(f324(f81(x66522),f324(f324(f82(x66522),x66523),x66523)),f324(f324(f82(x66522),x66521),x66521)),f2(x66522)) % 181.55/181.54 [6653]~P121(x66532)+E(x66531,f2(x66532))+~E(f324(f324(f81(x66532),f324(f324(f82(x66532),x66531),x66531)),f324(f324(f82(x66532),x66533),x66533)),f2(x66532)) % 181.55/181.54 [6698]E(x66981,f2(a865))+~P1(f324(x66982,f383(x66981,x66983,x66982)))+P1(f324(x66982,f324(f324(f38(a865),x66983),x66981))) % 181.55/181.54 [6703]~P105(x67031)+~P16(x67031,x67033)+P16(x67031,f324(f324(f142(x67031,x67031,f5(x67031)),x67032),x67033)) % 181.55/181.54 [6746]P1(f324(x67461,f382(x67462,x67463,x67461)))+P1(f324(x67461,f2(a865)))+~P1(f324(x67461,f324(f324(f38(a865),x67463),x67462))) % 181.55/181.54 [6752]~P92(x67521)+E(f324(f106(x67521),x67522),f324(f106(x67521),x67523))+~P32(x67521,f324(f106(x67521),f324(f324(f81(a1),x67522),f324(f80(a1),x67523)))) % 181.55/181.54 [6817]E(x68171,f2(a1))+E(x68172,f2(a1))+~P1(f324(f48(x68172,x68172),f324(f324(f259(a1,a1),x68173),x68171))) % 181.55/181.54 [6818]E(x68181,f79(a1))+E(x68182,f2(a1))+~P1(f324(f48(x68182,x68182),f324(f324(f259(a1,a1),x68181),x68183))) % 181.55/181.54 [6832]P1(f324(x68321,x68322))+P1(f324(f324(f239(a865),f444(x68321,x68323)),x68323))+~P1(f324(f324(f326(a865),x68322),f324(f294(a865,f2(a865)),x68323))) % 181.55/181.54 [6854]~P1(f324(x68541,f369(x68543,x68542,x68541)))+~P1(f324(x68541,f2(a865)))+P1(f324(x68541,f324(f324(f22(a865),x68542),x68543))) % 181.55/181.54 [6855]~P1(f324(x68551,f370(x68553,x68552,x68551)))+~P1(f324(x68551,f2(a865)))+P1(f324(x68551,f324(f324(f22(a865),x68552),x68553))) % 181.55/181.54 [6856]~P1(f324(x68561,f383(x68563,x68562,x68561)))+~P1(f324(x68561,f2(a865)))+P1(f324(x68561,f324(f324(f38(a865),x68562),x68563))) % 181.55/181.54 [6874]~P1(f324(x68741,x68743))+P1(f324(f324(f239(a865),f448(x68741,x68742)),x68742))+~P1(f324(f324(f326(a865),x68743),f324(f294(a865,f2(a865)),x68742))) % 181.55/181.54 [6875]E(f324(f324(f22(a865),f324(f324(f22(a865),x68751),x68752)),f324(f324(f22(a865),x68753),x68752)),f324(f324(f22(a865),x68751),x68753))+~P1(f324(f324(f238(a865),x68752),x68751))+~P1(f324(f324(f238(a865),x68752),x68753)) % 181.55/181.54 [6910]~P75(x69101)+~P1(f324(f324(f238(x69101),f324(f80(x69101),x69103)),x69102))+P1(f324(f324(f238(x69101),f324(f80(x69101),x69102)),x69103)) % 181.55/181.54 [6912]~P83(x69121)+~P1(f324(f324(f238(x69121),f324(f75(x69121),x69122)),x69123))+P1(f324(f324(f238(x69121),f324(f80(x69121),x69122)),x69123)) % 181.55/181.54 [6914]~P75(x69141)+~P1(f324(f324(f239(x69141),f324(f80(x69141),x69143)),x69142))+P1(f324(f324(f239(x69141),f324(f80(x69141),x69142)),x69143)) % 181.55/181.54 [6915]~P117(x69151)+~P1(f324(f324(f239(x69151),f324(f75(x69151),x69152)),x69153))+P1(f324(f324(f239(x69151),f324(f80(x69151),x69152)),x69153)) % 181.55/181.54 [6948]~P1(f324(x69483,f369(x69482,x69481,x69483)))+P1(f324(f324(f239(a865),x69481),x69482))+P1(f324(x69483,f324(f324(f22(a865),x69481),x69482))) % 181.55/181.54 [6949]~P1(f324(x69493,f370(x69492,x69491,x69493)))+P1(f324(f324(f239(a865),x69491),x69492))+P1(f324(x69493,f324(f324(f22(a865),x69491),x69492))) % 181.55/181.54 [6999]~E(f636(x69993,x69992,x69991),f637(x69993,x69992,x69991))+E(f324(f324(f104(f871(x69991,a859)),x69992),f39(f871(x69991,a859),x69993)),f191(f871(x69991,a859)))+P1(f324(f324(f326(f871(x69991,a859)),x69992),x69993)) % 181.55/181.54 [7008]~P1(f324(f61(x70081),x70083))+P1(f324(f61(x70081),f40(f871(x70081,a859),x70082)))+~P1(f324(f324(f326(f871(x70081,a859)),x70083),x70082)) % 181.55/181.54 [7067]~P105(x70671)+E(f324(f324(f113(f871(x70671,a859)),f324(f294(x70671,x70672),x70673)),f324(f324(f302(x70671),x70673),f191(f871(x70671,a859)))),f295(x70671,x70672,x70673))+~P1(f324(f324(f238(x70671),x70672),x70673)) % 181.55/181.54 [7068]E(x70681,f2(a865))+P1(f324(f324(f239(a865),f387(x70681,x70683,x70682)),x70681))+P1(f324(x70682,f324(f324(f38(a865),x70683),x70681))) % 181.55/181.54 [7103]E(x71031,x71032)+~P1(f324(f324(f238(f871(x71033,a859)),x71031),x71032))+P1(f324(f324(f239(f871(x71033,a859)),x71031),x71032)) % 181.55/181.54 [7115]E(x71151,x71152)+~E(f324(f192(f866(x71153)),x71151),f324(f192(f866(x71153)),x71152))+P1(f324(f324(f239(a865),f669(x71153,x71151,x71152)),f324(f192(f866(x71153)),x71152))) % 181.55/181.54 [7161]P9(x71611,x71612,x71613)+~E(f324(f257(x71611,x71611),x71613),x71612)+~E(f324(f324(f281(x71611,x71611,x71611),f324(f279(x71611,x71611),x71613)),x71613),x71613) % 181.55/181.54 [7233]~P1(f324(x72331,f2(a865)))+P1(f324(f324(f239(a865),f387(x72333,x72332,x72331)),x72333))+P1(f324(x72331,f324(f324(f38(a865),x72332),x72333))) % 181.55/181.54 [7242]~P105(x72421)+E(f324(f324(f113(f871(x72421,a859)),f298(x72421,x72422,x72423)),f324(f324(f302(x72421),x72423),f191(f871(x72421,a859)))),f297(x72421,x72422,x72423))+~P1(f324(f324(f239(x72421),x72422),x72423)) % 181.55/181.54 [7340]~P1(f324(f61(x73401),x73403))+P1(f324(f324(f238(a865),f324(f37(x73401),x73402)),f324(f37(x73401),x73403)))+~P1(f324(f324(f238(f871(x73401,a859)),x73402),x73403)) % 181.55/181.54 [7341]~P1(f324(f61(x73411),x73413))+P1(f324(f324(f239(a865),f324(f37(x73411),x73412)),f324(f37(x73411),x73413)))+~P1(f324(f324(f239(f871(x73411,a859)),x73412),x73413)) % 181.55/181.54 [7477]E(x74771,x74772)+~P1(f324(f324(f238(f871(x74773,a859)),x74772),x74771))+~P1(f324(f324(f238(f871(x74773,a859)),x74771),x74772)) % 181.55/181.54 [7480]~P105(x74801)+P16(x74801,x74802)+~P16(x74801,f324(f324(f142(x74801,x74801,f5(x74801)),x74803),x74802)) % 181.55/181.54 [7548]~P1(f324(f324(f239(a865),x75483),x75482))+~P1(f324(f324(f239(a865),x75483),x75481))+P1(f324(f324(f239(a865),f324(f324(f22(a865),x75481),x75482)),f324(f324(f22(a865),x75481),x75483))) % 181.55/181.54 [7549]~P1(f324(f324(f238(a865),x75492),x75491))+~P1(f324(f324(f239(a865),x75491),x75493))+P1(f324(f324(f239(a865),f324(f324(f22(a865),x75491),x75492)),f324(f324(f22(a865),x75493),x75492))) % 181.55/181.54 [7564]~P1(f324(f324(f239(a1),x75642),f2(a1)))+~P1(f324(f324(f238(a1),x75643),x75641))+P1(f324(f324(f238(a1),f324(f324(f38(a1),x75641),x75642)),f324(f324(f38(a1),x75643),x75642))) % 181.55/181.54 [7582]~P1(f324(f324(f239(a865),f2(a865)),x75823))+~P1(f324(f324(f238(a865),x75823),x75822))+P1(f324(f324(f238(a865),f324(f324(f38(a865),x75821),x75822)),f324(f324(f38(a865),x75821),x75823))) % 181.55/181.54 [7583]~P1(f324(f324(f239(a1),f2(a1)),x75832))+~P1(f324(f324(f238(a1),x75831),x75833))+P1(f324(f324(f238(a1),f324(f324(f38(a1),x75831),x75832)),f324(f324(f38(a1),x75833),x75832))) % 181.55/181.54 [7587]~P1(f324(f324(f239(a865),f2(a865)),x75872))+~P1(f324(f324(f239(a865),x75871),x75873))+P1(f324(f324(f239(a865),f324(f324(f82(a865),x75871),x75872)),f324(f324(f82(a865),x75873),x75872))) % 181.55/181.54 [7588]~P1(f324(f324(f239(a865),f2(a865)),x75881))+~P1(f324(f324(f239(a865),x75882),x75883))+P1(f324(f324(f239(a865),f324(f324(f82(a865),x75881),x75882)),f324(f324(f82(a865),x75881),x75883))) % 181.55/181.54 [7589]~P1(f324(f324(f239(a1),f2(a1)),x75891))+~P1(f324(f324(f239(a1),x75892),x75893))+P1(f324(f324(f239(a1),f324(f324(f82(a1),x75891),x75892)),f324(f324(f82(a1),x75891),x75893))) % 181.55/181.54 [7637]E(x76371,f2(a865))+E(f324(f324(f81(a865),f324(f324(f82(a865),x76371),f383(x76371,x76372,x76373))),f387(x76371,x76372,x76373)),x76372)+P1(f324(x76373,f324(f324(f38(a865),x76372),x76371))) % 181.55/181.54 [7693]E(f324(f324(f81(a865),f324(f324(f82(a865),x76931),f383(x76931,x76932,x76933))),f387(x76931,x76932,x76933)),x76932)+~P1(f324(x76933,f2(a865)))+P1(f324(x76933,f324(f324(f38(a865),x76932),x76931))) % 181.55/181.54 [7709]~P1(f324(f61(x77091),x77093))+P1(f324(f324(f326(x77091),f384(x77092,x77093,x77091)),x77093))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f9(x77091,a865),x77092),x77093))) % 181.55/181.54 [7710]~P1(f324(f61(x77101),x77103))+P1(f324(f324(f326(x77101),f537(x77102,x77103,x77101)),x77103))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f9(x77101,a865),x77102),x77103))) % 181.55/181.54 [8000]E(x80001,f191(f871(x80002,a859)))+E(x80001,f324(f324(f302(x80002),x80003),f191(f871(x80002,a859))))+~P1(f324(f324(f238(f871(x80002,a859)),x80001),f324(f324(f302(x80002),x80003),f191(f871(x80002,a859))))) % 181.55/181.54 [8017]~P61(x80171)+P13(x80171,x80172,x80173)+P1(f324(f324(f326(f866(x80171)),f725(x80173,x80172,x80171)),f324(f167(f866(x80171)),f54(x80171,x80173,f55(x80171))))) % 181.55/181.54 [8036]~P1(f324(f324(f239(a865),f2(a865)),x80363))+P1(f324(f324(f238(a865),x80361),x80362))+~P1(f324(f324(f238(a865),f324(f324(f82(a865),x80363),x80361)),f324(f324(f82(a865),x80363),x80362))) % 181.55/181.54 [8037]~P1(f324(f324(f239(a865),f2(a865)),x80373))+P1(f324(f324(f238(a865),x80371),x80372))+~P1(f324(f324(f238(a865),f324(f324(f82(a865),x80371),x80373)),f324(f324(f82(a865),x80372),x80373))) % 181.55/181.54 [8039]~P1(f324(f324(f239(a865),f2(a865)),x80393))+P1(f324(f324(f239(a865),x80391),x80392))+~P1(f324(f324(f239(a865),f324(f324(f249(a865),x80393),x80391)),f324(f324(f249(a865),x80393),x80392))) % 181.55/181.54 [8064]~P61(x80641)+~P12(x80641,x80643,x80642)+P1(f324(f324(f326(f866(x80641)),f717(x80642,x80643,x80641)),f324(f167(f866(x80641)),f54(x80641,x80642,f55(x80641))))) % 181.55/181.54 [8080]~E(f324(f324(f104(f871(x80801,a859)),f637(x80803,x80802,x80801)),f636(x80803,x80802,x80801)),f191(f871(x80801,a859)))+E(f324(f324(f104(f871(x80801,a859)),x80802),f39(f871(x80801,a859),x80803)),f191(f871(x80801,a859)))+P1(f324(f324(f326(f871(x80801,a859)),x80802),x80803)) % 181.55/181.54 [8097]E(x80971,f116(x80972))+~E(f324(f136(f866(x80972),f866(x80972),f124(x80972),f116(x80972)),x80973),f116(x80972))+~P1(f324(f324(f326(f866(x80972)),x80971),f324(f167(f866(x80972)),x80973))) % 181.55/181.54 [8154]E(x81541,f191(f871(f871(x81542,a859),a859)))+P1(f324(f324(f326(f871(x81542,a859)),f640(x81543,x81541,x81542)),x81541))+P1(f324(f324(f238(f871(x81542,a859)),f40(f871(x81542,a859),x81541)),x81543)) % 181.55/181.54 [8162]~P68(x81621)+~P72(x81621)+E(f324(f324(f9(a1,x81621),f324(f324(f8(a865,x81621,a1),x81622),a107)),f324(f303(a865,a1,f103(a1)),x81623)),f324(f324(f9(a865,x81621),x81622),x81623)) % 181.55/181.54 [8163]~P68(x81631)+~P72(x81631)+E(f324(f324(f6(a1,x81631),f324(f324(f8(a865,x81631,a1),x81632),a107)),f324(f303(a865,a1,f103(a1)),x81633)),f324(f324(f6(a865,x81631),x81632),x81633)) % 181.55/181.54 [8204]~P1(f324(f61(x82041),x82043))+~P1(f324(f324(f239(a865),f2(a865)),f324(x82042,f384(x82042,x82043,x82041))))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f9(x82041,a865),x82042),x82043))) % 181.55/181.54 [8205]~P1(f324(f61(x82051),x82053))+~P1(f324(f324(f239(a865),f2(a865)),f324(x82052,f537(x82052,x82053,x82051))))+P1(f324(f324(f239(a865),f2(a865)),f324(f324(f9(x82051,a865),x82052),x82053))) % 181.55/181.54 [8240]~P63(x82402)+E(x82401,f79(x82402))+E(f324(f324(f282(x82402),f324(f324(f22(x82402),f324(f324(f249(x82402),x82401),x82403)),f79(x82402))),f324(f324(f22(x82402),x82401),f79(x82402))),f324(f324(f6(a865,x82402),f324(f249(x82402),x82401)),f324(f294(a865,f2(a865)),x82403))) % 181.55/181.54 [8302]E(x83021,f2(a865))+~P1(f324(x83023,f324(f324(f38(a865),x83022),x83021)))+P1(f324(f324(f239(a865),x83022),f324(f324(f82(a865),x83021),f324(a115,f382(x83021,x83022,x83023))))) % 181.55/181.54 [8320]P1(f324(x83201,f2(a865)))+~P1(f324(x83201,f324(f324(f38(a865),x83202),x83203)))+P1(f324(f324(f239(a865),x83202),f324(f324(f82(a865),x83203),f324(a115,f382(x83203,x83202,x83201))))) % 181.55/181.54 [8358]E(x83581,f2(a865))+~P1(f324(x83583,f324(f324(f38(a865),x83582),x83581)))+P1(f324(f324(f238(a865),f324(f324(f82(a865),x83581),f382(x83581,x83582,x83583))),x83582)) % 181.55/181.54 [8390]P1(f324(x83901,f2(a865)))+~P1(f324(x83901,f324(f324(f38(a865),x83903),x83902)))+P1(f324(f324(f238(a865),f324(f324(f82(a865),x83902),f382(x83902,x83903,x83901))),x83903)) % 181.55/181.54 [8393]~P105(x83931)+E(f324(f324(f142(x83931,x83931,f5(x83931)),x83932),x83933),f143(x83931,x83931,f5(x83931),x83932,x83933))+P1(f324(f324(f326(x83931),x83932),f324(f167(x83931),x83933))) % 181.55/181.54 [8428]~E(f324(x84283,f558(x84282,x84283,x84281)),f324(x84283,f560(x84282,x84283,x84281)))+~P57(x84281,f324(x84283,f559(x84282,x84283,x84281)))+P57(x84281,f324(f324(f41(x84282,f871(x84281,f871(x84281,a859))),f247(f871(x84282,a859))),x84283)) % 181.55/181.54 [8436]E(x84361,f191(f871(f871(x84362,a859),a859)))+~P1(f324(f324(f238(f871(x84362,a859)),f640(x84363,x84361,x84362)),x84363))+P1(f324(f324(f238(f871(x84362,a859)),f40(f871(x84362,a859),x84361)),x84363)) % 181.55/181.54 [8495]~P65(x84951)+~P1(f324(f324(f239(x84951),x84952),x84953))+P1(f324(f324(f239(x84951),x84952),f324(f324(f282(x84951),f324(f324(f81(x84951),x84952),x84953)),f324(f324(f81(x84951),f79(x84951)),f79(x84951))))) % 181.55/181.54 [8555]~P1(f324(f324(x85551,f401(x85551,x85553,x85552)),f402(x85551,x85553,x85552)))+P1(f324(f324(x85551,x85552),x85553))+~P1(f324(f312(f870(a1,a1),a229),f324(f324(f259(a1,a1),x85552),x85553))) % 181.55/181.54 [8556]~P1(f324(f324(x85561,f412(x85561,x85563,x85562)),f413(x85561,x85563,x85562)))+P1(f324(f324(x85561,x85562),x85563))+~P1(f324(f312(f870(a1,a1),a56),f324(f324(f259(a1,a1),x85562),x85563))) % 181.55/181.54 [8557]~P1(f324(f324(x85571,f421(x85571,x85573,x85572)),f422(x85571,x85573,x85572)))+P1(f324(f324(x85571,x85572),x85573))+~P1(f324(f312(f870(a1,a1),a51),f324(f324(f259(a1,a1),x85572),x85573))) % 181.55/181.54 [8558]~P1(f324(f324(x85581,f512(x85581,x85583,x85582)),f514(x85581,x85583,x85582)))+P1(f324(f324(x85581,x85582),x85583))+~P1(f324(f312(f870(a865,a865),a224),f324(f324(f259(a865,a865),x85582),x85583))) % 181.55/181.54 [8559]~P1(f324(f324(x85591,f686(x85591,x85593,x85592)),f692(x85591,x85593,x85592)))+P1(f324(f324(x85591,x85592),x85593))+~P1(f324(f312(f870(a1,a1),a178),f324(f324(f259(a1,a1),x85592),x85593))) % 181.55/181.54 [8830]P1(f324(f324(x88301,x88302),x88303))+P1(f324(f312(f870(a865,a865),a224),f324(f324(f259(a865,a865),f512(x88301,x88303,x88302)),f514(x88301,x88303,x88302))))+~P1(f324(f312(f870(a865,a865),a224),f324(f324(f259(a865,a865),x88302),x88303))) % 181.55/181.54 [8831]P1(f324(f324(x88311,x88312),x88313))+P1(f324(f312(f870(a1,a1),a229),f324(f324(f259(a1,a1),f401(x88311,x88313,x88312)),f402(x88311,x88313,x88312))))+~P1(f324(f312(f870(a1,a1),a229),f324(f324(f259(a1,a1),x88312),x88313))) % 181.55/181.54 [8832]P1(f324(f324(x88321,x88322),x88323))+P1(f324(f312(f870(a1,a1),a56),f324(f324(f259(a1,a1),f412(x88321,x88323,x88322)),f413(x88321,x88323,x88322))))+~P1(f324(f312(f870(a1,a1),a56),f324(f324(f259(a1,a1),x88322),x88323))) % 181.55/181.54 [8833]P1(f324(f324(x88331,x88332),x88333))+P1(f324(f312(f870(a1,a1),a51),f324(f324(f259(a1,a1),f421(x88331,x88333,x88332)),f422(x88331,x88333,x88332))))+~P1(f324(f312(f870(a1,a1),a51),f324(f324(f259(a1,a1),x88332),x88333))) % 181.55/181.54 [8834]P1(f324(f324(x88341,x88342),x88343))+P1(f324(f312(f870(a1,a1),a178),f324(f324(f259(a1,a1),f686(x88341,x88343,x88342)),f692(x88341,x88343,x88342))))+~P1(f324(f312(f870(a1,a1),a178),f324(f324(f259(a1,a1),x88342),x88343))) % 181.55/181.54 [9174]~P1(f324(f61(x91741),x91743))+P1(f324(f324(f326(f870(f871(x91741,a859),f871(x91741,a859))),f324(f324(f259(f871(x91741,a859),f871(x91741,a859)),x91742),x91743)),f299(x91741)))+~P1(f324(f324(f239(f871(x91741,a859)),x91742),x91743)) % 181.55/181.54 [9243]~P57(x92431,f324(x92433,f559(x92432,x92433,x92431)))+P57(x92431,f324(f324(f41(x92432,f871(x92431,f871(x92431,a859))),f247(f871(x92432,a859))),x92433))+~E(f324(f324(f104(f871(x92431,a859)),f253(x92431,x92431,f324(x92433,f558(x92432,x92433,x92431)))),f254(x92431,x92431,f324(x92433,f560(x92432,x92433,x92431)))),f191(f871(x92431,a859))) % 181.55/181.54 [9446]P41(x94461,x94462,x94463)+P1(f324(f324(f326(f870(x94461,x94461)),f541(x94463,x94462,x94461)),x94463))+~P1(f324(f324(f326(f870(x94461,x94461)),f324(f324(f259(x94461,x94461),f540(x94463,x94462,x94461)),f540(x94463,x94462,x94461))),x94463)) % 181.55/181.54 [10035]P41(x100351,x100352,x100353)+~P1(f324(f324(f263(x100351,x100351,a859),f324(f324(f7(x100351,f871(x100351,a859),f871(x100351,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x100351,a859),f871(x100351,a859)),x100351),f8(a859,a859,x100351)),f324(f324(f8(a859,f871(a859,a859),x100351),a322),f324(f324(f7(x100351,f871(x100351,a859),a859),f326(x100351)),x100352)))),f324(f324(f7(x100351,f871(x100351,a859),a859),f326(x100351)),x100352))),f541(x100353,x100352,x100351)))+~P1(f324(f324(f326(f870(x100351,x100351)),f324(f324(f259(x100351,x100351),f540(x100353,x100352,x100351)),f540(x100353,x100352,x100351))),x100353)) % 181.55/181.54 [5610]~P59(x56102)+E(x56101,f2(x56102))+E(f324(f324(f38(x56102),f324(f324(f82(x56102),x56103),x56101)),x56101),x56103) % 181.55/181.54 [5611]~P59(x56112)+E(x56111,f2(x56112))+E(f324(f324(f38(x56112),f324(f324(f82(x56112),x56111),x56113)),x56111),x56113) % 181.55/181.54 [6387]~P72(x63871)+~E(f324(x63872,f2(a865)),f2(x63871))+E(f324(f324(f6(a865,x63871),x63872),f324(f294(a865,f324(a115,f2(a865))),x63873)),f324(f324(f6(a865,x63871),x63872),f324(f294(a865,f2(a865)),x63873))) % 181.55/181.54 [6515]~P59(x65152)+E(x65151,f2(x65152))+E(f324(f324(f38(x65152),f324(f324(f81(x65152),x65153),x65151)),x65151),f324(f324(f81(x65152),f324(f324(f38(x65152),x65153),x65151)),f79(x65152))) % 181.55/181.54 [6516]~P59(x65162)+E(x65161,f2(x65162))+E(f324(f324(f38(x65162),f324(f324(f81(x65162),x65161),x65163)),x65161),f324(f324(f81(x65162),f324(f324(f38(x65162),x65163),x65161)),f79(x65162))) % 181.55/181.54 [6734]~P1(f324(x67343,f2(a1)))+P1(f324(f324(f238(a865),x67341),x67342))+P1(f324(x67343,f324(f103(a1),f324(f324(f22(a865),x67342),x67341)))) % 181.55/181.54 [6838]P1(f324(f324(f239(a865),x68382),x68381))+P1(f324(f324(f238(a865),x68381),x68382))+P1(f324(x68383,f324(f103(a1),f324(f324(f22(a865),x68382),x68381)))) % 181.55/181.54 [6908]E(f324(f324(f81(a865),f324(f106(a865),x69081)),f324(f324(f81(a865),f324(f106(a865),x69082)),x69083)),f324(f324(f81(a865),f324(f106(a865),x69081)),x69083))+P1(f324(a196,f324(f106(a1),x69081)))+~P1(f324(a196,f324(f106(a1),x69082))) % 181.55/181.54 [6986]~E(x69862,f324(f324(f38(a865),x69863),x69861))+~P1(f324(f324(f239(a865),f2(a865)),x69861))+P1(f324(f324(f238(a865),f324(f324(f82(a865),x69861),x69862)),x69863)) % 181.55/181.54 [7101]~P1(f324(f61(x71011),x71013))+~P1(f324(f61(x71011),x71012))+P1(f324(f61(x71011),f324(f324(f113(f871(x71011,a859)),x71012),x71013))) % 181.55/181.54 [7391]~P105(x73911)+~P1(f324(f61(x73911),x73912))+E(f133(x73911,f324(f324(f22(f871(x73911,a859)),x73912),f324(f324(f302(x73911),x73913),f191(f871(x73911,a859))))),f164(x73911,x73913,f133(x73911,x73912))) % 181.55/181.54 [7457]P1(f324(x74571,f2(a1)))+~P1(f324(f324(f239(a865),x74572),x74573))+~P1(f324(x74571,f324(f103(a1),f324(f324(f22(a865),x74572),x74573)))) % 181.55/181.54 [7474]~P1(f324(f61(x74741),x74742))+E(f324(f37(x74741),f324(f324(f22(f871(x74741,a859)),x74742),f324(f324(f302(x74741),x74743),f191(f871(x74741,a859))))),f324(f37(x74741),x74742))+P1(f324(f324(f326(x74741),x74743),x74742)) % 181.55/181.54 [7604]~P120(x76041)+~P1(f324(f324(f239(x76041),f79(x76041)),x76042))+P1(f324(f324(f239(x76041),f79(x76041)),f324(f324(f82(x76041),x76042),f324(f324(f249(x76041),x76042),x76043)))) % 181.55/181.54 [7647]~P1(f324(f61(x76471),x76473))+E(f324(f324(f22(a865),f324(f37(x76471),x76472)),f324(f37(x76471),x76473)),f324(f37(x76471),f324(f324(f22(f871(x76471,a859)),x76472),x76473)))+~P1(f324(f324(f238(f871(x76471,a859)),x76473),x76472)) % 181.55/181.54 [7702]~P1(f324(f324(f238(a865),x77022),x77023))+~P1(f324(f324(f238(a865),x77021),f324(f324(f22(a865),x77023),x77022)))+P1(f324(f324(f238(a865),f324(f324(f81(a865),x77021),x77022)),x77023)) % 181.55/181.54 [7750]P1(f324(f61(x77501),x77502))+~P1(f324(f61(x77501),x77503))+~P1(f324(f61(x77501),f324(f324(f22(f871(x77501,a859)),x77502),x77503))) % 181.55/181.54 [7756]~P1(f324(f61(x77561),x77562))+E(f324(f37(x77561),f324(f324(f22(f871(x77561,a859)),x77562),f324(f324(f302(x77561),x77563),f191(f871(x77561,a859))))),f324(f324(f22(a865),f324(f37(x77561),x77562)),f79(a865)))+~P1(f324(f324(f326(x77561),x77563),x77562)) % 181.55/181.54 [7833]P57(x78331,x78332)+~P57(x78331,x78333)+~P1(f324(f324(f238(f871(x78331,f871(x78331,a859))),x78332),x78333)) % 181.55/181.54 [7878]~P1(f324(f324(f238(a865),x78783),x78782))+P1(f324(f324(f238(a865),x78781),f324(f324(f22(a865),x78782),x78783)))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),x78781),x78783)),x78782)) % 181.55/181.54 [7896]P39(x78961,x78962)+~P39(x78961,x78963)+~P1(f324(f324(f238(f871(f870(x78961,x78961),a859)),x78962),x78963)) % 181.55/181.54 [7897]P55(x78971,x78972)+~P55(x78971,x78973)+~P1(f324(f324(f238(f871(f870(x78971,x78971),a859)),x78972),x78973)) % 181.55/181.54 [8132]~P120(x81321)+~P1(f324(f324(f239(x81321),f79(x81321)),x81322))+P1(f324(f324(f239(x81321),f324(f324(f249(x81321),x81322),x81323)),f324(f324(f82(x81321),x81322),f324(f324(f249(x81321),x81322),x81323)))) % 181.55/181.54 [8222]~P1(f324(x82221,f2(a1)))+~P1(f324(x82221,f324(f324(f22(a1),f324(f103(a1),x82222)),f324(f103(a1),x82223))))+P1(f324(x82221,f324(f103(a1),f324(f324(f22(a865),x82222),x82223)))) % 181.55/181.54 [8237]~P1(f324(f324(f238(a865),x82373),x82372))+P1(f324(x82371,f324(f324(f22(a1),f324(f103(a1),x82372)),f324(f103(a1),x82373))))+~P1(f324(x82371,f324(f103(a1),f324(f324(f22(a865),x82372),x82373)))) % 181.55/181.54 [8256]P1(f324(f324(f239(a865),x82561),x82562))+~P1(f324(x82563,f324(f324(f22(a1),f324(f103(a1),x82561)),f324(f103(a1),x82562))))+P1(f324(x82563,f324(f103(a1),f324(f324(f22(a865),x82561),x82562)))) % 181.55/181.54 [8314]~P121(x83142)+E(x83141,f2(x83142))+P1(f324(f324(f239(x83142),f2(x83142)),f324(f324(f81(x83142),f324(f324(f82(x83142),x83143),x83143)),f324(f324(f82(x83142),x83141),x83141)))) % 181.55/181.54 [8315]~P121(x83152)+E(x83151,f2(x83152))+P1(f324(f324(f239(x83152),f2(x83152)),f324(f324(f81(x83152),f324(f324(f82(x83152),x83151),x83151)),f324(f324(f82(x83152),x83153),x83153)))) % 181.55/181.54 [8411]~P1(f324(f324(f239(a865),f2(a865)),x84111))+~P1(f324(f324(f239(a1),x84112),x84113))+P1(f324(f324(f239(a1),f324(f324(f82(a1),f324(f103(a1),x84111)),x84112)),f324(f324(f82(a1),f324(f103(a1),x84111)),x84113))) % 181.55/181.54 [8465]E(f324(f324(f104(f871(x84651,a859)),x84652),f39(f871(x84651,a859),x84653)),f191(f871(x84651,a859)))+P1(f324(f324(f326(f871(x84651,a859)),x84652),x84653))+P1(f324(f324(f326(f871(x84651,a859)),f637(x84653,x84652,x84651)),f324(f324(f302(f871(x84651,a859)),x84652),x84653))) % 181.55/181.54 [8466]E(f324(f324(f104(f871(x84661,a859)),x84662),f39(f871(x84661,a859),x84663)),f191(f871(x84661,a859)))+P1(f324(f324(f326(f871(x84661,a859)),x84662),x84663))+P1(f324(f324(f326(f871(x84661,a859)),f636(x84663,x84662,x84661)),f324(f324(f302(f871(x84661,a859)),x84662),x84663))) % 181.55/181.54 [8494]E(x84941,x84942)+~E(f324(f192(f866(x84943)),x84941),f324(f192(f866(x84943)),x84942))+P1(f324(f324(f326(f870(x84943,x84943)),f670(x84943,x84941,x84942)),f324(f167(f870(x84943,x84943)),f324(f324(f177(x84943,x84943),x84942),x84941)))) % 181.55/181.54 [8747]E(f300(x87471,x87472),f300(x87471,x87473))+~P1(f324(f324(f238(f871(f870(x87471,x87471),a859)),x87473),f300(x87471,x87472)))+~P1(f324(f324(f238(f871(f870(x87471,x87471),a859)),x87472),x87473)) % 181.55/181.54 [8809]~P41(x88091,f247(f871(x88091,a859)),x88093)+P1(f324(f324(f238(f871(f870(f866(x88091),f866(x88091)),a859)),f151(x88091,x88092)),f152(x88091,x88093)))+~P1(f324(f324(f238(f871(f870(x88091,x88091),a859)),x88092),x88093)) % 181.55/181.54 [9010]P39(x90101,x90102)+~P1(f324(f324(f326(x90101),x90103),f603(x90102,x90101)))+P1(f324(f324(f326(f870(x90101,x90101)),f324(f324(f259(x90101,x90101),f650(x90102,x90101,x90103)),x90103)),x90102)) % 181.55/181.54 [9045]~P1(f324(f61(x90451),x90452))+P1(f324(f61(f871(x90451,a859)),f324(f324(f60(x90451),x90452),x90453)))+~P1(f324(f324(f238(f871(f870(x90451,x90451),a859)),x90453),f324(f324(f261(x90451,x90451),x90452),f324(f16(f871(x90451,a859),x90451),x90452)))) % 181.55/181.54 [9079]P41(x90791,x90792,x90793)+P1(f324(f324(f326(x90791),f524(x90793,x90792,x90791)),x90792))+~P1(f324(f324(f238(f871(f870(x90791,x90791),a859)),x90793),f324(f324(f261(x90791,x90791),x90792),f324(f16(f871(x90791,a859),x90791),x90792)))) % 181.55/181.54 [9080]P41(x90801,x90802,x90803)+P1(f324(f324(f326(x90801),f527(x90802,x90803,x90801)),x90802))+~P1(f324(f324(f238(f871(f870(x90801,x90801),a859)),x90803),f324(f324(f261(x90801,x90801),x90802),f324(f16(f871(x90801,a859),x90801),x90802)))) % 181.55/181.54 [9116]~P65(x91161)+~P1(f324(f324(f239(x91161),x91162),x91163))+P1(f324(f324(f239(x91161),f324(f324(f282(x91161),f324(f324(f81(x91161),x91162),x91163)),f324(f324(f81(x91161),f79(x91161)),f79(x91161)))),x91163)) % 181.55/181.54 [9149]~P64(x91491)+P1(f324(f324(f238(x91491),x91492),x91493))+~P1(f324(f324(f238(x91491),f324(f324(f82(x91491),f488(x91493,x91492,x91491)),x91492)),x91493)) % 181.55/181.54 [9279]E(f324(f192(f866(f866(x92791))),f324(f130(f866(x92791),f324(f324(f8(a865,a859,f866(x92791)),f324(f239(a865),x92792)),f192(f866(x92791)))),f175(x92791,x92793))),f324(f192(f866(x92791)),f324(f324(f159(f866(x92791)),x92793),x92792)))+~P16(a865,f324(f163(a865),f324(f324(f148(f866(x92791),a865),f192(f866(x92791))),x92793)))+~P1(f324(f324(f239(a865),x92792),f324(f192(f866(f866(x92791))),x92793))) % 181.55/181.54 [9389]~P39(x93891,x93892)+P29(x93891,f324(f324(f259(f871(f870(x93891,x93891),a859),f871(f870(x93891,x93891),a859)),x93892),x93893))+~P1(f324(f324(f238(f871(f870(x93891,x93891),a859)),f324(f324(f281(x93891,x93891,x93891),x93892),x93893)),x93892)) % 181.55/181.54 [9396]E(f324(f324(f148(f866(x93961),x93961),f324(f324(f7(f866(x93961),a865,x93961),f159(x93961)),x93962)),f324(f130(f866(x93961),f324(f324(f8(a865,a859,f866(x93961)),f324(f239(a865),x93962)),f192(f866(x93961)))),f175(x93961,x93963))),f324(f324(f159(f866(x93961)),x93963),x93962))+~P16(a865,f324(f163(a865),f324(f324(f148(f866(x93961),a865),f192(f866(x93961))),x93963)))+~P1(f324(f324(f239(a865),x93962),f324(f192(f866(f866(x93961))),x93963))) % 181.55/181.54 [9538]P41(x95381,x95382,x95383)+~P1(f324(f324(f326(f870(x95381,x95381)),f324(f324(f259(x95381,x95381),f524(x95383,x95382,x95381)),f524(x95383,x95382,x95381))),x95383))+~P1(f324(f324(f238(f871(f870(x95381,x95381),a859)),x95383),f324(f324(f261(x95381,x95381),x95382),f324(f16(f871(x95381,a859),x95381),x95382)))) % 181.55/181.54 [9539]P41(x95391,x95392,x95393)+~P1(f324(f324(f326(f870(x95391,x95391)),f324(f324(f259(x95391,x95391),f527(x95392,x95393,x95391)),f527(x95392,x95393,x95391))),x95393))+~P1(f324(f324(f238(f871(f870(x95391,x95391),a859)),x95393),f324(f324(f261(x95391,x95391),x95392),f324(f16(f871(x95391,a859),x95391),x95392)))) % 181.55/181.54 [9718]~P135(x97181)+~P119(x97181)+E(f324(f324(f282(x97181),f324(f105(x97181),f324(f324(f73(f870(a1,a1),a1,x97182,f258(a1,a1)),f217(x97182)),x97183))),f324(f105(x97181),f324(f324(f73(f870(a1,a1),a1,x97182,f262(a1,a1)),f217(x97182)),x97183))),f230(x97182,x97181,x97183)) % 181.55/181.54 [9917]~E(x99173,f2(a865))+~E(f324(f192(f866(x99171)),f324(f324(f159(f866(x99171)),x99172),f720(x99173,x99171,x99172))),x99173)+E(f324(f324(f148(a865,f866(x99171)),f324(f324(f7(a865,f866(a865),f866(x99171)),f324(f324(f8(f871(a865,x99171),f871(f866(a865),f866(x99171)),a865),f148(a865,x99171)),f324(f7(a865,a865,x99171),f324(f324(f8(f866(x99171),f871(a865,x99171),a865),f159(x99171)),f324(f159(f866(x99171)),x99172))))),f133(a865,f324(f294(a865,f2(a865)),f324(f192(f866(f866(x99171))),x99172))))),f133(a865,f324(f294(a865,f2(a865)),x99173))),f175(x99171,x99172)) % 181.55/181.54 [9918]E(x99181,f116(f866(x99182)))+~E(f324(f192(f866(x99182)),f324(f324(f159(f866(x99182)),x99181),f720(x99183,x99182,x99181))),x99183)+E(f324(f324(f148(a865,f866(x99182)),f324(f324(f7(a865,f866(a865),f866(x99182)),f324(f324(f8(f871(a865,x99182),f871(f866(a865),f866(x99182)),a865),f148(a865,x99182)),f324(f7(a865,a865,x99182),f324(f324(f8(f866(x99182),f871(a865,x99182),a865),f159(x99182)),f324(f159(f866(x99182)),x99181))))),f133(a865,f324(f294(a865,f2(a865)),f324(f192(f866(f866(x99182))),x99181))))),f133(a865,f324(f294(a865,f2(a865)),x99183))),f175(x99182,x99181)) % 181.55/181.54 [9919]~E(x99193,f2(a865))+E(f324(f324(f148(a865,f866(x99191)),f324(f324(f7(a865,f866(a865),f866(x99191)),f324(f324(f8(f871(a865,x99191),f871(f866(a865),f866(x99191)),a865),f148(a865,x99191)),f324(f7(a865,a865,x99191),f324(f324(f8(f866(x99191),f871(a865,x99191),a865),f159(x99191)),f324(f159(f866(x99191)),x99192))))),f133(a865,f324(f294(a865,f2(a865)),f324(f192(f866(f866(x99191))),x99192))))),f133(a865,f324(f294(a865,f2(a865)),x99193))),f175(x99191,x99192))+P1(f324(f324(f239(a865),f720(x99193,x99191,x99192)),f324(f192(f866(f866(x99191))),x99192))) % 181.55/181.54 [9920]E(x99201,f116(f866(x99202)))+E(f324(f324(f148(a865,f866(x99202)),f324(f324(f7(a865,f866(a865),f866(x99202)),f324(f324(f8(f871(a865,x99202),f871(f866(a865),f866(x99202)),a865),f148(a865,x99202)),f324(f7(a865,a865,x99202),f324(f324(f8(f866(x99202),f871(a865,x99202),a865),f159(x99202)),f324(f159(f866(x99202)),x99201))))),f133(a865,f324(f294(a865,f2(a865)),f324(f192(f866(f866(x99202))),x99201))))),f133(a865,f324(f294(a865,f2(a865)),x99203))),f175(x99202,x99201))+P1(f324(f324(f239(a865),f720(x99203,x99202,x99201)),f324(f192(f866(f866(x99202))),x99201))) % 181.55/181.54 [7644]E(f324(f324(f81(a865),f324(f106(a865),x76441)),f324(f324(f81(a865),f324(f106(a865),x76442)),x76443)),f324(f324(f81(a865),f324(f106(a865),f324(f324(f81(a1),x76441),x76442))),x76443))+P1(f324(a196,f324(f106(a1),x76441)))+P1(f324(a196,f324(f106(a1),x76442))) % 181.55/181.54 [8402]~P1(f324(f61(x84021),x84022))+~P1(f324(f324(f326(x84021),x84023),x84022))+E(f324(a115,f324(f37(x84021),f324(f324(f22(f871(x84021,a859)),x84022),f324(f324(f302(x84021),x84023),f191(f871(x84021,a859)))))),f324(f37(x84021),x84022)) % 181.55/181.54 [8418]~P1(f324(f61(x84181),x84182))+~P1(f324(f324(f326(x84181),x84183),x84182))+E(f324(f324(f81(a865),f79(a865)),f324(f37(x84181),f324(f324(f22(f871(x84181,a859)),x84182),f324(f324(f302(x84181),x84183),f191(f871(x84181,a859)))))),f324(f37(x84181),x84182)) % 181.55/181.54 [8504]~P105(x85041)+~P1(f324(f61(x85041),x85043))+E(f324(f324(f142(x85041,x85041,f5(x85041)),x85042),f133(x85041,f324(f324(f22(f871(x85041,a859)),x85043),f324(f324(f302(x85041),x85042),f191(f871(x85041,a859)))))),f133(x85041,f324(f324(f302(x85041),x85042),x85043))) % 181.55/181.54 [8671]~P1(f324(f61(x86711),x86713))+~P1(f324(f61(x86711),x86712))+E(f324(f324(f81(a865),f324(f37(x86711),f324(f324(f113(f871(x86711,a859)),x86712),x86713))),f324(f37(x86711),f324(f324(f104(f871(x86711,a859)),x86712),x86713))),f324(f324(f81(a865),f324(f37(x86711),x86712)),f324(f37(x86711),x86713))) % 181.55/181.54 [9865]~P27(x98651,f871(f871(x98651,a859),a859),f324(f324(f7(x98651,f871(f870(x98651,x98651),a859),f871(f871(x98651,a859),a859)),f324(f324(f8(f871(x98651,a859),f871(f871(f870(x98651,x98651),a859),f871(f871(x98651,a859),a859)),x98651),f60(x98651)),f324(f324(f7(x98651,f871(x98651,a859),f871(x98651,a859)),f302(x98651)),f191(f871(x98651,a859))))),x98653),x98652)+~P1(f324(f61(x98651),x98652))+E(f324(f37(f871(x98651,a859)),f324(f324(f60(x98651),x98652),x98653)),f324(f37(x98651),x98652)) % 181.55/181.54 [7909]~P92(x79091)+P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x79093)))+E(f324(f324(f249(x79091),x79092),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),x79093),x79093)),a100))),f79(x79091)) % 181.55/181.54 [9374]~P92(x93741)+~P1(f324(f324(f238(a1),f2(a1)),f324(f106(a1),x93743)))+E(f324(f324(f249(x93741),x93742),f324(f106(a865),f324(f324(f22(a1),f324(f324(f81(a1),x93743),x93743)),a100))),f324(f324(f87(x93741,x93741),f324(f324(f249(x93741),x93742),f324(f106(a865),x93743))),f324(f324(f18(x93741,x93741,x93741),f324(f324(f8(x93741,f871(x93741,x93741),x93741),f82(x93741)),f324(f82(x93741),x93742))),f5(x93741)))) % 181.55/181.54 [9777]~P1(f324(f131(x97771),x97773))+~P1(f324(f324(f326(x97771),x97772),f324(f167(x97771),x97773)))+E(f324(f324(f132(x97771),f324(f192(f866(x97771)),f172(x97771,f324(f324(f8(a859,a859,x97771),a319),f324(f324(f7(x97771,x97771,a859),a321),x97772)),f324(f163(x97771),x97773)))),f324(f163(x97771),x97773)),f324(f324(f145(x97771),x97772),f324(f163(x97771),f172(x97771,f324(f324(f8(a859,a859,x97771),a319),f324(f324(f7(x97771,x97771,a859),a321),x97772)),x97773)))) % 181.55/181.54 [9845]P1(f324(f324(f238(f871(f870(x98451,x98451),a859)),f300(x98451,x98452)),x98453))+~P1(f324(f324(f238(f871(f870(x98451,x98451),a859)),f300(x98451,f191(f871(f870(x98451,x98451),a859)))),x98453))+~P1(f324(f324(f238(f871(f870(x98451,x98451),a859)),f324(f324(f281(x98451,x98451,x98451),f324(f324(f104(f871(f870(x98451,x98451),a859)),f300(x98451,x98452)),x98453)),x98452)),x98453)) % 181.55/181.54 [9689]~P1(f324(f61(x96891),f324(f244(x96891),x96893)))+~P1(f324(f61(x96891),f324(f244(x96891),x96892)))+P1(f324(f61(x96891),f324(f244(x96891),f324(f324(f18(x96891,a859,a859),f324(f324(f8(a859,f871(a859,a859),x96891),a323),x96892)),x96893)))) % 181.55/181.54 [9979]P1(f324(f324(f238(f871(f870(x99791,x99791),a859)),f324(f324(f281(x99791,x99791,x99791),x99792),f300(x99791,x99792))),x99793))+~P1(f324(f324(f238(f871(f870(x99791,x99791),a859)),x99792),x99793))+~P1(f324(f324(f238(f871(f870(x99791,x99791),a859)),f324(f324(f281(x99791,x99791,x99791),f324(f324(f104(f871(f870(x99791,x99791),a859)),f324(f324(f281(x99791,x99791,x99791),x99792),f300(x99791,x99792))),x99793)),x99792)),x99793)) % 181.55/181.54 [9933]~P117(x99332)+E(x99331,f2(x99332))+~E(f324(f324(f81(x99332),f324(f324(f249(x99332),x99333),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x99332),x99331),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f2(x99332)) % 181.55/181.54 [9934]~P117(x99342)+E(x99341,f2(x99342))+~E(f324(f324(f81(x99342),f324(f324(f249(x99342),x99341),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x99342),x99343),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f2(x99342)) % 181.55/181.54 [9939]~P1(f324(f131(x99391),x99393))+~P1(f324(f324(f326(x99391),x99392),f324(f167(x99391),x99393)))+E(f324(f163(x99391),f324(f166(x99391),f324(f324(f132(x99391),f324(f192(f866(x99391)),f172(x99391,f324(f324(f8(a859,a859,x99391),a319),f324(f324(f7(x99391,x99391,a859),a321),x99392)),x99393))),x99393))),f172(x99391,f324(f324(f8(a859,a859,x99391),a319),f324(f324(f7(x99391,x99391,a859),a321),x99392)),f324(f163(x99391),x99393))) % 181.55/181.54 [10023]~P117(x100232)+E(x100231,f2(x100232))+P1(f324(f324(f239(x100232),f2(x100232)),f324(f324(f81(x100232),f324(f324(f249(x100232),x100233),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100232),x100231),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))))) % 181.55/181.54 [10024]~P117(x100242)+E(x100241,f2(x100242))+P1(f324(f324(f239(x100242),f2(x100242)),f324(f324(f81(x100242),f324(f324(f249(x100242),x100241),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100242),x100243),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))))) % 181.55/181.54 [10065]~P117(x100651)+P1(f324(f324(f238(x100651),f2(x100651)),x100652))+~P1(f324(f324(f238(x100651),f2(x100651)),f324(f324(f249(x100651),x100652),f324(a115,f324(f324(f82(a865),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),x100653))))) % 181.55/181.54 [5453]~P26(x54531,x54534,x54533)+P26(x54531,x54532,x54533)+~P26(x54531,x54532,x54534) % 181.55/181.54 [4935]~E(x49352,f91(x49353,x49351))+P1(f324(x49351,x49352))+~P1(f324(x49351,x49354)) % 181.55/181.54 [6645]~P39(x66452,x66454)+~P39(x66451,x66453)+P39(f870(x66451,x66452),f316(x66451,x66452,x66453,x66454)) % 181.55/181.54 [5110]~P8(x51104,x51101)+~E(f324(x51101,x51102),f324(x51101,x51103))+P1(f324(f324(x51101,x51102),x51103)) % 181.55/181.54 [5269]~P8(x52694,x52691)+E(f324(x52691,x52692),f324(x52691,x52693))+~P1(f324(f324(x52691,x52692),x52693)) % 181.55/181.54 [5360]~P20(x53603,x53604,x53601)+E(f324(x53601,x53602),f324(f63(x53603,x53604),x53602))+~P1(f324(f61(x53603),x53602)) % 181.55/181.54 [5361]~P10(x53613,x53614,x53611)+E(f324(x53611,x53612),f324(f63(x53613,x53614),x53612))+~P1(f324(f61(x53613),x53612)) % 181.55/181.54 [5486]~P8(x54864,x54861)+~P1(f324(f324(x54861,x54863),x54862))+P1(f324(f324(x54861,x54862),x54863)) % 181.55/181.54 [5553]E(x55531,x55532)+~E(f324(f258(x55533,x55534),x55531),f324(f258(x55533,x55534),x55532))+~E(f324(f262(x55533,x55534),x55531),f324(f262(x55533,x55534),x55532)) % 181.55/181.54 [5578]E(x55781,x55782)+~P1(f324(f47(x55783,x55784),x55782))+~P1(f324(f47(x55783,x55784),x55781)) % 181.55/181.54 [5768]~P72(x57682)+E(f231(x57681,x57682,x57683,x57684),f2(x57682))+P1(f324(f61(x57681),x57684)) % 181.55/181.54 [5902]~P1(f324(f312(x59021,x59022),x59024))+P1(f324(f312(x59021,x59022),x59023))+~P1(f324(f324(x59022,x59023),x59024)) % 181.55/181.54 [6317]P51(x63171,x63172,x63173,x63174)+P1(f324(f324(x63172,x63174),x63173))+~P1(f324(f324(x63172,x63173),x63174)) % 181.55/181.54 [7828]~P105(x78282)+~P1(f324(f131(x78281),x78284))+P1(f324(f131(x78281),f144(x78281,x78282,x78283,x78284))) % 181.55/181.54 [8052]~P1(f324(f61(x80522),x80524))+~P1(f324(f61(x80521),x80523))+P1(f324(f61(f872(x80521,x80522)),f311(x80521,x80522,x80523,x80524))) % 181.55/181.54 [8053]~P1(f324(f131(x80532),x80534))+~P1(f324(f131(x80531),x80533))+P1(f324(f131(f870(x80531,x80532)),f59(x80531,x80532,x80533,x80534))) % 181.55/181.54 [8057]P1(f324(f324(f326(f866(x80571)),f324(f324(f124(x80571),x80572),x80573)),f155(x80571,x80574)))+~P1(f324(f324(f326(f866(x80571)),x80573),f155(x80571,x80574)))+~P1(f324(f324(f326(f866(x80571)),x80572),f155(x80571,x80574))) % 181.55/181.54 [8382]~P105(x83823)+~P1(f324(f131(x83821),f144(x83821,x83823,x83824,x83822)))+P1(f324(f131(x83821),x83822)) % 181.55/181.54 [8660]~P1(f324(f324(f326(f870(x86601,x86601)),f324(f324(f259(x86601,x86601),x86602),x86604)),f300(x86601,x86603)))+P1(f324(f324(f326(x86601),x86602),f313(x86601,x86603)))+~P1(f324(f324(f326(x86601),x86604),f313(x86601,x86603))) % 181.55/181.54 [5094]~P68(x50942)+E(f324(f324(f9(x50941,x50942),x50943),x50944),f79(x50942))+P1(f324(f61(x50941),x50944)) % 181.55/181.54 [5097]~P72(x50972)+E(f324(f324(f6(x50971,x50972),x50973),x50974),f2(x50972))+P1(f324(f61(x50971),x50974)) % 181.55/181.54 [5233]~P69(x52333)+E(x52331,x52332)+~E(f324(f324(f81(x52333),x52334),x52331),f324(f324(f81(x52333),x52334),x52332)) % 181.55/181.54 [5234]~P70(x52343)+E(x52341,x52342)+~E(f324(f324(f81(x52343),x52344),x52341),f324(f324(f81(x52343),x52344),x52342)) % 181.55/181.54 [5236]~P69(x52363)+E(x52361,x52362)+~E(f324(f324(f81(x52363),x52361),x52364),f324(f324(f81(x52363),x52362),x52364)) % 181.55/181.54 [5356]~P6(x53563)+E(x53561,f191(f871(x53562,a859)))+E(f324(f324(f41(x53562,x53563),x53561),f324(f16(x53563,x53562),x53564)),x53564) % 181.55/181.54 [5357]~P6(x53573)+E(x53571,f191(f871(x53572,a859)))+E(f324(f324(f42(x53572,x53573),x53571),f324(f16(x53573,x53572),x53574)),x53574) % 181.55/181.54 [5566]~P106(x55663)+E(x55661,x55662)+~E(f295(x55663,x55664,x55661),f324(f324(f302(x55663),x55662),f191(f871(x55663,a859)))) % 181.55/181.54 [5567]~P106(x55673)+E(x55671,x55672)+~E(f295(x55673,x55671,x55672),f324(f324(f302(x55673),x55674),f191(f871(x55673,a859)))) % 181.55/181.54 [5627]~P37(x56273,x56271,x56274)+P37(x56273,x56271,f324(f324(f145(x56273),x56272),x56274))+P1(f324(x56271,x56272)) % 181.55/181.54 [5728]~P33(x57281,x57282,x57284)+~P1(f324(x57282,x57283))+P33(x57281,x57282,f324(f324(f145(x57281),x57283),x57284)) % 181.55/181.54 [5859]P1(f324(x58591,x58592))+~P1(f324(f252(x58593,x58591),x58594))+~P1(f324(f324(f326(x58593),x58592),x58594)) % 181.55/181.54 [5868]~P33(x58681,x58682,x58684)+~P33(x58681,x58682,x58683)+P33(x58681,x58682,f324(f324(f124(x58681),x58683),x58684)) % 181.55/181.54 [5878]P35(x58781,x58782,x58783)+~P35(x58781,x58782,f324(f324(f145(x58781),x58784),x58783))+P1(f324(x58782,x58784)) % 181.55/181.54 [5879]P37(x58791,x58792,x58793)+~P37(x58791,x58792,f324(f324(f145(x58791),x58794),x58793))+P1(f324(x58792,x58794)) % 181.55/181.54 [5952]P35(x59521,x59522,x59523)+P35(x59521,x59522,x59524)+~P35(x59521,x59522,f324(f324(f124(x59521),x59524),x59523)) % 181.55/181.54 [5971]~P72(x59711)+E(f324(f324(f6(a865,x59711),x59712),f324(f294(a865,x59713),f324(a115,x59714))),f2(x59711))+~P1(f324(f324(f239(a865),x59714),x59713)) % 181.55/181.54 [5976]~P60(x59761)+~E(f44(x59761,x59762,x59763),f44(x59761,x59764,x59763))+E(f44(x59761,f324(f80(x59761),x59762),x59763),f44(x59761,f324(f80(x59761),x59764),x59763)) % 181.55/181.54 [6043]P1(f324(x60431,x60432))+~E(f324(f130(x60433,x60431),x60434),x60434)+~P1(f324(f324(f326(x60433),x60432),f324(f167(x60433),x60434))) % 181.55/181.54 [6062]~E(f324(f324(f81(a865),x60623),x60622),f324(f324(f81(a865),x60621),x60624))+~P1(f324(f324(f239(a865),x60623),x60624))+P1(f324(f324(f239(a865),x60621),x60622)) % 181.55/181.54 [6066]P35(x60661,x60662,x60663)+~P1(f324(x60662,x60664))+~P1(f324(f324(f326(x60661),x60664),f324(f167(x60661),x60663))) % 181.55/181.54 [6102]~P33(x61023,x61021,x61024)+P1(f324(x61021,x61022))+~P1(f324(f324(f326(x61023),x61022),f324(f167(x61023),x61024))) % 181.55/181.54 [6104]~E(f324(f130(x61041,x61042),x61043),f116(x61041))+~P1(f324(x61042,x61044))+~P1(f324(f324(f326(x61041),x61044),f324(f167(x61041),x61043))) % 181.55/181.54 [6105]~E(f172(x61053,x61051,x61054),x61054)+P1(f324(x61051,x61052))+~P1(f324(f324(f326(x61053),x61052),f324(f167(x61053),x61054))) % 181.55/181.54 [6133]~E(x61334,f191(f871(x61332,a859)))+~E(x61333,f191(f871(x61331,a859)))+E(f311(x61331,x61332,x61333,x61334),f191(f871(f872(x61331,x61332),a859))) % 181.55/181.54 [6276]P1(f324(x62761,x62762))+~P1(f324(f154(x62763,x62761),x62764))+~P1(f324(f324(f326(x62763),x62762),f324(f167(x62763),x62764))) % 181.55/181.54 [6544]~P72(x65441)+E(f324(f324(f6(a865,x65441),x65442),f295(a865,x65443,f324(a115,x65444))),f2(x65441))+~P1(f324(f324(f239(a865),f324(a115,x65444)),x65443)) % 181.55/181.54 [6684]~P105(x66841)+E(f324(f324(f22(f871(x66841,a859)),f324(f294(x66841,x66842),x66843)),f324(f294(x66841,x66842),x66844)),f324(f294(x66841,x66844),x66843))+~P1(f324(f324(f238(x66841),x66842),x66844)) % 181.55/181.54 [7032]~P1(f324(f324(f326(f866(x70321)),x70324),f155(x70321,x70323)))+P1(f324(f324(f326(x70321),x70322),x70323))+~P1(f324(f324(f326(x70321),x70322),f324(f167(x70321),x70324))) % 181.55/181.54 [7039]~P39(x70391,x70392)+P1(f324(f324(f326(x70391),f638(x70392,x70391,x70393)),x70393))+~P1(f324(f324(f326(x70391),x70394),x70393)) % 181.55/181.54 [7095]~P68(x70951)+E(f324(f324(f324(f65(x70951,x70952,f82(x70951)),x70953),f79(x70951)),x70954),f324(f324(f9(x70952,x70951),x70953),x70954))+~P1(f324(f61(x70952),x70954)) % 181.55/181.54 [7097]~P72(x70971)+E(f324(f324(f324(f65(x70971,x70972,f81(x70971)),x70973),f2(x70971)),x70974),f324(f324(f6(x70972,x70971),x70973),x70974))+~P1(f324(f61(x70972),x70974)) % 181.55/181.54 [7124]P27(x71241,x71242,x71243,x71244)+~E(f324(f37(x71242),f324(f303(x71241,x71242,x71243),x71244)),f324(f37(x71241),x71244))+~P1(f324(f61(x71241),x71244)) % 181.55/181.54 [7308]~P72(x73081)+E(f324(f324(f81(x73081),f324(x73082,x73083)),f324(f324(f6(a865,x73081),x73082),f297(a865,x73083,x73084))),f324(f324(f6(a865,x73081),x73082),f295(a865,x73083,x73084)))+~P1(f324(f324(f238(a865),x73083),x73084)) % 181.55/181.54 [7318]~P68(x73181)+~P27(x73182,x73181,x73183,x73184)+E(f324(f324(f9(x73181,x73181),f34(x73181)),f324(f303(x73182,x73181,x73183),x73184)),f324(f324(f9(x73182,x73181),x73183),x73184)) % 181.55/181.54 [7319]~P72(x73191)+~P27(x73192,x73191,x73193,x73194)+E(f324(f324(f6(x73191,x73191),f34(x73191)),f324(f303(x73192,x73191,x73193),x73194)),f324(f324(f6(x73192,x73191),x73193),x73194)) % 181.55/181.54 [7372]E(f324(f37(f872(x73721,x73722)),f311(x73721,x73722,x73723,x73724)),f324(f324(f81(a865),f324(f37(x73721),x73723)),f324(f37(x73722),x73724)))+~P1(f324(f61(x73722),x73724))+~P1(f324(f61(x73721),x73723)) % 181.55/181.54 [7458]E(x74581,x74582)+P1(f324(f324(f326(x74583),x74581),f324(f167(x74583),f164(x74583,x74582,x74584))))+~P1(f324(f324(f326(x74583),x74581),f324(f167(x74583),x74584))) % 181.55/181.54 [7680]~P72(x76801)+E(f324(f324(f81(x76801),f324(f324(f6(a865,x76801),x76802),f324(f294(a865,x76803),x76804))),f324(x76802,x76804)),f324(f324(f6(a865,x76801),x76802),f324(f294(a865,x76803),f324(a115,x76804))))+P1(f324(f324(f239(a865),x76804),x76803)) % 181.55/181.54 [7728]~P27(x77281,x77282,x77283,f247(f871(x77281,a859)))+~P1(f324(f61(x77282),x77284))+P1(f324(f61(x77281),f324(f304(x77281,x77282,x77283),x77284))) % 181.55/181.54 [7843]P1(f324(f324(f326(f866(x78431)),f324(f324(f145(x78431),x78432),x78433)),f155(x78431,x78434)))+~P1(f324(f324(f326(f866(x78431)),x78433),f155(x78431,x78434)))+~P1(f324(f324(f326(x78431),x78432),x78434)) % 181.55/181.54 [7933]~E(f324(f303(x79333,x79331,x79334),f247(f871(x79333,a859))),f247(f871(x79331,a859)))+P1(f324(f61(x79331),x79332))+~P1(f324(f61(x79333),f324(f304(x79333,x79331,x79334),x79332))) % 181.55/181.54 [8025]~P27(x80251,x80253,x80254,x80252)+P1(f324(f61(x80251),x80252))+~P1(f324(f61(x80253),f324(f303(x80251,x80253,x80254),x80252))) % 181.55/181.54 [8046]~E(x80462,x80463)+P1(f324(f324(f326(f870(x80461,x80461)),f324(f324(f259(x80461,x80461),x80462),x80463)),f256(x80461,x80464)))+~P1(f324(f324(f326(x80461),x80462),x80464)) % 181.55/181.54 [8082]~P72(x80821)+E(f324(f324(f81(x80821),f324(f324(f6(a865,x80821),x80822),f295(a865,x80823,x80824))),f324(x80822,f324(a115,x80824))),f324(f324(f6(a865,x80821),x80822),f295(a865,x80823,f324(a115,x80824))))+P1(f324(f324(f239(a865),f324(a115,x80824)),x80823)) % 181.55/181.54 [8146]P1(f324(x81461,x81462))+~P1(f324(x81461,f324(f324(f159(x81463),x81464),f679(x81461,x81464,x81463))))+~P1(f324(f324(f326(x81463),x81462),f324(f167(x81463),x81464))) % 181.55/181.54 [8290]~P1(f324(f324(f326(x82901),x82902),f313(x82901,x82904)))+P1(f324(f324(f326(f866(x82901)),f324(f324(f145(x82901),x82902),x82903)),f313(f866(x82901),f151(x82901,x82904))))+~P1(f324(f324(f326(f866(x82901)),x82903),f313(f866(x82901),f151(x82901,x82904)))) % 181.55/181.54 [8305]~P27(x83052,x83053,x83054,f641(x83054,x83053,x83052,x83051))+P27(x83052,x83053,x83054,f40(f871(x83052,a859),x83051))+E(x83051,f191(f871(f871(x83052,a859),a859))) % 181.55/181.54 [8569]E(x85691,x85692)+~P1(f324(f324(f326(f870(x85693,x85693)),f324(f324(f259(x85693,x85693),x85691),x85692)),f300(x85693,x85694)))+P1(f324(f324(f326(x85693),x85691),f324(f257(x85693,x85693),x85694))) % 181.55/181.54 [8850]~E(f324(x88504,f324(x88503,f562(x88504,x88503,x88502,x88501))),f562(x88504,x88503,x88502,x88501))+E(f94(x88501,x88502,f247(f871(x88501,a859)),x88503),x88504)+~E(f324(f303(x88501,x88502,x88503),f247(f871(x88501,a859))),f247(f871(x88502,a859))) % 181.55/181.54 [8863]~P28(x88631,x88632,x88633,f247(f871(x88631,a859)),f247(f871(x88632,a859)))+~P1(f324(f61(x88632),x88634))+P1(f324(f61(x88631),f324(f304(x88631,x88632,x88633),x88634))) % 181.55/181.54 [8867]P27(x88672,x88673,x88674,f40(f871(x88672,a859),x88671))+E(x88671,f191(f871(f871(x88672,a859),a859)))+P1(f324(f324(f326(f871(x88672,a859)),f641(x88674,x88673,x88672,x88671)),x88671)) % 181.55/181.54 [8911]~P27(x89111,x89112,x89113,f247(f871(x89111,a859)))+~E(f324(x89113,f324(x89114,f550(x89114,x89113,x89112,x89111))),f550(x89114,x89113,x89112,x89111))+E(f94(x89111,x89112,f247(f871(x89111,a859)),x89113),x89114) % 181.55/181.54 [8979]~P28(x89793,x89791,x89794,f247(f871(x89793,a859)),f247(f871(x89791,a859)))+P1(f324(f61(x89791),x89792))+~P1(f324(f61(x89793),f324(f304(x89793,x89791,x89794),x89792))) % 181.55/181.54 [8997]P1(f324(f61(x89971),x89972))+~P1(f324(f61(x89974),f324(f303(x89971,x89974,x89973),x89972)))+P1(f324(f324(f326(x89971),f347(x89973,x89974,x89972,x89971)),x89972)) % 181.55/181.54 [9093]~P6(x90932)+E(f324(f324(f64(x90931,x90932,f324(f324(f8(x90932,f871(x90932,x90932),x90931),f113(x90932)),x90933)),f191(x90932)),x90934),f324(f324(f41(x90931,x90932),x90934),x90933))+~P1(f324(f61(x90931),x90934)) % 181.55/181.54 [9094]~P6(x90942)+E(f324(f324(f64(x90941,x90942,f324(f324(f8(x90942,f871(x90942,x90942),x90941),f104(x90942)),x90943)),f247(x90942)),x90944),f324(f324(f42(x90941,x90942),x90944),x90943))+~P1(f324(f61(x90941),x90944)) % 181.55/181.54 [9177]P1(f324(x91771,x91772))+~P1(f324(x91771,f324(f324(f159(x91773),x91774),f751(x91772,x91771,x91774,x91773))))+~P1(f324(f324(f326(x91773),x91772),f324(f167(x91773),x91774))) % 181.55/181.54 [9197]E(x91971,x91972)+~P1(f324(f324(f326(f870(x91973,x91973)),f324(f324(f259(x91973,x91973),x91971),x91972)),f300(x91973,x91974)))+P1(f324(f324(f326(f870(x91973,x91973)),f324(f324(f259(x91973,x91973),x91971),x91972)),f324(f324(f281(x91973,x91973,x91973),x91974),f300(x91973,x91974)))) % 181.55/181.54 [9244]~E(f324(f192(f866(x92441)),x92442),f324(f192(f866(x92441)),x92443))+~P1(f324(f324(f326(f870(f866(x92441),f866(x92441))),f324(f324(f259(f866(x92441),f866(x92441)),x92442),x92443)),f141(x92441,x92444)))+P1(f324(f324(f326(f870(f866(x92441),f866(x92441))),f324(f324(f259(f866(x92441),f866(x92441)),x92442),x92443)),f139(x92441,x92444))) % 181.55/181.54 [9483]P33(x94831,f324(f324(f18(x94831,a859,a859),f324(f324(f8(a859,f871(a859,a859),x94831),a323),f324(f324(f8(a859,a859,x94831),a319),x94832))),f324(a321,x94833)),x94834)+~P1(f324(x94832,x94833))+~P37(x94831,x94832,f324(f324(f145(x94831),x94833),x94834)) % 181.55/181.54 [9651]~P33(x96511,f324(f324(f18(x96511,a859,a859),f324(f324(f8(a859,f871(a859,a859),x96511),a323),f324(f324(f8(a859,a859,x96511),a319),x96512))),f324(a321,x96513)),x96514)+~P1(f324(x96512,x96513))+P37(x96511,x96512,f324(f324(f145(x96511),x96513),x96514)) % 181.55/181.54 [9655]~P37(x96551,x96552,x96554)+~P33(x96551,f324(f324(f18(x96551,a859,a859),f324(f324(f8(a859,f871(a859,a859),x96551),a323),f324(f324(f8(a859,a859,x96551),a319),x96552))),f324(a321,x96553)),x96554)+P37(x96551,x96552,f324(f324(f145(x96551),x96553),x96554)) % 181.55/181.54 [9692]~P5(x96921)+E(f324(f324(f6(a865,x96921),f324(f324(f18(a865,x96921,x96921),f324(f324(f8(x96921,f871(x96921,x96921),a865),f22(x96921)),x96922)),f324(f324(f8(a865,x96921,a865),x96922),f324(f324(f7(a865,a865,a865),f81(a865)),f79(a865))))),f295(a865,x96923,x96924)),f2(x96921))+P1(f324(f324(f238(a865),x96923),x96924)) % 181.55/181.54 [9932]~P39(x99322,x99324)+~P27(x99322,x99321,x99323,f247(f871(x99322,a859)))+P39(x99321,f324(f303(f870(x99322,x99322),f870(x99321,x99321),f264(x99322,x99321,x99322,x99321,x99323,x99323)),x99324)) % 181.55/181.54 [10094]~E(f324(f192(f866(x100941)),x100943),f324(f192(f866(x100941)),x100942))+P1(f324(f324(f326(f870(f866(x100941),f866(x100941))),f324(f324(f259(f866(x100941),f866(x100941)),x100942),x100943)),f152(x100941,x100944)))+~P1(f324(f324(f263(x100941,x100941,a859),f324(f324(f7(x100941,f871(f870(x100941,x100941),a859),f871(x100941,a859)),f324(f324(f8(f871(x100941,f871(f871(f870(x100941,x100941),a859),a859)),f871(f871(f870(x100941,x100941),a859),f871(x100941,a859)),x100941),f7(x100941,f871(f870(x100941,x100941),a859),a859)),f324(f324(f8(f871(x100941,f870(x100941,x100941)),f871(x100941,f871(f871(f870(x100941,x100941),a859),a859)),x100941),f324(f8(f870(x100941,x100941),f871(f871(f870(x100941,x100941),a859),a859),x100941),f326(f870(x100941,x100941)))),f259(x100941,x100941)))),x100944)),f671(x100944,x100943,x100942,x100941))) % 181.55/181.54 [6027]~P59(x60271)+~E(x60272,f2(x60271))+E(f324(f324(f38(x60271),f324(f324(f82(x60271),x60272),x60273)),f324(f324(f82(x60271),x60272),x60274)),f2(x60271)) % 181.55/181.54 [6065]E(x60651,f116(x60652))+E(x60653,f324(f324(f22(a865),f324(f192(f866(x60652)),x60651)),f79(a865)))+E(f138(x60652,f324(f324(f153(x60652,x60651),x60653),x60654)),f138(x60652,x60651)) % 181.55/181.54 [6093]E(x60931,x60932)+P1(f324(x60933,x60932))+~P1(f324(f324(f324(f302(x60934),x60931),x60933),x60932)) % 181.55/181.54 [6109]~P72(x61091)+~P1(f324(f131(x61092),x61094))+E(f324(f160(x61091),f324(f324(f148(x61092,x61091),x61093),x61094)),f324(f324(f6(x61092,x61091),x61093),f324(f167(x61092),x61094))) % 181.55/181.54 [6126]~P68(x61262)+~P1(f324(f61(x61261),x61264))+E(f324(f324(f9(x61261,x61262),f324(f16(x61262,x61261),x61263)),x61264),f324(f324(f249(x61262),x61263),f324(f37(x61261),x61264))) % 181.55/181.54 [6180]~P59(x61802)+E(x61801,f2(x61802))+E(f324(f324(f38(x61802),f324(f324(f82(x61802),x61803),x61801)),f324(f324(f82(x61802),x61804),x61801)),f324(f324(f38(x61802),x61803),x61804)) % 181.55/181.54 [6182]~P62(x61822)+E(x61821,f2(x61822))+E(f324(f324(f282(x61822),f324(f324(f82(x61822),x61823),x61821)),f324(f324(f82(x61822),x61824),x61821)),f324(f324(f282(x61822),x61823),x61824)) % 181.55/181.54 [6183]~P62(x61832)+E(x61831,f2(x61832))+E(f324(f324(f282(x61832),f324(f324(f82(x61832),x61831),x61833)),f324(f324(f82(x61832),x61831),x61834)),f324(f324(f282(x61832),x61833),x61834)) % 181.55/181.54 [6184]~P59(x61842)+E(x61841,f2(x61842))+E(f324(f324(f38(x61842),f324(f324(f82(x61842),x61841),x61843)),f324(f324(f82(x61842),x61841),x61844)),f324(f324(f38(x61842),x61843),x61844)) % 181.55/181.54 [6246]P1(f324(x62461,x62462))+~E(x62463,f324(f324(f81(a865),x62464),x62462))+~P1(f324(x62461,f324(f324(f22(a865),x62463),x62464))) % 181.55/181.54 [6327]P31(x63271,x63272,x63273)+P30(x63271,f551(x63273,x63272,x63271),x63274)+~P1(f324(f324(f326(f864(x63271)),x63274),x63272)) % 181.55/181.54 [6329]~P1(f324(x63292,x63293))+~P1(f324(f154(x63291,x63292),x63294))+P1(f324(f154(x63291,x63292),f324(f324(f145(x63291),x63293),x63294))) % 181.55/181.54 [6370]E(x63701,f116(x63702))+~E(x63703,f324(f324(f22(a865),f324(f192(f866(x63702)),x63701)),f79(a865)))+E(f138(x63702,f324(f324(f153(x63702,x63701),x63703),x63704)),x63704) % 181.55/181.54 [6393]~P100(x63931)+~P1(f324(f324(f238(x63931),x63932),x63934))+P1(f324(f324(f238(x63931),x63932),f324(f324(f113(x63931),x63933),x63934))) % 181.55/181.54 [6394]~P100(x63941)+~P1(f324(f324(f238(x63941),x63942),x63943))+P1(f324(f324(f238(x63941),x63942),f324(f324(f113(x63941),x63943),x63944))) % 181.55/181.54 [6396]~P105(x63961)+~P1(f324(f324(f238(x63961),x63962),x63964))+P1(f324(f324(f238(x63961),x63962),f324(f324(f190(x63961),x63963),x63964))) % 181.55/181.54 [6398]~P105(x63981)+~P1(f324(f324(f238(x63981),x63982),x63983))+P1(f324(f324(f238(x63981),x63982),f324(f324(f190(x63981),x63983),x63984))) % 181.55/181.54 [6399]~P100(x63991)+~P1(f324(f324(f239(x63991),x63992),x63994))+P1(f324(f324(f239(x63991),x63992),f324(f324(f113(x63991),x63993),x63994))) % 181.55/181.54 [6400]~P100(x64001)+~P1(f324(f324(f239(x64001),x64002),x64003))+P1(f324(f324(f239(x64001),x64002),f324(f324(f113(x64001),x64003),x64004))) % 181.55/181.54 [6402]~P105(x64021)+~P1(f324(f324(f239(x64021),x64022),x64024))+P1(f324(f324(f239(x64021),x64022),f324(f324(f190(x64021),x64023),x64024))) % 181.55/181.54 [6404]~P105(x64041)+~P1(f324(f324(f239(x64041),x64042),x64043))+P1(f324(f324(f239(x64041),x64042),f324(f324(f190(x64041),x64043),x64044))) % 181.55/181.54 [6490]~E(f324(f324(f159(x64901),x64902),x64903),x64904)+E(f324(f324(f153(x64901,x64902),x64903),x64904),x64902)+~P1(f324(f324(f239(a865),x64903),f324(f192(f866(x64901)),x64902))) % 181.55/181.54 [6530]P1(f324(x65301,x65302))+~P1(f324(x65303,x65302))+~P1(f324(f324(f238(f871(x65304,a859)),x65303),x65301)) % 181.55/181.54 [6561]~E(f324(f324(f153(x65611,x65612),x65613),x65614),x65612)+E(f324(f324(f159(x65611),x65612),x65613),x65614)+~P1(f324(f324(f239(a865),x65613),f324(f192(f866(x65611)),x65612))) % 181.55/181.54 [6576]~P1(f324(f154(x65761,x65762),x65764))+~P1(f324(f154(x65761,x65762),x65763))+P1(f324(f154(x65761,x65762),f324(f324(f124(x65761),x65763),x65764))) % 181.55/181.54 [6672]P30(x66721,x66722,x66723)+~P30(x66721,f324(a115,x66722),f547(x66722,x66724,x66721))+~P1(f324(f324(f326(f864(x66721)),x66723),x66724)) % 181.55/181.54 [6681]E(x66811,f191(f871(x66812,a859)))+E(x66813,f191(f871(x66814,a859)))+~E(f324(f324(f261(x66814,x66812),x66813),f324(f16(f871(x66812,a859),x66814),x66811)),f191(f871(f870(x66814,x66812),a859))) % 181.55/181.54 [6700]E(x67001,x67002)+P1(f324(f324(f326(x67003),x67001),x67004))+~P1(f324(f324(f326(x67003),x67001),f324(f324(f302(x67003),x67002),x67004))) % 181.55/181.54 [6717]~P105(x67171)+P1(f324(f324(f238(x67171),x67172),x67173))+~P1(f324(f324(f238(x67171),x67172),f324(f324(f189(x67171),x67174),x67173))) % 181.55/181.54 [6719]~P105(x67191)+P1(f324(f324(f238(x67191),x67192),x67193))+~P1(f324(f324(f238(x67191),x67192),f324(f324(f189(x67191),x67193),x67194))) % 181.55/181.54 [6721]~P99(x67211)+P1(f324(f324(f238(x67211),x67212),x67213))+~P1(f324(f324(f238(x67211),x67212),f324(f324(f104(x67211),x67214),x67213))) % 181.55/181.54 [6723]~P99(x67231)+P1(f324(f324(f238(x67231),x67232),x67233))+~P1(f324(f324(f238(x67231),x67232),f324(f324(f104(x67231),x67233),x67234))) % 181.55/181.54 [6724]~P105(x67241)+P1(f324(f324(f239(x67241),x67242),x67243))+~P1(f324(f324(f239(x67241),x67242),f324(f324(f189(x67241),x67244),x67243))) % 181.55/181.54 [6725]~P105(x67251)+P1(f324(f324(f239(x67251),x67252),x67253))+~P1(f324(f324(f239(x67251),x67252),f324(f324(f189(x67251),x67253),x67254))) % 181.55/181.54 [6747]~E(f324(f324(f159(x67471),x67473),x67474),x67472)+P1(f324(f324(f326(x67471),x67472),f324(f167(x67471),x67473)))+~P1(f324(f324(f239(a865),x67474),f324(f192(f866(x67471)),x67473))) % 181.55/181.54 [6758]~P105(x67581)+~P16(x67581,f324(f324(f145(x67581),x67582),f324(f324(f145(x67581),x67583),x67584)))+P1(f324(f324(f238(x67581),x67582),x67583)) % 181.55/181.54 [6898]~P33(x68982,x68981,x68983)+P1(f324(x68981,f324(f324(f159(x68982),x68983),x68984)))+~P1(f324(f324(f239(a865),x68984),f324(f192(f866(x68982)),x68983))) % 181.55/181.54 [6917]E(x69171,f2(a1))+E(f324(f324(f38(a1),x69172),x69171),x69173)+~P1(f324(f48(x69172,x69171),f324(f324(f259(a1,a1),x69173),x69174))) % 181.55/181.54 [6938]E(f44(a1,x69382,x69381),x69383)+E(x69381,f2(a1))+~P1(f324(f48(x69382,x69381),f324(f324(f259(a1,a1),x69384),x69383))) % 181.55/181.54 [7056]P1(f324(f324(f326(x70561),x70562),x70563))+~P1(f324(f324(f326(x70561),x70562),x70564))+~P1(f324(f324(f239(f871(x70561,a859)),x70564),x70563)) % 181.55/181.54 [7057]P1(f324(f324(f326(x70571),x70572),x70573))+~P1(f324(f324(f326(x70571),x70572),x70574))+~P1(f324(f324(f238(f871(x70571,a859)),x70574),x70573)) % 181.55/181.54 [7164]P35(x71641,x71642,x71643)+~P1(f324(x71642,f324(f324(f159(x71641),x71643),x71644)))+~P1(f324(f324(f239(a865),x71644),f324(f192(f866(x71641)),x71643))) % 181.55/181.54 [7273]~P104(x72732)+~P1(f324(f324(f239(f871(x72731,x72732)),x72733),x72734))+P1(f324(f324(f238(f871(x72731,x72732)),x72733),x72734)) % 181.55/181.54 [7360]~P26(x73601,x73602,x73604)+P26(x73601,x73602,f324(f324(f302(f864(x73601)),x73603),x73604))+~P26(x73601,x73602,f324(f324(f302(f864(x73601)),x73603),f191(f871(f864(x73601),a859)))) % 181.55/181.54 [7404]~P1(f324(f324(f326(x74041),x74042),x74044))+P1(f324(f324(f326(x74041),x74042),f39(f871(x74041,a859),x74043)))+~P1(f324(f324(f326(f871(x74041,a859)),x74044),x74043)) % 181.55/181.54 [7416]P30(x74161,x74162,x74163)+P1(f324(f324(f326(f864(x74161)),f547(x74162,x74164,x74161)),x74164))+~P1(f324(f324(f326(f864(x74161)),x74163),x74164)) % 181.55/181.54 [7436]~P81(x74361)+~P1(f324(f324(f238(x74361),x74363),x74364))+P1(f324(f324(f238(x74361),f324(f324(f81(x74361),x74362),x74363)),f324(f324(f81(x74361),x74362),x74364))) % 181.55/181.54 [7437]~P82(x74371)+~P1(f324(f324(f238(x74371),x74373),x74374))+P1(f324(f324(f238(x74371),f324(f324(f81(x74371),x74372),x74373)),f324(f324(f81(x74371),x74372),x74374))) % 181.55/181.54 [7438]~P81(x74381)+~P1(f324(f324(f238(x74381),x74382),x74384))+P1(f324(f324(f238(x74381),f324(f324(f81(x74381),x74382),x74383)),f324(f324(f81(x74381),x74384),x74383))) % 181.55/181.54 [7439]~P82(x74391)+~P1(f324(f324(f238(x74391),x74392),x74394))+P1(f324(f324(f238(x74391),f324(f324(f81(x74391),x74392),x74393)),f324(f324(f81(x74391),x74394),x74393))) % 181.55/181.54 [7440]~P81(x74401)+~P1(f324(f324(f239(x74401),x74403),x74404))+P1(f324(f324(f239(x74401),f324(f324(f81(x74401),x74402),x74403)),f324(f324(f81(x74401),x74402),x74404))) % 181.55/181.54 [7441]~P84(x74411)+~P1(f324(f324(f239(x74411),x74413),x74414))+P1(f324(f324(f239(x74411),f324(f324(f81(x74411),x74412),x74413)),f324(f324(f81(x74411),x74412),x74414))) % 181.55/181.54 [7442]~P81(x74421)+~P1(f324(f324(f239(x74421),x74422),x74424))+P1(f324(f324(f239(x74421),f324(f324(f81(x74421),x74422),x74423)),f324(f324(f81(x74421),x74424),x74423))) % 181.55/181.54 [7443]~P84(x74431)+~P1(f324(f324(f239(x74431),x74432),x74434))+P1(f324(f324(f239(x74431),f324(f324(f81(x74431),x74432),x74433)),f324(f324(f81(x74431),x74434),x74433))) % 181.55/181.54 [7452]~P116(x74521)+~P90(x74521)+E(f324(f324(f22(x74521),f324(f324(f82(x74521),x74522),f324(f106(x74521),x74523))),f324(f324(f82(x74521),x74524),f324(f106(x74521),x74523))),f324(f324(f82(x74521),f324(f324(f22(x74521),x74522),x74524)),f324(f106(x74521),x74523))) % 181.55/181.54 [7453]~P137(x74531)+~P90(x74531)+E(f324(f324(f81(x74531),f324(f324(f82(x74531),x74532),f324(f106(x74531),x74533))),f324(f324(f82(x74531),x74534),f324(f106(x74531),x74533))),f324(f324(f82(x74531),f324(f324(f81(x74531),x74532),x74534)),f324(f106(x74531),x74533))) % 181.55/181.54 [7488]~P72(x74881)+E(f324(f324(f81(x74881),f324(x74882,x74883)),f324(f324(f6(a865,x74881),x74882),f295(a865,f324(a115,x74883),x74884))),f324(f324(f6(a865,x74881),x74882),f295(a865,x74883,x74884)))+~P1(f324(f324(f238(a865),x74883),x74884)) % 181.55/181.54 [7499]~P27(x74992,x74991,x74993,f324(f167(x74992),x74994))+~P1(f324(f131(x74992),x74994))+P1(f324(f131(x74991),f324(f324(f148(x74992,x74991),x74993),x74994))) % 181.55/181.54 [7546]~P1(f324(f324(f238(a865),x75462),x75464))+~P1(f324(f324(f238(a865),x75461),x75463))+P1(f324(f324(f238(a865),f324(f324(f82(a865),x75461),x75462)),f324(f324(f82(a865),x75463),x75464))) % 181.55/181.54 [7547]~P1(f324(f324(f238(a865),x75472),x75474))+~P1(f324(f324(f238(a865),x75471),x75473))+P1(f324(f324(f238(a865),f324(f324(f81(a865),x75471),x75472)),f324(f324(f81(a865),x75473),x75474))) % 181.55/181.54 [7550]~P1(f324(f324(f239(a865),x75502),x75504))+~P1(f324(f324(f239(a865),x75501),x75503))+P1(f324(f324(f239(a865),f324(f324(f81(a865),x75501),x75502)),f324(f324(f81(a865),x75503),x75504))) % 181.55/181.54 [7551]~P1(f324(f324(f238(a1),x75512),x75514))+~P1(f324(f324(f239(a1),x75511),x75513))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x75511),x75512)),f324(f324(f81(a1),x75513),x75514))) % 181.55/181.54 [7599]P1(f324(f324(f326(x75991),x75992),x75993))+~P1(f324(f324(f326(x75991),x75992),f40(f871(x75991,a859),x75994)))+~P1(f324(f324(f326(f871(x75991,a859)),x75993),x75994)) % 181.55/181.54 [7614]~P1(f324(x76141,f678(x76141,x76143,x76142)))+P1(f324(x76141,f324(f324(f159(x76142),x76143),x76144)))+~P1(f324(f324(f239(a865),x76144),f324(f192(f866(x76142)),x76143))) % 181.55/181.54 [7618]P1(f324(x76181,x76182))+~P1(f324(f324(f326(x76184),x76182),f324(f167(x76184),x76183)))+P1(f324(f324(f239(a865),f679(x76181,x76183,x76184)),f324(f192(f866(x76184)),x76183))) % 181.55/181.54 [7666]~P104(x76661)+~P1(f324(f324(f239(f871(x76662,x76661)),x76664),x76663))+~P1(f324(f324(f238(f871(x76662,x76661)),x76663),x76664)) % 181.55/181.54 [7707]~P1(f324(x77074,x77072))+~P1(f324(f324(f326(x77071),x77072),x77073))+P1(f324(f324(f326(x77071),x77072),f324(f324(f104(f871(x77071,a859)),x77073),f324(f244(x77071),x77074)))) % 181.55/181.54 [7852]~P1(f324(f324(f326(x78521),x78523),x78524))+~P1(f324(f324(f239(f871(x78521,a859)),x78522),x78524))+P1(f324(f324(f239(f871(x78521,a859)),x78522),f324(f324(f302(x78521),x78523),x78524))) % 181.55/181.54 [7854]E(f324(f324(f104(f871(x78541,a859)),x78542),x78543),f191(f871(x78541,a859)))+~E(f324(f324(f104(f871(x78541,a859)),f39(f871(x78541,a859),x78544)),x78543),f191(f871(x78541,a859)))+~P1(f324(f324(f326(f871(x78541,a859)),x78542),x78544)) % 181.55/181.54 [7929]P1(f324(f324(f326(x79291),x79292),x79293))+~P1(f324(f324(f238(f871(x79291,a859)),x79293),f324(f324(f302(x79291),x79292),x79294)))+P1(f324(f324(f238(f871(x79291,a859)),x79293),x79294)) % 181.55/181.54 [7946]P1(f324(f324(f326(x79462),f678(x79461,x79463,x79462)),f324(f167(x79462),x79463)))+P1(f324(x79461,f324(f324(f159(x79462),x79463),x79464)))+~P1(f324(f324(f239(a865),x79464),f324(f192(f866(x79462)),x79463))) % 181.55/181.54 [7954]~P1(f324(f324(f238(f871(x79541,a859)),x79542),x79544))+P1(f324(f324(f238(f871(x79541,a859)),x79542),x79543))+~P1(f324(f324(f238(f871(x79541,a859)),x79544),x79543)) % 181.55/181.54 [7955]~P1(f324(f324(f239(f871(x79551,a859)),x79552),x79554))+~P1(f324(f324(f238(f871(x79551,a859)),x79554),x79553))+P1(f324(f324(f239(f871(x79551,a859)),x79552),x79553)) % 181.55/181.54 [7956]~P1(f324(f324(f238(f871(x79561,a859)),x79562),x79564))+~P1(f324(f324(f239(f871(x79561,a859)),x79564),x79563))+P1(f324(f324(f239(f871(x79561,a859)),x79562),x79563)) % 181.55/181.54 [7957]~P1(f324(f324(f239(f871(x79571,a859)),x79572),x79574))+P1(f324(f324(f239(f871(x79571,a859)),x79572),x79573))+~P1(f324(f324(f239(f871(x79571,a859)),x79574),x79573)) % 181.55/181.54 [7999]~P1(f324(f324(f326(x79991),x79994),x79993))+~P1(f324(f324(f239(f871(x79991,a859)),x79992),f324(f324(f302(x79991),x79994),x79993)))+P1(f324(f324(f239(f871(x79991,a859)),x79992),x79993)) % 181.55/181.54 [8010]~P81(x80101)+P1(f324(f324(f238(x80101),x80102),x80103))+~P1(f324(f324(f238(x80101),f324(f324(f81(x80101),x80104),x80102)),f324(f324(f81(x80101),x80104),x80103))) % 181.55/181.54 [8012]~P81(x80121)+P1(f324(f324(f238(x80121),x80122),x80123))+~P1(f324(f324(f238(x80121),f324(f324(f81(x80121),x80122),x80124)),f324(f324(f81(x80121),x80123),x80124))) % 181.55/181.54 [8014]~P81(x80141)+P1(f324(f324(f239(x80141),x80142),x80143))+~P1(f324(f324(f239(x80141),f324(f324(f81(x80141),x80144),x80142)),f324(f324(f81(x80141),x80144),x80143))) % 181.55/181.54 [8016]~P81(x80161)+P1(f324(f324(f239(x80161),x80162),x80163))+~P1(f324(f324(f239(x80161),f324(f324(f81(x80161),x80162),x80164)),f324(f324(f81(x80161),x80163),x80164))) % 181.55/181.54 [8063]P1(f324(x80631,x80632))+~E(f324(f324(f132(x80633),f324(f192(f866(x80633)),f172(x80633,x80631,x80634))),x80634),f116(x80633))+~P1(f324(f324(f326(x80633),x80632),f324(f167(x80633),x80634))) % 181.55/181.54 [8189]P1(f324(x81891,x81892))+~P1(f324(f324(f326(x81893),x81892),f324(f167(x81893),x81894)))+P1(f324(f324(f239(a865),f324(f192(f866(x81893)),f324(f130(x81893,x81891),x81894))),f324(f192(f866(x81893)),x81894))) % 181.55/181.54 [8676]~P1(f324(x86761,f776(x86761,x86763,x86762,x86764)))+P1(f324(x86761,f324(f324(f159(x86762),x86763),x86764)))+~P1(f324(f324(f239(a865),x86764),f324(f192(f866(x86762)),x86763))) % 181.55/181.54 [8700]~P27(x87004,x87003,x87001,f247(f871(x87004,a859)))+E(f324(x87001,f408(x87002,x87001,x87003,x87004)),x87002)+~P1(f324(f324(f326(x87003),x87002),f324(f303(x87004,x87003,x87001),f247(f871(x87004,a859))))) % 181.55/181.54 [8769]E(f172(x87691,x87692,x87693),f324(f324(f170(x87691),x87694),x87693))+P1(f324(f324(f239(a865),f744(x87692,x87693,x87691,x87694)),x87694))+P1(f324(f324(f239(a865),x87694),f324(f192(f866(x87691)),x87693))) % 181.55/181.54 [8772]E(f172(x87721,x87722,x87723),f324(f324(f170(x87721),x87724),x87723))+P1(f324(f324(f239(a865),f744(x87722,x87723,x87721,x87724)),x87724))+P1(f324(x87722,f324(f324(f159(x87721),x87723),x87724))) % 181.55/181.54 [8801]P1(f324(x88011,x88012))+~P1(f324(f324(f326(x88014),x88012),f324(f167(x88014),x88013)))+P1(f324(f324(f239(a865),f751(x88012,x88011,x88013,x88014)),f324(f192(f866(x88014)),x88013))) % 181.55/181.54 [8804]E(f172(x88041,x88042,x88043),f324(f324(f170(x88041),x88044),x88043))+P1(f324(f324(f239(a865),x88044),f324(f192(f866(x88041)),x88043)))+P1(f324(f324(f239(a865),f744(x88042,x88043,x88041,x88044)),f324(f192(f866(x88041)),x88043))) % 181.55/181.54 [8811]E(f172(x88111,x88112,x88113),f324(f324(f170(x88111),x88114),x88113))+P1(f324(x88112,f324(f324(f159(x88111),x88113),x88114)))+P1(f324(f324(f239(a865),f744(x88112,x88113,x88111,x88114)),f324(f192(f866(x88111)),x88113))) % 181.55/181.54 [8837]~P120(x88374)+P1(f324(f324(f326(x88371),f786(x88372,x88373,x88371,x88374)),x88373))+P1(f324(f324(f239(x88374),f2(x88374)),f324(f324(f9(x88371,x88374),x88372),x88373))) % 181.55/181.54 [8838]~P120(x88384)+P1(f324(f324(f326(x88381),f798(x88382,x88383,x88381,x88384)),x88383))+P1(f324(f324(f238(x88384),f2(x88384)),f324(f324(f9(x88381,x88384),x88382),x88383))) % 181.55/181.54 [8869]~P1(f324(f61(x88691),x88694))+P1(f324(f324(f326(x88691),f490(x88692,x88693,x88694,x88691)),x88694))+P1(f324(f61(f870(x88691,x88693)),f324(f324(f261(x88691,x88693),x88694),x88692))) % 181.55/181.54 [8897]P1(f324(f324(f326(x88972),f776(x88971,x88973,x88972,x88974)),f324(f167(x88972),x88973)))+P1(f324(x88971,f324(f324(f159(x88972),x88973),x88974)))+~P1(f324(f324(f239(a865),x88974),f324(f192(f866(x88972)),x88973))) % 181.55/181.54 [9030]P1(f324(f324(f238(a865),x90304),f324(f192(f866(x90302)),f172(x90302,x90303,x90301))))+P1(f324(f324(f239(a865),f745(x90301,x90302,x90303,x90304)),x90304))+~P1(f324(f324(f238(a865),x90304),f324(f192(f866(x90302)),x90301))) % 181.55/181.54 [9136]~E(f324(f324(f173(x91361,x91362),x91363),f757(x91364,x91363,x91362,x91361)),f324(f324(f173(x91361,x91362),x91364),f757(x91364,x91363,x91362,x91361)))+E(f324(f173(x91361,x91362),x91363),f324(f173(x91361,x91362),x91364))+~E(f324(f167(x91361),f324(f324(f148(f870(x91361,x91362),x91361),f258(x91361,x91362)),x91363)),f324(f167(x91361),f324(f324(f148(f870(x91361,x91362),x91361),f258(x91361,x91362)),x91364))) % 181.55/181.54 [9180]E(f172(x91801,x91802,x91803),f324(f324(f170(x91801),x91804),x91803))+~P1(f324(x91802,f324(f324(f159(x91801),x91803),f744(x91802,x91803,x91801,x91804))))+P1(f324(f324(f239(a865),x91804),f324(f192(f866(x91801)),x91803))) % 181.55/181.54 [9184]E(f172(x91841,x91842,x91843),f324(f324(f170(x91841),x91844),x91843))+~P1(f324(x91842,f324(f324(f159(x91841),x91843),f744(x91842,x91843,x91841,x91844))))+P1(f324(x91842,f324(f324(f159(x91841),x91843),x91844))) % 181.55/181.54 [9191]~P1(f324(f61(x91911),x91913))+~P1(f324(f61(x91912),f324(x91914,f490(x91914,x91912,x91913,x91911))))+P1(f324(f61(f870(x91911,x91912)),f324(f324(f261(x91911,x91912),x91913),x91914))) % 181.55/181.54 [9199]~P120(x91991)+~P1(f324(f324(f238(x91991),f2(x91991)),f324(x91993,f798(x91993,x91994,x91992,x91991))))+P1(f324(f324(f238(x91991),f2(x91991)),f324(f324(f9(x91992,x91991),x91993),x91994))) % 181.55/181.54 [9200]~P120(x92001)+~P1(f324(f324(f239(x92001),f2(x92001)),f324(x92003,f786(x92003,x92004,x92002,x92001))))+P1(f324(f324(f239(x92001),f2(x92001)),f324(f324(f9(x92002,x92001),x92003),x92004))) % 181.55/181.54 [9208]~E(f324(f192(f866(x92084)),x92082),f324(f192(f866(x92084)),x92083))+P1(f324(f324(f326(f870(f866(x92084),f866(x92084))),f324(f324(f259(f866(x92084),f866(x92084)),x92083),x92082)),f152(x92084,x92081)))+P1(f324(f324(f239(a865),f687(x92081,x92082,x92083,x92084)),f324(f192(f866(x92084)),x92083))) % 181.55/181.54 [9258]~P1(f324(x92583,f324(f324(f159(x92582),x92584),f745(x92584,x92582,x92583,x92581))))+P1(f324(f324(f238(a865),x92581),f324(f192(f866(x92582)),f172(x92582,x92583,x92584))))+~P1(f324(f324(f238(a865),x92581),f324(f192(f866(x92582)),x92584))) % 181.55/181.54 [9336]E(f324(f324(f170(x93361),f691(x93362,x93363,x93364,x93361)),x93363),f324(f324(f170(x93361),f691(x93362,x93363,x93364,x93361)),x93364))+~P1(f324(f324(f326(f870(f866(x93361),f866(x93361))),f324(f324(f259(f866(x93361),f866(x93361)),x93364),x93363)),f141(x93361,x93362)))+P1(f324(f324(f239(a865),f324(f192(f866(x93361)),x93364)),f324(f192(f866(x93361)),x93363))) % 181.55/181.54 [9392]~P1(f324(f324(f239(a865),f2(a865)),x93923))+~P1(f324(f324(f239(a865),x93924),x93921))+P1(f324(f324(f239(a865),f324(f324(f81(a865),f324(f324(f82(a865),x93921),f44(a865,x93922,x93923))),x93924)),f324(f324(f82(a865),x93921),x93923))) % 181.55/181.54 [9593]~P104(x95932)+~P1(f324(f324(f238(x95932),f324(x95933,f378(x95934,x95933,x95931,x95932))),f324(x95934,f378(x95934,x95933,x95931,x95932))))+P1(f324(f324(f238(f871(x95931,x95932)),x95933),x95934)) % 181.55/181.54 [9699]~P5(x96991)+E(f324(f324(f6(a865,x96991),f324(f324(f18(a865,x96991,x96991),f324(f324(f8(x96991,f871(x96991,x96991),a865),f22(x96991)),x96992)),f324(f324(f8(a865,x96991,a865),x96992),f324(f324(f7(a865,a865,a865),f81(a865)),f79(a865))))),f295(a865,x96993,x96994)),f324(f324(f22(x96991),f324(x96992,x96993)),f324(x96992,f324(f324(f81(a865),x96994),f79(a865)))))+~P1(f324(f324(f238(a865),x96993),x96994)) % 181.55/181.54 [6751]E(f324(f324(f124(x67511),x67512),x67513),x67514)+~E(x67513,f324(f324(f132(x67511),f324(f192(f866(x67511)),x67512)),x67514))+~E(f324(f324(f170(x67511),f324(f192(f866(x67511)),x67512)),x67514),x67512) % 181.55/181.54 [6806]~P63(x68062)+E(x68061,f2(x68062))+E(f324(f324(f282(x68062),f324(f324(f249(x68062),x68063),x68064)),f324(f324(f249(x68062),x68061),x68064)),f324(f324(f249(x68062),f324(f324(f282(x68062),x68063),x68061)),x68064)) % 181.55/181.54 [6939]~E(f324(f192(f866(x69391)),x69393),f324(f192(f866(x69392)),x69394))+~P1(f324(f131(x69391),x69393))+E(f179(x69391,x69392,f324(f173(x69391,x69392),f324(f324(f177(x69391,x69392),x69393),x69394))),f324(f167(x69391),x69393)) % 181.55/181.54 [6956]~P99(x69561)+~P1(f324(f324(f238(x69561),x69563),x69564))+P1(f324(f324(f238(x69561),f324(f324(f104(x69561),x69562),x69563)),x69564)) % 181.55/181.54 [6957]~P99(x69571)+~P1(f324(f324(f238(x69571),x69572),x69574))+P1(f324(f324(f238(x69571),f324(f324(f104(x69571),x69572),x69573)),x69574)) % 181.55/181.54 [6959]~P105(x69591)+~P1(f324(f324(f238(x69591),x69593),x69594))+P1(f324(f324(f238(x69591),f324(f324(f189(x69591),x69592),x69593)),x69594)) % 181.55/181.54 [6961]~P105(x69611)+~P1(f324(f324(f238(x69611),x69612),x69614))+P1(f324(f324(f238(x69611),f324(f324(f189(x69611),x69612),x69613)),x69614)) % 181.55/181.54 [6962]~P99(x69621)+~P1(f324(f324(f239(x69621),x69623),x69624))+P1(f324(f324(f239(x69621),f324(f324(f104(x69621),x69622),x69623)),x69624)) % 181.55/181.54 [6963]~P99(x69631)+~P1(f324(f324(f239(x69631),x69632),x69634))+P1(f324(f324(f239(x69631),f324(f324(f104(x69631),x69632),x69633)),x69634)) % 181.55/181.54 [6965]~P105(x69651)+~P1(f324(f324(f239(x69651),x69653),x69654))+P1(f324(f324(f239(x69651),f324(f324(f189(x69651),x69652),x69653)),x69654)) % 181.55/181.54 [6967]~P105(x69671)+~P1(f324(f324(f239(x69671),x69672),x69674))+P1(f324(f324(f239(x69671),f324(f324(f189(x69671),x69672),x69673)),x69674)) % 181.55/181.54 [6987]~P1(f324(x69873,x69874))+~P1(f324(x69872,x69874))+P1(f324(f324(f324(f104(f871(x69871,a859)),x69872),x69873),x69874)) % 181.55/181.54 [7111]P26(x71111,x71112,x71113)+~P26(x71111,x71112,x71114)+~P1(f324(f324(f238(f871(f864(x71111),a859)),x71113),x71114)) % 181.55/181.54 [7478]~P72(x74781)+E(f324(f324(f81(x74781),f324(x74782,x74783)),f324(f324(f6(a865,x74781),x74782),f324(f294(a865,f324(a115,x74783)),x74784))),f324(f324(f6(a865,x74781),x74782),f324(f294(a865,x74783),x74784)))+~P1(f324(f324(f239(a865),x74783),x74784)) % 181.55/181.54 [7507]~P105(x75071)+P1(f324(f324(f238(x75071),x75072),x75073))+~P1(f324(f324(f238(x75071),f324(f324(f190(x75071),x75074),x75072)),x75073)) % 181.55/181.54 [7509]~P105(x75091)+P1(f324(f324(f238(x75091),x75092),x75093))+~P1(f324(f324(f238(x75091),f324(f324(f190(x75091),x75092),x75094)),x75093)) % 181.55/181.54 [7511]~P100(x75111)+P1(f324(f324(f238(x75111),x75112),x75113))+~P1(f324(f324(f238(x75111),f324(f324(f113(x75111),x75114),x75112)),x75113)) % 181.55/181.54 [7513]~P100(x75131)+P1(f324(f324(f238(x75131),x75132),x75133))+~P1(f324(f324(f238(x75131),f324(f324(f113(x75131),x75132),x75134)),x75133)) % 181.55/181.54 [7514]~P105(x75141)+P1(f324(f324(f239(x75141),x75142),x75143))+~P1(f324(f324(f239(x75141),f324(f324(f190(x75141),x75144),x75142)),x75143)) % 181.55/181.54 [7515]~P105(x75151)+P1(f324(f324(f239(x75151),x75152),x75153))+~P1(f324(f324(f239(x75151),f324(f324(f190(x75151),x75152),x75154)),x75153)) % 181.55/181.54 [7591]~P1(f324(f324(f326(x75911),x75912),x75914))+P1(f324(f324(f326(x75911),x75912),x75913))+P1(f324(f324(f326(x75911),x75912),f324(f324(f22(f871(x75911,a859)),x75914),x75913))) % 181.55/181.54 [7672]P1(f324(x76721,x76722))+P1(f324(x76723,x76722))+~P1(f324(f324(f324(f113(f871(x76724,a859)),x76723),x76721),x76722)) % 181.55/181.54 [7682]~P1(f324(f324(f326(x76821),x76822),x76824))+~P1(f324(f324(f326(x76821),x76822),x76823))+P1(f324(f324(f326(x76821),x76822),f324(f324(f104(f871(x76821,a859)),x76823),x76824))) % 181.55/181.54 [7729]~P99(x77291)+~P1(f324(f61(x77291),x77294))+E(f324(f324(f64(x77291,x77291,f104(x77291)),x77292),f324(f324(f302(x77291),x77293),x77294)),f324(f324(f104(x77291),x77293),f324(f324(f64(x77291,x77291,f104(x77291)),x77292),x77294))) % 181.55/181.54 [7730]~P100(x77301)+~P1(f324(f61(x77301),x77304))+E(f324(f324(f64(x77301,x77301,f113(x77301)),x77302),f324(f324(f302(x77301),x77303),x77304)),f324(f324(f113(x77301),x77303),f324(f324(f64(x77301,x77301,f113(x77301)),x77302),x77304))) % 181.55/181.54 [7731]~P105(x77311)+~P1(f324(f61(x77311),x77314))+E(f324(f324(f64(x77311,x77311,f189(x77311)),x77312),f324(f324(f302(x77311),x77313),x77314)),f324(f324(f189(x77311),x77313),f324(f324(f64(x77311,x77311,f189(x77311)),x77312),x77314))) % 181.55/181.54 [7732]~P105(x77321)+~P1(f324(f61(x77321),x77324))+E(f324(f324(f64(x77321,x77321,f190(x77321)),x77322),f324(f324(f302(x77321),x77323),x77324)),f324(f324(f190(x77321),x77323),f324(f324(f64(x77321,x77321,f190(x77321)),x77322),x77324))) % 181.55/181.54 [7733]~P116(x77331)+~P90(x77331)+E(f324(f324(f22(x77331),f324(f324(f82(x77331),f324(f106(x77331),x77332)),x77333)),f324(f324(f82(x77331),f324(f106(x77331),x77332)),x77334)),f324(f324(f82(x77331),f324(f106(x77331),x77332)),f324(f324(f22(x77331),x77333),x77334))) % 181.55/181.54 [7734]~P137(x77341)+~P90(x77341)+E(f324(f324(f81(x77341),f324(f324(f82(x77341),f324(f106(x77341),x77342)),x77343)),f324(f324(f82(x77341),f324(f106(x77341),x77342)),x77344)),f324(f324(f82(x77341),f324(f106(x77341),x77342)),f324(f324(f81(x77341),x77343),x77344))) % 181.55/181.54 [7850]E(x78501,x78502)+P1(f324(f324(f326(x78503),x78501),f324(f167(x78503),x78504)))+~P1(f324(f324(f326(x78503),x78501),f324(f167(x78503),f324(f324(f145(x78503),x78502),x78504)))) % 181.55/181.54 [7877]~P61(x78771)+~E(f324(f192(f866(x78772)),x78773),f324(f192(f866(x78771)),f55(x78771)))+E(f324(f324(f173(x78771,x78772),f324(f324(f177(x78771,x78772),f55(x78771)),x78773)),x78774),f324(f233(x78772),f742(x78774,x78773,x78772,x78771))) % 181.55/181.54 [8023]P52(x80231,x80232,x80233)+~P52(x80231,x80232,x80234)+~P1(f324(f324(f238(f871(f870(x80231,x80232),a859)),x80233),x80234)) % 181.55/181.54 [8066]P1(f324(f324(f326(x80661),x80662),x80663))+P1(f324(f324(f326(x80661),x80662),x80664))+~P1(f324(f324(f326(x80661),x80662),f324(f324(f113(f871(x80661,a859)),x80664),x80663))) % 181.55/181.54 [8076]~P41(x80761,x80764,x80763)+~P1(f324(f324(f326(x80761),x80762),x80764))+P1(f324(f324(f326(f870(x80761,x80761)),f324(f324(f259(x80761,x80761),x80762),x80762)),x80763)) % 181.55/181.54 [8091]~P1(f324(f61(x80912),x80914))+~P1(f324(f61(x80911),x80913))+P1(f324(f61(f870(x80911,x80912)),f324(f324(f261(x80911,x80912),x80913),f324(f16(f871(x80912,a859),x80911),x80914)))) % 181.55/181.54 [8092]~P1(f324(f324(f326(x80921),x80922),x80924))+~P1(f324(f324(f238(f871(x80921,a859)),x80923),x80924))+P1(f324(f324(f238(f871(x80921,a859)),f324(f324(f302(x80921),x80922),x80923)),x80924)) % 181.55/181.54 [8100]~P68(x81002)+~P135(x81002)+E(f324(f324(f9(x81001,x81002),f324(f324(f8(a1,x81002,x81001),f105(x81002)),x81003)),x81004),f324(f105(x81002),f324(f324(f9(x81001,a1),x81003),x81004))) % 181.55/181.54 [8101]~P68(x81012)+~P141(x81012)+E(f324(f324(f9(x81011,x81012),f324(f324(f8(a865,x81012,x81011),f103(x81012)),x81013)),x81014),f324(f103(x81012),f324(f324(f9(x81011,a865),x81013),x81014))) % 181.55/181.54 [8127]E(f324(f324(f22(f871(x81271,a859)),x81272),f324(f324(f22(f871(x81271,a859)),x81273),x81274)),x81274)+~P1(f324(f324(f238(f871(x81271,a859)),x81272),x81273))+~P1(f324(f324(f238(f871(x81271,a859)),x81274),x81272)) % 181.55/181.54 [8223]~P1(f324(f61(x82231),x82234))+E(f324(f324(f22(a865),f324(f324(f6(x82231,a865),x82232),x82233)),f324(f324(f6(x82231,a865),x82232),x82234)),f324(f324(f6(x82231,a865),x82232),f324(f324(f22(f871(x82231,a859)),x82233),x82234)))+~P1(f324(f324(f238(f871(x82231,a859)),x82234),x82233)) % 181.55/181.54 [8378]~P9(x83781,x83784,x83783)+~P1(f324(f324(f326(x83781),x83782),x83784))+P1(f324(f324(f326(x83781),x83782),f324(f278(x83781,x83781,x83783),f324(f324(f302(x83781),x83782),f191(f871(x83781,a859)))))) % 181.55/181.54 [8434]~P1(f324(f324(f238(f871(x84341,a859)),x84342),x84343))+~P1(f324(f324(f238(f871(x84341,a859)),x84342),x84344))+P1(f324(f324(f238(f871(x84341,a859)),x84342),f324(f324(f104(f871(x84341,a859)),x84343),x84344))) % 181.55/181.54 [8536]E(x85361,f191(f871(x85362,a859)))+P1(f324(f61(x85363),x85364))+~P1(f324(f61(f870(x85363,x85362)),f324(f324(f261(x85363,x85362),x85364),f324(f16(f871(x85362,a859),x85363),x85361)))) % 181.55/181.54 [8537]E(x85371,f191(f871(x85372,a859)))+P1(f324(f61(x85373),x85374))+~P1(f324(f61(f870(x85372,x85373)),f324(f324(f261(x85372,x85373),x85371),f324(f16(f871(x85373,a859),x85372),x85374)))) % 181.55/181.54 [8611]P1(f324(f324(f326(x86111),x86112),f313(x86111,x86113)))+~P1(f324(f324(f326(x86111),x86114),f313(x86111,x86113)))+~P1(f324(f324(f326(f870(x86111,x86111)),f324(f324(f259(x86111,x86111),x86112),x86114)),x86113)) % 181.55/181.54 [8668]~P39(x86681,x86684)+P1(f324(f324(f326(f870(x86681,x86681)),f324(f324(f259(x86681,x86681),x86683),x86682)),f300(x86681,x86684)))+P39(x86681,f324(f324(f302(f870(x86681,x86681)),f324(f324(f259(x86681,x86681),x86682),x86683)),x86684)) % 181.55/181.54 [8669]~P55(x86691,x86694)+P1(f324(f324(f326(f870(x86691,x86691)),f324(f324(f259(x86691,x86691),x86693),x86692)),f300(x86691,x86694)))+P55(x86691,f324(f324(f302(f870(x86691,x86691)),f324(f324(f259(x86691,x86691),x86692),x86693)),x86694)) % 181.55/181.54 [8752]~E(x87522,x87523)+~P1(f324(f324(f326(x87521),x87522),f324(f167(x87521),x87524)))+P1(f324(f324(f326(f870(x87521,x87521)),f324(f324(f259(x87521,x87521),x87522),x87523)),f324(f167(f870(x87521,x87521)),f324(f324(f177(x87521,x87521),x87524),x87524)))) % 181.55/181.54 [8835]~E(x88353,x88354)+P1(f324(f324(f263(x88351,x88351,a859),a321),x88352))+~P1(f324(f324(f326(f870(x88351,x88351)),x88352),f324(f167(f870(x88351,x88351)),f324(f324(f177(x88351,x88351),x88353),x88354)))) % 181.55/181.54 [8884]P1(f324(f324(f326(f870(f866(x88841),f866(x88841))),f324(f324(f259(f866(x88841),f866(x88841)),x88842),x88843)),f141(x88841,x88844)))+~E(f324(f324(f170(x88841),f324(f192(f866(x88841)),x88842)),x88843),x88842)+~P1(f324(f324(f239(a865),f324(f192(f866(x88841)),x88842)),f324(f192(f866(x88841)),x88843))) % 181.55/181.54 [8977]~P1(f324(f61(x89771),x89774))+P1(f324(f324(f326(x89771),f830(x89772,x89773,x89774,x89771)),x89774))+P1(f324(f61(x89773),f324(f324(f41(x89771,f871(x89773,a859)),x89774),x89772))) % 181.55/181.54 [8978]~P1(f324(f61(x89781),x89784))+P1(f324(f324(f326(x89781),f548(x89782,x89783,x89784,x89781)),x89784))+P1(f324(f61(x89783),f324(f324(f41(x89781,f871(x89783,a859)),x89784),x89782))) % 181.55/181.54 [9065]P1(f324(f324(f326(f870(x90651,x90651)),x90652),f324(f324(f281(x90651,x90651,x90651),x90653),f300(x90651,x90653))))+~P1(f324(f324(f239(a865),f2(a865)),x90654))+~P1(f324(f324(f326(f870(x90651,x90651)),x90652),f324(f324(f184(f870(x90651,x90651),a859),x90654),x90653))) % 181.55/181.54 [9073]~P39(x90731,x90732)+~P1(f324(f324(f326(f870(x90731,x90731)),f324(f324(f259(x90731,x90731),x90734),x90733)),x90732))+~P1(f324(f324(f326(f870(x90731,x90731)),f324(f324(f259(x90731,x90731),x90733),x90734)),x90732)) % 181.55/181.54 [9198]~P1(f324(f61(x91981),x91984))+E(f324(f324(f6(x91981,a865),f324(f324(f8(f871(x91982,a859),a865,x91981),f37(x91982)),x91983)),x91984),f324(f37(f870(x91981,x91982)),f324(f324(f261(x91981,x91982),x91984),x91983)))+P1(f324(f324(f326(x91981),f491(x91983,x91982,x91984,x91981)),x91984)) % 181.55/181.54 [9202]~P1(f324(f131(x92021),x92022))+P1(f324(f131(x92021),f324(f324(f153(x92021,x92022),x92023),x92024)))+P1(f324(f324(f326(x92021),x92024),f324(f324(f22(f871(x92021,a859)),f324(f167(x92021),x92022)),f324(f324(f302(x92021),f324(f324(f159(x92021),x92022),x92023)),f191(f871(x92021,a859)))))) % 181.55/181.54 [9218]~P1(f324(f61(x92182),x92183))+~P1(f324(f61(x92181),f324(x92184,f830(x92184,x92181,x92183,x92182))))+P1(f324(f61(x92181),f324(f324(f41(x92182,f871(x92181,a859)),x92183),x92184))) % 181.55/181.54 [9219]~P1(f324(f61(x92192),x92193))+~P1(f324(f61(x92191),f324(x92194,f548(x92194,x92191,x92193,x92192))))+P1(f324(f61(x92191),f324(f324(f41(x92192,f871(x92191,a859)),x92193),x92194))) % 181.55/181.54 [9297]~P1(f324(f324(f326(f870(x92971,x92971)),x92972),f324(f324(f281(x92971,x92971,x92971),x92974),f300(x92971,x92974))))+P1(f324(f324(f326(f870(x92971,x92971)),x92972),f324(f324(f281(x92971,x92971,x92971),x92973),f300(x92971,x92973))))+~P1(f324(f324(f238(f871(f870(x92971,x92971),a859)),x92974),x92973)) % 181.55/181.54 [9305]E(f324(f324(f170(x93051),f691(x93054,x93053,x93052,x93051)),x93053),f324(f324(f170(x93051),f691(x93054,x93053,x93052,x93051)),x93052))+~P1(f324(f324(f326(f870(f866(x93051),f866(x93051))),f324(f324(f259(f866(x93051),f866(x93051)),x93052),x93053)),f141(x93051,x93054)))+E(f324(f324(f170(x93051),f324(f192(f866(x93051)),x93052)),x93053),x93052) % 181.55/181.54 [9321]~P1(f324(f61(x93211),x93214))+E(f324(f324(f6(x93211,a865),f324(f324(f8(f871(x93212,a859),a865,x93211),f37(x93212)),x93213)),x93214),f324(f37(f870(x93211,x93212)),f324(f324(f261(x93211,x93212),x93214),x93213)))+~P1(f324(f61(x93212),f324(x93213,f491(x93213,x93212,x93214,x93211)))) % 181.55/181.54 [9325]~E(f324(f192(f866(x93251)),x93253),f324(f192(f866(x93251)),x93252))+P1(f324(f324(f326(f870(f866(x93251),f866(x93251))),f324(f324(f259(f866(x93251),f866(x93251)),x93252),x93253)),f152(x93251,x93254)))+P1(f324(f324(f326(f870(x93251,x93251)),f671(x93254,x93253,x93252,x93251)),f324(f167(f870(x93251,x93251)),f324(f324(f177(x93251,x93251),x93252),x93253)))) % 181.55/181.54 [9405]~P1(f324(f324(f326(f870(f866(x94051),f866(x94051))),f324(f324(f259(f866(x94051),f866(x94051)),x94052),x94053)),f141(x94051,x94054)))+E(f324(f324(f170(x94051),f324(f192(f866(x94051)),x94052)),x94053),x94052)+P1(f324(f324(f239(a865),f691(x94054,x94053,x94052,x94051)),f324(f324(f189(a865),f324(f192(f866(x94051)),x94052)),f324(f192(f866(x94051)),x94053)))) % 181.55/181.54 [9406]E(f324(f173(x94061,x94062),x94063),f324(f173(x94061,x94062),x94064))+~E(f324(f167(x94061),f324(f324(f148(f870(x94061,x94062),x94061),f258(x94061,x94062)),x94063)),f324(f167(x94061),f324(f324(f148(f870(x94061,x94062),x94061),f258(x94061,x94062)),x94064)))+P1(f324(f324(f326(x94061),f757(x94063,x94064,x94062,x94061)),f324(f167(x94061),f324(f324(f148(f870(x94061,x94062),x94061),f258(x94061,x94062)),x94064)))) % 181.55/181.54 [9431]~P1(f324(f324(f326(f870(f866(x94311),f866(x94311))),f324(f324(f259(f866(x94311),f866(x94311)),x94312),x94313)),f141(x94311,x94314)))+P1(f324(f324(f239(a865),f324(f192(f866(x94311)),x94312)),f324(f192(f866(x94311)),x94313)))+P1(f324(f324(f239(a865),f691(x94314,x94313,x94312,x94311)),f324(f324(f189(a865),f324(f192(f866(x94311)),x94312)),f324(f192(f866(x94311)),x94313)))) % 181.55/181.54 [9736]~P1(f324(f324(f324(x97361,f659(x97361,x97364,x97363,x97362)),f660(x97361,x97364,x97363,x97362)),f662(x97361,x97364,x97363,x97362)))+P1(f324(f324(f324(x97361,x97362),x97363),x97364))+~P1(f324(f312(f870(f871(a1,f869(f866(a320))),f870(a1,a1)),a310),f324(f324(f259(f871(a1,f869(f866(a320))),f870(a1,a1)),x97362),f324(f324(f259(a1,a1),x97363),x97364)))) % 181.55/181.54 [9813]P1(f324(f324(f324(x98131,x98132),x98133),x98134))+P1(f324(f312(f870(f871(a1,f869(f866(a320))),f870(a1,a1)),a310),f324(f324(f259(f871(a1,f869(f866(a320))),f870(a1,a1)),f659(x98131,x98134,x98133,x98132)),f324(f324(f259(a1,a1),f660(x98131,x98134,x98133,x98132)),f662(x98131,x98134,x98133,x98132)))))+~P1(f324(f312(f870(f871(a1,f869(f866(a320))),f870(a1,a1)),a310),f324(f324(f259(f871(a1,f869(f866(a320))),f870(a1,a1)),x98132),f324(f324(f259(a1,a1),x98133),x98134)))) % 181.55/181.54 [9851]~P1(f324(f324(f326(f870(f866(x98511),f866(x98511))),f324(f324(f259(f866(x98511),f866(x98511)),x98512),x98513)),f141(x98511,x98514)))+E(f324(f324(f170(x98511),f324(f192(f866(x98511)),x98512)),x98513),x98512)+P1(f324(f324(f326(f870(x98511,x98511)),f324(f324(f259(x98511,x98511),f324(f324(f159(x98511),x98512),f691(x98514,x98513,x98512,x98511))),f324(f324(f159(x98511),x98513),f691(x98514,x98513,x98512,x98511)))),x98514)) % 181.55/181.54 [9852]~P1(f324(f324(f326(f870(f866(x98521),f866(x98521))),f324(f324(f259(f866(x98521),f866(x98521)),x98522),x98523)),f141(x98521,x98524)))+P1(f324(f324(f239(a865),f324(f192(f866(x98521)),x98522)),f324(f192(f866(x98521)),x98523)))+P1(f324(f324(f326(f870(x98521,x98521)),f324(f324(f259(x98521,x98521),f324(f324(f159(x98521),x98522),f691(x98524,x98523,x98522,x98521))),f324(f324(f159(x98521),x98523),f691(x98524,x98523,x98522,x98521)))),x98524)) % 181.55/181.54 [9910]~E(f324(f192(f866(x99101)),x99102),f324(f192(f866(x99101)),x99103))+P1(f324(f324(f326(f870(f866(x99101),f866(x99101))),f324(f324(f259(f866(x99101),f866(x99101)),x99102),x99103)),f152(x99101,x99104)))+~P1(f324(f324(f326(f870(x99101,x99101)),f324(f324(f259(x99101,x99101),f324(f324(f159(x99101),x99102),f687(x99104,x99103,x99102,x99101))),f324(f324(f159(x99101),x99103),f687(x99104,x99103,x99102,x99101)))),x99104)) % 181.55/181.54 [10043]~P72(x100431)+~P1(f324(f61(x100432),x100434))+E(f324(f160(x100431),f324(f324(f148(x100432,x100431),x100433),f91(f866(x100432),f324(f324(f18(f866(x100432),a859,a859),f324(f324(f8(a859,f871(a859,a859),f866(x100432)),a322),f324(f324(f7(f866(x100432),f871(x100432,a859),a859),f324(f324(f8(f871(x100432,a859),f871(f871(x100432,a859),a859),f866(x100432)),a321),f167(x100432))),x100434))),f131(x100432))))),f231(x100432,x100431,x100433,x100434)) % 181.55/181.54 [7320]~P62(x73202)+E(x73201,f2(x73202))+E(f324(f324(f282(x73202),f324(f324(f81(x73202),x73203),f324(f324(f82(x73202),x73204),x73201))),x73201),f324(f324(f81(x73202),x73204),f324(f324(f282(x73202),x73203),x73201))) % 181.55/181.54 [7321]~P59(x73212)+E(x73211,f2(x73212))+E(f324(f324(f38(x73212),f324(f324(f81(x73212),x73213),f324(f324(f82(x73212),x73214),x73211))),x73211),f324(f324(f81(x73212),x73214),f324(f324(f38(x73212),x73213),x73211))) % 181.55/181.54 [7322]~P59(x73222)+E(x73221,f2(x73222))+E(f324(f324(f38(x73222),f324(f324(f81(x73222),x73223),f324(f324(f82(x73222),x73221),x73224))),x73221),f324(f324(f81(x73222),x73224),f324(f324(f38(x73222),x73223),x73221))) % 181.55/181.54 [7554]~P63(x75542)+E(x75541,f2(x75542))+E(f324(f324(f282(x75542),f324(f324(f22(x75542),x75543),f324(f324(f82(x75542),x75541),x75544))),x75541),f324(f324(f22(x75542),f324(f324(f282(x75542),x75543),x75541)),x75544)) % 181.55/181.54 [7555]~P62(x75552)+E(x75551,f2(x75552))+E(f324(f324(f282(x75552),f324(f324(f81(x75552),x75553),f324(f324(f82(x75552),x75554),x75551))),x75551),f324(f324(f81(x75552),f324(f324(f282(x75552),x75553),x75551)),x75554)) % 181.55/181.54 [7556]~P63(x75562)+E(x75561,f2(x75562))+E(f324(f324(f282(x75562),f324(f324(f81(x75562),x75563),f324(f324(f82(x75562),x75561),x75564))),x75561),f324(f324(f81(x75562),f324(f324(f282(x75562),x75563),x75561)),x75564)) % 181.55/181.54 [8254]~P1(f324(f154(x82541,x82543),x82544))+~P1(f324(f154(x82541,x82542),x82544))+P1(f324(f154(x82541,f324(f324(f104(f871(x82541,a859)),x82542),x82543)),x82544)) % 181.55/181.54 [8626]~E(f324(f324(f281(x86261,x86261,x86261),x86262),x86264),f191(f871(f870(x86261,x86261),a859)))+~E(f324(f324(f281(x86261,x86261,x86261),x86262),x86263),f191(f871(f870(x86261,x86261),a859)))+E(f324(f324(f281(x86261,x86261,x86261),x86262),f324(f324(f113(f871(f870(x86261,x86261),a859)),x86263),x86264)),f191(f871(f870(x86261,x86261),a859))) % 181.55/181.54 [8753]~P1(f324(f324(f238(f871(x87531,a859)),x87533),x87534))+~P1(f324(f324(f238(f871(x87531,a859)),x87532),x87534))+P1(f324(f324(f238(f871(x87531,a859)),f324(f324(f113(f871(x87531,a859)),x87532),x87533)),x87534)) % 181.55/181.54 [9130]~P1(f324(f61(x91301),x91304))+~P1(f324(f61(x91301),x91303))+E(f324(f324(f22(a865),f324(f324(f81(a865),f324(f324(f6(x91301,a865),x91302),x91303)),f324(f324(f6(x91301,a865),x91302),x91304))),f324(f324(f6(x91301,a865),x91302),f324(f324(f104(f871(x91301,a859)),x91303),x91304))),f324(f324(f6(x91301,a865),x91302),f324(f324(f113(f871(x91301,a859)),x91303),x91304))) % 181.55/181.54 [9215]~P1(f324(f324(f326(x92151),x92153),x92152))+~P1(f324(f324(f238(f871(x92151,a859)),x92152),f324(f324(f302(x92151),x92153),x92154)))+P1(f324(f324(f238(f871(x92151,a859)),f324(f324(f22(f871(x92151,a859)),x92152),f324(f324(f302(x92151),x92153),f191(f871(x92151,a859))))),x92154)) % 181.55/181.54 [9378]~P1(f324(f324(f326(x93781),x93783),x93782))+P1(f324(f324(f238(f871(x93781,a859)),x93782),f324(f324(f302(x93781),x93783),x93784)))+~P1(f324(f324(f238(f871(x93781,a859)),f324(f324(f22(f871(x93781,a859)),x93782),f324(f324(f302(x93781),x93783),f191(f871(x93781,a859))))),x93784)) % 181.55/181.54 [9470]~P1(f324(f324(f238(a865),x94701),x94703))+~P1(f324(f324(f239(a865),x94702),x94704))+P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),f324(f324(f259(a865,a865),x94701),x94702)),f324(f324(f259(a865,a865),x94703),x94704))),a35)) % 181.55/181.54 [9471]~P1(f324(f324(f238(a865),x94712),x94714))+~P1(f324(f324(f238(a865),x94711),x94713))+P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),f324(f324(f259(a865,a865),x94711),x94712)),f324(f324(f259(a865,a865),x94713),x94714))),a70)) % 181.55/181.54 [9775]~P1(f324(f324(f326(f866(x97751)),x97754),f155(x97751,x97753)))+~P1(f324(f324(f326(f866(x97751)),x97754),f155(x97751,x97752)))+P1(f324(f154(x97751,f324(f324(f104(f871(x97751,a859)),f324(f324(f7(x97751,f871(x97751,a859),a859),f326(x97751)),x97752)),f324(f324(f7(x97751,f871(x97751,a859),a859),f326(x97751)),x97753))),x97754)) % 181.55/181.54 [9875]~P27(x98751,f871(f871(x98751,a859),a859),f324(f324(f7(x98751,f871(f870(x98751,x98751),a859),f871(f871(x98751,a859),a859)),f324(f324(f8(f871(x98751,a859),f871(f871(f870(x98751,x98751),a859),f871(f871(x98751,a859),a859)),x98751),f60(x98751)),f324(f324(f7(x98751,f871(x98751,a859),f871(x98751,a859)),f302(x98751)),f191(f871(x98751,a859))))),x98753),x98752)+~P1(f324(f324(f326(x98751),x98754),x98752))+E(f324(f324(f22(f871(f871(x98751,a859),a859)),f324(f324(f60(x98751),x98752),x98753)),f324(f324(f60(x98751),f324(f324(f302(x98751),x98754),f191(f871(x98751,a859)))),x98753)),f324(f324(f60(x98751),f324(f324(f22(f871(x98751,a859)),x98752),f324(f324(f302(x98751),x98754),f191(f871(x98751,a859))))),x98753)) % 181.55/181.54 [10008]~P41(x100081,x100082,x100084)+~P1(f324(f324(f326(f870(x100081,x100081)),x100083),x100084))+P1(f324(f324(f263(x100081,x100081,a859),f324(f324(f7(x100081,f871(x100081,a859),f871(x100081,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x100081,a859),f871(x100081,a859)),x100081),f8(a859,a859,x100081)),f324(f324(f8(a859,f871(a859,a859),x100081),a322),f324(f324(f7(x100081,f871(x100081,a859),a859),f326(x100081)),x100082)))),f324(f324(f7(x100081,f871(x100081,a859),a859),f326(x100081)),x100082))),x100083)) % 181.55/181.54 [10020]P1(f324(f61(x100201),x100202))+~P1(f324(f61(x100203),f324(f303(x100201,x100203,x100204),x100202)))+~P1(f324(f61(x100201),f324(f244(x100201),f324(f324(f18(x100201,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100201),a322),f324(f324(f7(x100201,f871(x100201,a859),a859),f326(x100201)),x100202))),f324(f324(f7(x100201,x100203,a859),f324(f324(f8(x100203,f871(x100203,a859),x100201),a321),x100204)),f324(x100204,f347(x100204,x100203,x100202,x100201))))))) % 181.55/181.54 [8005]~P63(x80052)+E(x80051,f2(x80052))+E(f324(f324(f282(x80052),f324(f324(f22(x80052),f324(f324(f82(x80052),x80051),x80053)),x80054)),x80051),f324(f324(f22(x80052),x80053),f324(f324(f282(x80052),x80054),x80051))) % 181.55/181.54 [8006]~P63(x80062)+E(x80061,f2(x80062))+E(f324(f324(f282(x80062),f324(f324(f81(x80062),f324(f324(f82(x80062),x80061),x80063)),x80064)),x80061),f324(f324(f81(x80062),x80063),f324(f324(f282(x80062),x80064),x80061))) % 181.55/181.54 [8912]~E(f324(f324(f281(x89121,x89121,x89121),x89123),x89124),f191(f871(f870(x89121,x89121),a859)))+~E(f324(f324(f281(x89121,x89121,x89121),x89122),x89124),f191(f871(f870(x89121,x89121),a859)))+E(f324(f324(f281(x89121,x89121,x89121),f324(f324(f113(f871(f870(x89121,x89121),a859)),x89122),x89123)),x89124),f191(f871(f870(x89121,x89121),a859))) % 181.55/181.54 [9952]~P142(x99521)+~P142(x99522)+E(f324(f324(f309(x99521),f324(f324(f7(x99521,a102,f869(f866(a320))),f324(f324(f8(f871(x99522,f869(f866(a320))),f871(a102,f869(f866(a320))),x99521),f309(x99522)),f324(f324(f8(f871(x99522,f870(x99521,x99522)),f871(x99522,f869(f866(a320))),x99521),f324(f8(f870(x99521,x99522),f869(f866(a320)),x99522),x99523)),f259(x99521,x99522)))),x99524)),x99524),f324(f324(f309(f870(x99521,x99522)),x99523),x99524)) % 181.55/181.54 [9684]~P1(f324(f154(x96841,x96843),x96844))+~P1(f324(f154(x96841,x96842),x96844))+P1(f324(f154(x96841,f324(f324(f18(x96841,a859,a859),f324(f324(f8(a859,f871(a859,a859),x96841),a322),x96842)),x96843)),x96844)) % 181.55/181.54 [9944]P1(f324(x99441,f837(x99442,x99443,x99441,x99444)))+~P1(f324(f61(x99444),f324(f244(x99444),x99441)))+P1(f324(f61(x99443),f324(f244(x99443),f324(f324(f8(f871(x99444,a859),a859,x99443),f88(x99444)),f324(f324(f8(f871(x99444,a859),f871(x99444,a859),x99443),f324(f18(x99444,a859,a859),f324(f324(f8(a859,f871(a859,a859),x99444),a322),x99441))),x99442))))) % 181.55/181.54 [9965]~P1(f324(f61(x99652),f324(f244(x99652),x99653)))+~P1(f324(f61(x99651),f324(f244(x99651),f324(f324(f7(x99651,x99652,a859),x99654),f837(x99654,x99651,x99653,x99652)))))+P1(f324(f61(x99651),f324(f244(x99651),f324(f324(f8(f871(x99652,a859),a859,x99651),f88(x99652)),f324(f324(f8(f871(x99652,a859),f871(x99652,a859),x99651),f324(f18(x99652,a859,a859),f324(f324(f8(a859,f871(a859,a859),x99652),a322),x99653))),x99654))))) % 181.55/181.54 [6470]E(x64701,x64702)+~E(f324(x64703,x64701),f324(x64703,x64702))+~P27(x64704,x64705,x64703,f247(f871(x64704,a859))) % 181.55/181.54 [6629]~E(f324(x66293,x66295),f203(x66292))+~E(f324(x66294,x66295),f203(x66292))+E(f324(f180(x66291,x66292,x66293,x66294),x66295),f203(x66292)) % 181.55/181.54 [7355]E(x73551,x73552)+~P27(x73553,x73554,x73555,f247(f871(x73553,a859)))+~E(f324(f303(x73553,x73554,x73555),x73551),f324(f303(x73553,x73554,x73555),x73552)) % 181.55/181.54 [7608]P27(x76082,x76083,f449(x76084,x76083,x76082,x76081),x76081)+~E(f324(f303(x76083,x76082,x76085),x76084),x76081)+E(x76081,f191(f871(x76082,a859))) % 181.55/181.54 [8138]~P1(f324(f324(x81383,x81382),x81385))+~P1(f324(f324(x81383,x81384),x81382))+P1(f324(f324(f326(x81381),x81382),f288(x81381,x81383,x81384,x81385))) % 181.55/181.54 [8139]~P1(f324(f324(x81393,x81392),x81395))+~P1(f324(f324(x81393,x81394),x81392))+P1(f324(f324(f326(x81391),x81392),f291(x81391,x81393,x81394,x81395))) % 181.55/181.54 [8442]~P27(x84421,x84422,x84423,x84424)+P28(x84421,x84422,x84423,x84424,x84425)+~E(f324(f303(x84421,x84422,x84423),x84424),x84425) % 181.55/181.54 [8575]~P28(x85751,x85753,x85754,x85752,x85755)+~P1(f324(f61(x85753),x85755))+P1(f324(f61(x85751),x85752)) % 181.55/181.54 [8576]~P28(x85763,x85761,x85764,x85765,x85762)+~P1(f324(f61(x85763),x85765))+P1(f324(f61(x85761),x85762)) % 181.55/181.54 [8709]~P27(x87091,x87093,x87095,f247(f871(x87091,a859)))+~P27(x87093,x87092,x87094,f247(f871(x87093,a859)))+P27(x87091,x87092,f324(f73(x87093,x87092,x87091,x87094),x87095),f247(f871(x87091,a859))) % 181.55/181.54 [9273]P1(f324(f324(f326(f870(x92731,x92731)),f324(f324(f259(x92731,x92731),x92732),x92733)),f300(x92731,x92734)))+~P1(f324(f324(f326(f870(x92731,x92731)),f324(f324(f259(x92731,x92731),x92732),x92735)),f300(x92731,x92734)))+~P1(f324(f324(f326(f870(x92731,x92731)),f324(f324(f259(x92731,x92731),x92735),x92733)),f300(x92731,x92734))) % 181.55/181.54 [9312]~P105(x93122)+~P1(f324(f131(x93121),x93125))+P1(f324(f131(x93121),f143(x93121,x93122,x93123,x93124,x93125))) % 181.55/181.54 [5322]~E(x53222,f116(x53221))+E(f324(f324(f124(x53221),x53222),x53223),f324(f324(f145(x53221),x53224),x53225))+~E(x53223,f324(f324(f145(x53221),x53224),x53225)) % 181.55/181.54 [5323]~E(x53232,f116(x53231))+E(f324(f324(f124(x53231),x53232),x53233),f324(f324(f145(x53231),x53234),x53235))+~E(f324(f324(f145(x53231),x53234),x53235),x53233) % 181.55/181.54 [6427]~E(f324(f192(f866(x64271)),x64275),f324(f192(f866(x64272)),x64274))+E(f324(f324(f148(f870(x64271,x64272),x64272),f262(x64271,x64272)),x64273),x64274)+~E(f324(f324(f177(x64271,x64272),x64275),x64274),x64273) % 181.55/181.54 [6428]~E(f324(f192(f866(x64281)),x64284),f324(f192(f866(x64282)),x64285))+E(f324(f324(f148(f870(x64281,x64282),x64281),f258(x64281,x64282)),x64283),x64284)+~E(f324(f324(f177(x64281,x64282),x64284),x64285),x64283) % 181.55/181.54 [6899]~P105(x68991)+~P16(x68991,f324(f324(f148(x68992,x68991),x68993),x68995))+P16(x68991,f324(f324(f148(x68992,x68991),x68993),f324(f130(x68992,x68994),x68995))) % 181.55/181.54 [6943]~P1(f324(x69433,x69435))+~P1(f324(f324(x69432,x69434),x69435))+P1(f324(f324(f95(x69431,x69432,x69433),x69434),x69435)) % 181.55/181.54 [7040]~P105(x70401)+P16(x70401,f324(f324(f148(x70402,x70401),x70403),f164(x70402,x70404,x70405)))+~P16(x70401,f324(f324(f148(x70402,x70401),x70403),x70405)) % 181.55/181.54 [7063]~P52(x70633,x70632,x70635)+~P52(x70631,x70633,x70634)+P52(x70631,x70632,f324(f324(f281(x70631,x70633,x70632),x70634),x70635)) % 181.55/181.54 [7154]E(x71541,x71542)+~P27(x71543,x71544,x71545,f247(f871(x71543,a859)))+~E(f324(f324(f148(x71543,x71544),x71545),x71541),f324(f324(f148(x71543,x71544),x71545),x71542)) % 181.55/181.54 [7306]~P1(f324(f324(f238(a865),x73061),f324(x73063,x73065)))+P1(f324(f324(f238(a865),x73061),f149(x73062,x73063,x73064)))+~P1(f324(f324(f326(x73062),x73065),f324(f167(x73062),x73064))) % 181.55/181.54 [7307]~P1(f324(f324(f239(a865),x73071),f324(x73073,x73075)))+P1(f324(f324(f239(a865),x73071),f149(x73072,x73073,x73074)))+~P1(f324(f324(f326(x73072),x73075),f324(f167(x73072),x73074))) % 181.55/181.54 [7706]~P106(x77061)+P1(f324(f324(f238(f871(x77061,a859)),f295(x77061,x77062,x77063)),f295(x77061,x77064,x77065)))+P1(f324(f324(f238(x77061),x77062),x77063)) % 181.55/181.54 [7727]~P6(x77271)+P1(f324(f324(f238(x77271),f324(f324(f42(x77272,x77271),x77273),x77274)),f324(x77274,x77275)))+~P1(f324(f324(f326(x77272),x77275),x77273)) % 181.55/181.54 [7794]~P27(x77941,x77942,x77944,x77943)+E(f324(f78(x77941,x77942,x77943,x77944),f324(x77944,x77945)),x77945)+~P1(f324(f324(f326(x77941),x77945),x77943)) % 181.55/181.54 [7795]~P27(x77951,x77952,x77954,x77953)+E(f324(f94(x77951,x77952,x77953,x77954),f324(x77954,x77955)),x77955)+~P1(f324(f324(f326(x77951),x77955),x77953)) % 181.55/181.54 [7994]~P1(f324(x79941,x79945))+P1(f324(x79941,f814(x79941,x79942,x79943,x79944)))+~P1(f324(f324(f326(x79944),x79945),x79943)) % 181.55/181.54 [7995]~P1(f324(x79951,x79955))+P1(f324(x79951,f814(x79951,x79952,x79953,x79954)))+~P1(f324(f324(f326(x79954),x79955),x79952)) % 181.55/181.54 [8089]P1(f324(f61(x80891),x80892))+~P1(f324(f61(x80893),x80894))+~P1(f324(f324(f238(f871(x80891,a859)),x80892),f324(f303(x80893,x80891,x80895),x80894))) % 181.55/181.54 [8258]E(x82581,x82582)+~P27(x82583,x82584,x82585,f324(f324(f113(f871(x82583,a859)),f324(f167(x82583),x82581)),f324(f167(x82583),x82582)))+~E(f324(f324(f148(x82583,x82584),x82585),x82581),f324(f324(f148(x82583,x82584),x82585),x82582)) % 181.55/181.54 [8316]~P106(x83161)+~P1(f324(f324(f239(f871(x83161,a859)),f295(x83161,x83164,x83165)),f295(x83161,x83162,x83163)))+P1(f324(f324(f238(x83161),x83162),x83163)) % 181.55/181.54 [8377]~P27(x83771,x83774,x83775,f247(f871(x83771,a859)))+~P1(f324(f324(f326(x83774),f324(x83775,x83772)),f324(f303(x83771,x83774,x83775),x83773)))+P1(f324(f324(f326(x83771),x83772),x83773)) % 181.55/181.54 [8448]P1(f324(x84481,x84482))+~P1(f324(x84481,f820(x84481,x84483,x84484,x84485)))+~P1(f324(f324(f326(x84485),x84482),x84484)) % 181.55/181.54 [8449]P1(f324(x84491,x84492))+~P1(f324(x84491,f820(x84491,x84493,x84494,x84495)))+~P1(f324(f324(f326(x84495),x84492),x84493)) % 181.55/181.54 [8750]~P27(x87502,x87503,x87501,x87504)+E(f324(x87501,f324(f78(x87502,x87503,x87504,x87501),x87505)),x87505)+~P1(f324(f324(f326(x87503),x87505),f324(f303(x87502,x87503,x87501),x87504))) % 181.55/181.54 [8857]E(x88571,f116(x88572))+E(f324(f324(f145(x88572),x88573),f693(x88574,x88573,x88575,x88571,x88572)),x88571)+~E(f324(f324(f124(x88572),x88571),x88575),f324(f324(f145(x88572),x88573),x88574)) % 181.55/181.54 [8858]E(x88581,f116(x88582))+E(f324(f324(f145(x88582),x88583),f694(x88584,x88581,x88585,x88583,x88582)),x88581)+~E(f324(f324(f124(x88582),x88581),x88584),f324(f324(f145(x88582),x88583),x88585)) % 181.55/181.54 [8873]E(f324(f324(f145(x88732),x88733),f693(x88734,x88733,x88731,x88735,x88732)),x88735)+~E(f324(f324(f124(x88732),x88735),x88731),f324(f324(f145(x88732),x88733),x88734))+E(x88731,f324(f324(f145(x88732),x88733),x88734)) % 181.55/181.54 [8874]E(f324(f324(f145(x88741),x88742),f694(x88744,x88745,x88743,x88742,x88741)),x88745)+~E(f324(f324(f124(x88741),x88745),x88744),f324(f324(f145(x88741),x88742),x88743))+E(f324(f324(f145(x88741),x88742),x88743),x88744) % 181.55/181.54 [8948]~E(f324(f303(x89483,x89482,x89484),f247(f871(x89483,a859))),f247(f871(x89482,a859)))+~E(f324(f303(x89481,x89483,x89485),f247(f871(x89481,a859))),f247(f871(x89483,a859)))+E(f324(f303(x89481,x89482,f324(f73(x89483,x89482,x89481,x89484),x89485)),f247(f871(x89481,a859))),f247(f871(x89482,a859))) % 181.55/181.54 [9318]E(x93181,f116(x93182))+~E(f324(f324(f124(x93182),x93181),x93183),f324(f324(f145(x93182),x93185),x93184))+E(f324(f324(f124(x93182),f694(x93183,x93181,x93184,x93185,x93182)),x93183),x93184) % 181.55/181.54 [9319]E(x93191,f116(x93192))+~E(f324(f324(f124(x93192),x93191),x93195),f324(f324(f145(x93192),x93194),x93193))+E(f324(f324(f124(x93192),f693(x93193,x93194,x93195,x93191,x93192)),x93195),x93193) % 181.55/181.54 [9326]E(f324(f324(f124(x93262),f693(x93264,x93263,x93261,x93265,x93262)),x93261),x93264)+~E(f324(f324(f124(x93262),x93265),x93261),f324(f324(f145(x93262),x93263),x93264))+E(x93261,f324(f324(f145(x93262),x93263),x93264)) % 181.55/181.54 [9327]~E(f324(f324(f124(x93271),x93275),x93274),f324(f324(f145(x93271),x93272),x93273))+E(f324(f324(f124(x93271),f694(x93274,x93275,x93273,x93272,x93271)),x93274),x93273)+E(f324(f324(f145(x93271),x93272),x93273),x93274) % 181.55/181.54 [9328]E(f324(f324(f124(x93281),x93285),f696(x93283,x93282,x93284,x93285,x93281)),x93282)+E(f324(f324(f124(x93281),x93282),f695(x93283,x93282,x93284,x93285,x93281)),x93285)+~E(f324(f324(f124(x93281),x93285),x93284),f324(f324(f124(x93281),x93282),x93283)) % 181.55/181.54 [9360]~P105(x93601)+P16(x93601,f324(f324(f148(x93602,x93601),x93603),f143(x93602,x93601,x93603,x93604,x93605)))+~P16(x93601,f324(f324(f148(x93602,x93601),x93603),x93605)) % 181.55/181.54 [9375]~P56(x93755,x93751,x93754,x93753)+P1(f324(f324(x93751,x93752),f344(x93753,x93754,x93751,x93755,x93752)))+~P1(f324(f324(f326(x93755),x93752),x93754)) % 181.55/181.54 [9484]~P1(f324(f324(f326(f870(x94841,x94841)),f324(f324(f259(x94841,x94841),x94845),x94843)),f300(x94841,x94844)))+P1(f324(f324(f326(f870(x94841,x94841)),f324(f324(f259(x94841,x94841),x94842),x94843)),f324(f324(f281(x94841,x94841,x94841),x94844),f300(x94841,x94844))))+~P1(f324(f324(f326(f870(x94841,x94841)),f324(f324(f259(x94841,x94841),x94842),x94845)),f324(f324(f281(x94841,x94841,x94841),x94844),f300(x94841,x94844)))) % 181.55/181.54 [9485]~P1(f324(f324(f326(f870(x94851,x94851)),f324(f324(f259(x94851,x94851),x94852),x94855)),f300(x94851,x94854)))+P1(f324(f324(f326(f870(x94851,x94851)),f324(f324(f259(x94851,x94851),x94852),x94853)),f324(f324(f281(x94851,x94851,x94851),x94854),f300(x94851,x94854))))+~P1(f324(f324(f326(f870(x94851,x94851)),f324(f324(f259(x94851,x94851),x94855),x94853)),f324(f324(f281(x94851,x94851,x94851),x94854),f300(x94851,x94854)))) % 181.55/181.54 [9488]P1(f324(f324(f326(f870(f866(x94881),f866(x94881))),f324(f324(f259(f866(x94881),f866(x94881)),x94882),x94883)),f152(x94881,f300(x94881,x94884))))+~P1(f324(f324(f326(f870(f866(x94881),f866(x94881))),f324(f324(f259(f866(x94881),f866(x94881)),x94882),x94885)),f152(x94881,f300(x94881,x94884))))+~P1(f324(f324(f326(f870(f866(x94881),f866(x94881))),f324(f324(f259(f866(x94881),f866(x94881)),x94885),x94883)),f152(x94881,f300(x94881,x94884)))) % 181.55/181.54 [9492]E(f324(f324(f124(x94921),x94922),f695(x94923,x94922,x94924,x94925,x94921)),x94925)+E(f324(f324(f124(x94921),f696(x94923,x94922,x94924,x94925,x94921)),x94923),x94924)+~E(f324(f324(f124(x94921),x94922),x94923),f324(f324(f124(x94921),x94925),x94924)) % 181.55/181.54 [9493]E(f324(f324(f124(x94931),x94932),f696(x94933,x94934,x94935,x94932,x94931)),x94934)+E(f324(f324(f124(x94931),f695(x94933,x94934,x94935,x94932,x94931)),x94935),x94933)+~E(f324(f324(f124(x94931),x94932),x94935),f324(f324(f124(x94931),x94934),x94933)) % 181.55/181.54 [9550]P1(f324(f324(f326(f870(x95501,x95501)),f324(f324(f259(x95501,x95501),x95502),x95503)),f324(f324(f281(x95501,x95501,x95501),x95504),f300(x95501,x95504))))+~P1(f324(f324(f326(f870(x95501,x95501)),f324(f324(f259(x95501,x95501),x95502),x95505)),f324(f324(f281(x95501,x95501,x95501),x95504),f300(x95501,x95504))))+~P1(f324(f324(f326(f870(x95501,x95501)),f324(f324(f259(x95501,x95501),x95505),x95503)),f324(f324(f281(x95501,x95501,x95501),x95504),f300(x95501,x95504)))) % 181.55/181.54 [9578]P36(x95781,x95782,x95783,x95784,x95785)+~E(f324(f192(f866(x95781)),x95784),f324(f192(f866(x95782)),x95785))+~P1(f324(f324(f263(x95781,x95782,a859),x95783),f746(x95785,x95784,x95783,x95782,x95781))) % 181.55/181.54 [9579]P36(x95791,x95792,x95793,x95794,x95795)+~E(f324(f192(f866(x95791)),x95794),f324(f192(f866(x95792)),x95795))+~P1(f324(f324(f263(x95791,x95792,a859),x95793),f752(x95793,x95795,x95794,x95792,x95791))) % 181.55/181.54 [9584]E(f324(f324(f124(x95841),f695(x95842,x95843,x95844,x95845,x95841)),x95844),x95842)+~E(f324(f324(f124(x95841),x95843),x95842),f324(f324(f124(x95841),x95845),x95844))+E(f324(f324(f124(x95841),f696(x95842,x95843,x95844,x95845,x95841)),x95842),x95844) % 181.55/181.54 [9599]~P105(x95992)+E(f324(f324(f142(x95991,x95992,x95993),x95994),x95995),f324(f324(f145(x95991),x95994),x95995))+P1(f324(f324(f326(x95991),f771(x95994,x95993,x95995,x95991,x95992)),f324(f167(x95991),x95995))) % 181.55/181.54 [9604]~P56(x96041,x96044,x96043,x96042)+~P1(f324(f324(f326(x96041),x96045),x96043))+P1(f324(f324(f326(x96041),f344(x96042,x96043,x96044,x96041,x96045)),x96042)) % 181.55/181.54 [9727]~P1(f324(f324(f326(f870(f871(x97271,a859),f871(x97271,a859))),f324(f324(f259(f871(x97271,a859),f871(x97271,a859)),x97274),x97273)),f315(x97271,x97272)))+~P1(f324(f324(f326(x97271),x97275),x97274))+P1(f324(f324(f326(x97271),f577(x97272,x97273,x97274,x97271,x97275)),x97273)) % 181.55/181.54 [9738]~P105(x97382)+E(f324(f324(f142(x97381,x97382,x97383),x97384),x97385),f324(f324(f145(x97381),x97384),x97385))+~P1(f324(f324(f238(x97382),f324(x97383,x97384)),f324(x97383,f771(x97384,x97383,x97385,x97381,x97382)))) % 181.55/181.54 [9784]~P27(x97843,x97844,x97845,f247(f871(x97843,a859)))+P1(f324(x97841,x97842))+~P1(f324(x97841,f324(f94(x97843,x97844,f247(f871(x97843,a859)),x97845),f539(x97842,x97841,x97845,x97844,x97843)))) % 181.55/181.54 [9927]P36(x99271,x99272,x99273,x99274,x99275)+~E(f324(f192(f866(x99271)),x99274),f324(f192(f866(x99272)),x99275))+~P1(f324(f324(x99273,f324(f324(f159(x99271),x99274),f753(x99275,x99274,x99273,x99272,x99271))),f324(f324(f159(x99272),x99275),f753(x99275,x99274,x99273,x99272,x99271)))) % 181.55/181.54 [9928]P36(x99281,x99282,x99283,x99284,x99285)+~E(f324(f192(f866(x99281)),x99284),f324(f192(f866(x99282)),x99285))+~P1(f324(f324(x99283,f324(f324(f159(x99281),x99284),f760(x99283,x99285,x99282,x99284,x99281))),f324(f324(f159(x99282),x99285),f760(x99283,x99285,x99282,x99284,x99281)))) % 181.55/181.54 [6499]~P19(x64992,x64995,x64991)+~P1(f324(f61(x64992),x64994))+E(f324(x64991,f324(f324(f302(x64992),x64993),x64994)),f324(f324(f64(x64992,x64992,x64995),x64993),x64994)) % 181.55/181.54 [6500]~E(x65003,x65004)+~E(x65002,x65005)+E(f324(f324(f302(x65001),x65002),f324(f324(f302(x65001),x65003),f191(f871(x65001,a859)))),f324(f324(f302(x65001),x65004),f324(f324(f302(x65001),x65005),f191(f871(x65001,a859))))) % 181.55/181.54 [6510]P1(f324(x65102,x65105))+E(f172(x65101,x65102,f324(f324(f124(x65101),x65103),x65104)),f172(x65101,x65102,x65103))+~P1(f324(f324(f326(x65101),x65105),f324(f167(x65101),x65103))) % 181.55/181.54 [6547]E(f324(x65471,x65472),f191(f871(x65473,a859)))+~E(f324(f324(f41(x65474,f871(x65473,a859)),x65475),x65471),f191(f871(x65473,a859)))+~P1(f324(f324(f326(x65474),x65472),x65475)) % 181.55/181.54 [6548]E(f324(x65481,x65482),f247(f871(x65483,a859)))+~E(f324(f324(f42(x65484,f871(x65483,a859)),x65485),x65481),f247(f871(x65483,a859)))+~P1(f324(f324(f326(x65484),x65482),x65485)) % 181.55/181.54 [7050]~E(x70502,x70504)+~P136(x70501)+E(f324(f324(f81(x70501),f324(f324(f82(x70501),x70502),x70503)),f324(f324(f82(x70501),x70504),x70505)),f324(f324(f81(x70501),f324(f324(f82(x70501),x70502),x70505)),f324(f324(f82(x70501),x70504),x70503))) % 181.55/181.54 [7110]~P6(x71101)+~P1(f324(f324(f326(x71104),x71103),x71105))+P1(f324(f324(f238(x71101),f324(x71102,x71103)),f324(f324(f41(x71104,x71101),x71105),x71102))) % 181.55/181.54 [7159]~P104(x71591)+P1(f324(f324(f238(x71591),f324(x71592,x71593)),f324(x71594,x71593)))+~P1(f324(f324(f238(f871(x71595,x71591)),x71592),x71594)) % 181.55/181.54 [7274]E(x72741,x72742)+E(x72743,x72741)+~E(f324(f324(f302(x72744),x72741),f324(f324(f302(x72744),x72745),f191(f871(x72744,a859)))),f324(f324(f302(x72744),x72742),f324(f324(f302(x72744),x72743),f191(f871(x72744,a859))))) % 181.55/181.54 [7275]E(x72751,x72752)+E(x72753,x72751)+~E(f324(f324(f302(x72754),x72753),f324(f324(f302(x72754),x72752),f191(f871(x72754,a859)))),f324(f324(f302(x72754),x72755),f324(f324(f302(x72754),x72751),f191(f871(x72754,a859))))) % 181.55/181.54 [7276]E(x72761,x72762)+E(x72761,x72763)+~E(f324(f324(f302(x72764),x72763),f324(f324(f302(x72764),x72762),f191(f871(x72764,a859)))),f324(f324(f302(x72764),x72765),f324(f324(f302(x72764),x72761),f191(f871(x72764,a859))))) % 181.55/181.54 [7277]E(x72771,x72772)+E(x72771,x72773)+~E(f324(f324(f302(x72774),x72771),f324(f324(f302(x72774),x72775),f191(f871(x72774,a859)))),f324(f324(f302(x72774),x72772),f324(f324(f302(x72774),x72773),f191(f871(x72774,a859))))) % 181.55/181.54 [7805]P27(x78051,x78052,x78053,x78054)+~P27(x78051,x78052,x78053,x78055)+~P1(f324(f324(f238(f871(x78051,a859)),x78054),x78055)) % 181.55/181.54 [7834]~E(f324(x78343,x78345),x78344)+~P27(x78341,x78342,x78343,f247(f871(x78341,a859)))+E(f324(f94(x78341,x78342,f247(f871(x78341,a859)),x78343),x78344),x78345) % 181.55/181.54 [7984]E(x79841,x79842)+~E(f324(f303(x79843,x79844,x79845),x79841),f324(f303(x79843,x79844,x79845),x79842))+~P27(x79843,x79844,x79845,f324(f324(f113(f871(x79843,a859)),x79841),x79842)) % 181.55/181.54 [8056]P1(f324(x80562,x80564))+E(f324(f324(f132(x80561),f324(f192(f866(x80561)),f172(x80561,x80562,x80563))),x80563),f324(f324(f145(x80561),x80564),x80565))+~E(f324(f324(f124(x80561),f172(x80561,x80562,x80563)),f324(f324(f145(x80561),x80564),x80565)),x80563) % 181.55/181.54 [8086]~P27(x80861,x80862,x80863,x80865)+~P27(x80861,x80862,x80863,x80864)+P27(x80861,x80862,x80863,f324(f324(f104(f871(x80861,a859)),x80864),x80865)) % 181.55/181.54 [8198]~P72(x81981)+E(f324(f324(f81(x81981),f324(x81982,x81983)),f324(f160(x81981),f324(f324(f148(x81984,x81981),x81982),f164(x81984,x81983,x81985)))),f324(f160(x81981),f324(f324(f148(x81984,x81981),x81982),x81985)))+~P1(f324(f324(f326(x81984),x81983),f324(f167(x81984),x81985))) % 181.55/181.54 [8289]~P105(x82891)+~P16(x82891,f324(f324(f148(x82892,x82891),x82893),x82895))+P16(x82891,f324(f324(f148(x82892,x82891),x82893),f324(f324(f142(x82892,x82891,x82893),x82894),x82895))) % 181.55/181.54 [8373]~P6(x83731)+P1(f324(f324(f238(x83731),f324(f324(f41(x83732,x83731),x83733),x83734)),f324(f324(f41(x83732,x83731),x83735),x83734)))+~P1(f324(f324(f238(f871(x83732,a859)),x83733),x83735)) % 181.55/181.54 [8374]~P6(x83741)+P1(f324(f324(f238(x83741),f324(f324(f42(x83742,x83741),x83743),x83744)),f324(f324(f42(x83742,x83741),x83745),x83744)))+~P1(f324(f324(f238(f871(x83742,a859)),x83745),x83743)) % 181.55/181.54 [8404]~P105(x84043)+P1(f324(f131(x84041),x84042))+~P1(f324(f131(x84041),f324(f324(f142(x84041,x84043,x84044),x84045),x84042))) % 181.55/181.54 [8548]~P105(x85481)+~P1(f324(f324(f326(x85482),x85483),f324(f167(x85482),x85484)))+~P1(f324(f131(x85482),f324(f324(f142(x85482,x85481,x85485),x85483),x85484))) % 181.55/181.54 [8638]~P105(x86381)+P16(x86381,f324(f324(f148(x86382,x86381),x86383),x86384))+~P16(x86381,f324(f324(f148(x86382,x86381),x86383),f324(f324(f142(x86382,x86381,x86383),x86385),x86384))) % 181.55/181.54 [8685]~P27(x86852,x86851,x86854,x86853)+E(f324(f303(x86851,x86852,f94(x86852,x86851,x86853,x86854)),f324(f303(x86852,x86851,x86854),x86855)),x86855)+~P1(f324(f324(f238(f871(x86852,a859)),x86855),x86853)) % 181.55/181.54 [8738]~P105(x87382)+E(f324(f324(f142(x87381,x87382,x87383),x87384),x87385),f143(x87381,x87382,x87383,x87384,x87385))+P1(f324(f324(f326(x87382),f324(x87383,x87384)),f324(f303(x87381,x87382,x87383),f324(f167(x87381),x87385)))) % 181.55/181.54 [8814]~P105(x88142)+E(f143(x88141,x88142,x88143,x88144,x88145),x88145)+~P1(f324(f324(f326(x88142),f324(x88143,x88144)),f324(f303(x88141,x88142,x88143),f324(f167(x88141),x88145)))) % 181.55/181.54 [8829]~P27(x88292,x88291,x88293,x88295)+P1(f324(f324(f239(f871(x88291,a859)),f324(f303(x88292,x88291,x88293),x88294)),f324(f303(x88292,x88291,x88293),x88295)))+~P1(f324(f324(f239(f871(x88292,a859)),x88294),x88295)) % 181.55/181.54 [8990]~P27(x89901,x89902,x89903,f247(f871(x89901,a859)))+~P1(f324(f324(f238(f871(x89902,a859)),x89904),f324(f303(x89901,x89902,x89903),x89905)))+P1(f324(f324(f238(f871(x89901,a859)),f324(f304(x89901,x89902,x89903),x89904)),x89905)) % 181.55/181.54 [9014]~E(f324(f303(x90143,x90141,x90144),f247(f871(x90143,a859))),f247(f871(x90141,a859)))+P1(f324(f324(f238(f871(x90141,a859)),x90142),f324(f303(x90143,x90141,x90144),x90145)))+~P1(f324(f324(f238(f871(x90143,a859)),f324(f304(x90143,x90141,x90144),x90142)),x90145)) % 181.55/181.54 [9039]~E(f324(f233(x90392),x90394),f324(f324(f173(x90391,x90392),x90395),x90393))+~P1(f324(f131(x90391),f324(f324(f148(f870(x90391,x90392),x90391),f258(x90391,x90392)),x90395)))+P1(f324(f324(f326(f870(x90391,x90392)),f324(f324(f259(x90391,x90392),x90393),x90394)),f324(f167(f870(x90391,x90392)),x90395))) % 181.55/181.54 [9121]~P27(x91211,x91214,x91215,f247(f871(x91211,a859)))+~P1(f324(f324(f238(f871(x91214,a859)),f324(f303(x91211,x91214,x91215),x91212)),f324(f303(x91211,x91214,x91215),x91213)))+P1(f324(f324(f238(f871(x91211,a859)),x91212),x91213)) % 181.55/181.54 [9185]E(f324(f233(x91851),x91852),f324(f324(f173(x91853,x91851),x91854),x91855))+~P1(f324(f131(x91853),f324(f324(f148(f870(x91853,x91851),x91853),f258(x91853,x91851)),x91854)))+~P1(f324(f324(f326(f870(x91853,x91851)),f324(f324(f259(x91853,x91851),x91855),x91852)),f324(f167(f870(x91853,x91851)),x91854))) % 181.55/181.54 [9187]E(f324(f324(f173(x91871,x91872),x91873),x91874),f324(f233(x91872),x91875))+~P1(f324(f131(x91871),f324(f324(f148(f870(x91871,x91872),x91871),f258(x91871,x91872)),x91873)))+~P1(f324(f324(f326(f870(x91871,x91872)),f324(f324(f259(x91871,x91872),x91874),x91875)),f324(f167(f870(x91871,x91872)),x91873))) % 181.55/181.54 [9240]~P78(x92401)+~E(f324(x92403,f722(x92403,x92404,x92405,x92402,x92401)),f2(x92401))+E(f324(f160(x92401),f324(f324(f148(x92402,x92401),x92403),f324(f130(x92402,x92404),x92405))),f324(f160(x92401),f324(f324(f148(x92402,x92401),x92403),x92405))) % 181.55/181.54 [9268]~P28(x92681,x92682,x92683,f247(f871(x92681,a859)),f247(f871(x92682,a859)))+~P1(f324(f324(f238(f871(x92682,a859)),x92684),f324(f303(x92681,x92682,x92683),x92685)))+P1(f324(f324(f238(f871(x92681,a859)),f324(f304(x92681,x92682,x92683),x92684)),x92685)) % 181.55/181.54 [9298]~P28(x92983,x92981,x92984,f247(f871(x92983,a859)),f247(f871(x92981,a859)))+P1(f324(f324(f238(f871(x92981,a859)),x92982),f324(f303(x92983,x92981,x92984),x92985)))+~P1(f324(f324(f238(f871(x92983,a859)),f324(f304(x92983,x92981,x92984),x92982)),x92985)) % 181.55/181.54 [9425]~P18(x94251,x94252,x94253)+~P1(f324(f61(x94251),x94255))+P1(f324(f66(x94251,x94252,x94253,x94254,x94255),f324(f324(f64(x94251,x94252,x94253),x94254),x94255))) % 181.55/181.54 [9505]~P28(x95052,x95051,x95054,f247(f871(x95052,a859)),f247(f871(x95051,a859)))+~P28(x95051,x95053,x95055,f247(f871(x95051,a859)),f247(f871(x95053,a859)))+E(f324(f73(x95051,x95052,x95053,f94(x95052,x95051,f247(f871(x95052,a859)),x95054)),f94(x95051,x95053,f247(f871(x95051,a859)),x95055)),f94(x95052,x95053,f247(f871(x95052,a859)),f324(f73(x95051,x95053,x95052,x95055),x95054))) % 181.55/181.54 [9506]P1(f324(x95061,f818(x95062,x95061,x95063,x95064,x95065)))+~P1(f324(f324(f238(f871(x95065,a859)),x95064),x95063))+P1(f324(f324(f238(f871(x95065,a859)),f324(f324(f104(f871(x95065,a859)),x95064),f324(f244(x95065),x95061))),f324(f324(f104(f871(x95065,a859)),x95063),f324(f244(x95065),x95062)))) % 181.55/181.54 [9521]~P78(x95211)+~P1(f324(x95214,f722(x95213,x95214,x95215,x95212,x95211)))+E(f324(f160(x95211),f324(f324(f148(x95212,x95211),x95213),f324(f130(x95212,x95214),x95215))),f324(f160(x95211),f324(f324(f148(x95212,x95211),x95213),x95215))) % 181.55/181.54 [9602]~P6(x96025)+P1(f324(f324(f326(x96021),f619(x96022,x96023,x96021,x96024,x96025)),x96023))+P1(f324(f324(f238(x96025),x96024),f324(f324(f42(x96021,x96025),x96023),x96022))) % 181.55/181.54 [9605]~P78(x96051)+E(f324(f160(x96051),f324(f324(f148(x96052,x96051),x96053),f324(f130(x96052,x96054),x96055))),f324(f160(x96051),f324(f324(f148(x96052,x96051),x96053),x96055)))+P1(f324(f324(f326(x96052),f722(x96053,x96054,x96055,x96052,x96051)),f324(f167(x96052),x96055))) % 181.55/181.54 [9615]~P1(f324(x96155,f818(x96155,x96153,x96154,x96152,x96151)))+~P1(f324(f324(f238(f871(x96151,a859)),x96152),x96154))+P1(f324(f324(f238(f871(x96151,a859)),f324(f324(f104(f871(x96151,a859)),x96152),f324(f244(x96151),x96153))),f324(f324(f104(f871(x96151,a859)),x96154),f324(f244(x96151),x96155)))) % 181.55/181.54 [9630]~P27(x96305,x96303,x96304,f247(f871(x96305,a859)))+P1(f324(x96301,x96302))+P1(f324(f324(f326(x96303),f539(x96302,x96301,x96304,x96303,x96305)),f324(f303(x96305,x96303,x96304),f247(f871(x96305,a859))))) % 181.55/181.54 [9652]P36(x96521,x96522,x96523,x96524,x96525)+~E(f324(f192(f866(x96522)),x96525),f324(f192(f866(x96521)),x96524))+P1(f324(f324(f239(a865),f753(x96525,x96524,x96523,x96522,x96521)),f324(f192(f866(x96521)),x96524))) % 181.55/181.54 [9653]P36(x96531,x96532,x96533,x96534,x96535)+~E(f324(f192(f866(x96532)),x96535),f324(f192(f866(x96531)),x96534))+P1(f324(f324(f239(a865),f760(x96533,x96535,x96532,x96534,x96531)),f324(f192(f866(x96531)),x96534))) % 181.55/181.54 [9686]P1(f324(f324(f326(x96861),f818(x96862,x96863,x96864,x96865,x96861)),x96865))+~P1(f324(f324(f238(f871(x96861,a859)),x96865),x96864))+P1(f324(f324(f238(f871(x96861,a859)),f324(f324(f104(f871(x96861,a859)),x96865),f324(f244(x96861),x96863))),f324(f324(f104(f871(x96861,a859)),x96864),f324(f244(x96861),x96862)))) % 181.55/181.54 [9739]~P6(x97391)+~P1(f324(f324(f238(x97391),x97392),f324(x97395,f619(x97395,x97394,x97393,x97392,x97391))))+P1(f324(f324(f238(x97391),x97392),f324(f324(f42(x97393,x97391),x97394),x97395))) % 181.55/181.54 [9773]~P68(x97731)+~P1(f324(f61(x97732),x97735))+E(f324(f324(f324(f65(x97731,x97732,f82(x97731)),f324(f324(f18(x97732,x97731,x97731),f324(f324(f8(x97731,f871(x97731,x97731),x97732),f82(x97731)),x97733)),x97734)),f79(x97731)),x97735),f324(f324(f82(x97731),f324(f324(f324(f65(x97731,x97732,f82(x97731)),x97733),f79(x97731)),x97735)),f324(f324(f324(f65(x97731,x97732,f82(x97731)),x97734),f79(x97731)),x97735))) % 181.55/181.54 [9834]~P1(f324(f324(f326(f870(f871(x98341,a859),f871(x98341,a859))),f324(f324(f259(f871(x98341,a859),f871(x98341,a859)),x98345),x98344)),f315(x98341,x98343)))+~P1(f324(f324(f326(x98341),x98342),x98345))+P1(f324(f324(f326(f870(x98341,x98341)),f324(f324(f259(x98341,x98341),x98342),f577(x98343,x98344,x98345,x98341,x98342))),x98343)) % 181.55/181.54 [9962]~P1(f324(f324(f326(f870(f866(x99621),f866(x99621))),f324(f324(f259(f866(x99621),f866(x99621)),f324(f324(f124(x99621),x99625),x99622)),f324(f324(f124(x99621),x99625),x99623))),f141(x99621,x99624)))+P1(f324(f324(f326(f870(f866(x99621),f866(x99621))),f324(f324(f259(f866(x99621),f866(x99621)),x99622),x99623)),f141(x99621,x99624)))+P1(f324(f324(f326(f870(x99621,x99621)),f324(f324(f259(x99621,x99621),f702(x99624,x99623,x99622,x99625,x99621)),f702(x99624,x99623,x99622,x99625,x99621))),x99624)) % 181.55/181.54 [7090]~E(f324(f192(f866(x70901)),x70903),f324(f192(f866(x70902)),x70904))+E(f324(f324(f173(x70901,x70902),f324(f324(f177(x70901,x70902),x70903),x70904)),x70905),f203(x70902))+P1(f324(f324(f326(x70901),x70905),f324(f167(x70901),x70903))) % 181.55/181.54 [7162]~E(x71623,x71625)+E(f324(f324(f159(x71621),f324(f324(f153(x71621,x71622),x71623),x71624)),x71625),x71624)+~P1(f324(f324(f239(a865),x71623),f324(f192(f866(x71621)),x71622))) % 181.55/181.54 [7271]~E(f324(f324(f124(x72711),x72712),x72714),f324(f324(f124(x72711),x72713),x72715))+E(f324(f324(f170(x72711),f324(f192(f866(x72711)),x72712)),x72713),x72712)+P1(f324(f324(f238(a865),f324(f192(f866(x72711)),x72713)),f324(f192(f866(x72711)),x72712))) % 181.55/181.54 [7764]~E(f324(f324(f124(x77641),x77642),x77644),f324(f324(f124(x77641),x77643),x77645))+E(f324(f324(f170(x77641),f324(f192(f866(x77641)),x77642)),x77643),x77642)+~P1(f324(f324(f238(a865),f324(f192(f866(x77641)),x77642)),f324(f192(f866(x77641)),x77643))) % 181.55/181.54 [7788]~P1(f324(f61(x77881),f324(x77884,x77885)))+~P1(f324(f324(f326(x77882),x77885),x77883))+P1(f324(f61(x77881),f324(f324(f42(x77882,f871(x77881,a859)),x77883),x77884))) % 181.55/181.54 [7844]~E(f324(f192(f866(x78441)),x78442),f324(f192(f866(x78443)),x78444))+~E(f324(f324(f173(x78441,x78443),f324(f324(f177(x78441,x78443),x78442),x78444)),x78445),f203(x78443))+~P1(f324(f324(f326(x78441),x78445),f324(f167(x78441),x78442))) % 181.55/181.54 [7968]~P41(x79681,x79683,x79685)+~P41(x79681,x79682,x79684)+P41(x79681,f324(f324(f104(f871(x79681,a859)),x79682),x79683),f324(f324(f104(f871(f870(x79681,x79681),a859)),x79684),x79685)) % 181.55/181.54 [7969]~P41(x79691,x79693,x79695)+~P41(x79691,x79692,x79694)+P41(x79691,f324(f324(f113(f871(x79691,a859)),x79692),x79693),f324(f324(f113(f871(f870(x79691,x79691),a859)),x79694),x79695)) % 181.55/181.54 [8328]E(f324(f324(f259(x83281,x83282),f324(f324(f159(x83281),x83283),x83284)),f324(f324(f159(x83282),x83285),x83284)),f324(f324(f159(f870(x83281,x83282)),f324(f324(f177(x83281,x83282),x83283),x83285)),x83284))+~P1(f324(f324(f239(a865),x83284),f324(f192(f866(x83281)),x83283)))+~P1(f324(f324(f239(a865),x83284),f324(f192(f866(x83282)),x83285))) % 181.55/181.54 [8476]~P41(x84761,x84763,x84764)+P1(f324(f324(f326(x84761),x84762),x84763))+~P1(f324(f324(f326(f870(x84761,x84761)),f324(f324(f259(x84761,x84761),x84765),x84762)),x84764)) % 181.55/181.54 [8477]~P41(x84771,x84773,x84774)+P1(f324(f324(f326(x84771),x84772),x84773))+~P1(f324(f324(f326(f870(x84771,x84771)),f324(f324(f259(x84771,x84771),x84772),x84775)),x84774)) % 181.55/181.54 [8478]~P9(x84781,x84783,x84784)+P1(f324(f324(f326(x84781),x84782),x84783))+~P1(f324(f324(f326(f870(x84781,x84781)),f324(f324(f259(x84781,x84781),x84785),x84782)),x84784)) % 181.55/181.54 [8479]~P9(x84791,x84793,x84794)+P1(f324(f324(f326(x84791),x84792),x84793))+~P1(f324(f324(f326(f870(x84791,x84791)),f324(f324(f259(x84791,x84791),x84792),x84795)),x84794)) % 181.55/181.54 [8762]~P9(x87621,x87625,x87622)+E(f324(f278(x87621,x87621,x87622),f324(f324(f302(x87621),x87623),f191(f871(x87621,a859)))),f324(f278(x87621,x87621,x87622),f324(f324(f302(x87621),x87624),f191(f871(x87621,a859)))))+~P1(f324(f324(f326(f870(x87621,x87621)),f324(f324(f259(x87621,x87621),x87623),x87624)),x87622)) % 181.55/181.54 [8945]P1(f324(x89451,x89452))+~P1(f324(f324(f326(x89453),x89452),x89455))+P1(f324(f324(f326(x89453),f820(x89451,x89454,x89455,x89453)),f324(f324(f113(f871(x89453,a859)),x89455),x89454))) % 181.55/181.54 [8946]P1(f324(x89461,x89462))+~P1(f324(f324(f326(x89463),x89462),x89464))+P1(f324(f324(f326(x89463),f820(x89461,x89464,x89465,x89463)),f324(f324(f113(f871(x89463,a859)),x89465),x89464))) % 181.55/181.54 [8954]~P1(f324(x89542,x89545))+~P1(f324(f324(f326(x89541),x89545),x89544))+P1(f324(f324(f326(x89541),f814(x89542,x89543,x89544,x89541)),f324(f324(f113(f871(x89541,a859)),x89544),x89543))) % 181.55/181.54 [8955]~P1(f324(x89552,x89555))+~P1(f324(f324(f326(x89551),x89555),x89553))+P1(f324(f324(f326(x89551),f814(x89552,x89553,x89554,x89551)),f324(f324(f113(f871(x89551,a859)),x89554),x89553))) % 181.55/181.54 [8970]~P1(f324(f324(f238(f871(x89701,a859)),x89705),x89703))+~P1(f324(f324(f238(f871(x89701,a859)),x89702),x89704))+P1(f324(f324(f238(f871(x89701,a859)),f324(f324(f22(f871(x89701,a859)),x89702),x89703)),f324(f324(f22(f871(x89701,a859)),x89704),x89705))) % 181.55/181.54 [8971]~P1(f324(f324(f238(f871(x89711,a859)),x89713),x89715))+~P1(f324(f324(f238(f871(x89711,a859)),x89712),x89714))+P1(f324(f324(f238(f871(x89711,a859)),f324(f324(f104(f871(x89711,a859)),x89712),x89713)),f324(f324(f104(f871(x89711,a859)),x89714),x89715))) % 181.55/181.54 [8972]~P1(f324(f324(f238(f871(x89721,a859)),x89723),x89725))+~P1(f324(f324(f238(f871(x89721,a859)),x89722),x89724))+P1(f324(f324(f238(f871(x89721,a859)),f324(f324(f113(f871(x89721,a859)),x89722),x89723)),f324(f324(f113(f871(x89721,a859)),x89724),x89725))) % 181.55/181.54 [9064]~E(f324(f192(f866(x90641)),x90643),f324(f192(f866(x90642)),x90644))+E(f324(f324(f173(x90641,x90642),f324(f324(f177(x90641,x90642),x90643),x90644)),x90645),f324(f233(x90642),f672(x90645,x90644,x90642,x90643,x90641)))+~P1(f324(f324(f326(x90641),x90645),f324(f167(x90641),x90643))) % 181.55/181.54 [9068]P1(f324(f324(f326(f870(x90681,x90681)),f324(f324(f259(x90681,x90681),x90682),x90683)),f318(x90681,x90684,x90685)))+~P1(f324(f324(f238(a865),f324(x90684,x90682)),f324(x90684,x90683)))+~P1(f324(f324(f326(f870(x90681,x90681)),f324(f324(f259(x90681,x90681),x90682),x90683)),x90685)) % 181.55/181.54 [9250]P1(f324(f324(f326(f870(x92501,x92501)),f324(f324(f259(x92501,x92501),x92502),x92503)),f300(x92501,x92504)))+~P1(f324(f324(f326(f870(x92501,x92501)),f324(f324(f259(x92501,x92501),x92502),x92505)),f300(x92501,x92504)))+~P1(f324(f324(f326(f870(x92501,x92501)),f324(f324(f259(x92501,x92501),x92505),x92503)),x92504)) % 181.55/181.54 [9251]P1(f324(f324(f326(f870(x92511,x92511)),f324(f324(f259(x92511,x92511),x92512),x92513)),f300(x92511,x92514)))+~P1(f324(f324(f326(f870(x92511,x92511)),f324(f324(f259(x92511,x92511),x92515),x92513)),f300(x92511,x92514)))+~P1(f324(f324(f326(f870(x92511,x92511)),f324(f324(f259(x92511,x92511),x92512),x92515)),x92514)) % 181.55/181.54 [9349]E(x93491,x93492)+E(f324(a115,f591(x93493,x93494,x93491,x93492,x93495)),x93494)+~P1(f324(f324(f326(f870(x93495,x93495)),f324(f324(f259(x93495,x93495),x93492),x93491)),f324(f324(f184(f870(x93495,x93495),a859),x93494),x93493))) % 181.55/181.54 [9350]E(x93501,x93502)+E(f324(a115,f596(x93503,x93504,x93501,x93502,x93505)),x93504)+~P1(f324(f324(f326(f870(x93505,x93505)),f324(f324(f259(x93505,x93505),x93502),x93501)),f324(f324(f184(f870(x93505,x93505),a859),x93504),x93503))) % 181.55/181.54 [9351]E(x93511,f2(a865))+E(f324(a115,f591(x93512,x93511,x93513,x93514,x93515)),x93511)+~P1(f324(f324(f326(f870(x93515,x93515)),f324(f324(f259(x93515,x93515),x93514),x93513)),f324(f324(f184(f870(x93515,x93515),a859),x93511),x93512))) % 181.55/181.54 [9352]E(x93521,f2(a865))+E(f324(a115,f596(x93522,x93521,x93523,x93524,x93525)),x93521)+~P1(f324(f324(f326(f870(x93525,x93525)),f324(f324(f259(x93525,x93525),x93524),x93523)),f324(f324(f184(f870(x93525,x93525),a859),x93521),x93522))) % 181.55/181.54 [9372]P1(f324(f324(f326(f870(x93721,x93721)),f324(f324(f259(x93721,x93721),x93722),x93723)),f324(f324(f281(x93721,x93721,x93721),x93724),f300(x93721,x93724))))+~P1(f324(f324(f326(f870(x93721,x93721)),f324(f324(f259(x93721,x93721),x93722),x93725)),x93724))+~P1(f324(f324(f326(f870(x93721,x93721)),f324(f324(f259(x93721,x93721),x93725),x93723)),x93724)) % 181.55/181.54 [9379]~P1(f324(f324(f326(f870(x93791,x93791)),f324(f324(f259(x93791,x93791),x93792),x93795)),f300(x93791,x93794)))+P1(f324(f324(f326(f870(x93791,x93791)),f324(f324(f259(x93791,x93791),x93792),x93793)),f324(f324(f281(x93791,x93791,x93791),x93794),f300(x93791,x93794))))+~P1(f324(f324(f326(f870(x93791,x93791)),f324(f324(f259(x93791,x93791),x93795),x93793)),x93794)) % 181.55/181.54 [9419]~P9(x94191,x94195,x94192)+~P1(f324(f324(f326(f870(x94191,x94191)),f324(f324(f259(x94191,x94191),x94193),x94194)),x94192))+P1(f324(f324(f238(f871(x94191,a859)),f324(f278(x94191,x94191,x94192),f324(f324(f302(x94191),x94193),f191(f871(x94191,a859))))),f324(f278(x94191,x94191,x94192),f324(f324(f302(x94191),x94194),f191(f871(x94191,a859)))))) % 181.55/181.54 [9476]P1(f324(f324(f326(f870(x94761,x94761)),f324(f324(f259(x94761,x94761),x94762),x94763)),f324(f324(f281(x94761,x94761,x94761),x94764),f300(x94761,x94764))))+~P1(f324(f324(f326(f870(x94761,x94761)),f324(f324(f259(x94761,x94761),x94762),x94765)),f324(f324(f281(x94761,x94761,x94761),x94764),f300(x94761,x94764))))+~P1(f324(f324(f326(f870(x94761,x94761)),f324(f324(f259(x94761,x94761),x94765),x94763)),x94764)) % 181.55/181.54 [9477]P1(f324(f324(f326(f870(x94771,x94771)),f324(f324(f259(x94771,x94771),x94772),x94773)),f324(f324(f281(x94771,x94771,x94771),x94774),f300(x94771,x94774))))+~P1(f324(f324(f326(f870(x94771,x94771)),f324(f324(f259(x94771,x94771),x94775),x94773)),f324(f324(f281(x94771,x94771,x94771),x94774),f300(x94771,x94774))))+~P1(f324(f324(f326(f870(x94771,x94771)),f324(f324(f259(x94771,x94771),x94772),x94775)),x94774)) % 181.55/181.54 [9530]~P1(f324(f66(x95301,x95301,x95304,x95302,x95303),x95305))+P1(f324(f324(f326(x95301),x95302),x95303))+P1(f324(f62(x95301,x95304,f324(f324(f302(x95301),x95302),x95303)),x95305)) % 181.55/181.54 [9570]~E(f324(f303(x95703,x95702,x95705),x95704),x95701)+E(x95701,f191(f871(x95702,a859)))+P1(f324(f324(f238(f871(x95703,a859)),f324(f303(x95702,x95703,f449(x95704,x95703,x95702,x95701)),x95701)),x95704)) % 181.55/181.54 [9618]~P6(x96185)+P1(f324(f324(f326(x96181),f673(x96182,x96183,x96184,x96181,x96185)),x96184))+P1(f324(f324(f238(x96185),f324(f324(f41(x96181,x96185),x96184),x96183)),x96182)) % 181.55/181.54 [9672]P36(x96721,x96722,x96723,x96724,x96725)+~E(f324(f192(f866(x96721)),x96724),f324(f192(f866(x96722)),x96725))+P1(f324(f324(f326(f870(x96721,x96722)),f746(x96725,x96724,x96723,x96722,x96721)),f324(f167(f870(x96721,x96722)),f324(f324(f177(x96721,x96722),x96724),x96725)))) % 181.55/181.54 [9673]P36(x96731,x96732,x96733,x96734,x96735)+~E(f324(f192(f866(x96731)),x96734),f324(f192(f866(x96732)),x96735))+P1(f324(f324(f326(f870(x96731,x96732)),f752(x96733,x96735,x96734,x96732,x96731)),f324(f167(f870(x96731,x96732)),f324(f324(f177(x96731,x96732),x96734),x96735)))) % 181.55/181.54 [9811]E(x98111,x98112)+P1(f324(f324(f326(f870(x98113,x98113)),f324(f324(f259(x98113,x98113),x98111),f592(x98114,x98115,x98112,x98111,x98113))),x98114))+~P1(f324(f324(f326(f870(x98113,x98113)),f324(f324(f259(x98113,x98113),x98111),x98112)),f324(f324(f184(f870(x98113,x98113),a859),x98115),x98114))) % 181.55/181.54 [9812]E(x98121,f2(a865))+P1(f324(f324(f326(f870(x98122,x98122)),f324(f324(f259(x98122,x98122),x98123),f592(x98124,x98121,x98125,x98123,x98122))),x98124))+~P1(f324(f324(f326(f870(x98122,x98122)),f324(f324(f259(x98122,x98122),x98123),x98125)),f324(f324(f184(f870(x98122,x98122),a859),x98121),x98124))) % 181.55/181.54 [9854]~P6(x98541)+~P1(f324(f324(f238(x98541),f324(x98544,f673(x98545,x98544,x98543,x98542,x98541))),x98545))+P1(f324(f324(f238(x98541),f324(f324(f41(x98542,x98541),x98543),x98544)),x98545)) % 181.55/181.54 [9897]E(x98971,x98972)+P1(f324(f324(f326(f870(x98973,x98973)),f324(f324(f259(x98973,x98973),f593(x98974,x98975,x98971,x98972,x98973)),x98971)),x98974))+~P1(f324(f324(f326(f870(x98973,x98973)),f324(f324(f259(x98973,x98973),x98972),x98971)),f324(f324(f184(f870(x98973,x98973),a859),x98975),x98974))) % 181.55/181.54 [9898]E(x98981,f2(a865))+P1(f324(f324(f326(f870(x98982,x98982)),f324(f324(f259(x98982,x98982),f593(x98983,x98981,x98984,x98985,x98982)),x98984)),x98983))+~P1(f324(f324(f326(f870(x98982,x98982)),f324(f324(f259(x98982,x98982),x98985),x98984)),f324(f324(f184(f870(x98982,x98982),a859),x98981),x98983))) % 181.55/181.54 [9902]E(x99021,x99022)+P1(f324(f324(f326(f870(x99023,x99023)),f324(f324(f259(x99023,x99023),x99021),f593(x99024,x99025,x99022,x99021,x99023))),f324(f324(f184(f870(x99023,x99023),a859),f596(x99024,x99025,x99022,x99021,x99023)),x99024)))+~P1(f324(f324(f326(f870(x99023,x99023)),f324(f324(f259(x99023,x99023),x99021),x99022)),f324(f324(f184(f870(x99023,x99023),a859),x99025),x99024))) % 181.55/181.54 [9903]E(x99031,f2(a865))+P1(f324(f324(f326(f870(x99032,x99032)),f324(f324(f259(x99032,x99032),x99033),f593(x99034,x99031,x99035,x99033,x99032))),f324(f324(f184(f870(x99032,x99032),a859),f596(x99034,x99031,x99035,x99033,x99032)),x99034)))+~P1(f324(f324(f326(f870(x99032,x99032)),f324(f324(f259(x99032,x99032),x99033),x99035)),f324(f324(f184(f870(x99032,x99032),a859),x99031),x99034))) % 181.55/181.54 [9953]E(x99531,x99532)+P1(f324(f324(f326(f870(x99533,x99533)),f324(f324(f259(x99533,x99533),f592(x99534,x99535,x99531,x99532,x99533)),x99531)),f324(f324(f184(f870(x99533,x99533),a859),f591(x99534,x99535,x99531,x99532,x99533)),x99534)))+~P1(f324(f324(f326(f870(x99533,x99533)),f324(f324(f259(x99533,x99533),x99532),x99531)),f324(f324(f184(f870(x99533,x99533),a859),x99535),x99534))) % 181.55/181.54 [9954]E(x99541,f2(a865))+P1(f324(f324(f326(f870(x99542,x99542)),f324(f324(f259(x99542,x99542),f592(x99543,x99541,x99544,x99545,x99542)),x99544)),f324(f324(f184(f870(x99542,x99542),a859),f591(x99543,x99541,x99544,x99545,x99542)),x99543)))+~P1(f324(f324(f326(f870(x99542,x99542)),f324(f324(f259(x99542,x99542),x99545),x99544)),f324(f324(f184(f870(x99542,x99542),a859),x99541),x99543))) % 181.55/181.54 [9987]~P72(x99872)+~P1(f324(f61(x99871),x99875))+E(f324(f324(f6(x99871,x99872),f324(f324(f7(x99871,x99872,x99872),f324(f324(f18(x99871,x99872,f871(x99872,x99872)),f324(f324(f8(a859,f871(x99872,f871(x99872,x99872)),x99871),f99(x99872)),f324(f324(f7(x99871,f871(x99871,a859),a859),f326(x99871)),x99873))),x99874)),f2(x99872))),x99875),f324(f324(f6(x99871,x99872),x99874),f324(f324(f104(f871(x99871,a859)),x99875),x99873))) % 181.55/181.54 [8544]~P68(x85441)+~P1(f324(f61(x85444),x85445))+E(f324(f324(f82(x85441),f324(x85442,x85443)),f324(f324(f9(x85444,x85441),x85442),f324(f324(f22(f871(x85444,a859)),x85445),f324(f324(f302(x85444),x85443),f191(f871(x85444,a859)))))),f324(f324(f9(x85444,x85441),x85442),f324(f324(f302(x85444),x85443),x85445))) % 181.55/181.54 [8545]~P72(x85451)+~P1(f324(f61(x85454),x85455))+E(f324(f324(f81(x85451),f324(x85452,x85453)),f324(f324(f6(x85454,x85451),x85452),f324(f324(f22(f871(x85454,a859)),x85455),f324(f324(f302(x85454),x85453),f191(f871(x85454,a859)))))),f324(f324(f6(x85454,x85451),x85452),f324(f324(f302(x85454),x85453),x85455))) % 181.55/181.54 [8879]~P105(x88792)+~P16(x88792,f324(f163(x88792),f324(f324(f148(x88791,x88792),x88794),x88795)))+E(f324(f130(x88791,f324(f324(f8(x88792,a859,x88791),f324(f239(x88792),x88793)),x88794)),x88795),f172(x88791,f324(f324(f8(x88792,a859,x88791),f324(f239(x88792),x88793)),x88794),x88795)) % 181.55/181.54 [8901]~P72(x89011)+E(f324(f324(f81(x89011),f324(f324(f6(a865,x89011),x89012),f295(a865,x89013,x89014))),f324(f324(f6(a865,x89011),x89012),f295(a865,f324(f324(f81(a865),x89014),f79(a865)),f324(f324(f81(a865),x89014),x89015)))),f324(f324(f6(a865,x89011),x89012),f295(a865,x89013,f324(f324(f81(a865),x89014),x89015))))+~P1(f324(f324(f238(a865),x89013),f324(f324(f81(a865),x89014),f79(a865)))) % 181.55/181.54 [8902]~P1(f324(f324(f326(x89021),x89024),x89025))+~P1(f324(f324(f238(f871(x89021,a859)),f324(f167(x89021),x89022)),x89025))+P1(f324(f324(f238(f871(x89021,a859)),f324(f167(x89021),f324(f324(f153(x89021,x89022),x89023),x89024))),x89025)) % 181.55/181.54 [9132]~P6(x91322)+~P1(f324(f61(x91321),x91325))+E(f324(f324(f64(x91321,x91322,f324(f324(f8(x91322,f871(x91322,x91322),x91321),f104(x91322)),x91323)),x91324),x91325),f324(f324(f104(x91322),x91324),f324(f324(f42(x91321,x91322),x91325),x91323))) % 181.55/181.54 [9133]~P6(x91332)+~P1(f324(f61(x91331),x91335))+E(f324(f324(f64(x91331,x91332,f324(f324(f8(x91332,f871(x91332,x91332),x91331),f113(x91332)),x91333)),x91334),x91335),f324(f324(f113(x91332),x91334),f324(f324(f41(x91331,x91332),x91335),x91333))) % 181.55/181.54 [9178]E(f324(x91781,x91782),f324(x91781,x91783))+P1(f324(f324(f239(a865),f324(x91781,x91782)),f324(x91781,x91783)))+~P1(f324(f324(f326(f870(x91784,x91784)),f324(f324(f259(x91784,x91784),x91782),x91783)),f147(x91784,f324(f324(f145(f871(x91784,a865)),x91781),x91785)))) % 181.55/181.54 [9211]~E(f324(x92114,x92112),f324(x92114,x92113))+~P1(f324(f324(f326(f870(x92111,x92111)),f324(f324(f259(x92111,x92111),x92112),x92113)),f147(x92111,x92115)))+P1(f324(f324(f326(f870(x92111,x92111)),f324(f324(f259(x92111,x92111),x92112),x92113)),f147(x92111,f324(f324(f145(f871(x92111,a865)),x92114),x92115)))) % 181.55/181.54 [9230]~P27(x92301,x92302,x92303,x92305)+P27(x92301,x92302,x92303,f324(f324(f302(x92301),x92304),x92305))+P1(f324(f324(f326(x92302),f324(x92303,x92304)),f324(f303(x92301,x92302,x92303),f324(f324(f22(f871(x92301,a859)),x92305),f324(f324(f302(x92301),x92304),f191(f871(x92301,a859))))))) % 181.55/181.54 [9233]P1(f324(x92332,x92335))+~P1(f324(f324(f326(x92331),x92335),f324(f167(x92331),x92333)))+E(f324(f324(f132(x92331),f324(f192(f866(x92331)),f172(x92331,x92332,f324(f324(f124(x92331),x92333),x92334)))),f324(f324(f124(x92331),x92333),x92334)),f324(f324(f124(x92331),f324(f324(f132(x92331),f324(f192(f866(x92331)),f172(x92331,x92332,x92333))),x92333)),x92334)) % 181.55/181.54 [9236]~P1(f324(f324(f326(f870(x92361,x92361)),f324(f324(f259(x92361,x92361),x92362),x92363)),f147(x92361,x92365)))+~P1(f324(f324(f238(a865),f324(x92364,x92362)),f324(x92364,x92363)))+P1(f324(f324(f326(f870(x92361,x92361)),f324(f324(f259(x92361,x92361),x92362),x92363)),f147(x92361,f324(f324(f145(f871(x92361,a865)),x92364),x92365)))) % 181.55/181.54 [9303]P1(f324(f324(f326(f870(x93034,x93034)),f324(f324(f259(x93034,x93034),x93032),x93033)),f147(x93034,x93035)))+P1(f324(f324(f239(a865),f324(x93031,x93032)),f324(x93031,x93033)))+~P1(f324(f324(f326(f870(x93034,x93034)),f324(f324(f259(x93034,x93034),x93032),x93033)),f147(x93034,f324(f324(f145(f871(x93034,a865)),x93031),x93035)))) % 181.55/181.54 [9448]~P1(f324(f324(f326(f870(f866(x94481),f866(x94481))),f324(f324(f259(f866(x94481),f866(x94481)),x94482),x94484)),f152(x94481,x94485)))+~P1(f324(f324(f239(a865),x94483),f324(f192(f866(x94481)),x94482)))+P1(f324(f324(f326(f870(x94481,x94481)),f324(f324(f259(x94481,x94481),f324(f324(f159(x94481),x94482),x94483)),f324(f324(f159(x94481),x94484),x94483))),x94485)) % 181.55/181.54 [9700]E(x97001,f2(a1))+~P1(f324(f48(x97003,x97001),f324(f324(f259(a1,a1),x97004),x97005)))+P1(f324(f48(f324(f324(f82(a1),x97002),x97003),x97001),f324(f324(f259(a1,a1),f324(f324(f81(a1),f324(f324(f82(a1),x97002),x97004)),f324(f324(f38(a1),f324(f324(f82(a1),x97002),x97005)),x97001))),f44(a1,f324(f324(f82(a1),x97002),x97005),x97001)))) % 181.55/181.54 [9702]~P1(f324(f324(f239(a865),f2(a865)),x97023))+~P1(f324(f47(x97022,x97023),f324(f324(f259(a865,a865),x97024),x97025)))+P1(f324(f47(f324(f324(f82(a865),x97021),x97022),x97023),f324(f324(f259(a865,a865),f324(f324(f81(a865),f324(f324(f82(a865),x97021),x97024)),f324(f324(f38(a865),f324(f324(f82(a865),x97021),x97025)),x97023))),f44(a865,f324(f324(f82(a865),x97021),x97025),x97023)))) % 181.55/181.54 [10009]~P72(x100092)+~P1(f324(f61(x100091),x100094))+E(f324(f324(f6(x100091,x100092),x100093),f324(f244(x100091),f324(f324(f18(x100091,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100091),a322),f324(f324(f7(x100091,f871(x100091,a859),a859),f326(x100091)),x100094))),f324(f324(f7(x100091,f871(x100091,a859),a859),f326(x100091)),x100095)))),f324(f324(f6(x100091,x100092),f324(f324(f7(x100091,x100092,x100092),f324(f324(f18(x100091,x100092,f871(x100092,x100092)),f324(f324(f8(a859,f871(x100092,f871(x100092,x100092)),x100091),f99(x100092)),f324(f324(f7(x100091,f871(x100091,a859),a859),f326(x100091)),x100095))),x100093)),f2(x100092))),x100094)) % 181.55/181.54 [8178]~E(f324(f324(f124(x81781),x81782),x81785),f324(f324(f124(x81781),x81783),x81784))+E(f324(f324(f124(x81781),f324(f324(f132(x81781),f324(f192(f866(x81781)),x81782)),x81783)),x81784),x81785)+P1(f324(f324(f238(a865),f324(f192(f866(x81781)),x81783)),f324(f192(f866(x81781)),x81782))) % 181.55/181.54 [8376]~E(f324(f324(f124(x83762),x83763),x83761),f324(f324(f124(x83762),x83764),x83765))+E(x83761,f324(f324(f124(x83762),f324(f324(f132(x83762),f324(f192(f866(x83762)),x83763)),x83764)),x83765))+~P1(f324(f324(f238(a865),f324(f192(f866(x83762)),x83763)),f324(f192(f866(x83762)),x83764))) % 181.55/181.54 [8459]~E(f324(f324(f81(a865),f324(f324(f82(a865),x84593),x84594)),x84591),f324(f324(f81(a865),f324(f324(f82(a865),x84592),x84594)),x84595))+~P1(f324(f324(f238(a865),x84593),x84592))+E(x84591,f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x84592),x84593)),x84594)),x84595)) % 181.55/181.54 [8460]~E(f324(f324(f81(a865),f324(f324(f82(a865),x84601),x84603)),x84604),f324(f324(f81(a865),f324(f324(f82(a865),x84602),x84603)),x84605))+~P1(f324(f324(f238(a865),x84602),x84601))+E(f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x84601),x84602)),x84603)),x84604),x84605) % 181.55/181.54 [8629]E(f324(f324(f81(a865),f324(f324(f82(a865),x86291),x86292)),x86293),f324(f324(f81(a865),f324(f324(f82(a865),x86294),x86292)),x86295))+~P1(f324(f324(f238(a865),x86294),x86291))+~E(x86295,f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x86291),x86294)),x86292)),x86293)) % 181.55/181.54 [8630]E(f324(f324(f81(a865),f324(f324(f82(a865),x86301),x86302)),x86303),f324(f324(f81(a865),f324(f324(f82(a865),x86304),x86302)),x86305))+~P1(f324(f324(f238(a865),x86304),x86301))+~E(f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x86301),x86304)),x86302)),x86303),x86305) % 181.55/181.54 [9503]~P62(x95032)+~P1(f324(f61(x95031),x95035))+E(f324(f324(f9(x95031,x95032),f324(f324(f18(x95031,x95032,x95032),f324(f324(f8(x95032,f871(x95032,x95032),x95031),f282(x95032)),x95033)),x95034)),x95035),f324(f324(f282(x95032),f324(f324(f9(x95031,x95032),x95033),x95035)),f324(f324(f9(x95031,x95032),x95034),x95035))) % 181.55/181.54 [9635]~E(f610(x96355,x96354,x96353,x96352,x96351),f611(x96355,x96354,x96353,x96352,x96351))+P1(f324(f324(f326(f870(x96351,x96351)),f324(f324(f259(x96351,x96351),x96352),x96353)),f300(x96351,x96354)))+~P1(f324(f324(f326(f870(x96351,x96351)),f324(f324(f259(x96351,x96351),x96352),x96353)),f300(x96351,f324(f324(f113(f871(f870(x96351,x96351),a859)),x96354),x96355)))) % 181.55/181.54 [9636]~E(f615(x96365,x96364,x96363,x96362,x96361),f612(x96365,x96364,x96363,x96362,x96361))+P1(f324(f324(f326(f870(x96361,x96361)),f324(f324(f259(x96361,x96361),x96362),x96363)),f300(x96361,x96364)))+~P1(f324(f324(f326(f870(x96361,x96361)),f324(f324(f259(x96361,x96361),x96362),x96363)),f300(x96361,f324(f324(f113(f871(f870(x96361,x96361),a859)),x96364),x96365)))) % 181.55/181.54 [9844]P1(f324(f324(f326(f870(x98441,x98441)),f324(f324(f259(x98441,x98441),x98442),f611(x98445,x98444,x98443,x98442,x98441))),f300(x98441,x98444)))+P1(f324(f324(f326(f870(x98441,x98441)),f324(f324(f259(x98441,x98441),x98442),x98443)),f300(x98441,x98444)))+~P1(f324(f324(f326(f870(x98441,x98441)),f324(f324(f259(x98441,x98441),x98442),x98443)),f300(x98441,f324(f324(f113(f871(f870(x98441,x98441),a859)),x98444),x98445)))) % 181.55/181.54 [9924]P1(f324(f324(f326(f870(x99241,x99241)),f324(f324(f259(x99241,x99241),f612(x99245,x99244,x99243,x99242,x99241)),x99243)),f300(x99241,x99244)))+P1(f324(f324(f326(f870(x99241,x99241)),f324(f324(f259(x99241,x99241),x99242),x99243)),f300(x99241,x99244)))+~P1(f324(f324(f326(f870(x99241,x99241)),f324(f324(f259(x99241,x99241),x99242),x99243)),f300(x99241,f324(f324(f113(f871(f870(x99241,x99241),a859)),x99244),x99245)))) % 181.55/181.54 [9960]P1(f324(f324(f326(f870(x99601,x99601)),f324(f324(f259(x99601,x99601),x99602),x99603)),f300(x99601,x99604)))+P1(f324(f324(f326(f870(x99601,x99601)),f324(f324(f259(x99601,x99601),f611(x99605,x99604,x99603,x99602,x99601)),f610(x99605,x99604,x99603,x99602,x99601))),x99605))+~P1(f324(f324(f326(f870(x99601,x99601)),f324(f324(f259(x99601,x99601),x99602),x99603)),f300(x99601,f324(f324(f113(f871(f870(x99601,x99601),a859)),x99604),x99605)))) % 181.55/181.54 [9961]P1(f324(f324(f326(f870(x99611,x99611)),f324(f324(f259(x99611,x99611),x99612),x99613)),f300(x99611,x99614)))+P1(f324(f324(f326(f870(x99611,x99611)),f324(f324(f259(x99611,x99611),f615(x99615,x99614,x99613,x99612,x99611)),f612(x99615,x99614,x99613,x99612,x99611))),x99615))+~P1(f324(f324(f326(f870(x99611,x99611)),f324(f324(f259(x99611,x99611),x99612),x99613)),f300(x99611,f324(f324(f113(f871(f870(x99611,x99611),a859)),x99614),x99615)))) % 181.55/181.54 [10081]~P1(f324(f324(f326(f870(f866(x100811),f866(x100811))),f324(f324(f259(f866(x100811),f866(x100811)),x100814),x100815)),f152(x100811,x100812)))+~P1(f324(f324(f326(f870(x100811,x100811)),x100813),f324(f167(f870(x100811,x100811)),f324(f324(f177(x100811,x100811),x100814),x100815))))+P1(f324(f324(f263(x100811,x100811,a859),f324(f324(f7(x100811,f871(f870(x100811,x100811),a859),f871(x100811,a859)),f324(f324(f8(f871(x100811,f871(f871(f870(x100811,x100811),a859),a859)),f871(f871(f870(x100811,x100811),a859),f871(x100811,a859)),x100811),f7(x100811,f871(f870(x100811,x100811),a859),a859)),f324(f324(f8(f871(x100811,f870(x100811,x100811)),f871(x100811,f871(f871(f870(x100811,x100811),a859),a859)),x100811),f324(f8(f870(x100811,x100811),f871(f871(f870(x100811,x100811),a859),a859),x100811),f326(f870(x100811,x100811)))),f259(x100811,x100811)))),x100812)),x100813)) % 181.55/181.54 [9534]~P1(f324(f324(f238(a865),x95343),x95342))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),f324(f324(f82(a865),x95343),x95344)),x95341)),f324(f324(f81(a865),f324(f324(f82(a865),x95342),x95344)),x95345)))+P1(f324(f324(f238(a865),x95341),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x95342),x95343)),x95344)),x95345))) % 181.55/181.54 [9535]~P1(f324(f324(f238(a865),x95353),x95352))+~P1(f324(f324(f239(a865),f324(f324(f81(a865),f324(f324(f82(a865),x95353),x95354)),x95351)),f324(f324(f81(a865),f324(f324(f82(a865),x95352),x95354)),x95355)))+P1(f324(f324(f239(a865),x95351),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x95352),x95353)),x95354)),x95355))) % 181.55/181.54 [9554]~P1(f324(f324(f238(a865),x95541),x95544))+P1(f324(f324(f238(a865),f324(f324(f81(a865),f324(f324(f82(a865),x95541),x95542)),x95543)),f324(f324(f81(a865),f324(f324(f82(a865),x95544),x95542)),x95545)))+~P1(f324(f324(f238(a865),x95543),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x95544),x95541)),x95542)),x95545))) % 181.55/181.54 [9555]~P1(f324(f324(f238(a865),x95551),x95554))+P1(f324(f324(f239(a865),f324(f324(f81(a865),f324(f324(f82(a865),x95551),x95552)),x95553)),f324(f324(f81(a865),f324(f324(f82(a865),x95554),x95552)),x95555)))+~P1(f324(f324(f239(a865),x95553),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x95554),x95551)),x95552)),x95555))) % 181.55/181.54 [9670]~P1(f324(f324(f238(a865),x96702),x96701))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),f324(f324(f82(a865),x96701),x96703)),x96704)),f324(f324(f81(a865),f324(f324(f82(a865),x96702),x96703)),x96705)))+P1(f324(f324(f238(a865),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x96701),x96702)),x96703)),x96704)),x96705)) % 181.55/181.54 [9671]~P1(f324(f324(f238(a865),x96712),x96711))+~P1(f324(f324(f239(a865),f324(f324(f81(a865),f324(f324(f82(a865),x96711),x96713)),x96714)),f324(f324(f81(a865),f324(f324(f82(a865),x96712),x96713)),x96715)))+P1(f324(f324(f239(a865),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x96711),x96712)),x96713)),x96714)),x96715)) % 181.55/181.54 [9724]~P1(f324(f324(f238(a865),x97244),x97241))+P1(f324(f324(f238(a865),f324(f324(f81(a865),f324(f324(f82(a865),x97241),x97242)),x97243)),f324(f324(f81(a865),f324(f324(f82(a865),x97244),x97242)),x97245)))+~P1(f324(f324(f238(a865),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x97241),x97244)),x97242)),x97243)),x97245)) % 181.55/181.54 [9725]~P1(f324(f324(f238(a865),x97254),x97251))+P1(f324(f324(f239(a865),f324(f324(f81(a865),f324(f324(f82(a865),x97251),x97252)),x97253)),f324(f324(f81(a865),f324(f324(f82(a865),x97254),x97252)),x97255)))+~P1(f324(f324(f239(a865),f324(f324(f81(a865),f324(f324(f82(a865),f324(f324(f22(a865),x97251),x97254)),x97252)),x97253)),x97255)) % 181.55/181.54 [9945]~P14(x99451,x99452,x99455,x99453)+~P1(f324(f324(f326(f870(x99451,x99451)),x99454),x99455))+P1(f324(f324(f263(x99451,x99451,a859),f324(f324(f7(x99451,f871(x99451,x99452),f871(x99451,a859)),f324(f324(f8(f871(x99452,a859),f871(f871(x99451,x99452),f871(x99451,a859)),x99451),f8(x99452,a859,x99451)),f324(f324(f8(x99452,f871(x99452,a859),x99451),a321),x99453))),x99453)),x99454)) % 181.55/181.54 [6739]~E(f324(x67394,x67395),f203(x67392))+E(f324(f180(x67391,x67392,x67393,x67394),x67395),f324(f233(x67392),x67396))+~E(f324(x67393,x67395),f324(f233(x67392),x67396)) % 181.55/181.54 [6839]~E(f324(x68393,x68396),f203(x68391))+E(f324(f235(f869(x68391),x68392,f203(x68391),x68393),f324(x68394,x68395)),f203(x68391))+~E(f324(x68394,x68395),f324(f233(x68392),x68396)) % 181.55/181.54 [7415]E(f324(x74151,x74152),f203(x74153))+~E(f324(f180(x74155,x74153,x74156,x74151),x74152),f324(f233(x74153),x74154))+E(f324(x74151,x74152),f324(f233(x74153),x74154)) % 181.55/181.54 [7451]~E(f324(f180(x74516,x74513,x74515,x74511),x74512),f324(f233(x74513),x74514))+E(f324(x74511,x74512),f324(f233(x74513),x74514))+E(f324(x74515,x74512),f324(f233(x74513),x74514)) % 181.55/181.54 [8340]~P21(x83406,x83401,x83402,x83404)+E(f324(f73(x83401,x83401,x83401,f324(x83402,x83403)),f324(x83404,x83405)),f324(f73(x83401,x83401,x83401,f324(x83404,x83405)),f324(x83402,x83403)))+~P1(f324(f61(x83406),x83405)) % 181.55/181.54 [8774]~P27(x87741,x87743,x87745,x87746)+~P27(x87743,x87742,x87744,f324(f303(x87741,x87743,x87745),x87746))+P27(x87741,x87742,f324(f73(x87743,x87742,x87741,x87744),x87745),x87746) % 181.55/181.54 [9334]~P1(f324(f324(x93344,x93342),x93346))+~P1(f324(f324(x93343,x93345),x93342))+P1(f324(f324(f326(x93341),x93342),f289(x93341,x93343,x93344,x93345,x93346))) % 181.55/181.54 [9335]~P1(f324(f324(x93353,x93352),x93356))+~P1(f324(f324(x93354,x93355),x93352))+P1(f324(f324(f326(x93351),x93352),f292(x93351,x93353,x93354,x93355,x93356))) % 181.55/181.54 [9449]E(x94491,x94492)+E(x94493,x94494)+~P1(f324(f324(f326(f870(f866(x94495),f866(x94495))),f324(f324(f259(f866(x94495),f866(x94495)),f324(f324(f145(x94495),x94493),x94491)),f324(f324(f145(x94495),x94494),x94492))),f151(x94495,x94496))) % 181.55/181.54 [9459]~E(x94592,x94594)+P1(f324(f324(f326(f870(f866(x94591),f866(x94591))),f324(f324(f259(f866(x94591),f866(x94591)),f324(f324(f145(x94591),x94592),x94593)),f324(f324(f145(x94591),x94594),x94595))),f139(x94591,x94596)))+~P1(f324(f324(f326(f870(f866(x94591),f866(x94591))),f324(f324(f259(f866(x94591),f866(x94591)),x94593),x94595)),f139(x94591,x94596))) % 181.55/181.54 [9460]~E(x94602,x94604)+P1(f324(f324(f326(f870(f866(x94601),f866(x94601))),f324(f324(f259(f866(x94601),f866(x94601)),f324(f324(f145(x94601),x94602),x94603)),f324(f324(f145(x94601),x94604),x94605))),f141(x94601,x94606)))+~P1(f324(f324(f326(f870(f866(x94601),f866(x94601))),f324(f324(f259(f866(x94601),f866(x94601)),x94603),x94605)),f141(x94601,x94606))) % 181.55/181.54 [9461]~E(x94612,x94614)+P1(f324(f324(f326(f870(f866(x94611),f866(x94611))),f324(f324(f259(f866(x94611),f866(x94611)),f324(f324(f145(x94611),x94612),x94613)),f324(f324(f145(x94611),x94614),x94615))),f151(x94611,x94616)))+~P1(f324(f324(f326(f870(f866(x94611),f866(x94611))),f324(f324(f259(f866(x94611),f866(x94611)),x94613),x94615)),f151(x94611,x94616))) % 181.55/181.54 [9462]~E(x94622,x94624)+P1(f324(f324(f326(f870(f866(x94621),f866(x94621))),f324(f324(f259(f866(x94621),f866(x94621)),f324(f324(f124(x94621),x94622),x94623)),f324(f324(f124(x94621),x94624),x94625))),f151(x94621,x94626)))+~P1(f324(f324(f326(f870(f866(x94621),f866(x94621))),f324(f324(f259(f866(x94621),f866(x94621)),x94623),x94625)),f151(x94621,x94626))) % 181.55/181.54 [9463]~E(x94633,x94635)+P1(f324(f324(f326(f870(f866(x94631),f866(x94631))),f324(f324(f259(f866(x94631),f866(x94631)),f324(f324(f124(x94631),x94632),x94633)),f324(f324(f124(x94631),x94634),x94635))),f151(x94631,x94636)))+~P1(f324(f324(f326(f870(f866(x94631),f866(x94631))),f324(f324(f259(f866(x94631),f866(x94631)),x94632),x94634)),f151(x94631,x94636))) % 181.55/181.54 [9522]E(x95221,x95222)+P1(f324(f324(f326(f870(f866(x95223),f866(x95223))),f324(f324(f259(f866(x95223),f866(x95223)),x95221),x95222)),f151(x95223,x95224)))+~P1(f324(f324(f326(f870(f866(x95223),f866(x95223))),f324(f324(f259(f866(x95223),f866(x95223)),f324(f324(f145(x95223),x95225),x95221)),f324(f324(f145(x95223),x95226),x95222))),f151(x95223,x95224))) % 181.55/181.54 [9674]~E(x96743,x96745)+P1(f324(f324(f326(f870(f866(x96741),f866(x96741))),f324(f324(f259(f866(x96741),f866(x96741)),f324(f324(f124(x96741),x96742),f324(f324(f145(x96741),x96743),f116(x96741)))),f324(f324(f124(x96741),x96744),f324(f324(f145(x96741),x96745),f116(x96741))))),f151(x96741,x96746)))+~P1(f324(f324(f326(f870(f866(x96741),f866(x96741))),f324(f324(f259(f866(x96741),f866(x96741)),x96742),x96744)),f151(x96741,x96746))) % 181.55/181.54 [9690]E(f324(x96901,x96902),f203(x96903))+~E(f324(f235(f869(x96906),x96903,f203(x96906),x96904),f324(x96901,x96902)),f203(x96906))+E(f324(x96904,f665(x96902,x96901,x96904,x96905,x96906,x96903)),f203(x96906)) % 181.55/181.54 [9691]E(f324(x96911,x96912),f203(x96913))+~E(f324(f235(f869(x96916),x96913,f203(x96916),x96914),f324(x96911,x96912)),f203(x96916))+E(f324(f233(x96913),f665(x96912,x96911,x96914,x96915,x96916,x96913)),f324(x96911,x96912)) % 181.55/181.54 [9728]E(x97281,x97282)+E(x97283,x97284)+~P1(f324(f324(f326(f870(f866(x97285),f866(x97285))),f324(f324(f259(f866(x97285),f866(x97285)),f324(f324(f124(x97285),x97283),f324(f324(f145(x97285),x97281),f116(x97285)))),f324(f324(f124(x97285),x97284),f324(f324(f145(x97285),x97282),f116(x97285))))),f151(x97285,x97286))) % 181.55/181.54 [9752]E(x97521,x97522)+~P1(f324(f324(f326(f870(f866(x97523),f866(x97523))),f324(f324(f259(f866(x97523),f866(x97523)),f324(f324(f124(x97523),x97521),f324(f324(f145(x97523),x97525),f116(x97523)))),f324(f324(f124(x97523),x97522),f324(f324(f145(x97523),x97526),f116(x97523))))),f151(x97523,x97524)))+P1(f324(f324(f326(f870(f866(x97523),f866(x97523))),f324(f324(f259(f866(x97523),f866(x97523)),x97521),x97522)),f151(x97523,x97524))) % 181.55/181.54 [9790]~P1(f324(f324(f326(f870(f871(x97901,a859),f871(x97901,a859))),f324(f324(f259(f871(x97901,a859),f871(x97901,a859)),x97902),x97904)),f315(x97901,x97906)))+~P1(f324(f324(f326(f870(f871(x97901,a859),f871(x97901,a859))),f324(f324(f259(f871(x97901,a859),f871(x97901,a859)),x97903),x97905)),f315(x97901,x97906)))+P1(f324(f324(f326(f870(f871(x97901,a859),f871(x97901,a859))),f324(f324(f259(f871(x97901,a859),f871(x97901,a859)),f324(f324(f113(f871(x97901,a859)),x97902),x97903)),f324(f324(f113(f871(x97901,a859)),x97904),x97905))),f315(x97901,x97906))) % 181.55/181.54 [5210]~E(f324(x52103,x52106),x52105)+~E(x52104,f324(f233(x52101),x52106))+E(f324(f324(f204(x52101,x52102),x52103),x52104),f324(f233(x52102),x52105)) % 181.55/181.54 [5619]~E(f324(f324(f124(x56191),x56196),x56193),x56195)+E(f324(f324(f124(x56191),x56192),x56193),f324(f324(f145(x56191),x56194),x56195))+~E(x56192,f324(f324(f145(x56191),x56194),x56196)) % 181.55/181.54 [5620]~E(f324(f324(f124(x56201),x56206),x56203),x56205)+E(f324(f324(f124(x56201),x56202),x56203),f324(f324(f124(x56201),x56204),x56205))+~E(x56202,f324(f324(f124(x56201),x56204),x56206)) % 181.55/181.54 [5622]E(f324(f324(f124(x56221),x56222),x56223),f324(f324(f145(x56221),x56224),x56225))+~E(f324(f324(f145(x56221),x56224),x56226),x56222)+~E(x56225,f324(f324(f124(x56221),x56226),x56223)) % 181.55/181.54 [5624]~E(f324(f324(f124(x56241),x56242),x56246),x56244)+E(f324(f324(f124(x56241),x56242),x56243),f324(f324(f124(x56241),x56244),x56245))+~E(x56243,f324(f324(f124(x56241),x56246),x56245)) % 181.55/181.54 [6733]E(f324(x67331,x67332),f324(x67333,x67332))+~E(f324(f324(f148(x67334,x67335),x67331),x67336),f324(f324(f148(x67334,x67335),x67333),x67336))+~P1(f324(f324(f326(x67334),x67332),f324(f167(x67334),x67336))) % 181.55/181.54 [7112]~P21(x71124,x71125,x71126,x71121)+E(f324(f324(x71121,x71122),x71123),f324(f324(f64(x71124,x71125,x71126),x71123),x71122))+~P1(f324(f61(x71124),x71122)) % 181.55/181.54 [7178]~E(x71782,f324(x71784,x71786))+~P1(f324(f324(f326(x71783),x71786),x71785))+P1(f324(f324(f326(x71781),x71782),f324(f303(x71783,x71781,x71784),x71785))) % 181.55/181.54 [7179]~E(f324(x71794,x71792),x71796)+~P1(f324(f324(f326(x71793),x71796),x71795))+P1(f324(f324(f326(x71791),x71792),f324(f304(x71791,x71793,x71794),x71795))) % 181.55/181.54 [7628]~P34(x76281,x76282,x76284,x76286)+P34(x76281,x76282,f324(f324(f145(x76281),x76283),x76284),f324(f324(f145(x76281),x76285),x76286))+~P1(f324(f324(x76282,x76283),x76285)) % 181.55/181.54 [8639]~P54(x86394,x86395,x86391,x86392,x86396)+E(f324(x86391,f324(x86392,x86393)),x86393)+~P1(f324(f324(f326(x86395),x86393),x86396)) % 181.55/181.54 [9143]~P28(x91432,x91431,x91435,x91434,x91433)+E(f324(f94(x91431,x91432,x91433,f94(x91432,x91431,x91434,x91435)),x91436),f324(x91435,x91436))+~P1(f324(f324(f326(x91432),x91436),x91434)) % 181.55/181.54 [9366]E(f324(f303(x93661,x93662,f76(x93661,x93662,x93663,x93664,x93665)),x93666),f324(f303(x93661,x93662,x93665),x93666))+~P1(f324(f324(f326(x93661),x93664),x93666))+~P1(f324(f324(f326(x93661),x93663),x93666)) % 181.55/181.54 [9451]E(x94511,x94512)+E(f324(f192(f866(x94513)),x94514),f324(f192(f866(x94513)),x94515))+~P1(f324(f324(f326(f870(f866(x94513),f866(x94513))),f324(f324(f259(f866(x94513),f866(x94513)),f324(f324(f145(x94513),x94511),x94514)),f324(f324(f145(x94513),x94512),x94515))),f139(x94513,x94516))) % 181.55/181.54 [9516]~P18(x95161,x95162,x95163)+E(f324(f324(f64(x95161,x95162,x95163),x95164),x95165),x95166)+~P1(f324(f66(x95161,x95162,x95163,x95164,x95165),x95166)) % 181.55/181.54 [9525]E(f324(f192(f866(x95251)),x95252),f324(f192(f866(x95251)),x95253))+P1(f324(f324(f326(f870(f866(x95251),f866(x95251))),f324(f324(f259(f866(x95251),f866(x95251)),x95252),x95253)),f139(x95251,x95254)))+~P1(f324(f324(f326(f870(f866(x95251),f866(x95251))),f324(f324(f259(f866(x95251),f866(x95251)),f324(f324(f145(x95251),x95255),x95252)),f324(f324(f145(x95251),x95256),x95253))),f139(x95251,x95254))) % 181.55/181.54 [9548]~P1(f324(f324(f326(f870(x95481,x95481)),f324(f324(f259(x95481,x95481),x95482),x95484)),f300(x95481,x95486)))+P1(f324(f324(f326(f870(f866(x95481),f866(x95481))),f324(f324(f259(f866(x95481),f866(x95481)),f324(f324(f145(x95481),x95482),x95483)),f324(f324(f145(x95481),x95484),x95485))),f300(f866(x95481),f151(x95481,x95486))))+~P1(f324(f324(f326(f870(f866(x95481),f866(x95481))),f324(f324(f259(f866(x95481),f866(x95481)),x95483),x95485)),f300(f866(x95481),f151(x95481,x95486)))) % 181.55/181.54 [9577]E(x95771,x95772)+E(x95773,x95771)+E(f76(x95774,x95775,x95773,x95772,f76(x95774,x95775,x95772,x95771,f76(x95774,x95775,x95773,x95772,x95776))),f76(x95774,x95775,x95773,x95771,x95776)) % 181.55/181.54 [9734]~P1(f324(x97342,x97346))+~E(f324(f130(x97341,x97342),x97343),f324(f324(f145(x97341),x97344),x97345))+~P1(f324(f324(f326(x97341),x97346),f324(f167(x97341),f772(x97345,x97344,x97343,x97342,x97341)))) % 181.55/181.54 [9735]~P1(f324(x97354,x97356))+~E(f324(f324(f145(x97351),x97352),x97353),f324(f130(x97351,x97354),x97355))+~P1(f324(f324(f326(x97351),x97356),f324(f167(x97351),f770(x97355,x97354,x97353,x97352,x97351)))) % 181.55/181.54 [10036]~P72(x100362)+E(f324(f324(f6(x100361,x100362),f324(f324(f8(f871(x100363,a859),x100362,x100361),f324(f6(x100363,x100362),x100364)),f324(f324(f8(f871(x100363,a859),f871(x100363,a859),x100361),f244(x100363)),f324(f324(f8(f871(x100363,a859),f871(x100363,a859),x100361),f324(f18(x100363,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100363),a322),f324(f324(f7(x100363,f871(x100363,a859),a859),f326(x100363)),x100365)))),f324(f7(x100363,x100361,a859),f324(f324(f8(x100361,f871(x100361,a859),x100363),a321),x100366)))))),f324(f303(x100363,x100361,x100366),x100365)),f324(f324(f6(x100363,x100362),x100364),x100365))+~P1(f324(f61(x100363),x100365)) % 181.55/181.54 [6790]~P105(x67903)+P1(f324(x67902,x67905))+E(f324(f130(x67901,x67902),f324(f324(f142(x67901,x67903,x67904),x67905),x67906)),f324(f130(x67901,x67902),x67906)) % 181.55/181.54 [6792]P1(f324(x67921,x67922))+~E(f161(x67923,x67921,x67924),f324(f324(f259(f866(x67923),f866(x67923)),x67925),x67926))+~P1(f324(f324(f326(x67923),x67922),f324(f167(x67923),x67925))) % 181.55/181.54 [6836]~P1(f324(x68362,x68366))+~E(f161(x68361,x68362,x68363),f324(f324(f259(f866(x68361),f866(x68361)),x68364),x68365))+~P1(f324(f324(f326(x68361),x68366),f324(f167(x68361),x68365))) % 181.55/181.54 [7495]~P17(x74951,x74952,x74953)+~P1(f324(f61(x74951),x74956))+E(f324(f324(f64(x74951,x74952,x74953),x74954),f324(f324(f302(x74951),x74955),x74956)),f324(f324(f64(x74951,x74952,x74953),f324(f324(x74953,x74955),x74954)),x74956)) % 181.55/181.54 [7545]~P105(x75452)+~P1(f324(f324(f238(x75452),f324(x75453,x75454)),f324(x75453,x75455)))+E(f324(f324(f142(x75451,x75452,x75453),x75454),f324(f324(f145(x75451),x75455),x75456)),f324(f324(f145(x75451),x75454),f324(f324(f145(x75451),x75455),x75456))) % 181.55/181.54 [7658]E(x76581,x76582)+~E(f324(f324(f261(x76583,x76584),x76581),f324(f16(f871(x76584,a859),x76583),x76585)),f324(f324(f261(x76583,x76584),x76582),f324(f16(f871(x76584,a859),x76583),x76585)))+~P1(f324(f324(f326(x76584),x76586),x76585)) % 181.55/181.54 [7719]~P17(x77191,x77192,x77193)+~P1(f324(f61(x77191),x77196))+E(f324(f324(f64(x77191,x77192,x77193),x77194),f324(f324(f302(x77191),x77195),x77196)),f324(f324(x77193,x77195),f324(f324(f64(x77191,x77192,x77193),x77194),x77196))) % 181.55/181.54 [7835]~P18(x78351,x78352,x78353)+~P1(f324(f61(x78351),x78356))+E(f324(f324(f64(x78351,x78352,x78353),f324(f324(x78353,x78354),x78355)),x78356),f324(f324(x78353,x78354),f324(f324(f64(x78351,x78352,x78353),x78355),x78356))) % 181.55/181.54 [7907]~P22(x79072,x79075,x79076,x79071)+~P1(f324(f61(x79072),x79074))+E(f324(x79071,f324(f324(f302(x79072),x79073),x79074)),f324(f73(x79075,x79075,x79075,f324(x79071,x79074)),f324(x79076,x79073))) % 181.55/181.54 [7939]~P105(x79392)+P1(f324(f324(f238(x79392),f324(x79393,x79394)),f324(x79393,x79395)))+E(f324(f324(f142(x79391,x79392,x79393),x79394),f324(f324(f145(x79391),x79395),x79396)),f324(f324(f145(x79391),x79395),f324(f324(f142(x79391,x79392,x79393),x79394),x79396))) % 181.55/181.54 [8078]~E(f324(f192(f866(x80781)),x80785),f324(f192(f866(x80782)),x80786))+~E(f324(f192(f866(x80781)),x80783),f324(f192(f866(x80782)),x80784))+E(f324(f324(f124(f870(x80781,x80782)),f324(f324(f177(x80781,x80782),x80783),x80784)),f324(f324(f177(x80781,x80782),x80785),x80786)),f324(f324(f177(x80781,x80782),f324(f324(f124(x80781),x80783),x80785)),f324(f324(f124(x80782),x80784),x80786))) % 181.55/181.54 [8193]~E(x81932,f324(f303(x81933,x81931,x81934),x81936))+P1(f324(f324(f238(f871(x81931,a859)),x81932),f324(f303(x81933,x81931,x81934),x81935)))+~P1(f324(f324(f238(f871(x81933,a859)),x81936),x81935)) % 181.55/181.54 [8300]~P105(x83005)+E(f324(x83001,x83002),f324(x83001,x83003))+E(f324(f324(f142(x83004,x83005,x83001),x83002),f324(f324(f142(x83004,x83005,x83001),x83003),x83006)),f324(f324(f142(x83004,x83005,x83001),x83003),f324(f324(f142(x83004,x83005,x83001),x83002),x83006))) % 181.55/181.54 [8333]~P27(x83333,x83331,x83334,x83335)+P27(x83333,x83331,f324(f324(f324(f72(x83333,x83331),x83334),x83336),x83332),x83335)+P1(f324(f324(f326(x83331),x83332),f324(f303(x83333,x83331,x83334),x83335))) % 181.55/181.54 [8468]~P1(f324(f324(f326(x84682),x84684),f324(x84686,x84683)))+~P1(f324(f324(f326(x84681),x84683),x84685))+P1(f324(f324(f326(f870(x84681,x84682)),f324(f324(f259(x84681,x84682),x84683),x84684)),f324(f324(f261(x84681,x84682),x84685),x84686))) % 181.55/181.54 [8943]~P68(x89432)+~P27(x89434,x89431,x89435,x89436)+E(f324(f324(f9(x89431,x89432),x89433),f324(f303(x89434,x89431,x89435),x89436)),f324(f324(f9(x89434,x89432),f324(f73(x89431,x89432,x89434,x89433),x89435)),x89436)) % 181.55/181.54 [8944]~P72(x89442)+~P27(x89444,x89441,x89445,x89446)+E(f324(f324(f6(x89441,x89442),x89443),f324(f303(x89444,x89441,x89445),x89446)),f324(f324(f6(x89444,x89442),f324(f73(x89441,x89442,x89444,x89443),x89445)),x89446)) % 181.55/181.54 [8992]~P36(x89922,x89925,x89921,x89923,x89926)+P1(f324(f324(x89921,f324(f324(f159(x89922),x89923),x89924)),f324(f324(f159(x89925),x89926),x89924)))+~P1(f324(f324(f239(a865),x89924),f324(f192(f866(x89925)),x89926))) % 181.55/181.54 [8993]~P36(x89932,x89935,x89931,x89933,x89936)+P1(f324(f324(x89931,f324(f324(f159(x89932),x89933),x89934)),f324(f324(f159(x89935),x89936),x89934)))+~P1(f324(f324(f239(a865),x89934),f324(f192(f866(x89932)),x89933))) % 181.55/181.54 [9004]~E(f324(f303(x90041,x90042,x90043),x90044),x90046)+E(f324(f303(x90041,x90042,x90043),f324(f303(x90042,x90041,f94(x90041,x90042,x90044,x90043)),x90045)),x90045)+~P1(f324(f324(f238(f871(x90042,a859)),x90045),x90046)) % 181.55/181.54 [9206]~P21(x92063,x92061,x92066,x92062)+~P1(f324(f61(x92063),x92064))+E(f324(f73(x92061,x92061,x92061,f324(x92062,f324(f324(f22(f871(x92063,a859)),x92064),f324(f324(f302(x92063),x92065),f191(f871(x92063,a859)))))),f324(x92066,x92065)),f324(x92062,f324(f324(f302(x92063),x92065),x92064))) % 181.55/181.54 [9825]~E(f324(f303(x98252,x98254,x98256),f247(f871(x98252,a859))),f247(f871(x98254,a859)))+~E(f324(f303(x98251,x98253,x98255),f247(f871(x98251,a859))),f247(f871(x98253,a859)))+E(f324(f303(f870(x98251,x98252),f870(x98253,x98254),f264(x98251,x98253,x98252,x98254,x98255,x98256)),f247(f871(f870(x98251,x98252),a859))),f247(f871(f870(x98253,x98254),a859))) % 181.55/181.54 [9873]~P27(x98733,x98734,x98735,f324(x98736,f645(x98736,x98735,x98734,x98733,x98732,x98731)))+P27(x98733,x98734,x98735,f324(f324(f42(x98732,f871(x98733,a859)),x98731),x98736))+E(x98731,f191(f871(x98732,a859))) % 181.55/181.54 [9931]P27(x99316,x99315,x99314,f324(f324(f42(x99312,f871(x99316,a859)),x99311),x99313))+E(x99311,f191(f871(x99312,a859)))+P1(f324(f324(f326(x99312),f645(x99313,x99314,x99315,x99316,x99312,x99311)),x99311)) % 181.55/181.54 [9936]P1(f324(f324(f326(x99361),f571(x99362,x99363,x99364,x99365,x99366,x99361)),x99366))+P1(f324(f324(f238(f871(f870(x99361,x99364),a859)),f324(f324(f261(x99361,x99364),x99366),x99363)),f324(f324(f261(x99361,x99364),x99365),x99362)))+~P1(f324(f324(f238(f871(x99361,a859)),x99366),x99365)) % 181.55/181.54 [9974]P26(x99746,x99745,f324(f324(f302(f864(x99746)),f324(f324(f324(f93(x99746),x99741),x99743),x99742)),f191(f871(f864(x99746),a859))))+~P26(x99746,x99745,f324(f324(f302(f864(x99746)),f324(f324(f324(f93(x99746),x99744),x99743),x99742)),f191(f871(f864(x99746),a859))))+P1(f324(f324(x99741,f816(x99741,x99742,x99743,x99744,x99745,x99746)),f828(x99741,x99742,x99743,x99744,x99745,x99746))) % 181.55/181.54 [9975]P26(x99756,x99755,f324(f324(f302(f864(x99756)),f324(f324(f324(f93(x99756),x99754),x99753),x99752)),f191(f871(f864(x99756),a859))))+~P26(x99756,x99755,f324(f324(f302(f864(x99756)),f324(f324(f324(f93(x99756),x99754),x99753),x99751)),f191(f871(f864(x99756),a859))))+P1(f324(f324(x99751,f839(x99752,x99751,x99753,x99754,x99755,x99756)),f850(x99752,x99751,x99753,x99754,x99755,x99756))) % 181.55/181.54 [10012]~P26(x100121,x100122,f324(f324(f302(f864(x100121)),f324(f324(f324(f93(x100121),x100123),x100124),x100126)),f191(f871(f864(x100121),a859))))+P26(x100121,x100122,f324(f324(f302(f864(x100121)),f324(f324(f324(f93(x100121),x100123),x100124),x100125)),f191(f871(f864(x100121),a859))))+~P1(f324(f324(x100125,f839(x100125,x100126,x100124,x100123,x100122,x100121)),f850(x100125,x100126,x100124,x100123,x100122,x100121))) % 181.55/181.54 [10013]~P26(x100131,x100132,f324(f324(f302(f864(x100131)),f324(f324(f324(f93(x100131),x100136),x100134),x100135)),f191(f871(f864(x100131),a859))))+P26(x100131,x100132,f324(f324(f302(f864(x100131)),f324(f324(f324(f93(x100131),x100133),x100134),x100135)),f191(f871(f864(x100131),a859))))+~P1(f324(f324(x100136,f816(x100133,x100135,x100134,x100136,x100132,x100131)),f828(x100133,x100135,x100134,x100136,x100132,x100131))) % 181.55/181.54 [10047]~P1(f324(f324(f238(f871(x100472,a859)),f324(x100474,f571(x100476,x100474,x100472,x100475,x100473,x100471))),f324(x100476,f571(x100476,x100474,x100472,x100475,x100473,x100471))))+~P1(f324(f324(f238(f871(x100471,a859)),x100473),x100475))+P1(f324(f324(f238(f871(f870(x100471,x100472),a859)),f324(f324(f261(x100471,x100472),x100473),x100474)),f324(f324(f261(x100471,x100472),x100475),x100476))) % 181.55/181.54 [7677]~P1(f324(x76771,x76775))+~P1(f324(x76776,x76774))+P1(f324(x76771,f324(f262(x76772,x76773),f324(f324(f259(x76772,x76773),x76774),x76775)))) % 181.55/181.54 [7678]~P1(f324(x76781,x76784))+~P1(f324(x76786,x76785))+P1(f324(x76781,f324(f258(x76782,x76783),f324(f324(f259(x76782,x76783),x76784),x76785)))) % 181.55/181.54 [7698]~E(f324(f192(f866(x76981)),x76983),f324(f192(f866(x76984)),x76985))+~E(f324(f324(f173(x76981,x76984),f324(f324(f177(x76981,x76984),x76983),x76985)),x76982),f324(f233(x76984),x76986))+P1(f324(f324(f326(x76981),x76982),f324(f167(x76981),x76983))) % 181.55/181.54 [7724]~P1(f324(f324(x77244,x77246),x77245))+~P1(f324(f324(f326(x77241),x77246),x77243))+P1(f324(f324(f324(f41(x77241,f871(x77242,a859)),x77243),x77244),x77245)) % 181.55/181.54 [8029]~P1(f324(f324(f326(x80291),x80292),f324(x80295,x80296)))+~P1(f324(f324(f326(x80293),x80296),x80294))+P1(f324(f324(f326(x80291),x80292),f324(f324(f41(x80293,f871(x80291,a859)),x80294),x80295))) % 181.55/181.54 [8071]P1(f324(f324(x80711,x80712),x80713))+~P1(f324(f324(x80714,x80712),x80713))+~P1(f324(f324(f238(f871(x80715,f871(x80716,a859))),x80714),x80711)) % 181.55/181.54 [8217]P1(f324(f324(x82171,x82172),x82173))+~P1(f324(f324(f326(x82174),x82172),x82175))+~P1(f324(f324(f324(f42(x82174,f871(x82176,a859)),x82175),x82171),x82173)) % 181.55/181.54 [8355]P1(f324(f324(f326(x83551),x83552),f324(x83553,x83554)))+~P1(f324(f324(f326(x83555),x83554),x83556))+~P1(f324(f324(f326(x83551),x83552),f324(f324(f42(x83555,f871(x83551,a859)),x83556),x83553))) % 181.55/181.54 [8618]~P14(x86184,x86185,x86186,x86181)+E(f324(x86181,x86182),f324(x86181,x86183))+~P1(f324(f324(f326(f870(x86184,x86184)),f324(f324(f259(x86184,x86184),x86182),x86183)),x86186)) % 181.55/181.54 [8652]P1(f324(f324(f238(f871(x86521,a859)),x86522),f324(x86523,x86524)))+~P1(f324(f324(f326(x86525),x86524),x86526))+~P1(f324(f324(f238(f871(x86521,a859)),x86522),f324(f324(f42(x86525,f871(x86521,a859)),x86526),x86523))) % 181.55/181.54 [8686]~P52(x86863,x86864,f324(f279(x86864,x86863),x86865))+E(x86861,f191(f871(x86862,a859)))+E(f324(f324(f42(x86862,f871(x86863,a859)),x86861),f324(f324(f8(f871(x86864,a859),f871(x86863,a859),x86862),f278(x86864,x86863,x86865)),x86866)),f324(f278(x86864,x86863,x86865),f324(f324(f42(x86862,f871(x86864,a859)),x86861),x86866))) % 181.55/181.54 [8765]P1(f324(f324(f326(x87651),x87652),f324(f278(x87653,x87651,x87654),x87655)))+~P1(f324(f324(f326(x87653),x87656),x87655))+~P1(f324(f324(f326(f870(x87653,x87651)),f324(f324(f259(x87653,x87651),x87656),x87652)),x87654)) % 181.55/181.54 [9070]P1(f324(f324(f238(f871(x90701,a859)),f324(f278(x90702,x90701,x90703),x90704)),f324(f278(x90702,x90701,x90705),x90706)))+~P1(f324(f324(f238(f871(x90702,a859)),x90704),x90706))+~P1(f324(f324(f238(f871(f870(x90702,x90701),a859)),x90703),x90705)) % 181.55/181.54 [9252]~P1(f324(f324(f326(x92522),x92526),x92524))+~P1(f324(f324(f238(f871(x92521,a859)),x92523),x92525))+P1(f324(f324(f238(f871(f870(x92521,x92522),a859)),f324(f324(f261(x92521,x92522),x92523),f324(f16(f871(x92522,a859),x92521),x92524))),f324(f324(f261(x92521,x92522),x92525),f324(f16(f871(x92522,a859),x92521),x92524)))) % 181.55/181.54 [9265]~P36(x92651,x92652,x92653,x92655,x92656)+P1(f324(f324(f263(x92651,x92652,a859),x92653),x92654))+~P1(f324(f324(f326(f870(x92651,x92652)),x92654),f324(f167(f870(x92651,x92652)),f324(f324(f177(x92651,x92652),x92655),x92656)))) % 181.55/181.54 [9403]~E(x94033,x94035)+P1(f324(f324(f326(f870(f866(x94031),f866(x94031))),f324(f324(f259(f866(x94031),f866(x94031)),f324(f324(f145(x94031),x94032),x94033)),f324(f324(f145(x94031),x94034),x94035))),f151(x94031,x94036)))+~P1(f324(f324(f326(f870(x94031,x94031)),f324(f324(f259(x94031,x94031),x94032),x94034)),x94036)) % 181.55/181.54 [9411]~E(f324(f192(f866(x94111)),x94115),f324(f192(f866(x94112)),x94116))+E(f182(x94111,x94112,f183(x94111,x94112,x94113,f324(f324(f22(f871(x94111,a859)),x94114),f324(f167(x94111),x94115))),x94115,x94116),f183(x94111,x94112,f182(x94111,x94112,x94113,x94115,x94116),x94114))+~P1(f324(f324(f238(f871(x94111,a859)),f324(f167(x94111),x94115)),x94114)) % 181.55/181.54 [9412]~E(f324(f192(f866(x94121)),x94123),f324(f192(f866(x94121)),x94125))+P1(f324(f324(f326(f870(f866(x94121),f866(x94121))),f324(f324(f259(f866(x94121),f866(x94121)),f324(f324(f145(x94121),x94122),x94123)),f324(f324(f145(x94121),x94124),x94125))),f139(x94121,x94126)))+~P1(f324(f324(f326(f870(x94121,x94121)),f324(f324(f259(x94121,x94121),x94122),x94124)),x94126)) % 181.55/181.54 [9443]P1(f324(f324(f326(f870(x94431,x94431)),f324(f324(f259(x94431,x94431),x94432),x94433)),f324(f324(f184(f870(x94431,x94431),a859),f324(a115,x94434)),x94435)))+~P1(f324(f324(f326(f870(x94431,x94431)),f324(f324(f259(x94431,x94431),x94436),x94433)),x94435))+~P1(f324(f324(f326(f870(x94431,x94431)),f324(f324(f259(x94431,x94431),x94432),x94436)),f324(f324(f184(f870(x94431,x94431),a859),x94434),x94435))) % 181.55/181.54 [9444]P1(f324(f324(f326(f870(x94441,x94441)),f324(f324(f259(x94441,x94441),x94442),x94443)),f324(f324(f184(f870(x94441,x94441),a859),f324(a115,x94444)),x94445)))+~P1(f324(f324(f326(f870(x94441,x94441)),f324(f324(f259(x94441,x94441),x94442),x94446)),x94445))+~P1(f324(f324(f326(f870(x94441,x94441)),f324(f324(f259(x94441,x94441),x94446),x94443)),f324(f324(f184(f870(x94441,x94441),a859),x94444),x94445))) % 181.55/181.54 [9447]~P1(f324(f324(f326(x94474),x94475),x94476))+P1(f324(f324(f238(f871(x94471,a859)),x94472),x94473))+~P1(f324(f324(f238(f871(f870(x94471,x94474),a859)),f324(f324(f261(x94471,x94474),x94472),f324(f16(f871(x94474,a859),x94471),x94476))),f324(f324(f261(x94471,x94474),x94473),f324(f16(f871(x94474,a859),x94471),x94476)))) % 181.55/181.54 [9494]E(x94941,x94942)+~P1(f324(f324(f326(f870(f866(x94943),f866(x94943))),f324(f324(f259(f866(x94943),f866(x94943)),f324(f324(f145(x94943),x94941),x94945)),f324(f324(f145(x94943),x94942),x94946))),f139(x94943,x94944)))+P1(f324(f324(f326(f870(x94943,x94943)),f324(f324(f259(x94943,x94943),x94941),x94942)),x94944)) % 181.55/181.54 [9495]E(x94951,x94952)+~P1(f324(f324(f326(f870(f866(x94953),f866(x94953))),f324(f324(f259(f866(x94953),f866(x94953)),f324(f324(f145(x94953),x94951),x94955)),f324(f324(f145(x94953),x94952),x94956))),f141(x94953,x94954)))+P1(f324(f324(f326(f870(x94953,x94953)),f324(f324(f259(x94953,x94953),x94951),x94952)),x94954)) % 181.55/181.54 [9496]E(x94961,x94962)+~P1(f324(f324(f326(f870(f866(x94963),f866(x94963))),f324(f324(f259(f866(x94963),f866(x94963)),f324(f324(f145(x94963),x94961),x94965)),f324(f324(f145(x94963),x94962),x94966))),f151(x94963,x94964)))+P1(f324(f324(f326(f870(x94963,x94963)),f324(f324(f259(x94963,x94963),x94961),x94962)),x94964)) % 181.55/181.54 [9533]P1(f324(f324(f326(f870(f866(x95331),f866(x95331))),f324(f324(f259(f866(x95331),f866(x95331)),f324(f324(f145(x95331),x95332),x95333)),f324(f324(f145(x95331),x95334),x95335))),f152(x95331,x95336)))+~P1(f324(f324(f326(f870(f866(x95331),f866(x95331))),f324(f324(f259(f866(x95331),f866(x95331)),x95333),x95335)),f152(x95331,x95336)))+~P1(f324(f324(f326(f870(x95331,x95331)),f324(f324(f259(x95331,x95331),x95332),x95334)),x95336)) % 181.55/181.54 [9552]P1(f324(x95521,x95522))+~P1(f324(x95521,f658(x95521,x95523,x95524,x95525,x95526)))+~P1(f324(f324(f326(x95526),x95522),f324(f324(f41(x95525,f871(x95526,a859)),x95524),x95523))) % 181.55/181.54 [9557]~P1(f324(f324(f326(f870(f866(x95571),f866(x95571))),f324(f324(f259(f866(x95571),f866(x95571)),f324(f324(f145(x95571),x95572),x95575)),f324(f324(f145(x95571),x95573),x95576))),f139(x95571,x95574)))+P1(f324(f324(f326(f870(f866(x95571),f866(x95571))),f324(f324(f259(f866(x95571),f866(x95571)),x95575),x95576)),f139(x95571,x95574)))+P1(f324(f324(f326(f870(x95571,x95571)),f324(f324(f259(x95571,x95571),x95572),x95573)),x95574)) % 181.55/181.54 [9558]~P1(f324(f324(f326(f870(f866(x95581),f866(x95581))),f324(f324(f259(f866(x95581),f866(x95581)),f324(f324(f145(x95581),x95582),x95585)),f324(f324(f145(x95581),x95583),x95586))),f141(x95581,x95584)))+P1(f324(f324(f326(f870(f866(x95581),f866(x95581))),f324(f324(f259(f866(x95581),f866(x95581)),x95585),x95586)),f141(x95581,x95584)))+P1(f324(f324(f326(f870(x95581,x95581)),f324(f324(f259(x95581,x95581),x95582),x95583)),x95584)) % 181.55/181.54 [9559]~P1(f324(f324(f326(f870(f866(x95591),f866(x95591))),f324(f324(f259(f866(x95591),f866(x95591)),f324(f324(f145(x95591),x95592),x95595)),f324(f324(f145(x95591),x95593),x95596))),f151(x95591,x95594)))+P1(f324(f324(f326(f870(f866(x95591),f866(x95591))),f324(f324(f259(f866(x95591),f866(x95591)),x95595),x95596)),f151(x95591,x95594)))+P1(f324(f324(f326(f870(x95591,x95591)),f324(f324(f259(x95591,x95591),x95592),x95593)),x95594)) % 181.55/181.54 [9646]P1(f324(x96461,x96462))+P1(f324(f324(f326(x96463),f651(x96461,x96464,x96465,x96463,x96466)),x96465))+~P1(f324(f324(f326(x96466),x96462),f324(f324(f41(x96463,f871(x96466,a859)),x96465),x96464))) % 181.55/181.54 [9657]~E(x96572,x96574)+P1(f324(f324(f326(f870(f866(x96571),f866(x96571))),f324(f324(f259(f866(x96571),f866(x96571)),f324(f324(f124(x96571),x96572),f324(f324(f145(x96571),x96573),f116(x96571)))),f324(f324(f124(x96571),x96574),f324(f324(f145(x96571),x96575),f116(x96571))))),f151(x96571,x96576)))+~P1(f324(f324(f326(f870(x96571,x96571)),f324(f324(f259(x96571,x96571),x96573),x96575)),x96576)) % 181.55/181.54 [9743]E(x97431,x97432)+~P1(f324(f324(f326(f870(f866(x97433),f866(x97433))),f324(f324(f259(f866(x97433),f866(x97433)),f324(f324(f124(x97433),x97435),f324(f324(f145(x97433),x97431),f116(x97433)))),f324(f324(f124(x97433),x97436),f324(f324(f145(x97433),x97432),f116(x97433))))),f151(x97433,x97434)))+P1(f324(f324(f326(f870(x97433,x97433)),f324(f324(f259(x97433,x97433),x97431),x97432)),x97434)) % 181.55/181.54 [9771]~P1(f324(f324(f326(f870(f866(x97711),f866(x97711))),f324(f324(f259(f866(x97711),f866(x97711)),f324(f324(f124(x97711),x97715),f324(f324(f145(x97711),x97712),f116(x97711)))),f324(f324(f124(x97711),x97716),f324(f324(f145(x97711),x97713),f116(x97711))))),f151(x97711,x97714)))+P1(f324(f324(f326(f870(f866(x97711),f866(x97711))),f324(f324(f259(f866(x97711),f866(x97711)),x97715),x97716)),f151(x97711,x97714)))+P1(f324(f324(f326(f870(x97711,x97711)),f324(f324(f259(x97711,x97711),x97712),x97713)),x97714)) % 181.55/181.54 [9791]P1(f324(x97911,x97912))+P1(f324(f324(f326(x97913),f658(x97911,x97914,x97915,x97916,x97913)),f324(x97914,f651(x97911,x97914,x97915,x97916,x97913))))+~P1(f324(f324(f326(x97913),x97912),f324(f324(f41(x97916,f871(x97913,a859)),x97915),x97914))) % 181.55/181.54 [8780]~P18(x87803,x87804,x87801)+~P1(f324(f61(x87803),x87806))+E(f324(f324(x87801,x87802),f324(f324(f64(x87803,x87804,x87801),x87805),f324(f324(f22(f871(x87803,a859)),x87806),f324(f324(f302(x87803),x87802),f191(f871(x87803,a859)))))),f324(f324(f64(x87803,x87804,x87801),x87805),f324(f324(f302(x87803),x87802),x87806))) % 181.55/181.54 [8864]~E(f324(f324(f173(x88641,x88642),x88644),x88645),f324(f233(x88642),x88646))+~P1(f324(f324(x88643,x88645),x88646))+E(f324(f324(f173(x88641,x88642),f324(f130(f870(x88641,x88642),f324(f263(x88641,x88642,a859),x88643)),x88644)),x88645),f324(f233(x88642),x88646)) % 181.55/181.54 [9077]~P1(f324(f324(f326(x90775),x90773),x90776))+P1(f324(f324(f238(f871(x90771,a859)),f324(x90772,x90773)),x90774))+~P1(f324(f324(f238(f871(x90771,a859)),f324(f324(f41(x90775,f871(x90771,a859)),x90776),x90772)),x90774)) % 181.55/181.54 [9717]~P9(x97171,x97175,x97174)+P1(f324(f324(f326(f870(x97171,x97171)),f324(f324(f259(x97171,x97171),x97172),x97173)),x97174))+~P1(f324(f324(f326(x97171),x97176),f324(f324(f104(f871(x97171,a859)),f324(f278(x97171,x97171,x97174),f324(f324(f302(x97171),x97172),f191(f871(x97171,a859))))),f324(f278(x97171,x97171,x97174),f324(f324(f302(x97171),x97173),f191(f871(x97171,a859))))))) % 181.55/181.54 [8505]~P116(x85052)+~E(f324(f324(f81(x85052),f324(f324(f82(x85052),x85054),x85055)),x85051),f324(f324(f81(x85052),f324(f324(f82(x85052),x85053),x85055)),x85056))+E(x85051,f324(f324(f81(x85052),f324(f324(f82(x85052),f324(f324(f22(x85052),x85053),x85054)),x85055)),x85056)) % 181.55/181.54 [8506]~P116(x85061)+~E(f324(f324(f81(x85061),f324(f324(f82(x85061),x85062),x85064)),x85065),f324(f324(f81(x85061),f324(f324(f82(x85061),x85063),x85064)),x85066))+E(f324(f324(f81(x85061),f324(f324(f82(x85061),f324(f324(f22(x85061),x85062),x85063)),x85064)),x85065),x85066) % 181.55/181.54 [8689]~P116(x86891)+E(f324(f324(f81(x86891),f324(f324(f82(x86891),x86892),x86893)),x86894),f324(f324(f81(x86891),f324(f324(f82(x86891),x86895),x86893)),x86896))+~E(x86896,f324(f324(f81(x86891),f324(f324(f82(x86891),f324(f324(f22(x86891),x86892),x86895)),x86893)),x86894)) % 181.55/181.54 [8690]~P116(x86901)+E(f324(f324(f81(x86901),f324(f324(f82(x86901),x86902),x86903)),x86904),f324(f324(f81(x86901),f324(f324(f82(x86901),x86905),x86903)),x86906))+~E(f324(f324(f81(x86901),f324(f324(f82(x86901),f324(f324(f22(x86901),x86902),x86905)),x86903)),x86904),x86906) % 181.55/181.54 [9016]~P1(f324(f324(x90164,x90165),x90166))+~P1(f324(f324(x90163,x90165),x90166))+P1(f324(f324(f324(f324(f104(f871(x90161,f871(x90162,a859))),x90163),x90164),x90165),x90166)) % 181.55/181.54 [9274]P1(f324(f324(x92741,x92742),x92743))+P1(f324(f324(x92744,x92742),x92743))+~P1(f324(f324(f324(f324(f113(f871(x92745,f871(x92746,a859))),x92744),x92741),x92742),x92743)) % 181.55/181.54 [9572]~P123(x95721)+~P1(f324(f324(f238(x95721),f324(f324(f81(x95721),f324(f324(f82(x95721),x95724),x95725)),x95722)),f324(f324(f81(x95721),f324(f324(f82(x95721),x95723),x95725)),x95726)))+P1(f324(f324(f238(x95721),x95722),f324(f324(f81(x95721),f324(f324(f82(x95721),f324(f324(f22(x95721),x95723),x95724)),x95725)),x95726))) % 181.55/181.54 [9573]~P123(x95731)+~P1(f324(f324(f239(x95731),f324(f324(f81(x95731),f324(f324(f82(x95731),x95734),x95735)),x95732)),f324(f324(f81(x95731),f324(f324(f82(x95731),x95733),x95735)),x95736)))+P1(f324(f324(f239(x95731),x95732),f324(f324(f81(x95731),f324(f324(f82(x95731),f324(f324(f22(x95731),x95733),x95734)),x95735)),x95736))) % 181.55/181.54 [9597]~P123(x95971)+P1(f324(f324(f238(x95971),f324(f324(f81(x95971),f324(f324(f82(x95971),x95972),x95973)),x95974)),f324(f324(f81(x95971),f324(f324(f82(x95971),x95975),x95973)),x95976)))+~P1(f324(f324(f238(x95971),x95974),f324(f324(f81(x95971),f324(f324(f82(x95971),f324(f324(f22(x95971),x95975),x95972)),x95973)),x95976))) % 181.55/181.54 [9598]~P123(x95981)+P1(f324(f324(f239(x95981),f324(f324(f81(x95981),f324(f324(f82(x95981),x95982),x95983)),x95984)),f324(f324(f81(x95981),f324(f324(f82(x95981),x95985),x95983)),x95986)))+~P1(f324(f324(f239(x95981),x95984),f324(f324(f81(x95981),f324(f324(f82(x95981),f324(f324(f22(x95981),x95985),x95982)),x95983)),x95986))) % 181.55/181.54 [9705]~P123(x97051)+~P1(f324(f324(f238(x97051),f324(f324(f81(x97051),f324(f324(f82(x97051),x97052),x97054)),x97055)),f324(f324(f81(x97051),f324(f324(f82(x97051),x97053),x97054)),x97056)))+P1(f324(f324(f238(x97051),f324(f324(f81(x97051),f324(f324(f82(x97051),f324(f324(f22(x97051),x97052),x97053)),x97054)),x97055)),x97056)) % 181.55/181.54 [9706]~P123(x97061)+~P1(f324(f324(f239(x97061),f324(f324(f81(x97061),f324(f324(f82(x97061),x97062),x97064)),x97065)),f324(f324(f81(x97061),f324(f324(f82(x97061),x97063),x97064)),x97066)))+P1(f324(f324(f239(x97061),f324(f324(f81(x97061),f324(f324(f82(x97061),f324(f324(f22(x97061),x97062),x97063)),x97064)),x97065)),x97066)) % 181.55/181.54 [9754]~P123(x97541)+P1(f324(f324(f238(x97541),f324(f324(f81(x97541),f324(f324(f82(x97541),x97542),x97543)),x97544)),f324(f324(f81(x97541),f324(f324(f82(x97541),x97545),x97543)),x97546)))+~P1(f324(f324(f238(x97541),f324(f324(f81(x97541),f324(f324(f82(x97541),f324(f324(f22(x97541),x97542),x97545)),x97543)),x97544)),x97546)) % 181.55/181.54 [9755]~P123(x97551)+P1(f324(f324(f239(x97551),f324(f324(f81(x97551),f324(f324(f82(x97551),x97552),x97553)),x97554)),f324(f324(f81(x97551),f324(f324(f82(x97551),x97555),x97553)),x97556)))+~P1(f324(f324(f239(x97551),f324(f324(f81(x97551),f324(f324(f82(x97551),f324(f324(f22(x97551),x97552),x97555)),x97553)),x97554)),x97556)) % 181.55/181.54 [9925]~P72(x99252)+~P1(f324(f61(x99251),x99256))+E(f324(f324(f6(x99251,x99252),f324(f324(f18(x99251,x99252,x99252),f324(f324(f18(x99251,x99252,f871(x99252,x99252)),f324(f324(f8(a859,f871(x99252,f871(x99252,x99252)),x99251),f99(x99252)),x99253)),x99254)),x99255)),x99256),f324(f324(f81(x99252),f324(f324(f6(x99251,x99252),x99254),f324(f324(f104(f871(x99251,a859)),x99256),f324(f244(x99251),x99253)))),f324(f324(f6(x99251,x99252),x99255),f324(f324(f104(f871(x99251,a859)),x99256),f324(f80(f871(x99251,a859)),f324(f244(x99251),x99253)))))) % 181.55/181.54 [9983]P1(f324(f324(f326(x99832),x99834),x99836))+P1(f324(f324(f326(x99832),x99835),x99836))+E(f324(f304(x99831,x99832,f324(f324(f7(x99831,x99832,x99832),f324(f324(f7(x99831,x99832,f871(x99832,x99832)),f324(f324(f8(a859,f871(x99832,f871(x99832,x99832)),x99831),f99(x99832)),f324(f324(f7(x99831,f871(x99831,a859),a859),f326(x99831)),x99833))),x99834)),x99835)),x99836),f191(f871(x99831,a859))) % 181.55/181.54 [9984]P1(f324(f324(f326(x99842),x99845),x99846))+~P1(f324(f324(f326(x99842),x99844),x99846))+E(f324(f304(x99841,x99842,f324(f324(f7(x99841,x99842,x99842),f324(f324(f7(x99841,x99842,f871(x99842,x99842)),f324(f324(f8(a859,f871(x99842,f871(x99842,x99842)),x99841),f99(x99842)),f324(f324(f7(x99841,f871(x99841,a859),a859),f326(x99841)),x99843))),x99844)),x99845)),x99846),x99843) % 181.55/181.54 [9985]P1(f324(f324(f326(x99852),x99854),x99856))+~P1(f324(f324(f326(x99852),x99855),x99856))+E(f324(f304(x99851,x99852,f324(f324(f7(x99851,x99852,x99852),f324(f324(f7(x99851,x99852,f871(x99852,x99852)),f324(f324(f8(a859,f871(x99852,f871(x99852,x99852)),x99851),f99(x99852)),f324(f324(f7(x99851,f871(x99851,a859),a859),f326(x99851)),x99853))),x99854)),x99855)),x99856),f324(f80(f871(x99851,a859)),x99853)) % 181.55/181.54 [9986]~P1(f324(f324(f326(x99862),x99864),x99866))+~P1(f324(f324(f326(x99862),x99865),x99866))+E(f324(f304(x99861,x99862,f324(f324(f7(x99861,x99862,x99862),f324(f324(f7(x99861,x99862,f871(x99862,x99862)),f324(f324(f8(a859,f871(x99862,f871(x99862,x99862)),x99861),f99(x99862)),f324(f324(f7(x99861,f871(x99861,a859),a859),f326(x99861)),x99863))),x99864)),x99865)),x99866),f247(f871(x99861,a859))) % 181.55/181.54 [8538]E(x85381,x85382)+~P54(x85384,x85385,x85383,x85386,x85387)+~E(f324(x85383,x85381),f324(x85383,x85382)) % 181.55/181.54 [6941]E(f324(f235(f869(x69411),x69412,f203(x69411),x69413),f324(x69414,x69415)),f324(f233(x69411),x69416))+~E(f324(x69414,x69415),f324(f233(x69412),x69417))+~E(f324(x69413,x69417),f324(f233(x69411),x69416)) % 181.55/181.54 [8567]~P11(x85676,x85675,x85677,x85674,x85671)+E(f324(f324(x85671,x85672),x85673),x85674)+P1(f324(f61(x85675),x85673)) % 181.55/181.54 [9434]P44(x94341,x94342,x94343,x94344,x94345,f324(f324(x94343,x94346),x94347))+~E(f324(f324(x94343,x94346),x94347),x94344)+~E(x94345,f191(f871(x94341,a859))) % 181.55/181.54 [9619]~P1(f324(x96196,x96193))+~P1(f324(f324(f326(f870(x96192,x96192)),f324(f324(f259(x96192,x96192),x96194),x96195)),f324(x96197,x96193)))+P1(f324(f324(f326(f870(f870(x96191,x96192),f870(x96191,x96192))),f324(f324(f259(f870(x96191,x96192),f870(x96191,x96192)),f324(f324(f259(x96191,x96192),x96193),x96194)),f324(f324(f259(x96191,x96192),x96193),x96195))),f276(x96191,x96192,x96196,x96197))) % 181.55/181.54 [10038]~P44(x100382,x100387,x100383,x100386,x100381,f324(f324(x100383,x100385),x100384))+E(f324(f324(x100383,f465(x100384,x100385,x100381,x100386,x100383,x100387,x100382)),f478(x100384,x100385,x100381,x100386,x100383,x100387,x100382)),f324(f324(x100383,x100385),x100384))+E(x100381,f191(f871(x100382,a859))) % 181.55/181.54 [10039]~P44(x100397,x100396,x100391,x100394,x100395,f324(f324(x100391,x100392),x100393))+E(f324(f324(x100391,f465(x100393,x100392,x100395,x100394,x100391,x100396,x100397)),f478(x100393,x100392,x100395,x100394,x100391,x100396,x100397)),f324(f324(x100391,x100392),x100393))+E(f324(f324(x100391,x100392),x100393),x100394) % 181.55/181.54 [9114]~P36(x91141,x91142,x91143,x91145,x91147)+P36(x91141,x91142,x91143,f324(f324(f145(x91141),x91144),x91145),f324(f324(f145(x91142),x91146),x91147))+~P1(f324(f324(x91143,x91144),x91146)) % 181.55/181.54 [9134]P36(x91341,x91342,x91343,x91344,x91345)+~P36(x91341,x91342,x91343,f324(f324(f124(x91341),x91346),x91344),f324(f324(f124(x91342),x91347),x91345))+~E(f324(f192(f866(x91341)),x91346),f324(f192(f866(x91342)),x91347)) % 181.55/181.54 [9135]P36(x91351,x91352,x91353,x91354,x91355)+~P36(x91351,x91352,x91353,f324(f324(f124(x91351),x91354),x91356),f324(f324(f124(x91352),x91355),x91357))+~E(f324(f192(f866(x91351)),x91354),f324(f192(f866(x91352)),x91355)) % 181.55/181.54 [9337]~P36(x93371,x93372,x93373,x93375,x93377)+~P36(x93371,x93372,x93373,x93374,x93376)+P36(x93371,x93372,x93373,f324(f324(f124(x93371),x93374),x93375),f324(f324(f124(x93372),x93376),x93377)) % 181.55/181.54 [9694]~P1(f324(f66(x96941,x96944,x96945,x96946,x96943),x96947))+P1(f324(f66(x96941,x96944,x96945,x96946,f324(f324(f302(x96941),x96942),x96943)),f324(f324(x96945,x96942),x96947)))+P1(f324(f324(f326(x96941),x96942),x96943)) % 181.55/181.54 [9823]~P27(x98233,x98231,x98234,f247(f871(x98233,a859)))+E(f324(f324(f173(x98231,x98232),f324(f324(f148(f870(x98233,x98232),f870(x98231,x98232)),f324(f263(x98233,x98232,f870(x98231,x98232)),f324(f324(f8(x98231,f871(x98232,f870(x98231,x98232)),x98233),f259(x98231,x98232)),x98234))),x98235)),f324(x98234,x98236)),f324(f233(x98232),x98237))+~E(f324(f324(f173(x98233,x98232),x98235),x98236),f324(f233(x98232),x98237)) % 181.55/181.54 [10059]~P44(x100592,x100597,x100596,x100595,x100591,f324(f324(x100596,x100594),x100593))+E(x100591,f191(f871(x100592,a859)))+P1(f324(f324(f326(x100592),f465(x100593,x100594,x100591,x100595,x100596,x100597,x100592)),x100591)) % 181.55/181.54 [10060]~P44(x100605,x100607,x100601,x100604,x100606,f324(f324(x100601,x100602),x100603))+E(f324(f324(x100601,x100602),x100603),x100604)+P1(f324(f324(f326(x100605),f465(x100603,x100602,x100606,x100604,x100601,x100607,x100605)),x100606)) % 181.55/181.54 [6732]~E(x67325,x67327)+~E(x67326,x67324)+E(f324(f324(f324(f324(f72(x67321,f869(x67322)),x67323),x67324),f324(f233(x67322),x67325)),x67326),f324(f233(x67322),x67327)) % 181.55/181.54 [6858]E(x68581,x68582)+~E(f324(x68585,x68581),f324(f233(x68584),x68587))+E(f324(f324(f324(f324(f72(x68583,f869(x68584)),x68585),x68582),f324(f233(x68584),x68586)),x68581),f324(f233(x68584),x68587)) % 181.55/181.54 [7570]E(x75701,x75702)+~E(x75703,x75704)+~E(f324(f324(f324(f324(f72(x75705,f869(x75706)),x75707),x75704),f324(f233(x75706),x75701)),x75703),f324(f233(x75706),x75702)) % 181.55/181.54 [7634]E(x76341,x76342)+E(f324(x76343,x76344),f324(f233(x76345),x76341))+~E(f324(f324(f324(f324(f72(x76346,f869(x76345)),x76343),x76347),f324(f233(x76345),x76342)),x76344),f324(f233(x76345),x76341)) % 181.55/181.54 [7635]E(x76351,x76352)+E(f324(x76353,x76351),f324(f233(x76354),x76355))+~E(f324(f324(f324(f324(f72(x76356,f869(x76354)),x76353),x76352),f324(f233(x76354),x76357)),x76351),f324(f233(x76354),x76355)) % 181.55/181.54 [8805]~P23(x88054,x88055,x88056,x88057,x88051)+~P1(f324(f61(x88055),x88053))+E(f324(f324(x88051,x88052),x88053),f324(f324(f324(f65(x88054,x88055,x88056),x88052),x88057),x88053)) % 181.55/181.54 [8806]~P11(x88064,x88065,x88066,x88067,x88061)+~P1(f324(f61(x88065),x88063))+E(f324(f324(x88061,x88062),x88063),f324(f324(f324(f65(x88064,x88065,x88066),x88062),x88067),x88063)) % 181.55/181.54 [9395]~P26(x93951,x93952,f324(f324(f302(f864(x93951)),f324(f324(f324(f93(x93951),x93953),x93954),x93957)),f191(f871(f864(x93951),a859))))+P26(x93951,x93952,f324(f324(f302(f864(x93951)),f324(f324(f324(f93(x93951),x93953),f33(x93954,x93955)),x93956)),f191(f871(f864(x93951),a859))))+~P26(x93951,x93952,f324(f324(f302(f864(x93951)),f324(f324(f324(f93(x93951),x93957),x93955),x93956)),f191(f871(f864(x93951),a859)))) % 181.55/181.54 [9592]~P25(x95923,x95924,x95925,x95927,x95926,x95921)+~P1(f324(f61(x95924),x95922))+E(f324(x95921,x95922),f324(f324(f324(f65(x95923,x95924,x95925),x95926),x95927),x95922)) % 181.55/181.54 [9749]P44(x97491,x97492,x97493,x97494,x97495,f324(f324(x97493,x97496),x97497))+~P44(x97491,x97492,x97493,x97494,f324(f324(f22(f871(x97491,a859)),x97495),f324(f324(f302(x97491),x97496),f191(f871(x97491,a859)))),x97497)+~P1(f324(f324(f326(x97491),x97496),x97495)) % 181.55/181.54 [10014]~P26(x100141,x100142,f324(f324(f302(f864(x100141)),f324(f324(f324(f93(x100141),f95(x100141,x100143,x100144)),x100145),x100147)),f191(f871(f864(x100141),a859))))+P26(x100141,x100142,f324(f324(f302(f864(x100141)),f324(f324(f324(f93(x100141),x100143),f30(x100144,x100145,x100146)),x100147)),f191(f871(f864(x100141),a859))))+~P26(x100141,x100142,f324(f324(f302(f864(x100141)),f324(f324(f324(f93(x100141),f95(x100141,x100143,f324(f73(a859,a859,a860,a319),x100144))),x100146),x100147)),f191(f871(f864(x100141),a859)))) % 181.55/181.54 [10077]P26(x100777,x100776,f324(f324(f302(f864(x100777)),f324(f324(f324(f93(x100777),x100771),x100774),x100772)),f191(f871(f864(x100777),a859))))+~P26(x100777,x100776,f324(f324(f302(f864(x100777)),f324(f324(f324(f93(x100777),x100775),x100774),x100773)),f191(f871(f864(x100777),a859))))+P1(f324(f324(x100771,f346(x100772,x100771,x100773,x100774,x100775,x100776,x100777)),f356(x100772,x100771,x100773,x100774,x100775,x100776,x100777))) % 181.55/181.54 [10086]~P44(x100862,x100863,x100864,x100865,x100861,f324(f324(x100864,x100867),x100866))+P44(x100862,x100863,x100864,x100865,f324(f324(f22(f871(x100862,a859)),x100861),f324(f324(f302(x100862),f465(x100866,x100867,x100861,x100865,x100864,x100863,x100862)),f191(f871(x100862,a859)))),f478(x100866,x100867,x100861,x100865,x100864,x100863,x100862))+E(x100861,f191(f871(x100862,a859))) % 181.55/181.54 [10087]~P44(x100875,x100876,x100871,x100874,x100877,f324(f324(x100871,x100872),x100873))+P44(x100875,x100876,x100871,x100874,f324(f324(f22(f871(x100875,a859)),x100877),f324(f324(f302(x100875),f465(x100873,x100872,x100877,x100874,x100871,x100876,x100875)),f191(f871(x100875,a859)))),f478(x100873,x100872,x100877,x100874,x100871,x100876,x100875))+E(f324(f324(x100871,x100872),x100873),x100874) % 181.55/181.54 [10088]~P26(x100881,x100882,f324(f324(f302(f864(x100881)),f324(f324(f324(f93(x100881),x100887),x100884),x100886)),f191(f871(f864(x100881),a859))))+P26(x100881,x100882,f324(f324(f302(f864(x100881)),f324(f324(f324(f93(x100881),x100883),x100884),x100885)),f191(f871(f864(x100881),a859))))+~P1(f324(f324(x100885,f346(x100885,x100883,x100886,x100884,x100887,x100882,x100881)),f366(x100885,x100883,x100886,x100884,x100887,x100882,x100881))) % 181.55/181.54 [9122]E(f182(x91221,x91222,x91223,x91224,f324(f324(f153(x91222,x91225),x91226),x91227)),f182(x91221,x91222,x91223,x91224,x91225))+~P1(f324(f324(f239(a865),x91226),f324(f192(f866(x91222)),x91225)))+~P1(f324(f324(f238(a865),f324(f192(f866(x91221)),x91224)),x91226)) % 181.55/181.54 [9420]P1(f324(f324(f238(f871(f870(x94201,x94202),a859)),f324(f324(f281(x94201,x94203,x94202),x94204),x94205)),f324(f324(f281(x94201,x94203,x94202),x94206),x94207)))+~P1(f324(f324(f238(f871(f870(x94203,x94202),a859)),x94205),x94207))+~P1(f324(f324(f238(f871(f870(x94201,x94203),a859)),x94204),x94206)) % 181.55/181.54 [9760]~P1(f324(f324(f326(x97601),x97606),x97605))+P1(f324(f66(x97601,x97602,x97603,x97604,x97605),f324(f324(x97603,x97606),x97607)))+~P1(f324(f66(x97601,x97602,x97603,x97604,f324(f324(f22(f871(x97601,a859)),x97605),f324(f324(f302(x97601),x97606),f191(f871(x97601,a859))))),x97607)) % 181.55/181.54 [10141]~P140(x101411)+~P27(f870(x101412,x101413),x101411,f324(f263(x101412,x101413,x101411),f324(f324(f7(x101412,f871(x101413,x101411),f871(x101413,x101411)),f324(f324(f8(f871(x101411,x101411),f871(f871(x101413,x101411),f871(x101413,x101411)),x101412),f8(x101411,x101411,x101413)),f324(f324(f8(x101411,f871(x101411,x101411),x101412),f82(x101411)),x101414))),x101415)),f324(f324(f261(x101412,x101413),x101416),f324(f16(f871(x101413,a859),x101412),x101417)))+E(f324(f324(f6(x101411,x101411),f34(x101411)),f324(f244(x101411),f324(f324(f8(f871(x101412,a859),a859,x101411),f88(x101412)),f324(f324(f8(f871(x101412,f871(x101413,a859)),f871(x101412,a859),x101411),f324(f8(f871(x101413,a859),a859,x101412),f88(x101413))),f324(f324(f7(x101411,f871(x101412,f871(x101413,a859)),f871(x101412,f871(x101413,a859))),f324(f324(f8(f871(x101412,f871(f871(x101413,a859),f871(x101413,a859))),f871(f871(x101412,f871(x101413,a859)),f871(x101412,f871(x101413,a859))),x101411),f18(x101412,f871(x101413,a859),f871(x101413,a859))),f324(f324(f8(f871(x101412,f871(x101413,f871(a859,a859))),f871(x101412,f871(f871(x101413,a859),f871(x101413,a859))),x101411),f324(f8(f871(x101413,f871(a859,a859)),f871(f871(x101413,a859),f871(x101413,a859)),x101412),f18(x101413,a859,a859))),f324(f324(f8(f871(x101412,f871(x101413,a859)),f871(x101412,f871(x101413,f871(a859,a859))),x101411),f324(f8(f871(x101413,a859),f871(x101413,f871(a859,a859)),x101412),f324(f8(a859,f871(a859,a859),x101413),a322))),f324(f324(f7(x101411,f871(x101412,f871(x101413,x101411)),f871(x101412,f871(x101413,a859))),f324(f324(f8(f871(f871(x101413,x101411),f871(x101413,a859)),f871(f871(x101412,f871(x101413,x101411)),f871(x101412,f871(x101413,a859))),x101411),f8(f871(x101413,x101411),f871(x101413,a859),x101412)),f324(f324(f8(f871(x101411,a859),f871(f871(x101413,x101411),f871(x101413,a859)),x101411),f8(x101411,a859,x101413)),a321))),f324(f324(f7(x101412,f871(x101413,x101411),f871(x101413,x101411)),f324(f324(f8(f871(x101411,x101411),f871(f871(x101413,x101411),f871(x101413,x101411)),x101412),f8(x101411,x101411,x101413)),f324(f324(f8(x101411,f871(x101411,x101411),x101412),f82(x101411)),x101414))),x101415)))))),f324(f324(f7(x101412,f871(x101413,a859),f871(x101413,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x101413,a859),f871(x101413,a859)),x101412),f8(a859,a859,x101413)),f324(f324(f8(a859,f871(a859,a859),x101412),a322),f324(f324(f7(x101412,f871(x101412,a859),a859),f326(x101412)),x101416)))),f324(f324(f7(x101413,f871(x101413,a859),a859),f326(x101413)),x101417))))))),f324(f324(f82(x101411),f324(f324(f6(x101412,x101411),x101414),x101416)),f324(f324(f6(x101413,x101411),x101415),x101417))) % 181.55/181.54 [9424]~P28(x94241,x94243,x94245,x94246,x94248)+~P28(x94243,x94242,x94244,x94248,x94247)+P28(x94241,x94242,f324(f73(x94243,x94242,x94241,x94244),x94245),x94246,x94247) % 181.55/181.54 [9453]P28(x94531,x94532,x94533,x94534,x94535)+~P28(x94536,x94531,x94537,x94538,x94534)+~P28(x94536,x94532,f324(f73(x94531,x94532,x94536,x94533),x94537),x94538,x94535) % 181.55/181.54 [9590]~P1(f324(f324(x95904,x95906),x95908))+~P1(f324(f324(x95905,x95908),x95907))+P1(f324(f324(f260(x95901,x95902,x95903,x95904,x95905),x95906),x95907)) % 181.55/181.54 [9182]~P21(x91828,x91821,x91823,x91825)+~P1(f324(f61(x91828),x91826))+E(f324(f73(x91821,x91821,x91822,f324(x91823,x91824)),f324(f73(x91821,x91821,x91822,f324(x91825,x91826)),x91827)),f324(f73(x91821,x91821,x91822,f324(x91825,x91826)),f324(f73(x91821,x91821,x91822,f324(x91823,x91824)),x91827))) % 181.55/181.54 [9580]~P24(x95807,x95802,x95805,x95808,x95806,x95801)+~P1(f324(f61(x95802),x95804))+E(f324(x95801,f324(f324(f302(x95802),x95803),x95804)),f324(f324(x95805,f324(x95806,x95803)),f324(x95801,x95804))) % 181.55/181.54 [9703]~P27(x97032,x97034,x97036,x97038)+~P27(x97031,x97033,x97035,x97037)+P27(f870(x97031,x97032),f870(x97033,x97034),f264(x97031,x97033,x97032,x97034,x97035,x97036),f324(f324(f261(x97031,x97032),x97037),f324(f16(f871(x97032,a859),x97031),x97038))) % 181.55/181.54 [9361]P1(f324(f324(f326(f870(x93611,x93612)),f324(f324(f259(x93611,x93612),x93613),x93614)),f324(f324(f281(x93611,x93615,x93612),x93616),x93617)))+~P1(f324(f324(f326(f870(x93611,x93615)),f324(f324(f259(x93611,x93615),x93613),x93618)),x93616))+~P1(f324(f324(f326(f870(x93615,x93612)),f324(f324(f259(x93615,x93612),x93618),x93614)),x93617)) % 181.55/181.54 [9560]~P1(f324(f324(f238(f871(f870(x95603,x95602),a859)),x95605),f324(f324(f261(x95603,x95602),x95608),f324(f16(f871(x95602,a859),x95603),x95607))))+~P1(f324(f324(f238(f871(f870(x95601,x95603),a859)),x95604),f324(f324(f261(x95601,x95603),x95606),f324(f16(f871(x95603,a859),x95601),x95608))))+P1(f324(f324(f238(f871(f870(x95601,x95602),a859)),f324(f324(f281(x95601,x95603,x95602),x95604),x95605)),f324(f324(f261(x95601,x95602),x95606),f324(f16(f871(x95602,a859),x95601),x95607)))) % 181.55/181.54 [9614]~E(x96143,x96145)+P1(f324(f324(f326(f870(f870(x96141,x96142),f870(x96141,x96142))),f324(f324(f259(f870(x96141,x96142),f870(x96141,x96142)),f324(f324(f259(x96141,x96142),x96143),x96144)),f324(f324(f259(x96141,x96142),x96145),x96146))),f316(x96141,x96142,x96147,x96148)))+~P1(f324(f324(f326(f870(x96142,x96142)),f324(f324(f259(x96142,x96142),x96144),x96146)),x96148)) % 181.55/181.54 [9726]E(x97261,x97262)+~P1(f324(f324(f326(f870(f870(x97263,x97265),f870(x97263,x97265))),f324(f324(f259(f870(x97263,x97265),f870(x97263,x97265)),f324(f324(f259(x97263,x97265),x97261),x97266)),f324(f324(f259(x97263,x97265),x97262),x97267))),f316(x97263,x97265,x97264,x97268)))+P1(f324(f324(f326(f870(x97263,x97263)),f324(f324(f259(x97263,x97263),x97261),x97262)),x97264)) % 181.55/181.54 [9742]~P1(f324(f324(f326(f870(f870(x97421,x97425),f870(x97421,x97425))),f324(f324(f259(f870(x97421,x97425),f870(x97421,x97425)),f324(f324(f259(x97421,x97425),x97422),x97426)),f324(f324(f259(x97421,x97425),x97423),x97427))),f316(x97421,x97425,x97424,x97428)))+P1(f324(f324(f326(f870(x97421,x97421)),f324(f324(f259(x97421,x97421),x97422),x97423)),x97424))+P1(f324(f324(f326(f870(x97425,x97425)),f324(f324(f259(x97425,x97425),x97426),x97427)),x97428)) % 181.55/181.54 [9647]~P25(x96477,x96475,x96471,x96478,x96472,x96474)+~P1(f324(f61(x96475),x96476))+E(f324(f324(x96471,f324(x96472,x96473)),f324(x96474,f324(f324(f22(f871(x96475,a859)),x96476),f324(f324(f302(x96475),x96473),f191(f871(x96475,a859)))))),f324(x96474,f324(f324(f302(x96475),x96473),x96476))) % 181.55/181.54 [9142]~P1(f324(f324(f324(x91425,x91428),x91426),x91427))+~P1(f324(f324(f326(x91421),x91428),x91424))+P1(f324(f324(f324(f324(f41(x91421,f871(x91422,f871(x91423,a859))),x91424),x91425),x91426),x91427)) % 181.55/181.54 [9348]P1(f324(f324(f324(x93481,x93482),x93483),x93484))+~P1(f324(f324(f326(x93485),x93482),x93486))+~P1(f324(f324(f324(f324(f42(x93485,f871(x93487,f871(x93488,a859))),x93486),x93481),x93483),x93484)) % 181.55/181.54 [9553]~P23(x95533,x95532,x95534,x95538,x95531)+~P1(f324(f61(x95532),x95537))+E(f324(f324(x95531,f324(f324(f18(x95532,x95533,x95533),f324(f324(f8(x95533,f871(x95533,x95533),x95532),x95534),x95535)),x95536)),x95537),f324(f324(x95534,f324(f324(x95531,x95535),x95537)),f324(f324(x95531,x95536),x95537))) % 181.55/181.54 [9831]~E(f324(f303(x98312,x98314,x98316),x98318),x983110)+~E(f324(f303(x98311,x98313,x98315),x98317),x98319)+E(f324(f303(f870(x98311,x98312),f870(x98313,x98314),f264(x98311,x98313,x98312,x98314,x98315,x98316)),f324(f324(f261(x98311,x98312),x98317),f324(f16(f871(x98312,a859),x98311),x98318))),f324(f324(f261(x98313,x98314),x98319),f324(f16(f871(x98314,a859),x98313),x983110))) % 181.55/181.54 [4822]~P105(x48222)+~P16(x48222,x48221)+P16(x48222,f117(x48222,x48221))+E(x48221,f116(x48222)) % 181.55/181.54 [4823]~P105(x48232)+~P16(x48232,x48231)+P16(x48232,f715(x48231,x48232))+E(x48231,f116(x48232)) % 181.55/181.54 [5050]~P6(x50502)+E(f10(x50502,x50501),f40(x50502,x50501))+E(x50501,f191(f871(x50502,a859)))+~P1(f324(f61(x50502),x50501)) % 181.55/181.54 [5051]~P6(x50512)+E(f13(x50512,x50511),f39(x50512,x50511))+E(x50511,f191(f871(x50512,a859)))+~P1(f324(f61(x50512),x50511)) % 181.55/181.54 [5198]~P105(x51982)+~P16(x51982,x51981)+E(x51981,f116(x51982))+E(f324(f324(f145(x51982),f748(x51981,x51982)),f715(x51981,x51982)),x51981) % 181.55/181.54 [5980]~P94(x59802)+E(x59801,f191(f871(x59802,a859)))+P1(f324(f324(f238(x59802),f10(x59802,x59801)),f13(x59802,x59801)))+~P1(f324(f61(x59802),x59801)) % 181.55/181.54 [5992]~P40(x59922)+~P40(x59921)+E(x59921,x59922)+~E(f324(f303(a1,a865,a107),x59921),f324(f303(a1,a865,a107),x59922)) % 181.55/181.54 [8994]~P117(x89941)+~P1(f324(f324(f326(x89941),x89942),f112(x89941)))+P1(f324(f324(f239(x89941),f324(f324(f81(x89941),f324(f324(f81(x89941),f79(x89941)),x89942)),x89942)),f2(x89941)))+~P1(f324(f324(f239(x89941),x89942),f2(x89941))) % 181.55/181.54 [9235]~P117(x92351)+~P1(f324(f324(f326(x92351),x92352),f112(x92351)))+~P1(f324(f324(f239(x92351),f324(f324(f81(x92351),f324(f324(f81(x92351),f79(x92351)),x92352)),x92352)),f2(x92351)))+P1(f324(f324(f239(x92351),x92352),f2(x92351))) % 181.55/181.54 [4878]~P110(x48782)+~P140(x48782)+E(x48781,f2(a865))+E(f324(f324(f249(x48782),f2(x48782)),x48781),f2(x48782)) % 181.55/181.54 [4881]~P110(x48811)+~P140(x48811)+~E(x48812,f2(a865))+E(f324(f324(f249(x48811),f2(x48811)),x48812),f79(x48811)) % 181.55/181.54 [5037]~P134(x50372)+E(x50371,f79(x50372))+E(x50371,f324(f80(x50372),f79(x50372)))+~E(f324(f324(f82(x50372),x50371),x50371),f79(x50372)) % 181.55/181.54 [5278]~P86(x52782)+E(x52781,f2(x52782))+E(f83(x52782,x52781),f324(f80(x52782),f79(x52782)))+P1(f324(f324(f239(x52782),f2(x52782)),x52781)) % 181.55/181.54 [5511]~P86(x55112)+E(f83(x55112,x55111),f79(x55112))+E(x55111,f2(x55112))+~P1(f324(f324(f239(x55112),f2(x55112)),x55111)) % 181.55/181.54 [5520]E(x55201,x55202)+~E(f324(f106(a865),x55201),f324(f106(a865),x55202))+P1(f324(a196,f324(f106(a1),x55202)))+P1(f324(a196,f324(f106(a1),x55201))) % 181.55/181.54 [5569]~P89(x55691)+~E(x55692,f2(x55691))+E(f324(f324(f81(x55691),x55692),x55692),f2(x55691))+~P1(f324(f324(f326(x55691),x55692),f112(x55691))) % 181.55/181.54 [5607]E(x56071,f2(a1))+~E(f324(f324(f38(a1),x56072),x56071),f2(a1))+P1(f324(f324(f239(a1),x56071),x56072))+P1(f324(f324(f239(a1),x56072),x56071)) % 181.55/181.54 [5638]E(x56381,f2(a1))+~E(f324(f324(f38(a1),x56382),x56381),f2(a1))+P1(f324(f324(f238(a1),x56382),f2(a1)))+P1(f324(f324(f239(a1),x56382),x56381)) % 181.55/181.54 [5672]E(x56721,f2(a1))+~E(f324(f324(f38(a1),x56722),x56721),f2(a1))+P1(f324(f324(f238(a1),f2(a1)),x56722))+P1(f324(f324(f239(a1),x56721),x56722)) % 181.55/181.54 [5706]~P89(x57062)+E(x57061,f2(x57062))+~E(f324(f324(f81(x57062),x57061),x57061),f2(x57062))+~P1(f324(f324(f326(x57062),x57061),f112(x57062))) % 181.55/181.54 [5766]E(f324(f106(a865),x57661),f324(f106(a865),x57662))+~E(f324(f106(a1),x57662),f2(a1))+P1(f324(a196,f324(f106(a1),x57662)))+~P1(f324(a196,f324(f106(a1),x57661))) % 181.55/181.54 [5793]~E(f324(f106(a865),x57932),f324(f106(a865),x57931))+E(f324(f106(a1),x57931),f2(a1))+P1(f324(a196,f324(f106(a1),x57931)))+~P1(f324(a196,f324(f106(a1),x57932))) % 181.55/181.54 [5802]~P105(x58022)+E(x58021,f191(f871(x58022,a859)))+~P1(f324(f61(x58022),x58021))+P1(f324(f324(f326(x58022),f14(x58022,x58021)),x58021)) % 181.55/181.54 [5803]~P105(x58032)+E(x58031,f191(f871(x58032,a859)))+~P1(f324(f61(x58032),x58031))+P1(f324(f324(f326(x58032),f15(x58032,x58031)),x58031)) % 181.55/181.54 [5960]~P117(x59601)+~P92(x59601)+P1(f324(f324(f238(x59601),f2(x59601)),f324(f106(x59601),x59602)))+~P1(f324(f324(f238(a1),a84),x59602)) % 181.55/181.54 [5961]~P117(x59611)+~P92(x59611)+P1(f324(f324(f239(x59611),f2(x59611)),f324(f106(x59611),x59612)))+~P1(f324(f324(f239(a1),a84),x59612)) % 181.55/181.54 [5979]~P117(x59791)+~P92(x59791)+E(f324(f75(x59791),f324(f106(x59791),x59792)),f324(f106(x59791),x59792))+P1(f324(f324(f239(x59791),f324(f106(x59791),x59792)),f2(x59791))) % 181.55/181.54 [6019]E(x60191,x60192)+~E(f324(a107,x60191),f324(a107,x60192))+~P1(f324(f324(f238(a1),f2(a1)),x60192))+~P1(f324(f324(f238(a1),f2(a1)),x60191)) % 181.55/181.54 [6206]~P92(x62062)+~P117(x62062)+~P1(f324(f324(f238(x62062),f2(x62062)),f324(f106(x62062),x62061)))+P1(f324(f324(f238(a1),a84),x62061)) % 181.55/181.54 [6207]~P92(x62072)+~P117(x62072)+~P1(f324(f324(f239(x62072),f2(x62072)),f324(f106(x62072),x62071)))+P1(f324(f324(f239(a1),a84),x62071)) % 181.55/181.54 [6212]~P117(x62121)+~P92(x62121)+P1(f324(f324(f238(x62121),f324(f106(x62121),x62122)),f2(x62121)))+~P1(f324(f324(f238(a1),x62122),a84)) % 181.55/181.54 [6213]~P117(x62131)+~P92(x62131)+P1(f324(f324(f239(x62131),f324(f106(x62131),x62132)),f2(x62131)))+~P1(f324(f324(f239(a1),x62132),a84)) % 181.55/181.54 [6521]~P92(x65212)+~P117(x65212)+~P1(f324(f324(f238(x65212),f324(f106(x65212),x65211)),f2(x65212)))+P1(f324(f324(f238(a1),x65211),a84)) % 181.55/181.54 [6522]~P92(x65222)+~P117(x65222)+~P1(f324(f324(f239(x65222),f324(f106(x65222),x65221)),f2(x65222)))+P1(f324(f324(f239(a1),x65221),a84)) % 181.55/181.54 [6612]~P117(x66121)+~P92(x66121)+E(f324(f75(x66121),f324(f106(x66121),x66122)),f324(f80(x66121),f324(f106(x66121),x66122)))+~P1(f324(f324(f239(x66121),f324(f106(x66121),x66122)),f2(x66121))) % 181.55/181.54 [6630]E(f324(f106(a865),x66301),f324(f106(a865),x66302))+~E(f324(f106(a1),x66302),f2(a1))+~P1(f324(f324(f238(a1),f324(f106(a1),x66301)),f2(a1)))+~P1(f324(a196,f324(f106(a1),x66301))) % 181.55/181.54 [7501]~P105(x75012)+E(x75011,f191(f871(x75012,a859)))+~P1(f324(f61(x75012),x75011))+P1(f324(f324(f238(x75012),f12(x75012,f189(x75012),x75011)),f11(x75012,f190(x75012),x75011))) % 181.55/181.54 [7811]~P40(x78112)+~P7(x78111)+P1(f324(f324(f326(a1),x78111),x78112))+~P1(f324(f324(f326(a865),f324(a107,x78111)),f324(f303(a1,a865,a107),x78112))) % 181.55/181.54 [8081]~P61(x80812)+P1(f324(x80811,f203(x80812)))+~P1(f324(f57(f869(x80812)),x80811))+P1(f324(f57(x80812),f324(f324(f8(f869(x80812),a859,x80812),x80811),f233(x80812)))) % 181.55/181.54 [8547]~P61(x85471)+~P1(f324(x85472,f203(x85471)))+P1(f324(f58(f869(x85471)),x85472))+~P1(f324(f58(x85471),f324(f324(f8(f869(x85471),a859,x85471),x85472),f233(x85471)))) % 181.55/181.54 [5799]~P135(x57992)+E(x57991,f2(a1))+E(f324(f80(x57992),f324(f105(x57992),f324(f80(a1),x57991))),f324(f105(x57992),x57991))+~P1(f324(f324(f239(a1),x57991),f2(a1))) % 181.55/181.54 [5870]~P89(x58701)+~P92(x58701)+~P32(x58701,f324(f106(x58701),x58702))+P32(x58701,f324(f106(x58701),f324(f324(f81(a1),x58702),x58702))) % 181.55/181.54 [6195]~P74(x61952)+E(x61951,f191(f871(x61952,a859)))+E(f15(x61952,f324(f303(x61952,x61952,f80(x61952)),x61951)),f324(f80(x61952),f14(x61952,x61951)))+~P1(f324(f61(x61952),x61951)) % 181.55/181.54 [6196]~P74(x61962)+E(x61961,f191(f871(x61962,a859)))+E(f14(x61962,f324(f303(x61962,x61962,f80(x61962)),x61961)),f324(f80(x61962),f15(x61962,x61961)))+~P1(f324(f61(x61962),x61961)) % 181.55/181.54 [6227]~P89(x62271)+~P92(x62271)+P32(x62271,f324(f106(x62271),x62272))+~P32(x62271,f324(f106(x62271),f324(f324(f81(a1),x62272),x62272))) % 181.55/181.54 [6315]E(x63151,f2(a1))+E(f324(a50,f49(f324(f80(a1),x63151),f324(f80(a1),x63152))),f45(x63151,x63152))+P1(f324(f324(f238(a1),f2(a1)),x63152))+~P1(f324(f324(f238(a1),f2(a1)),x63151)) % 181.55/181.54 [8596]~P40(x85962)+~P40(x85961)+P1(f324(f324(f239(f871(a865,a859)),f324(f303(a1,a865,a107),x85961)),f324(f303(a1,a865,a107),x85962)))+~P1(f324(f324(f239(f871(a1,a859)),x85961),x85962)) % 181.55/181.54 [8824]~E(f754(x88242,x88241),f755(x88242,x88241))+~P1(f324(f131(x88241),f756(x88242,x88241)))+~P1(f324(f131(f866(x88241)),x88242))+P1(f324(f131(x88241),f324(f136(f866(x88241),f866(x88241),f124(x88241),f116(x88241)),x88242))) % 181.55/181.54 [8913]~P40(x89132)+~P40(x89131)+~P1(f324(f324(f238(f871(a865,a859)),f324(f303(a1,a865,a107),x89131)),f324(f303(a1,a865,a107),x89132)))+P1(f324(f324(f238(f871(a1,a859)),x89131),x89132)) % 181.55/181.54 [8914]~P40(x89142)+~P40(x89141)+~P1(f324(f324(f239(f871(a865,a859)),f324(f303(a1,a865,a107),x89141)),f324(f303(a1,a865,a107),x89142)))+P1(f324(f324(f239(f871(a1,a859)),x89141),x89142)) % 181.55/181.54 [8920]~E(f754(x89202,x89201),f755(x89202,x89201))+~P1(f324(f131(f866(x89201)),x89202))+P1(f324(f131(x89201),f324(f136(f866(x89201),f866(x89201),f124(x89201),f116(x89201)),x89202)))+P1(f324(f324(f326(f866(x89201)),f756(x89202,x89201)),f324(f167(f866(x89201)),x89202))) % 181.55/181.54 [8961]~P1(f324(f131(x89611),f756(x89612,x89611)))+~P1(f324(f131(f866(x89611)),x89612))+P1(f324(f131(x89611),f324(f136(f866(x89611),f866(x89611),f124(x89611),f116(x89611)),x89612)))+P1(f324(f324(f326(f866(x89611)),f755(x89612,x89611)),f324(f167(f866(x89611)),x89612))) % 181.55/181.54 [8962]~P1(f324(f131(x89621),f756(x89622,x89621)))+~P1(f324(f131(f866(x89621)),x89622))+P1(f324(f131(x89621),f324(f136(f866(x89621),f866(x89621),f124(x89621),f116(x89621)),x89622)))+P1(f324(f324(f326(f866(x89621)),f754(x89622,x89621)),f324(f167(f866(x89621)),x89622))) % 181.55/181.54 [9042]~P1(f324(f131(f866(x90421)),x90422))+P1(f324(f131(x90421),f324(f136(f866(x90421),f866(x90421),f124(x90421),f116(x90421)),x90422)))+P1(f324(f324(f326(f866(x90421)),f755(x90422,x90421)),f324(f167(f866(x90421)),x90422)))+P1(f324(f324(f326(f866(x90421)),f756(x90422,x90421)),f324(f167(f866(x90421)),x90422))) % 181.55/181.54 [9043]~P1(f324(f131(f866(x90431)),x90432))+P1(f324(f131(x90431),f324(f136(f866(x90431),f866(x90431),f124(x90431),f116(x90431)),x90432)))+P1(f324(f324(f326(f866(x90431)),f754(x90432,x90431)),f324(f167(f866(x90431)),x90432)))+P1(f324(f324(f326(f866(x90431)),f756(x90432,x90431)),f324(f167(f866(x90431)),x90432))) % 181.55/181.54 [9056]~E(f324(f324(f104(f871(x90561,a859)),f324(f167(x90561),f755(x90562,x90561))),f324(f167(x90561),f754(x90562,x90561))),f191(f871(x90561,a859)))+~P1(f324(f131(x90561),f756(x90562,x90561)))+~P1(f324(f131(f866(x90561)),x90562))+P1(f324(f131(x90561),f324(f136(f866(x90561),f866(x90561),f124(x90561),f116(x90561)),x90562))) % 181.55/181.54 [9118]~E(f324(f324(f104(f871(x91181,a859)),f324(f167(x91181),f755(x91182,x91181))),f324(f167(x91181),f754(x91182,x91181))),f191(f871(x91181,a859)))+~P1(f324(f131(f866(x91181)),x91182))+P1(f324(f131(x91181),f324(f136(f866(x91181),f866(x91181),f124(x91181),f116(x91181)),x91182)))+P1(f324(f324(f326(f866(x91181)),f756(x91182,x91181)),f324(f167(f866(x91181)),x91182))) % 181.55/181.54 [9387]E(x93871,f2(a1))+E(x93872,f2(a1))+E(f324(f324(f87(a1,f870(a1,a1)),f324(f324(a222,x93872),x93871)),f324(f324(f18(a1,a1,f870(a1,a1)),f324(f324(f8(a1,f871(a1,f870(a1,a1)),a1),f259(a1,a1)),f324(f38(a1),x93872))),f324(f38(a1),x93871))),f220(x93872,x93871))+P1(f324(f324(f239(a1),x93871),f2(a1))) % 181.55/181.54 [8142]~P92(x81422)+~P117(x81422)+~P1(f324(f324(f238(x81422),f324(f106(x81422),x81421)),f79(x81422)))+P1(f324(f324(f238(a1),x81421),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))) % 181.55/181.54 [8143]~P92(x81432)+~P117(x81432)+~P1(f324(f324(f239(x81432),f324(f106(x81432),x81431)),f79(x81432)))+P1(f324(f324(f239(a1),x81431),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))) % 181.55/181.54 [8413]~P117(x84131)+~P92(x84131)+P1(f324(f324(f238(x84131),f324(f106(x84131),x84132)),f79(x84131)))+~P1(f324(f324(f238(a1),x84132),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))) % 181.55/181.54 [8414]~P117(x84141)+~P92(x84141)+P1(f324(f324(f239(x84141),f324(f106(x84141),x84142)),f79(x84141)))+~P1(f324(f324(f239(a1),x84142),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))) % 181.55/181.54 [8624]~P92(x86242)+~P117(x86242)+~P1(f324(f324(f238(x86242),f79(x86242)),f324(f106(x86242),x86241)))+P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),x86241)) % 181.55/181.54 [8625]~P92(x86252)+~P117(x86252)+~P1(f324(f324(f239(x86252),f79(x86252)),f324(f106(x86252),x86251)))+P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),x86251)) % 181.55/181.54 [9000]~P117(x90001)+~P92(x90001)+P1(f324(f324(f238(x90001),f79(x90001)),f324(f106(x90001),x90002)))+~P1(f324(f324(f238(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),x90002)) % 181.55/181.54 [9001]~P117(x90011)+~P92(x90011)+P1(f324(f324(f239(x90011),f79(x90011)),f324(f106(x90011),x90012)))+~P1(f324(f324(f239(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),x90012)) % 181.55/181.54 [9524]~P134(x95242)+E(x95241,f79(x95242))+E(x95241,f324(f80(x95242),f79(x95242)))+~E(f324(f324(f249(x95242),x95241),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f79(x95242)) % 181.55/181.54 [9801]~P64(x98011)+~P92(x98011)+~P1(f324(f324(f239(x98011),f2(x98011)),x98012))+P1(f324(f324(f239(x98011),f2(x98011)),f324(f324(f282(x98011),x98012),f324(f106(x98011),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.54 [9861]~P64(x98611)+~P92(x98611)+P1(f324(f324(f239(x98611),f2(x98611)),x98612))+~P1(f324(f324(f239(x98611),f2(x98611)),f324(f324(f282(x98611),x98612),f324(f106(x98611),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.54 [10114]~P135(x101142)+E(x101141,f2(a1))+P1(f324(f324(f239(a1),x101141),f2(a1)))+E(f324(f324(f263(a1,a1,x101142),f324(f324(f7(a1,f871(a1,f871(x101142,x101142)),f871(a1,x101142)),f324(f324(f8(f871(f871(x101142,x101142),x101142),f871(f871(a1,f871(x101142,x101142)),f871(a1,x101142)),a1),f8(f871(x101142,x101142),x101142,a1)),f324(f324(f8(x101142,f871(f871(x101142,x101142),x101142),a1),f87(x101142,x101142)),f105(x101142)))),f324(f324(f7(a1,f871(x101142,x101142),f871(x101142,x101142)),f324(f324(f8(f871(x101142,f871(x101142,x101142)),f871(f871(x101142,x101142),f871(x101142,x101142)),a1),f18(x101142,x101142,x101142)),f324(f324(f7(a1,f871(x101142,x101142),f871(x101142,f871(x101142,x101142))),f324(f324(f8(f871(x101142,f871(x101142,x101142)),f871(f871(x101142,x101142),f871(x101142,f871(x101142,x101142))),a1),f8(x101142,f871(x101142,x101142),x101142)),f324(f324(f8(a859,f871(x101142,f871(x101142,x101142)),a1),f99(x101142)),f324(f324(f7(a1,a1,a859),a321),f2(a1))))),f324(f324(f18(x101142,x101142,x101142),f81(x101142)),f5(x101142))))),f324(f324(f7(x101142,x101142,x101142),f324(f324(f8(x101142,f871(x101142,x101142),x101142),f81(x101142)),f324(f324(f18(x101142,x101142,x101142),f81(x101142)),f5(x101142)))),f79(x101142))))),f45(x101141,f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f105(x101142),x101141)) % 181.55/181.54 [5193]~P61(x51933)+~P37(x51933,x51932,f55(x51933))+E(x51931,f762(x51932,x51933))+~P1(f324(x51932,x51931)) % 181.55/181.54 [5348]~P61(x53481)+P37(x53481,x53482,f55(x53481))+~E(f763(x53482,x53481,x53483),x53483)+~P1(f324(x53482,x53483)) % 181.55/181.54 [4849]~P89(x48493)+~P92(x48493)+E(x48491,x48492)+~E(f324(f106(x48493),x48491),f324(f106(x48493),x48492)) % 181.55/181.54 [5959]~P61(x59591)+P37(x59591,x59592,f55(x59591))+~P1(f324(x59592,x59593))+P1(f324(x59592,f763(x59592,x59591,x59593))) % 181.55/181.54 [5969]~P1(f324(x59691,x59692))+~P1(f324(x59691,x59693))+~P1(f324(f324(f238(a865),x59693),f376(x59692,x59691)))+P1(f324(x59691,f2(a865))) % 181.55/181.54 [6380]P144(x63802,x63801,x63803)+E(x63801,f2(a1))+P1(f324(f324(f238(a1),f2(a1)),f793(x63803,x63801,x63802)))+P1(f324(f324(f239(a1),x63801),f2(a1))) % 181.55/181.54 [6381]P143(x63812,x63811,x63813)+E(x63811,f2(a1))+P1(f324(f324(f238(a1),f2(a1)),f804(x63813,x63811,x63812)))+P1(f324(f324(f239(a1),x63811),f2(a1))) % 181.55/181.54 [6501]P143(x65011,x65012,x65013)+~P1(f324(x65011,x65013))+P1(f324(f324(f238(a1),f2(a1)),f804(x65013,x65012,x65011)))+P1(f324(f324(f239(a1),x65012),f2(a1))) % 181.55/181.54 [6527]P144(x65271,x65272,x65273)+P1(f324(f324(f238(a1),f2(a1)),f793(x65273,x65272,x65271)))+~P1(f324(x65271,f2(a1)))+P1(f324(f324(f239(a1),x65272),f2(a1))) % 181.55/181.54 [6555]P144(x65552,x65551,x65553)+E(x65551,f2(a1))+~P1(f324(x65552,f794(x65553,x65551,x65552)))+P1(f324(f324(f239(a1),x65551),f2(a1))) % 181.55/181.54 [6556]P143(x65562,x65561,x65563)+E(x65561,f2(a1))+~P1(f324(x65562,f804(x65563,x65561,x65562)))+P1(f324(f324(f239(a1),x65561),f2(a1))) % 181.55/181.54 [6655]~P105(x66551)+~P6(x66551)+~P1(f324(f324(f239(x66551),x66552),f39(x66551,x66553)))+P1(f324(f324(f239(x66551),x66552),f605(x66553,x66552,x66551))) % 181.55/181.54 [6664]P143(x66641,x66642,x66643)+~P1(f324(x66641,x66643))+~P1(f324(x66641,f804(x66643,x66642,x66641)))+P1(f324(f324(f239(a1),x66642),f2(a1))) % 181.55/181.54 [6696]P144(x66961,x66962,x66963)+~P1(f324(x66961,f794(x66963,x66962,x66961)))+~P1(f324(x66961,f2(a1)))+P1(f324(f324(f239(a1),x66962),f2(a1))) % 181.55/181.54 [6944]P144(x69442,x69441,x69443)+E(x69441,f2(a1))+P1(f324(f324(f238(a1),f2(a1)),f793(x69443,x69441,x69442)))+P1(f324(f324(f239(a1),x69441),f792(x69443,x69441,x69442))) % 181.55/181.54 [6945]P143(x69452,x69451,x69453)+E(x69451,f2(a1))+P1(f324(f324(f238(a1),f2(a1)),f804(x69453,x69451,x69452)))+P1(f324(f324(f239(a1),x69451),f803(x69453,x69451,x69452))) % 181.55/181.54 [7062]P143(x70621,x70622,x70623)+~P1(f324(x70621,x70623))+P1(f324(f324(f238(a1),f2(a1)),f804(x70623,x70622,x70621)))+P1(f324(f324(f239(a1),x70622),f803(x70623,x70622,x70621))) % 181.55/181.54 [7081]P144(x70811,x70812,x70813)+P1(f324(f324(f238(a1),f2(a1)),f793(x70813,x70812,x70811)))+P1(f324(f324(f239(a1),x70812),f792(x70813,x70812,x70811)))+~P1(f324(x70811,f2(a1))) % 181.55/181.54 [7113]P144(x71132,x71131,x71133)+E(x71131,f2(a1))+~P1(f324(x71132,f794(x71133,x71131,x71132)))+P1(f324(f324(f239(a1),x71131),f792(x71133,x71131,x71132))) % 181.55/181.54 [7114]P143(x71142,x71141,x71143)+E(x71141,f2(a1))+~P1(f324(x71142,f804(x71143,x71141,x71142)))+P1(f324(f324(f239(a1),x71141),f803(x71143,x71141,x71142))) % 181.55/181.54 [7155]P144(x71552,x71551,x71553)+E(x71551,f2(a1))+P1(f324(f324(f238(a1),f2(a1)),f793(x71553,x71551,x71552)))+~P1(f324(x71552,f802(x71553,x71551,x71552))) % 181.55/181.54 [7156]P143(x71562,x71561,x71563)+E(x71561,f2(a1))+P1(f324(f324(f238(a1),f2(a1)),f804(x71563,x71561,x71562)))+~P1(f324(x71562,f803(x71563,x71561,x71562))) % 181.55/181.54 [7244]P143(x72441,x72442,x72443)+~P1(f324(x72441,x72443))+~P1(f324(x72441,f804(x72443,x72442,x72441)))+P1(f324(f324(f239(a1),x72442),f803(x72443,x72442,x72441))) % 181.55/181.54 [7260]P144(x72601,x72602,x72603)+~P1(f324(x72601,f794(x72603,x72602,x72601)))+P1(f324(f324(f239(a1),x72602),f792(x72603,x72602,x72601)))+~P1(f324(x72601,f2(a1))) % 181.55/181.54 [7264]P143(x72641,x72642,x72643)+~P1(f324(x72641,x72643))+P1(f324(f324(f238(a1),f2(a1)),f804(x72643,x72642,x72641)))+~P1(f324(x72641,f803(x72643,x72642,x72641))) % 181.55/181.54 [7280]P144(x72801,x72802,x72803)+P1(f324(f324(f238(a1),f2(a1)),f793(x72803,x72802,x72801)))+~P1(f324(x72801,f802(x72803,x72802,x72801)))+~P1(f324(x72801,f2(a1))) % 181.55/181.54 [7304]P144(x73042,x73041,x73043)+E(x73041,f2(a1))+~P1(f324(x73042,f794(x73043,x73041,x73042)))+~P1(f324(x73042,f802(x73043,x73041,x73042))) % 181.55/181.54 [7305]P143(x73052,x73051,x73053)+E(x73051,f2(a1))+~P1(f324(x73052,f804(x73053,x73051,x73052)))+~P1(f324(x73052,f803(x73053,x73051,x73052))) % 181.55/181.54 [7396]P143(x73961,x73962,x73963)+~P1(f324(x73961,x73963))+~P1(f324(x73961,f804(x73963,x73962,x73961)))+~P1(f324(x73961,f803(x73963,x73962,x73961))) % 181.55/181.54 [7413]P144(x74131,x74132,x74133)+~P1(f324(x74131,f794(x74133,x74132,x74131)))+~P1(f324(x74131,f802(x74133,x74132,x74131)))+~P1(f324(x74131,f2(a1))) % 181.55/181.54 [7461]P144(x74612,x74611,x74613)+E(x74611,f2(a1))+P1(f324(f324(f238(a1),f2(a1)),f793(x74613,x74611,x74612)))+P1(f324(f324(f238(a1),f792(x74613,x74611,x74612)),f2(a1))) % 181.55/181.54 [7462]P143(x74622,x74621,x74623)+E(x74621,f2(a1))+P1(f324(f324(f238(a1),f2(a1)),f804(x74623,x74621,x74622)))+P1(f324(f324(f238(a1),f803(x74623,x74621,x74622)),f2(a1))) % 181.55/181.54 [7463]~P135(x74631)+~P1(f324(f324(f326(x74631),x74633),f112(x74631)))+~P1(f324(f324(f326(x74631),x74632),f112(x74631)))+P1(f324(f324(f326(x74631),f324(f324(f22(x74631),x74632),x74633)),f112(x74631))) % 181.55/181.54 [7464]~P135(x74641)+~P1(f324(f324(f326(x74641),x74643),f112(x74641)))+~P1(f324(f324(f326(x74641),x74642),f112(x74641)))+P1(f324(f324(f326(x74641),f324(f324(f82(x74641),x74642),x74643)),f112(x74641))) % 181.55/181.54 [7465]~P141(x74651)+~P1(f324(f324(f326(x74651),x74653),f187(x74651)))+~P1(f324(f324(f326(x74651),x74652),f187(x74651)))+P1(f324(f324(f326(x74651),f324(f324(f82(x74651),x74652),x74653)),f187(x74651))) % 181.55/181.54 [7466]~P135(x74661)+~P1(f324(f324(f326(x74661),x74663),f112(x74661)))+~P1(f324(f324(f326(x74661),x74662),f112(x74661)))+P1(f324(f324(f326(x74661),f324(f324(f81(x74661),x74662),x74663)),f112(x74661))) % 181.55/181.54 [7467]~P141(x74671)+~P1(f324(f324(f326(x74671),x74673),f187(x74671)))+~P1(f324(f324(f326(x74671),x74672),f187(x74671)))+P1(f324(f324(f326(x74671),f324(f324(f81(x74671),x74672),x74673)),f187(x74671))) % 181.55/181.54 [7468]~P85(x74681)+~P1(f324(f324(f238(x74681),x74683),f2(x74681)))+~P1(f324(f324(f238(x74681),x74682),f2(x74681)))+P1(f324(f324(f238(x74681),f324(f324(f81(x74681),x74682),x74683)),f2(x74681))) % 181.55/181.54 [7469]~P85(x74691)+~P1(f324(f324(f238(x74691),x74693),f2(x74691)))+~P1(f324(f324(f239(x74691),x74692),f2(x74691)))+P1(f324(f324(f239(x74691),f324(f324(f81(x74691),x74692),x74693)),f2(x74691))) % 181.55/181.54 [7470]~P85(x74701)+~P1(f324(f324(f238(x74701),x74702),f2(x74701)))+~P1(f324(f324(f239(x74701),x74703),f2(x74701)))+P1(f324(f324(f239(x74701),f324(f324(f81(x74701),x74702),x74703)),f2(x74701))) % 181.55/181.54 [7471]~P85(x74711)+~P1(f324(f324(f239(x74711),x74713),f2(x74711)))+~P1(f324(f324(f239(x74711),x74712),f2(x74711)))+P1(f324(f324(f239(x74711),f324(f324(f81(x74711),x74712),x74713)),f2(x74711))) % 181.55/181.54 [7497]P144(x74973,x74971,x74972)+E(x74971,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x74971),f794(x74972,x74971,x74973))),f793(x74972,x74971,x74973)),x74972)+P1(f324(f324(f239(a1),x74971),f2(a1))) % 181.55/181.54 [7498]P143(x74983,x74981,x74982)+E(x74981,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x74981),f805(x74982,x74981,x74983))),f804(x74982,x74981,x74983)),x74982)+P1(f324(f324(f239(a1),x74981),f2(a1))) % 181.55/181.54 [7580]P143(x75801,x75802,x75803)+~P1(f324(x75801,x75803))+P1(f324(f324(f238(a1),f2(a1)),f804(x75803,x75802,x75801)))+P1(f324(f324(f238(a1),f803(x75803,x75802,x75801)),f2(a1))) % 181.55/181.54 [7609]P144(x76091,x76092,x76093)+P1(f324(f324(f238(a1),f2(a1)),f793(x76093,x76092,x76091)))+~P1(f324(x76091,f2(a1)))+P1(f324(f324(f238(a1),f792(x76093,x76092,x76091)),f2(a1))) % 181.55/181.54 [7617]P143(x76173,x76171,x76172)+~P1(f324(x76173,x76172))+E(f324(f324(f81(a1),f324(f324(f82(a1),x76171),f805(x76172,x76171,x76173))),f804(x76172,x76171,x76173)),x76172)+P1(f324(f324(f239(a1),x76171),f2(a1))) % 181.55/181.54 [7623]P144(x76232,x76231,x76233)+E(x76231,f2(a1))+~P1(f324(x76232,f794(x76233,x76231,x76232)))+P1(f324(f324(f238(a1),f792(x76233,x76231,x76232)),f2(a1))) % 181.55/181.54 [7624]P143(x76242,x76241,x76243)+E(x76241,f2(a1))+~P1(f324(x76242,f804(x76243,x76241,x76242)))+P1(f324(f324(f238(a1),f803(x76243,x76241,x76242)),f2(a1))) % 181.55/181.54 [7629]P144(x76293,x76291,x76292)+E(f324(f324(f81(a1),f324(f324(f82(a1),x76291),f794(x76292,x76291,x76293))),f793(x76292,x76291,x76293)),x76292)+~P1(f324(x76293,f2(a1)))+P1(f324(f324(f239(a1),x76291),f2(a1))) % 181.55/181.54 [7683]P143(x76831,x76832,x76833)+~P1(f324(x76831,x76833))+~P1(f324(x76831,f804(x76833,x76832,x76831)))+P1(f324(f324(f238(a1),f803(x76833,x76832,x76831)),f2(a1))) % 181.55/181.54 [7687]P144(x76871,x76872,x76873)+~P1(f324(x76871,f794(x76873,x76872,x76871)))+~P1(f324(x76871,f2(a1)))+P1(f324(f324(f238(a1),f792(x76873,x76872,x76871)),f2(a1))) % 181.55/181.54 [7751]~P121(x77511)+~P1(f324(f324(f238(x77511),f324(f324(f82(x77511),x77513),x77512)),f2(x77511)))+P1(f324(f324(f238(x77511),x77512),f2(x77511)))+P1(f324(f324(f238(x77511),x77513),f2(x77511))) % 181.55/181.54 [7752]~P64(x77521)+~P1(f324(f324(f238(x77521),f324(f324(f282(x77521),x77523),x77522)),f2(x77521)))+P1(f324(f324(f238(x77521),x77522),f2(x77521)))+P1(f324(f324(f238(x77521),x77523),f2(x77521))) % 181.55/181.54 [7753]~P64(x77531)+~P1(f324(f324(f239(x77531),f324(f324(f282(x77531),x77533),x77532)),f2(x77531)))+P1(f324(f324(f239(x77531),x77532),f2(x77531)))+P1(f324(f324(f239(x77531),x77533),f2(x77531))) % 181.55/181.54 [7870]P144(x78703,x78701,x78702)+E(x78701,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x78701),f794(x78702,x78701,x78703))),f793(x78702,x78701,x78703)),x78702)+P1(f324(f324(f239(a1),x78701),f792(x78702,x78701,x78703))) % 181.55/181.54 [7871]P143(x78713,x78711,x78712)+E(x78711,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x78711),f805(x78712,x78711,x78713))),f804(x78712,x78711,x78713)),x78712)+P1(f324(f324(f239(a1),x78711),f803(x78712,x78711,x78713))) % 181.55/181.54 [7885]P144(x78853,x78851,x78852)+E(x78851,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x78851),f802(x78852,x78851,x78853))),f792(x78852,x78851,x78853)),x78852)+P1(f324(f324(f238(a1),f2(a1)),f793(x78852,x78851,x78853))) % 181.55/181.54 [7886]P143(x78863,x78861,x78862)+E(x78861,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x78861),f806(x78862,x78861,x78863))),f803(x78862,x78861,x78863)),x78862)+P1(f324(f324(f238(a1),f2(a1)),f804(x78862,x78861,x78863))) % 181.55/181.54 [7927]P143(x79273,x79271,x79272)+~P1(f324(x79273,x79272))+E(f324(f324(f81(a1),f324(f324(f82(a1),x79271),f805(x79272,x79271,x79273))),f804(x79272,x79271,x79273)),x79272)+P1(f324(f324(f239(a1),x79271),f803(x79272,x79271,x79273))) % 181.55/181.54 [7936]P144(x79363,x79361,x79362)+E(f324(f324(f81(a1),f324(f324(f82(a1),x79361),f794(x79362,x79361,x79363))),f793(x79362,x79361,x79363)),x79362)+P1(f324(f324(f239(a1),x79361),f792(x79362,x79361,x79363)))+~P1(f324(x79363,f2(a1))) % 181.55/181.54 [7942]P143(x79423,x79421,x79422)+~P1(f324(x79423,x79422))+E(f324(f324(f81(a1),f324(f324(f82(a1),x79421),f806(x79422,x79421,x79423))),f803(x79422,x79421,x79423)),x79422)+P1(f324(f324(f238(a1),f2(a1)),f804(x79422,x79421,x79423))) % 181.55/181.54 [7948]P144(x79483,x79481,x79482)+E(f324(f324(f81(a1),f324(f324(f82(a1),x79481),f802(x79482,x79481,x79483))),f792(x79482,x79481,x79483)),x79482)+P1(f324(f324(f238(a1),f2(a1)),f793(x79482,x79481,x79483)))+~P1(f324(x79483,f2(a1))) % 181.55/181.54 [7959]P144(x79593,x79591,x79592)+E(x79591,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x79591),f794(x79592,x79591,x79593))),f793(x79592,x79591,x79593)),x79592)+~P1(f324(x79593,f802(x79592,x79591,x79593))) % 181.55/181.54 [7960]P143(x79603,x79601,x79602)+E(x79601,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x79601),f805(x79602,x79601,x79603))),f804(x79602,x79601,x79603)),x79602)+~P1(f324(x79603,f803(x79602,x79601,x79603))) % 181.55/181.54 [7961]P144(x79613,x79611,x79612)+E(x79611,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x79611),f802(x79612,x79611,x79613))),f792(x79612,x79611,x79613)),x79612)+~P1(f324(x79613,f794(x79612,x79611,x79613))) % 181.55/181.54 [7962]P143(x79623,x79621,x79622)+E(x79621,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x79621),f806(x79622,x79621,x79623))),f803(x79622,x79621,x79623)),x79622)+~P1(f324(x79623,f804(x79622,x79621,x79623))) % 181.55/181.54 [8021]P143(x80213,x80211,x80212)+~P1(f324(x80213,x80212))+E(f324(f324(f81(a1),f324(f324(f82(a1),x80211),f805(x80212,x80211,x80213))),f804(x80212,x80211,x80213)),x80212)+~P1(f324(x80213,f803(x80212,x80211,x80213))) % 181.55/181.54 [8022]P143(x80223,x80221,x80222)+~P1(f324(x80223,x80222))+E(f324(f324(f81(a1),f324(f324(f82(a1),x80221),f806(x80222,x80221,x80223))),f803(x80222,x80221,x80223)),x80222)+~P1(f324(x80223,f804(x80222,x80221,x80223))) % 181.55/181.54 [8032]P144(x80323,x80321,x80322)+E(f324(f324(f81(a1),f324(f324(f82(a1),x80321),f794(x80322,x80321,x80323))),f793(x80322,x80321,x80323)),x80322)+~P1(f324(x80323,f802(x80322,x80321,x80323)))+~P1(f324(x80323,f2(a1))) % 181.55/181.54 [8033]P144(x80333,x80331,x80332)+E(f324(f324(f81(a1),f324(f324(f82(a1),x80331),f802(x80332,x80331,x80333))),f792(x80332,x80331,x80333)),x80332)+~P1(f324(x80333,f794(x80332,x80331,x80333)))+~P1(f324(x80333,f2(a1))) % 181.55/181.54 [8135]P144(x81353,x81351,x81352)+E(x81351,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x81351),f794(x81352,x81351,x81353))),f793(x81352,x81351,x81353)),x81352)+P1(f324(f324(f238(a1),f792(x81352,x81351,x81353)),f2(a1))) % 181.55/181.54 [8136]P143(x81363,x81361,x81362)+E(x81361,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x81361),f805(x81362,x81361,x81363))),f804(x81362,x81361,x81363)),x81362)+P1(f324(f324(f238(a1),f803(x81362,x81361,x81363)),f2(a1))) % 181.55/181.54 [8177]P143(x81773,x81771,x81772)+~P1(f324(x81773,x81772))+E(f324(f324(f81(a1),f324(f324(f82(a1),x81771),f805(x81772,x81771,x81773))),f804(x81772,x81771,x81773)),x81772)+P1(f324(f324(f238(a1),f803(x81772,x81771,x81773)),f2(a1))) % 181.55/181.54 [8182]P144(x81823,x81821,x81822)+E(f324(f324(f81(a1),f324(f324(f82(a1),x81821),f794(x81822,x81821,x81823))),f793(x81822,x81821,x81823)),x81822)+~P1(f324(x81823,f2(a1)))+P1(f324(f324(f238(a1),f792(x81822,x81821,x81823)),f2(a1))) % 181.55/181.54 [8318]P144(x83183,x83181,x83182)+E(x83181,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x83181),f802(x83182,x83181,x83183))),f792(x83182,x83181,x83183)),x83182)+E(f324(f324(f81(a1),f324(f324(f82(a1),x83181),f794(x83182,x83181,x83183))),f793(x83182,x83181,x83183)),x83182) % 181.55/181.54 [8319]P143(x83193,x83191,x83192)+E(x83191,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x83191),f806(x83192,x83191,x83193))),f803(x83192,x83191,x83193)),x83192)+E(f324(f324(f81(a1),f324(f324(f82(a1),x83191),f805(x83192,x83191,x83193))),f804(x83192,x83191,x83193)),x83192) % 181.55/181.54 [8339]P143(x83393,x83391,x83392)+~P1(f324(x83393,x83392))+E(f324(f324(f81(a1),f324(f324(f82(a1),x83391),f806(x83392,x83391,x83393))),f803(x83392,x83391,x83393)),x83392)+E(f324(f324(f81(a1),f324(f324(f82(a1),x83391),f805(x83392,x83391,x83393))),f804(x83392,x83391,x83393)),x83392) % 181.55/181.54 [8350]P144(x83503,x83501,x83502)+E(f324(f324(f81(a1),f324(f324(f82(a1),x83501),f802(x83502,x83501,x83503))),f792(x83502,x83501,x83503)),x83502)+E(f324(f324(f81(a1),f324(f324(f82(a1),x83501),f794(x83502,x83501,x83503))),f793(x83502,x83501,x83503)),x83502)+~P1(f324(x83503,f2(a1))) % 181.55/181.54 [9009]~P121(x90091)+~E(x90093,f2(x90091))+~E(x90092,f2(x90091))+P1(f324(f324(f238(x90091),f324(f324(f81(x90091),f324(f324(f82(x90091),x90092),x90092)),f324(f324(f82(x90091),x90093),x90093))),f2(x90091))) % 181.55/181.54 [10062]~P117(x100621)+~E(x100623,f2(x100621))+~E(x100622,f2(x100621))+P1(f324(f324(f238(x100621),f324(f324(f81(x100621),f324(f324(f249(x100621),x100622),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100621),x100623),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))),f2(x100621))) % 181.55/181.54 [4798]~E(x47983,x47981)+~P114(x47982)+E(x47981,f2(x47982))+E(f324(f324(f282(x47982),x47983),x47981),f79(x47982)) % 181.55/181.54 [4850]~P97(x48501)+~E(x48503,f247(x48501))+~E(x48502,f247(x48501))+E(f324(f324(f104(x48501),x48502),x48503),f247(x48501)) % 181.55/181.54 [4851]~P95(x48511)+~E(x48513,f191(x48511))+~E(x48512,f191(x48511))+E(f324(f324(f113(x48511),x48512),x48513),f191(x48511)) % 181.55/181.54 [4936]~P114(x49363)+E(x49361,x49362)+E(x49362,f2(x49363))+~E(f324(f324(f282(x49363),x49361),x49362),f79(x49363)) % 181.55/181.54 [4955]~P124(x49552)+E(x49551,f2(x49552))+E(x49553,f2(x49552))+~E(f324(f324(f82(x49552),x49553),x49551),f2(x49552)) % 181.55/181.54 [4956]~P138(x49562)+E(x49561,f2(x49562))+E(x49563,f2(x49562))+~E(f324(f324(f82(x49562),x49563),x49561),f2(x49562)) % 181.55/181.54 [5315]~P108(x53153)+E(x53151,x53152)+E(x53151,f324(f80(x53153),x53152))+~E(f324(f324(f82(x53153),x53151),x53151),f324(f324(f82(x53153),x53152),x53152)) % 181.55/181.54 [5355]~P79(x53551)+E(f324(f80(x53551),x53552),x53553)+~E(f324(f324(f104(x53551),x53552),x53553),f191(x53551))+~E(f324(f324(f113(x53551),x53552),x53553),f247(x53551)) % 181.55/181.54 [5434]~P117(x54343)+E(x54341,x54342)+P1(f324(f324(f239(x54343),x54342),x54341))+P1(f324(f324(f239(x54343),x54341),x54342)) % 181.55/181.54 [5435]~P105(x54353)+E(x54351,x54352)+P1(f324(f324(f239(x54353),x54352),x54351))+P1(f324(f324(f239(x54353),x54351),x54352)) % 181.55/181.54 [5436]~E(x54362,x54363)+~P105(x54361)+P1(f324(f324(f239(x54361),x54362),x54363))+P1(f324(f324(f238(x54361),x54362),x54363)) % 181.55/181.54 [5688]~P106(x56883)+E(x56881,x56882)+~P1(f324(f324(f238(x56883),x56882),x56881))+P1(f324(f324(f239(x56883),x56882),x56881)) % 181.55/181.54 [5690]~P105(x56903)+E(x56901,x56902)+~P1(f324(f324(f238(x56903),x56901),x56902))+P1(f324(f324(f239(x56903),x56901),x56902)) % 181.55/181.54 [5696]~P106(x56963)+E(x56961,x56962)+~P1(f324(f324(f238(x56963),x56961),x56962))+P1(f324(f324(f239(x56963),x56961),x56962)) % 181.55/181.54 [5796]P143(x57961,x57962,x57963)+~P1(f324(x57961,x57963))+P1(f324(f324(f239(a1),x57962),f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x57962)) % 181.55/181.54 [5843]P144(x58431,x58432,x58433)+~P1(f324(x58431,f2(a1)))+P1(f324(f324(f239(a1),x58432),f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x58432)) % 181.55/181.54 [5847]~P94(x58471)+E(f324(f324(f104(x58471),x58472),f13(x58471,x58473)),x58472)+~P1(f324(f61(x58471),x58473))+~P1(f324(f324(f326(x58471),x58472),x58473)) % 181.55/181.54 [5848]~P94(x58481)+E(f324(f324(f113(x58481),x58482),f10(x58481,x58483)),x58482)+~P1(f324(f61(x58481),x58483))+~P1(f324(f324(f326(x58481),x58482),x58483)) % 181.55/181.54 [5882]~P94(x58821)+E(f324(f324(f104(x58821),x58822),f10(x58821,x58823)),f10(x58821,x58823))+~P1(f324(f61(x58821),x58823))+~P1(f324(f324(f326(x58821),x58822),x58823)) % 181.55/181.54 [5883]~P94(x58831)+E(f324(f324(f113(x58831),x58832),f13(x58831,x58833)),f13(x58831,x58833))+~P1(f324(f61(x58831),x58833))+~P1(f324(f324(f326(x58831),x58832),x58833)) % 181.55/181.54 [5884]~P105(x58841)+E(f324(f324(f189(x58841),x58842),f15(x58841,x58843)),f15(x58841,x58843))+~P1(f324(f61(x58841),x58843))+~P1(f324(f324(f326(x58841),x58842),x58843)) % 181.55/181.54 [5885]~P105(x58851)+E(f324(f324(f190(x58851),x58852),f14(x58851,x58853)),f14(x58851,x58853))+~P1(f324(f61(x58851),x58853))+~P1(f324(f324(f326(x58851),x58852),x58853)) % 181.55/181.54 [5926]E(x59261,x59262)+~P106(x59263)+~P1(f324(f324(f238(x59263),x59262),x59261))+~P1(f324(f324(f238(x59263),x59261),x59262)) % 181.55/181.54 [6063]~P103(x60631)+P1(f324(f324(f239(x60631),x60633),x60632))+~P1(f324(f324(f238(x60631),x60633),x60632))+P1(f324(f324(f238(x60631),x60632),x60633)) % 181.55/181.54 [6084]~P105(x60841)+~P1(f324(f61(x60841),x60843))+P1(f324(f324(f238(x60841),x60842),f14(x60841,x60843)))+~P1(f324(f324(f326(x60841),x60842),x60843)) % 181.55/181.54 [6131]~P105(x61311)+E(f324(f324(f189(x61311),x61312),f11(x61311,f190(x61311),x61313)),x61312)+~P1(f324(f61(x61311),x61313))+~P1(f324(f324(f326(x61311),x61312),x61313)) % 181.55/181.54 [6132]~P105(x61321)+E(f324(f324(f190(x61321),x61322),f12(x61321,f189(x61321),x61323)),x61322)+~P1(f324(f61(x61321),x61323))+~P1(f324(f324(f326(x61321),x61322),x61323)) % 181.55/181.54 [6268]E(x62681,x62682)+~E(f324(f324(f22(a865),x62681),x62683),f324(f324(f22(a865),x62682),x62683))+~P1(f324(f324(f238(a865),x62683),x62681))+~P1(f324(f324(f238(a865),x62683),x62682)) % 181.55/181.54 [6295]~P105(x62951)+~P1(f324(f61(x62951),x62952))+~P1(f324(f324(f326(x62951),x62953),x62952))+P1(f324(f324(f238(x62951),f15(x62951,x62952)),x62953)) % 181.55/181.54 [6359]P144(x63592,x63591,x63593)+E(x63591,f2(a1))+P1(f324(f324(f239(a1),x63591),f792(x63593,x63591,x63592)))+P1(f324(f324(f239(a1),f2(a1)),x63591)) % 181.55/181.54 [6360]P143(x63602,x63601,x63603)+E(x63601,f2(a1))+P1(f324(f324(f239(a1),x63601),f803(x63603,x63601,x63602)))+P1(f324(f324(f239(a1),f2(a1)),x63601)) % 181.55/181.54 [6361]~P105(x63611)+E(f324(f324(f189(x63611),x63612),f12(x63611,f189(x63611),x63613)),f12(x63611,f189(x63611),x63613))+~P1(f324(f61(x63611),x63613))+~P1(f324(f324(f326(x63611),x63612),x63613)) % 181.55/181.54 [6362]~P105(x63621)+E(f324(f324(f190(x63621),x63622),f11(x63621,f190(x63621),x63623)),f11(x63621,f190(x63621),x63623))+~P1(f324(f61(x63621),x63623))+~P1(f324(f324(f326(x63621),x63622),x63623)) % 181.55/181.54 [6368]~P1(f324(x63681,x63682))+P1(f324(x63681,f575(x63682,x63681,x63683)))+P1(f324(x63681,f2(a865)))+~P1(f324(f324(f239(a865),x63682),x63683)) % 181.55/181.54 [6422]~P1(f324(x64221,x64222))+~P1(f324(f61(x64223),x64222))+P1(f324(x64221,f826(x64221,x64222,x64223)))+P1(f324(x64221,f191(f871(x64223,a859)))) % 181.55/181.54 [6435]~P117(x64351)+~P92(x64351)+P1(f324(f324(f238(x64351),f324(f106(x64351),x64352)),f324(f106(x64351),x64353)))+~P1(f324(f324(f238(a1),x64352),x64353)) % 181.55/181.54 [6436]~P117(x64361)+~P92(x64361)+P1(f324(f324(f239(x64361),f324(f106(x64361),x64362)),f324(f106(x64361),x64363)))+~P1(f324(f324(f239(a1),x64362),x64363)) % 181.55/181.54 [6439]~P1(f324(x64391,x64393))+~P1(f324(f61(x64392),x64393))+P1(f324(f61(x64392),f826(x64391,x64393,x64392)))+P1(f324(x64391,f191(f871(x64392,a859)))) % 181.55/181.54 [6472]P143(x64721,x64722,x64723)+~P1(f324(x64721,x64723))+P1(f324(f324(f239(a1),x64722),f803(x64723,x64722,x64721)))+P1(f324(f324(f239(a1),f2(a1)),x64722)) % 181.55/181.54 [6507]P144(x65071,x65072,x65073)+P1(f324(f324(f239(a1),x65072),f792(x65073,x65072,x65071)))+~P1(f324(x65071,f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x65072)) % 181.55/181.54 [6538]~P104(x65381)+~P90(x65381)+E(f324(f324(f189(x65381),f324(f106(x65381),x65382)),f324(f106(x65381),x65383)),f324(f106(x65381),x65383))+P1(f324(f324(f238(x65381),f324(f106(x65381),x65382)),f324(f106(x65381),x65383))) % 181.55/181.54 [6539]~P104(x65391)+~P90(x65391)+E(f324(f324(f190(x65391),f324(f106(x65391),x65392)),f324(f106(x65391),x65393)),f324(f106(x65391),x65392))+P1(f324(f324(f238(x65391),f324(f106(x65391),x65392)),f324(f106(x65391),x65393))) % 181.55/181.54 [6596]P144(x65962,x65961,x65963)+E(x65961,f2(a1))+~P1(f324(x65962,f802(x65963,x65961,x65962)))+P1(f324(f324(f239(a1),f2(a1)),x65961)) % 181.55/181.54 [6597]P143(x65972,x65971,x65973)+E(x65971,f2(a1))+~P1(f324(x65972,f803(x65973,x65971,x65972)))+P1(f324(f324(f239(a1),f2(a1)),x65971)) % 181.55/181.54 [6601]P1(f324(x66011,x66012))+~P1(f324(f61(x66013),x66012))+P1(f324(x66011,f795(x66011,x66012,x66013)))+~P1(f324(x66011,f191(f871(x66013,a859)))) % 181.55/181.54 [6620]P1(f324(x66201,x66202))+P1(f324(f61(x66203),f795(x66201,x66202,x66203)))+~P1(f324(f61(x66203),x66202))+~P1(f324(x66201,f191(f871(x66203,a859)))) % 181.55/181.54 [6685]P143(x66851,x66852,x66853)+~P1(f324(x66851,x66853))+~P1(f324(x66851,f803(x66853,x66852,x66851)))+P1(f324(f324(f239(a1),f2(a1)),x66852)) % 181.55/181.54 [6715]P144(x67151,x67152,x67153)+~P1(f324(x67151,f802(x67153,x67152,x67151)))+~P1(f324(x67151,f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x67152)) % 181.55/181.54 [6822]~P92(x68223)+~P117(x68223)+~P1(f324(f324(f238(x68223),f324(f106(x68223),x68221)),f324(f106(x68223),x68222)))+P1(f324(f324(f238(a1),x68221),x68222)) % 181.55/181.54 [6823]~P92(x68233)+~P117(x68233)+~P1(f324(f324(f239(x68233),f324(f106(x68233),x68231)),f324(f106(x68233),x68232)))+P1(f324(f324(f239(a1),x68231),x68232)) % 181.55/181.54 [6850]~P105(x68501)+~P16(x68501,x68503)+P16(x68501,f324(f324(f145(x68501),x68502),x68503))+~P1(f324(f324(f238(x68501),x68502),f732(x68503,x68502,x68501))) % 181.55/181.54 [6851]~P105(x68511)+~P16(x68511,x68513)+P16(x68511,f324(f324(f145(x68511),x68512),x68513))+~P1(f324(f324(f238(x68511),x68512),f733(x68513,x68512,x68511))) % 181.55/181.54 [6852]~P105(x68521)+~P16(x68521,x68523)+P16(x68521,f324(f324(f145(x68521),x68522),x68523))+~P1(f324(f324(f238(x68521),x68522),f765(x68522,x68523,x68521))) % 181.55/181.54 [6936]P144(x69362,x69361,x69363)+E(x69361,f2(a1))+P1(f324(f324(f239(a1),x69361),f2(a1)))+P1(f324(f324(f239(a1),f793(x69363,x69361,x69362)),x69361)) % 181.55/181.54 [6937]P143(x69372,x69371,x69373)+E(x69371,f2(a1))+P1(f324(f324(f239(a1),x69371),f2(a1)))+P1(f324(f324(f239(a1),f804(x69373,x69371,x69372)),x69371)) % 181.55/181.54 [6975]P144(x69752,x69751,x69753)+E(x69751,f2(a1))+P1(f324(f324(f238(a1),f792(x69753,x69751,x69752)),f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x69751)) % 181.55/181.54 [6976]P143(x69762,x69761,x69763)+E(x69761,f2(a1))+P1(f324(f324(f238(a1),f803(x69763,x69761,x69762)),f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x69761)) % 181.55/181.54 [6998]~P105(x69981)+~P16(x69981,x69983)+E(f324(f324(f142(x69981,x69981,f5(x69981)),x69982),f164(x69981,x69982,x69983)),x69983)+~P1(f324(f324(f326(x69981),x69982),f324(f167(x69981),x69983))) % 181.55/181.54 [7045]P143(x70451,x70452,x70453)+~P1(f324(x70451,x70453))+P1(f324(f324(f239(a1),x70452),f2(a1)))+P1(f324(f324(f239(a1),f804(x70453,x70452,x70451)),x70452)) % 181.55/181.54 [7051]~P104(x70511)+~P90(x70511)+E(f324(f324(f189(x70511),f324(f106(x70511),x70512)),f324(f106(x70511),x70513)),f324(f106(x70511),x70512))+~P1(f324(f324(f238(x70511),f324(f106(x70511),x70512)),f324(f106(x70511),x70513))) % 181.55/181.54 [7052]~P104(x70521)+~P90(x70521)+E(f324(f324(f190(x70521),f324(f106(x70521),x70522)),f324(f106(x70521),x70523)),f324(f106(x70521),x70523))+~P1(f324(f324(f238(x70521),f324(f106(x70521),x70522)),f324(f106(x70521),x70523))) % 181.55/181.54 [7066]P144(x70661,x70662,x70663)+~P1(f324(x70661,f2(a1)))+P1(f324(f324(f239(a1),x70662),f2(a1)))+P1(f324(f324(f239(a1),f793(x70663,x70662,x70661)),x70662)) % 181.55/181.54 [7074]P143(x70741,x70742,x70743)+~P1(f324(x70741,x70743))+P1(f324(f324(f238(a1),f803(x70743,x70742,x70741)),f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x70742)) % 181.55/181.54 [7098]P144(x70981,x70982,x70983)+~P1(f324(x70981,f2(a1)))+P1(f324(f324(f238(a1),f792(x70983,x70982,x70981)),f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x70982)) % 181.55/181.54 [7125]~P1(f324(x71251,x71252))+P1(f324(x71251,f2(a865)))+~P1(f324(f324(f239(a865),x71252),x71253))+P1(f324(f324(f239(a865),f575(x71252,x71251,x71253)),x71253)) % 181.55/181.54 [7142]~P105(x71421)+~P16(x71421,x71423)+P16(x71421,f324(f324(f145(x71421),x71422),x71423))+P1(f324(f324(f326(x71421),f732(x71423,x71422,x71421)),f324(f167(x71421),x71423))) % 181.55/181.54 [7143]~P105(x71431)+~P16(x71431,x71433)+P16(x71431,f324(f324(f145(x71431),x71432),x71433))+P1(f324(f324(f326(x71431),f733(x71433,x71432,x71431)),f324(f167(x71431),x71433))) % 181.55/181.54 [7144]~P105(x71441)+~P16(x71441,x71443)+P16(x71441,f324(f324(f145(x71441),x71442),x71443))+P1(f324(f324(f326(x71441),f765(x71442,x71443,x71441)),f324(f167(x71441),x71443))) % 181.55/181.54 [7248]~P105(x72481)+~P6(x72481)+~P1(f324(f324(f239(x72481),x72483),f39(x72481,x72482)))+P1(f324(f324(f326(x72481),f605(x72482,x72483,x72481)),x72482)) % 181.55/181.54 [7411]~P105(x74111)+~P6(x74111)+~P1(f324(f324(f239(x74111),f40(x74111,x74113)),x74112))+P1(f324(f324(f326(x74111),f630(x74112,x74113,x74111)),x74113)) % 181.55/181.54 [7412]~P105(x74121)+~P6(x74121)+~P1(f324(f324(f239(x74121),f40(x74121,x74123)),x74122))+P1(f324(f324(f239(x74121),f630(x74122,x74123,x74121)),x74122)) % 181.55/181.54 [7427]P144(x74272,x74271,x74273)+E(x74271,f2(a1))+P1(f324(f324(f239(a1),x74271),f792(x74273,x74271,x74272)))+P1(f324(f324(f239(a1),f793(x74273,x74271,x74272)),x74271)) % 181.55/181.54 [7428]P143(x74282,x74281,x74283)+E(x74281,f2(a1))+P1(f324(f324(f239(a1),x74281),f803(x74283,x74281,x74282)))+P1(f324(f324(f239(a1),f804(x74283,x74281,x74282)),x74281)) % 181.55/181.54 [7518]P144(x75183,x75181,x75182)+E(x75181,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x75181),f802(x75182,x75181,x75183))),f792(x75182,x75181,x75183)),x75182)+P1(f324(f324(f239(a1),f2(a1)),x75181)) % 181.55/181.54 [7519]P143(x75193,x75191,x75192)+E(x75191,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x75191),f806(x75192,x75191,x75193))),f803(x75192,x75191,x75193)),x75192)+P1(f324(f324(f239(a1),f2(a1)),x75191)) % 181.55/181.54 [7522]~P130(x75221)+~P1(f324(f324(f238(x75221),x75223),f2(x75221)))+P1(f324(f324(f238(x75221),f324(f324(f82(x75221),x75222),x75223)),f2(x75221)))+~P1(f324(f324(f238(x75221),f2(x75221)),x75222)) % 181.55/181.54 [7524]~P130(x75241)+~P1(f324(f324(f238(x75241),x75242),f2(x75241)))+P1(f324(f324(f238(x75241),f324(f324(f82(x75241),x75242),x75243)),f2(x75241)))+~P1(f324(f324(f238(x75241),f2(x75241)),x75243)) % 181.55/181.54 [7525]~P121(x75251)+~P1(f324(f324(f238(x75251),x75253),f2(x75251)))+P1(f324(f324(f238(x75251),f324(f324(f82(x75251),x75252),x75253)),f2(x75251)))+~P1(f324(f324(f238(x75251),f2(x75251)),x75252)) % 181.55/181.54 [7526]~P121(x75261)+~P1(f324(f324(f238(x75261),x75262),f2(x75261)))+P1(f324(f324(f238(x75261),f324(f324(f82(x75261),x75262),x75263)),f2(x75261)))+~P1(f324(f324(f238(x75261),f2(x75261)),x75263)) % 181.55/181.54 [7527]~P64(x75271)+~P1(f324(f324(f238(x75271),x75273),f2(x75271)))+P1(f324(f324(f238(x75271),f324(f324(f282(x75271),x75272),x75273)),f2(x75271)))+~P1(f324(f324(f238(x75271),f2(x75271)),x75272)) % 181.55/181.54 [7528]~P64(x75281)+~P1(f324(f324(f238(x75281),x75282),f2(x75281)))+P1(f324(f324(f238(x75281),f324(f324(f282(x75281),x75282),x75283)),f2(x75281)))+~P1(f324(f324(f238(x75281),f2(x75281)),x75283)) % 181.55/181.54 [7529]~P65(x75291)+~P1(f324(f324(f238(x75291),x75292),f2(x75291)))+P1(f324(f324(f238(x75291),f324(f324(f282(x75291),x75292),x75293)),f2(x75291)))+~P1(f324(f324(f239(x75291),f2(x75291)),x75293)) % 181.55/181.54 [7530]~P65(x75301)+~P1(f324(f324(f239(x75301),x75303),f2(x75301)))+P1(f324(f324(f238(x75301),f324(f324(f282(x75301),x75302),x75303)),f2(x75301)))+~P1(f324(f324(f238(x75301),f2(x75301)),x75302)) % 181.55/181.54 [7532]~P126(x75321)+~P1(f324(f324(f239(x75321),x75323),f2(x75321)))+P1(f324(f324(f239(x75321),f324(f324(f82(x75321),x75322),x75323)),f2(x75321)))+~P1(f324(f324(f239(x75321),f2(x75321)),x75322)) % 181.55/181.54 [7533]~P126(x75331)+~P1(f324(f324(f239(x75331),x75332),f2(x75331)))+P1(f324(f324(f239(x75331),f324(f324(f82(x75331),x75332),x75333)),f2(x75331)))+~P1(f324(f324(f239(x75331),f2(x75331)),x75333)) % 181.55/181.54 [7534]~P64(x75341)+~P1(f324(f324(f239(x75341),x75343),f2(x75341)))+P1(f324(f324(f239(x75341),f324(f324(f282(x75341),x75342),x75343)),f2(x75341)))+~P1(f324(f324(f239(x75341),f2(x75341)),x75342)) % 181.55/181.54 [7535]~P64(x75351)+~P1(f324(f324(f239(x75351),x75352),f2(x75351)))+P1(f324(f324(f239(x75351),f324(f324(f282(x75351),x75352),x75353)),f2(x75351)))+~P1(f324(f324(f239(x75351),f2(x75351)),x75353)) % 181.55/181.54 [7536]~P65(x75361)+~P1(f324(f324(f239(x75361),x75363),f2(x75361)))+P1(f324(f324(f239(x75361),f324(f324(f282(x75361),x75362),x75363)),f2(x75361)))+~P1(f324(f324(f239(x75361),f2(x75361)),x75362)) % 181.55/181.54 [7537]~P65(x75371)+~P1(f324(f324(f239(x75371),x75372),f2(x75371)))+P1(f324(f324(f239(x75371),f324(f324(f282(x75371),x75372),x75373)),f2(x75371)))+~P1(f324(f324(f239(x75371),f2(x75371)),x75373)) % 181.55/181.54 [7552]P143(x75521,x75522,x75523)+~P1(f324(x75521,x75523))+P1(f324(f324(f239(a1),x75522),f803(x75523,x75522,x75521)))+P1(f324(f324(f239(a1),f804(x75523,x75522,x75521)),x75522)) % 181.55/181.54 [7565]P144(x75651,x75652,x75653)+P1(f324(f324(f239(a1),x75652),f792(x75653,x75652,x75651)))+~P1(f324(x75651,f2(a1)))+P1(f324(f324(f239(a1),f793(x75653,x75652,x75651)),x75652)) % 181.55/181.54 [7615]P144(x76152,x76151,x76153)+E(x76151,f2(a1))+~P1(f324(x76152,f802(x76153,x76151,x76152)))+P1(f324(f324(f239(a1),f793(x76153,x76151,x76152)),x76151)) % 181.55/181.54 [7616]P143(x76162,x76161,x76163)+E(x76161,f2(a1))+~P1(f324(x76162,f803(x76163,x76161,x76162)))+P1(f324(f324(f239(a1),f804(x76163,x76161,x76162)),x76161)) % 181.55/181.54 [7626]P143(x76263,x76261,x76262)+~P1(f324(x76263,x76262))+E(f324(f324(f81(a1),f324(f324(f82(a1),x76261),f806(x76262,x76261,x76263))),f803(x76262,x76261,x76263)),x76262)+P1(f324(f324(f239(a1),f2(a1)),x76261)) % 181.55/181.54 [7643]P144(x76433,x76431,x76432)+E(f324(f324(f81(a1),f324(f324(f82(a1),x76431),f802(x76432,x76431,x76433))),f792(x76432,x76431,x76433)),x76432)+~P1(f324(x76433,f2(a1)))+P1(f324(f324(f239(a1),f2(a1)),x76431)) % 181.55/181.54 [7668]~P1(f324(x76681,x76683))+~P1(f324(f61(x76682),x76683))+P1(f324(f324(f326(x76682),f829(x76681,x76683,x76682)),f826(x76681,x76683,x76682)))+P1(f324(x76681,f191(f871(x76682,a859)))) % 181.55/181.54 [7679]P143(x76791,x76792,x76793)+~P1(f324(x76791,x76793))+~P1(f324(x76791,f803(x76793,x76792,x76791)))+P1(f324(f324(f239(a1),f804(x76793,x76792,x76791)),x76792)) % 181.55/181.54 [7684]P144(x76841,x76842,x76843)+~P1(f324(x76841,f802(x76843,x76842,x76841)))+~P1(f324(x76841,f2(a1)))+P1(f324(f324(f239(a1),f793(x76843,x76842,x76841)),x76842)) % 181.55/181.54 [7782]~P121(x77821)+~P1(f324(f324(f238(x77821),f324(f324(f82(x77821),x77823),x77822)),f2(x77821)))+P1(f324(f324(f238(x77821),x77822),f2(x77821)))+P1(f324(f324(f238(x77821),f2(x77821)),x77822)) % 181.55/181.54 [7783]~P121(x77831)+~P1(f324(f324(f238(x77831),f324(f324(f82(x77831),x77832),x77833)),f2(x77831)))+P1(f324(f324(f238(x77831),x77832),f2(x77831)))+P1(f324(f324(f238(x77831),f2(x77831)),x77832)) % 181.55/181.54 [7784]~P64(x77841)+~P1(f324(f324(f238(x77841),f324(f324(f282(x77841),x77843),x77842)),f2(x77841)))+P1(f324(f324(f238(x77841),x77842),f2(x77841)))+P1(f324(f324(f238(x77841),f2(x77841)),x77842)) % 181.55/181.54 [7785]~P64(x77851)+~P1(f324(f324(f238(x77851),f324(f324(f282(x77851),x77852),x77853)),f2(x77851)))+P1(f324(f324(f238(x77851),x77852),f2(x77851)))+P1(f324(f324(f238(x77851),f2(x77851)),x77852)) % 181.55/181.54 [7786]~P64(x77861)+~P1(f324(f324(f239(x77861),f324(f324(f282(x77861),x77863),x77862)),f2(x77861)))+P1(f324(f324(f239(x77861),x77862),f2(x77861)))+P1(f324(f324(f239(x77861),f2(x77861)),x77862)) % 181.55/181.54 [7787]~P64(x77871)+~P1(f324(f324(f239(x77871),f324(f324(f282(x77871),x77872),x77873)),f2(x77871)))+P1(f324(f324(f239(x77871),x77872),f2(x77871)))+P1(f324(f324(f239(x77871),f2(x77871)),x77872)) % 181.55/181.54 [7812]~P121(x78121)+~P1(f324(f324(f238(x78121),f324(f324(f82(x78121),x78122),x78123)),f2(x78121)))+P1(f324(f324(f238(x78121),f2(x78121)),x78122))+P1(f324(f324(f238(x78121),f2(x78121)),x78123)) % 181.55/181.54 [7813]~P64(x78131)+~P1(f324(f324(f238(x78131),f324(f324(f282(x78131),x78132),x78133)),f2(x78131)))+P1(f324(f324(f238(x78131),f2(x78131)),x78132))+P1(f324(f324(f238(x78131),f2(x78131)),x78133)) % 181.55/181.54 [7814]~P64(x78141)+~P1(f324(f324(f239(x78141),f324(f324(f282(x78141),x78142),x78143)),f2(x78141)))+P1(f324(f324(f239(x78141),f2(x78141)),x78142))+P1(f324(f324(f239(x78141),f2(x78141)),x78143)) % 181.55/181.54 [7836]P144(x78362,x78361,x78363)+E(x78361,f2(a1))+P1(f324(f324(f238(a1),f792(x78363,x78361,x78362)),f2(a1)))+P1(f324(f324(f239(a1),f793(x78363,x78361,x78362)),x78361)) % 181.55/181.54 [7837]P143(x78372,x78371,x78373)+E(x78371,f2(a1))+P1(f324(f324(f238(a1),f803(x78373,x78371,x78372)),f2(a1)))+P1(f324(f324(f239(a1),f804(x78373,x78371,x78372)),x78371)) % 181.55/181.54 [7845]~P120(x78451)+~P1(f324(f324(f239(x78451),x78452),f79(x78451)))+P1(f324(f324(f239(x78451),f324(f324(f249(x78451),x78452),f324(a115,x78453))),f79(x78451)))+~P1(f324(f324(f239(x78451),f2(x78451)),x78452)) % 181.55/181.54 [7902]~P105(x79021)+~E(x79023,f116(x79021))+~P16(x79021,f324(f163(x79021),x79023))+E(f324(f136(x79021,x79021,f324(f7(x79021,x79021,x79021),f190(x79021)),x79022),f324(f163(x79021),x79023)),x79022) % 181.55/181.54 [7904]P143(x79041,x79042,x79043)+~P1(f324(x79041,x79043))+P1(f324(f324(f238(a1),f803(x79043,x79042,x79041)),f2(a1)))+P1(f324(f324(f239(a1),f804(x79043,x79042,x79041)),x79042)) % 181.55/181.54 [7911]P144(x79111,x79112,x79113)+~P1(f324(x79111,f2(a1)))+P1(f324(f324(f238(a1),f792(x79113,x79112,x79111)),f2(a1)))+P1(f324(f324(f239(a1),f793(x79113,x79112,x79111)),x79112)) % 181.55/181.54 [8130]P144(x81303,x81301,x81302)+E(x81301,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x81301),f802(x81302,x81301,x81303))),f792(x81302,x81301,x81303)),x81302)+P1(f324(f324(f239(a1),f793(x81302,x81301,x81303)),x81301)) % 181.55/181.54 [8131]P143(x81313,x81311,x81312)+E(x81311,f2(a1))+E(f324(f324(f81(a1),f324(f324(f82(a1),x81311),f806(x81312,x81311,x81313))),f803(x81312,x81311,x81313)),x81312)+P1(f324(f324(f239(a1),f804(x81312,x81311,x81313)),x81311)) % 181.55/181.54 [8168]P143(x81683,x81681,x81682)+~P1(f324(x81683,x81682))+E(f324(f324(f81(a1),f324(f324(f82(a1),x81681),f806(x81682,x81681,x81683))),f803(x81682,x81681,x81683)),x81682)+P1(f324(f324(f239(a1),f804(x81682,x81681,x81683)),x81681)) % 181.55/181.54 [8169]~P68(x81691)+~P72(x81691)+~P40(x81693)+E(f324(f324(f9(a865,x81691),f324(f324(f8(a1,x81691,a865),x81692),f103(a1))),f324(f303(a1,a865,a107),x81693)),f324(f324(f9(a1,x81691),x81692),x81693)) % 181.55/181.54 [8170]~P68(x81701)+~P72(x81701)+~P40(x81703)+E(f324(f324(f6(a865,x81701),f324(f324(f8(a1,x81701,a865),x81702),f103(a1))),f324(f303(a1,a865,a107),x81703)),f324(f324(f6(a1,x81701),x81702),x81703)) % 181.55/181.54 [8179]P144(x81793,x81791,x81792)+E(f324(f324(f81(a1),f324(f324(f82(a1),x81791),f802(x81792,x81791,x81793))),f792(x81792,x81791,x81793)),x81792)+~P1(f324(x81793,f2(a1)))+P1(f324(f324(f239(a1),f793(x81792,x81791,x81793)),x81791)) % 181.55/181.54 [8200]~E(x82002,f2(a865))+~E(f324(f258(a865,a865),x82003),f2(a865))+~E(x82001,f324(f324(f81(a865),f324(f324(f82(a865),f324(f258(a865,a865),x82003)),x82002)),f324(f262(a865,a865),x82003)))+P1(f324(f47(x82001,x82002),x82003)) % 181.55/181.54 [8255]P1(f324(x82551,x82552))+~P1(f324(f324(f326(x82553),f797(x82551,x82552,x82553)),f795(x82551,x82552,x82553)))+~P1(f324(f61(x82553),x82552))+~P1(f324(x82551,f191(f871(x82553,a859)))) % 181.55/181.54 [8880]P1(f324(x88801,x88802))+~P1(f324(f61(x88803),x88802))+~P1(f324(x88801,f324(f324(f302(x88803),f797(x88801,x88802,x88803)),f795(x88801,x88802,x88803))))+~P1(f324(x88801,f191(f871(x88803,a859)))) % 181.55/181.54 [9113]P1(f324(f324(f238(a1),x91131),f2(a1)))+~P1(f324(f324(f239(a1),f324(f324(f81(a1),f324(f324(f82(a1),x91133),x91131)),x91132)),f2(a1)))+~P1(f324(f324(f238(a1),f2(a1)),x91132))+~P1(f324(f324(f239(a1),f2(a1)),x91133)) % 181.55/181.54 [5757]~P94(x57572)+E(x57571,f191(f871(x57572,a859)))+~P1(f324(f61(x57572),x57571))+E(f13(x57572,f324(f324(f302(x57572),x57573),x57571)),f324(f324(f113(x57572),x57573),f13(x57572,x57571))) % 181.55/181.54 [5758]~P94(x57582)+E(x57581,f191(f871(x57582,a859)))+~P1(f324(f61(x57582),x57581))+E(f10(x57582,f324(f324(f302(x57582),x57583),x57581)),f324(f324(f104(x57582),x57583),f10(x57582,x57581))) % 181.55/181.54 [5759]~P105(x57592)+E(x57591,f191(f871(x57592,a859)))+~P1(f324(f61(x57592),x57591))+E(f14(x57592,f324(f324(f302(x57592),x57593),x57591)),f324(f324(f190(x57592),x57593),f14(x57592,x57591))) % 181.55/181.54 [5760]~P105(x57602)+E(x57601,f191(f871(x57602,a859)))+~P1(f324(f61(x57602),x57601))+E(f15(x57602,f324(f324(f302(x57602),x57603),x57601)),f324(f324(f189(x57602),x57603),f15(x57602,x57601))) % 181.55/181.54 [6060]~P121(x60601)+~E(x60603,f2(x60601))+~E(x60602,f2(x60601))+E(f324(f324(f81(x60601),f324(f324(f82(x60601),x60602),x60602)),f324(f324(f82(x60601),x60603),x60603)),f2(x60601)) % 181.55/181.54 [6125]~P93(x61252)+E(x61251,f191(f871(x61252,a859)))+~P1(f324(f61(x61252),x61251))+E(f324(f63(x61252,f82(x61252)),f324(f324(f302(x61252),x61253),x61251)),f324(f324(f82(x61252),x61253),f324(f63(x61252,f82(x61252)),x61251))) % 181.55/181.54 [6247]~P105(x62472)+E(x62471,f191(f871(x62472,a859)))+~P1(f324(f61(x62472),x62471))+E(f11(x62472,f190(x62472),f324(f324(f302(x62472),x62473),x62471)),f324(f324(f190(x62472),x62473),f11(x62472,f190(x62472),x62471))) % 181.55/181.54 [6248]~P105(x62482)+E(x62481,f191(f871(x62482,a859)))+~P1(f324(f61(x62482),x62481))+E(f12(x62482,f189(x62482),f324(f324(f302(x62482),x62483),x62481)),f324(f324(f189(x62482),x62483),f12(x62482,f189(x62482),x62481))) % 181.55/181.54 [6750]~P66(x67501)+~P1(f324(f61(x67501),x67503))+E(f324(f63(x67501,f82(x67501)),f324(f324(f302(x67501),x67502),x67503)),f324(f324(f64(x67501,x67501,f82(x67501)),x67502),x67503))+P1(f324(f324(f326(x67501),x67502),x67503)) % 181.55/181.54 [6830]~E(f324(f324(f81(a1),x68302),f324(f324(f82(a1),x68303),x68301)),x68303)+~P1(f324(f324(f239(a1),f2(a1)),x68303))+P1(f324(f324(f238(a1),f79(a1)),x68301))+~P1(f324(f324(f239(a1),x68302),x68303)) % 181.55/181.54 [6857]~E(f324(f324(f81(a1),x68572),f324(f324(f82(a1),x68573),x68571)),x68573)+P1(f324(f324(f238(a1),x68571),f79(a1)))+~P1(f324(f324(f238(a1),f2(a1)),x68572))+~P1(f324(f324(f239(a1),f2(a1)),x68573)) % 181.55/181.54 [6873]E(x68731,f2(a865))+~P1(f324(f47(x68733,x68731),x68732))+~P1(f324(f324(f239(a865),f2(a865)),x68731))+P1(f324(f324(f239(a865),f324(f262(a865,a865),x68732)),x68731)) % 181.55/181.54 [6903]~P133(x69031)+~P1(f324(f324(f238(x69031),x69032),f2(x69031)))+~P1(f324(f324(f238(x69031),x69033),f2(x69031)))+E(f324(f324(f82(x69031),f324(f75(x69031),x69032)),f324(f75(x69031),x69033)),f324(f75(x69031),f324(f324(f82(x69031),x69032),x69033))) % 181.55/181.54 [6952]~P133(x69521)+~P1(f324(f324(f238(x69521),x69522),f2(x69521)))+E(f324(f324(f82(x69521),f324(f75(x69521),x69522)),f324(f75(x69521),x69523)),f324(f75(x69521),f324(f324(f82(x69521),x69522),x69523)))+~P1(f324(f324(f238(x69521),f2(x69521)),x69523)) % 181.55/181.54 [6953]~P133(x69531)+~P1(f324(f324(f238(x69531),x69533),f2(x69531)))+E(f324(f324(f82(x69531),f324(f75(x69531),x69532)),f324(f75(x69531),x69533)),f324(f75(x69531),f324(f324(f82(x69531),x69532),x69533)))+~P1(f324(f324(f238(x69531),f2(x69531)),x69532)) % 181.55/181.54 [7007]~P133(x70071)+E(f324(f324(f82(x70071),f324(f75(x70071),x70072)),f324(f75(x70071),x70073)),f324(f75(x70071),f324(f324(f82(x70071),x70072),x70073)))+~P1(f324(f324(f238(x70071),f2(x70071)),x70072))+~P1(f324(f324(f238(x70071),f2(x70071)),x70073)) % 181.55/181.54 [7024]~P123(x70241)+~P1(f324(f324(f238(x70241),x70243),f2(x70241)))+~P1(f324(f324(f238(x70241),x70242),f2(x70241)))+P1(f324(f324(f238(x70241),f2(x70241)),f324(f324(f82(x70241),x70242),x70243))) % 181.55/181.54 [7025]~P121(x70251)+~P1(f324(f324(f238(x70251),x70253),f2(x70251)))+~P1(f324(f324(f238(x70251),x70252),f2(x70251)))+P1(f324(f324(f238(x70251),f2(x70251)),f324(f324(f82(x70251),x70252),x70253))) % 181.55/181.54 [7026]~P64(x70261)+~P1(f324(f324(f238(x70261),x70263),f2(x70261)))+~P1(f324(f324(f238(x70261),x70262),f2(x70261)))+P1(f324(f324(f238(x70261),f2(x70261)),f324(f324(f282(x70261),x70262),x70263))) % 181.55/181.54 [7027]~P65(x70271)+~P1(f324(f324(f239(x70271),x70273),f2(x70271)))+~P1(f324(f324(f238(x70271),x70272),f2(x70271)))+P1(f324(f324(f238(x70271),f2(x70271)),f324(f324(f282(x70271),x70272),x70273))) % 181.55/181.54 [7028]~P121(x70281)+~P1(f324(f324(f239(x70281),x70283),f2(x70281)))+~P1(f324(f324(f239(x70281),x70282),f2(x70281)))+P1(f324(f324(f239(x70281),f2(x70281)),f324(f324(f82(x70281),x70282),x70283))) % 181.55/181.54 [7029]~P64(x70291)+~P1(f324(f324(f239(x70291),x70293),f2(x70291)))+~P1(f324(f324(f239(x70291),x70292),f2(x70291)))+P1(f324(f324(f239(x70291),f2(x70291)),f324(f324(f282(x70291),x70292),x70293))) % 181.55/181.54 [7030]~P65(x70301)+~P1(f324(f324(f239(x70301),x70303),f2(x70301)))+~P1(f324(f324(f239(x70301),x70302),f2(x70301)))+P1(f324(f324(f239(x70301),f2(x70301)),f324(f324(f282(x70301),x70302),x70303))) % 181.55/181.54 [7031]~P120(x70311)+~P1(f324(f324(f239(a865),f2(a865)),x70313))+~P1(f324(f324(f239(x70311),f79(x70311)),x70312))+P1(f324(f324(f239(x70311),f79(x70311)),f324(f324(f249(x70311),x70312),x70313))) % 181.55/181.54 [7126]~P123(x71261)+~P1(f324(f324(f238(x71261),f2(x71261)),x71263))+~P1(f324(f324(f238(x71261),f2(x71261)),x71262))+P1(f324(f324(f238(x71261),f2(x71261)),f324(f324(f82(x71261),x71262),x71263))) % 181.55/181.54 [7127]~P130(x71271)+~P1(f324(f324(f238(x71271),f2(x71271)),x71273))+~P1(f324(f324(f238(x71271),f2(x71271)),x71272))+P1(f324(f324(f238(x71271),f2(x71271)),f324(f324(f82(x71271),x71272),x71273))) % 181.55/181.54 [7128]~P121(x71281)+~P1(f324(f324(f238(x71281),f2(x71281)),x71283))+~P1(f324(f324(f238(x71281),f2(x71281)),x71282))+P1(f324(f324(f238(x71281),f2(x71281)),f324(f324(f82(x71281),x71282),x71283))) % 181.55/181.54 [7130]~P64(x71301)+~P1(f324(f324(f238(x71301),f2(x71301)),x71303))+~P1(f324(f324(f238(x71301),f2(x71301)),x71302))+P1(f324(f324(f238(x71301),f2(x71301)),f324(f324(f282(x71301),x71302),x71303))) % 181.55/181.54 [7131]~P65(x71311)+~P1(f324(f324(f239(x71311),f2(x71311)),x71313))+~P1(f324(f324(f238(x71311),f2(x71311)),x71312))+P1(f324(f324(f238(x71311),f2(x71311)),f324(f324(f282(x71311),x71312),x71313))) % 181.55/181.54 [7132]~P120(x71321)+~P1(f324(f324(f239(x71321),f79(x71321)),x71323))+~P1(f324(f324(f239(x71321),f79(x71321)),x71322))+P1(f324(f324(f239(x71321),f79(x71321)),f324(f324(f82(x71321),x71322),x71323))) % 181.55/181.54 [7133]~P126(x71331)+~P1(f324(f324(f239(x71331),f2(x71331)),x71333))+~P1(f324(f324(f239(x71331),f2(x71331)),x71332))+P1(f324(f324(f239(x71331),f2(x71331)),f324(f324(f82(x71331),x71332),x71333))) % 181.55/181.54 [7136]~P85(x71361)+~P1(f324(f324(f239(x71361),f2(x71361)),x71363))+~P1(f324(f324(f239(x71361),f2(x71361)),x71362))+P1(f324(f324(f239(x71361),f2(x71361)),f324(f324(f81(x71361),x71362),x71363))) % 181.55/181.54 [7137]~P64(x71371)+~P1(f324(f324(f239(x71371),f2(x71371)),x71373))+~P1(f324(f324(f239(x71371),f2(x71371)),x71372))+P1(f324(f324(f239(x71371),f2(x71371)),f324(f324(f282(x71371),x71372),x71373))) % 181.55/181.54 [7138]~P65(x71381)+~P1(f324(f324(f239(x71381),f2(x71381)),x71383))+~P1(f324(f324(f239(x71381),f2(x71381)),x71382))+P1(f324(f324(f239(x71381),f2(x71381)),f324(f324(f282(x71381),x71382),x71383))) % 181.55/181.54 [7209]~P94(x72091)+~P1(f324(f61(x72091),x72093))+E(f13(x72091,f324(f324(f302(x72091),x72092),x72093)),x72092)+~E(f324(f324(f22(f871(x72091,a859)),x72093),f324(f324(f302(x72091),x72092),f191(f871(x72091,a859)))),f191(f871(x72091,a859))) % 181.55/181.54 [7210]~P94(x72101)+~P1(f324(f61(x72101),x72103))+E(f10(x72101,f324(f324(f302(x72101),x72102),x72103)),x72102)+~E(f324(f324(f22(f871(x72101,a859)),x72103),f324(f324(f302(x72101),x72102),f191(f871(x72101,a859)))),f191(f871(x72101,a859))) % 181.55/181.54 [7211]~P105(x72111)+~P1(f324(f61(x72111),x72113))+E(f14(x72111,f324(f324(f302(x72111),x72112),x72113)),x72112)+~E(f324(f324(f22(f871(x72111,a859)),x72113),f324(f324(f302(x72111),x72112),f191(f871(x72111,a859)))),f191(f871(x72111,a859))) % 181.55/181.54 [7212]~P105(x72121)+~P1(f324(f61(x72121),x72123))+E(f15(x72121,f324(f324(f302(x72121),x72122),x72123)),x72122)+~E(f324(f324(f22(f871(x72121,a859)),x72123),f324(f324(f302(x72121),x72122),f191(f871(x72121,a859)))),f191(f871(x72121,a859))) % 181.55/181.54 [7213]~P121(x72131)+P1(f324(f324(f238(x72131),x72132),f2(x72131)))+P1(f324(f324(f238(x72131),f2(x72131)),x72133))+~P1(f324(f324(f238(x72131),f2(x72131)),f324(f324(f82(x72131),x72133),x72132))) % 181.55/181.54 [7214]~P121(x72141)+P1(f324(f324(f238(x72141),x72142),f2(x72141)))+P1(f324(f324(f238(x72141),f2(x72141)),x72143))+~P1(f324(f324(f238(x72141),f2(x72141)),f324(f324(f82(x72141),x72142),x72143))) % 181.55/181.54 [7215]~P64(x72151)+P1(f324(f324(f238(x72151),x72152),f2(x72151)))+P1(f324(f324(f238(x72151),f2(x72151)),x72153))+~P1(f324(f324(f238(x72151),f2(x72151)),f324(f324(f282(x72151),x72153),x72152))) % 181.55/181.54 [7216]~P64(x72161)+P1(f324(f324(f238(x72161),x72162),f2(x72161)))+P1(f324(f324(f238(x72161),f2(x72161)),x72163))+~P1(f324(f324(f238(x72161),f2(x72161)),f324(f324(f282(x72161),x72162),x72163))) % 181.55/181.54 [7217]~P121(x72171)+P1(f324(f324(f238(x72171),x72172),f2(x72171)))+P1(f324(f324(f238(x72171),f2(x72171)),x72172))+~P1(f324(f324(f238(x72171),f2(x72171)),f324(f324(f82(x72171),x72173),x72172))) % 181.55/181.54 [7218]~P121(x72181)+P1(f324(f324(f238(x72181),x72182),f2(x72181)))+P1(f324(f324(f238(x72181),f2(x72181)),x72182))+~P1(f324(f324(f238(x72181),f2(x72181)),f324(f324(f82(x72181),x72182),x72183))) % 181.55/181.54 [7219]~P64(x72191)+P1(f324(f324(f238(x72191),x72192),f2(x72191)))+P1(f324(f324(f238(x72191),f2(x72191)),x72192))+~P1(f324(f324(f238(x72191),f2(x72191)),f324(f324(f282(x72191),x72193),x72192))) % 181.55/181.54 [7220]~P64(x72201)+P1(f324(f324(f238(x72201),x72202),f2(x72201)))+P1(f324(f324(f238(x72201),f2(x72201)),x72202))+~P1(f324(f324(f238(x72201),f2(x72201)),f324(f324(f282(x72201),x72202),x72203))) % 181.55/181.54 [7221]~P64(x72211)+P1(f324(f324(f239(x72211),x72212),f2(x72211)))+P1(f324(f324(f239(x72211),f2(x72211)),x72213))+~P1(f324(f324(f239(x72211),f2(x72211)),f324(f324(f282(x72211),x72213),x72212))) % 181.55/181.54 [7222]~P64(x72221)+P1(f324(f324(f239(x72221),x72222),f2(x72221)))+P1(f324(f324(f239(x72221),f2(x72221)),x72223))+~P1(f324(f324(f239(x72221),f2(x72221)),f324(f324(f282(x72221),x72222),x72223))) % 181.55/181.54 [7223]~P64(x72231)+P1(f324(f324(f239(x72231),x72232),f2(x72231)))+P1(f324(f324(f239(x72231),f2(x72231)),x72232))+~P1(f324(f324(f239(x72231),f2(x72231)),f324(f324(f282(x72231),x72233),x72232))) % 181.55/181.54 [7224]~P64(x72241)+P1(f324(f324(f239(x72241),x72242),f2(x72241)))+P1(f324(f324(f239(x72241),f2(x72241)),x72242))+~P1(f324(f324(f239(x72241),f2(x72241)),f324(f324(f282(x72241),x72242),x72243))) % 181.55/181.54 [7312]~E(f324(f324(f104(f871(x73121,a859)),f324(f167(x73121),x73122)),f324(f167(x73121),x73123)),f191(f871(x73121,a859)))+~P1(f324(f131(x73121),x73123))+~P1(f324(f131(x73121),x73122))+P1(f324(f131(x73121),f324(f324(f124(x73121),x73122),x73123))) % 181.55/181.54 [7313]~P105(x73131)+~P1(f324(f61(x73131),x73133))+E(f11(x73131,f190(x73131),f324(f324(f302(x73131),x73132),x73133)),x73132)+~E(f324(f324(f22(f871(x73131,a859)),x73133),f324(f324(f302(x73131),x73132),f191(f871(x73131,a859)))),f191(f871(x73131,a859))) % 181.55/181.54 [7314]~P105(x73141)+~P1(f324(f61(x73141),x73143))+E(f12(x73141,f189(x73141),f324(f324(f302(x73141),x73142),x73143)),x73142)+~E(f324(f324(f22(f871(x73141,a859)),x73143),f324(f324(f302(x73141),x73142),f191(f871(x73141,a859)))),f191(f871(x73141,a859))) % 181.55/181.54 [7330]~P83(x73301)+~P1(f324(f324(f238(x73301),x73302),x73303))+~P1(f324(f324(f238(x73301),f324(f80(x73301),x73302)),x73303))+P1(f324(f324(f238(x73301),f324(f75(x73301),x73302)),x73303)) % 181.55/181.54 [7331]~P117(x73311)+~P1(f324(f324(f239(x73311),x73312),x73313))+~P1(f324(f324(f239(x73311),f324(f80(x73311),x73312)),x73313))+P1(f324(f324(f239(x73311),f324(f75(x73311),x73312)),x73313)) % 181.55/181.54 [7401]~P126(x74011)+P1(f324(f324(f239(x74011),f2(x74011)),x74012))+~P1(f324(f324(f239(x74011),f2(x74011)),x74013))+~P1(f324(f324(f239(x74011),f2(x74011)),f324(f324(f82(x74011),x74013),x74012))) % 181.55/181.54 [7402]~P126(x74021)+P1(f324(f324(f239(x74021),f2(x74021)),x74022))+~P1(f324(f324(f239(x74021),f2(x74021)),x74023))+~P1(f324(f324(f239(x74021),f2(x74021)),f324(f324(f82(x74021),x74022),x74023))) % 181.55/181.54 [7700]E(x77001,x77002)+~P1(f324(f61(x77003),x77001))+~P1(f324(f324(f238(a865),f324(f37(x77003),x77001)),f324(f37(x77003),x77002)))+~P1(f324(f324(f238(f871(x77003,a859)),x77002),x77001)) % 181.55/181.54 [7841]~P1(f324(f324(f239(a1),x78411),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x78412))+~P1(f324(f324(f238(a1),x78412),x78413))+P1(f324(f324(f238(a1),f324(f324(f38(a1),x78411),x78412)),f324(f324(f38(a1),x78411),x78413))) % 181.55/181.54 [7853]~P1(f324(f324(f238(a1),f2(a1)),x78531))+~P1(f324(f324(f239(a1),f2(a1)),x78533))+~P1(f324(f324(f238(a1),x78533),x78532))+P1(f324(f324(f238(a1),f324(f324(f38(a1),x78531),x78532)),f324(f324(f38(a1),x78531),x78533))) % 181.55/181.54 [7989]E(f324(x79891,f519(x79892,x79891,x79893)),x79892)+~P1(f324(f324(f238(a1),x79892),f324(x79891,x79893)))+P1(f324(f324(f239(a865),f520(x79892,x79891,x79893)),x79893))+~P1(f324(f324(f238(a1),f324(x79891,f2(a865))),x79892)) % 181.55/181.54 [7990]E(f324(x79901,f529(x79902,x79901,x79903)),x79902)+~P1(f324(f324(f238(a1),x79902),f324(x79901,x79903)))+P1(f324(f324(f239(a865),f530(x79902,x79901,x79903)),x79903))+~P1(f324(f324(f238(a1),f324(x79901,f2(a865))),x79902)) % 181.55/181.54 [8090]~P1(f324(f61(x80901),x80903))+~P1(f324(f324(f239(a865),f324(f37(x80901),x80902)),f324(f37(x80901),x80903)))+~P1(f324(f324(f238(f871(x80901,a859)),x80902),x80903))+P1(f324(f324(f239(f871(x80901,a859)),x80902),x80903)) % 181.55/181.54 [8119]E(f324(f324(f81(a1),f453(x81193,x81191,x81192)),f454(x81193,x81191,x81192)),x81191)+E(f324(f324(f22(a1),x81191),x81192),x81191)+~P1(f324(f324(f239(a1),f2(a1)),x81192))+~P1(f324(f324(f326(a1),f324(f324(f22(a1),x81191),f79(a1))),x81193)) % 181.55/181.54 [8120]E(f324(f324(f22(a1),f458(x81203,x81201,x81202)),f459(x81203,x81201,x81202)),x81201)+E(f324(f324(f81(a1),x81201),x81202),x81201)+~P1(f324(f324(f239(a1),f2(a1)),x81202))+~P1(f324(f324(f326(a1),f324(f324(f81(a1),x81201),f79(a1))),x81203)) % 181.55/181.54 [8174]~P1(f324(f324(f238(a865),x81743),x81741))+P1(f324(f324(f238(a865),x81741),x81742))+~P1(f324(f324(f238(a865),x81743),x81742))+~P1(f324(f324(f238(a865),f324(f324(f22(a865),x81741),x81743)),f324(f324(f22(a865),x81742),x81743))) % 181.55/181.54 [8175]~P1(f324(f324(f238(a865),x81753),x81751))+P1(f324(f324(f239(a865),x81751),x81752))+~P1(f324(f324(f238(a865),x81753),x81752))+~P1(f324(f324(f239(a865),f324(f324(f22(a865),x81751),x81753)),f324(f324(f22(a865),x81752),x81753))) % 181.55/181.54 [8191]~P105(x81912)+E(x81911,f116(x81912))+~P16(x81912,f324(f163(x81912),x81911))+E(f324(f136(x81912,x81912,f324(f7(x81912,x81912,x81912),f190(x81912)),x81913),f324(f163(x81912),x81911)),f324(f324(f190(x81912),f324(f324(f159(x81912),x81911),f2(a865))),x81913)) % 181.55/181.54 [8260]E(f324(f324(f22(a1),x82601),x82602),x82601)+~P1(f324(f324(f239(a1),f2(a1)),x82602))+P1(f324(f324(f326(a1),f453(x82603,x82601,x82602)),x82603))+~P1(f324(f324(f326(a1),f324(f324(f22(a1),x82601),f79(a1))),x82603)) % 181.55/181.54 [8261]E(f324(f324(f81(a1),x82611),x82612),x82611)+~P1(f324(f324(f239(a1),f2(a1)),x82612))+P1(f324(f324(f326(a1),f458(x82613,x82611,x82612)),x82613))+~P1(f324(f324(f326(a1),f324(f324(f81(a1),x82611),f79(a1))),x82613)) % 181.55/181.54 [8337]~P1(f324(f324(f238(a1),x83371),f324(x83372,x83373)))+P1(f324(f324(f239(a865),f520(x83371,x83372,x83373)),x83373))+P1(f324(f324(f238(a865),f519(x83371,x83372,x83373)),x83373))+~P1(f324(f324(f238(a1),f324(x83372,f2(a865))),x83371)) % 181.55/181.54 [8338]~P1(f324(f324(f238(a1),x83381),f324(x83382,x83383)))+P1(f324(f324(f239(a865),f530(x83381,x83382,x83383)),x83383))+P1(f324(f324(f238(a865),f529(x83381,x83382,x83383)),x83383))+~P1(f324(f324(f238(a1),f324(x83382,f2(a865))),x83381)) % 181.55/181.54 [8407]E(f324(f324(f22(a1),x84071),x84072),x84071)+~P1(f324(f324(f239(a1),f2(a1)),x84072))+P1(f324(f324(f326(a1),f454(x84073,x84071,x84072)),f295(a1,f79(a1),x84072)))+~P1(f324(f324(f326(a1),f324(f324(f22(a1),x84071),f79(a1))),x84073)) % 181.55/181.54 [8408]E(f324(f324(f81(a1),x84081),x84082),x84081)+~P1(f324(f324(f239(a1),f2(a1)),x84082))+P1(f324(f324(f326(a1),f459(x84083,x84081,x84082)),f295(a1,f79(a1),x84082)))+~P1(f324(f324(f326(a1),f324(f324(f81(a1),x84081),f79(a1))),x84083)) % 181.55/181.54 [8539]~P120(x85391)+~P1(f324(f324(f239(x85391),x85392),f79(x85391)))+~P1(f324(f324(f239(x85391),f2(x85391)),x85392))+P1(f324(f324(f239(x85391),f324(f324(f82(x85391),x85392),f324(f324(f249(x85391),x85392),x85393))),f324(f324(f249(x85391),x85392),x85393))) % 181.55/181.54 [8633]~P1(f324(x86331,x86332))+P1(f324(x86331,f2(a865)))+~P1(f324(f324(f239(a865),x86332),x86333))+~P1(f324(x86331,f44(a865,f324(a115,f575(x86332,x86331,x86333)),x86333))) % 181.55/181.54 [8781]E(f514(x87811,x87812,x87813),f2(a865))+P1(f324(f324(x87811,x87813),x87812))+P1(f324(f324(x87811,f514(x87811,x87812,x87813)),f44(a865,f512(x87811,x87812,x87813),f514(x87811,x87812,x87813))))+~P1(f324(f312(f870(a865,a865),a224),f324(f324(f259(a865,a865),x87813),x87812))) % 181.55/181.54 [8819]~P27(x88191,x88191,x88192,x88193)+E(f324(f303(x88191,x88191,x88192),x88193),x88193)+~P1(f324(f61(x88191),x88193))+~P1(f324(f324(f238(f871(x88191,a859)),f324(f303(x88191,x88191,x88192),x88193)),x88193)) % 181.55/181.54 [9055]P1(f324(f324(x90551,x90552),x90553))+~P1(f324(f324(f239(a1),f402(x90551,x90553,x90552)),f2(a1)))+P1(f324(f324(x90551,f324(f80(a1),f401(x90551,x90553,x90552))),f324(f80(a1),f402(x90551,x90553,x90552))))+~P1(f324(f312(f870(a1,a1),a229),f324(f324(f259(a1,a1),x90552),x90553))) % 181.55/181.54 [9239]P1(f324(f324(x92391,x92392),x92393))+P1(f324(f324(x92391,f324(f324(f81(a1),f686(x92391,x92393,x92392)),f79(a1))),f692(x92391,x92393,x92392)))+~P1(f324(f324(f238(a1),f686(x92391,x92393,x92392)),f692(x92391,x92393,x92392)))+~P1(f324(f312(f870(a1,a1),a178),f324(f324(f259(a1,a1),x92392),x92393))) % 181.55/181.54 [9679]~P61(x96792)+~P61(x96791)+~P1(f324(f58(f870(x96791,x96792)),x96793))+P1(f324(f58(x96791),f324(f324(f8(f871(x96792,a859),a859,x96791),f58(x96792)),f324(f324(f8(f871(x96792,f870(x96791,x96792)),f871(x96792,a859),x96791),f324(f8(f870(x96791,x96792),a859,x96792),x96793)),f259(x96791,x96792))))) % 181.55/181.54 [9680]~P61(x96802)+~P61(x96801)+~P1(f324(f57(f870(x96801,x96802)),x96803))+P1(f324(f57(x96801),f324(f324(f8(f871(x96802,a859),a859,x96801),f57(x96802)),f324(f324(f8(f871(x96802,f870(x96801,x96802)),f871(x96802,a859),x96801),f324(f8(f870(x96801,x96802),a859,x96802),x96803)),f259(x96801,x96802))))) % 181.55/181.54 [9782]~P61(x97822)+~P61(x97821)+P1(f324(f58(f870(x97821,x97822)),x97823))+~P1(f324(f58(x97821),f324(f324(f8(f871(x97822,a859),a859,x97821),f58(x97822)),f324(f324(f8(f871(x97822,f870(x97821,x97822)),f871(x97822,a859),x97821),f324(f8(f870(x97821,x97822),a859,x97822),x97823)),f259(x97821,x97822))))) % 181.55/181.54 [9783]~P61(x97832)+~P61(x97831)+P1(f324(f57(f870(x97831,x97832)),x97833))+~P1(f324(f57(x97831),f324(f324(f8(f871(x97832,a859),a859,x97831),f57(x97832)),f324(f324(f8(f871(x97832,f870(x97831,x97832)),f871(x97832,a859),x97831),f324(f8(f870(x97831,x97832),a859,x97832),x97833)),f259(x97831,x97832))))) % 181.55/181.54 [9950]E(f324(x99501,f519(x99502,x99501,x99503)),x99502)+~P1(f324(f324(f238(a1),x99502),f324(x99501,x99503)))+~P1(f324(f324(f238(a1),f324(f75(a1),f324(f324(f22(a1),f324(x99501,f324(f324(f81(a865),f520(x99502,x99501,x99503)),f79(a865)))),f324(x99501,f520(x99502,x99501,x99503))))),f79(a1)))+~P1(f324(f324(f238(a1),f324(x99501,f2(a865))),x99502)) % 181.55/181.54 [9951]E(f324(x99511,f529(x99512,x99511,x99513)),x99512)+~P1(f324(f324(f238(a1),x99512),f324(x99511,x99513)))+~P1(f324(f324(f238(a1),f324(f75(a1),f324(f324(f22(a1),f324(x99511,f324(f324(f81(a865),f530(x99512,x99511,x99513)),f79(a865)))),f324(x99511,f530(x99512,x99511,x99513))))),f79(a1)))+~P1(f324(f324(f238(a1),f324(x99511,f2(a865))),x99512)) % 181.55/181.54 [9955]~P1(f324(f324(f238(a1),x99551),f324(x99552,x99553)))+~P1(f324(f324(f238(a1),f324(f75(a1),f324(f324(f22(a1),f324(x99552,f324(f324(f81(a865),f520(x99551,x99552,x99553)),f79(a865)))),f324(x99552,f520(x99551,x99552,x99553))))),f79(a1)))+P1(f324(f324(f238(a865),f519(x99551,x99552,x99553)),x99553))+~P1(f324(f324(f238(a1),f324(x99552,f2(a865))),x99551)) % 181.55/181.54 [9956]~P1(f324(f324(f238(a1),x99561),f324(x99562,x99563)))+~P1(f324(f324(f238(a1),f324(f75(a1),f324(f324(f22(a1),f324(x99562,f324(f324(f81(a865),f530(x99561,x99562,x99563)),f79(a865)))),f324(x99562,f530(x99561,x99562,x99563))))),f79(a1)))+P1(f324(f324(f238(a865),f529(x99561,x99562,x99563)),x99563))+~P1(f324(f324(f238(a1),f324(x99562,f2(a865))),x99561)) % 181.55/181.54 [10010]E(x100101,x100102)+~E(f324(f136(f866(x100103),f866(x100103),f124(x100103),f116(x100103)),x100101),f324(f136(f866(x100103),f866(x100103),f124(x100103),f116(x100103)),x100102))+~E(f324(f192(f866(f866(x100103))),x100101),f324(f192(f866(f866(x100103))),x100102))+~P1(f324(f324(f263(f866(x100103),f866(x100103),a859),f324(f324(f7(f866(x100103),f871(f866(x100103),a865),f871(f866(x100103),a859)),f324(f324(f8(f871(a865,a859),f871(f871(f866(x100103),a865),f871(f866(x100103),a859)),f866(x100103)),f8(a865,a859,f866(x100103))),f324(f324(f8(a865,f871(a865,a859),f866(x100103)),a321),f192(f866(x100103))))),f192(f866(x100103)))),f723(x100102,x100101,x100103))) % 181.55/181.54 [10011]E(x100111,x100112)+~E(f324(f136(f866(x100113),f866(x100113),f124(x100113),f116(x100113)),x100111),f324(f136(f866(x100113),f866(x100113),f124(x100113),f116(x100113)),x100112))+~E(f324(f192(f866(f866(x100113))),x100111),f324(f192(f866(f866(x100113))),x100112))+~P1(f324(f324(f263(f866(x100113),f866(x100113),a859),f324(f324(f7(f866(x100113),f871(f866(x100113),a865),f871(f866(x100113),a859)),f324(f324(f8(f871(a865,a859),f871(f871(f866(x100113),a865),f871(f866(x100113),a859)),f866(x100113)),f8(a865,a859,f866(x100113))),f324(f324(f8(a865,f871(a865,a859),f866(x100113)),a321),f192(f866(x100113))))),f192(f866(x100113)))),f724(x100111,x100112,x100113))) % 181.55/181.54 [6737]~E(f79(a865),f2(a865))+~P1(f324(f61(x67371),x67373))+~P1(f324(f61(x67371),x67372))+E(f324(f324(f81(a865),f324(f37(x67371),x67372)),f324(f37(x67371),x67373)),f324(f37(x67371),f324(f324(f113(f871(x67371,a859)),x67372),x67373))) % 181.55/181.54 [7145]~P99(x71451)+~P1(f324(f61(x71451),x71452))+~P1(f324(f324(f326(x71451),x71453),x71452))+P1(f324(f324(f238(x71451),f324(f63(x71451,f104(x71451)),x71452)),x71453)) % 181.55/181.54 [7146]~P105(x71461)+~P1(f324(f61(x71461),x71462))+~P1(f324(f324(f326(x71461),x71463),x71462))+P1(f324(f324(f238(x71461),f324(f63(x71461,f189(x71461)),x71462)),x71463)) % 181.55/181.54 [7395]~P1(f324(f61(x73951),x73953))+~P1(f324(f61(x73951),x73952))+~E(f324(f324(f104(f871(x73951,a859)),x73952),x73953),f191(f871(x73951,a859)))+E(f324(f324(f81(a865),f324(f37(x73951),x73952)),f324(f37(x73951),x73953)),f324(f37(x73951),f324(f324(f113(f871(x73951,a859)),x73952),x73953))) % 181.55/181.54 [8180]~P39(x81801,x81803)+~P39(x81801,x81802)+~E(f324(f324(f104(f871(x81801,a859)),f324(f257(x81801,x81801),x81802)),f324(f255(x81801,x81801),x81803)),f191(f871(x81801,a859)))+P39(x81801,f324(f324(f113(f871(f870(x81801,x81801),a859)),x81802),x81803)) % 181.55/181.54 [8275]E(x82751,f324(f324(f38(a865),x82752),x82753))+~P1(f324(f324(f239(a865),f2(a865)),x82753))+~P1(f324(f324(f239(a865),x82752),f324(f324(f82(a865),x82753),f324(a115,x82751))))+~P1(f324(f324(f238(a865),f324(f324(f82(a865),x82753),x82751)),x82752)) % 181.55/181.54 [8405]~P1(f324(f61(x84051),x84052))+~P1(f324(f61(x84051),x84053))+E(f324(f324(f81(a865),f324(f37(x84051),x84052)),f324(f37(x84051),x84053)),f324(f37(x84051),f324(f324(f113(f871(x84051,a859)),x84052),x84053)))+P1(f324(f324(f326(x84051),f372(x84053,x84052,x84051)),f324(f324(f104(f871(x84051,a859)),x84052),x84053))) % 181.55/181.54 [8793]~P121(x87932)+~E(x87931,f2(x87932))+~E(x87933,f2(x87932))+~P1(f324(f324(f239(x87932),f2(x87932)),f324(f324(f81(x87932),f324(f324(f82(x87932),x87933),x87933)),f324(f324(f82(x87932),x87931),x87931)))) % 181.55/181.54 [9320]~P39(x93201,x93203)+~P39(x93201,x93202)+P39(x93201,f324(f324(f113(f871(f870(x93201,x93201),a859)),x93202),x93203))+~P1(f324(f324(f238(f871(f870(x93201,x93201),a859)),f324(f324(f281(x93201,x93201,x93201),x93202),x93203)),x93202)) % 181.55/181.54 [9450]~P1(f324(x94501,x94503))+~P1(f324(f61(x94502),x94503))+P1(f324(x94501,f191(f871(x94502,a859))))+~P1(f324(x94501,f324(f324(f22(f871(x94502,a859)),f826(x94501,x94503,x94502)),f324(f324(f302(x94502),f829(x94501,x94503,x94502)),f191(f871(x94502,a859)))))) % 181.55/181.54 [9709]~P61(x97091)+~P61(x97092)+P12(x97091,f324(f324(f8(f871(x97092,x97091),a859,f866(x97091)),x97093),f324(f324(f8(f871(x97092,f869(x97091)),f871(x97092,x97091),f866(x97091)),f73(f869(x97091),x97091,x97092,f237(x97091))),f324(f324(f8(f866(f870(x97092,x97091)),f871(x97092,f869(x97091)),f866(x97091)),f173(x97092,x97091)),f324(f177(x97092,x97091),f55(x97092))))),f324(f192(f866(x97092)),f55(x97092)))+~P1(f324(f57(f871(x97092,x97091)),x97093)) % 181.55/181.54 [9710]~P61(x97101)+~P61(x97102)+P13(x97101,f324(f324(f8(f871(x97102,x97101),a859,f866(x97101)),x97103),f324(f324(f8(f871(x97102,f869(x97101)),f871(x97102,x97101),f866(x97101)),f73(f869(x97101),x97101,x97102,f237(x97101))),f324(f324(f8(f866(f870(x97102,x97101)),f871(x97102,f869(x97101)),f866(x97101)),f173(x97102,x97101)),f324(f177(x97102,x97101),f55(x97102))))),f324(f192(f866(x97102)),f55(x97102)))+~P1(f324(f58(f871(x97102,x97101)),x97103)) % 181.55/181.54 [9804]~P61(x98041)+~P61(x98042)+~P13(x98042,f324(f324(f8(f871(x98041,x98042),a859,f866(x98042)),x98043),f324(f324(f8(f871(x98041,f869(x98042)),f871(x98041,x98042),f866(x98042)),f73(f869(x98042),x98042,x98041,f237(x98042))),f324(f324(f8(f866(f870(x98041,x98042)),f871(x98041,f869(x98042)),f866(x98042)),f173(x98041,x98042)),f324(f177(x98041,x98042),f55(x98041))))),f324(f192(f866(x98041)),f55(x98041)))+P1(f324(f58(f871(x98041,x98042)),x98043)) % 181.55/181.54 [9805]~P61(x98051)+~P61(x98052)+~P12(x98052,f324(f324(f8(f871(x98051,x98052),a859,f866(x98052)),x98053),f324(f324(f8(f871(x98051,f869(x98052)),f871(x98051,x98052),f866(x98052)),f73(f869(x98052),x98052,x98051,f237(x98052))),f324(f324(f8(f866(f870(x98051,x98052)),f871(x98051,f869(x98052)),f866(x98052)),f173(x98051,x98052)),f324(f177(x98051,x98052),f55(x98051))))),f324(f192(f866(x98051)),f55(x98051)))+P1(f324(f57(f871(x98051,x98052)),x98053)) % 181.55/181.54 [8579]~P1(f324(f324(f239(a1),f2(a1)),x85793))+P1(f324(f324(f238(a1),f2(a1)),x85791))+~P1(f324(f324(f239(a1),x85792),x85793))+~P1(f324(f324(f238(a1),f2(a1)),f324(f324(f81(a1),f324(f324(f82(a1),x85793),x85791)),x85792))) % 181.55/181.54 [8604]~P94(x86041)+~P1(f324(f61(x86041),x86042))+E(f324(f324(f22(f871(x86041,a859)),x86042),f324(f324(f302(x86041),x86043),f191(f871(x86041,a859)))),f191(f871(x86041,a859)))+E(f324(f324(f113(x86041),x86043),f13(x86041,f324(f324(f22(f871(x86041,a859)),x86042),f324(f324(f302(x86041),x86043),f191(f871(x86041,a859)))))),f13(x86041,f324(f324(f302(x86041),x86043),x86042))) % 181.55/181.54 [8605]~P94(x86051)+~P1(f324(f61(x86051),x86052))+E(f324(f324(f22(f871(x86051,a859)),x86052),f324(f324(f302(x86051),x86053),f191(f871(x86051,a859)))),f191(f871(x86051,a859)))+E(f324(f324(f104(x86051),x86053),f10(x86051,f324(f324(f22(f871(x86051,a859)),x86052),f324(f324(f302(x86051),x86053),f191(f871(x86051,a859)))))),f10(x86051,f324(f324(f302(x86051),x86053),x86052))) % 181.55/181.54 [8606]~P105(x86061)+~P1(f324(f61(x86061),x86062))+E(f324(f324(f22(f871(x86061,a859)),x86062),f324(f324(f302(x86061),x86063),f191(f871(x86061,a859)))),f191(f871(x86061,a859)))+E(f324(f324(f190(x86061),x86063),f14(x86061,f324(f324(f22(f871(x86061,a859)),x86062),f324(f324(f302(x86061),x86063),f191(f871(x86061,a859)))))),f14(x86061,f324(f324(f302(x86061),x86063),x86062))) % 181.55/181.54 [8607]~P105(x86071)+~P1(f324(f61(x86071),x86072))+E(f324(f324(f22(f871(x86071,a859)),x86072),f324(f324(f302(x86071),x86073),f191(f871(x86071,a859)))),f191(f871(x86071,a859)))+E(f324(f324(f189(x86071),x86073),f15(x86071,f324(f324(f22(f871(x86071,a859)),x86072),f324(f324(f302(x86071),x86073),f191(f871(x86071,a859)))))),f15(x86071,f324(f324(f302(x86071),x86073),x86072))) % 181.55/181.54 [8679]~P105(x86791)+~P1(f324(f61(x86791),x86792))+E(f324(f324(f22(f871(x86791,a859)),x86792),f324(f324(f302(x86791),x86793),f191(f871(x86791,a859)))),f191(f871(x86791,a859)))+E(f324(f324(f190(x86791),x86793),f11(x86791,f190(x86791),f324(f324(f22(f871(x86791,a859)),x86792),f324(f324(f302(x86791),x86793),f191(f871(x86791,a859)))))),f11(x86791,f190(x86791),f324(f324(f302(x86791),x86793),x86792))) % 181.55/181.54 [8680]~P105(x86801)+~P1(f324(f61(x86801),x86802))+E(f324(f324(f22(f871(x86801,a859)),x86802),f324(f324(f302(x86801),x86803),f191(f871(x86801,a859)))),f191(f871(x86801,a859)))+E(f324(f324(f189(x86801),x86803),f12(x86801,f189(x86801),f324(f324(f22(f871(x86801,a859)),x86802),f324(f324(f302(x86801),x86803),f191(f871(x86801,a859)))))),f12(x86801,f189(x86801),f324(f324(f302(x86801),x86803),x86802))) % 181.55/181.54 [9259]E(x92591,x92592)+~E(f324(f136(f866(x92593),f866(x92593),f124(x92593),f116(x92593)),x92591),f324(f136(f866(x92593),f866(x92593),f124(x92593),f116(x92593)),x92592))+~E(f324(f192(f866(f866(x92593))),x92591),f324(f192(f866(f866(x92593))),x92592))+P1(f324(f324(f326(f870(f866(x92593),f866(x92593))),f723(x92592,x92591,x92593)),f324(f167(f870(f866(x92593),f866(x92593))),f324(f324(f177(f866(x92593),f866(x92593)),x92591),x92592)))) % 181.55/181.54 [9260]E(x92601,x92602)+~E(f324(f136(f866(x92603),f866(x92603),f124(x92603),f116(x92603)),x92601),f324(f136(f866(x92603),f866(x92603),f124(x92603),f116(x92603)),x92602))+~E(f324(f192(f866(f866(x92603))),x92601),f324(f192(f866(f866(x92603))),x92602))+P1(f324(f324(f326(f870(f866(x92603),f866(x92603))),f724(x92601,x92602,x92603)),f324(f167(f870(f866(x92603),f866(x92603))),f324(f324(f177(f866(x92603),f866(x92603)),x92602),x92601)))) % 181.55/181.54 [10096]~P98(x100962)+E(x100961,f191(f871(x100962,a859)))+~P1(f324(f61(x100962),x100961))+E(f13(x100962,f324(f244(x100962),f324(f324(f8(f871(x100962,a859),a859,x100962),f88(x100962)),f324(f324(f7(x100962,f871(x100962,a859),f871(x100962,a859)),f324(f324(f8(f871(x100962,f871(a859,a859)),f871(f871(x100962,a859),f871(x100962,a859)),x100962),f18(x100962,a859,a859)),f324(f324(f8(f871(x100962,a859),f871(x100962,f871(a859,a859)),x100962),f324(f8(a859,f871(a859,a859),x100962),a322)),f324(f324(f7(x100962,f871(x100962,x100962),f871(x100962,a859)),f324(f324(f8(f871(x100962,a859),f871(f871(x100962,x100962),f871(x100962,a859)),x100962),f8(x100962,a859,x100962)),a321)),f324(f104(x100962),x100963))))),f324(f324(f7(x100962,f871(x100962,a859),a859),f326(x100962)),x100961))))),f324(f324(f104(x100962),x100963),f13(x100962,x100961))) % 181.55/181.54 [10097]~P98(x100972)+E(x100971,f191(f871(x100972,a859)))+~P1(f324(f61(x100972),x100971))+E(f10(x100972,f324(f244(x100972),f324(f324(f8(f871(x100972,a859),a859,x100972),f88(x100972)),f324(f324(f7(x100972,f871(x100972,a859),f871(x100972,a859)),f324(f324(f8(f871(x100972,f871(a859,a859)),f871(f871(x100972,a859),f871(x100972,a859)),x100972),f18(x100972,a859,a859)),f324(f324(f8(f871(x100972,a859),f871(x100972,f871(a859,a859)),x100972),f324(f8(a859,f871(a859,a859),x100972),a322)),f324(f324(f7(x100972,f871(x100972,x100972),f871(x100972,a859)),f324(f324(f8(f871(x100972,a859),f871(f871(x100972,x100972),f871(x100972,a859)),x100972),f8(x100972,a859,x100972)),a321)),f324(f113(x100972),x100973))))),f324(f324(f7(x100972,f871(x100972,a859),a859),f326(x100972)),x100971))))),f324(f324(f113(x100972),x100973),f10(x100972,x100971))) % 181.55/181.54 [10098]~P73(x100982)+E(x100981,f191(f871(x100982,a859)))+~P1(f324(f61(x100982),x100981))+E(f14(x100982,f324(f244(x100982),f324(f324(f8(f871(x100982,a859),a859,x100982),f88(x100982)),f324(f324(f7(x100982,f871(x100982,a859),f871(x100982,a859)),f324(f324(f8(f871(x100982,f871(a859,a859)),f871(f871(x100982,a859),f871(x100982,a859)),x100982),f18(x100982,a859,a859)),f324(f324(f8(f871(x100982,a859),f871(x100982,f871(a859,a859)),x100982),f324(f8(a859,f871(a859,a859),x100982),a322)),f324(f324(f7(x100982,f871(x100982,x100982),f871(x100982,a859)),f324(f324(f8(f871(x100982,a859),f871(f871(x100982,x100982),f871(x100982,a859)),x100982),f8(x100982,a859,x100982)),a321)),f324(f81(x100982),x100983))))),f324(f324(f7(x100982,f871(x100982,a859),a859),f326(x100982)),x100981))))),f324(f324(f81(x100982),x100983),f14(x100982,x100981))) % 181.55/181.54 [10099]~P73(x100992)+E(x100991,f191(f871(x100992,a859)))+~P1(f324(f61(x100992),x100991))+E(f15(x100992,f324(f244(x100992),f324(f324(f8(f871(x100992,a859),a859,x100992),f88(x100992)),f324(f324(f7(x100992,f871(x100992,a859),f871(x100992,a859)),f324(f324(f8(f871(x100992,f871(a859,a859)),f871(f871(x100992,a859),f871(x100992,a859)),x100992),f18(x100992,a859,a859)),f324(f324(f8(f871(x100992,a859),f871(x100992,f871(a859,a859)),x100992),f324(f8(a859,f871(a859,a859),x100992),a322)),f324(f324(f7(x100992,f871(x100992,x100992),f871(x100992,a859)),f324(f324(f8(f871(x100992,a859),f871(f871(x100992,x100992),f871(x100992,a859)),x100992),f8(x100992,a859,x100992)),a321)),f324(f81(x100992),x100993))))),f324(f324(f7(x100992,f871(x100992,a859),a859),f326(x100992)),x100991))))),f324(f324(f81(x100992),x100993),f15(x100992,x100991))) % 181.55/181.54 [10100]~P105(x101002)+E(x101001,f191(f871(x101002,a859)))+~P1(f324(f61(x101002),x101001))+E(f11(x101002,f190(x101002),f324(f244(x101002),f324(f324(f8(f871(x101002,a859),a859,x101002),f88(x101002)),f324(f324(f7(x101002,f871(x101002,a859),f871(x101002,a859)),f324(f324(f8(f871(x101002,f871(a859,a859)),f871(f871(x101002,a859),f871(x101002,a859)),x101002),f18(x101002,a859,a859)),f324(f324(f8(f871(x101002,a859),f871(x101002,f871(a859,a859)),x101002),f324(f8(a859,f871(a859,a859),x101002),a322)),f324(f324(f7(x101002,f871(x101002,x101002),f871(x101002,a859)),f324(f324(f8(f871(x101002,a859),f871(f871(x101002,x101002),f871(x101002,a859)),x101002),f8(x101002,a859,x101002)),a321)),f324(f189(x101002),x101003))))),f324(f324(f7(x101002,f871(x101002,a859),a859),f326(x101002)),x101001))))),f324(f324(f189(x101002),x101003),f11(x101002,f190(x101002),x101001))) % 181.55/181.54 [10101]~P105(x101012)+E(x101011,f191(f871(x101012,a859)))+~P1(f324(f61(x101012),x101011))+E(f12(x101012,f189(x101012),f324(f244(x101012),f324(f324(f8(f871(x101012,a859),a859,x101012),f88(x101012)),f324(f324(f7(x101012,f871(x101012,a859),f871(x101012,a859)),f324(f324(f8(f871(x101012,f871(a859,a859)),f871(f871(x101012,a859),f871(x101012,a859)),x101012),f18(x101012,a859,a859)),f324(f324(f8(f871(x101012,a859),f871(x101012,f871(a859,a859)),x101012),f324(f8(a859,f871(a859,a859),x101012),a322)),f324(f324(f7(x101012,f871(x101012,x101012),f871(x101012,a859)),f324(f324(f8(f871(x101012,a859),f871(f871(x101012,x101012),f871(x101012,a859)),x101012),f8(x101012,a859,x101012)),a321)),f324(f190(x101012),x101013))))),f324(f324(f7(x101012,f871(x101012,a859),a859),f326(x101012)),x101011))))),f324(f324(f190(x101012),x101013),f12(x101012,f189(x101012),x101011))) % 181.55/181.54 [9853]~P117(x98531)+~E(x98533,f2(x98531))+~E(x98532,f2(x98531))+E(f324(f324(f81(x98531),f324(f324(f249(x98531),x98532),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x98531),x98533),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f2(x98531)) % 181.55/181.54 [9994]~P120(x99941)+~P1(f324(f324(f238(x99941),f2(x99941)),x99943))+P1(f324(f324(f238(x99941),x99942),x99943))+~P1(f324(f324(f238(x99941),f324(f324(f249(x99941),x99942),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x99941),x99943),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))))) % 181.55/181.54 [10040]~P117(x100402)+~E(x100401,f2(x100402))+~E(x100403,f2(x100402))+~P1(f324(f324(f239(x100402),f2(x100402)),f324(f324(f81(x100402),f324(f324(f249(x100402),x100403),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))),f324(f324(f249(x100402),x100401),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))))) % 181.55/181.54 [8514]P28(x85141,x85142,f848(x85143,x85142,x85144,x85141),x85144,x85143)+~E(f324(f37(x85141),x85144),f324(f37(x85142),x85143))+~P1(f324(f61(x85142),x85143))+~P1(f324(f61(x85141),x85144)) % 181.55/181.54 [9223]E(x92231,x92232)+~E(f707(x92231,x92232,x92234,x92233),f709(x92231,x92232,x92234,x92233))+P1(f324(f324(f326(f870(f866(x92233),f866(x92233))),f324(f324(f259(f866(x92233),f866(x92233)),x92232),x92231)),f141(x92233,x92234)))+P1(f324(f324(f326(f870(f866(x92233),f866(x92233))),f324(f324(f259(f866(x92233),f866(x92233)),x92231),x92232)),f141(x92233,x92234))) % 181.55/181.54 [4836]~P62(x48362)+~E(x48364,f2(x48362))+~E(x48361,f2(x48362))+E(x48361,f324(f324(f282(x48362),x48363),x48364)) % 181.55/181.54 [4837]~P62(x48371)+~E(x48373,f2(x48371))+~E(x48374,f2(x48371))+E(f324(f324(f282(x48371),x48372),x48373),x48374) % 181.55/181.54 [4945]~P62(x49452)+E(x49451,f2(x49452))+~E(x49453,f2(x49452))+~E(x49451,f324(f324(f282(x49452),x49454),x49453)) % 181.55/181.54 [4946]~P62(x49462)+E(x49461,f2(x49462))+~E(x49463,f2(x49462))+~E(f324(f324(f282(x49462),x49464),x49463),x49461) % 181.55/181.54 [5117]~P114(x51172)+E(x51171,f2(x51172))+~E(f324(f324(f282(x51172),x51173),x51171),x51174)+E(x51173,f324(f324(f82(x51172),x51174),x51171)) % 181.55/181.54 [5119]~P114(x51192)+E(x51191,f2(x51192))+~E(f324(f324(f82(x51192),x51193),x51191),x51194)+E(x51193,f324(f324(f282(x51192),x51194),x51191)) % 181.55/181.54 [5120]~P62(x51202)+E(x51201,f2(x51202))+~E(f324(f324(f282(x51202),x51203),x51201),x51204)+E(x51203,f324(f324(f82(x51202),x51204),x51201)) % 181.55/181.54 [5121]~P62(x51212)+E(x51211,f2(x51212))+~E(f324(f324(f82(x51212),x51213),x51211),x51214)+E(x51213,f324(f324(f282(x51212),x51214),x51211)) % 181.55/181.54 [5122]~P114(x51222)+E(x51221,f2(x51222))+~E(x51223,f324(f324(f282(x51222),x51224),x51221))+E(f324(f324(f82(x51222),x51223),x51221),x51224) % 181.55/181.54 [5124]~P114(x51242)+E(x51241,f2(x51242))+~E(x51243,f324(f324(f82(x51242),x51244),x51241))+E(f324(f324(f282(x51242),x51243),x51241),x51244) % 181.55/181.54 [5125]~P62(x51252)+E(x51251,f2(x51252))+~E(x51253,f324(f324(f282(x51252),x51254),x51251))+E(f324(f324(f82(x51252),x51253),x51251),x51254) % 181.55/181.54 [5126]~P62(x51262)+E(x51261,f2(x51262))+~E(x51263,f324(f324(f82(x51262),x51264),x51261))+E(f324(f324(f282(x51262),x51263),x51261),x51264) % 181.55/181.54 [5150]~P62(x51502)+~E(x51501,f2(x51502))+~E(f324(f324(f82(x51502),x51501),x51504),x51503)+E(x51501,f324(f324(f282(x51502),x51503),x51504)) % 181.55/181.54 [5151]~P62(x51511)+~E(x51514,f2(x51511))+~E(x51512,f324(f324(f82(x51511),x51514),x51513))+E(f324(f324(f282(x51511),x51512),x51513),x51514) % 181.55/181.54 [5221]~E(x52213,x52214)+~E(x52212,x52213)+~P106(x52211)+E(f295(x52211,x52212,x52213),f324(f324(f302(x52211),x52214),f191(f871(x52211,a859)))) % 181.55/181.54 [5424]~E(f138(x54242,x54241),x54244)+~E(f117(x54242,x54241),x54243)+E(x54241,f116(x54242))+E(f324(f324(f124(x54242),x54243),f324(f324(f145(x54242),x54244),f116(x54242))),x54241) % 181.55/181.54 [6028]~P120(x60283)+E(x60281,x60282)+~E(f324(f324(f249(x60283),x60284),x60281),f324(f324(f249(x60283),x60284),x60282))+~P1(f324(f324(f239(x60283),f79(x60283)),x60284)) % 181.55/181.54 [6029]E(x60291,x60292)+~E(f324(f324(f302(x60293),x60294),x60291),f324(f324(f302(x60293),x60294),x60292))+P1(f324(f324(f326(x60293),x60294),x60292))+P1(f324(f324(f326(x60293),x60294),x60291)) % 181.55/181.54 [6067]E(f324(x60671,x60672),f79(a865))+~E(f324(f324(f9(x60673,a865),x60671),x60674),f79(a865))+~P1(f324(f61(x60673),x60674))+~P1(f324(f324(f326(x60673),x60672),x60674)) % 181.55/181.54 [6068]E(f324(x60681,x60682),f2(a865))+~E(f324(f324(f6(x60683,a865),x60681),x60684),f2(a865))+~P1(f324(f61(x60683),x60684))+~P1(f324(f324(f326(x60683),x60682),x60684)) % 181.55/181.54 [6280]~P106(x62801)+~P1(f324(f324(f238(x62801),x62804),x62803))+P1(f324(f324(f238(x62801),x62802),x62803))+~P1(f324(f324(f238(x62801),x62802),x62804)) % 181.55/181.54 [6281]~P103(x62811)+~P1(f324(f324(f238(x62811),x62812),x62814))+P1(f324(f324(f238(x62811),x62812),x62813))+~P1(f324(f324(f238(x62811),x62814),x62813)) % 181.55/181.54 [6282]~P106(x62821)+~P1(f324(f324(f239(x62821),x62824),x62823))+P1(f324(f324(f239(x62821),x62822),x62823))+~P1(f324(f324(f238(x62821),x62822),x62824)) % 181.55/181.54 [6283]~P106(x62831)+~P1(f324(f324(f239(x62831),x62832),x62834))+P1(f324(f324(f239(x62831),x62832),x62833))+~P1(f324(f324(f238(x62831),x62834),x62833)) % 181.55/181.54 [6284]~P106(x62841)+~P1(f324(f324(f239(x62841),x62844),x62843))+P1(f324(f324(f239(x62841),x62842),x62843))+~P1(f324(f324(f239(x62841),x62842),x62844)) % 181.55/181.54 [6285]~P103(x62851)+~P1(f324(f324(f239(x62851),x62852),x62854))+P1(f324(f324(f239(x62851),x62852),x62853))+~P1(f324(f324(f238(x62851),x62854),x62853)) % 181.55/181.54 [6286]~P103(x62861)+~P1(f324(f324(f239(x62861),x62864),x62863))+P1(f324(f324(f239(x62861),x62862),x62863))+~P1(f324(f324(f238(x62861),x62862),x62864)) % 181.55/181.54 [6287]~P103(x62871)+~P1(f324(f324(f239(x62871),x62872),x62874))+P1(f324(f324(f239(x62871),x62872),x62873))+~P1(f324(f324(f239(x62871),x62874),x62873)) % 181.55/181.54 [6369]~P37(x63694,x63693,x63692)+E(x63691,f791(x63692,x63693,x63694))+~P1(f324(x63693,x63691))+~P1(f324(f324(f326(x63694),x63691),f324(f167(x63694),x63692))) % 181.55/181.54 [6513]~P6(x65131)+~P1(f324(f324(f238(x65131),x65132),f40(x65131,x65134)))+P1(f324(f324(f238(x65131),x65132),x65133))+~P1(f324(f324(f326(x65131),x65133),x65134)) % 181.55/181.54 [6658]~P105(x66581)+~P16(x66581,f324(f324(f145(x66581),x66582),x66584))+~P1(f324(f324(f326(x66581),x66583),f324(f167(x66581),x66584)))+P1(f324(f324(f238(x66581),x66582),x66583)) % 181.55/181.54 [6748]~P6(x67481)+~P1(f324(f324(f238(x67481),f39(x67481,x67484)),x67483))+P1(f324(f324(f238(x67481),x67482),x67483))+~P1(f324(f324(f326(x67481),x67482),x67484)) % 181.55/181.54 [7148]~P105(x71481)+E(f324(f324(f113(f871(x71481,a859)),f324(f294(x71481,x71482),x71483)),f324(f294(x71481,x71483),x71484)),f324(f294(x71481,x71482),x71484))+~P1(f324(f324(f238(x71481),x71483),x71484))+~P1(f324(f324(f238(x71481),x71482),x71483)) % 181.55/181.54 [7185]P37(x71851,x71852,x71853)+~E(f796(x71853,x71852,x71851,x71854),x71854)+~P1(f324(x71852,x71854))+~P1(f324(f324(f326(x71851),x71854),f324(f167(x71851),x71853))) % 181.55/181.54 [7259]~P105(x72591)+E(f324(f324(f113(f871(x72591,a859)),f324(f294(x72591,x72592),x72593)),f295(x72591,x72593,x72594)),f295(x72591,x72592,x72594))+~P1(f324(f324(f238(x72591),x72593),x72594))+~P1(f324(f324(f238(x72591),x72592),x72593)) % 181.55/181.54 [7323]~P105(x73231)+E(f324(f324(f113(f871(x73231,a859)),f298(x73231,x73232,x73233)),f324(f294(x73231,x73233),x73234)),f298(x73231,x73232,x73234))+~P1(f324(f324(f238(x73231),x73233),x73234))+~P1(f324(f324(f239(x73231),x73232),x73233)) % 181.55/181.54 [7343]~P105(x73431)+E(f324(f324(f113(f871(x73431,a859)),f295(x73431,x73432,x73433)),f298(x73431,x73433,x73434)),f324(f294(x73431,x73432),x73434))+~P1(f324(f324(f238(x73431),x73432),x73433))+~P1(f324(f324(f239(x73431),x73433),x73434)) % 181.55/181.54 [7375]~P105(x73751)+E(f324(f324(f113(f871(x73751,a859)),f298(x73751,x73752,x73753)),f295(x73751,x73753,x73754)),f297(x73751,x73752,x73754))+~P1(f324(f324(f238(x73751),x73753),x73754))+~P1(f324(f324(f239(x73751),x73752),x73753)) % 181.55/181.54 [7376]~P105(x73761)+E(f324(f324(f113(f871(x73761,a859)),f297(x73761,x73762,x73763)),f298(x73761,x73763,x73764)),f298(x73761,x73762,x73764))+~P1(f324(f324(f238(x73761),x73762),x73763))+~P1(f324(f324(f239(x73761),x73763),x73764)) % 181.55/181.54 [7377]~P105(x73771)+E(f324(f324(f113(f871(x73771,a859)),f297(x73771,x73772,x73773)),f297(x73771,x73773,x73774)),f297(x73771,x73772,x73774))+~P1(f324(f324(f238(x73771),x73773),x73774))+~P1(f324(f324(f238(x73771),x73772),x73773)) % 181.55/181.54 [7378]~P105(x73781)+E(f324(f324(f113(f871(x73781,a859)),f295(x73781,x73782,x73783)),f297(x73781,x73783,x73784)),f295(x73781,x73782,x73784))+~P1(f324(f324(f238(x73781),x73783),x73784))+~P1(f324(f324(f238(x73781),x73782),x73783)) % 181.55/181.54 [8164]P27(x81641,x81642,f847(x81643,x81642,x81644,x81641),x81644)+~P1(f324(f61(x81642),x81643))+~P1(f324(f61(x81641),x81644))+~P1(f324(f324(f238(a865),f324(f37(x81641),x81644)),f324(f37(x81642),x81643))) % 181.55/181.54 [8185]P37(x81851,x81852,x81853)+~P1(f324(x81852,x81854))+P1(f324(x81852,f796(x81853,x81852,x81851,x81854)))+~P1(f324(f324(f326(x81851),x81854),f324(f167(x81851),x81853))) % 181.55/181.54 [8238]~P68(x82381)+~E(f324(x82383,f574(x82383,x82384,x82382,x82381)),f79(x82381))+E(f324(f324(f324(f65(x82381,x82382,f82(x82381)),x82383),f79(x82381)),x82384),f79(x82381))+~P1(f324(f61(x82382),x82384)) % 181.55/181.54 [8503]~P120(x85031)+~P1(f324(f324(f238(x85031),f2(x85031)),x85033))+P1(f324(f324(f238(x85031),x85032),x85033))+~P1(f324(f324(f238(x85031),f324(f324(f249(x85031),x85032),f324(a115,x85034))),f324(f324(f249(x85031),x85033),f324(a115,x85034)))) % 181.55/181.54 [8820]P37(x88201,x88202,x88203)+~P1(f324(x88202,x88204))+~P1(f324(f324(f326(x88201),x88204),f324(f167(x88201),x88203)))+P1(f324(f324(f326(x88201),f796(x88203,x88202,x88201,x88204)),f324(f167(x88201),x88203))) % 181.55/181.54 [8898]~P68(x88981)+E(f324(f324(f324(f65(x88981,x88982,f82(x88981)),x88983),f79(x88981)),x88984),f79(x88981))+~P1(f324(f61(x88982),x88984))+P1(f324(f324(f326(x88982),f574(x88983,x88984,x88982,x88981)),x88984)) % 181.55/181.54 [9388]~P1(f324(f324(f238(a1),x93884),f2(a1)))+P1(f324(f324(f238(a1),f324(f324(f81(a1),f324(f324(f82(a1),x93881),f44(a1,x93882,x93883))),x93884)),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x93883))+~P1(f324(f324(f239(a1),x93881),x93884)) % 181.55/181.54 [9846]~P1(f324(f61(x98461),x98462))+~P1(f324(f324(f326(x98461),x98464),x98462))+~P1(f324(f324(f326(x98461),x98463),x98462))+P1(f324(f324(f239(a865),f324(f37(x98461),f324(f324(f22(f871(x98461,a859)),f324(f324(f22(f871(x98461,a859)),x98462),f324(f324(f302(x98461),x98463),f191(f871(x98461,a859))))),f324(f324(f302(x98461),x98464),f191(f871(x98461,a859)))))),f324(f37(x98461),x98462))) % 181.55/181.54 [6862]~P99(x68621)+~P1(f324(f324(f238(x68621),x68622),x68624))+~P1(f324(f324(f238(x68621),x68622),x68623))+P1(f324(f324(f238(x68621),x68622),f324(f324(f104(x68621),x68623),x68624))) % 181.55/181.54 [6865]~P105(x68651)+~P1(f324(f324(f238(x68651),x68652),x68654))+~P1(f324(f324(f238(x68651),x68652),x68653))+P1(f324(f324(f238(x68651),x68652),f324(f324(f189(x68651),x68653),x68654))) % 181.55/181.54 [6866]~P105(x68661)+~P1(f324(f324(f239(x68661),x68662),x68664))+~P1(f324(f324(f239(x68661),x68662),x68663))+P1(f324(f324(f239(x68661),x68662),f324(f324(f189(x68661),x68663),x68664))) % 181.55/181.54 [6885]~P63(x68852)+E(x68851,f2(x68852))+E(f324(f324(f282(x68852),f324(f324(f249(x68852),x68851),x68853)),f324(f324(f249(x68852),x68851),x68854)),f324(f324(f249(x68852),x68851),f324(f324(f22(a865),x68853),x68854)))+~P1(f324(f324(f238(a865),x68854),x68853)) % 181.55/181.54 [6930]~P105(x69301)+~P16(x69301,f324(f324(f145(x69301),x69303),x69304))+P16(x69301,f324(f324(f145(x69301),x69302),f324(f324(f145(x69301),x69303),x69304)))+~P1(f324(f324(f238(x69301),x69302),x69303)) % 181.55/181.54 [6968]~P85(x69681)+~P1(f324(f324(f238(x69681),f2(x69681)),x69684))+~P1(f324(f324(f238(x69681),x69682),x69683))+P1(f324(f324(f238(x69681),x69682),f324(f324(f81(x69681),x69683),x69684))) % 181.55/181.54 [6969]~P85(x69691)+~P1(f324(f324(f238(x69691),f2(x69691)),x69693))+~P1(f324(f324(f238(x69691),x69692),x69694))+P1(f324(f324(f238(x69691),x69692),f324(f324(f81(x69691),x69693),x69694))) % 181.55/181.54 [6970]~P120(x69701)+~P1(f324(f324(f239(x69701),f2(x69701)),x69703))+~P1(f324(f324(f239(x69701),x69702),x69704))+P1(f324(f324(f239(x69701),x69702),f324(f324(f81(x69701),x69703),x69704))) % 181.55/181.54 [6971]~P85(x69711)+~P1(f324(f324(f238(x69711),x69712),x69714))+~P1(f324(f324(f239(x69711),f2(x69711)),x69713))+P1(f324(f324(f239(x69711),x69712),f324(f324(f81(x69711),x69713),x69714))) % 181.55/181.54 [6972]~P85(x69721)+~P1(f324(f324(f238(x69721),f2(x69721)),x69723))+~P1(f324(f324(f239(x69721),x69722),x69724))+P1(f324(f324(f239(x69721),x69722),f324(f324(f81(x69721),x69723),x69724))) % 181.55/181.54 [7011]~P105(x70111)+P1(f324(f324(f238(x70111),x70112),x70113))+P1(f324(f324(f238(x70111),x70112),x70114))+~P1(f324(f324(f238(x70111),x70112),f324(f324(f190(x70111),x70114),x70113))) % 181.55/181.54 [7012]~P105(x70121)+P1(f324(f324(f239(x70121),x70122),x70123))+P1(f324(f324(f239(x70121),x70122),x70124))+~P1(f324(f324(f239(x70121),x70122),f324(f324(f190(x70121),x70124),x70123))) % 181.55/181.54 [7295]~P106(x72952)+~P61(x72951)+~P1(f324(f324(f239(f871(x72951,x72952)),x72953),x72954))+P1(f324(f324(f238(f871(x72951,x72952)),x72953),x72954)) % 181.55/181.54 [7662]~P65(x76621)+~P1(f324(f324(f239(x76621),x76624),f2(x76621)))+~P1(f324(f324(f238(x76621),x76623),f324(f324(f282(x76621),x76622),x76624)))+P1(f324(f324(f238(x76621),x76622),f324(f324(f82(x76621),x76623),x76624))) % 181.55/181.54 [7663]~P65(x76631)+~P1(f324(f324(f239(x76631),x76634),f2(x76631)))+~P1(f324(f324(f238(x76631),x76633),f324(f324(f82(x76631),x76632),x76634)))+P1(f324(f324(f238(x76631),x76632),f324(f324(f282(x76631),x76633),x76634))) % 181.55/181.54 [7664]~P65(x76641)+~P1(f324(f324(f239(x76641),x76644),f2(x76641)))+~P1(f324(f324(f239(x76641),x76643),f324(f324(f282(x76641),x76642),x76644)))+P1(f324(f324(f239(x76641),x76642),f324(f324(f82(x76641),x76643),x76644))) % 181.55/181.54 [7665]~P65(x76651)+~P1(f324(f324(f239(x76651),x76654),f2(x76651)))+~P1(f324(f324(f239(x76651),x76653),f324(f324(f82(x76651),x76652),x76654)))+P1(f324(f324(f239(x76651),x76652),f324(f324(f282(x76651),x76653),x76654))) % 181.55/181.54 [7765]~P123(x77651)+~P1(f324(f324(f238(x77651),x77652),f2(x77651)))+~P1(f324(f324(f238(x77651),x77654),x77653))+P1(f324(f324(f238(x77651),f324(f324(f82(x77651),x77652),x77653)),f324(f324(f82(x77651),x77652),x77654))) % 181.55/181.54 [7766]~P121(x77661)+~P1(f324(f324(f239(x77661),x77662),f2(x77661)))+~P1(f324(f324(f238(x77661),x77664),x77663))+P1(f324(f324(f238(x77661),f324(f324(f82(x77661),x77662),x77663)),f324(f324(f82(x77661),x77662),x77664))) % 181.55/181.54 [7767]~P123(x77671)+~P1(f324(f324(f238(x77671),x77673),f2(x77671)))+~P1(f324(f324(f238(x77671),x77674),x77672))+P1(f324(f324(f238(x77671),f324(f324(f82(x77671),x77672),x77673)),f324(f324(f82(x77671),x77674),x77673))) % 181.55/181.54 [7768]~P64(x77681)+~P1(f324(f324(f238(x77681),x77683),f2(x77681)))+~P1(f324(f324(f238(x77681),x77684),x77682))+P1(f324(f324(f238(x77681),f324(f324(f282(x77681),x77682),x77683)),f324(f324(f282(x77681),x77684),x77683))) % 181.55/181.54 [7772]~P121(x77721)+~P1(f324(f324(f239(x77721),x77723),f2(x77721)))+~P1(f324(f324(f239(x77721),x77724),x77722))+P1(f324(f324(f239(x77721),f324(f324(f82(x77721),x77722),x77723)),f324(f324(f82(x77721),x77724),x77723))) % 181.55/181.54 [7773]~P121(x77731)+~P1(f324(f324(f239(x77731),x77732),f2(x77731)))+~P1(f324(f324(f239(x77731),x77734),x77733))+P1(f324(f324(f239(x77731),f324(f324(f82(x77731),x77732),x77733)),f324(f324(f82(x77731),x77732),x77734))) % 181.55/181.54 [7774]~P65(x77741)+~P1(f324(f324(f239(x77741),x77743),f2(x77741)))+~P1(f324(f324(f239(x77741),x77744),x77742))+P1(f324(f324(f239(x77741),f324(f324(f282(x77741),x77742),x77743)),f324(f324(f282(x77741),x77744),x77743))) % 181.55/181.55 [7775]~P120(x77751)+~P1(f324(f324(f239(x77751),f79(x77751)),x77752))+~P1(f324(f324(f238(a865),x77753),x77754))+P1(f324(f324(f238(x77751),f324(f324(f249(x77751),x77752),x77753)),f324(f324(f249(x77751),x77752),x77754))) % 181.55/181.55 [7776]~P120(x77761)+~P1(f324(f324(f238(x77761),f79(x77761)),x77762))+~P1(f324(f324(f238(a865),x77763),x77764))+P1(f324(f324(f238(x77761),f324(f324(f249(x77761),x77762),x77763)),f324(f324(f249(x77761),x77762),x77764))) % 181.55/181.55 [7778]~P120(x77781)+~P1(f324(f324(f239(x77781),f79(x77781)),x77782))+~P1(f324(f324(f239(a865),x77783),x77784))+P1(f324(f324(f239(x77781),f324(f324(f249(x77781),x77782),x77783)),f324(f324(f249(x77781),x77782),x77784))) % 181.55/181.55 [7807]P1(f324(f324(f239(a865),f2(a865)),f324(x78071,x78072)))+~P1(f324(f61(x78073),x78074))+~P1(f324(f324(f326(x78073),x78072),x78074))+~P1(f324(f324(f239(a865),f2(a865)),f324(f324(f9(x78073,a865),x78071),x78074))) % 181.55/181.55 [7815]~P132(x78151)+~P1(f324(f324(f238(x78151),x78153),x78154))+~P1(f324(f324(f238(x78151),f2(x78151)),x78152))+P1(f324(f324(f238(x78151),f324(f324(f82(x78151),x78152),x78153)),f324(f324(f82(x78151),x78152),x78154))) % 181.55/181.55 [7816]~P131(x78161)+~P1(f324(f324(f238(x78161),x78163),x78164))+~P1(f324(f324(f238(x78161),f2(x78161)),x78162))+P1(f324(f324(f238(x78161),f324(f324(f82(x78161),x78162),x78163)),f324(f324(f82(x78161),x78162),x78164))) % 181.55/181.55 [7817]~P121(x78171)+~P1(f324(f324(f239(x78171),f2(x78171)),x78172))+~P1(f324(f324(f238(x78171),x78173),x78174))+P1(f324(f324(f238(x78171),f324(f324(f82(x78171),x78172),x78173)),f324(f324(f82(x78171),x78172),x78174))) % 181.55/181.55 [7818]~P132(x78181)+~P1(f324(f324(f238(x78181),x78182),x78184))+~P1(f324(f324(f238(x78181),f2(x78181)),x78183))+P1(f324(f324(f238(x78181),f324(f324(f82(x78181),x78182),x78183)),f324(f324(f82(x78181),x78184),x78183))) % 181.55/181.55 [7819]~P120(x78191)+~P1(f324(f324(f238(x78191),x78192),x78194))+~P1(f324(f324(f238(x78191),f2(x78191)),x78192))+P1(f324(f324(f238(x78191),f324(f324(f249(x78191),x78192),x78193)),f324(f324(f249(x78191),x78194),x78193))) % 181.55/181.55 [7820]~P64(x78201)+~P1(f324(f324(f238(x78201),x78202),x78204))+~P1(f324(f324(f238(x78201),f2(x78201)),x78203))+P1(f324(f324(f238(x78201),f324(f324(f282(x78201),x78202),x78203)),f324(f324(f282(x78201),x78204),x78203))) % 181.55/181.55 [7822]~P118(x78221)+~P1(f324(f324(f239(x78221),x78223),x78224))+~P1(f324(f324(f239(x78221),f2(x78221)),x78222))+P1(f324(f324(f239(x78221),f324(f324(f82(x78221),x78222),x78223)),f324(f324(f82(x78221),x78222),x78224))) % 181.55/181.55 [7823]~P126(x78231)+~P1(f324(f324(f239(x78231),x78233),x78234))+~P1(f324(f324(f239(x78231),f2(x78231)),x78232))+P1(f324(f324(f239(x78231),f324(f324(f82(x78231),x78232),x78233)),f324(f324(f82(x78231),x78232),x78234))) % 181.55/181.55 [7824]~P121(x78241)+~P1(f324(f324(f239(x78241),x78242),x78244))+~P1(f324(f324(f239(x78241),f2(x78241)),x78243))+P1(f324(f324(f239(x78241),f324(f324(f82(x78241),x78242),x78243)),f324(f324(f82(x78241),x78244),x78243))) % 181.55/181.55 [7825]~P126(x78251)+~P1(f324(f324(f239(x78251),x78252),x78254))+~P1(f324(f324(f239(x78251),f2(x78251)),x78253))+P1(f324(f324(f239(x78251),f324(f324(f82(x78251),x78252),x78253)),f324(f324(f82(x78251),x78254),x78253))) % 181.55/181.55 [7826]~P121(x78261)+~P1(f324(f324(f239(x78261),x78263),x78264))+~P1(f324(f324(f239(x78261),f2(x78261)),x78262))+P1(f324(f324(f239(x78261),f324(f324(f82(x78261),x78262),x78263)),f324(f324(f82(x78261),x78262),x78264))) % 181.55/181.55 [7827]~P65(x78271)+~P1(f324(f324(f239(x78271),x78272),x78274))+~P1(f324(f324(f239(x78271),f2(x78271)),x78273))+P1(f324(f324(f239(x78271),f324(f324(f282(x78271),x78272),x78273)),f324(f324(f282(x78271),x78274),x78273))) % 181.55/181.55 [7873]~P104(x78732)+P1(f324(f324(f239(f871(x78731,x78732)),x78734),x78733))+~P1(f324(f324(f238(f871(x78731,x78732)),x78734),x78733))+P1(f324(f324(f238(f871(x78731,x78732)),x78733),x78734)) % 181.55/181.55 [7913]P1(f324(f324(f326(x79131),x79132),x79133))+P1(f324(f324(f326(x79131),x79132),x79134))+~P1(f324(f324(f238(f871(x79131,a859)),x79134),x79133))+P1(f324(f324(f239(f871(x79131,a859)),x79134),f324(f324(f302(x79131),x79132),x79133))) % 181.55/181.55 [8069]P1(f324(f324(f326(x80691),x80692),x80693))+P1(f324(f324(f326(x80691),x80692),x80694))+~P1(f324(f324(f239(f871(x80691,a859)),x80694),f324(f324(f302(x80691),x80692),x80693)))+P1(f324(f324(f238(f871(x80691,a859)),x80694),x80693)) % 181.55/181.55 [8077]~P61(x80771)+P12(x80771,x80772,x80773)+~P1(f324(x80772,x80774))+~P1(f324(f324(f326(f866(x80771)),x80774),f324(f167(f866(x80771)),f54(x80771,x80773,f55(x80771))))) % 181.55/181.55 [8087]~P13(x80873,x80871,x80874)+~P61(x80873)+P1(f324(x80871,x80872))+~P1(f324(f324(f326(f866(x80873)),x80872),f324(f167(f866(x80873)),f54(x80873,x80874,f55(x80873))))) % 181.55/181.55 [8140]~P121(x81401)+P1(f324(f324(f239(x81401),x81403),x81402))+P1(f324(f324(f239(x81401),x81402),x81403))+~P1(f324(f324(f239(x81401),f324(f324(f82(x81401),x81404),x81402)),f324(f324(f82(x81401),x81404),x81403))) % 181.55/181.55 [8141]~P121(x81411)+P1(f324(f324(f239(x81411),x81413),x81412))+P1(f324(f324(f239(x81411),x81412),x81413))+~P1(f324(f324(f239(x81411),f324(f324(f82(x81411),x81412),x81414)),f324(f324(f82(x81411),x81413),x81414))) % 181.55/181.55 [8152]~P121(x81521)+P1(f324(f324(f239(x81521),x81524),f2(x81521)))+P1(f324(f324(f239(x81521),x81522),x81523))+~P1(f324(f324(f239(x81521),f324(f324(f82(x81521),x81522),x81524)),f324(f324(f82(x81521),x81523),x81524))) % 181.55/181.55 [8153]~P121(x81531)+P1(f324(f324(f239(x81531),x81534),f2(x81531)))+P1(f324(f324(f239(x81531),x81532),x81533))+~P1(f324(f324(f239(x81531),f324(f324(f82(x81531),x81534),x81532)),f324(f324(f82(x81531),x81534),x81533))) % 181.55/181.55 [8158]~P121(x81581)+P1(f324(f324(f239(x81581),x81582),x81583))+P1(f324(f324(f239(x81581),f2(x81581)),x81584))+~P1(f324(f324(f239(x81581),f324(f324(f82(x81581),x81584),x81583)),f324(f324(f82(x81581),x81584),x81582))) % 181.55/181.55 [8159]~P121(x81591)+P1(f324(f324(f239(x81591),x81592),x81593))+P1(f324(f324(f239(x81591),f2(x81591)),x81594))+~P1(f324(f324(f239(x81591),f324(f324(f82(x81591),x81593),x81594)),f324(f324(f82(x81591),x81592),x81594))) % 181.55/181.55 [8172]~P121(x81721)+P1(f324(f324(f239(x81721),x81722),f2(x81721)))+P1(f324(f324(f239(x81721),f2(x81721)),x81722))+~P1(f324(f324(f239(x81721),f324(f324(f82(x81721),x81723),x81722)),f324(f324(f82(x81721),x81724),x81722))) % 181.55/181.55 [8173]~P121(x81731)+P1(f324(f324(f239(x81731),x81732),f2(x81731)))+P1(f324(f324(f239(x81731),f2(x81731)),x81732))+~P1(f324(f324(f239(x81731),f324(f324(f82(x81731),x81732),x81733)),f324(f324(f82(x81731),x81732),x81734))) % 181.55/181.55 [8201]~P121(x82011)+~P1(f324(f324(f239(x82011),x82014),f2(x82011)))+P1(f324(f324(f238(x82011),x82012),x82013))+~P1(f324(f324(f238(x82011),f324(f324(f82(x82011),x82014),x82013)),f324(f324(f82(x82011),x82014),x82012))) % 181.55/181.55 [8202]~P121(x82021)+~P1(f324(f324(f239(x82021),x82024),f2(x82021)))+P1(f324(f324(f239(x82021),x82022),x82023))+~P1(f324(f324(f239(x82021),f324(f324(f82(x82021),x82024),x82023)),f324(f324(f82(x82021),x82024),x82022))) % 181.55/181.55 [8212]~P120(x82123)+~P1(f324(f324(f239(x82123),f79(x82123)),x82124))+P1(f324(f324(f238(a865),x82121),x82122))+~P1(f324(f324(f238(x82123),f324(f324(f249(x82123),x82124),x82121)),f324(f324(f249(x82123),x82124),x82122))) % 181.55/181.55 [8214]~P120(x82143)+~P1(f324(f324(f239(x82143),f79(x82143)),x82144))+P1(f324(f324(f239(a865),x82141),x82142))+~P1(f324(f324(f239(x82143),f324(f324(f249(x82143),x82144),x82141)),f324(f324(f249(x82143),x82144),x82142))) % 181.55/181.55 [8224]~P121(x82241)+P1(f324(f324(f238(x82241),x82242),x82243))+~P1(f324(f324(f239(x82241),f2(x82241)),x82244))+~P1(f324(f324(f238(x82241),f324(f324(f82(x82241),x82244),x82242)),f324(f324(f82(x82241),x82244),x82243))) % 181.55/181.55 [8225]~P126(x82251)+P1(f324(f324(f238(x82251),x82252),x82253))+~P1(f324(f324(f239(x82251),f2(x82251)),x82254))+~P1(f324(f324(f238(x82251),f324(f324(f82(x82251),x82254),x82252)),f324(f324(f82(x82251),x82254),x82253))) % 181.55/181.55 [8226]~P126(x82261)+P1(f324(f324(f238(x82261),x82262),x82263))+~P1(f324(f324(f239(x82261),f2(x82261)),x82264))+~P1(f324(f324(f238(x82261),f324(f324(f82(x82261),x82262),x82264)),f324(f324(f82(x82261),x82263),x82264))) % 181.55/181.55 [8227]~P121(x82271)+P1(f324(f324(f239(x82271),x82272),x82273))+~P1(f324(f324(f239(x82271),f2(x82271)),x82274))+~P1(f324(f324(f239(x82271),f324(f324(f82(x82271),x82274),x82272)),f324(f324(f82(x82271),x82274),x82273))) % 181.55/181.55 [8228]~P126(x82281)+P1(f324(f324(f239(x82281),x82282),x82283))+~P1(f324(f324(f238(x82281),f2(x82281)),x82284))+~P1(f324(f324(f239(x82281),f324(f324(f82(x82281),x82284),x82282)),f324(f324(f82(x82281),x82284),x82283))) % 181.55/181.55 [8229]~P127(x82291)+P1(f324(f324(f239(x82291),x82292),x82293))+~P1(f324(f324(f238(x82291),f2(x82291)),x82294))+~P1(f324(f324(f239(x82291),f324(f324(f82(x82291),x82294),x82292)),f324(f324(f82(x82291),x82294),x82293))) % 181.55/181.55 [8230]~P120(x82301)+~P1(f324(f324(f238(x82301),f2(x82301)),x82303))+P1(f324(f324(f239(x82301),x82302),x82303))+~P1(f324(f324(f239(x82301),f324(f324(f249(x82301),x82302),x82304)),f324(f324(f249(x82301),x82303),x82304))) % 181.55/181.55 [8231]~P126(x82311)+P1(f324(f324(f239(x82311),x82312),x82313))+~P1(f324(f324(f238(x82311),f2(x82311)),x82314))+~P1(f324(f324(f239(x82311),f324(f324(f82(x82311),x82312),x82314)),f324(f324(f82(x82311),x82313),x82314))) % 181.55/181.55 [8232]~P127(x82321)+P1(f324(f324(f239(x82321),x82322),x82323))+~P1(f324(f324(f238(x82321),f2(x82321)),x82324))+~P1(f324(f324(f239(x82321),f324(f324(f82(x82321),x82322),x82324)),f324(f324(f82(x82321),x82323),x82324))) % 181.55/181.55 [8278]P1(f324(f324(f326(x82781),x82782),x82783))+~P1(f324(f324(f238(f871(x82781,a859)),x82783),x82784))+~P1(f324(f324(f239(f871(x82781,a859)),x82783),x82784))+P1(f324(f324(f239(f871(x82781,a859)),x82783),f324(f324(f302(x82781),x82782),x82784))) % 181.55/181.55 [8528]~P61(x85281)+~P91(x85282)+~E(f324(x85283,f801(x85284,x85283,x85281,x85282)),f324(x85284,f801(x85284,x85283,x85281,x85282)))+P1(f324(f324(f92(f871(x85281,x85282)),x85283),x85284)) % 181.55/181.55 [8654]E(f324(f324(f22(a1),f461(x86541,x86542,x86543,x86544)),f462(x86541,x86542,x86543,x86544)),x86544)+~P1(f324(f324(f239(a1),f2(a1)),x86543))+~P1(f324(f324(f238(a1),x86541),x86544))+P1(f324(f324(f238(a1),x86541),f324(f324(f81(a1),x86544),x86543))) % 181.55/181.55 [8655]E(f324(f324(f22(a1),f470(x86551,x86552,x86553,x86554)),f471(x86551,x86552,x86553,x86554)),x86554)+~P1(f324(f324(f239(a1),f2(a1)),x86553))+~P1(f324(f324(f239(a1),x86551),x86554))+P1(f324(f324(f239(a1),x86551),f324(f324(f81(a1),x86554),x86553))) % 181.55/181.55 [8800]~E(f324(f324(f159(x88001),x88003),f712(x88004,x88003,x88001,x88002)),f324(f324(f159(x88001),x88004),f712(x88004,x88003,x88001,x88002)))+E(f324(f324(f170(x88001),x88002),x88003),f324(f324(f170(x88001),x88002),x88004))+~P1(f324(f324(f238(a865),x88002),f324(f192(f866(x88001)),x88003)))+~P1(f324(f324(f238(a865),x88002),f324(f192(f866(x88001)),x88004))) % 181.55/181.55 [8870]~P1(f324(f324(f239(a1),f2(a1)),x88703))+~P1(f324(f324(f238(a1),x88701),x88704))+P1(f324(f324(f326(a1),f461(x88701,x88702,x88703,x88704)),x88702))+P1(f324(f324(f238(a1),x88701),f324(f324(f81(a1),x88704),x88703))) % 181.55/181.55 [8871]~P1(f324(f324(f239(a1),f2(a1)),x88713))+~P1(f324(f324(f239(a1),x88711),x88714))+P1(f324(f324(f326(a1),f470(x88711,x88712,x88713,x88714)),x88712))+P1(f324(f324(f239(a1),x88711),f324(f324(f81(a1),x88714),x88713))) % 181.55/181.55 [8907]~P99(x89071)+~P1(f324(f61(x89071),x89073))+~P1(f324(f324(f326(x89071),x89074),x89073))+P1(f324(f324(f238(x89071),f324(f324(f64(x89071,x89071,f104(x89071)),x89072),x89073)),f324(f324(f104(x89071),x89074),x89072))) % 181.55/181.55 [8908]~P105(x89081)+~P1(f324(f61(x89081),x89083))+~P1(f324(f324(f326(x89081),x89084),x89083))+P1(f324(f324(f238(x89081),f324(f324(f64(x89081,x89081,f189(x89081)),x89082),x89083)),f324(f324(f189(x89081),x89084),x89082))) % 181.55/181.55 [8953]E(f324(f324(f170(x89531),x89532),x89533),f324(f324(f170(x89531),x89532),x89534))+P1(f324(f324(f239(a865),f712(x89533,x89534,x89531,x89532)),x89532))+~P1(f324(f324(f238(a865),x89532),f324(f192(f866(x89531)),x89533)))+~P1(f324(f324(f238(a865),x89532),f324(f192(f866(x89531)),x89534))) % 181.55/181.55 [8958]~P1(f324(f324(f239(a1),f2(a1)),x89583))+~P1(f324(f324(f238(a1),x89581),x89582))+P1(f324(f324(f326(a1),f462(x89581,x89584,x89583,x89582)),f295(a1,f79(a1),x89583)))+P1(f324(f324(f238(a1),x89581),f324(f324(f81(a1),x89582),x89583))) % 181.55/181.55 [8959]~P1(f324(f324(f239(a1),f2(a1)),x89593))+~P1(f324(f324(f239(a1),x89591),x89592))+P1(f324(f324(f326(a1),f471(x89591,x89594,x89593,x89592)),f295(a1,f79(a1),x89593)))+P1(f324(f324(f239(a1),x89591),f324(f324(f81(a1),x89592),x89593))) % 181.55/181.55 [9128]~E(f324(f173(x91281,x91282),x91283),f324(f173(x91281,x91282),x91284))+E(f324(f167(f870(x91281,x91282)),x91283),f324(f167(f870(x91281,x91282)),x91284))+~P1(f324(f131(x91281),f324(f324(f148(f870(x91281,x91282),x91281),f258(x91281,x91282)),x91284)))+~P1(f324(f131(x91281),f324(f324(f148(f870(x91281,x91282),x91281),f258(x91281,x91282)),x91283))) % 181.55/181.55 [9140]E(f324(f173(x91401,x91402),x91403),f324(f173(x91401,x91402),x91404))+~E(f324(f167(f870(x91401,x91402)),x91403),f324(f167(f870(x91401,x91402)),x91404))+~P1(f324(f131(x91401),f324(f324(f148(f870(x91401,x91402),x91401),f258(x91401,x91402)),x91404)))+~P1(f324(f131(x91401),f324(f324(f148(f870(x91401,x91402),x91401),f258(x91401,x91402)),x91403))) % 181.55/181.55 [9280]~P105(x92801)+~P1(f324(f61(x92801),x92804))+P1(f324(f324(f326(x92801),f643(x92802,x92803,x92804,x92801)),x92804))+P1(f324(f324(f238(x92801),f324(f324(f64(x92801,x92801,f190(x92801)),x92802),x92804)),f324(f324(f190(x92801),x92803),x92802))) % 181.55/181.55 [9281]~P100(x92811)+~P1(f324(f61(x92811),x92814))+P1(f324(f324(f326(x92811),f648(x92812,x92813,x92814,x92811)),x92814))+P1(f324(f324(f238(x92811),f324(f324(f64(x92811,x92811,f113(x92811)),x92812),x92814)),f324(f324(f113(x92811),x92813),x92812))) % 181.55/181.55 [9409]~P100(x94091)+~P1(f324(f61(x94091),x94093))+~P1(f324(f324(f238(x94091),f648(x94092,x94094,x94093,x94091)),x94094))+P1(f324(f324(f238(x94091),f324(f324(f64(x94091,x94091,f113(x94091)),x94092),x94093)),f324(f324(f113(x94091),x94094),x94092))) % 181.55/181.55 [9410]~P105(x94101)+~P1(f324(f61(x94101),x94103))+~P1(f324(f324(f238(x94101),f643(x94102,x94104,x94103,x94101)),x94104))+P1(f324(f324(f238(x94101),f324(f324(f64(x94101,x94101,f190(x94101)),x94102),x94103)),f324(f324(f190(x94101),x94104),x94102))) % 181.55/181.55 [9413]~P1(f324(f324(f238(a1),f2(a1)),x94134))+~P1(f324(f324(f239(a1),f2(a1)),x94133))+~P1(f324(f324(f239(a1),x94134),x94131))+P1(f324(f324(f239(a1),f324(f324(f81(a1),f324(f324(f82(a1),x94131),f44(a1,x94132,x94133))),x94134)),f324(f324(f82(a1),x94131),x94133))) % 181.55/181.55 [9816]E(x98161,x98162)+P1(f324(f324(f326(f870(f866(x98163),f866(x98163))),f324(f324(f259(f866(x98163),f866(x98163)),x98162),x98161)),f141(x98163,x98164)))+P1(f324(f324(f326(f870(f866(x98163),f866(x98163))),f324(f324(f259(f866(x98163),f866(x98163)),x98161),x98162)),f141(x98163,x98164)))+~P1(f324(f324(f326(f870(x98163,x98163)),f324(f324(f259(x98163,x98163),f707(x98161,x98162,x98164,x98163)),f709(x98161,x98162,x98164,x98163))),x98164)) % 181.55/181.55 [9817]E(x98171,x98172)+P1(f324(f324(f326(f870(f866(x98173),f866(x98173))),f324(f324(f259(f866(x98173),f866(x98173)),x98172),x98171)),f141(x98173,x98174)))+P1(f324(f324(f326(f870(f866(x98173),f866(x98173))),f324(f324(f259(f866(x98173),f866(x98173)),x98171),x98172)),f141(x98173,x98174)))+~P1(f324(f324(f326(f870(x98173,x98173)),f324(f324(f259(x98173,x98173),f709(x98171,x98172,x98174,x98173)),f707(x98171,x98172,x98174,x98173))),x98174)) % 181.55/181.55 [7365]~P100(x73651)+~P1(f324(f324(f238(x73651),x73653),x73654))+~P1(f324(f324(f238(x73651),x73652),x73654))+P1(f324(f324(f238(x73651),f324(f324(f113(x73651),x73652),x73653)),x73654)) % 181.55/181.55 [7368]~P105(x73681)+~P1(f324(f324(f238(x73681),x73683),x73684))+~P1(f324(f324(f238(x73681),x73682),x73684))+P1(f324(f324(f238(x73681),f324(f324(f190(x73681),x73682),x73683)),x73684)) % 181.55/181.55 [7369]~P105(x73691)+~P1(f324(f324(f239(x73691),x73693),x73694))+~P1(f324(f324(f239(x73691),x73692),x73694))+P1(f324(f324(f239(x73691),f324(f324(f190(x73691),x73692),x73693)),x73694)) % 181.55/181.55 [7685]~E(x76851,x76853)+E(f133(a865,f324(f294(a865,x76851),x76852)),f324(f324(f145(a865),x76853),x76854))+~E(f133(a865,f324(f294(a865,f324(f324(f81(a865),x76851),f79(a865))),x76852)),x76854)+~P1(f324(f324(f239(a865),x76851),x76852)) % 181.55/181.55 [7694]~P105(x76941)+P1(f324(f324(f238(x76941),x76942),x76943))+P1(f324(f324(f238(x76941),x76944),x76943))+~P1(f324(f324(f238(x76941),f324(f324(f189(x76941),x76944),x76942)),x76943)) % 181.55/181.55 [7695]~P105(x76951)+P1(f324(f324(f239(x76951),x76952),x76953))+P1(f324(f324(f239(x76951),x76954),x76953))+~P1(f324(f324(f239(x76951),f324(f324(f189(x76951),x76954),x76952)),x76953)) % 181.55/181.55 [7971]~P64(x79711)+~P1(f324(f324(f239(x79711),f2(x79711)),x79713))+~P1(f324(f324(f238(x79711),x79712),f324(f324(f282(x79711),x79714),x79713)))+P1(f324(f324(f238(x79711),f324(f324(f82(x79711),x79712),x79713)),x79714)) % 181.55/181.55 [7972]~P65(x79721)+~P1(f324(f324(f239(x79721),f2(x79721)),x79723))+~P1(f324(f324(f238(x79721),x79722),f324(f324(f282(x79721),x79724),x79723)))+P1(f324(f324(f238(x79721),f324(f324(f82(x79721),x79722),x79723)),x79724)) % 181.55/181.55 [7973]~P64(x79731)+~P1(f324(f324(f239(x79731),f2(x79731)),x79733))+~P1(f324(f324(f238(x79731),x79732),f324(f324(f82(x79731),x79734),x79733)))+P1(f324(f324(f238(x79731),f324(f324(f282(x79731),x79732),x79733)),x79734)) % 181.55/181.55 [7975]~P65(x79751)+~P1(f324(f324(f239(x79751),f2(x79751)),x79753))+~P1(f324(f324(f238(x79751),x79752),f324(f324(f82(x79751),x79754),x79753)))+P1(f324(f324(f238(x79751),f324(f324(f282(x79751),x79752),x79753)),x79754)) % 181.55/181.55 [7976]~P64(x79761)+~P1(f324(f324(f239(x79761),f2(x79761)),x79763))+~P1(f324(f324(f239(x79761),x79762),f324(f324(f282(x79761),x79764),x79763)))+P1(f324(f324(f239(x79761),f324(f324(f82(x79761),x79762),x79763)),x79764)) % 181.55/181.55 [7977]~P65(x79771)+~P1(f324(f324(f239(x79771),f2(x79771)),x79773))+~P1(f324(f324(f239(x79771),x79772),f324(f324(f282(x79771),x79774),x79773)))+P1(f324(f324(f239(x79771),f324(f324(f82(x79771),x79772),x79773)),x79774)) % 181.55/181.55 [7978]~P64(x79781)+~P1(f324(f324(f239(x79781),f2(x79781)),x79783))+~P1(f324(f324(f239(x79781),x79782),f324(f324(f82(x79781),x79784),x79783)))+P1(f324(f324(f239(x79781),f324(f324(f282(x79781),x79782),x79783)),x79784)) % 181.55/181.55 [7980]~P65(x79801)+~P1(f324(f324(f239(x79801),f2(x79801)),x79803))+~P1(f324(f324(f239(x79801),x79802),f324(f324(f82(x79801),x79804),x79803)))+P1(f324(f324(f239(x79801),f324(f324(f282(x79801),x79802),x79803)),x79804)) % 181.55/181.55 [8109]~P64(x81091)+~P1(f324(f324(f239(x81091),f2(x81091)),x81094))+P1(f324(f324(f238(x81091),x81092),f324(f324(f82(x81091),x81093),x81094)))+~P1(f324(f324(f238(x81091),f324(f324(f282(x81091),x81092),x81094)),x81093)) % 181.55/181.55 [8110]~P64(x81101)+~P1(f324(f324(f239(x81101),f2(x81101)),x81104))+P1(f324(f324(f238(x81101),x81102),f324(f324(f282(x81101),x81103),x81104)))+~P1(f324(f324(f238(x81101),f324(f324(f82(x81101),x81102),x81104)),x81103)) % 181.55/181.55 [8112]~P65(x81121)+~P1(f324(f324(f239(x81121),f2(x81121)),x81124))+P1(f324(f324(f238(x81121),x81122),f324(f324(f82(x81121),x81123),x81124)))+~P1(f324(f324(f238(x81121),f324(f324(f282(x81121),x81122),x81124)),x81123)) % 181.55/181.55 [8113]~P65(x81131)+~P1(f324(f324(f239(x81131),f2(x81131)),x81134))+P1(f324(f324(f238(x81131),x81132),f324(f324(f282(x81131),x81133),x81134)))+~P1(f324(f324(f238(x81131),f324(f324(f82(x81131),x81132),x81134)),x81133)) % 181.55/181.55 [8114]~P64(x81141)+~P1(f324(f324(f239(x81141),f2(x81141)),x81144))+P1(f324(f324(f239(x81141),x81142),f324(f324(f82(x81141),x81143),x81144)))+~P1(f324(f324(f239(x81141),f324(f324(f282(x81141),x81142),x81144)),x81143)) % 181.55/181.55 [8115]~P64(x81151)+~P1(f324(f324(f239(x81151),f2(x81151)),x81154))+P1(f324(f324(f239(x81151),x81152),f324(f324(f282(x81151),x81153),x81154)))+~P1(f324(f324(f239(x81151),f324(f324(f82(x81151),x81152),x81154)),x81153)) % 181.55/181.55 [8117]~P65(x81171)+~P1(f324(f324(f239(x81171),f2(x81171)),x81174))+P1(f324(f324(f239(x81171),x81172),f324(f324(f82(x81171),x81173),x81174)))+~P1(f324(f324(f239(x81171),f324(f324(f282(x81171),x81172),x81174)),x81173)) % 181.55/181.55 [8118]~P65(x81181)+~P1(f324(f324(f239(x81181),f2(x81181)),x81184))+P1(f324(f324(f239(x81181),x81182),f324(f324(f282(x81181),x81183),x81184)))+~P1(f324(f324(f239(x81181),f324(f324(f82(x81181),x81182),x81184)),x81183)) % 181.55/181.55 [8283]~P65(x82831)+~P1(f324(f324(f239(x82831),x82833),f2(x82831)))+~P1(f324(f324(f238(x82831),f324(f324(f282(x82831),x82834),x82833)),x82832))+P1(f324(f324(f238(x82831),f324(f324(f82(x82831),x82832),x82833)),x82834)) % 181.55/181.55 [8284]~P65(x82841)+~P1(f324(f324(f239(x82841),x82843),f2(x82841)))+~P1(f324(f324(f238(x82841),f324(f324(f82(x82841),x82844),x82843)),x82842))+P1(f324(f324(f238(x82841),f324(f324(f282(x82841),x82842),x82843)),x82844)) % 181.55/181.55 [8285]~P65(x82851)+~P1(f324(f324(f239(x82851),x82853),f2(x82851)))+~P1(f324(f324(f239(x82851),f324(f324(f282(x82851),x82854),x82853)),x82852))+P1(f324(f324(f239(x82851),f324(f324(f82(x82851),x82852),x82853)),x82854)) % 181.55/181.55 [8286]~P65(x82861)+~P1(f324(f324(f239(x82861),x82863),f2(x82861)))+~P1(f324(f324(f239(x82861),f324(f324(f82(x82861),x82864),x82863)),x82862))+P1(f324(f324(f239(x82861),f324(f324(f282(x82861),x82862),x82863)),x82864)) % 181.55/181.55 [8298]~P1(f324(x82981,x82984))+~P1(f324(f324(f239(a865),x82982),f324(f324(f82(a865),x82983),f324(a115,x82984))))+P1(f324(x82981,f324(f324(f38(a865),x82982),x82983)))+~P1(f324(f324(f238(a865),f324(f324(f82(a865),x82983),x82984)),x82982)) % 181.55/181.55 [8500]~P100(x85001)+~P1(f324(f61(x85001),x85004))+~P1(f324(f324(f326(x85001),x85002),x85004))+P1(f324(f324(f238(x85001),f324(f324(f113(x85001),x85002),x85003)),f324(f324(f64(x85001,x85001,f113(x85001)),x85003),x85004))) % 181.55/181.55 [8501]~P105(x85011)+~P1(f324(f61(x85011),x85014))+~P1(f324(f324(f326(x85011),x85012),x85014))+P1(f324(f324(f238(x85011),f324(f324(f190(x85011),x85012),x85013)),f324(f324(f64(x85011,x85011,f190(x85011)),x85013),x85014))) % 181.55/181.55 [8656]~P1(f324(f61(x86561),x86562))+E(f324(f37(x86561),f324(f324(f22(f871(x86561,a859)),x86562),f324(f324(f302(x86561),x86563),x86564))),f324(f324(f22(a865),f324(f37(x86561),f324(f324(f22(f871(x86561,a859)),x86562),x86564))),f79(a865)))+P1(f324(f324(f326(x86561),x86563),x86564))+~P1(f324(f324(f326(x86561),x86563),x86562)) % 181.55/181.55 [8734]E(f324(f324(f81(a1),f463(x87341,x87342,x87343,x87344)),f464(x87341,x87342,x87343,x87344)),x87344)+~P1(f324(f324(f239(a1),f2(a1)),x87343))+~P1(f324(f324(f238(a1),x87344),x87341))+P1(f324(f324(f238(a1),f324(f324(f22(a1),x87344),x87343)),x87341)) % 181.55/181.55 [8735]E(f324(f324(f81(a1),f472(x87351,x87352,x87353,x87354)),f473(x87351,x87352,x87353,x87354)),x87354)+~P1(f324(f324(f239(a1),f2(a1)),x87353))+~P1(f324(f324(f239(a1),x87354),x87351))+P1(f324(f324(f239(a1),f324(f324(f22(a1),x87354),x87353)),x87351)) % 181.55/181.55 [8938]~P1(f324(f324(f239(a1),f2(a1)),x89383))+~P1(f324(f324(f238(a1),x89384),x89381))+P1(f324(f324(f326(a1),f463(x89381,x89382,x89383,x89384)),x89382))+P1(f324(f324(f238(a1),f324(f324(f22(a1),x89384),x89383)),x89381)) % 181.55/181.55 [8939]~P1(f324(f324(f239(a1),f2(a1)),x89393))+~P1(f324(f324(f239(a1),x89394),x89391))+P1(f324(f324(f326(a1),f472(x89391,x89392,x89393,x89394)),x89392))+P1(f324(f324(f239(a1),f324(f324(f22(a1),x89394),x89393)),x89391)) % 181.55/181.55 [9028]~P1(f324(f324(f239(a1),f2(a1)),x90282))+~P1(f324(f324(f238(a1),x90281),x90283))+P1(f324(f324(f326(a1),f464(x90283,x90284,x90282,x90281)),f295(a1,f79(a1),x90282)))+P1(f324(f324(f238(a1),f324(f324(f22(a1),x90281),x90282)),x90283)) % 181.55/181.55 [9029]~P1(f324(f324(f239(a1),f2(a1)),x90292))+~P1(f324(f324(f239(a1),x90291),x90293))+P1(f324(f324(f326(a1),f473(x90293,x90294,x90292,x90291)),f295(a1,f79(a1),x90292)))+P1(f324(f324(f239(a1),f324(f324(f22(a1),x90291),x90292)),x90293)) % 181.55/181.55 [9046]~P1(f324(f324(f238(a1),f2(a1)),x90464))+~P1(f324(f324(f239(a1),f2(a1)),x90463))+~P1(f324(f324(f239(a1),x90464),x90461))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f81(a1),f324(f324(f82(a1),x90461),f44(a1,x90462,x90463))),x90464))) % 181.55/181.55 [9109]~P99(x91091)+~P1(f324(f61(x91091),x91094))+~P1(f324(f324(f238(x91091),x91092),f647(x91093,x91092,x91094,x91091)))+P1(f324(f324(f238(x91091),f324(f324(f104(x91091),x91092),x91093)),f324(f324(f64(x91091,x91091,f104(x91091)),x91093),x91094))) % 181.55/181.55 [9110]~P105(x91101)+~P1(f324(f61(x91101),x91104))+~P1(f324(f324(f238(x91101),x91102),f642(x91103,x91102,x91104,x91101)))+P1(f324(f324(f238(x91101),f324(f324(f189(x91101),x91102),x91103)),f324(f324(f64(x91101,x91101,f189(x91101)),x91103),x91104))) % 181.55/181.55 [9126]~P1(f324(f324(f238(a1),x91264),f2(a1)))+~P1(f324(f324(f239(a1),f2(a1)),x91262))+~P1(f324(f324(f239(a1),x91261),x91264))+P1(f324(f324(f239(a1),f324(f324(f82(a1),x91261),x91262)),f324(f324(f81(a1),f324(f324(f82(a1),x91261),f44(a1,x91263,x91262))),x91264))) % 181.55/181.55 [9152]P1(f324(f61(x91521),x91522))+~P1(f324(f61(x91521),x91523))+~P1(f324(f324(f326(f871(x91521,a859)),x91522),f324(f324(f60(x91521),x91523),x91524)))+~P1(f324(f324(f238(f871(f870(x91521,x91521),a859)),x91524),f324(f324(f261(x91521,x91521),x91523),f324(f16(f871(x91521,a859),x91521),x91523)))) % 181.55/181.55 [9175]~P105(x91751)+~P1(f324(f61(x91751),x91754))+P1(f324(f324(f326(x91751),f642(x91752,x91753,x91754,x91751)),x91754))+P1(f324(f324(f238(x91751),f324(f324(f189(x91751),x91753),x91752)),f324(f324(f64(x91751,x91751,f189(x91751)),x91752),x91754))) % 181.55/181.55 [9176]~P99(x91761)+~P1(f324(f61(x91761),x91764))+P1(f324(f324(f326(x91761),f647(x91762,x91763,x91764,x91761)),x91764))+P1(f324(f324(f238(x91761),f324(f324(f104(x91761),x91763),x91762)),f324(f324(f64(x91761,x91761,f104(x91761)),x91762),x91764))) % 181.55/181.55 [9582]~P1(f324(f61(x95822),x95824))+~P1(f324(f61(x95821),x95823))+~P1(f324(f324(f238(a865),f324(f37(x95822),x95824)),f324(f37(x95821),x95823)))+P1(f324(f324(f238(f871(x95821,a859)),f324(f303(x95822,x95821,f847(x95823,x95821,x95824,x95822)),x95824)),x95823)) % 181.55/181.55 [9222]~P1(f324(f324(f326(x92221),x92222),x92224))+P1(f324(f324(f326(x92221),x92222),x92223))+~P1(f324(f324(f239(f871(x92221,a859)),x92224),f324(f324(f302(x92221),x92222),x92223)))+P1(f324(f324(f239(f871(x92221,a859)),f324(f324(f22(f871(x92221,a859)),x92224),f324(f324(f302(x92221),x92222),f191(f871(x92221,a859))))),x92223)) % 181.55/181.55 [9385]~P1(f324(f324(f326(x93851),x93852),x93854))+P1(f324(f324(f326(x93851),x93852),x93853))+P1(f324(f324(f239(f871(x93851,a859)),x93854),f324(f324(f302(x93851),x93852),x93853)))+~P1(f324(f324(f239(f871(x93851,a859)),f324(f324(f22(f871(x93851,a859)),x93854),f324(f324(f302(x93851),x93852),f191(f871(x93851,a859))))),x93853)) % 181.55/181.55 [9416]P1(f324(f324(f326(x94161),x94162),x94163))+~P1(f324(f324(f238(f871(x94161,a859)),x94164),x94163))+P1(f324(f324(f239(f871(x94161,a859)),x94164),f324(f324(f302(x94161),x94162),x94163)))+~P1(f324(f324(f239(f871(x94161,a859)),f324(f324(f22(f871(x94161,a859)),x94164),f324(f324(f302(x94161),x94162),f191(f871(x94161,a859))))),x94163)) % 181.55/181.55 [9421]~P1(f324(f324(f326(x94211),x94213),x94212))+~P1(f324(f324(f239(f871(x94211,a859)),x94212),x94214))+P1(f324(f324(f239(f871(x94211,a859)),x94212),f324(f324(f302(x94211),x94213),x94214)))+~P1(f324(f324(f239(f871(x94211,a859)),f324(f324(f22(f871(x94211,a859)),x94212),f324(f324(f302(x94211),x94213),f191(f871(x94211,a859))))),x94214)) % 181.55/181.55 [9436]~P1(f324(f324(f238(f871(x94361,a859)),x94362),x94364))+~P1(f324(f324(f239(f871(x94361,a859)),x94362),x94364))+P1(f324(f324(f239(f871(x94361,a859)),x94362),f324(f324(f302(x94361),x94363),x94364)))+~P1(f324(f324(f239(f871(x94361,a859)),f324(f324(f22(f871(x94361,a859)),x94362),f324(f324(f302(x94361),x94363),f191(f871(x94361,a859))))),x94364)) % 181.55/181.55 [9481]~P106(x94812)+~P61(x94811)+~P1(f324(f324(f238(f871(x94811,x94812)),x94813),x94814))+P1(f324(f58(x94811),f324(f324(f18(x94811,x94812,a859),f324(f324(f8(x94812,f871(x94812,a859),x94811),f238(x94812)),x94813)),x94814))) % 181.55/181.55 [9629]~P106(x96292)+~P61(x96291)+P1(f324(f324(f238(f871(x96291,x96292)),x96293),x96294))+~P1(f324(f58(x96291),f324(f324(f18(x96291,x96292,a859),f324(f324(f8(x96292,f871(x96292,a859),x96291),f238(x96292)),x96293)),x96294))) % 181.55/181.55 [9802]E(f324(f324(f159(x98021),f324(f324(f159(f866(x98021)),f175(x98021,x98022)),x98023)),x98024),f324(f324(f159(x98021),f324(f324(f159(f866(x98021)),x98022),x98024)),x98023))+~P1(f324(f324(f239(a865),x98023),f324(f192(f866(f866(x98021))),f175(x98021,x98022))))+~P16(a865,f324(f163(a865),f324(f324(f148(f866(x98021),a865),f192(f866(x98021))),x98022)))+~P1(f324(f324(f239(a865),x98024),f324(f192(f866(f866(x98021))),f324(f130(f866(x98021),f324(f324(f8(a865,a859,f866(x98021)),f324(f239(a865),x98023)),f192(f866(x98021)))),x98022)))) % 181.55/181.55 [9829]~P1(f324(f324(f326(f870(a865,a865)),x98294),x98291))+~P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),x98294),x98292)),a35))+~P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),x98291),x98293)),a68))+P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),x98291),f324(f324(f302(f870(a865,a865)),x98292),x98293))),a68)) % 181.55/181.55 [9830]~P1(f324(f324(f326(f870(a865,a865)),x98304),x98301))+~P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),x98304),x98302)),a70))+~P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),x98301),x98303)),a71))+P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),x98301),f324(f324(f302(f870(a865,a865)),x98302),x98303))),a71)) % 181.55/181.55 [9716]~P106(x97162)+~P61(x97161)+~P1(f324(f324(f239(f871(x97161,x97162)),x97163),x97164))+P1(f324(f57(x97161),f324(f324(f8(a859,a859,x97161),a319),f324(f324(f18(x97161,x97162,a859),f324(f324(f8(x97162,f871(x97162,a859),x97161),a321),x97163)),x97164)))) % 181.55/181.55 [9842]~P1(f324(f324(f326(f870(a865,a865)),x98424),x98423))+~P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),x98421),x98424)),a35))+~P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),x98422),x98423)),a36))+P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),f324(f324(f302(f870(a865,a865)),x98421),x98422)),x98423)),a36)) % 181.55/181.55 [9843]~P1(f324(f324(f326(f870(a865,a865)),x98434),x98433))+~P1(f324(f324(f326(f870(f870(a865,a865),f870(a865,a865))),f324(f324(f259(f870(a865,a865),f870(a865,a865)),x98431),x98434)),a70))+~P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),x98432),x98433)),a69))+P1(f324(f324(f326(f870(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859))),f324(f324(f259(f871(f870(a865,a865),a859),f871(f870(a865,a865),a859)),f324(f324(f302(f870(a865,a865)),x98431),x98432)),x98433)),a69)) % 181.55/181.55 [5978]~P8(x59784,x59781)+~P1(f324(f324(x59781,x59782),x59785))+P1(f324(f324(x59781,x59782),x59783))+~P1(f324(f324(x59781,x59785),x59783)) % 181.55/181.55 [5252]~P5(x52525)+E(x52521,x52522)+~E(x52523,x52524)+~E(f324(f324(f22(x52525),x52523),x52524),f324(f324(f22(x52525),x52521),x52522)) % 181.55/181.55 [6085]~P19(x60855,x60851,x60853)+E(f324(f324(x60851,x60852),f324(x60853,x60854)),f324(x60853,x60854))+~P1(f324(f61(x60855),x60854))+~P1(f324(f324(f326(x60855),x60852),x60854)) % 181.55/181.55 [6271]~P75(x62711)+~E(f324(f324(f22(x62711),x62714),x62715),f324(f324(f22(x62711),x62712),x62713))+~P1(f324(f324(f238(x62711),x62714),x62715))+P1(f324(f324(f238(x62711),x62712),x62713)) % 181.55/181.55 [6273]~P75(x62731)+~E(f324(f324(f22(x62731),x62734),x62735),f324(f324(f22(x62731),x62732),x62733))+~P1(f324(f324(f239(x62731),x62734),x62735))+P1(f324(f324(f239(x62731),x62732),x62733)) % 181.55/181.55 [7226]~E(x72262,f324(f324(f145(x72261),x72264),x72265))+P1(f324(f324(f326(f866(x72261)),x72262),f155(x72261,x72263)))+~P1(f324(f324(f326(f866(x72261)),x72265),f155(x72261,x72263)))+~P1(f324(f324(f326(x72261),x72264),x72263)) % 181.55/181.55 [7638]~E(f324(f192(f866(x76381)),x76383),f324(f192(f866(x76382)),x76384))+~E(f324(f324(f148(f870(x76381,x76382),x76382),f262(x76381,x76382)),x76385),x76384)+~E(f324(f324(f148(f870(x76381,x76382),x76381),f258(x76381,x76382)),x76385),x76383)+E(f324(f324(f177(x76381,x76382),x76383),x76384),x76385) % 181.55/181.55 [7967]~P106(x79671)+P1(f324(f324(f239(f871(x79671,a859)),f295(x79671,x79672,x79673)),f295(x79671,x79674,x79675)))+~P1(f324(f324(f238(x79671),x79674),x79675))+P1(f324(f324(f238(x79671),x79672),x79673)) % 181.55/181.55 [8062]~P106(x80621)+P1(f324(f324(f238(f871(x80621,a859)),f295(x80621,x80622,x80623)),f295(x80621,x80624,x80625)))+~P1(f324(f324(f238(x80621),x80623),x80625))+~P1(f324(f324(f238(x80621),x80624),x80622)) % 181.55/181.55 [8187]~P105(x81871)+P1(f324(f324(f238(x81871),x81872),x81873))+P1(f324(f324(f238(x81871),x81874),x81873))+~P1(f324(f324(f238(f871(x81871,a859)),f324(f294(x81871,x81873),x81872)),f324(f294(x81871,x81874),x81875))) % 181.55/181.55 [8188]~P105(x81881)+P1(f324(f324(f238(x81881),x81882),x81883))+P1(f324(f324(f238(x81881),x81882),x81884))+~P1(f324(f324(f238(f871(x81881,a859)),f324(f294(x81881,x81883),x81882)),f324(f294(x81881,x81885),x81884))) % 181.55/181.55 [8419]~P106(x84191)+~P1(f324(f324(f238(f871(x84191,a859)),f295(x84191,x84194,x84192)),f295(x84191,x84195,x84193)))+P1(f324(f324(f238(x84191),x84192),x84193))+~P1(f324(f324(f238(x84191),x84194),x84192)) % 181.55/181.55 [8420]~P106(x84201)+~P1(f324(f324(f239(f871(x84201,a859)),f295(x84201,x84204,x84202)),f295(x84201,x84205,x84203)))+P1(f324(f324(f238(x84201),x84202),x84203))+~P1(f324(f324(f238(x84201),x84204),x84202)) % 181.55/181.55 [8421]~P106(x84211)+~P1(f324(f324(f238(f871(x84211,a859)),f295(x84211,x84213,x84214)),f295(x84211,x84212,x84215)))+P1(f324(f324(f238(x84211),x84212),x84213))+~P1(f324(f324(f238(x84211),x84213),x84214)) % 181.55/181.55 [8422]~P106(x84221)+~P1(f324(f324(f239(f871(x84221,a859)),f295(x84221,x84223,x84224)),f295(x84221,x84222,x84225)))+P1(f324(f324(f238(x84221),x84222),x84223))+~P1(f324(f324(f238(x84221),x84223),x84224)) % 181.55/181.55 [5977]~P19(x59772,x59775,x59773)+E(x59771,f191(f871(x59772,a859)))+~P1(f324(f61(x59772),x59771))+E(f324(x59773,f324(f324(f302(x59772),x59774),x59771)),f324(f324(x59775,x59774),f324(x59773,x59771))) % 181.55/181.55 [6735]~E(x67351,x67352)+~E(f324(f324(f104(f871(x67353,a859)),x67354),x67355),f191(f871(x67353,a859)))+~P1(f324(f324(f326(x67353),x67352),x67355))+~P1(f324(f324(f326(x67353),x67351),x67354)) % 181.55/181.55 [6816]~P20(x68162,x68165,x68161)+~P1(f324(f61(x68162),x68164))+E(f324(x68161,f324(f324(f302(x68162),x68163),x68164)),f324(f324(f64(x68162,x68162,x68165),x68163),x68164))+P1(f324(f324(f326(x68162),x68163),x68164)) % 181.55/181.55 [6881]~P68(x68812)+~P1(f324(f61(x68811),x68815))+E(f324(f324(f9(x68811,x68812),x68813),f324(f324(f302(x68811),x68814),x68815)),f324(f324(f82(x68812),f324(x68813,x68814)),f324(f324(f9(x68811,x68812),x68813),x68815)))+P1(f324(f324(f326(x68811),x68814),x68815)) % 181.55/181.55 [6883]~P72(x68832)+~P1(f324(f61(x68831),x68835))+E(f324(f324(f6(x68831,x68832),x68833),f324(f324(f302(x68831),x68834),x68835)),f324(f324(f81(x68832),f324(x68833,x68834)),f324(f324(f6(x68831,x68832),x68833),x68835)))+P1(f324(f324(f326(x68831),x68834),x68835)) % 181.55/181.55 [7380]~P20(x73802,x73805,x73801)+~P1(f324(f61(x73802),x73804))+E(f324(x73801,f324(f324(f302(x73802),x73803),x73804)),x73803)+~E(f324(f324(f22(f871(x73802,a859)),x73804),f324(f324(f302(x73802),x73803),f191(f871(x73802,a859)))),f191(f871(x73802,a859))) % 181.55/181.55 [7736]~P99(x77361)+~P1(f324(f324(f238(x77361),x77363),x77365))+~P1(f324(f324(f238(x77361),x77362),x77364))+P1(f324(f324(f238(x77361),f324(f324(f104(x77361),x77362),x77363)),f324(f324(f104(x77361),x77364),x77365))) % 181.55/181.55 [7737]~P100(x77371)+~P1(f324(f324(f238(x77371),x77373),x77375))+~P1(f324(f324(f238(x77371),x77372),x77374))+P1(f324(f324(f238(x77371),f324(f324(f113(x77371),x77372),x77373)),f324(f324(f113(x77371),x77374),x77375))) % 181.55/181.55 [7738]~P82(x77381)+~P1(f324(f324(f238(x77381),x77383),x77385))+~P1(f324(f324(f238(x77381),x77382),x77384))+P1(f324(f324(f238(x77381),f324(f324(f81(x77381),x77382),x77383)),f324(f324(f81(x77381),x77384),x77385))) % 181.55/181.55 [7739]~P105(x77391)+~P1(f324(f324(f238(x77391),x77393),x77395))+~P1(f324(f324(f238(x77391),x77392),x77394))+P1(f324(f324(f238(x77391),f324(f324(f189(x77391),x77392),x77393)),f324(f324(f189(x77391),x77394),x77395))) % 181.55/181.55 [7740]~P105(x77401)+~P1(f324(f324(f238(x77401),x77403),x77405))+~P1(f324(f324(f238(x77401),x77402),x77404))+P1(f324(f324(f238(x77401),f324(f324(f190(x77401),x77402),x77403)),f324(f324(f190(x77401),x77404),x77405))) % 181.55/181.55 [7741]~P84(x77411)+~P1(f324(f324(f238(x77411),x77413),x77415))+~P1(f324(f324(f239(x77411),x77412),x77414))+P1(f324(f324(f239(x77411),f324(f324(f81(x77411),x77412),x77413)),f324(f324(f81(x77411),x77414),x77415))) % 181.55/181.55 [7742]~P84(x77421)+~P1(f324(f324(f238(x77421),x77422),x77424))+~P1(f324(f324(f239(x77421),x77423),x77425))+P1(f324(f324(f239(x77421),f324(f324(f81(x77421),x77422),x77423)),f324(f324(f81(x77421),x77424),x77425))) % 181.55/181.55 [7743]~P84(x77431)+~P1(f324(f324(f239(x77431),x77433),x77435))+~P1(f324(f324(f239(x77431),x77432),x77434))+P1(f324(f324(f239(x77431),f324(f324(f81(x77431),x77432),x77433)),f324(f324(f81(x77431),x77434),x77435))) % 181.55/181.55 [7884]~P136(x78845)+E(x78841,x78842)+E(x78843,x78844)+~E(f324(f324(f81(x78845),f324(f324(f82(x78845),x78843),x78841)),f324(f324(f82(x78845),x78844),x78842)),f324(f324(f81(x78845),f324(f324(f82(x78845),x78843),x78842)),f324(f324(f82(x78845),x78844),x78841))) % 181.55/181.55 [8018]P30(x80181,x80182,x80183)+~P31(x80181,x80184,x80185)+~P30(x80181,x80182,f549(x80185,x80184,x80181,x80182))+~P1(f324(f324(f326(f864(x80181)),x80183),x80185)) % 181.55/181.55 [8084]~P105(x80844)+~P1(f324(f131(x80841),x80843))+P1(f324(f324(f326(x80841),x80842),f324(f167(x80841),x80843)))+P1(f324(f131(x80841),f324(f324(f142(x80841,x80844,x80845),x80842),x80843))) % 181.55/181.55 [8233]~P5(x82331)+E(f324(f324(f22(x82331),f324(f324(f6(a865,x82331),x82332),f324(f294(a865,x82333),x82334))),f324(f324(f6(a865,x82331),x82332),f324(f294(a865,x82333),x82335))),f324(f324(f6(a865,x82331),x82332),f324(f294(a865,x82335),x82334)))+~P1(f324(f324(f238(a865),x82335),x82334))+~P1(f324(f324(f238(a865),x82333),x82335)) % 181.55/181.55 [8234]~P72(x82341)+E(f324(f324(f81(x82341),f324(f324(f6(a865,x82341),x82342),f324(f294(a865,x82343),x82344))),f324(f324(f6(a865,x82341),x82342),f324(f294(a865,x82344),x82345))),f324(f324(f6(a865,x82341),x82342),f324(f294(a865,x82343),x82345)))+~P1(f324(f324(f238(a865),x82344),x82345))+~P1(f324(f324(f238(a865),x82343),x82344)) % 181.55/181.55 [8561]~P63(x85612)+E(x85611,f2(x85612))+E(x85613,f2(x85612))+E(f324(f324(f282(x85612),f324(f324(f22(x85612),f324(f324(f82(x85612),x85614),x85611)),f324(f324(f82(x85612),x85615),x85613))),f324(f324(f82(x85612),x85613),x85611)),f324(f324(f22(x85612),f324(f324(f282(x85612),x85614),x85613)),f324(f324(f282(x85612),x85615),x85611))) % 181.55/181.55 [8562]~P63(x85622)+E(x85621,f2(x85622))+E(x85623,f2(x85622))+E(f324(f324(f282(x85622),f324(f324(f81(x85622),f324(f324(f82(x85622),x85624),x85621)),f324(f324(f82(x85622),x85625),x85623))),f324(f324(f82(x85622),x85623),x85621)),f324(f324(f81(x85622),f324(f324(f282(x85622),x85624),x85623)),f324(f324(f282(x85622),x85625),x85621))) % 181.55/181.55 [8571]~E(x85712,f324(x85713,x85711))+E(x85711,f408(x85712,x85713,x85714,x85715))+~P27(x85715,x85714,x85713,f247(f871(x85715,a859)))+~P1(f324(f324(f326(x85714),x85712),f324(f303(x85715,x85714,x85713),f247(f871(x85715,a859))))) % 181.55/181.55 [8785]~P117(x87851)+~P1(f324(f324(f239(x87851),f324(f75(x87851),x87852)),x87854))+P1(f324(f324(f239(x87851),f324(f324(f82(x87851),f324(f75(x87851),x87852)),f324(f75(x87851),x87853))),f324(f324(f82(x87851),x87854),x87855)))+~P1(f324(f324(f239(x87851),f324(f75(x87851),x87853)),x87855)) % 181.55/181.55 [8802]~P31(x88021,x88025,x88024)+P30(x88021,x88022,x88023)+P1(f324(f324(f326(f864(x88021)),f549(x88024,x88025,x88021,x88022)),x88025))+~P1(f324(f324(f326(f864(x88021)),x88023),x88024)) % 181.55/181.55 [8899]~P27(x88991,x88993,x88995,x88992)+~P1(f324(f61(x88993),x88994))+P1(f324(f324(f238(a865),f324(f37(x88991),x88992)),f324(f37(x88993),x88994)))+~P1(f324(f324(f238(f871(x88993,a859)),f324(f303(x88991,x88993,x88995),x88992)),x88994)) % 181.55/181.55 [8967]~P68(x89672)+~P27(x89671,x89671,x89674,x89675)+~P1(f324(f61(x89671),x89675))+E(f324(f324(f9(x89671,x89672),f324(f73(x89671,x89672,x89671,x89673),x89674)),x89675),f324(f324(f9(x89671,x89672),x89673),f324(f303(x89671,x89671,x89674),x89675))) % 181.55/181.55 [8968]~P72(x89682)+~P27(x89681,x89681,x89684,x89685)+~P1(f324(f61(x89681),x89685))+E(f324(f324(f6(x89681,x89682),f324(f73(x89681,x89682,x89681,x89683),x89684)),x89685),f324(f324(f6(x89681,x89682),x89683),f324(f303(x89681,x89681,x89684),x89685))) % 181.55/181.55 [9086]~P39(x90861,x90862)+~P1(f324(f324(f326(x90861),x90863),x90864))+~P1(f324(f324(f326(x90861),x90865),x90864))+~P1(f324(f324(f326(f870(x90861,x90861)),f324(f324(f259(x90861,x90861),x90865),f638(x90862,x90861,x90864))),x90862)) % 181.55/181.55 [9125]~P27(x91252,x91253,x91255,x91251)+E(x91251,f191(f871(x91252,a859)))+E(f324(f303(x91253,x91252,f439(x91254,x91253,x91252,x91251)),x91254),x91251)+~P1(f324(f324(f238(f871(x91253,a859)),f324(f303(x91252,x91253,x91255),x91251)),x91254)) % 181.55/181.55 [9611]~P105(x96115)+~P6(x96115)+P1(f324(f324(f326(x96111),f688(x96112,x96113,x96111,x96114,x96115)),x96113))+~P1(f324(f324(f239(x96115),x96114),f324(f324(f41(x96111,x96115),x96113),x96112))) % 181.55/181.55 [9616]~P105(x96161)+~P6(x96161)+P1(f324(f324(f239(x96161),x96162),f324(x96163,f688(x96163,x96164,x96165,x96162,x96161))))+~P1(f324(f324(f239(x96161),x96162),f324(f324(f41(x96165,x96161),x96164),x96163))) % 181.55/181.55 [9696]~P66(x96961)+~P1(f324(f66(x96961,x96961,f82(x96961),x96962,x96963),x96965))+P1(f324(f324(f326(x96961),x96962),x96963))+P1(f324(f66(x96961,x96961,f82(x96961),x96964,f324(f324(f302(x96961),x96962),x96963)),f324(f324(f82(x96961),x96964),x96965))) % 181.55/181.55 [9911]~P68(x99112)+~P1(f324(f61(x99111),x99115))+E(f324(f324(f9(x99111,x99112),f324(f324(f7(x99111,x99112,x99112),f324(f324(f18(x99111,x99112,f871(x99112,x99112)),f324(f324(f8(a859,f871(x99112,f871(x99112,x99112)),x99111),f99(x99112)),f324(a321,x99113))),x99114)),f79(x99112))),x99115),f79(x99112))+P1(f324(f324(f326(x99111),x99113),x99115)) % 181.55/181.55 [9912]~P72(x99122)+~P1(f324(f61(x99121),x99125))+E(f324(f324(f6(x99121,x99122),f324(f324(f7(x99121,x99122,x99122),f324(f324(f18(x99121,x99122,f871(x99122,x99122)),f324(f324(f8(a859,f871(x99122,f871(x99122,x99122)),x99121),f99(x99122)),f324(a321,x99123))),x99124)),f2(x99122))),x99125),f2(x99122))+P1(f324(f324(f326(x99121),x99123),x99125)) % 181.55/181.55 [9913]~P68(x99132)+~P1(f324(f61(x99131),x99135))+E(f324(f324(f9(x99131,x99132),f324(f324(f7(x99131,x99132,x99132),f324(f324(f18(x99131,x99132,f871(x99132,x99132)),f324(f324(f8(a859,f871(x99132,f871(x99132,x99132)),x99131),f99(x99132)),f324(a321,x99133))),x99134)),f79(x99132))),x99135),f324(x99134,x99133))+~P1(f324(f324(f326(x99131),x99133),x99135)) % 181.55/181.55 [9914]~P72(x99142)+~P1(f324(f61(x99141),x99145))+E(f324(f324(f6(x99141,x99142),f324(f324(f7(x99141,x99142,x99142),f324(f324(f18(x99141,x99142,f871(x99142,x99142)),f324(f324(f8(a859,f871(x99142,f871(x99142,x99142)),x99141),f99(x99142)),f324(a321,x99143))),x99144)),f2(x99142))),x99145),f324(x99144,x99143))+~P1(f324(f324(f326(x99141),x99143),x99145)) % 181.55/181.55 [9969]~P68(x99692)+~P1(f324(f61(x99691),x99695))+E(f324(f324(f9(x99691,x99692),f324(f324(f7(x99691,x99692,x99692),f324(f324(f18(x99691,x99692,f871(x99692,x99692)),f324(f324(f8(a859,f871(x99692,f871(x99692,x99692)),x99691),f99(x99692)),f324(f324(f7(x99691,x99691,a859),a321),x99693))),x99694)),f79(x99692))),x99695),f79(x99692))+P1(f324(f324(f326(x99691),x99693),x99695)) % 181.55/181.55 [9970]~P72(x99702)+~P1(f324(f61(x99701),x99705))+E(f324(f324(f6(x99701,x99702),f324(f324(f7(x99701,x99702,x99702),f324(f324(f18(x99701,x99702,f871(x99702,x99702)),f324(f324(f8(a859,f871(x99702,f871(x99702,x99702)),x99701),f99(x99702)),f324(f324(f7(x99701,x99701,a859),a321),x99703))),x99704)),f2(x99702))),x99705),f2(x99702))+P1(f324(f324(f326(x99701),x99703),x99705)) % 181.55/181.55 [9972]~P68(x99722)+~P1(f324(f61(x99721),x99725))+E(f324(f324(f9(x99721,x99722),f324(f324(f7(x99721,x99722,x99722),f324(f324(f18(x99721,x99722,f871(x99722,x99722)),f324(f324(f8(a859,f871(x99722,f871(x99722,x99722)),x99721),f99(x99722)),f324(f324(f7(x99721,x99721,a859),a321),x99723))),x99724)),f79(x99722))),x99725),f324(x99724,x99723))+~P1(f324(f324(f326(x99721),x99723),x99725)) % 181.55/181.55 [9973]~P72(x99732)+~P1(f324(f61(x99731),x99735))+E(f324(f324(f6(x99731,x99732),f324(f324(f7(x99731,x99732,x99732),f324(f324(f18(x99731,x99732,f871(x99732,x99732)),f324(f324(f8(a859,f871(x99732,f871(x99732,x99732)),x99731),f99(x99732)),f324(f324(f7(x99731,x99731,a859),a321),x99733))),x99734)),f2(x99732))),x99735),f324(x99734,x99733))+~P1(f324(f324(f326(x99731),x99733),x99735)) % 181.55/181.55 [7735]~P5(x77352)+~P1(f324(f61(x77351),x77354))+E(f324(f324(f6(x77351,x77352),x77353),f324(f324(f22(f871(x77351,a859)),x77354),f324(f324(f302(x77351),x77355),f191(f871(x77351,a859))))),f324(f324(f6(x77351,x77352),x77353),x77354))+P1(f324(f324(f326(x77351),x77355),x77354)) % 181.55/181.55 [8241]~P116(x82412)+~P1(f324(f61(x82411),x82414))+E(f324(f324(f6(x82411,x82412),x82413),f324(f324(f22(f871(x82411,a859)),x82414),f324(f324(f302(x82411),x82415),f191(f871(x82411,a859))))),f324(f324(f22(x82412),f324(f324(f6(x82411,x82412),x82413),x82414)),f324(x82413,x82415)))+~P1(f324(f324(f326(x82411),x82415),x82414)) % 181.55/181.55 [8242]~P5(x82422)+~P1(f324(f61(x82421),x82424))+E(f324(f324(f6(x82421,x82422),x82423),f324(f324(f22(f871(x82421,a859)),x82424),f324(f324(f302(x82421),x82425),f191(f871(x82421,a859))))),f324(f324(f22(x82422),f324(f324(f6(x82421,x82422),x82423),x82424)),f324(x82423,x82425)))+~P1(f324(f324(f326(x82421),x82425),x82424)) % 181.55/181.55 [8274]~P5(x82741)+~P1(f324(f61(x82742),x82744))+E(f324(f324(f22(x82741),f324(f324(f6(x82742,x82741),x82743),x82744)),f324(f324(f6(x82742,x82741),x82743),x82745)),f324(f324(f6(x82742,x82741),x82743),f324(f324(f22(f871(x82742,a859)),x82744),x82745)))+~P1(f324(f324(f238(f871(x82742,a859)),x82745),x82744)) % 181.55/181.55 [8295]P1(f324(f61(x82951),f324(x82952,x82953)))+~P1(f324(f61(x82954),x82955))+~P1(f324(f324(f326(x82954),x82953),x82955))+~P1(f324(f61(x82951),f324(f324(f41(x82954,f871(x82951,a859)),x82955),x82952))) % 181.55/181.55 [8746]~P9(x87461,x87465,x87464)+~E(f324(f278(x87461,x87461,x87464),f324(f324(f302(x87461),x87462),f191(f871(x87461,a859)))),f324(f278(x87461,x87461,x87464),f324(f324(f302(x87461),x87463),f191(f871(x87461,a859)))))+~P1(f324(f324(f326(x87461),x87463),x87465))+P1(f324(f324(f326(f870(x87461,x87461)),f324(f324(f259(x87461,x87461),x87462),x87463)),x87464)) % 181.55/181.55 [9044]~P1(f324(x90441,x90445))+P1(f324(x90441,f819(x90441,x90442,x90443,x90444)))+P1(f324(x90441,f817(x90441,x90442,x90443,x90444)))+~P1(f324(f324(f326(x90444),x90445),f324(f324(f113(f871(x90444,a859)),x90443),x90442))) % 181.55/181.55 [9227]~P1(f324(x92271,x92275))+P1(f324(x92271,f817(x92271,x92272,x92273,x92274)))+P1(f324(f324(f326(x92274),f819(x92271,x92272,x92273,x92274)),x92272))+~P1(f324(f324(f326(x92274),x92275),f324(f324(f113(f871(x92274,a859)),x92273),x92272))) % 181.55/181.55 [9228]~P1(f324(x92281,x92285))+P1(f324(x92281,f819(x92281,x92282,x92283,x92284)))+P1(f324(f324(f326(x92284),f817(x92281,x92282,x92283,x92284)),x92283))+~P1(f324(f324(f326(x92284),x92285),f324(f324(f113(f871(x92284,a859)),x92283),x92282))) % 181.55/181.55 [9232]P1(f324(x92321,x92322))+~P1(f324(x92321,f822(x92321,x92323,x92324,x92325)))+~P1(f324(x92321,f821(x92321,x92323,x92324,x92325)))+~P1(f324(f324(f326(x92325),x92322),f324(f324(f113(f871(x92325,a859)),x92324),x92323))) % 181.55/181.55 [9275]E(x92751,x92752)+~P1(f324(f324(f326(f870(x92753,x92753)),f324(f324(f259(x92753,x92753),x92751),x92752)),f300(x92753,x92755)))+P1(f324(f324(f326(x92753),x92751),x92754))+~P1(f324(f324(f238(f871(f870(x92753,x92753),a859)),x92755),f324(f324(f261(x92753,x92753),x92754),f324(f16(f871(x92753,a859),x92753),x92754)))) % 181.55/181.55 [9294]P1(f324(x92941,x92942))+~P1(f324(x92941,f821(x92941,x92944,x92945,x92943)))+P1(f324(f324(f326(x92943),f822(x92941,x92944,x92945,x92943)),x92944))+~P1(f324(f324(f326(x92943),x92942),f324(f324(f113(f871(x92943,a859)),x92945),x92944))) % 181.55/181.55 [9295]P1(f324(x92951,x92952))+~P1(f324(x92951,f822(x92951,x92954,x92955,x92953)))+P1(f324(f324(f326(x92953),f821(x92951,x92954,x92955,x92953)),x92955))+~P1(f324(f324(f326(x92953),x92952),f324(f324(f113(f871(x92953,a859)),x92955),x92954))) % 181.55/181.55 [9356]P1(f324(x93561,x93562))+P1(f324(f324(f326(x93563),f822(x93561,x93564,x93565,x93563)),x93564))+P1(f324(f324(f326(x93563),f821(x93561,x93564,x93565,x93563)),x93565))+~P1(f324(f324(f326(x93563),x93562),f324(f324(f113(f871(x93563,a859)),x93565),x93564))) % 181.55/181.55 [9358]~P1(f324(x93582,x93585))+P1(f324(f324(f326(x93581),f819(x93582,x93583,x93584,x93581)),x93583))+P1(f324(f324(f326(x93581),f817(x93582,x93583,x93584,x93581)),x93584))+~P1(f324(f324(f326(x93581),x93585),f324(f324(f113(f871(x93581,a859)),x93584),x93583))) % 181.55/181.55 [9514]~P9(x95141,x95145,x95144)+~P1(f324(f324(f326(x95141),x95143),x95145))+P1(f324(f324(f326(f870(x95141,x95141)),f324(f324(f259(x95141,x95141),x95142),x95143)),x95144))+~P1(f324(f324(f238(f871(x95141,a859)),f324(f278(x95141,x95141,x95144),f324(f324(f302(x95141),x95143),f191(f871(x95141,a859))))),f324(f278(x95141,x95141,x95144),f324(f324(f302(x95141),x95142),f191(f871(x95141,a859)))))) % 181.55/181.55 [9643]~P105(x96435)+~P6(x96435)+P1(f324(f324(f326(x96431),f620(x96432,x96433,x96434,x96431,x96435)),x96434))+~P1(f324(f324(f239(x96435),f324(f324(f42(x96431,x96435),x96434),x96433)),x96432)) % 181.55/181.55 [9676]~P82(x96765)+~P78(x96765)+P1(f324(f324(f326(x96761),f708(x96762,x96763,x96764,x96761,x96765)),f324(f167(x96761),x96764)))+P1(f324(f324(f238(x96765),f324(f160(x96765),f324(f324(f148(x96761,x96765),x96763),x96764))),f324(f160(x96765),f324(f324(f148(x96761,x96765),x96762),x96764)))) % 181.55/181.55 [9792]~P105(x97921)+~P6(x97921)+P1(f324(f324(f239(x97921),f324(x97922,f620(x97923,x97922,x97924,x97925,x97921))),x97923))+~P1(f324(f324(f239(x97921),f324(f324(f42(x97925,x97921),x97924),x97922)),x97923)) % 181.55/181.55 [9929]~P82(x99291)+~P78(x99291)+~P1(f324(f324(f238(x99291),f324(x99293,f708(x99295,x99293,x99294,x99292,x99291))),f324(x99295,f708(x99295,x99293,x99294,x99292,x99291))))+P1(f324(f324(f238(x99291),f324(f160(x99291),f324(f324(f148(x99292,x99291),x99293),x99294))),f324(f160(x99291),f324(f324(f148(x99292,x99291),x99295),x99294)))) % 181.55/181.55 [8583]~P68(x85831)+~P1(f324(f61(x85834),x85835))+~P1(f324(f324(f326(x85834),x85833),x85835))+E(f324(f324(f82(x85831),f324(x85832,x85833)),f324(f324(f9(x85834,x85831),x85832),f324(f324(f22(f871(x85834,a859)),x85835),f324(f324(f302(x85834),x85833),f191(f871(x85834,a859)))))),f324(f324(f9(x85834,x85831),x85832),x85835)) % 181.55/181.55 [8585]~P72(x85851)+~P1(f324(f61(x85854),x85855))+~P1(f324(f324(f326(x85854),x85853),x85855))+E(f324(f324(f81(x85851),f324(x85852,x85853)),f324(f324(f6(x85854,x85851),x85852),f324(f324(f22(f871(x85854,a859)),x85855),f324(f324(f302(x85854),x85853),f191(f871(x85854,a859)))))),f324(f324(f6(x85854,x85851),x85852),x85855)) % 181.55/181.55 [8645]~P20(x86451,x86454,x86455)+~P1(f324(f61(x86451),x86452))+E(f324(f324(f22(f871(x86451,a859)),x86452),f324(f324(f302(x86451),x86453),f191(f871(x86451,a859)))),f191(f871(x86451,a859)))+E(f324(f324(x86454,x86453),f324(x86455,f324(f324(f22(f871(x86451,a859)),x86452),f324(f324(f302(x86451),x86453),f191(f871(x86451,a859)))))),f324(x86455,f324(f324(f302(x86451),x86453),x86452))) % 181.55/181.55 [9024]~P68(x90241)+~P1(f324(f61(x90242),x90245))+~P1(f324(f61(x90242),x90244))+E(f324(f324(f82(x90241),f324(f324(f9(x90242,x90241),x90243),f324(f324(f113(f871(x90242,a859)),x90244),x90245))),f324(f324(f9(x90242,x90241),x90243),f324(f324(f104(f871(x90242,a859)),x90244),x90245))),f324(f324(f82(x90241),f324(f324(f9(x90242,x90241),x90243),x90244)),f324(f324(f9(x90242,x90241),x90243),x90245))) % 181.55/181.55 [9025]~P72(x90251)+~P1(f324(f61(x90252),x90255))+~P1(f324(f61(x90252),x90254))+E(f324(f324(f81(x90251),f324(f324(f6(x90252,x90251),x90253),f324(f324(f113(f871(x90252,a859)),x90254),x90255))),f324(f324(f6(x90252,x90251),x90253),f324(f324(f104(f871(x90252,a859)),x90254),x90255))),f324(f324(f81(x90251),f324(f324(f6(x90252,x90251),x90253),x90254)),f324(f324(f6(x90252,x90251),x90253),x90255))) % 181.55/181.55 [9165]~P5(x91651)+~P1(f324(f61(x91652),x91655))+~P1(f324(f61(x91652),x91654))+E(f324(f324(f22(x91651),f324(f324(f81(x91651),f324(f324(f6(x91652,x91651),x91653),x91654)),f324(f324(f6(x91652,x91651),x91653),x91655))),f324(f324(f6(x91652,x91651),x91653),f324(f324(f104(f871(x91652,a859)),x91654),x91655))),f324(f324(f6(x91652,x91651),x91653),f324(f324(f113(f871(x91652,a859)),x91654),x91655))) % 181.55/181.55 [9371]~P27(x93711,x93712,x93713,x93715)+~P27(x93711,x93712,x93713,x93714)+P27(x93711,x93712,x93713,f324(f324(f113(f871(x93711,a859)),x93714),x93715))+~E(f324(f324(f104(f871(x93712,a859)),f324(f303(x93711,x93712,x93713),f324(f324(f22(f871(x93711,a859)),x93714),x93715))),f324(f303(x93711,x93712,x93713),f324(f324(f22(f871(x93711,a859)),x93715),x93714))),f191(f871(x93712,a859))) % 181.55/181.55 [9489]E(x94891,f2(a1))+~P1(f324(f324(f239(a1),f2(a1)),x94893))+~P1(f324(f48(x94892,x94891),f324(f324(f259(a1,a1),x94894),x94895)))+P1(f324(f48(x94892,f324(f324(f82(a1),x94891),x94893)),f324(f324(f259(a1,a1),f324(f324(f38(a1),x94894),x94893)),f324(f324(f81(a1),f324(f324(f82(a1),x94891),f44(a1,x94894,x94893))),x94895)))) % 181.55/181.55 [9497]~P1(f324(f324(f239(a865),f2(a865)),x94973))+~P1(f324(f324(f239(a865),f2(a865)),x94972))+~P1(f324(f47(x94971,x94972),f324(f324(f259(a865,a865),x94974),x94975)))+P1(f324(f47(x94971,f324(f324(f82(a865),x94972),x94973)),f324(f324(f259(a865,a865),f324(f324(f38(a865),x94974),x94973)),f324(f324(f81(a865),f324(f324(f82(a865),x94972),f44(a865,x94974,x94973))),x94975)))) % 181.55/181.55 [9549]~P68(x95491)+~P1(f324(f61(x95492),x95495))+~P1(f324(f61(x95492),x95494))+E(f324(f324(f82(x95491),f324(f324(f324(f65(x95491,x95492,f82(x95491)),x95493),f79(x95491)),f324(f324(f113(f871(x95492,a859)),x95494),x95495))),f324(f324(f324(f65(x95491,x95492,f82(x95491)),x95493),f79(x95491)),f324(f324(f104(f871(x95492,a859)),x95494),x95495))),f324(f324(f82(x95491),f324(f324(f324(f65(x95491,x95492,f82(x95491)),x95493),f79(x95491)),x95494)),f324(f324(f324(f65(x95491,x95492,f82(x95491)),x95493),f79(x95491)),x95495))) % 181.55/181.55 [9551]~E(f324(f324(f170(x95511),x95515),x95512),f324(f324(f170(x95511),x95515),x95513))+P1(f324(f324(f326(f870(f866(x95511),f866(x95511))),f324(f324(f259(f866(x95511),f866(x95511)),x95512),x95513)),f141(x95511,x95514)))+~P1(f324(f324(f239(a865),x95515),f324(f324(f189(a865),f324(f192(f866(x95511)),x95512)),f324(f192(f866(x95511)),x95513))))+~P1(f324(f324(f326(f870(x95511,x95511)),f324(f324(f259(x95511,x95511),f324(f324(f159(x95511),x95512),x95515)),f324(f324(f159(x95511),x95513),x95515))),x95514)) % 181.55/181.55 [9664]~P82(x96645)+~P141(x96645)+P1(f324(f324(f326(x96641),f474(x96642,x96643,x96644,x96641,x96645)),x96644))+P1(f324(f324(f238(x96645),f324(f324(f6(x96641,x96645),x96643),x96644)),f324(f324(f82(x96645),f324(f103(x96645),f324(f37(x96641),x96644))),x96642))) % 181.55/181.55 [9857]~P82(x98571)+~P141(x98571)+~P1(f324(f324(f238(x98571),f324(x98573,f474(x98575,x98573,x98574,x98572,x98571))),x98575))+P1(f324(f324(f238(x98571),f324(f324(f6(x98572,x98571),x98573),x98574)),f324(f324(f82(x98571),f324(f103(x98571),f324(f37(x98572),x98574))),x98575))) % 181.55/181.55 [8614]E(f324(f324(f124(x86141),x86142),x86143),f324(f324(f124(x86141),x86144),x86145))+~E(f324(f324(f170(x86141),f324(f192(f866(x86141)),x86142)),x86144),x86142)+~E(f324(f324(f124(x86141),f324(f324(f132(x86141),f324(f192(f866(x86141)),x86142)),x86144)),x86145),x86143)+P1(f324(f324(f238(a865),f324(f192(f866(x86141)),x86144)),f324(f192(f866(x86141)),x86142))) % 181.55/181.55 [8745]E(f324(f324(f124(x87451),x87452),x87453),f324(f324(f124(x87451),x87454),x87455))+~E(f324(f324(f170(x87451),f324(f192(f866(x87451)),x87452)),x87454),x87452)+~E(x87453,f324(f324(f124(x87451),f324(f324(f132(x87451),f324(f192(f866(x87451)),x87452)),x87454)),x87455))+~P1(f324(f324(f238(a865),f324(f192(f866(x87451)),x87452)),f324(f192(f866(x87451)),x87454))) % 181.55/181.55 [9990]~P1(f324(x99905,x99904))+~P1(f324(f61(x99902),f324(f244(x99902),x99905)))+P1(f324(f61(x99901),f324(f244(x99901),f324(f324(f7(x99901,x99902,a859),x99903),x99904))))+~P1(f324(f61(x99901),f324(f244(x99901),f324(f324(f8(f871(x99902,a859),a859,x99901),f88(x99902)),f324(f324(f8(f871(x99902,a859),f871(x99902,a859),x99901),f324(f18(x99902,a859,a859),f324(f324(f8(a859,f871(a859,a859),x99902),a322),x99905))),x99903))))) % 181.55/181.55 [8400]~P21(x84005,x84001,x84006,x84002)+E(f324(f73(x84001,x84001,x84001,f324(x84002,x84003)),f324(x84002,x84004)),f324(f73(x84001,x84001,x84001,f324(x84002,x84004)),f324(x84002,x84003)))+~P1(f324(f61(x84005),x84004))+~P1(f324(f61(x84005),x84003)) % 181.55/181.55 [7790]~P27(x77901,x77902,x77904,x77903)+~E(f324(x77904,x77906),x77905)+E(f324(f78(x77901,x77902,x77903,x77904),x77905),x77906)+~P1(f324(f324(f326(x77901),x77906),x77903)) % 181.55/181.55 [7791]~P27(x77911,x77912,x77914,x77913)+~E(f324(x77914,x77916),x77915)+E(f324(f94(x77911,x77912,x77913,x77914),x77915),x77916)+~P1(f324(f324(f326(x77911),x77916),x77913)) % 181.55/181.55 [7988]~P22(x79886,x79881,x79884,x79882)+E(f324(f73(x79881,x79881,x79881,f324(x79882,x79883)),f324(x79884,x79885)),f324(x79882,x79883))+~P1(f324(f61(x79886),x79883))+~P1(f324(f324(f326(x79886),x79885),x79883)) % 181.55/181.55 [9092]~P27(x90921,x90922,x90925,x90926)+P27(x90921,x90922,f76(x90921,x90922,x90923,x90924,x90925),x90926)+~P1(f324(f324(f326(x90921),x90924),x90926))+~P1(f324(f324(f326(x90921),x90923),x90926)) % 181.55/181.55 [9115]E(x91151,x91152)+~E(f324(f94(x91153,x91154,x91155,x91156),x91151),f324(f94(x91153,x91154,x91155,x91156),x91152))+~P1(f324(f324(f326(x91154),x91152),f324(f303(x91153,x91154,x91156),x91155)))+~P1(f324(f324(f326(x91154),x91151),f324(f303(x91153,x91154,x91156),x91155))) % 181.55/181.55 [9212]~P21(x92123,x92121,x92126,x92122)+E(f324(f73(x92121,x92121,x92121,f324(x92122,f324(f324(f22(f871(x92123,a859)),x92124),f324(f324(f302(x92123),x92125),f191(f871(x92123,a859)))))),f324(x92126,x92125)),f324(x92122,x92124))+~P1(f324(f61(x92123),x92124))+~P1(f324(f324(f326(x92123),x92125),x92124)) % 181.55/181.55 [9293]P27(x92931,x92932,x92933,x92934)+~P27(x92931,x92932,f76(x92931,x92932,x92936,x92935,x92933),x92934)+~P1(f324(f324(f326(x92931),x92935),x92934))+~P1(f324(f324(f326(x92931),x92936),x92934)) % 181.55/181.55 [6886]~P60(x68861)+~E(f44(x68861,x68863,x68864),f44(x68861,x68866,x68864))+~E(f44(x68861,x68862,x68864),f44(x68861,x68865,x68864))+E(f44(x68861,f324(f324(f22(x68861),x68862),x68863),x68864),f44(x68861,f324(f324(f22(x68861),x68865),x68866),x68864)) % 181.55/181.55 [6887]~P59(x68871)+~E(f44(x68871,x68873,x68874),f44(x68871,x68876,x68874))+~E(f44(x68871,x68872,x68874),f44(x68871,x68875,x68874))+E(f44(x68871,f324(f324(f82(x68871),x68872),x68873),x68874),f44(x68871,f324(f324(f82(x68871),x68875),x68876),x68874)) % 181.55/181.55 [6888]~P59(x68881)+~E(f44(x68881,x68883,x68884),f44(x68881,x68886,x68884))+~E(f44(x68881,x68882,x68884),f44(x68881,x68885,x68884))+E(f44(x68881,f324(f324(f81(x68881),x68882),x68883),x68884),f44(x68881,f324(f324(f81(x68881),x68885),x68886),x68884)) % 181.55/181.55 [7689]~P18(x76891,x76892,x76893)+~P1(f324(f61(x76891),x76896))+E(f324(f324(f64(x76891,x76892,x76893),x76894),f324(f324(f302(x76891),x76895),x76896)),f324(f324(f64(x76891,x76892,x76893),f324(f324(x76893,x76895),x76894)),x76896))+P1(f324(f324(f326(x76891),x76895),x76896)) % 181.55/181.55 [7748]~P6(x77481)+P1(f324(f324(f238(x77481),x77482),f324(x77483,x77484)))+~P1(f324(f324(f326(x77485),x77484),x77486))+~P1(f324(f324(f238(x77481),x77482),f324(f324(f42(x77485,x77481),x77486),x77483))) % 181.55/181.55 [7910]~P18(x79101,x79102,x79103)+~P1(f324(f61(x79101),x79106))+E(f324(f324(f64(x79101,x79102,x79103),x79104),f324(f324(f302(x79101),x79105),x79106)),f324(f324(x79103,x79105),f324(f324(f64(x79101,x79102,x79103),x79104),x79106)))+P1(f324(f324(f326(x79101),x79105),x79106)) % 181.55/181.55 [8004]~P105(x80043)+~P1(f324(x80042,x80045))+~P16(x80043,f324(f324(f148(x80041,x80043),x80044),x80046))+E(f324(f130(x80041,x80042),f324(f324(f142(x80041,x80043,x80044),x80045),x80046)),f324(f324(f142(x80041,x80043,x80044),x80045),f324(f130(x80041,x80042),x80046))) % 181.55/181.55 [8026]E(x80261,x80262)+E(x80263,f2(a1))+~P1(f324(f48(x80264,x80263),f324(f324(f259(a1,a1),x80265),x80262)))+~P1(f324(f48(x80264,x80263),f324(f324(f259(a1,a1),x80266),x80261))) % 181.55/181.55 [8027]E(x80271,x80272)+E(x80273,f2(a1))+~P1(f324(f48(x80274,x80273),f324(f324(f259(a1,a1),x80272),x80275)))+~P1(f324(f48(x80274,x80273),f324(f324(f259(a1,a1),x80271),x80276))) % 181.55/181.55 [8047]~P21(x80472,x80475,x80476,x80471)+~P1(f324(f61(x80472),x80474))+E(f324(x80471,f324(f324(f302(x80472),x80473),x80474)),f324(f73(x80475,x80475,x80475,f324(x80471,x80474)),f324(x80476,x80473)))+P1(f324(f324(f326(x80472),x80473),x80474)) % 181.55/181.55 [8277]~P22(x82775,x82771,x82776,x82772)+E(f324(f73(x82771,x82771,x82771,f324(x82772,x82773)),f324(x82772,x82774)),f324(x82772,x82773))+~P1(f324(f61(x82775),x82773))+~P1(f324(f324(f238(f871(x82775,a859)),x82774),x82773)) % 181.55/181.55 [9418]~P27(x94181,x94182,x94184,x94183)+~P1(f324(f324(f326(x94182),x94185),f324(f303(x94181,x94182,x94184),x94183)))+P1(f324(f324(f326(x94181),f324(f78(x94181,x94182,x94183,x94184),x94185)),x94186))+~P1(f324(f324(f238(f871(x94181,a859)),x94183),x94186)) % 181.55/181.55 [9803]~P72(x98032)+~E(f499(x98031,x98033,x98035,x98036,x98034,x98032),f498(x98031,x98033,x98035,x98036,x98034,x98032))+~P1(f324(f61(x98034),x98036))+E(f324(f324(f6(x98031,x98032),x98033),f324(f303(x98034,x98031,x98035),x98036)),f324(f324(f6(x98034,x98032),f324(f73(x98031,x98032,x98034,x98033),x98035)),x98036)) % 181.55/181.55 [9838]~P72(x98386)+E(f324(x98381,f499(x98382,x98383,x98381,x98384,x98385,x98386)),f324(x98381,f498(x98382,x98383,x98381,x98384,x98385,x98386)))+E(f324(f324(f6(x98382,x98386),x98383),f324(f303(x98385,x98382,x98381),x98384)),f324(f324(f6(x98385,x98386),f324(f73(x98382,x98386,x98385,x98383),x98381)),x98384))+~P1(f324(f61(x98385),x98384)) % 181.55/181.55 [9879]~P72(x98792)+~E(f324(x98793,f324(x98795,f498(x98791,x98793,x98795,x98796,x98794,x98792))),f2(x98792))+~P1(f324(f61(x98794),x98796))+E(f324(f324(f6(x98791,x98792),x98793),f324(f303(x98794,x98791,x98795),x98796)),f324(f324(f6(x98794,x98792),f324(f73(x98791,x98792,x98794,x98793),x98795)),x98796)) % 181.55/181.55 [9937]~P72(x99372)+~P1(f324(f61(x99374),x99376))+E(f324(f324(f6(x99371,x99372),x99373),f324(f303(x99374,x99371,x99375),x99376)),f324(f324(f6(x99374,x99372),f324(f73(x99371,x99372,x99374,x99373),x99375)),x99376))+P1(f324(f324(f326(x99374),f498(x99371,x99373,x99375,x99376,x99374,x99372)),x99376)) % 181.55/181.55 [9938]~P72(x99382)+~P1(f324(f61(x99384),x99386))+E(f324(f324(f6(x99381,x99382),x99383),f324(f303(x99384,x99381,x99385),x99386)),f324(f324(f6(x99384,x99382),f324(f73(x99381,x99382,x99384,x99383),x99385)),x99386))+P1(f324(f324(f326(x99384),f499(x99381,x99383,x99385,x99386,x99384,x99382)),x99386)) % 181.55/181.55 [10048]~P68(x100481)+~P1(f324(f61(x100482),x100486))+E(f324(f324(f324(f65(x100481,x100482,f82(x100481)),f324(f324(f18(x100482,f871(x100483,a859),x100481),f324(f324(f7(x100482,x100481,f871(f871(x100483,a859),x100481)),f324(f324(f8(f871(x100483,x100481),f871(x100481,f871(f871(x100483,a859),x100481)),x100482),f65(x100481,x100483,f82(x100481))),x100484)),f79(x100481))),x100485)),f79(x100481)),x100486),f324(f324(f324(f65(x100481,f870(x100482,x100483),f82(x100481)),f324(f263(x100482,x100483,x100481),x100484)),f79(x100481)),f324(f324(f261(x100482,x100483),x100486),x100485)))+P1(f324(f324(f326(x100482),f485(x100484,x100485,x100483,x100486,x100482,x100481)),x100486)) % 181.55/181.55 [10066]~P68(x100661)+~P1(f324(f61(x100662),x100666))+E(f324(f324(f324(f65(x100661,x100662,f82(x100661)),f324(f324(f18(x100662,f871(x100663,a859),x100661),f324(f324(f7(x100662,x100661,f871(f871(x100663,a859),x100661)),f324(f324(f8(f871(x100663,x100661),f871(x100661,f871(f871(x100663,a859),x100661)),x100662),f65(x100661,x100663,f82(x100661))),x100664)),f79(x100661))),x100665)),f79(x100661)),x100666),f324(f324(f324(f65(x100661,f870(x100662,x100663),f82(x100661)),f324(f263(x100662,x100663,x100661),x100664)),f79(x100661)),f324(f324(f261(x100662,x100663),x100666),x100665)))+~P1(f324(f61(x100663),f324(x100665,f485(x100664,x100665,x100663,x100666,x100662,x100661)))) % 181.55/181.55 [8186]~P22(x81862,x81865,x81866,x81861)+~P1(f324(f61(x81862),x81864))+~P1(f324(f61(x81862),x81863))+E(f324(x81861,f324(f324(f113(f871(x81862,a859)),x81863),x81864)),f324(f73(x81865,x81865,x81865,f324(x81861,x81863)),f324(x81861,x81864))) % 181.55/181.55 [8401]~P6(x84011)+P1(f324(f324(f238(x84011),f324(x84012,x84013)),x84014))+~P1(f324(f324(f326(x84015),x84013),x84016))+~P1(f324(f324(f238(x84011),f324(f324(f41(x84015,x84011),x84016),x84012)),x84014)) % 181.55/181.55 [8827]~P27(x88272,x88271,x88273,x88276)+E(f324(f324(f22(f871(x88271,a859)),f324(f303(x88272,x88271,x88273),x88274)),f324(f303(x88272,x88271,x88273),x88275)),f324(f303(x88272,x88271,x88273),f324(f324(f22(f871(x88272,a859)),x88274),x88275)))+~P1(f324(f324(f238(f871(x88272,a859)),x88275),x88276))+~P1(f324(f324(f238(f871(x88272,a859)),x88274),x88276)) % 181.55/181.55 [8828]~P27(x88282,x88281,x88283,x88286)+E(f324(f324(f104(f871(x88281,a859)),f324(f303(x88282,x88281,x88283),x88284)),f324(f303(x88282,x88281,x88283),x88285)),f324(f303(x88282,x88281,x88283),f324(f324(f104(f871(x88282,a859)),x88284),x88285)))+~P1(f324(f324(f238(f871(x88282,a859)),x88285),x88286))+~P1(f324(f324(f238(f871(x88282,a859)),x88284),x88286)) % 181.55/181.55 [9088]E(x90881,x90882)+~P52(x90883,x90884,x90885)+~P1(f324(f324(f326(f870(x90883,x90884)),f324(f324(f259(x90883,x90884),x90886),x90882)),x90885))+~P1(f324(f324(f326(f870(x90883,x90884)),f324(f324(f259(x90883,x90884),x90886),x90881)),x90885)) % 181.55/181.55 [9874]~P66(x98741)+~E(f324(x98743,f579(x98744,x98746,x98743,x98745,x98742,x98741)),f324(x98746,f579(x98744,x98746,x98743,x98745,x98742,x98741)))+~P1(f324(f61(x98742),x98745))+E(f324(f324(f324(f65(x98741,x98742,f82(x98741)),x98743),x98744),x98745),f324(f324(f324(f65(x98741,x98742,f82(x98741)),x98746),x98744),x98745)) % 181.55/181.55 [9935]~P66(x99351)+~P1(f324(f61(x99352),x99355))+E(f324(f324(f324(f65(x99351,x99352,f82(x99351)),x99353),x99354),x99355),f324(f324(f324(f65(x99351,x99352,f82(x99351)),x99356),x99354),x99355))+P1(f324(f324(f326(x99352),f579(x99354,x99353,x99356,x99355,x99352,x99351)),x99355)) % 181.55/181.55 [8628]~P66(x86281)+~P1(f324(f61(x86282),x86286))+P1(f324(f324(f326(x86282),x86285),x86286))+E(f324(f324(f324(f65(x86281,x86282,f82(x86281)),x86283),x86284),f324(f324(f302(x86282),x86285),x86286)),f324(f324(f82(x86281),f324(x86283,x86285)),f324(f324(f324(f65(x86281,x86282,f82(x86281)),x86283),x86284),x86286))) % 181.55/181.55 [8681]~P9(x86811,x86816,x86813)+~P14(x86811,f871(x86812,a859),x86813,x86815)+~P1(f324(f324(f326(x86811),x86814),x86816))+E(f324(f324(f41(x86811,f871(x86812,a859)),f324(f278(x86811,x86811,x86813),f324(f324(f302(x86811),x86814),f191(f871(x86811,a859))))),x86815),f324(x86815,x86814)) % 181.55/181.55 [8803]~P18(x88033,x88034,x88031)+~P1(f324(f61(x88033),x88036))+~P1(f324(f324(f326(x88033),x88032),x88036))+E(f324(f324(x88031,x88032),f324(f324(f64(x88033,x88034,x88031),x88035),f324(f324(f22(f871(x88033,a859)),x88036),f324(f324(f302(x88033),x88032),f191(f871(x88033,a859)))))),f324(f324(f64(x88033,x88034,x88031),x88035),x88036)) % 181.55/181.55 [9101]~P21(x91013,x91011,x91016,x91012)+~P1(f324(f61(x91013),x91015))+~P1(f324(f61(x91013),x91014))+E(f324(f73(x91011,x91011,x91011,f324(x91012,f324(f324(f113(f871(x91013,a859)),x91014),x91015))),f324(x91012,f324(f324(f104(f871(x91013,a859)),x91014),x91015))),f324(f73(x91011,x91011,x91011,f324(x91012,x91014)),f324(x91012,x91015))) % 181.55/181.55 [9440]~E(x94403,f324(f324(f153(x94401,x94402),x94405),x94406))+P1(f324(f324(f326(f870(f866(x94401),f866(x94401))),f324(f324(f259(f866(x94401),f866(x94401)),x94402),x94403)),f151(x94401,x94404)))+~P1(f324(f324(f239(a865),x94405),f324(f192(f866(x94401)),x94402)))+~P1(f324(f324(f326(f870(x94401,x94401)),f324(f324(f259(x94401,x94401),f324(f324(f159(x94401),x94402),x94405)),x94406)),x94404)) % 181.55/181.55 [9948]~P68(x99482)+~P1(f324(f61(x99481),x99486))+P1(f324(f324(f326(x99481),f492(x99484,x99485,x99483,x99486,x99481,x99482)),x99486))+E(f324(f324(f9(x99481,x99482),f324(f324(f18(x99481,f871(x99483,a859),x99482),f324(f324(f8(f871(x99483,x99482),f871(f871(x99483,a859),x99482),x99481),f9(x99483,x99482)),x99484)),x99485)),x99486),f324(f324(f9(f870(x99481,x99483),x99482),f324(f263(x99481,x99483,x99482),x99484)),f324(f324(f261(x99481,x99483),x99486),x99485))) % 181.55/181.55 [9949]~P72(x99492)+~P1(f324(f61(x99491),x99496))+P1(f324(f324(f326(x99491),f493(x99494,x99495,x99493,x99496,x99491,x99492)),x99496))+E(f324(f324(f6(x99491,x99492),f324(f324(f18(x99491,f871(x99493,a859),x99492),f324(f324(f8(f871(x99493,x99492),f871(f871(x99493,a859),x99492),x99491),f6(x99493,x99492)),x99494)),x99495)),x99496),f324(f324(f6(f870(x99491,x99493),x99492),f324(f263(x99491,x99493,x99492),x99494)),f324(f324(f261(x99491,x99493),x99496),x99495))) % 181.55/181.55 [9988]~P68(x99882)+~P1(f324(f61(x99881),x99886))+~P1(f324(f61(x99883),f324(x99885,f492(x99884,x99885,x99883,x99886,x99881,x99882))))+E(f324(f324(f9(x99881,x99882),f324(f324(f18(x99881,f871(x99883,a859),x99882),f324(f324(f8(f871(x99883,x99882),f871(f871(x99883,a859),x99882),x99881),f9(x99883,x99882)),x99884)),x99885)),x99886),f324(f324(f9(f870(x99881,x99883),x99882),f324(f263(x99881,x99883,x99882),x99884)),f324(f324(f261(x99881,x99883),x99886),x99885))) % 181.55/181.55 [9989]~P72(x99892)+~P1(f324(f61(x99891),x99896))+~P1(f324(f61(x99893),f324(x99895,f493(x99894,x99895,x99893,x99896,x99891,x99892))))+E(f324(f324(f6(x99891,x99892),f324(f324(f18(x99891,f871(x99893,a859),x99892),f324(f324(f8(f871(x99893,x99892),f871(f871(x99893,a859),x99892),x99891),f6(x99893,x99892)),x99894)),x99895)),x99896),f324(f324(f6(f870(x99891,x99893),x99892),f324(f263(x99891,x99893,x99892),x99894)),f324(f324(f261(x99891,x99893),x99896),x99895))) % 181.55/181.55 [9971]~P68(x99712)+~P1(f324(f61(x99711),x99716))+P1(f324(f324(f326(x99711),x99713),x99716))+E(f324(f324(f9(x99711,x99712),f324(f324(f7(x99711,x99712,x99712),f324(f324(f18(x99711,x99712,f871(x99712,x99712)),f324(f324(f8(a859,f871(x99712,f871(x99712,x99712)),x99711),f99(x99712)),f324(f324(f7(x99711,x99711,a859),a321),x99713))),x99714)),x99715)),x99716),f324(f324(f249(x99712),x99715),f324(f37(x99711),x99716))) % 181.55/181.55 [9976]~P68(x99762)+~P1(f324(f61(x99761),x99766))+~P1(f324(f324(f326(x99761),x99763),x99766))+E(f324(f324(f9(x99761,x99762),f324(f324(f7(x99761,x99762,x99762),f324(f324(f18(x99761,x99762,f871(x99762,x99762)),f324(f324(f8(a859,f871(x99762,f871(x99762,x99762)),x99761),f99(x99762)),f324(f324(f7(x99761,x99761,a859),a321),x99763))),x99764)),x99765)),x99766),f324(f324(f82(x99762),f324(x99764,x99763)),f324(f324(f249(x99762),x99765),f324(f324(f22(a865),f324(f37(x99761),x99766)),f79(a865))))) % 181.55/181.55 [10041]~P1(f324(f61(x100411),x100415))+~P1(f324(f61(x100412),x100413))+P1(f324(f324(f326(x100412),f484(x100416,x100414,x100413,x100412,x100415,x100411)),x100413))+E(f324(f324(f6(x100411,a865),f324(f324(f8(f871(x100412,a859),a865,x100411),f37(x100412)),f324(f324(f8(f871(x100412,a859),f871(x100412,a859),x100411),f244(x100412)),f324(f324(f8(f871(x100412,a859),f871(x100412,a859),x100411),f324(f18(x100412,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100412),a322),f324(f324(f7(x100412,f871(x100412,a859),a859),f326(x100412)),x100413)))),x100414)))),x100415),f324(f324(f82(a865),x100416),f324(f37(x100412),x100413))) % 181.55/181.55 [10042]~P1(f324(f61(x100421),x100425))+~P1(f324(f61(x100422),x100423))+P1(f324(f324(f326(x100422),f504(x100426,x100424,x100423,x100422,x100425,x100421)),x100423))+E(f324(f324(f6(x100421,a865),f324(f324(f8(f871(x100422,a859),a865,x100421),f37(x100422)),f324(f324(f8(f871(x100422,a859),f871(x100422,a859),x100421),f244(x100422)),f324(f324(f8(f871(x100422,a859),f871(x100422,a859),x100421),f324(f18(x100422,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100422),a322),f324(f324(f7(x100422,f871(x100422,a859),a859),f326(x100422)),x100423)))),x100424)))),x100425),f324(f324(f6(x100422,a865),x100426),x100423)) % 181.55/181.55 [10073]~P1(f324(f61(x100732),x100733))+~P1(f324(f61(x100731),x100735))+~E(f324(f37(x100731),f324(f244(x100731),f324(f324(f18(x100731,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100731),a322),f324(f324(f7(x100731,f871(x100731,a859),a859),f326(x100731)),x100735))),f324(f324(f7(x100731,x100732,a859),x100734),f484(x100736,x100734,x100733,x100732,x100735,x100731))))),x100736)+E(f324(f324(f6(x100731,a865),f324(f324(f8(f871(x100732,a859),a865,x100731),f37(x100732)),f324(f324(f8(f871(x100732,a859),f871(x100732,a859),x100731),f244(x100732)),f324(f324(f8(f871(x100732,a859),f871(x100732,a859),x100731),f324(f18(x100732,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100732),a322),f324(f324(f7(x100732,f871(x100732,a859),a859),f326(x100732)),x100733)))),x100734)))),x100735),f324(f324(f82(a865),x100736),f324(f37(x100732),x100733))) % 181.55/181.55 [10075]~P1(f324(f61(x100752),x100753))+~P1(f324(f61(x100751),x100755))+~E(f324(f37(x100751),f324(f244(x100751),f324(f324(f18(x100751,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100751),a322),f324(f324(f7(x100751,f871(x100751,a859),a859),f326(x100751)),x100755))),f324(f324(f7(x100751,x100752,a859),x100754),f504(x100756,x100754,x100753,x100752,x100755,x100751))))),f324(x100756,f504(x100756,x100754,x100753,x100752,x100755,x100751)))+E(f324(f324(f6(x100751,a865),f324(f324(f8(f871(x100752,a859),a865,x100751),f37(x100752)),f324(f324(f8(f871(x100752,a859),f871(x100752,a859),x100751),f244(x100752)),f324(f324(f8(f871(x100752,a859),f871(x100752,a859),x100751),f324(f18(x100752,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100752),a322),f324(f324(f7(x100752,f871(x100752,a859),a859),f326(x100752)),x100753)))),x100754)))),x100755),f324(f324(f6(x100752,a865),x100756),x100753)) % 181.55/181.55 [9731]E(x97311,x97312)+~P18(x97313,x97314,x97315)+~P1(f324(f66(x97313,x97314,x97315,x97316,x97317),x97312))+~P1(f324(f66(x97313,x97314,x97315,x97316,x97317),x97311)) % 181.55/181.55 [9408]~P28(x94081,x94082,x94085,x94086,x94087)+P28(x94081,x94082,f76(x94081,x94082,x94083,x94084,x94085),x94086,x94087)+~P1(f324(f324(f326(x94081),x94084),x94086))+~P1(f324(f324(f326(x94081),x94083),x94086)) % 181.55/181.55 [9479]P28(x94791,x94792,x94793,x94794,x94795)+~P28(x94791,x94792,f76(x94791,x94792,x94797,x94796,x94793),x94794,x94795)+~P1(f324(f324(f326(x94791),x94796),x94794))+~P1(f324(f324(f326(x94791),x94797),x94794)) % 181.55/181.55 [9518]P1(f324(x95181,x95182))+~P1(f324(f324(f326(x95187),x95182),f324(x95186,x95184)))+~P1(f324(x95181,f644(x95181,x95186,x95185,x95183,x95187)))+~P1(f324(f324(f326(x95183),x95184),x95185)) % 181.55/181.55 [9963]~P18(x99637,x99636,x99631)+E(f324(f324(x99631,x99632),f621(x99632,x99633,x99634,x99635,x99631,x99636,x99637)),x99633)+~P1(f324(f66(x99637,x99636,x99631,x99635,x99634),x99633))+~P1(f324(f324(f326(x99637),x99632),x99634)) % 181.55/181.55 [10027]~P18(x100271,x100272,x100273)+~P1(f324(f66(x100271,x100272,x100273,x100274,x100275),x100277))+P1(f324(f66(x100271,x100272,x100273,x100274,f324(f324(f22(f871(x100271,a859)),x100275),f324(f324(f302(x100271),x100276),f191(f871(x100271,a859))))),f621(x100276,x100277,x100275,x100274,x100273,x100272,x100271)))+~P1(f324(f324(f326(x100271),x100276),x100275)) % 181.55/181.55 [9172]P28(x91721,x91722,x91723,x91724,x91725)+~P28(x91721,x91722,x91723,x91726,x91727)+~E(f324(f303(x91721,x91722,x91723),x91724),x91725)+~P1(f324(f324(f238(f871(x91721,a859)),x91724),x91726)) % 181.55/181.55 [9407]~P28(x94071,x94072,x94073,x94075,x94077)+~P28(x94071,x94072,x94073,x94074,x94076)+P28(x94071,x94072,x94073,f324(f324(f113(f871(x94071,a859)),x94074),x94075),f324(f324(f113(f871(x94072,a859)),x94076),x94077))+~E(f324(f324(f104(f871(x94072,a859)),x94076),x94077),f191(f871(x94072,a859))) % 181.55/181.55 [9414]~P66(x94141)+~P27(x94145,x94142,x94146,x94147)+~P1(f324(f61(x94145),x94147))+E(f324(f324(f324(f65(x94141,x94142,f82(x94141)),x94143),x94144),f324(f303(x94145,x94142,x94146),x94147)),f324(f324(f324(f65(x94141,x94145,f82(x94141)),f324(f73(x94142,x94141,x94145,x94143),x94146)),x94144),x94147)) % 181.55/181.55 [9543]~E(f324(f324(f302(x95431),x95435),x95436),f324(f324(f302(x95431),x95432),x95433))+~P1(f324(f66(x95431,x95431,x95434,x95432,x95433),x95437))+P1(f324(f324(f326(x95431),x95432),x95433))+P1(f324(f62(x95431,x95434,f324(f324(f302(x95431),x95435),x95436)),x95437)) % 181.55/181.55 [9628]P1(f324(x96281,x96282))+~P1(f324(f324(f326(x96283),x96282),f324(x96284,x96287)))+~P1(f324(f324(f326(x96286),x96287),x96285))+P1(f324(f324(f326(x96283),f644(x96281,x96284,x96285,x96286,x96283)),f324(f324(f41(x96286,f871(x96283,a859)),x96285),x96284))) % 181.55/181.55 [9644]~P27(x96442,x96441,x96445,x96444)+~P27(x96441,x96443,x96446,f324(f303(x96442,x96441,x96445),x96444))+E(f324(f324(f73(x96441,x96442,x96443,f78(x96442,x96441,x96444,x96445)),f78(x96441,x96443,f324(f303(x96442,x96441,x96445),x96444),x96446)),x96447),f324(f78(x96442,x96443,x96444,f324(f73(x96441,x96443,x96442,x96446),x96445)),x96447))+~P1(f324(f324(f326(x96443),x96447),f324(f303(x96441,x96443,x96446),f324(f303(x96442,x96441,x96445),x96444)))) % 181.55/181.55 [9645]~P27(x96452,x96451,x96455,x96454)+~P27(x96451,x96453,x96456,f324(f303(x96452,x96451,x96455),x96454))+E(f324(f324(f73(x96451,x96452,x96453,f94(x96452,x96451,x96454,x96455)),f94(x96451,x96453,f324(f303(x96452,x96451,x96455),x96454),x96456)),x96457),f324(f94(x96452,x96453,x96454,f324(f73(x96451,x96453,x96452,x96456),x96455)),x96457))+~P1(f324(f324(f326(x96453),x96457),f324(f303(x96451,x96453,x96456),f324(f303(x96452,x96451,x96455),x96454)))) % 181.55/181.55 [9964]~P18(x99647,x99646,x99641)+E(f324(f324(x99641,x99642),f646(x99643,x99644,x99642,x99645,x99641,x99646,x99647)),x99643)+P1(f324(f324(f326(x99647),x99642),x99644))+~P1(f324(f66(x99647,x99646,x99641,x99645,f324(f324(f302(x99647),x99642),x99644)),x99643)) % 181.55/181.55 [10026]~P18(x100261,x100264,x100265)+P1(f324(f66(x100261,x100264,x100265,x100266,x100263),f646(x100267,x100263,x100262,x100266,x100265,x100264,x100261)))+P1(f324(f324(f326(x100261),x100262),x100263))+~P1(f324(f66(x100261,x100264,x100265,x100266,f324(f324(f302(x100261),x100262),x100263)),x100267)) % 181.55/181.55 [9713]E(x97131,f2(a1))+~P1(f324(f48(x97133,x97131),f324(f324(f259(a1,a1),x97135),x97137)))+~P1(f324(f48(x97132,x97131),f324(f324(f259(a1,a1),x97134),x97136)))+P1(f324(f48(f324(f324(f81(a1),x97132),x97133),x97131),f324(f324(f259(a1,a1),f324(f324(f81(a1),f324(f324(f81(a1),x97134),x97135)),f324(f324(f38(a1),f324(f324(f81(a1),x97136),x97137)),x97131))),f44(a1,f324(f324(f81(a1),x97136),x97137),x97131)))) % 181.55/181.55 [9715]~P1(f324(f324(f239(a865),f2(a865)),x97153))+~P1(f324(f47(x97152,x97153),f324(f324(f259(a865,a865),x97155),x97157)))+~P1(f324(f47(x97151,x97153),f324(f324(f259(a865,a865),x97154),x97156)))+P1(f324(f47(f324(f324(f81(a865),x97151),x97152),x97153),f324(f324(f259(a865,a865),f324(f324(f81(a865),f324(f324(f81(a865),x97154),x97155)),f324(f324(f38(a865),f324(f324(f81(a865),x97156),x97157)),x97153))),f44(a865,f324(f324(f81(a865),x97156),x97157),x97153)))) % 181.55/181.55 [10072]~P72(x100722)+~P1(f324(f61(x100723),x100725))+~P1(f324(f61(x100721),x100727))+E(f324(f324(f6(x100721,x100722),f324(f324(f18(x100721,f871(x100723,a859),x100722),f324(f324(f8(f871(x100723,x100722),f871(f871(x100723,a859),x100722),x100721),f6(x100723,x100722)),x100724)),f324(f324(f8(f871(x100723,a859),f871(x100723,a859),x100721),f244(x100723)),f324(f324(f8(f871(x100723,a859),f871(x100723,a859),x100721),f324(f18(x100723,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100723),a322),f324(f324(f7(x100723,f871(x100723,a859),a859),f326(x100723)),x100725)))),x100726)))),x100727),f324(f324(f6(x100723,x100722),f324(f324(f18(x100723,f871(x100721,a859),x100722),f324(f324(f8(f871(x100721,x100722),f871(f871(x100721,a859),x100722),x100723),f6(x100721,x100722)),f324(f7(x100721,x100723,x100722),x100724))),f324(f324(f8(f871(x100721,a859),f871(x100721,a859),x100723),f244(x100721)),f324(f324(f8(f871(x100721,a859),f871(x100721,a859),x100723),f324(f18(x100721,a859,a859),f324(f324(f8(a859,f871(a859,a859),x100721),a322),f324(f324(f7(x100721,f871(x100721,a859),a859),f326(x100721)),x100727)))),f324(f7(x100721,x100723,a859),x100726))))),x100725)) % 181.55/181.55 [9581]~P24(x95817,x95816,x95811,x95818,x95812,x95814)+E(f324(f324(x95811,f324(x95812,x95813)),f324(x95814,x95815)),f324(x95814,x95815))+~P1(f324(f61(x95816),x95815))+~P1(f324(f324(f326(x95816),x95813),x95815)) % 181.55/181.55 [9585]~P15(x95856,x95851,x95852,x95858,x95853,x95854)+~P9(x95856,x95857,x95858)+P14(x95851,x95852,x95853,f324(x95854,x95855))+~P1(f324(f324(f326(x95856),x95855),x95857)) % 181.55/181.55 [9195]~P21(x91957,x91951,x91958,x91953)+~P1(f324(f61(x91957),x91955))+~P1(f324(f61(x91957),x91954))+E(f324(f73(x91951,x91951,x91952,f324(x91953,x91954)),f324(f73(x91951,x91951,x91952,f324(x91953,x91955)),x91956)),f324(f73(x91951,x91951,x91952,f324(x91953,x91955)),f324(f73(x91951,x91951,x91952,f324(x91953,x91954)),x91956))) % 181.55/181.55 [9204]~P36(x92041,x92042,x92043,x92044,x92047)+P36(x92041,x92042,x92043,f324(f324(f153(x92041,x92044),x92045),x92046),f324(f324(f153(x92042,x92047),x92045),x92048))+~P1(f324(f324(x92043,x92046),x92048))+~P1(f324(f324(f239(a865),x92045),f324(f192(f866(x92041)),x92044))) % 181.55/181.55 [9205]~P36(x92051,x92052,x92053,x92054,x92057)+P36(x92051,x92052,x92053,f324(f324(f153(x92051,x92054),x92055),x92056),f324(f324(f153(x92052,x92057),x92055),x92058))+~P1(f324(f324(x92053,x92056),x92058))+~P1(f324(f324(f239(a865),x92055),f324(f192(f866(x92052)),x92057))) % 181.55/181.55 [9282]~P27(x92822,x92822,x92825,x92826)+~P23(x92823,x92822,x92827,x92828,x92821)+~P1(f324(f61(x92822),x92826))+E(f324(f324(x92821,f324(f73(x92822,x92823,x92822,x92824),x92825)),x92826),f324(f324(x92821,x92824),f324(f303(x92822,x92822,x92825),x92826))) % 181.55/181.55 [9544]P28(x95441,x95442,x95443,x95444,x95445)+~P28(x95442,x95446,x95447,x95445,x95448)+~P28(x95441,x95446,f324(f73(x95442,x95446,x95441,x95447),x95443),x95444,x95448)+~P1(f324(f324(f238(f871(x95442,a859)),f324(f303(x95441,x95442,x95443),x95444)),x95445)) % 181.55/181.55 [9583]~P25(x95837,x95832,x95835,x95838,x95836,x95831)+~P1(f324(f61(x95832),x95834))+E(f324(x95831,f324(f324(f302(x95832),x95833),x95834)),f324(f324(x95835,f324(x95836,x95833)),f324(x95831,x95834)))+P1(f324(f324(f326(x95832),x95833),x95834)) % 181.55/181.55 [9594]~P24(x95946,x95945,x95941,x95947,x95948,x95942)+E(f324(f324(x95941,f324(x95942,x95943)),f324(x95942,x95944)),f324(x95942,x95944))+~P1(f324(f61(x95945),x95944))+~P1(f324(f324(f238(f871(x95945,a859)),x95943),x95944)) % 181.55/181.55 [10070]P26(x100708,x100707,f324(f324(f302(f864(x100708)),f324(f324(f324(f93(x100708),x100704),x100705),x100703)),f191(f871(f864(x100708),a859))))+~P26(x100708,x100707,f324(f324(f302(f864(x100708)),f324(f324(f324(f93(x100708),x100706),x100705),x100701)),f191(f871(f864(x100708),a859))))+~P1(f324(f324(x100706,x100702),f356(x100703,x100704,x100701,x100705,x100706,x100707,x100708)))+P1(f324(f324(x100701,x100702),f366(x100703,x100704,x100701,x100705,x100706,x100707,x100708))) % 181.55/181.55 [9181]P1(f324(f324(f326(f870(f866(x91811),f866(x91811))),f324(f324(f259(f866(x91811),f866(x91811)),x91812),x91813)),f151(x91811,x91814)))+~E(x91813,f324(f324(f124(x91811),x91815),f324(f324(f145(x91811),x91816),x91817)))+~E(x91812,f324(f324(f124(x91811),x91815),f324(f324(f145(x91811),x91818),x91817)))+~P1(f324(f324(f326(f870(x91811,x91811)),f324(f324(f259(x91811,x91811),x91818),x91816)),x91814)) % 181.55/181.55 [9588]~P24(x95886,x95882,x95885,x95887,x95888,x95881)+~P1(f324(f61(x95882),x95884))+~P1(f324(f61(x95882),x95883))+E(f324(x95881,f324(f324(f113(f871(x95882,a859)),x95883),x95884)),f324(f324(x95885,f324(x95881,x95883)),f324(x95881,x95884))) % 181.55/181.55 [10111]~P27(x101114,x101112,x101115,x101118)+E(f324(f324(f42(x101111,f871(x101112,a859)),x101113),f324(f324(f8(f871(x101114,a859),f871(x101112,a859),x101111),f303(x101114,x101112,x101115)),x101116)),f324(f303(x101114,x101112,x101115),f324(f324(f42(x101111,f871(x101114,a859)),x101113),x101116)))+~P1(f324(f324(f326(x101111),x101117),x101113))+P1(f324(f324(f326(x101111),f635(x101117,x101116,x101113,x101111,x101118,x101115,x101112,x101114)),x101113)) % 181.55/181.55 [10133]~P27(x101334,x101332,x101335,x101337)+E(f324(f324(f42(x101331,f871(x101332,a859)),x101333),f324(f324(f8(f871(x101334,a859),f871(x101332,a859),x101331),f303(x101334,x101332,x101335)),x101336)),f324(f303(x101334,x101332,x101335),f324(f324(f42(x101331,f871(x101334,a859)),x101333),x101336)))+~P1(f324(f324(f326(x101331),x101338),x101333))+~P1(f324(f324(f238(f871(x101334,a859)),f324(x101336,f635(x101338,x101336,x101333,x101331,x101337,x101335,x101332,x101334))),x101337)) % 181.55/181.55 [9654]~P25(x96547,x96545,x96541,x96548,x96542,x96544)+~P1(f324(f61(x96545),x96546))+~P1(f324(f324(f326(x96545),x96543),x96546))+E(f324(f324(x96541,f324(x96542,x96543)),f324(x96544,f324(f324(f22(f871(x96545,a859)),x96546),f324(f324(f302(x96545),x96543),f191(f871(x96545,a859)))))),f324(x96544,x96546)) % 181.55/181.55 [9662]~P25(x96626,x96623,x96621,x96627,x96628,x96622)+~P1(f324(f61(x96623),x96625))+~P1(f324(f61(x96623),x96624))+E(f324(f324(x96621,f324(x96622,f324(f324(f113(f871(x96623,a859)),x96624),x96625))),f324(x96622,f324(f324(f104(f871(x96623,a859)),x96624),x96625))),f324(f324(x96621,f324(x96622,x96624)),f324(x96622,x96625))) % 181.55/181.55 [9753]P44(x97531,x97532,x97533,x97534,x97535,f324(f324(x97533,x97536),x97537))+~P44(x97531,x97532,x97533,x97534,f324(f324(f22(f871(x97531,a859)),x97535),f324(f324(f302(x97531),x97538),f191(f871(x97531,a859)))),x97539)+~E(f324(f324(x97533,x97536),x97537),f324(f324(x97533,x97538),x97539))+~P1(f324(f324(f326(x97531),x97538),x97535)) % 181.55/181.55 [9688]~P15(x96886,x96887,x96888,x96889,x968810,x96881)+E(f324(f324(x96881,x96882),x96883),f324(f324(x96881,x96884),x96885))+~P1(f324(f324(f326(f870(x96887,x96887)),f324(f324(f259(x96887,x96887),x96883),x96885)),x968810))+~P1(f324(f324(f326(f870(x96886,x96886)),f324(f324(f259(x96886,x96886),x96882),x96884)),x96889)) % 181.55/181.55 [9284]~P94(x92842)+E(x92841,f191(f871(x92842,a859)))+~P1(f324(f61(x92842),x92841))+P1(f324(f324(f326(x92842),f13(x92842,x92841)),x92841))+~P1(f324(f324(f326(x92842),f324(f324(f113(x92842),f338(x92841,x92842)),f341(x92841,x92842))),f324(f324(f302(x92842),f338(x92841,x92842)),f324(f324(f302(x92842),f341(x92841,x92842)),f191(f871(x92842,a859)))))) % 181.55/181.55 [9285]~P94(x92852)+E(x92851,f191(f871(x92852,a859)))+~P1(f324(f61(x92852),x92851))+P1(f324(f324(f326(x92852),f10(x92852,x92851)),x92851))+~P1(f324(f324(f326(x92852),f324(f324(f104(x92852),f339(x92851,x92852)),f340(x92851,x92852))),f324(f324(f302(x92852),f339(x92851,x92852)),f324(f324(f302(x92852),f340(x92851,x92852)),f191(f871(x92852,a859)))))) % 181.55/181.55 [9317]~P66(x93172)+E(x93171,f191(f871(x93172,a859)))+~P1(f324(f61(x93172),x93171))+P1(f324(f324(f326(x93172),f324(f63(x93172,f82(x93172)),x93171)),x93171))+~P1(f324(f324(f326(x93172),f324(f324(f82(x93172),f856(x93171,x93172)),f857(x93171,x93172))),f324(f324(f302(x93172),f856(x93171,x93172)),f324(f324(f302(x93172),f857(x93171,x93172)),f191(f871(x93172,a859)))))) % 181.55/181.55 [9322]~P105(x93222)+E(x93221,f191(f871(x93222,a859)))+~P1(f324(f61(x93222),x93221))+P1(f324(f324(f326(x93222),f11(x93222,f190(x93222),x93221)),x93221))+~P1(f324(f324(f326(x93222),f324(f324(f190(x93222),f359(x93221,x93222)),f360(x93221,x93222))),f324(f324(f302(x93222),f359(x93221,x93222)),f324(f324(f302(x93222),f360(x93221,x93222)),f191(f871(x93222,a859)))))) % 181.55/181.55 [9323]~P105(x93232)+E(x93231,f191(f871(x93232,a859)))+~P1(f324(f61(x93232),x93231))+P1(f324(f324(f326(x93232),f12(x93232,f189(x93232),x93231)),x93231))+~P1(f324(f324(f326(x93232),f324(f324(f189(x93232),f361(x93231,x93232)),f362(x93231,x93232))),f324(f324(f302(x93232),f361(x93231,x93232)),f324(f324(f302(x93232),f362(x93231,x93232)),f191(f871(x93232,a859)))))) % 181.55/181.55 [6458]~P85(x64582)+E(x64581,f2(x64582))+~E(f324(f324(f81(x64582),x64583),x64581),f2(x64582))+~P1(f324(f324(f238(x64582),f2(x64582)),x64583))+~P1(f324(f324(f238(x64582),f2(x64582)),x64581)) % 181.55/181.55 [6459]~P85(x64592)+E(x64591,f2(x64592))+~E(f324(f324(f81(x64592),x64591),x64593),f2(x64592))+~P1(f324(f324(f238(x64592),f2(x64592)),x64593))+~P1(f324(f324(f238(x64592),f2(x64592)),x64591)) % 181.55/181.55 [6985]~P105(x69852)+~P16(x69852,x69851)+E(x69851,f116(x69852))+~P1(f324(f324(f326(x69852),x69853),f324(f167(x69852),f715(x69851,x69852))))+P1(f324(f324(f238(x69852),f748(x69851,x69852)),x69853)) % 181.55/181.55 [7150]~P105(x71501)+E(f15(x71501,x71502),x71503)+~P1(f324(f61(x71501),x71502))+~P1(f324(f324(f238(x71501),x71503),f578(x71503,x71502,x71501)))+~P1(f324(f324(f326(x71501),x71503),x71502)) % 181.55/181.55 [7181]~P105(x71811)+~P16(x71811,x71812)+~P16(x71811,x71813)+P16(x71811,f324(f324(f124(x71811),x71812),x71813))+P1(f324(f324(f326(x71811),f734(x71813,x71812,x71811)),f324(f167(x71811),x71812))) % 181.55/181.55 [7182]~P105(x71821)+~P16(x71821,x71822)+~P16(x71821,x71823)+P16(x71821,f324(f324(f124(x71821),x71822),x71823))+P1(f324(f324(f326(x71821),f735(x71823,x71822,x71821)),f324(f167(x71821),x71823))) % 181.55/181.55 [7238]~P105(x72381)+E(f14(x72381,x72382),x72383)+~P1(f324(f61(x72381),x72382))+P1(f324(f324(f326(x72381),f580(x72383,x72382,x72381)),x72382))+~P1(f324(f324(f326(x72381),x72383),x72382)) % 181.55/181.55 [7239]~P105(x72391)+E(f15(x72391,x72392),x72393)+~P1(f324(f61(x72391),x72392))+P1(f324(f324(f326(x72391),f578(x72393,x72392,x72391)),x72392))+~P1(f324(f324(f326(x72391),x72393),x72392)) % 181.55/181.55 [7810]~P105(x78101)+E(f14(x78101,x78102),x78103)+~P1(f324(f61(x78101),x78102))+~P1(f324(f324(f326(x78101),x78103),x78102))+~P1(f324(f324(f238(x78101),f580(x78103,x78102,x78101)),x78103)) % 181.55/181.55 [8133]~P105(x81331)+~P16(x81331,x81332)+~P16(x81331,x81333)+P16(x81331,f324(f324(f124(x81331),x81332),x81333))+~P1(f324(f324(f238(x81331),f734(x81333,x81332,x81331)),f735(x81333,x81332,x81331))) % 181.55/181.55 [8923]~P94(x89232)+E(x89231,f191(f871(x89232,a859)))+~E(f324(f324(f113(x89232),f324(x89233,f336(x89231,x89233,x89232))),f324(x89233,f343(x89231,x89233,x89232))),f324(x89233,f324(f324(f113(x89232),f336(x89231,x89233,x89232)),f343(x89231,x89233,x89232))))+E(f13(x89232,f324(f303(x89232,x89232,x89233),x89231)),f324(x89233,f13(x89232,x89231)))+~P1(f324(f61(x89232),x89231)) % 181.55/181.55 [8924]~P94(x89242)+E(x89241,f191(f871(x89242,a859)))+~E(f324(f324(f104(x89242),f324(x89243,f337(x89241,x89243,x89242))),f324(x89243,f342(x89241,x89243,x89242))),f324(x89243,f324(f324(f104(x89242),f337(x89241,x89243,x89242)),f342(x89241,x89243,x89242))))+E(f10(x89242,f324(f303(x89242,x89242,x89243),x89241)),f324(x89243,f10(x89242,x89241)))+~P1(f324(f61(x89242),x89241)) % 181.55/181.55 [8925]~P105(x89252)+E(x89251,f191(f871(x89252,a859)))+~E(f324(f324(f190(x89252),f324(x89253,f352(x89251,x89253,x89252))),f324(x89253,f367(x89251,x89253,x89252))),f324(x89253,f324(f324(f190(x89252),f352(x89251,x89253,x89252)),f367(x89251,x89253,x89252))))+E(f14(x89252,f324(f303(x89252,x89252,x89253),x89251)),f324(x89253,f14(x89252,x89251)))+~P1(f324(f61(x89252),x89251)) % 181.55/181.55 [8926]~P105(x89262)+E(x89261,f191(f871(x89262,a859)))+~E(f324(f324(f189(x89262),f324(x89263,f377(x89261,x89263,x89262))),f324(x89263,f379(x89261,x89263,x89262))),f324(x89263,f324(f324(f189(x89262),f377(x89261,x89263,x89262)),f379(x89261,x89263,x89262))))+E(f15(x89262,f324(f303(x89262,x89262,x89263),x89261)),f324(x89263,f15(x89262,x89261)))+~P1(f324(f61(x89262),x89261)) % 181.55/181.55 [8995]~P105(x89952)+E(x89951,f191(f871(x89952,a859)))+~E(f324(f324(f190(x89952),f324(x89953,f353(x89951,x89953,x89952))),f324(x89953,f363(x89951,x89953,x89952))),f324(x89953,f324(f324(f190(x89952),f353(x89951,x89953,x89952)),f363(x89951,x89953,x89952))))+E(f11(x89952,f190(x89952),f324(f303(x89952,x89952,x89953),x89951)),f324(x89953,f11(x89952,f190(x89952),x89951)))+~P1(f324(f61(x89952),x89951)) % 181.55/181.55 [8996]~P105(x89962)+E(x89961,f191(f871(x89962,a859)))+~E(f324(f324(f189(x89962),f324(x89963,f364(x89961,x89963,x89962))),f324(x89963,f365(x89961,x89963,x89962))),f324(x89963,f324(f324(f189(x89962),f364(x89961,x89963,x89962)),f365(x89961,x89963,x89962))))+E(f12(x89962,f189(x89962),f324(f303(x89962,x89962,x89963),x89961)),f324(x89963,f12(x89962,f189(x89962),x89961)))+~P1(f324(f61(x89962),x89961)) % 181.55/181.55 [6474]~P66(x64742)+E(x64741,f191(f871(x64742,a859)))+~P1(f324(f61(x64742),x64741))+E(f324(f63(x64742,f82(x64742)),f324(f324(f302(x64742),x64743),x64741)),f324(f324(f82(x64742),x64743),f324(f63(x64742,f82(x64742)),x64741)))+P1(f324(f324(f326(x64742),x64743),x64741)) % 181.55/181.55 [6991]~P94(x69912)+E(f324(f324(f104(x69912),f10(x69912,x69911)),f10(x69912,x69913)),f10(x69912,x69913))+E(x69911,f191(f871(x69912,a859)))+~P1(f324(f61(x69912),x69913))+~P1(f324(f324(f238(f871(x69912,a859)),x69911),x69913)) % 181.55/181.55 [6992]~P94(x69922)+E(f324(f324(f113(x69922),f13(x69922,x69921)),f13(x69922,x69923)),f13(x69922,x69923))+E(x69921,f191(f871(x69922,a859)))+~P1(f324(f61(x69922),x69923))+~P1(f324(f324(f238(f871(x69922,a859)),x69921),x69923)) % 181.55/181.55 [6993]~P105(x69932)+E(f324(f324(f189(x69932),f15(x69932,x69931)),f15(x69932,x69933)),f15(x69932,x69933))+E(x69931,f191(f871(x69932,a859)))+~P1(f324(f61(x69932),x69933))+~P1(f324(f324(f238(f871(x69932,a859)),x69931),x69933)) % 181.55/181.55 [6994]~P105(x69942)+E(f324(f324(f190(x69942),f14(x69942,x69941)),f14(x69942,x69943)),f14(x69942,x69943))+E(x69941,f191(f871(x69942,a859)))+~P1(f324(f61(x69942),x69943))+~P1(f324(f324(f238(f871(x69942,a859)),x69941),x69943)) % 181.55/181.55 [7287]~P105(x72872)+E(x72871,f191(f871(x72872,a859)))+~P1(f324(f61(x72872),x72873))+P1(f324(f324(f238(x72872),f14(x72872,x72871)),f14(x72872,x72873)))+~P1(f324(f324(f238(f871(x72872,a859)),x72871),x72873)) % 181.55/181.55 [7288]~P105(x72882)+E(x72881,f191(f871(x72882,a859)))+~P1(f324(f61(x72882),x72883))+P1(f324(f324(f238(x72882),f15(x72882,x72883)),f15(x72882,x72881)))+~P1(f324(f324(f238(f871(x72882,a859)),x72881),x72883)) % 181.55/181.55 [7347]~P94(x73471)+E(f13(x73471,x73472),x73473)+~P1(f324(f61(x73471),x73472))+~E(f324(f324(f22(f871(x73471,a859)),x73472),f324(f324(f302(x73471),x73473),f191(f871(x73471,a859)))),f191(f871(x73471,a859)))+~P1(f324(f324(f326(x73471),x73473),x73472)) % 181.55/181.55 [7348]~P94(x73481)+E(f10(x73481,x73482),x73483)+~P1(f324(f61(x73481),x73482))+~E(f324(f324(f22(f871(x73481,a859)),x73482),f324(f324(f302(x73481),x73483),f191(f871(x73481,a859)))),f191(f871(x73481,a859)))+~P1(f324(f324(f326(x73481),x73483),x73482)) % 181.55/181.55 [7349]~P105(x73491)+E(f14(x73491,x73492),x73493)+~P1(f324(f61(x73491),x73492))+~E(f324(f324(f22(f871(x73491,a859)),x73492),f324(f324(f302(x73491),x73493),f191(f871(x73491,a859)))),f191(f871(x73491,a859)))+~P1(f324(f324(f326(x73491),x73493),x73492)) % 181.55/181.55 [7350]~P105(x73501)+E(f15(x73501,x73502),x73503)+~P1(f324(f61(x73501),x73502))+~E(f324(f324(f22(f871(x73501,a859)),x73502),f324(f324(f302(x73501),x73503),f191(f871(x73501,a859)))),f191(f871(x73501,a859)))+~P1(f324(f324(f326(x73501),x73503),x73502)) % 181.55/181.55 [7448]~P105(x74481)+E(f11(x74481,f190(x74481),x74482),x74483)+~P1(f324(f61(x74481),x74482))+~E(f324(f324(f22(f871(x74481,a859)),x74482),f324(f324(f302(x74481),x74483),f191(f871(x74481,a859)))),f191(f871(x74481,a859)))+~P1(f324(f324(f326(x74481),x74483),x74482)) % 181.55/181.55 [7449]~P105(x74491)+E(f12(x74491,f189(x74491),x74492),x74493)+~P1(f324(f61(x74491),x74492))+~E(f324(f324(f22(f871(x74491,a859)),x74492),f324(f324(f302(x74491),x74493),f191(f871(x74491,a859)))),f191(f871(x74491,a859)))+~P1(f324(f324(f326(x74491),x74493),x74492)) % 181.55/181.55 [7485]~P99(x74852)+E(x74851,f191(f871(x74852,a859)))+~P1(f324(f61(x74852),x74851))+~P1(f324(f324(f238(x74852),x74853),f842(x74853,x74851,x74852)))+P1(f324(f324(f238(x74852),x74853),f324(f63(x74852,f104(x74852)),x74851))) % 181.55/181.55 [7486]~P105(x74862)+E(x74861,f191(f871(x74862,a859)))+~P1(f324(f61(x74862),x74861))+~P1(f324(f324(f238(x74862),x74863),f348(x74863,x74861,x74862)))+P1(f324(f324(f238(x74862),x74863),f324(f63(x74862,f189(x74862)),x74861))) % 181.55/181.55 [7487]~P105(x74872)+E(x74871,f191(f871(x74872,a859)))+~P1(f324(f61(x74872),x74871))+~P1(f324(f324(f239(x74872),x74873),f349(x74873,x74871,x74872)))+P1(f324(f324(f239(x74872),x74873),f324(f63(x74872,f189(x74872)),x74871))) % 181.55/181.55 [7572]~P99(x75722)+E(x75721,f191(f871(x75722,a859)))+~P1(f324(f61(x75722),x75721))+P1(f324(f324(f326(x75722),f842(x75723,x75721,x75722)),x75721))+P1(f324(f324(f238(x75722),x75723),f324(f63(x75722,f104(x75722)),x75721))) % 181.55/181.55 [7573]~P105(x75732)+E(x75731,f191(f871(x75732,a859)))+~P1(f324(f61(x75732),x75731))+P1(f324(f324(f326(x75732),f348(x75733,x75731,x75732)),x75731))+P1(f324(f324(f238(x75732),x75733),f324(f63(x75732,f189(x75732)),x75731))) % 181.55/181.55 [7574]~P105(x75742)+E(x75741,f191(f871(x75742,a859)))+~P1(f324(f61(x75742),x75741))+P1(f324(f324(f326(x75742),f349(x75743,x75741,x75742)),x75741))+P1(f324(f324(f239(x75742),x75743),f324(f63(x75742,f189(x75742)),x75741))) % 181.55/181.55 [7691]~P105(x76912)+E(x76911,f191(f871(x76912,a859)))+E(f324(f324(f189(x76912),f12(x76912,f189(x76912),x76911)),f12(x76912,f189(x76912),x76913)),f12(x76912,f189(x76912),x76913))+~P1(f324(f61(x76912),x76913))+~P1(f324(f324(f238(f871(x76912,a859)),x76911),x76913)) % 181.55/181.55 [7692]~P105(x76922)+E(x76921,f191(f871(x76922,a859)))+E(f324(f324(f190(x76922),f11(x76922,f190(x76922),x76921)),f11(x76922,f190(x76922),x76923)),f11(x76922,f190(x76922),x76923))+~P1(f324(f61(x76922),x76923))+~P1(f324(f324(f238(f871(x76922,a859)),x76921),x76923)) % 181.55/181.55 [7892]~E(f632(x78921,x78923,x78922),f633(x78921,x78923,x78922))+~E(f324(f37(x78922),f634(x78921,x78923,x78922)),x78921)+E(f324(f324(f82(a865),x78921),f324(f37(f871(x78922,a859)),x78923)),f324(f37(x78922),f39(f871(x78922,a859),x78923)))+~P1(f324(f61(x78922),f39(f871(x78922,a859),x78923)))+~P1(f324(f61(f871(x78922,a859)),x78923)) % 181.55/181.55 [8067]~P105(x80672)+E(x80671,f191(f871(x80672,a859)))+~P1(f324(f61(x80672),x80673))+P1(f324(f324(f238(x80672),f324(f63(x80672,f189(x80672)),x80673)),f324(f63(x80672,f189(x80672)),x80671)))+~P1(f324(f324(f238(f871(x80672,a859)),x80671),x80673)) % 181.55/181.55 [8375]~E(f632(x83751,x83753,x83752),f633(x83751,x83753,x83752))+E(f324(f324(f82(a865),x83751),f324(f37(f871(x83752,a859)),x83753)),f324(f37(x83752),f39(f871(x83752,a859),x83753)))+P1(f324(f324(f326(f871(x83752,a859)),f634(x83751,x83753,x83752)),x83753))+~P1(f324(f61(x83752),f39(f871(x83752,a859),x83753)))+~P1(f324(f61(f871(x83752,a859)),x83753)) % 181.55/181.55 [8397]~E(f324(f37(x83972),f634(x83971,x83973,x83972)),x83971)+E(f324(f324(f82(a865),x83971),f324(f37(f871(x83972,a859)),x83973)),f324(f37(x83972),f39(f871(x83972,a859),x83973)))+P1(f324(f324(f326(f871(x83972,a859)),f633(x83971,x83973,x83972)),x83973))+~P1(f324(f61(x83972),f39(f871(x83972,a859),x83973)))+~P1(f324(f61(f871(x83972,a859)),x83973)) % 181.55/181.55 [8398]~E(f324(f37(x83982),f634(x83981,x83983,x83982)),x83981)+E(f324(f324(f82(a865),x83981),f324(f37(f871(x83982,a859)),x83983)),f324(f37(x83982),f39(f871(x83982,a859),x83983)))+P1(f324(f324(f326(f871(x83982,a859)),f632(x83981,x83983,x83982)),x83983))+~P1(f324(f61(x83982),f39(f871(x83982,a859),x83983)))+~P1(f324(f61(f871(x83982,a859)),x83983)) % 181.55/181.55 [8423]~E(f324(f37(x84232),f634(x84231,x84233,x84232)),x84231)+~E(f324(f324(f104(f871(x84232,a859)),f633(x84231,x84233,x84232)),f632(x84231,x84233,x84232)),f191(f871(x84232,a859)))+E(f324(f324(f82(a865),x84231),f324(f37(f871(x84232,a859)),x84233)),f324(f37(x84232),f39(f871(x84232,a859),x84233)))+~P1(f324(f61(f871(x84232,a859)),x84233))+~P1(f324(f61(x84232),f39(f871(x84232,a859),x84233))) % 181.55/181.55 [8687]E(f324(f324(f82(a865),x86871),f324(f37(f871(x86872,a859)),x86873)),f324(f37(x86872),f39(f871(x86872,a859),x86873)))+P1(f324(f324(f326(f871(x86872,a859)),f634(x86871,x86873,x86872)),x86873))+P1(f324(f324(f326(f871(x86872,a859)),f633(x86871,x86873,x86872)),x86873))+~P1(f324(f61(f871(x86872,a859)),x86873))+~P1(f324(f61(x86872),f39(f871(x86872,a859),x86873))) % 181.55/181.55 [8688]E(f324(f324(f82(a865),x86881),f324(f37(f871(x86882,a859)),x86883)),f324(f37(x86882),f39(f871(x86882,a859),x86883)))+P1(f324(f324(f326(f871(x86882,a859)),f634(x86881,x86883,x86882)),x86883))+P1(f324(f324(f326(f871(x86882,a859)),f632(x86881,x86883,x86882)),x86883))+~P1(f324(f61(f871(x86882,a859)),x86883))+~P1(f324(f61(x86882),f39(f871(x86882,a859),x86883))) % 181.55/181.55 [8715]~E(f324(f324(f104(f871(x87152,a859)),f633(x87151,x87153,x87152)),f632(x87151,x87153,x87152)),f191(f871(x87152,a859)))+E(f324(f324(f82(a865),x87151),f324(f37(f871(x87152,a859)),x87153)),f324(f37(x87152),f39(f871(x87152,a859),x87153)))+~P1(f324(f61(f871(x87152,a859)),x87153))+P1(f324(f324(f326(f871(x87152,a859)),f634(x87151,x87153,x87152)),x87153))+~P1(f324(f61(x87152),f39(f871(x87152,a859),x87153))) % 181.55/181.55 [8969]~P93(x89692)+E(x89691,f191(f871(x89692,a859)))+~E(f324(f324(f82(x89692),f324(x89693,f855(x89691,x89693,x89692))),f324(x89693,f333(x89691,x89693,x89692))),f324(x89693,f324(f324(f82(x89692),f855(x89691,x89693,x89692)),f333(x89691,x89693,x89692))))+~P1(f324(f61(x89692),x89691))+E(f324(f63(x89692,f82(x89692)),f324(f303(x89692,x89692,x89693),x89691)),f324(x89693,f324(f63(x89692,f82(x89692)),x89691))) % 181.55/181.55 [9909]P1(f324(f324(x99091,x99092),x99093))+P1(f324(f324(f239(a1),f412(x99091,x99093,x99092)),f413(x99091,x99093,x99092)))+P1(f324(f324(f238(a1),f413(x99091,x99093,x99092)),f2(a1)))+P1(f324(f324(x99091,f412(x99091,x99093,x99092)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f413(x99091,x99093,x99092))))+~P1(f324(f312(f870(a1,a1),a56),f324(f324(f259(a1,a1),x99092),x99093))) % 181.55/181.55 [9915]P1(f324(f324(x99151,x99152),x99153))+P1(f324(f324(f238(a1),f422(x99151,x99153,x99152)),f2(a1)))+P1(f324(f324(x99151,f421(x99151,x99153,x99152)),f324(f324(f82(a1),f324(f106(a1),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f422(x99151,x99153,x99152))))+P1(f324(f324(f238(a1),f2(a1)),f324(f324(f81(a1),f421(x99151,x99153,x99152)),f422(x99151,x99153,x99152))))+~P1(f324(f312(f870(a1,a1),a51),f324(f324(f259(a1,a1),x99152),x99153))) % 181.55/181.55 [7861]~P117(x78611)+~P1(f324(f324(f238(x78611),x78612),f79(x78611)))+~P1(f324(f324(f238(x78611),f2(x78611)),x78612))+~P1(f324(f324(f238(x78611),f2(x78611)),x78613))+P1(f324(f324(f238(x78611),f324(f324(f82(x78611),x78612),x78613)),x78613)) % 181.55/181.55 [7862]~P117(x78621)+~P1(f324(f324(f238(x78621),x78623),f79(x78621)))+~P1(f324(f324(f238(x78621),f2(x78621)),x78623))+~P1(f324(f324(f238(x78621),f2(x78621)),x78622))+P1(f324(f324(f238(x78621),f324(f324(f82(x78621),x78622),x78623)),x78622)) % 181.55/181.55 [8218]~P105(x82182)+E(x82181,f191(f871(x82182,a859)))+~P1(f324(f61(x82182),x82181))+P1(f324(f324(f326(x82182),f350(x82183,x82181,x82182)),x82181))+~P1(f324(f324(f238(x82182),f324(f63(x82182,f189(x82182)),x82181)),x82183)) % 181.55/181.55 [8219]~P105(x82192)+E(x82191,f191(f871(x82192,a859)))+~P1(f324(f61(x82192),x82191))+P1(f324(f324(f326(x82192),f351(x82193,x82191,x82192)),x82191))+~P1(f324(f324(f239(x82192),f324(f63(x82192,f189(x82192)),x82191)),x82193)) % 181.55/181.55 [8220]~P105(x82202)+E(x82201,f191(f871(x82202,a859)))+~P1(f324(f61(x82202),x82201))+P1(f324(f324(f238(x82202),f350(x82203,x82201,x82202)),x82203))+~P1(f324(f324(f238(x82202),f324(f63(x82202,f189(x82202)),x82201)),x82203)) % 181.55/181.55 [8221]~P105(x82212)+E(x82211,f191(f871(x82212,a859)))+~P1(f324(f61(x82212),x82211))+P1(f324(f324(f239(x82212),f351(x82213,x82211,x82212)),x82213))+~P1(f324(f324(f239(x82212),f324(f63(x82212,f189(x82212)),x82211)),x82213)) % 181.55/181.55 [8312]~P1(f324(x83121,x83123))+P1(f324(x83121,f467(x83121,x83122)))+P1(f324(x83121,f460(x83121,x83122)))+~P1(f324(f324(f239(a1),f2(a1)),x83122))+P1(f324(x83121,f324(f324(f22(a1),f460(x83121,x83122)),f324(f324(f82(a1),f468(x83121,x83122)),x83122)))) % 181.55/181.55 [8522]~P1(f324(x85221,x85223))+P1(f324(x85221,f460(x85221,x85222)))+~P1(f324(f324(f239(a1),f2(a1)),x85222))+P1(f324(f324(f326(a1),f467(x85221,x85222)),f295(a1,f79(a1),x85222)))+P1(f324(x85221,f324(f324(f22(a1),f460(x85221,x85222)),f324(f324(f82(a1),f468(x85221,x85222)),x85222)))) % 181.55/181.55 [8737]~P1(f324(x87371,x87373))+~P1(f324(x87371,f460(x87371,x87372)))+P1(f324(x87371,f467(x87371,x87372)))+~P1(f324(f324(f239(a1),f2(a1)),x87372))+~P1(f324(x87371,f324(f324(f22(a1),f460(x87371,x87372)),f324(f324(f82(a1),f468(x87371,x87372)),x87372)))) % 181.55/181.55 [8862]~P1(f324(x88621,x88623))+~P1(f324(x88621,f460(x88621,x88622)))+~P1(f324(f324(f239(a1),f2(a1)),x88622))+P1(f324(f324(f326(a1),f467(x88621,x88622)),f295(a1,f79(a1),x88622)))+~P1(f324(x88621,f324(f324(f22(a1),f460(x88621,x88622)),f324(f324(f82(a1),f468(x88621,x88622)),x88622)))) % 181.55/181.55 [8641]~P94(x86411)+~P1(f324(f61(x86411),x86412))+E(f324(f324(f22(f871(x86411,a859)),x86412),f324(f324(f302(x86411),x86413),f191(f871(x86411,a859)))),f191(f871(x86411,a859)))+~P1(f324(f324(f326(x86411),x86413),x86412))+E(f324(f324(f113(x86411),x86413),f13(x86411,f324(f324(f22(f871(x86411,a859)),x86412),f324(f324(f302(x86411),x86413),f191(f871(x86411,a859)))))),f13(x86411,x86412)) % 181.55/181.55 [8642]~P94(x86421)+~P1(f324(f61(x86421),x86422))+E(f324(f324(f22(f871(x86421,a859)),x86422),f324(f324(f302(x86421),x86423),f191(f871(x86421,a859)))),f191(f871(x86421,a859)))+~P1(f324(f324(f326(x86421),x86423),x86422))+E(f324(f324(f104(x86421),x86423),f10(x86421,f324(f324(f22(f871(x86421,a859)),x86422),f324(f324(f302(x86421),x86423),f191(f871(x86421,a859)))))),f10(x86421,x86422)) % 181.55/181.55 [8643]~P105(x86431)+~P1(f324(f61(x86431),x86432))+E(f324(f324(f22(f871(x86431,a859)),x86432),f324(f324(f302(x86431),x86433),f191(f871(x86431,a859)))),f191(f871(x86431,a859)))+~P1(f324(f324(f326(x86431),x86433),x86432))+E(f324(f324(f190(x86431),x86433),f14(x86431,f324(f324(f22(f871(x86431,a859)),x86432),f324(f324(f302(x86431),x86433),f191(f871(x86431,a859)))))),f14(x86431,x86432)) % 181.55/181.55 [8644]~P105(x86441)+~P1(f324(f61(x86441),x86442))+E(f324(f324(f22(f871(x86441,a859)),x86442),f324(f324(f302(x86441),x86443),f191(f871(x86441,a859)))),f191(f871(x86441,a859)))+~P1(f324(f324(f326(x86441),x86443),x86442))+E(f324(f324(f189(x86441),x86443),f15(x86441,f324(f324(f22(f871(x86441,a859)),x86442),f324(f324(f302(x86441),x86443),f191(f871(x86441,a859)))))),f15(x86441,x86442)) % 181.55/181.55 [8707]~P105(x87071)+~P1(f324(f61(x87071),x87072))+E(f324(f324(f22(f871(x87071,a859)),x87072),f324(f324(f302(x87071),x87073),f191(f871(x87071,a859)))),f191(f871(x87071,a859)))+~P1(f324(f324(f326(x87071),x87073),x87072))+E(f324(f324(f190(x87071),x87073),f11(x87071,f190(x87071),f324(f324(f22(f871(x87071,a859)),x87072),f324(f324(f302(x87071),x87073),f191(f871(x87071,a859)))))),f11(x87071,f190(x87071),x87072)) % 181.55/181.55 [8708]~P105(x87081)+~P1(f324(f61(x87081),x87082))+E(f324(f324(f22(f871(x87081,a859)),x87082),f324(f324(f302(x87081),x87083),f191(f871(x87081,a859)))),f191(f871(x87081,a859)))+~P1(f324(f324(f326(x87081),x87083),x87082))+E(f324(f324(f189(x87081),x87083),f12(x87081,f189(x87081),f324(f324(f22(f871(x87081,a859)),x87082),f324(f324(f302(x87081),x87083),f191(f871(x87081,a859)))))),f12(x87081,f189(x87081),x87082)) % 181.55/181.55 [8724]~P94(x87241)+~P1(f324(f61(x87241),x87243))+~P1(f324(f61(x87241),x87242))+E(f324(f324(f104(f871(x87241,a859)),x87242),x87243),f191(f871(x87241,a859)))+E(f324(f324(f104(x87241),f10(x87241,f324(f324(f113(f871(x87241,a859)),x87242),x87243))),f10(x87241,f324(f324(f104(f871(x87241,a859)),x87242),x87243))),f324(f324(f104(x87241),f10(x87241,x87242)),f10(x87241,x87243))) % 181.55/181.55 [8725]~P94(x87251)+~P1(f324(f61(x87251),x87253))+~P1(f324(f61(x87251),x87252))+E(f324(f324(f104(f871(x87251,a859)),x87252),x87253),f191(f871(x87251,a859)))+E(f324(f324(f113(x87251),f13(x87251,f324(f324(f113(f871(x87251,a859)),x87252),x87253))),f13(x87251,f324(f324(f104(f871(x87251,a859)),x87252),x87253))),f324(f324(f113(x87251),f13(x87251,x87252)),f13(x87251,x87253))) % 181.55/181.55 [8726]~P105(x87261)+~P1(f324(f61(x87261),x87263))+~P1(f324(f61(x87261),x87262))+E(f324(f324(f104(f871(x87261,a859)),x87262),x87263),f191(f871(x87261,a859)))+E(f324(f324(f189(x87261),f15(x87261,f324(f324(f113(f871(x87261,a859)),x87262),x87263))),f15(x87261,f324(f324(f104(f871(x87261,a859)),x87262),x87263))),f324(f324(f189(x87261),f15(x87261,x87262)),f15(x87261,x87263))) % 181.55/181.55 [8727]~P105(x87271)+~P1(f324(f61(x87271),x87273))+~P1(f324(f61(x87271),x87272))+E(f324(f324(f104(f871(x87271,a859)),x87272),x87273),f191(f871(x87271,a859)))+E(f324(f324(f190(x87271),f14(x87271,f324(f324(f113(f871(x87271,a859)),x87272),x87273))),f14(x87271,f324(f324(f104(f871(x87271,a859)),x87272),x87273))),f324(f324(f190(x87271),f14(x87271,x87272)),f14(x87271,x87273))) % 181.55/181.55 [8941]~P105(x89411)+~P1(f324(f61(x89411),x89413))+~P1(f324(f61(x89411),x89412))+E(f324(f324(f104(f871(x89411,a859)),x89412),x89413),f191(f871(x89411,a859)))+E(f324(f324(f189(x89411),f12(x89411,f189(x89411),f324(f324(f113(f871(x89411,a859)),x89412),x89413))),f12(x89411,f189(x89411),f324(f324(f104(f871(x89411,a859)),x89412),x89413))),f324(f324(f189(x89411),f12(x89411,f189(x89411),x89412)),f12(x89411,f189(x89411),x89413))) % 181.55/181.55 [8942]~P105(x89421)+~P1(f324(f61(x89421),x89423))+~P1(f324(f61(x89421),x89422))+E(f324(f324(f104(f871(x89421,a859)),x89422),x89423),f191(f871(x89421,a859)))+E(f324(f324(f190(x89421),f11(x89421,f190(x89421),f324(f324(f113(f871(x89421,a859)),x89422),x89423))),f11(x89421,f190(x89421),f324(f324(f104(f871(x89421,a859)),x89422),x89423))),f324(f324(f190(x89421),f11(x89421,f190(x89421),x89422)),f11(x89421,f190(x89421),x89423))) % 181.55/181.55 [9750]~P120(x97503)+E(x97501,x97502)+~P1(f324(f324(f238(x97503),f2(x97503)),x97502))+~P1(f324(f324(f238(x97503),f2(x97503)),x97501))+~E(f324(f324(f249(x97503),x97501),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)))),f324(f324(f249(x97503),x97502),f324(f106(a865),f324(f324(f81(a1),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100)),f324(f324(f22(a1),f324(f324(f81(a1),a84),a84)),a100))))) % 181.55/181.55 [6275]E(f446(x62751,x62752,x62753),x62754)+E(f324(x62751,x62754),f2(a865))+~E(f324(f324(f6(x62753,a865),x62751),x62752),f79(a865))+~P1(f324(f61(x62753),x62752))+~P1(f324(f324(f326(x62753),x62754),x62752)) % 181.55/181.55 [6337]E(f479(x63371,x63372,x63373),x63374)+E(f324(x63371,x63374),f2(a865))+~E(f324(f324(f6(x63373,a865),x63371),x63372),f324(a115,f2(a865)))+~P1(f324(f61(x63373),x63372))+~P1(f324(f324(f326(x63373),x63374),x63372)) % 181.55/181.55 [6443]~P105(x64431)+~P6(x64431)+P1(f324(f324(f239(x64431),x64432),f39(x64431,x64433)))+~P1(f324(f324(f239(x64431),x64432),x64434))+~P1(f324(f324(f326(x64431),x64434),x64433)) % 181.55/181.55 [6615]~P105(x66151)+~P6(x66151)+~P1(f324(f324(f239(x66151),x66154),x66153))+P1(f324(f324(f239(x66151),f40(x66151,x66152)),x66153))+~P1(f324(f324(f326(x66151),x66154),x66152)) % 181.55/181.55 [6872]~P120(x68723)+E(x68721,x68722)+~E(f324(f324(f249(x68723),x68721),f324(a115,x68724)),f324(f324(f249(x68723),x68722),f324(a115,x68724)))+~P1(f324(f324(f238(x68723),f2(x68723)),x68722))+~P1(f324(f324(f238(x68723),f2(x68723)),x68721)) % 181.55/181.55 [7080]~E(f481(x70802,x70803,x70801,x70804),x70804)+~E(f324(x70802,x70804),f79(a865))+E(f324(f324(f6(x70801,a865),x70802),x70803),f79(a865))+~P1(f324(f61(x70801),x70803))+~P1(f324(f324(f326(x70801),x70804),x70803)) % 181.55/181.55 [7087]~P112(x70874)+~P124(x70874)+E(f324(x70871,f381(x70871,x70872,x70873,x70874)),f2(x70874))+~E(f324(f324(f9(x70873,x70874),x70871),x70872),f2(x70874))+~P1(f324(f61(x70873),x70872)) % 181.55/181.55 [7172]~E(f480(x71722,x71723,x71721,x71724),x71724)+~E(f324(x71722,x71724),f324(a115,f2(a865)))+E(f324(f324(f6(x71721,a865),x71722),x71723),f324(a115,f2(a865)))+~P1(f324(f61(x71721),x71723))+~P1(f324(f324(f326(x71721),x71724),x71723)) % 181.55/181.55 [7903]~E(f324(x79032,x79034),f79(a865))+~E(f324(x79032,f481(x79032,x79033,x79031,x79034)),f2(a865))+E(f324(f324(f6(x79031,a865),x79032),x79033),f79(a865))+~P1(f324(f61(x79031),x79033))+~P1(f324(f324(f326(x79031),x79034),x79033)) % 181.55/181.55 [7941]~E(f324(x79412,x79414),f324(a115,f2(a865)))+~E(f324(x79412,f480(x79412,x79413,x79411,x79414)),f2(a865))+E(f324(f324(f6(x79411,a865),x79412),x79413),f324(a115,f2(a865)))+~P1(f324(f61(x79411),x79413))+~P1(f324(f324(f326(x79411),x79414),x79413)) % 181.55/181.55 [8489]~P105(x84891)+~P16(x84891,x84894)+P16(x84891,x84892)+~E(x84892,f324(f324(f145(x84891),x84893),x84894))+~P1(f324(f324(f238(x84891),x84893),f749(x84892,x84891,x84894,x84893))) % 181.55/181.55 [8526]E(x85261,x85262)+E(f324(f324(f22(a1),f433(x85263,x85262,x85264,x85261)),f434(x85263,x85262,x85264,x85261)),x85261)+~E(f324(f324(f81(a1),x85261),x85264),x85262)+~P1(f324(f324(f239(a1),f2(a1)),x85264))+~P1(f324(f324(f326(a1),x85262),x85263)) % 181.55/181.55 [8527]E(x85271,x85272)+E(f324(f324(f81(a1),f450(x85273,x85272,x85274,x85271)),f451(x85273,x85272,x85274,x85271)),x85271)+~E(f324(f324(f22(a1),x85271),x85274),x85272)+~P1(f324(f324(f239(a1),f2(a1)),x85274))+~P1(f324(f324(f326(a1),x85272),x85273)) % 181.55/181.55 [8722]E(f324(x87221,f584(x87222,x87221,x87223,x87224)),x87222)+P1(f324(f324(f238(a865),x87224),f585(x87222,x87221,x87223,x87224)))+~P1(f324(f324(f238(a1),x87222),f324(x87221,x87223)))+~P1(f324(f324(f239(a865),x87224),x87223))+~P1(f324(f324(f238(a1),f324(x87221,x87224)),x87222)) % 181.55/181.55 [8723]~P105(x87231)+~P16(x87231,x87233)+P16(x87231,x87232)+~E(x87232,f324(f324(f145(x87231),x87234),x87233))+P1(f324(f324(f326(x87231),f749(x87232,x87231,x87233,x87234)),f324(f167(x87231),x87233))) % 181.55/181.55 [8741]~P112(x87414)+~P124(x87414)+~E(f324(f324(f9(x87411,x87414),x87412),x87413),f2(x87414))+~P1(f324(f61(x87411),x87413))+P1(f324(f324(f326(x87411),f381(x87412,x87413,x87411,x87414)),x87413)) % 181.55/181.55 [8777]~E(f324(x87772,x87774),f79(a865))+E(f324(f324(f6(x87771,a865),x87772),x87773),f79(a865))+~P1(f324(f61(x87771),x87773))+~P1(f324(f324(f326(x87771),x87774),x87773))+P1(f324(f324(f326(x87771),f481(x87772,x87773,x87771,x87774)),x87773)) % 181.55/181.55 [8786]E(x87861,x87862)+~E(f324(f324(f81(a1),x87862),x87864),x87861)+~P1(f324(f324(f239(a1),f2(a1)),x87864))+~P1(f324(f324(f326(a1),x87861),x87863))+P1(f324(f324(f326(a1),f433(x87863,x87861,x87864,x87862)),x87863)) % 181.55/181.55 [8787]E(x87871,x87872)+~E(f324(f324(f22(a1),x87872),x87874),x87871)+~P1(f324(f324(f239(a1),f2(a1)),x87874))+~P1(f324(f324(f326(a1),x87871),x87873))+P1(f324(f324(f326(a1),f450(x87873,x87871,x87874,x87872)),x87873)) % 181.55/181.55 [8789]~E(f324(x87892,x87894),f324(a115,f2(a865)))+E(f324(f324(f6(x87891,a865),x87892),x87893),f324(a115,f2(a865)))+~P1(f324(f61(x87891),x87893))+~P1(f324(f324(f326(x87891),x87894),x87893))+P1(f324(f324(f326(x87891),f480(x87892,x87893,x87891,x87894)),x87893)) % 181.55/181.55 [8794]P56(x87942,x87943,x87944,x87941)+E(x87941,f191(f871(x87942,a859)))+~P1(f324(f61(x87942),x87944))+~P1(f324(f61(x87942),x87941))+P1(f324(f324(f326(x87942),f335(x87941,x87944,x87943,x87942)),x87944)) % 181.55/181.55 [8875]E(x88751,x88752)+~E(f324(f324(f81(a1),x88752),x88754),x88751)+~P1(f324(f324(f239(a1),f2(a1)),x88754))+~P1(f324(f324(f326(a1),x88751),x88753))+P1(f324(f324(f326(a1),f434(x88753,x88751,x88754,x88752)),f295(a1,f79(a1),x88754))) % 181.55/181.55 [8876]E(x88761,x88762)+~E(f324(f324(f22(a1),x88762),x88764),x88761)+~P1(f324(f324(f239(a1),f2(a1)),x88764))+~P1(f324(f324(f326(a1),x88761),x88763))+P1(f324(f324(f326(a1),f451(x88763,x88761,x88764,x88762)),f295(a1,f79(a1),x88764))) % 181.55/181.55 [8947]P1(f324(f324(f238(a865),x89471),f584(x89472,x89473,x89474,x89471)))+~P1(f324(f324(f238(a1),x89472),f324(x89473,x89474)))+P1(f324(f324(f238(a865),x89471),f585(x89472,x89473,x89474,x89471)))+~P1(f324(f324(f239(a865),x89471),x89474))+~P1(f324(f324(f238(a1),f324(x89473,x89471)),x89472)) % 181.55/181.55 [9062]E(f324(x90621,f584(x90622,x90621,x90623,x90624)),x90622)+~P1(f324(f324(f238(a1),x90622),f324(x90621,x90623)))+P1(f324(f324(f239(a865),f585(x90622,x90621,x90623,x90624)),x90623))+~P1(f324(f324(f239(a865),x90624),x90623))+~P1(f324(f324(f238(a1),f324(x90621,x90624)),x90622)) % 181.55/181.55 [9192]~P1(f324(f324(f238(a1),x91922),f324(x91923,x91924)))+P1(f324(f324(f238(a865),x91921),f585(x91922,x91923,x91924,x91921)))+P1(f324(f324(f238(a865),f584(x91922,x91923,x91924,x91921)),x91924))+~P1(f324(f324(f239(a865),x91921),x91924))+~P1(f324(f324(f238(a1),f324(x91923,x91921)),x91922)) % 181.55/181.55 [9193]~P1(f324(f324(f238(a1),x91932),f324(x91933,x91934)))+P1(f324(f324(f238(a865),x91931),f584(x91932,x91933,x91934,x91931)))+P1(f324(f324(f239(a865),f585(x91932,x91933,x91934,x91931)),x91934))+~P1(f324(f324(f239(a865),x91931),x91934))+~P1(f324(f324(f238(a1),f324(x91933,x91931)),x91932)) % 181.55/181.55 [9300]~P1(f324(f324(f238(a1),x93001),f324(x93002,x93003)))+P1(f324(f324(f239(a865),f585(x93001,x93002,x93003,x93004)),x93003))+~P1(f324(f324(f239(a865),x93004),x93003))+~P1(f324(f324(f238(a1),f324(x93002,x93004)),x93001))+P1(f324(f324(f238(a865),f584(x93001,x93002,x93003,x93004)),x93003)) % 181.55/181.55 [9381]E(x93811,f191(f871(x93812,a859)))+~P1(f324(f61(x93812),x93814))+~P1(f324(f61(x93812),x93811))+P1(f324(f324(f326(f870(f871(x93812,a859),f871(x93812,a859))),f324(f324(f259(f871(x93812,a859),f871(x93812,a859)),x93814),x93811)),f315(x93812,x93813)))+P1(f324(f324(f326(x93812),f849(x93813,x93811,x93814,x93812)),x93814)) % 181.55/181.55 [9382]E(x93821,f191(f871(x93822,a859)))+~P1(f324(f61(x93822),x93824))+~P1(f324(f61(x93822),x93821))+P1(f324(f324(f326(f870(f871(x93822,a859),f871(x93822,a859))),f324(f324(f259(f871(x93822,a859),f871(x93822,a859)),x93824),x93821)),f315(x93822,x93823)))+P1(f324(f324(f326(x93822),f576(x93823,x93821,x93824,x93822)),x93824)) % 181.55/181.55 [10049]E(f324(x100491,f584(x100492,x100491,x100493,x100494)),x100492)+~P1(f324(f324(f238(a1),x100492),f324(x100491,x100493)))+~P1(f324(f324(f238(a1),f324(f75(a1),f324(f324(f22(a1),f324(x100491,f324(f324(f81(a865),f585(x100492,x100491,x100493,x100494)),f79(a865)))),f324(x100491,f585(x100492,x100491,x100493,x100494))))),f79(a1)))+~P1(f324(f324(f239(a865),x100494),x100493))+~P1(f324(f324(f238(a1),f324(x100491,x100494)),x100492)) % 181.55/181.55 [10050]~P1(f324(f324(f238(a1),x100502),f324(x100503,x100504)))+P1(f324(f324(f238(a865),x100501),f584(x100502,x100503,x100504,x100501)))+~P1(f324(f324(f238(a1),f324(f75(a1),f324(f324(f22(a1),f324(x100503,f324(f324(f81(a865),f585(x100502,x100503,x100504,x100501)),f79(a865)))),f324(x100503,f585(x100502,x100503,x100504,x100501))))),f79(a1)))+~P1(f324(f324(f239(a865),x100501),x100504))+~P1(f324(f324(f238(a1),f324(x100503,x100501)),x100502)) % 181.55/181.55 [10051]~P1(f324(f324(f238(a1),x100511),f324(x100512,x100513)))+~P1(f324(f324(f238(a1),f324(f75(a1),f324(f324(f22(a1),f324(x100512,f324(f324(f81(a865),f585(x100511,x100512,x100513,x100514)),f79(a865)))),f324(x100512,f585(x100511,x100512,x100513,x100514))))),f79(a1)))+~P1(f324(f324(f239(a865),x100514),x100513))+~P1(f324(f324(f238(a1),f324(x100512,x100514)),x100511))+P1(f324(f324(f238(a865),f584(x100511,x100512,x100513,x100514)),x100513)) % 181.55/181.55 [7139]~P64(x71391)+P1(f324(f324(f239(x71391),x71392),f2(x71391)))+~P1(f324(f324(f238(x71391),x71393),f2(x71391)))+P1(f324(f324(f239(x71391),f2(x71391)),x71392))+P1(f324(f324(f238(x71391),x71393),f324(f324(f282(x71391),x71394),x71392))) % 181.55/181.55 [7140]~P64(x71401)+P1(f324(f324(f239(x71401),x71402),f2(x71401)))+~P1(f324(f324(f239(x71401),x71403),f2(x71401)))+P1(f324(f324(f239(x71401),f2(x71401)),x71402))+P1(f324(f324(f239(x71401),x71403),f324(f324(f282(x71401),x71404),x71402))) % 181.55/181.55 [7386]~P64(x73861)+P1(f324(f324(f238(x73861),x73862),f2(x73861)))+P1(f324(f324(f239(x73861),x73863),f2(x73861)))+P1(f324(f324(f239(x73861),f2(x73861)),x73863))+~P1(f324(f324(f238(x73861),x73862),f324(f324(f282(x73861),x73864),x73863))) % 181.55/181.55 [7387]~P64(x73871)+P1(f324(f324(f239(x73871),x73872),f2(x73871)))+P1(f324(f324(f239(x73871),x73873),f2(x73871)))+P1(f324(f324(f239(x73871),f2(x73871)),x73873))+~P1(f324(f324(f239(x73871),x73872),f324(f324(f282(x73871),x73874),x73873))) % 181.55/181.55 [7505]E(x75051,x75052)+~E(f324(f324(f159(x75053),x75054),x75051),f324(f324(f159(x75053),x75054),x75052))+~P1(f324(f131(x75053),x75054))+~P1(f324(f324(f239(a865),x75052),f324(f192(f866(x75053)),x75054)))+~P1(f324(f324(f239(a865),x75051),f324(f192(f866(x75053)),x75054))) % 181.55/181.55 [7863]~P64(x78631)+~P1(f324(f324(f238(x78631),x78633),f2(x78631)))+P1(f324(f324(f239(x78631),f2(x78631)),x78632))+~P1(f324(f324(f238(x78631),x78634),f324(f324(f82(x78631),x78633),x78632)))+P1(f324(f324(f238(x78631),x78633),f324(f324(f282(x78631),x78634),x78632))) % 181.55/181.55 [7864]~P64(x78641)+~P1(f324(f324(f239(x78641),x78643),f2(x78641)))+P1(f324(f324(f239(x78641),f2(x78641)),x78642))+~P1(f324(f324(f239(x78641),x78644),f324(f324(f82(x78641),x78643),x78642)))+P1(f324(f324(f239(x78641),x78643),f324(f324(f282(x78641),x78644),x78642))) % 181.55/181.55 [7865]~P64(x78651)+~P1(f324(f324(f239(x78651),x78652),f2(x78651)))+P1(f324(f324(f239(x78651),f2(x78651)),x78652))+~P1(f324(f324(f238(x78651),x78654),f324(f324(f82(x78651),x78653),x78652)))+P1(f324(f324(f238(x78651),x78653),f324(f324(f282(x78651),x78654),x78652))) % 181.55/181.55 [7866]~P64(x78661)+~P1(f324(f324(f239(x78661),x78662),f2(x78661)))+P1(f324(f324(f239(x78661),f2(x78661)),x78662))+~P1(f324(f324(f238(x78661),x78664),f324(f324(f282(x78661),x78663),x78662)))+P1(f324(f324(f238(x78661),x78663),f324(f324(f82(x78661),x78664),x78662))) % 181.55/181.55 [7867]~P64(x78671)+~P1(f324(f324(f239(x78671),x78672),f2(x78671)))+P1(f324(f324(f239(x78671),f2(x78671)),x78672))+~P1(f324(f324(f239(x78671),x78674),f324(f324(f82(x78671),x78673),x78672)))+P1(f324(f324(f239(x78671),x78673),f324(f324(f282(x78671),x78674),x78672))) % 181.55/181.55 [7868]~P64(x78681)+~P1(f324(f324(f239(x78681),x78682),f2(x78681)))+P1(f324(f324(f239(x78681),f2(x78681)),x78682))+~P1(f324(f324(f239(x78681),x78684),f324(f324(f282(x78681),x78683),x78682)))+P1(f324(f324(f239(x78681),x78683),f324(f324(f82(x78681),x78684),x78682))) % 181.55/181.55 [8008]~P105(x80081)+~P16(x80081,x80082)+~P1(f324(f324(f238(a865),x80083),x80084))+P1(f324(f324(f238(x80081),f324(f324(f159(x80081),x80082),x80083)),f324(f324(f159(x80081),x80082),x80084)))+~P1(f324(f324(f239(a865),x80084),f324(f192(f866(x80081)),x80082))) % 181.55/181.55 [8058]~P120(x80581)+~P1(f324(f324(f238(x80581),x80582),f79(x80581)))+~P1(f324(f324(f238(x80581),f2(x80581)),x80582))+~P1(f324(f324(f238(a865),x80584),x80583))+P1(f324(f324(f238(x80581),f324(f324(f249(x80581),x80582),x80583)),f324(f324(f249(x80581),x80582),x80584))) % 181.55/181.55 [8059]~P120(x80591)+~P1(f324(f324(f239(x80591),x80592),f79(x80591)))+~P1(f324(f324(f239(x80591),f2(x80591)),x80592))+~P1(f324(f324(f239(a865),x80594),x80593))+P1(f324(f324(f239(x80591),f324(f324(f249(x80591),x80592),x80593)),f324(f324(f249(x80591),x80592),x80594))) % 181.55/181.55 [8060]~P120(x80601)+~P1(f324(f324(f238(x80601),f2(x80601)),x80602))+~P1(f324(f324(f239(a865),f2(a865)),x80603))+~P1(f324(f324(f239(x80601),x80602),x80604))+P1(f324(f324(f239(x80601),f324(f324(f249(x80601),x80602),x80603)),f324(f324(f249(x80601),x80604),x80603))) % 181.55/181.55 [8079]~P105(x80791)+~P16(x80791,f324(f163(x80791),x80792))+~P1(f324(f324(f238(a865),x80794),x80793))+P1(f324(f324(f238(x80791),f324(f324(f159(x80791),x80792),x80793)),f324(f324(f159(x80791),x80792),x80794)))+~P1(f324(f324(f239(a865),x80793),f324(f192(f866(x80791)),x80792))) % 181.55/181.55 [8331]~P64(x83311)+~P1(f324(f324(f238(x83311),x83312),f2(x83311)))+~P1(f324(f324(f238(x83311),x83313),x83314))+~P1(f324(f324(f239(x83311),f2(x83311)),f324(f324(f82(x83311),x83313),x83314)))+P1(f324(f324(f238(x83311),f324(f324(f282(x83311),x83312),x83313)),f324(f324(f282(x83311),x83312),x83314))) % 181.55/181.55 [8332]~P65(x83321)+~P1(f324(f324(f239(x83321),x83322),f2(x83321)))+~P1(f324(f324(f239(x83321),x83323),x83324))+~P1(f324(f324(f239(x83321),f2(x83321)),f324(f324(f82(x83321),x83323),x83324)))+P1(f324(f324(f239(x83321),f324(f324(f282(x83321),x83322),x83323)),f324(f324(f282(x83321),x83322),x83324))) % 181.55/181.55 [8342]~P65(x83421)+~P1(f324(f324(f238(x83421),x83424),x83423))+~P1(f324(f324(f238(x83421),f2(x83421)),x83422))+~P1(f324(f324(f239(x83421),f2(x83421)),f324(f324(f82(x83421),x83423),x83424)))+P1(f324(f324(f238(x83421),f324(f324(f282(x83421),x83422),x83423)),f324(f324(f282(x83421),x83422),x83424))) % 181.55/181.55 [8343]~P65(x83431)+~P1(f324(f324(f239(x83431),x83434),x83433))+~P1(f324(f324(f239(x83431),f2(x83431)),x83432))+~P1(f324(f324(f239(x83431),f2(x83431)),f324(f324(f82(x83431),x83433),x83434)))+P1(f324(f324(f239(x83431),f324(f324(f282(x83431),x83432),x83433)),f324(f324(f282(x83431),x83432),x83434))) % 181.55/181.55 [8438]P1(f324(x84381,x84382))+~P1(f324(f61(x84384),x84382))+P1(f324(x84381,f845(x84381,x84383,x84382,x84384)))+~P1(f324(x84381,f191(f871(x84384,a859))))+~P1(f324(f324(f238(f871(x84384,a859)),x84382),x84383)) % 181.55/181.55 [8447]P1(f324(x84471,x84472))+P1(f324(f61(x84473),f845(x84471,x84474,x84472,x84473)))+~P1(f324(f61(x84473),x84472))+~P1(f324(x84471,f191(f871(x84473,a859))))+~P1(f324(f324(f238(f871(x84473,a859)),x84472),x84474)) % 181.55/181.55 [8717]E(f324(f324(f81(a1),f455(x87171,x87172,x87173,x87174)),f452(x87171,x87172,x87173,x87174)),x87174)+~P1(f324(f324(f239(a1),f2(a1)),x87173))+~P1(f324(f324(f239(a1),x87172),x87174))+~P1(f324(f324(f326(a1),x87172),x87171))+P1(f324(f324(f239(a1),x87172),f324(f324(f22(a1),x87174),x87173))) % 181.55/181.55 [8929]~P1(f324(f324(f239(a1),f2(a1)),x89293))+~P1(f324(f324(f239(a1),x89292),x89294))+~P1(f324(f324(f326(a1),x89292),x89291))+P1(f324(f324(f326(a1),f455(x89291,x89292,x89293,x89294)),x89291))+P1(f324(f324(f239(a1),x89292),f324(f324(f22(a1),x89294),x89293))) % 181.55/181.55 [8940]P1(f324(x89401,x89402))+~P1(f324(f61(x89403),x89402))+P1(f324(f324(f326(x89403),f846(x89401,x89404,x89402,x89403)),x89404))+~P1(f324(x89401,f191(f871(x89403,a859))))+~P1(f324(f324(f238(f871(x89403,a859)),x89402),x89404)) % 181.55/181.55 [8957]E(f324(f324(f81(a1),f435(x89571,x89572,x89573,x89574)),f436(x89571,x89572,x89573,x89574)),x89574)+~P1(f324(f324(f239(a1),f2(a1)),x89573))+~P1(f324(f324(f238(a1),x89572),x89574))+P1(f324(f324(f238(a1),x89572),f324(f324(f22(a1),x89574),x89573)))+~P1(f324(f324(f326(a1),f324(f324(f22(a1),x89572),f79(a1))),x89571)) % 181.55/181.55 [9013]~P1(f324(f324(f239(a1),f2(a1)),x90133))+~P1(f324(f324(f239(a1),x90131),x90132))+~P1(f324(f324(f326(a1),x90131),x90134))+P1(f324(f324(f326(a1),f452(x90134,x90131,x90133,x90132)),f295(a1,f79(a1),x90133)))+P1(f324(f324(f239(a1),x90131),f324(f324(f22(a1),x90132),x90133))) % 181.55/181.55 [9108]~P1(f324(f324(f239(a1),f2(a1)),x91083))+~P1(f324(f324(f238(a1),x91082),x91084))+P1(f324(f324(f326(a1),f435(x91081,x91082,x91083,x91084)),x91081))+P1(f324(f324(f238(a1),x91082),f324(f324(f22(a1),x91084),x91083)))+~P1(f324(f324(f326(a1),f324(f324(f22(a1),x91082),f79(a1))),x91081)) % 181.55/181.55 [9153]~P1(f324(f324(f239(a1),f2(a1)),x91533))+~P1(f324(f324(f238(a1),x91531),x91532))+P1(f324(f324(f326(a1),f436(x91534,x91531,x91533,x91532)),f295(a1,f79(a1),x91533)))+P1(f324(f324(f238(a1),x91531),f324(f324(f22(a1),x91532),x91533)))+~P1(f324(f324(f326(a1),f324(f324(f22(a1),x91531),f79(a1))),x91534)) % 181.55/181.55 [9384]P1(f324(x93841,x93842))+~P1(f324(f324(f326(x93843),f846(x93841,x93844,x93842,x93843)),f845(x93841,x93844,x93842,x93843)))+~P1(f324(f61(x93843),x93842))+~P1(f324(x93841,f191(f871(x93843,a859))))+~P1(f324(f324(f238(f871(x93843,a859)),x93842),x93844)) % 181.55/181.55 [9608]P1(f324(x96081,x96082))+~P1(f324(f61(x96083),x96082))+~P1(f324(x96081,f324(f324(f302(x96083),f846(x96081,x96084,x96082,x96083)),f845(x96081,x96084,x96082,x96083))))+~P1(f324(x96081,f191(f871(x96083,a859))))+~P1(f324(f324(f238(f871(x96083,a859)),x96082),x96084)) % 181.55/181.55 [7639]~P64(x76391)+P1(f324(f324(f239(x76391),x76392),f2(x76391)))+~P1(f324(f324(f238(x76391),f2(x76391)),x76394))+P1(f324(f324(f239(x76391),f2(x76391)),x76392))+P1(f324(f324(f238(x76391),f324(f324(f282(x76391),x76393),x76392)),x76394)) % 181.55/181.55 [7640]~P64(x76401)+P1(f324(f324(f239(x76401),x76402),f2(x76401)))+P1(f324(f324(f239(x76401),f2(x76401)),x76402))+~P1(f324(f324(f239(x76401),f2(x76401)),x76404))+P1(f324(f324(f239(x76401),f324(f324(f282(x76401),x76403),x76402)),x76404)) % 181.55/181.55 [7916]~P1(f324(f324(f238(a1),x79164),f2(a1)))+~E(x79162,f324(f324(f81(a1),f324(f324(f82(a1),x79161),x79163)),x79164))+P1(f324(f324(f239(a1),f2(a1)),x79161))+~P1(f324(f324(f239(a1),x79161),x79164))+P1(f324(f48(x79162,x79161),f324(f324(f259(a1,a1),x79163),x79164))) % 181.55/181.55 [7950]~P1(f324(x79501,x79504))+P1(f324(x79501,f426(x79502,x79501,x79503)))+~P1(f324(f324(f238(a1),f2(a1)),x79502))+~P1(f324(f324(f239(a1),f2(a1)),x79503))+P1(f324(x79501,f324(f324(f22(a1),x79504),f324(f324(f82(a1),x79502),x79503)))) % 181.55/181.55 [7951]~P1(f324(x79511,x79514))+P1(f324(x79511,f428(x79512,x79511,x79513)))+~P1(f324(f324(f238(a1),f2(a1)),x79512))+~P1(f324(f324(f239(a1),f2(a1)),x79513))+P1(f324(x79511,f324(f324(f81(a1),x79514),f324(f324(f82(a1),x79512),x79513)))) % 181.55/181.55 [7952]~P64(x79521)+P1(f324(f324(f239(x79521),x79522),f2(x79521)))+P1(f324(f324(f239(x79521),f2(x79521)),x79522))+P1(f324(f324(f238(x79521),f2(x79521)),x79523))+~P1(f324(f324(f238(x79521),f324(f324(f282(x79521),x79524),x79522)),x79523)) % 181.55/181.55 [7953]~P64(x79531)+P1(f324(f324(f239(x79531),x79532),f2(x79531)))+P1(f324(f324(f239(x79531),f2(x79531)),x79532))+P1(f324(f324(f239(x79531),f2(x79531)),x79533))+~P1(f324(f324(f239(x79531),f324(f324(f282(x79531),x79534),x79532)),x79533)) % 181.55/181.55 [8003]~E(x80031,f324(f324(f81(a1),f324(f324(f82(a1),x80032),x80033)),x80034))+~P1(f324(f324(f238(a1),f2(a1)),x80034))+~P1(f324(f324(f239(a1),f2(a1)),x80032))+~P1(f324(f324(f239(a1),x80034),x80032))+P1(f324(f48(x80031,x80032),f324(f324(f259(a1,a1),x80033),x80034))) % 181.55/181.55 [8123]~P64(x81231)+P1(f324(f324(f239(x81231),x81232),f2(x81231)))+~P1(f324(f324(f238(x81231),f2(x81231)),x81234))+~P1(f324(f324(f238(x81231),x81233),f324(f324(f82(x81231),x81234),x81232)))+P1(f324(f324(f238(x81231),f324(f324(f282(x81231),x81233),x81232)),x81234)) % 181.55/181.55 [8124]~P64(x81241)+P1(f324(f324(f239(x81241),x81242),f2(x81241)))+~P1(f324(f324(f239(x81241),f2(x81241)),x81244))+~P1(f324(f324(f239(x81241),x81243),f324(f324(f82(x81241),x81244),x81242)))+P1(f324(f324(f239(x81241),f324(f324(f282(x81241),x81243),x81242)),x81244)) % 181.55/181.55 [8208]~P64(x82081)+P1(f324(f324(f239(x82081),x82082),f2(x82081)))+~P1(f324(f324(f238(x82081),x82083),f2(x82081)))+P1(f324(f324(f238(x82081),x82083),f324(f324(f282(x82081),x82084),x82082)))+~P1(f324(f324(f238(x82081),f324(f324(f82(x82081),x82083),x82082)),x82084)) % 181.55/181.55 [8209]~P64(x82091)+P1(f324(f324(f239(x82091),x82092),f2(x82091)))+~P1(f324(f324(f239(x82091),x82093),f2(x82091)))+P1(f324(f324(f239(x82091),x82093),f324(f324(f282(x82091),x82094),x82092)))+~P1(f324(f324(f239(x82091),f324(f324(f82(x82091),x82093),x82092)),x82094)) % 181.55/181.55 [8364]~P64(x83641)+~P1(f324(f324(f239(x83641),x83642),f2(x83641)))+P1(f324(f324(f239(x83641),f2(x83641)),x83642))+~P1(f324(f324(f238(x83641),f324(f324(f282(x83641),x83644),x83642)),x83643))+P1(f324(f324(f238(x83641),f324(f324(f82(x83641),x83643),x83642)),x83644)) % 181.55/181.55 [8365]~P64(x83651)+~P1(f324(f324(f239(x83651),x83652),f2(x83651)))+P1(f324(f324(f239(x83651),f2(x83651)),x83652))+~P1(f324(f324(f238(x83651),f324(f324(f82(x83651),x83654),x83652)),x83653))+P1(f324(f324(f238(x83651),f324(f324(f282(x83651),x83653),x83652)),x83654)) % 181.55/181.55 [8366]~P64(x83661)+~P1(f324(f324(f239(x83661),x83662),f2(x83661)))+P1(f324(f324(f239(x83661),f2(x83661)),x83662))+~P1(f324(f324(f239(x83661),f324(f324(f282(x83661),x83664),x83662)),x83663))+P1(f324(f324(f239(x83661),f324(f324(f82(x83661),x83663),x83662)),x83664)) % 181.55/181.55 [8367]~P64(x83671)+~P1(f324(f324(f239(x83671),x83672),f2(x83671)))+P1(f324(f324(f239(x83671),f2(x83671)),x83672))+~P1(f324(f324(f239(x83671),f324(f324(f82(x83671),x83674),x83672)),x83673))+P1(f324(f324(f239(x83671),f324(f324(f282(x83671),x83673),x83672)),x83674)) % 181.55/181.55 [8384]~P64(x83841)+~P1(f324(f324(f238(x83841),f2(x83841)),x83844))+P1(f324(f324(f239(x83841),f2(x83841)),x83842))+~P1(f324(f324(f238(x83841),f324(f324(f82(x83841),x83844),x83842)),x83843))+P1(f324(f324(f238(x83841),f324(f324(f282(x83841),x83843),x83842)),x83844)) % 181.55/181.55 [8385]~P64(x83851)+~P1(f324(f324(f239(x83851),f2(x83851)),x83854))+P1(f324(f324(f239(x83851),f2(x83851)),x83852))+~P1(f324(f324(f239(x83851),f324(f324(f82(x83851),x83854),x83852)),x83853))+P1(f324(f324(f239(x83851),f324(f324(f282(x83851),x83853),x83852)),x83854)) % 181.55/181.55 [8455]~P64(x84551)+~P1(f324(f324(f239(x84551),x84554),f2(x84551)))+~P1(f324(f324(f238(x84551),x84553),f324(f324(f82(x84551),x84552),x84554)))+P1(f324(f324(f238(x84551),x84552),f324(f324(f282(x84551),x84553),x84554)))+~P1(f324(f324(f238(x84551),f324(f324(f82(x84551),x84552),x84554)),x84553)) % 181.55/181.55 [8456]~P64(x84561)+~P1(f324(f324(f238(x84561),x84562),f2(x84561)))+~P1(f324(f324(f238(x84561),x84563),f324(f324(f82(x84561),x84562),x84564)))+P1(f324(f324(f238(x84561),x84562),f324(f324(f282(x84561),x84563),x84564)))+~P1(f324(f324(f238(x84561),f324(f324(f82(x84561),x84562),x84564)),x84563)) % 181.55/181.55 [8457]~P64(x84571)+~P1(f324(f324(f239(x84571),x84574),f2(x84571)))+~P1(f324(f324(f239(x84571),x84573),f324(f324(f82(x84571),x84572),x84574)))+P1(f324(f324(f239(x84571),x84572),f324(f324(f282(x84571),x84573),x84574)))+~P1(f324(f324(f239(x84571),f324(f324(f82(x84571),x84572),x84574)),x84573)) % 181.55/181.55 [8458]~P64(x84581)+~P1(f324(f324(f239(x84581),x84582),f2(x84581)))+~P1(f324(f324(f239(x84581),x84583),f324(f324(f82(x84581),x84582),x84584)))+P1(f324(f324(f239(x84581),x84582),f324(f324(f282(x84581),x84583),x84584)))+~P1(f324(f324(f239(x84581),f324(f324(f82(x84581),x84582),x84584)),x84583)) % 181.55/181.55 [8580]~P64(x85801)+~P1(f324(f324(f239(x85801),x85803),f2(x85801)))+~P1(f324(f324(f238(x85801),x85802),f324(f324(f82(x85801),x85804),x85803)))+~P1(f324(f324(f238(x85801),f324(f324(f82(x85801),x85804),x85803)),x85802))+P1(f324(f324(f238(x85801),f324(f324(f282(x85801),x85802),x85803)),x85804)) % 181.55/181.55 [8581]~P64(x85811)+~P1(f324(f324(f239(x85811),x85813),f2(x85811)))+~P1(f324(f324(f239(x85811),x85812),f324(f324(f82(x85811),x85814),x85813)))+~P1(f324(f324(f239(x85811),f324(f324(f82(x85811),x85814),x85813)),x85812))+P1(f324(f324(f239(x85811),f324(f324(f282(x85811),x85812),x85813)),x85814)) % 181.55/181.55 [8599]~P64(x85991)+~P1(f324(f324(f238(x85991),f2(x85991)),x85994))+~P1(f324(f324(f238(x85991),x85992),f324(f324(f82(x85991),x85994),x85993)))+~P1(f324(f324(f238(x85991),f324(f324(f82(x85991),x85994),x85993)),x85992))+P1(f324(f324(f238(x85991),f324(f324(f282(x85991),x85992),x85993)),x85994)) % 181.55/181.55 [8600]~P64(x86001)+~P1(f324(f324(f239(x86001),f2(x86001)),x86004))+~P1(f324(f324(f239(x86001),x86002),f324(f324(f82(x86001),x86004),x86003)))+~P1(f324(f324(f239(x86001),f324(f324(f82(x86001),x86004),x86003)),x86002))+P1(f324(f324(f239(x86001),f324(f324(f282(x86001),x86002),x86003)),x86004)) % 181.55/181.55 [8779]E(f324(f324(f22(a1),f456(x87791,x87792,x87793,x87794)),f457(x87791,x87792,x87793,x87794)),x87794)+~P1(f324(f324(f239(a1),f2(a1)),x87793))+~P1(f324(f324(f326(a1),x87792),x87791))+~P1(f324(f324(f239(a1),x87794),x87792))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x87794),x87793)),x87792)) % 181.55/181.55 [8859]~P1(f324(x88591,x88592))+~P1(f324(f324(f238(a1),f2(a1)),x88593))+~P1(f324(f324(f239(a1),f2(a1)),x88594))+~P1(f324(x88591,f324(f324(f22(a1),f426(x88593,x88591,x88594)),x88594)))+P1(f324(x88591,f324(f324(f22(a1),x88592),f324(f324(f82(a1),x88593),x88594)))) % 181.55/181.55 [8860]~P1(f324(x88601,x88602))+~P1(f324(f324(f238(a1),f2(a1)),x88603))+~P1(f324(f324(f239(a1),f2(a1)),x88604))+~P1(f324(x88601,f324(f324(f81(a1),f428(x88603,x88601,x88604)),x88604)))+P1(f324(x88601,f324(f324(f81(a1),x88602),f324(f324(f82(a1),x88603),x88604)))) % 181.55/181.55 [9006]~P1(f324(f324(f239(a1),f2(a1)),x90063))+~P1(f324(f324(f326(a1),x90062),x90061))+~P1(f324(f324(f239(a1),x90064),x90062))+P1(f324(f324(f326(a1),f456(x90061,x90062,x90063,x90064)),x90061))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x90064),x90063)),x90062)) % 181.55/181.55 [9027]E(f324(f324(f22(a1),f437(x90271,x90272,x90273,x90274)),f438(x90271,x90272,x90273,x90274)),x90274)+~P1(f324(f324(f239(a1),f2(a1)),x90273))+~P1(f324(f324(f238(a1),x90274),x90272))+~P1(f324(f324(f326(a1),f324(f324(f81(a1),x90272),f79(a1))),x90271))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x90274),x90273)),x90272)) % 181.55/181.55 [9054]~P1(f324(f324(f239(a1),f2(a1)),x90542))+~P1(f324(f324(f326(a1),x90543),x90544))+~P1(f324(f324(f239(a1),x90541),x90543))+P1(f324(f324(f326(a1),f457(x90544,x90543,x90542,x90541)),f295(a1,f79(a1),x90542)))+P1(f324(f324(f239(a1),f324(f324(f81(a1),x90541),x90542)),x90543)) % 181.55/181.55 [9148]~P1(f324(f324(f239(a1),f2(a1)),x91483))+~P1(f324(f324(f238(a1),x91484),x91482))+P1(f324(f324(f326(a1),f437(x91481,x91482,x91483,x91484)),x91481))+~P1(f324(f324(f326(a1),f324(f324(f81(a1),x91482),f79(a1))),x91481))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x91484),x91483)),x91482)) % 181.55/181.55 [9188]~P1(f324(f324(f239(a1),f2(a1)),x91882))+~P1(f324(f324(f238(a1),x91881),x91883))+P1(f324(f324(f326(a1),f438(x91884,x91883,x91882,x91881)),f295(a1,f79(a1),x91882)))+~P1(f324(f324(f326(a1),f324(f324(f81(a1),x91883),f79(a1))),x91884))+P1(f324(f324(f238(a1),f324(f324(f81(a1),x91881),x91882)),x91883)) % 181.55/181.55 [9480]~P39(x94801,x94803)+~P29(x94801,x94804)+P39(x94801,f324(f324(f113(f871(f870(x94801,x94801),a859)),x94802),x94803))+~P1(f324(f324(f238(f871(f870(x94801,x94801),a859)),x94802),f324(f258(f871(f870(x94801,x94801),a859),f871(f870(x94801,x94801),a859)),x94804)))+~P1(f324(f324(f238(f871(f870(x94801,x94801),a859)),x94803),f324(f262(f871(f870(x94801,x94801),a859),f871(f870(x94801,x94801),a859)),x94804))) % 181.55/181.55 [9779]~E(f324(f659(x97791,x97794,x97793,x97792),f662(x97791,x97794,x97793,x97792)),f203(f866(a320)))+P1(f324(f324(f239(a1),f660(x97791,x97794,x97793,x97792)),f662(x97791,x97794,x97793,x97792)))+P1(f324(f324(f324(x97791,x97792),x97793),x97794))+P1(f324(f324(f324(x97791,f659(x97791,x97794,x97793,x97792)),f660(x97791,x97794,x97793,x97792)),f324(f324(f81(a1),f662(x97791,x97794,x97793,x97792)),f79(a1))))+~P1(f324(f312(f870(f871(a1,f869(f866(a320))),f870(a1,a1)),a310),f324(f324(f259(f871(a1,f869(f866(a320))),f870(a1,a1)),x97792),f324(f324(f259(a1,a1),x97793),x97794)))) % 181.55/181.55 [9878]~P20(x98782,x98784,x98783)+E(x98781,f191(f871(x98782,a859)))+~P1(f324(f61(x98782),x98781))+P1(f324(f324(f326(x98782),f324(x98783,x98781)),x98781))+~P1(f324(f324(f326(x98782),f324(f324(x98784,f836(x98781,x98783,x98784,x98782)),f838(x98781,x98783,x98784,x98782))),f324(f324(f302(x98782),f836(x98781,x98783,x98784,x98782)),f324(f324(f302(x98782),f838(x98781,x98783,x98784,x98782)),f191(f871(x98782,a859)))))) % 181.55/181.55 [9809]~P106(x98092)+~P61(x98091)+~P1(f324(f324(f238(f871(x98091,x98092)),x98093),x98094))+P1(f324(f324(f239(f871(x98091,x98092)),x98093),x98094))+~P1(f324(f57(x98091),f324(f324(f8(a859,a859,x98091),a319),f324(f324(f18(x98091,x98092,a859),f324(f324(f8(x98092,f871(x98092,a859),x98091),a321),x98093)),x98094)))) % 181.55/181.55 [9390]~P52(x93901,x93901,x93904)+P1(f324(f324(f326(f870(x93901,x93901)),f324(f324(f259(x93901,x93901),x93902),x93903)),f300(x93901,x93904)))+P1(f324(f324(f326(f870(x93901,x93901)),f324(f324(f259(x93901,x93901),x93903),x93902)),f300(x93901,x93904)))+~P1(f324(f324(f326(f870(x93901,x93901)),f324(f324(f259(x93901,x93901),x93905),x93902)),f300(x93901,x93904)))+~P1(f324(f324(f326(f870(x93901,x93901)),f324(f324(f259(x93901,x93901),x93905),x93903)),f300(x93901,x93904))) % 181.55/181.55 [5576]E(x55761,f2(a865))+~E(f324(f37(x55762),x55765),x55761)+E(f324(f37(x55762),x55763),f324(a115,x55761))+~E(x55763,f324(f324(f302(x55762),x55764),x55765))+P1(f324(f324(f326(x55762),x55764),x55765)) % 181.55/181.55 [5700]~P63(x57002)+E(x57001,f2(x57002))+E(x57003,f2(x57002))+~E(f324(f324(f282(x57002),x57004),x57003),f324(f324(f282(x57002),x57005),x57001))+E(f324(f324(f82(x57002),x57004),x57001),f324(f324(f82(x57002),x57005),x57003)) % 181.55/181.55 [5701]~P63(x57012)+E(x57011,f2(x57012))+E(x57013,f2(x57012))+~E(f324(f324(f82(x57012),x57014),x57013),f324(f324(f82(x57012),x57015),x57011))+E(f324(f324(f282(x57012),x57014),x57011),f324(f324(f282(x57012),x57015),x57013)) % 181.55/181.55 [5767]~E(f324(f37(x57671),x57675),x57673)+~E(x57675,f191(f871(x57671,a859)))+E(f324(f37(x57671),x57672),f324(a115,x57673))+~E(x57672,f324(f324(f302(x57671),x57674),x57675))+P1(f324(f324(f326(x57671),x57674),x57675)) % 181.55/181.55 [5987]~P112(x59872)+~E(f324(x59873,x59875),f2(x59872))+E(f324(f324(f9(x59871,x59872),x59873),x59874),f2(x59872))+~P1(f324(f61(x59871),x59874))+~P1(f324(f324(f326(x59871),x59875),x59874)) % 181.55/181.55 [6350]~P105(x63503)+E(x63501,x63502)+~E(f324(f294(x63503,x63504),x63501),f324(f294(x63503,x63505),x63502))+~P1(f324(f324(f239(x63503),x63505),x63502))+~P1(f324(f324(f239(x63503),x63504),x63501)) % 181.55/181.55 [6351]~P105(x63513)+E(x63511,x63512)+~E(f324(f294(x63513,x63511),x63514),f324(f294(x63513,x63512),x63515))+~P1(f324(f324(f239(x63513),x63512),x63515))+~P1(f324(f324(f239(x63513),x63511),x63514)) % 181.55/181.55 [7403]~P105(x74031)+~P16(x74031,f324(f324(f124(x74031),x74034),x74035))+~P1(f324(f324(f326(x74031),x74033),f324(f167(x74031),x74035)))+~P1(f324(f324(f326(x74031),x74032),f324(f167(x74031),x74034)))+P1(f324(f324(f238(x74031),x74032),x74033)) % 181.55/181.55 [8491]~P106(x84911)+~P1(f324(f324(f239(f871(x84911,a859)),f295(x84911,x84915,x84912)),f295(x84911,x84914,x84913)))+~P1(f324(f324(f238(x84911),x84915),x84912))+P1(f324(f324(f239(x84911),x84912),x84913))+P1(f324(f324(f239(x84911),x84914),x84915)) % 181.55/181.55 [9921]~P19(x99212,x99215,x99213)+E(x99211,f191(f871(x99212,a859)))+~E(f324(f324(x99215,f324(x99214,f851(x99211,x99214,x99213,x99215,x99212))),f324(x99214,f852(x99211,x99214,x99213,x99215,x99212))),f324(x99214,f324(f324(x99215,f851(x99211,x99214,x99213,x99215,x99212)),f852(x99211,x99214,x99213,x99215,x99212))))+E(f324(x99213,f324(f303(x99212,x99212,x99214),x99211)),f324(x99214,f324(x99213,x99211)))+~P1(f324(f61(x99212),x99211)) % 181.55/181.55 [6347]~P20(x63472,x63475,x63473)+E(x63471,f191(f871(x63472,a859)))+~P1(f324(f61(x63472),x63471))+E(f324(x63473,f324(f324(f302(x63472),x63474),x63471)),f324(f324(x63475,x63474),f324(x63473,x63471)))+P1(f324(f324(f326(x63472),x63474),x63471)) % 181.55/181.55 [7163]~P19(x71632,x71633,x71634)+E(f324(f324(x71633,f324(x71634,x71631)),f324(x71634,x71635)),f324(x71634,x71635))+E(x71631,f191(f871(x71632,a859)))+~P1(f324(f61(x71632),x71635))+~P1(f324(f324(f238(f871(x71632,a859)),x71631),x71635)) % 181.55/181.55 [7379]~P61(x73794)+~P91(x73795)+E(f324(x73791,x73792),f324(x73793,x73792))+~P1(f324(f324(f326(x73794),x73792),f324(f167(x73794),f55(x73794))))+~P1(f324(f324(f92(f871(x73794,x73795)),x73791),x73793)) % 181.55/181.55 [7538]~P20(x75384,x75385,x75381)+E(f324(x75381,x75382),x75383)+~P1(f324(f61(x75384),x75382))+~E(f324(f324(f22(f871(x75384,a859)),x75382),f324(f324(f302(x75384),x75383),f191(f871(x75384,a859)))),f191(f871(x75384,a859)))+~P1(f324(f324(f326(x75384),x75383),x75382)) % 181.55/181.55 [7622]E(x76221,x76222)+~E(f324(f192(f866(x76223)),x76222),f324(f192(f866(x76224)),x76225))+~E(f324(f192(f866(x76223)),x76221),f324(f192(f866(x76224)),x76225))+~E(f324(f173(x76224,x76223),f324(f324(f177(x76224,x76223),x76225),x76221)),f324(f173(x76224,x76223),f324(f324(f177(x76224,x76223),x76225),x76222)))+~P1(f324(f131(x76224),x76225)) % 181.55/181.55 [8462]E(x84621,x84622)+~P9(x84623,x84624,x84625)+E(f324(f324(f104(f871(x84623,a859)),x84621),x84622),f191(f871(x84623,a859)))+~P1(f324(f324(f326(f871(x84623,a859)),x84622),f324(f324(f60(x84623),x84624),x84625)))+~P1(f324(f324(f326(f871(x84623,a859)),x84621),f324(f324(f60(x84623),x84624),x84625))) % 181.55/181.55 [9269]~P68(x92692)+~E(f324(x92693,f430(x92693,x92694,x92695,x92691,x92692)),f79(x92692))+E(f324(f324(f9(x92691,x92692),x92693),x92694),f324(f324(f9(x92691,x92692),x92693),x92695))+~P1(f324(f61(x92691),x92695))+~P1(f324(f324(f238(f871(x92691,a859)),x92694),x92695)) % 181.55/181.55 [9270]~P68(x92702)+~E(f324(x92703,f431(x92703,x92704,x92705,x92701,x92702)),f79(x92702))+E(f324(f324(f9(x92701,x92702),x92703),x92704),f324(f324(f9(x92701,x92702),x92703),x92705))+~P1(f324(f61(x92701),x92705))+~P1(f324(f324(f238(f871(x92701,a859)),x92704),x92705)) % 181.55/181.55 [9271]~P72(x92712)+~E(f324(x92713,f500(x92713,x92714,x92715,x92711,x92712)),f2(x92712))+E(f324(f324(f6(x92711,x92712),x92713),x92714),f324(f324(f6(x92711,x92712),x92713),x92715))+~P1(f324(f61(x92711),x92715))+~P1(f324(f324(f238(f871(x92711,a859)),x92714),x92715)) % 181.55/181.55 [9272]~P72(x92722)+~E(f324(x92723,f507(x92723,x92724,x92725,x92721,x92722)),f2(x92722))+E(f324(f324(f6(x92721,x92722),x92723),x92724),f324(f324(f6(x92721,x92722),x92723),x92725))+~P1(f324(f61(x92721),x92725))+~P1(f324(f324(f238(f871(x92721,a859)),x92724),x92725)) % 181.55/181.55 [9758]~P85(x97581)+~P1(f324(f61(x97582),x97585))+~P1(f324(f324(f238(x97581),f2(x97581)),f324(x97583,f475(x97583,x97584,x97585,x97582,x97581))))+P1(f324(f324(f238(x97581),f324(f324(f6(x97582,x97581),x97583),x97584)),f324(f324(f6(x97582,x97581),x97583),x97585)))+~P1(f324(f324(f238(f871(x97582,a859)),x97584),x97585)) % 181.55/181.55 [7400]E(x74001,f2(a865))+P1(f324(x74002,x74003))+~E(x74004,f324(f324(f81(a865),f324(f324(f82(a865),x74001),x74003)),x74005))+~P1(f324(f324(f239(a865),x74005),x74001))+~P1(f324(x74002,f324(f324(f38(a865),x74004),x74001))) % 181.55/181.55 [7479]E(x74791,f2(a865))+P1(f324(x74792,x74793))+~P1(f324(x74792,f44(a865,x74794,x74791)))+~E(x74794,f324(f324(f81(a865),f324(f324(f82(a865),x74791),x74795)),x74793))+~P1(f324(f324(f239(a865),x74793),x74791)) % 181.55/181.55 [7761]~P63(x77613)+E(f324(x77611,x77612),f2(x77613))+~P1(f324(f61(x77614),x77615))+E(f324(f324(f9(x77614,x77613),x77611),f324(f324(f22(f871(x77614,a859)),x77615),f324(f324(f302(x77614),x77612),f191(f871(x77614,a859))))),f324(f324(f9(x77614,x77613),x77611),x77615))+P1(f324(f324(f326(x77614),x77612),x77615)) % 181.55/181.55 [8166]~P68(x81661)+~P1(f324(f61(x81662),x81665))+~P1(f324(f61(x81662),x81664))+~E(f324(f324(f104(f871(x81662,a859)),x81664),x81665),f191(f871(x81662,a859)))+E(f324(f324(f82(x81661),f324(f324(f9(x81662,x81661),x81663),x81664)),f324(f324(f9(x81662,x81661),x81663),x81665)),f324(f324(f9(x81662,x81661),x81663),f324(f324(f113(f871(x81662,a859)),x81664),x81665))) % 181.55/181.55 [8167]~P72(x81671)+~P1(f324(f61(x81672),x81675))+~P1(f324(f61(x81672),x81674))+~E(f324(f324(f104(f871(x81672,a859)),x81674),x81675),f191(f871(x81672,a859)))+E(f324(f324(f81(x81671),f324(f324(f6(x81672,x81671),x81673),x81674)),f324(f324(f6(x81672,x81671),x81673),x81675)),f324(f324(f6(x81672,x81671),x81673),f324(f324(f113(f871(x81672,a859)),x81674),x81675))) % 181.55/181.55 [8263]~P63(x82633)+E(f324(x82631,x82632),f2(x82633))+~P1(f324(f61(x82634),x82635))+E(f324(f324(f9(x82634,x82633),x82631),f324(f324(f22(f871(x82634,a859)),x82635),f324(f324(f302(x82634),x82632),f191(f871(x82634,a859))))),f324(f324(f282(x82633),f324(f324(f9(x82634,x82633),x82631),x82635)),f324(x82631,x82632)))+~P1(f324(f324(f326(x82634),x82632),x82635)) % 181.55/181.55 [8982]~P9(x89821,x89825,x89824)+~E(f324(f324(f60(x89821),f324(f324(f302(x89821),x89822),f191(f871(x89821,a859)))),x89824),f324(f324(f60(x89821),f324(f324(f302(x89821),x89823),f191(f871(x89821,a859)))),x89824))+~P1(f324(f324(f326(x89821),x89823),x89825))+~P1(f324(f324(f326(x89821),x89822),x89825))+P1(f324(f324(f326(f870(x89821,x89821)),f324(f324(f259(x89821,x89821),x89822),x89823)),x89824)) % 181.55/181.55 [9005]~P9(x90051,x90055,x90053)+E(f324(f324(f60(x90051),f324(f324(f302(x90051),x90052),f191(f871(x90051,a859)))),x90053),f324(f324(f60(x90051),f324(f324(f302(x90051),x90054),f191(f871(x90051,a859)))),x90053))+~P1(f324(f324(f326(x90051),x90054),x90055))+~P1(f324(f324(f326(x90051),x90052),x90055))+~P1(f324(f324(f326(f870(x90051,x90051)),f324(f324(f259(x90051,x90051),x90052),x90054)),x90053)) % 181.55/181.55 [9299]~P68(x92991)+~P1(f324(f61(x92992),x92995))+~P1(f324(f61(x92992),x92994))+~E(f324(f324(f104(f871(x92992,a859)),x92994),x92995),f191(f871(x92992,a859)))+E(f324(f324(f82(x92991),f324(f324(f324(f65(x92991,x92992,f82(x92991)),x92993),f79(x92991)),x92994)),f324(f324(f324(f65(x92991,x92992,f82(x92991)),x92993),f79(x92991)),x92995)),f324(f324(f324(f65(x92991,x92992,f82(x92991)),x92993),f79(x92991)),f324(f324(f113(f871(x92992,a859)),x92994),x92995))) % 181.55/181.55 [9308]~P68(x93081)+~E(f324(x93083,f385(x93083,x93085,x93084,x93082,x93081)),f79(x93081))+~P1(f324(f61(x93082),x93084))+~P1(f324(f61(x93082),x93085))+E(f324(f324(f82(x93081),f324(f324(f9(x93082,x93081),x93083),x93084)),f324(f324(f9(x93082,x93081),x93083),x93085)),f324(f324(f9(x93082,x93081),x93083),f324(f324(f113(f871(x93082,a859)),x93084),x93085))) % 181.55/181.55 [9309]~P68(x93091)+~E(f324(x93093,f386(x93093,x93095,x93094,x93092,x93091)),f79(x93091))+~P1(f324(f61(x93092),x93094))+~P1(f324(f61(x93092),x93095))+E(f324(f324(f82(x93091),f324(f324(f9(x93092,x93091),x93093),x93094)),f324(f324(f9(x93092,x93091),x93093),x93095)),f324(f324(f9(x93092,x93091),x93093),f324(f324(f113(f871(x93092,a859)),x93094),x93095))) % 181.55/181.55 [9310]~P72(x93101)+~E(f324(x93103,f494(x93103,x93105,x93104,x93102,x93101)),f2(x93101))+~P1(f324(f61(x93102),x93104))+~P1(f324(f61(x93102),x93105))+E(f324(f324(f81(x93101),f324(f324(f6(x93102,x93101),x93103),x93104)),f324(f324(f6(x93102,x93101),x93103),x93105)),f324(f324(f6(x93102,x93101),x93103),f324(f324(f113(f871(x93102,a859)),x93104),x93105))) % 181.55/181.55 [9311]~P72(x93111)+~E(f324(x93113,f495(x93113,x93115,x93114,x93112,x93111)),f2(x93111))+~P1(f324(f61(x93112),x93114))+~P1(f324(f61(x93112),x93115))+E(f324(f324(f81(x93111),f324(f324(f6(x93112,x93111),x93113),x93114)),f324(f324(f6(x93112,x93111),x93113),x93115)),f324(f324(f6(x93112,x93111),x93113),f324(f324(f113(f871(x93112,a859)),x93114),x93115))) % 181.55/181.55 [9526]~P68(x95261)+~E(f324(x95263,f345(x95263,x95265,x95264,x95262,x95261)),f79(x95261))+~P1(f324(f61(x95262),x95264))+~P1(f324(f61(x95262),x95265))+E(f324(f324(f82(x95261),f324(f324(f324(f65(x95261,x95262,f82(x95261)),x95263),f79(x95261)),x95264)),f324(f324(f324(f65(x95261,x95262,f82(x95261)),x95263),f79(x95261)),x95265)),f324(f324(f324(f65(x95261,x95262,f82(x95261)),x95263),f79(x95261)),f324(f324(f113(f871(x95262,a859)),x95264),x95265))) % 181.55/181.55 [9637]~P68(x96372)+E(f324(f324(f9(x96371,x96372),x96373),x96374),f324(f324(f9(x96371,x96372),x96373),x96375))+~P1(f324(f61(x96371),x96375))+~P1(f324(f324(f238(f871(x96371,a859)),x96374),x96375))+P1(f324(f324(f326(x96371),f430(x96373,x96374,x96375,x96371,x96372)),f324(f324(f22(f871(x96371,a859)),x96375),x96374))) % 181.55/181.55 [9638]~P68(x96382)+E(f324(f324(f9(x96381,x96382),x96383),x96384),f324(f324(f9(x96381,x96382),x96383),x96385))+~P1(f324(f61(x96381),x96385))+~P1(f324(f324(f238(f871(x96381,a859)),x96384),x96385))+P1(f324(f324(f326(x96381),f431(x96383,x96384,x96385,x96381,x96382)),f324(f324(f22(f871(x96381,a859)),x96385),x96384))) % 181.55/181.55 [9639]~P72(x96392)+E(f324(f324(f6(x96391,x96392),x96393),x96394),f324(f324(f6(x96391,x96392),x96393),x96395))+~P1(f324(f61(x96391),x96395))+~P1(f324(f324(f238(f871(x96391,a859)),x96394),x96395))+P1(f324(f324(f326(x96391),f500(x96393,x96394,x96395,x96391,x96392)),f324(f324(f22(f871(x96391,a859)),x96395),x96394))) % 181.55/181.55 [9640]~P72(x96402)+E(f324(f324(f6(x96401,x96402),x96403),x96404),f324(f324(f6(x96401,x96402),x96403),x96405))+~P1(f324(f61(x96401),x96405))+~P1(f324(f324(f238(f871(x96401,a859)),x96404),x96405))+P1(f324(f324(f326(x96401),f507(x96403,x96404,x96405,x96401,x96402)),f324(f324(f22(f871(x96401,a859)),x96405),x96404))) % 181.55/181.55 [9658]~P68(x96581)+~P1(f324(f61(x96582),x96584))+~P1(f324(f61(x96582),x96585))+E(f324(f324(f82(x96581),f324(f324(f9(x96582,x96581),x96583),x96584)),f324(f324(f9(x96582,x96581),x96583),x96585)),f324(f324(f9(x96582,x96581),x96583),f324(f324(f113(f871(x96582,a859)),x96584),x96585)))+P1(f324(f324(f326(x96582),f385(x96583,x96585,x96584,x96582,x96581)),f324(f324(f104(f871(x96582,a859)),x96584),x96585))) % 181.55/181.55 [9659]~P68(x96591)+~P1(f324(f61(x96592),x96594))+~P1(f324(f61(x96592),x96595))+E(f324(f324(f82(x96591),f324(f324(f9(x96592,x96591),x96593),x96594)),f324(f324(f9(x96592,x96591),x96593),x96595)),f324(f324(f9(x96592,x96591),x96593),f324(f324(f113(f871(x96592,a859)),x96594),x96595)))+P1(f324(f324(f326(x96592),f386(x96593,x96595,x96594,x96592,x96591)),f324(f324(f104(f871(x96592,a859)),x96594),x96595))) % 181.55/181.55 [9660]~P72(x96601)+~P1(f324(f61(x96602),x96604))+~P1(f324(f61(x96602),x96605))+E(f324(f324(f81(x96601),f324(f324(f6(x96602,x96601),x96603),x96604)),f324(f324(f6(x96602,x96601),x96603),x96605)),f324(f324(f6(x96602,x96601),x96603),f324(f324(f113(f871(x96602,a859)),x96604),x96605)))+P1(f324(f324(f326(x96602),f494(x96603,x96605,x96604,x96602,x96601)),f324(f324(f104(f871(x96602,a859)),x96604),x96605))) % 181.55/181.55 [9661]~P72(x96611)+~P1(f324(f61(x96612),x96614))+~P1(f324(f61(x96612),x96615))+E(f324(f324(f81(x96611),f324(f324(f6(x96612,x96611),x96613),x96614)),f324(f324(f6(x96612,x96611),x96613),x96615)),f324(f324(f6(x96612,x96611),x96613),f324(f324(f113(f871(x96612,a859)),x96614),x96615)))+P1(f324(f324(f326(x96612),f495(x96613,x96615,x96614,x96612,x96611)),f324(f324(f104(f871(x96612,a859)),x96614),x96615))) % 181.55/181.55 [9668]~P85(x96685)+~P1(f324(f61(x96681),x96684))+P1(f324(f324(f238(x96685),f324(f324(f6(x96681,x96685),x96682),x96683)),f324(f324(f6(x96681,x96685),x96682),x96684)))+~P1(f324(f324(f238(f871(x96681,a859)),x96683),x96684))+P1(f324(f324(f326(x96681),f475(x96682,x96683,x96684,x96681,x96685)),f324(f324(f22(f871(x96681,a859)),x96684),x96683))) % 181.55/181.55 [9722]~P68(x97221)+~P1(f324(f61(x97222),x97224))+~P1(f324(f61(x97222),x97225))+E(f324(f324(f82(x97221),f324(f324(f324(f65(x97221,x97222,f82(x97221)),x97223),f79(x97221)),x97224)),f324(f324(f324(f65(x97221,x97222,f82(x97221)),x97223),f79(x97221)),x97225)),f324(f324(f324(f65(x97221,x97222,f82(x97221)),x97223),f79(x97221)),f324(f324(f113(f871(x97222,a859)),x97224),x97225)))+P1(f324(f324(f326(x97222),f345(x97223,x97225,x97224,x97222,x97221)),f324(f324(f104(f871(x97222,a859)),x97224),x97225))) % 181.55/181.55 [8672]~P20(x86721,x86724,x86725)+~P1(f324(f61(x86721),x86722))+E(f324(f324(f22(f871(x86721,a859)),x86722),f324(f324(f302(x86721),x86723),f191(f871(x86721,a859)))),f191(f871(x86721,a859)))+~P1(f324(f324(f326(x86721),x86723),x86722))+E(f324(f324(x86724,x86723),f324(x86725,f324(f324(f22(f871(x86721,a859)),x86722),f324(f324(f302(x86721),x86723),f191(f871(x86721,a859)))))),f324(x86725,x86722)) % 181.55/181.55 [8751]~P20(x87511,x87514,x87515)+~P1(f324(f61(x87511),x87513))+~P1(f324(f61(x87511),x87512))+E(f324(f324(f104(f871(x87511,a859)),x87512),x87513),f191(f871(x87511,a859)))+E(f324(f324(x87514,f324(x87515,f324(f324(f113(f871(x87511,a859)),x87512),x87513))),f324(x87515,f324(f324(f104(f871(x87511,a859)),x87512),x87513))),f324(f324(x87514,f324(x87515,x87512)),f324(x87515,x87513))) % 181.55/181.55 [9313]~P1(f324(f324(f238(a1),x93134),f2(a1)))+~P1(f324(f324(f239(a1),x93133),x93135))+P1(f324(f324(f238(a1),x93131),x93132))+~P1(f324(f324(f239(a1),x93133),x93134))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),f324(f324(f82(a1),x93133),x93132)),x93135)),f324(f324(f81(a1),f324(f324(f82(a1),x93133),x93131)),x93134))) % 181.55/181.55 [9315]~P1(f324(f324(f238(a1),f2(a1)),x93155))+P1(f324(f324(f238(a1),x93151),x93152))+~P1(f324(f324(f239(a1),x93153),x93154))+~P1(f324(f324(f239(a1),x93155),x93154))+~P1(f324(f324(f238(a1),f324(f324(f81(a1),f324(f324(f82(a1),x93154),x93151)),x93155)),f324(f324(f81(a1),f324(f324(f82(a1),x93154),x93152)),x93153))) % 181.55/181.55 [9432]~P63(x94325)+E(f324(x94321,f389(x94321,x94322,x94323,x94324,x94325)),f2(x94325))+~P1(f324(f61(x94324),x94323))+~P1(f324(f61(x94324),x94322))+E(f324(f324(f282(x94325),f324(f324(f82(x94325),f324(f324(f9(x94324,x94325),x94321),x94323)),f324(f324(f9(x94324,x94325),x94321),x94322))),f324(f324(f9(x94324,x94325),x94321),f324(f324(f104(f871(x94324,a859)),x94323),x94322))),f324(f324(f9(x94324,x94325),x94321),f324(f324(f113(f871(x94324,a859)),x94323),x94322))) % 181.55/181.55 [9714]~P63(x97141)+~P1(f324(f61(x97142),x97144))+~P1(f324(f61(x97142),x97145))+E(f324(f324(f282(x97141),f324(f324(f82(x97141),f324(f324(f9(x97142,x97141),x97143),x97144)),f324(f324(f9(x97142,x97141),x97143),x97145))),f324(f324(f9(x97142,x97141),x97143),f324(f324(f104(f871(x97142,a859)),x97144),x97145))),f324(f324(f9(x97142,x97141),x97143),f324(f324(f113(f871(x97142,a859)),x97144),x97145)))+P1(f324(f324(f326(x97142),f389(x97143,x97145,x97144,x97142,x97141)),f324(f324(f104(f871(x97142,a859)),x97144),x97145))) % 181.55/181.55 [9026]E(f324(f324(f124(x90261),x90262),x90263),f324(f324(f124(x90261),x90264),x90265))+~E(f324(f324(f170(x90261),f324(f192(f866(x90261)),x90264)),x90262),x90264)+~E(f324(f324(f170(x90261),f324(f192(f866(x90261)),x90262)),x90264),x90262)+~E(x90265,f324(f324(f124(x90261),f324(f324(f132(x90261),f324(f192(f866(x90261)),x90264)),x90262)),x90263))+~E(f324(f324(f124(x90261),f324(f324(f132(x90261),f324(f192(f866(x90261)),x90262)),x90264)),x90265),x90263) % 181.55/181.55 [9430]~P105(x94302)+E(f324(f324(f142(x94301,x94302,x94303),x94304),f164(x94301,x94304,x94305)),x94305)+~P16(x94302,f324(f324(f148(x94301,x94302),x94303),x94305))+~P1(f324(f324(f326(x94301),x94304),f324(f167(x94301),x94305)))+~E(f324(f135(x94301),f324(f130(x94301,f324(f324(f8(x94302,a859,x94301),f324(a321,f324(x94303,x94304))),x94303)),x94305)),x94304) % 181.55/181.55 [9776]~P66(x97761)+~P1(f324(f66(x97761,x97761,f82(x97761),x97762,x97763),x97765))+~P1(f324(f324(f326(x97761),x97764),x97763))+P1(f324(f324(f326(x97761),x97762),x97763))+P1(f324(f66(x97761,x97761,f82(x97761),x97764,f324(f324(f302(x97761),x97762),f324(f324(f22(f871(x97761,a859)),x97763),f324(f324(f302(x97761),x97764),f191(f871(x97761,a859)))))),x97765)) % 181.55/181.55 [7171]E(x71711,x71712)+~P27(x71714,x71715,x71713,x71716)+~E(f324(x71713,x71711),f324(x71713,x71712))+~P1(f324(f324(f326(x71714),x71712),x71716))+~P1(f324(f324(f326(x71714),x71711),x71716)) % 181.55/181.55 [6438]~P136(x64384)+E(x64381,x64382)+~E(x64385,x64386)+E(x64383,f2(x64384))+~E(f324(f324(f81(x64384),x64385),f324(f324(f82(x64384),x64383),x64381)),f324(f324(f81(x64384),x64386),f324(f324(f82(x64384),x64383),x64382))) % 181.55/181.55 [7460]~P105(x74601)+~P6(x74601)+~P1(f324(f324(f239(x74601),x74602),f324(x74605,x74606)))+~P1(f324(f324(f326(x74603),x74606),x74604))+P1(f324(f324(f239(x74601),x74602),f324(f324(f41(x74603,x74601),x74604),x74605))) % 181.55/181.55 [9772]~P27(x97722,x97721,x97723,x97724)+~P27(x97721,x97722,x97726,x97725)+P28(x97721,x97722,f497(x97723,x97724,x97725,x97726,x97722,x97721),x97725,x97724)+~P1(f324(f324(f238(f871(x97722,a859)),f324(f303(x97721,x97722,x97726),x97725)),x97724))+~P1(f324(f324(f238(f871(x97721,a859)),f324(f303(x97722,x97721,x97723),x97724)),x97725)) % 181.55/181.55 [8134]~P105(x81341)+~P6(x81341)+~P1(f324(f324(f239(x81341),f324(x81344,x81346)),x81345))+~P1(f324(f324(f326(x81342),x81346),x81343))+P1(f324(f324(f239(x81341),f324(f324(f42(x81342,x81341),x81343),x81344)),x81345)) % 181.55/181.55 [8391]~P21(x83912,x83915,x83916,x83911)+~P1(f324(f61(x83912),x83914))+~P1(f324(f61(x83912),x83913))+~E(f324(f324(f104(f871(x83912,a859)),x83913),x83914),f191(f871(x83912,a859)))+E(f324(x83911,f324(f324(f113(f871(x83912,a859)),x83913),x83914)),f324(f73(x83915,x83915,x83915,f324(x83911,x83913)),f324(x83911,x83914))) % 181.55/181.55 [8721]E(x87211,x87212)+~P54(x87214,x87215,x87216,x87213,x87217)+~E(f324(x87213,x87211),f324(x87213,x87212))+~P1(f324(f324(f326(x87215),x87212),x87217))+~P1(f324(f324(f326(x87215),x87211),x87217)) % 181.55/181.55 [10018]~P1(f324(x100182,x100184))+~E(x100185,f324(f130(x100181,x100182),x100187))+E(f324(f130(x100181,x100182),x100183),f324(f324(f145(x100181),x100184),x100185))+~E(x100183,f324(f324(f124(x100181),x100186),f324(f324(f145(x100181),x100184),x100187)))+P1(f324(x100182,f775(x100185,x100184,x100183,x100182,x100181,x100186,x100187))) % 181.55/181.55 [10019]~P1(f324(x100194,x100192))+~E(x100193,f324(f130(x100191,x100194),x100197))+E(f324(f324(f145(x100191),x100192),x100193),f324(f130(x100191,x100194),x100195))+~E(x100195,f324(f324(f124(x100191),x100196),f324(f324(f145(x100191),x100192),x100197)))+P1(f324(x100194,f773(x100195,x100194,x100193,x100192,x100191,x100196,x100197))) % 181.55/181.55 [10052]~P1(f324(x100522,x100524))+~E(x100525,f324(f130(x100521,x100522),x100527))+E(f324(f130(x100521,x100522),x100523),f324(f324(f145(x100521),x100524),x100525))+~E(x100523,f324(f324(f124(x100521),x100526),f324(f324(f145(x100521),x100524),x100527)))+P1(f324(f324(f326(x100521),f775(x100525,x100524,x100523,x100522,x100521,x100526,x100527)),f324(f167(x100521),x100526))) % 181.55/181.55 [10053]~P1(f324(x100534,x100532))+~E(x100533,f324(f130(x100531,x100534),x100537))+E(f324(f324(f145(x100531),x100532),x100533),f324(f130(x100531,x100534),x100535))+~E(x100535,f324(f324(f124(x100531),x100536),f324(f324(f145(x100531),x100532),x100537)))+P1(f324(f324(f326(x100531),f773(x100535,x100534,x100533,x100532,x100531,x100536,x100537)),f324(f167(x100531),x100536))) % 181.55/181.55 [10056]~P9(x100561,x100567,x100566)+~P14(x100561,f871(x100565,a859),x100566,x100564)+P1(f324(f324(f326(x100561),f761(x100562,x100563,x100564,x100565,x100566,x100567,x100561)),x100567))+~P1(f324(f324(f326(f871(x100561,a859)),x100563),f324(f324(f60(x100561),x100567),x100566)))+P1(f324(f324(f326(f871(x100565,a859)),f324(f324(f41(x100561,f871(x100565,a859)),x100563),x100564)),x100562)) % 181.55/181.55 [10103]~P9(x101032,x101036,x101037)+~P14(x101032,f871(x101031,a859),x101037,x101034)+~P1(f324(f324(f326(f871(x101032,a859)),x101033),f324(f324(f60(x101032),x101036),x101037)))+~P1(f324(f324(f326(f871(x101031,a859)),f324(x101034,f761(x101035,x101033,x101034,x101031,x101037,x101036,x101032))),x101035))+P1(f324(f324(f326(f871(x101031,a859)),f324(f324(f41(x101032,f871(x101031,a859)),x101033),x101034)),x101035)) % 181.55/181.55 [8311]~P68(x83112)+~P27(x83111,x83115,x83118,x83114)+~E(x83113,f324(f73(x83115,x83112,x83111,x83116),x83118))+~E(x83117,f324(f303(x83111,x83115,x83118),x83114))+E(f324(f324(f9(x83111,x83112),x83113),x83114),f324(f324(f9(x83115,x83112),x83116),x83117)) % 181.55/181.55 [10107]~P68(x101072)+~P27(x101075,x101071,x101078,x101077)+~E(f324(x101076,f390(x101073,x101076,x101074,x101077,x101078,x101071,x101075,x101072)),f324(f324(f73(x101071,x101072,x101075,x101073),x101078),f390(x101073,x101076,x101074,x101077,x101078,x101071,x101075,x101072)))+~E(x101074,f324(f303(x101075,x101071,x101078),x101077))+E(f324(f324(f9(x101071,x101072),x101073),x101074),f324(f324(f9(x101075,x101072),x101076),x101077)) % 181.55/181.55 [10109]~P68(x101092)+~P27(x101091,x101095,x101098,x101094)+~E(x101097,f324(f303(x101091,x101095,x101098),x101094))+E(f324(f324(f9(x101091,x101092),x101093),x101094),f324(f324(f9(x101095,x101092),x101096),x101097))+P1(f324(f324(f326(x101091),f390(x101096,x101093,x101097,x101094,x101098,x101095,x101091,x101092)),x101094)) % 181.55/181.55 [10110]~P72(x101102)+~P27(x101101,x101105,x101108,x101104)+~E(x101107,f324(f303(x101101,x101105,x101108),x101104))+E(f324(f324(f6(x101101,x101102),x101103),x101104),f324(f324(f6(x101105,x101102),x101106),x101107))+P1(f324(f324(f326(x101101),f582(x101106,x101103,x101107,x101104,x101108,x101105,x101101,x101102)),x101104)) % 181.55/181.55 [10115]~P72(x101152)+~P27(x101155,x101151,x101158,x101157)+~E(x101154,f324(f303(x101155,x101151,x101158),x101157))+~E(f324(x101156,f582(x101153,x101156,x101154,x101157,x101158,x101151,x101155,x101152)),f324(x101153,f324(x101158,f582(x101153,x101156,x101154,x101157,x101158,x101151,x101155,x101152))))+E(f324(f324(f6(x101151,x101152),x101153),x101154),f324(f324(f6(x101155,x101152),x101156),x101157)) % 181.55/181.55 [9486]~E(f324(f192(f866(x94862)),x94865),f324(f192(f866(x94861)),x94863))+~E(f324(f192(f866(x94862)),x94864),f324(f192(f866(x94861)),x94863))+~E(f324(f324(f324(f72(x94861,f869(x94862)),f324(f173(x94861,x94862),f324(f324(f177(x94861,x94862),x94863),x94864))),x94866),f324(f233(x94862),x94867)),f324(f324(f324(f72(x94861,f869(x94862)),f324(f173(x94861,x94862),f324(f324(f177(x94861,x94862),x94863),x94865))),x94866),f324(f233(x94862),x94868)))+E(f324(f173(x94861,x94862),f324(f324(f177(x94861,x94862),x94863),x94864)),f324(f173(x94861,x94862),f324(f324(f177(x94861,x94862),x94863),x94865)))+P1(f324(f324(f326(x94861),x94866),f324(f167(x94861),x94863))) % 181.55/181.55 [9603]~P25(x96036,x96032,x96035,x96037,x96038,x96031)+~P1(f324(f61(x96032),x96034))+~P1(f324(f61(x96032),x96033))+~E(f324(f324(f104(f871(x96032,a859)),x96033),x96034),f191(f871(x96032,a859)))+E(f324(x96031,f324(f324(f113(f871(x96032,a859)),x96033),x96034)),f324(f324(x96035,f324(x96031,x96033)),f324(x96031,x96034))) % 181.55/181.55 [10005]~P25(x100058,x100052,x100055,x100057,x100056,x100051)+~E(f324(x100056,f853(x100054,x100053,x100051,x100056,x100057,x100055,x100052)),x100057)+~P1(f324(f61(x100052),x100053))+~P1(f324(f61(x100052),x100054))+E(f324(x100051,f324(f324(f113(f871(x100052,a859)),x100053),x100054)),f324(f324(x100055,f324(x100051,x100053)),f324(x100051,x100054))) % 181.55/181.55 [10061]~P25(x100618,x100612,x100615,x100617,x100616,x100611)+~P1(f324(f61(x100612),x100613))+~P1(f324(f61(x100612),x100614))+E(f324(x100611,f324(f324(f113(f871(x100612,a859)),x100613),x100614)),f324(f324(x100615,f324(x100611,x100613)),f324(x100611,x100614)))+P1(f324(f324(f326(x100612),f853(x100614,x100613,x100611,x100616,x100617,x100615,x100612)),f324(f324(f104(f871(x100612,a859)),x100613),x100614))) % 181.55/181.55 [9763]~P9(x97634,x97638,x97635)+~P9(x97631,x97639,x97633)+~P15(x97631,x97634,f871(x97632,a859),x97633,x97635,x97637)+P14(x97631,f871(x97632,a859),x97633,f324(f324(f8(f871(x97634,f871(x97632,a859)),f871(x97632,a859),x97631),f324(f41(x97634,f871(x97632,a859)),f324(f278(x97634,x97634,x97635),f324(f324(f302(x97634),x97636),f191(f871(x97634,a859)))))),x97637))+~P1(f324(f324(f326(x97634),x97636),x97638)) % 181.55/181.55 [5384]~P105(x53843)+~P16(x53843,x53841)+E(x53841,f747(x53842,x53843))+~E(f324(f167(x53843),x53841),x53842)+~P1(f324(f61(x53843),x53842))+~P1(f324(f131(x53843),x53841)) % 181.55/181.55 [5022]~P124(x50222)+~P125(x50222)+~P139(x50222)+~P110(x50222)+E(x50221,f2(x50222))+~E(f324(f324(f249(x50222),x50221),x50223),f2(x50222)) % 181.55/181.55 [5023]~P124(x50232)+~P125(x50232)+~P139(x50232)+~P110(x50232)+~E(x50231,f2(a865))+~E(f324(f324(f249(x50232),x50233),x50231),f2(x50232)) % 181.55/181.55 [6420]~P85(x64201)+~E(x64203,f2(x64201))+~E(x64202,f2(x64201))+E(f324(f324(f81(x64201),x64202),x64203),f2(x64201))+~P1(f324(f324(f238(x64201),f2(x64201)),x64203))+~P1(f324(f324(f238(x64201),f2(x64201)),x64202)) % 181.55/181.55 [8784]~E(f324(f258(a865,a865),x87843),f2(a865))+~E(x87841,f324(f324(f81(a865),f324(f324(f82(a865),f324(f258(a865,a865),x87843)),x87842)),f324(f262(a865,a865),x87843)))+P1(f324(f47(x87841,x87842),x87843))+~P1(f324(f324(f238(a865),f324(f262(a865,a865),x87843)),f2(a865)))+P1(f324(f324(f239(a865),f2(a865)),x87842))+~P1(f324(f324(f239(a865),x87842),f324(f262(a865,a865),x87843))) % 181.55/181.55 [8792]E(x87921,f2(a865))+~E(x87922,f324(f324(f81(a865),f324(f324(f82(a865),f324(f258(a865,a865),x87923)),x87921)),f324(f262(a865,a865),x87923)))+P1(f324(f47(x87922,x87921),x87923))+~P1(f324(f324(f239(a865),f2(a865)),x87921))+~P1(f324(f324(f238(a865),f2(a865)),f324(f262(a865,a865),x87923)))+~P1(f324(f324(f239(a865),f324(f262(a865,a865),x87923)),x87921)) % 181.55/181.55 [8810]~E(f324(f258(a865,a865),x88103),f2(a865))+~E(x88101,f324(f324(f81(a865),f324(f324(f82(a865),f324(f258(a865,a865),x88103)),x88102)),f324(f262(a865,a865),x88103)))+P1(f324(f47(x88101,x88102),x88103))+~P1(f324(f324(f239(a865),f2(a865)),x88102))+~P1(f324(f324(f238(a865),f2(a865)),f324(f262(a865,a865),x88103)))+~P1(f324(f324(f239(a865),f324(f262(a865,a865),x88103)),x88102)) % 181.55/181.55 [6800]~P94(x68002)+E(x68001,f191(f871(x68002,a859)))+E(x68003,f191(f871(x68002,a859)))+~P1(f324(f61(x68002),x68001))+~P1(f324(f61(x68002),x68003))+E(f13(x68002,f324(f324(f113(f871(x68002,a859)),x68003),x68001)),f324(f324(f113(x68002),f13(x68002,x68003)),f13(x68002,x68001))) % 181.55/181.55 [6801]~P94(x68012)+E(x68011,f191(f871(x68012,a859)))+E(x68013,f191(f871(x68012,a859)))+~P1(f324(f61(x68012),x68011))+~P1(f324(f61(x68012),x68013))+E(f10(x68012,f324(f324(f113(f871(x68012,a859)),x68013),x68011)),f324(f324(f104(x68012),f10(x68012,x68013)),f10(x68012,x68011))) % 181.55/181.55 [6802]~P105(x68022)+E(x68021,f191(f871(x68022,a859)))+E(x68023,f191(f871(x68022,a859)))+~P1(f324(f61(x68022),x68021))+~P1(f324(f61(x68022),x68023))+E(f14(x68022,f324(f324(f113(f871(x68022,a859)),x68023),x68021)),f324(f324(f190(x68022),f14(x68022,x68023)),f14(x68022,x68021))) % 181.55/181.55 [6803]~P105(x68032)+E(x68031,f191(f871(x68032,a859)))+E(x68033,f191(f871(x68032,a859)))+~P1(f324(f61(x68032),x68031))+~P1(f324(f61(x68032),x68033))+E(f15(x68032,f324(f324(f113(f871(x68032,a859)),x68033),x68031)),f324(f324(f189(x68032),f15(x68032,x68033)),f15(x68032,x68031))) % 181.55/181.55 [7435]~P93(x74352)+E(x74351,f191(f871(x74352,a859)))+E(x74353,f191(f871(x74352,a859)))+~P1(f324(f61(x74352),x74351))+~P1(f324(f61(x74352),x74353))+E(f324(f324(f82(x74352),f324(f63(x74352,f82(x74352)),x74353)),f324(f63(x74352,f82(x74352)),x74351)),f324(f63(x74352,f82(x74352)),f324(f324(f113(f871(x74352,a859)),x74353),x74351))) % 181.55/181.55 [7592]~P105(x75922)+E(x75921,f191(f871(x75922,a859)))+E(x75923,f191(f871(x75922,a859)))+~P1(f324(f61(x75922),x75921))+~P1(f324(f61(x75922),x75923))+E(f324(f324(f190(x75922),f11(x75922,f190(x75922),x75923)),f11(x75922,f190(x75922),x75921)),f11(x75922,f190(x75922),f324(f324(f113(f871(x75922,a859)),x75923),x75921))) % 181.55/181.55 [7593]~P105(x75932)+E(x75931,f191(f871(x75932,a859)))+E(x75933,f191(f871(x75932,a859)))+~P1(f324(f61(x75932),x75931))+~P1(f324(f61(x75932),x75933))+E(f324(f324(f189(x75932),f12(x75932,f189(x75932),x75933)),f12(x75932,f189(x75932),x75931)),f12(x75932,f189(x75932),f324(f324(f113(f871(x75932,a859)),x75933),x75931))) % 181.55/181.55 [8621]~P1(f324(x86211,x86213))+P1(f324(x86211,f469(x86211,x86212)))+P1(f324(x86211,f460(x86211,x86212)))+~P1(f324(f324(f239(a1),f2(a1)),x86212))+~P1(f324(f324(f326(a1),x86213),f295(a1,f79(a1),x86212)))+P1(f324(x86211,f324(f324(f22(a1),f460(x86211,x86212)),f324(f324(f82(a1),f468(x86211,x86212)),x86212)))) % 181.55/181.55 [8922]~P1(f324(x89221,x89223))+~P1(f324(x89221,f460(x89221,x89222)))+P1(f324(x89221,f469(x89221,x89222)))+~P1(f324(f324(f239(a1),f2(a1)),x89222))+~P1(f324(f324(f326(a1),x89223),f295(a1,f79(a1),x89222)))+~P1(f324(x89221,f324(f324(f22(a1),f460(x89221,x89222)),f324(f324(f82(a1),f468(x89221,x89222)),x89222)))) % 181.55/181.55 [10137]~P98(x101372)+E(x101371,f191(f871(x101372,a859)))+E(x101373,f191(f871(x101372,a859)))+~P1(f324(f61(x101372),x101371))+~P1(f324(f61(x101372),x101373))+E(f13(x101372,f324(f244(x101372),f324(f324(f8(f871(x101372,a859),a859,x101372),f88(x101372)),f324(f324(f8(f871(x101372,f871(x101372,a859)),f871(x101372,a859),x101372),f324(f8(f871(x101372,a859),a859,x101372),f88(x101372))),f324(f324(f7(x101372,f871(x101372,f871(x101372,a859)),f871(x101372,f871(x101372,a859))),f324(f324(f8(f871(x101372,f871(f871(x101372,a859),f871(x101372,a859))),f871(f871(x101372,f871(x101372,a859)),f871(x101372,f871(x101372,a859))),x101372),f18(x101372,f871(x101372,a859),f871(x101372,a859))),f324(f324(f8(f871(x101372,f871(x101372,f871(a859,a859))),f871(x101372,f871(f871(x101372,a859),f871(x101372,a859))),x101372),f324(f8(f871(x101372,f871(a859,a859)),f871(f871(x101372,a859),f871(x101372,a859)),x101372),f18(x101372,a859,a859))),f324(f324(f8(f871(x101372,f871(x101372,a859)),f871(x101372,f871(x101372,f871(a859,a859))),x101372),f324(f8(f871(x101372,a859),f871(x101372,f871(a859,a859)),x101372),f324(f8(a859,f871(a859,a859),x101372),a322))),f324(f324(f7(x101372,f871(x101372,f871(x101372,x101372)),f871(x101372,f871(x101372,a859))),f324(f324(f8(f871(f871(x101372,x101372),f871(x101372,a859)),f871(f871(x101372,f871(x101372,x101372)),f871(x101372,f871(x101372,a859))),x101372),f8(f871(x101372,x101372),f871(x101372,a859),x101372)),f324(f324(f8(f871(x101372,a859),f871(f871(x101372,x101372),f871(x101372,a859)),x101372),f8(x101372,a859,x101372)),a321))),f104(x101372)))))),f324(f324(f7(x101372,f871(x101372,a859),f871(x101372,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x101372,a859),f871(x101372,a859)),x101372),f8(a859,a859,x101372)),f324(f324(f8(a859,f871(a859,a859),x101372),a322),f324(f324(f7(x101372,f871(x101372,a859),a859),f326(x101372)),x101373)))),f324(f324(f7(x101372,f871(x101372,a859),a859),f326(x101372)),x101371))))))),f324(f324(f104(x101372),f13(x101372,x101373)),f13(x101372,x101371))) % 181.55/181.55 [10138]~P98(x101382)+E(x101381,f191(f871(x101382,a859)))+E(x101383,f191(f871(x101382,a859)))+~P1(f324(f61(x101382),x101381))+~P1(f324(f61(x101382),x101383))+E(f10(x101382,f324(f244(x101382),f324(f324(f8(f871(x101382,a859),a859,x101382),f88(x101382)),f324(f324(f8(f871(x101382,f871(x101382,a859)),f871(x101382,a859),x101382),f324(f8(f871(x101382,a859),a859,x101382),f88(x101382))),f324(f324(f7(x101382,f871(x101382,f871(x101382,a859)),f871(x101382,f871(x101382,a859))),f324(f324(f8(f871(x101382,f871(f871(x101382,a859),f871(x101382,a859))),f871(f871(x101382,f871(x101382,a859)),f871(x101382,f871(x101382,a859))),x101382),f18(x101382,f871(x101382,a859),f871(x101382,a859))),f324(f324(f8(f871(x101382,f871(x101382,f871(a859,a859))),f871(x101382,f871(f871(x101382,a859),f871(x101382,a859))),x101382),f324(f8(f871(x101382,f871(a859,a859)),f871(f871(x101382,a859),f871(x101382,a859)),x101382),f18(x101382,a859,a859))),f324(f324(f8(f871(x101382,f871(x101382,a859)),f871(x101382,f871(x101382,f871(a859,a859))),x101382),f324(f8(f871(x101382,a859),f871(x101382,f871(a859,a859)),x101382),f324(f8(a859,f871(a859,a859),x101382),a322))),f324(f324(f7(x101382,f871(x101382,f871(x101382,x101382)),f871(x101382,f871(x101382,a859))),f324(f324(f8(f871(f871(x101382,x101382),f871(x101382,a859)),f871(f871(x101382,f871(x101382,x101382)),f871(x101382,f871(x101382,a859))),x101382),f8(f871(x101382,x101382),f871(x101382,a859),x101382)),f324(f324(f8(f871(x101382,a859),f871(f871(x101382,x101382),f871(x101382,a859)),x101382),f8(x101382,a859,x101382)),a321))),f113(x101382)))))),f324(f324(f7(x101382,f871(x101382,a859),f871(x101382,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x101382,a859),f871(x101382,a859)),x101382),f8(a859,a859,x101382)),f324(f324(f8(a859,f871(a859,a859),x101382),a322),f324(f324(f7(x101382,f871(x101382,a859),a859),f326(x101382)),x101383)))),f324(f324(f7(x101382,f871(x101382,a859),a859),f326(x101382)),x101381))))))),f324(f324(f113(x101382),f10(x101382,x101383)),f10(x101382,x101381))) % 181.55/181.55 [10139]~P105(x101392)+E(x101391,f191(f871(x101392,a859)))+E(x101393,f191(f871(x101392,a859)))+~P1(f324(f61(x101392),x101391))+~P1(f324(f61(x101392),x101393))+E(f11(x101392,f190(x101392),f324(f244(x101392),f324(f324(f8(f871(x101392,a859),a859,x101392),f88(x101392)),f324(f324(f8(f871(x101392,f871(x101392,a859)),f871(x101392,a859),x101392),f324(f8(f871(x101392,a859),a859,x101392),f88(x101392))),f324(f324(f7(x101392,f871(x101392,f871(x101392,a859)),f871(x101392,f871(x101392,a859))),f324(f324(f8(f871(x101392,f871(f871(x101392,a859),f871(x101392,a859))),f871(f871(x101392,f871(x101392,a859)),f871(x101392,f871(x101392,a859))),x101392),f18(x101392,f871(x101392,a859),f871(x101392,a859))),f324(f324(f8(f871(x101392,f871(x101392,f871(a859,a859))),f871(x101392,f871(f871(x101392,a859),f871(x101392,a859))),x101392),f324(f8(f871(x101392,f871(a859,a859)),f871(f871(x101392,a859),f871(x101392,a859)),x101392),f18(x101392,a859,a859))),f324(f324(f8(f871(x101392,f871(x101392,a859)),f871(x101392,f871(x101392,f871(a859,a859))),x101392),f324(f8(f871(x101392,a859),f871(x101392,f871(a859,a859)),x101392),f324(f8(a859,f871(a859,a859),x101392),a322))),f324(f324(f7(x101392,f871(x101392,f871(x101392,x101392)),f871(x101392,f871(x101392,a859))),f324(f324(f8(f871(f871(x101392,x101392),f871(x101392,a859)),f871(f871(x101392,f871(x101392,x101392)),f871(x101392,f871(x101392,a859))),x101392),f8(f871(x101392,x101392),f871(x101392,a859),x101392)),f324(f324(f8(f871(x101392,a859),f871(f871(x101392,x101392),f871(x101392,a859)),x101392),f8(x101392,a859,x101392)),a321))),f189(x101392)))))),f324(f324(f7(x101392,f871(x101392,a859),f871(x101392,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x101392,a859),f871(x101392,a859)),x101392),f8(a859,a859,x101392)),f324(f324(f8(a859,f871(a859,a859),x101392),a322),f324(f324(f7(x101392,f871(x101392,a859),a859),f326(x101392)),x101393)))),f324(f324(f7(x101392,f871(x101392,a859),a859),f326(x101392)),x101391))))))),f324(f324(f189(x101392),f11(x101392,f190(x101392),x101393)),f11(x101392,f190(x101392),x101391))) % 181.55/181.55 [10140]~P105(x101402)+E(x101401,f191(f871(x101402,a859)))+E(x101403,f191(f871(x101402,a859)))+~P1(f324(f61(x101402),x101401))+~P1(f324(f61(x101402),x101403))+E(f12(x101402,f189(x101402),f324(f244(x101402),f324(f324(f8(f871(x101402,a859),a859,x101402),f88(x101402)),f324(f324(f8(f871(x101402,f871(x101402,a859)),f871(x101402,a859),x101402),f324(f8(f871(x101402,a859),a859,x101402),f88(x101402))),f324(f324(f7(x101402,f871(x101402,f871(x101402,a859)),f871(x101402,f871(x101402,a859))),f324(f324(f8(f871(x101402,f871(f871(x101402,a859),f871(x101402,a859))),f871(f871(x101402,f871(x101402,a859)),f871(x101402,f871(x101402,a859))),x101402),f18(x101402,f871(x101402,a859),f871(x101402,a859))),f324(f324(f8(f871(x101402,f871(x101402,f871(a859,a859))),f871(x101402,f871(f871(x101402,a859),f871(x101402,a859))),x101402),f324(f8(f871(x101402,f871(a859,a859)),f871(f871(x101402,a859),f871(x101402,a859)),x101402),f18(x101402,a859,a859))),f324(f324(f8(f871(x101402,f871(x101402,a859)),f871(x101402,f871(x101402,f871(a859,a859))),x101402),f324(f8(f871(x101402,a859),f871(x101402,f871(a859,a859)),x101402),f324(f8(a859,f871(a859,a859),x101402),a322))),f324(f324(f7(x101402,f871(x101402,f871(x101402,x101402)),f871(x101402,f871(x101402,a859))),f324(f324(f8(f871(f871(x101402,x101402),f871(x101402,a859)),f871(f871(x101402,f871(x101402,x101402)),f871(x101402,f871(x101402,a859))),x101402),f8(f871(x101402,x101402),f871(x101402,a859),x101402)),f324(f324(f8(f871(x101402,a859),f871(f871(x101402,x101402),f871(x101402,a859)),x101402),f8(x101402,a859,x101402)),a321))),f190(x101402)))))),f324(f324(f7(x101402,f871(x101402,a859),f871(x101402,a859)),f324(f324(f8(f871(a859,a859),f871(f871(x101402,a859),f871(x101402,a859)),x101402),f8(a859,a859,x101402)),f324(f324(f8(a859,f871(a859,a859),x101402),a322),f324(f324(f7(x101402,f871(x101402,a859),a859),f326(x101402)),x101403)))),f324(f324(f7(x101402,f871(x101402,a859),a859),f326(x101402)),x101401))))))),f324(f324(f190(x101402),f12(x101402,f189(x101402),x101403)),f12(x101402,f189(x101402),x101401))) % 181.55/181.55 [7122]~P120(x71223)+E(x71221,x71222)+~E(f324(f324(f249(x71223),x71221),x71224),f324(f324(f249(x71223),x71222),x71224))+~P1(f324(f324(f238(x71223),f2(x71223)),x71222))+~P1(f324(f324(f238(x71223),f2(x71223)),x71221))+~P1(f324(f324(f239(a865),f2(a865)),x71224)) % 181.55/181.55 [7392]~P105(x73922)+E(x73921,f191(f871(x73922,a859)))+~P1(f324(f61(x73922),x73921))+~P1(f324(f324(f326(x73922),x73924),x73921))+P1(f324(f324(f238(x73922),x73923),x73924))+~P1(f324(f324(f238(x73922),x73923),f324(f63(x73922,f189(x73922)),x73921))) % 181.55/181.55 [7393]~P99(x73932)+E(x73931,f191(f871(x73932,a859)))+~P1(f324(f61(x73932),x73931))+~P1(f324(f324(f326(x73932),x73934),x73931))+P1(f324(f324(f238(x73932),x73933),x73934))+~P1(f324(f324(f238(x73932),x73933),f324(f63(x73932,f104(x73932)),x73931))) % 181.55/181.55 [7394]~P105(x73942)+E(x73941,f191(f871(x73942,a859)))+~P1(f324(f61(x73942),x73941))+~P1(f324(f324(f326(x73942),x73944),x73941))+P1(f324(f324(f239(x73942),x73943),x73944))+~P1(f324(f324(f239(x73942),x73943),f324(f63(x73942,f189(x73942)),x73941))) % 181.55/181.55 [7293]E(x72931,f2(a1))+E(f324(f324(f38(a1),x72932),x72931),x72933)+~P1(f324(f324(f238(a1),x72934),f2(a1)))+~E(x72932,f324(f324(f81(a1),f324(f324(f82(a1),x72931),x72933)),x72934))+P1(f324(f324(f239(a1),f2(a1)),x72931))+~P1(f324(f324(f239(a1),x72931),x72934)) % 181.55/181.55 [7309]E(f44(a1,x73092,x73091),x73093)+E(x73091,f2(a1))+~P1(f324(f324(f238(a1),x73093),f2(a1)))+~E(x73092,f324(f324(f81(a1),f324(f324(f82(a1),x73091),x73094)),x73093))+P1(f324(f324(f239(a1),f2(a1)),x73091))+~P1(f324(f324(f239(a1),x73091),x73093)) % 181.55/181.55 [7434]E(x74341,f2(a1))+E(f324(f324(f38(a1),x74342),x74341),x74343)+~E(x74342,f324(f324(f81(a1),f324(f324(f82(a1),x74341),x74343)),x74344))+~P1(f324(f324(f238(a1),f2(a1)),x74344))+~P1(f324(f324(f239(a1),f2(a1)),x74341))+~P1(f324(f324(f239(a1),x74344),x74341)) % 181.55/181.55 [7456]E(f44(a1,x74562,x74561),x74563)+E(x74561,f2(a1))+~E(x74562,f324(f324(f81(a1),f324(f324(f82(a1),x74561),x74564)),x74563))+~P1(f324(f324(f238(a1),f2(a1)),x74563))+~P1(f324(f324(f239(a1),f2(a1)),x74561))+~P1(f324(f324(f239(a1),x74563),x74561)) % 181.55/181.55 [7596]~P105(x75962)+E(x75961,f191(f871(x75962,a859)))+~P1(f324(f61(x75962),x75961))+~P1(f324(f324(f238(x75962),x75964),x75963))+~P1(f324(f324(f326(x75962),x75964),x75961))+P1(f324(f324(f238(x75962),f324(f63(x75962,f189(x75962)),x75961)),x75963)) % 181.55/181.55 [7597]~P105(x75972)+E(x75971,f191(f871(x75972,a859)))+~P1(f324(f61(x75972),x75971))+~P1(f324(f324(f239(x75972),x75974),x75973))+~P1(f324(f324(f326(x75972),x75974),x75971))+P1(f324(f324(f239(x75972),f324(f63(x75972,f189(x75972)),x75971)),x75973)) % 181.55/181.55 [8160]~P1(f324(f324(f238(a1),x81604),f2(a1)))+~E(x81601,f324(f324(f81(a1),f324(f324(f82(a1),x81602),x81603)),x81604))+~P1(f324(f324(f238(a1),f2(a1)),x81604))+~P1(f324(f324(f239(a1),x81604),x81602))+~P1(f324(f324(f239(a1),x81602),x81604))+P1(f324(f48(x81601,x81602),f324(f324(f259(a1,a1),x81603),x81604))) % 181.55/181.55 [9119]~P61(x91193)+~P61(x91194)+E(x91191,x91192)+~E(f324(f192(f866(x91193)),x91192),f324(f192(f866(x91194)),f55(x91194)))+~E(f324(f192(f866(x91193)),x91191),f324(f192(f866(x91194)),f55(x91194)))+~E(f324(f73(f869(x91193),x91193,x91194,f237(x91193)),f324(f173(x91194,x91193),f324(f324(f177(x91194,x91193),f55(x91194)),x91191))),f324(f73(f869(x91193),x91193,x91194,f237(x91193)),f324(f173(x91194,x91193),f324(f324(f177(x91194,x91193),f55(x91194)),x91192)))) % 181.55/181.55 [8329]~P106(x83291)+P1(f324(f324(f239(f871(x83291,a859)),f295(x83291,x83292,x83293)),f295(x83291,x83294,x83295)))+~P1(f324(f324(f238(x83291),x83294),x83292))+~P1(f324(f324(f238(x83291),x83294),x83295))+~P1(f324(f324(f238(x83291),x83293),x83295))+~P1(f324(f324(f239(x83291),x83293),x83295)) % 181.55/181.55 [8330]~P106(x83301)+P1(f324(f324(f239(f871(x83301,a859)),f295(x83301,x83302,x83303)),f295(x83301,x83304,x83305)))+~P1(f324(f324(f238(x83301),x83303),x83305))+~P1(f324(f324(f238(x83301),x83304),x83305))+~P1(f324(f324(f238(x83301),x83304),x83302))+~P1(f324(f324(f239(x83301),x83304),x83302)) % 181.55/181.55 [9183]P56(x91832,x91833,x91834,x91831)+E(x91831,f191(f871(x91832,a859)))+~P1(f324(f61(x91832),x91834))+~P1(f324(f61(x91832),x91831))+~P1(f324(f324(x91833,f335(x91831,x91834,x91833,x91832)),x91835))+~P1(f324(f324(f326(x91832),x91835),x91831)) % 181.55/181.55 [9331]~E(x93313,x93315)+~P68(x93311)+~P72(x93311)+~P40(x93313)+E(f324(f324(f9(a1,x93311),x93312),x93313),f324(f324(f9(a1,x93311),x93314),x93315))+P1(f324(f324(f238(a1),f2(a1)),f513(x93312,x93314,x93313,x93315,x93311))) % 181.55/181.55 [9332]~E(x93323,x93325)+~P68(x93321)+~P72(x93321)+~P40(x93323)+E(f324(f324(f6(a1,x93321),x93322),x93323),f324(f324(f6(a1,x93321),x93324),x93325))+P1(f324(f324(f238(a1),f2(a1)),f515(x93322,x93324,x93323,x93325,x93321))) % 181.55/181.55 [9508]~E(x95085,x95083)+~P68(x95081)+~P72(x95081)+~P40(x95085)+~E(f324(x95082,f513(x95084,x95082,x95085,x95083,x95081)),f324(x95084,f513(x95084,x95082,x95085,x95083,x95081)))+E(f324(f324(f9(a1,x95081),x95082),x95083),f324(f324(f9(a1,x95081),x95084),x95085)) % 181.55/181.55 [9509]~E(x95095,x95093)+~P68(x95091)+~P72(x95091)+~P40(x95095)+~E(f324(x95092,f515(x95094,x95092,x95095,x95093,x95091)),f324(x95094,f515(x95094,x95092,x95095,x95093,x95091)))+E(f324(f324(f6(a1,x95091),x95092),x95093),f324(f324(f6(a1,x95091),x95094),x95095)) % 181.55/181.55 [9600]~P75(x96003)+E(f324(x96001,x96002),f2(x96003))+~E(f324(f324(f6(x96004,x96003),x96001),x96005),f2(x96003))+~P1(f324(f61(x96004),x96005))+P1(f324(f324(f326(x96004),f503(x96002,x96001,x96005,x96004,x96003)),x96005))+~P1(f324(f324(f326(x96004),x96002),x96005)) % 181.55/181.55 [9737]~P75(x97373)+E(f324(x97371,x97372),f2(x97373))+~E(f324(f324(f6(x97374,x97373),x97371),x97375),f2(x97373))+~P1(f324(f61(x97374),x97375))+~P1(f324(f324(f326(x97374),x97372),x97375))+~P1(f324(f324(f238(x97373),f2(x97373)),f324(x97371,f503(x97372,x97371,x97375,x97374,x97373)))) % 181.55/181.55 [8243]~P132(x82431)+~P1(f324(f324(f238(x82431),x82433),x82435))+~P1(f324(f324(f238(x82431),x82432),x82434))+~P1(f324(f324(f238(x82431),f2(x82431)),x82433))+~P1(f324(f324(f238(x82431),f2(x82431)),x82434))+P1(f324(f324(f238(x82431),f324(f324(f82(x82431),x82432),x82433)),f324(f324(f82(x82431),x82434),x82435))) % 181.55/181.55 [8244]~P132(x82441)+~P1(f324(f324(f238(x82441),x82443),x82445))+~P1(f324(f324(f238(x82441),x82442),x82444))+~P1(f324(f324(f238(x82441),f2(x82441)),x82443))+~P1(f324(f324(f238(x82441),f2(x82441)),x82442))+P1(f324(f324(f238(x82441),f324(f324(f82(x82441),x82442),x82443)),f324(f324(f82(x82441),x82444),x82445))) % 181.55/181.55 [8245]~P65(x82451)+~P1(f324(f324(f239(x82451),f2(x82451)),x82455))+~P1(f324(f324(f238(x82451),x82455),x82453))+~P1(f324(f324(f238(x82451),x82452),x82454))+~P1(f324(f324(f238(x82451),f2(x82451)),x82452))+P1(f324(f324(f238(x82451),f324(f324(f282(x82451),x82452),x82453)),f324(f324(f282(x82451),x82454),x82455))) % 181.55/181.55 [8246]~P126(x82461)+~P1(f324(f324(f238(x82461),x82463),x82465))+~P1(f324(f324(f238(x82461),f2(x82461)),x82462))+~P1(f324(f324(f239(x82461),x82462),x82464))+~P1(f324(f324(f239(x82461),f2(x82461)),x82463))+P1(f324(f324(f239(x82461),f324(f324(f82(x82461),x82462),x82463)),f324(f324(f82(x82461),x82464),x82465))) % 181.55/181.55 [8247]~P126(x82471)+~P1(f324(f324(f238(x82471),x82472),x82474))+~P1(f324(f324(f238(x82471),f2(x82471)),x82473))+~P1(f324(f324(f239(x82471),x82473),x82475))+~P1(f324(f324(f239(x82471),f2(x82471)),x82472))+P1(f324(f324(f239(x82471),f324(f324(f82(x82471),x82472),x82473)),f324(f324(f82(x82471),x82474),x82475))) % 181.55/181.55 [8248]~P126(x82481)+~P1(f324(f324(f238(x82481),f2(x82481)),x82483))+~P1(f324(f324(f238(x82481),f2(x82481)),x82482))+~P1(f324(f324(f239(x82481),x82483),x82485))+~P1(f324(f324(f239(x82481),x82482),x82484))+P1(f324(f324(f239(x82481),f324(f324(f82(x82481),x82482),x82483)),f324(f324(f82(x82481),x82484),x82485))) % 181.55/181.55 [8249]~P126(x82491)+~P1(f324(f324(f238(x82491),f2(x82491)),x82493))+~P1(f324(f324(f239(x82491),x82493),x82495))+~P1(f324(f324(f239(x82491),x82492),x82494))+~P1(f324(f324(f239(x82491),f2(x82491)),x82494))+P1(f324(f324(f239(x82491),f324(f324(f82(x82491),x82492),x82493)),f324(f324(f82(x82491),x82494),x82495))) % 181.55/181.55 [8250]~P65(x82501)+~P1(f324(f324(f238(x82501),x82505),x82503))+~P1(f324(f324(f238(x82501),f2(x82501)),x82502))+~P1(f324(f324(f239(x82501),x82502),x82504))+~P1(f324(f324(f239(x82501),f2(x82501)),x82505))+P1(f324(f324(f239(x82501),f324(f324(f282(x82501),x82502),x82503)),f324(f324(f282(x82501),x82504),x82505))) % 181.55/181.55 [8251]~P65(x82511)+~P1(f324(f324(f238(x82511),x82512),x82514))+~P1(f324(f324(f239(x82511),x82515),x82513))+~P1(f324(f324(f239(x82511),f2(x82511)),x82515))+~P1(f324(f324(f239(x82511),f2(x82511)),x82512))+P1(f324(f324(f239(x82511),f324(f324(f282(x82511),x82512),x82513)),f324(f324(f282(x82511),x82514),x82515))) % 181.55/181.55 [9641]~P84(x96415)+~P72(x96415)+E(x96411,f191(f871(x96412,a859)))+~P1(f324(f61(x96412),x96411))+P1(f324(f324(f326(x96412),f508(x96413,x96414,x96411,x96412,x96415)),x96411))+P1(f324(f324(f239(x96415),f324(f324(f6(x96412,x96415),x96414),x96411)),f324(f324(f6(x96412,x96415),x96413),x96411))) % 181.55/181.55 [9759]~P82(x97591)+~P72(x97591)+~P1(f324(f61(x97592),x97595))+~P1(f324(f324(f238(x97591),f2(x97591)),f324(x97593,f496(x97593,x97594,x97595,x97592,x97591))))+P1(f324(f324(f238(x97591),f324(f324(f6(x97592,x97591),x97593),x97594)),f324(f324(f6(x97592,x97591),x97593),x97595)))+~P1(f324(f324(f238(f871(x97592,a859)),x97594),x97595)) % 181.55/181.55 [9926]~P84(x99263)+~P72(x99263)+E(x99261,f191(f871(x99262,a859)))+~P1(f324(f61(x99262),x99261))+~P1(f324(f324(f239(x99263),f324(x99264,f508(x99265,x99264,x99261,x99262,x99263))),f324(x99265,f508(x99265,x99264,x99261,x99262,x99263))))+P1(f324(f324(f239(x99263),f324(f324(f6(x99262,x99263),x99264),x99261)),f324(f324(f6(x99262,x99263),x99265),x99261))) % 181.55/181.55 [6982]~P19(x69822,x69825,x69824)+E(x69821,f191(f871(x69822,a859)))+E(x69823,f191(f871(x69822,a859)))+~P1(f324(f61(x69822),x69821))+~P1(f324(f61(x69822),x69823))+E(f324(x69824,f324(f324(f113(f871(x69822,a859)),x69823),x69821)),f324(f324(x69825,f324(x69824,x69823)),f324(x69824,x69821))) % 181.55/181.55 [7562]~P144(x75621,x75624,x75623)+P1(f324(x75621,x75622))+~P1(f324(f324(f239(a1),x75624),f2(a1)))+~P1(f324(f324(f238(a1),x75625),f2(a1)))+~E(x75623,f324(f324(f81(a1),f324(f324(f82(a1),x75624),x75622)),x75625))+~P1(f324(f324(f239(a1),x75624),x75625)) % 181.55/181.55 [7563]~P143(x75631,x75634,x75633)+P1(f324(x75631,x75632))+~P1(f324(f324(f239(a1),x75634),f2(a1)))+~P1(f324(f324(f238(a1),x75632),f2(a1)))+~E(x75633,f324(f324(f81(a1),f324(f324(f82(a1),x75634),x75635)),x75632))+~P1(f324(f324(f239(a1),x75634),x75632)) % 181.55/181.55 [7605]~P144(x76051,x76054,x76053)+P1(f324(x76051,x76052))+~E(x76053,f324(f324(f81(a1),f324(f324(f82(a1),x76054),x76052)),x76055))+~P1(f324(f324(f238(a1),f2(a1)),x76055))+~P1(f324(f324(f239(a1),f2(a1)),x76054))+~P1(f324(f324(f239(a1),x76055),x76054)) % 181.55/181.55 [7606]~P143(x76061,x76064,x76063)+P1(f324(x76061,x76062))+~E(x76063,f324(f324(f81(a1),f324(f324(f82(a1),x76064),x76065)),x76062))+~P1(f324(f324(f238(a1),f2(a1)),x76062))+~P1(f324(f324(f239(a1),f2(a1)),x76064))+~P1(f324(f324(f239(a1),x76062),x76064)) % 181.55/181.55 [8533]P1(f324(f324(x85331,x85332),x85333))+~P1(f324(f324(x85331,f324(f324(f38(a1),x85334),x85335)),f44(a1,x85334,x85335)))+~P1(f324(f324(f239(a1),x85335),f2(a1)))+~P1(f324(f324(f238(a1),x85333),f2(a1)))+~E(x85334,f324(f324(f81(a1),f324(f324(f82(a1),x85335),x85332)),x85333))+~P1(f324(f324(f239(a1),x85335),x85333)) % 181.55/181.55 [8542]P1(f324(f324(x85421,x85422),x85423))+~P1(f324(f324(x85421,f324(f324(f38(a1),x85424),x85425)),f44(a1,x85424,x85425)))+~E(x85424,f324(f324(f81(a1),f324(f324(f82(a1),x85425),x85422)),x85423))+~P1(f324(f324(f238(a1),f2(a1)),x85423))+~P1(f324(f324(f239(a1),f2(a1)),x85425))+~P1(f324(f324(f239(a1),x85423),x85425)) % 181.55/181.55 [8798]E(x87981,x87982)+~P53(x87983,x87985,x87984)+~P1(f324(f324(f326(x87983),x87982),x87985))+~P1(f324(f324(f326(x87983),x87981),x87985))+P1(f324(f324(f326(f870(x87983,x87983)),f324(f324(f259(x87983,x87983),x87981),x87982)),x87984))+P1(f324(f324(f326(f870(x87983,x87983)),f324(f324(f259(x87983,x87983),x87982),x87981)),x87984)) % 181.55/181.55 [9669]~P82(x96695)+~P72(x96695)+~P1(f324(f61(x96691),x96694))+P1(f324(f324(f238(x96695),f324(f324(f6(x96691,x96695),x96692),x96693)),f324(f324(f6(x96691,x96695),x96692),x96694)))+~P1(f324(f324(f238(f871(x96691,a859)),x96693),x96694))+P1(f324(f324(f326(x96691),f496(x96692,x96693,x96694,x96691,x96695)),f324(f324(f22(f871(x96691,a859)),x96694),x96693))) % 181.55/181.55 [9767]E(x97671,f191(f871(x97672,a859)))+~P1(f324(f61(x97672),x97673))+~P1(f324(f61(x97672),x97671))+P1(f324(f324(f326(f870(f871(x97672,a859),f871(x97672,a859))),f324(f324(f259(f871(x97672,a859),f871(x97672,a859)),x97673),x97671)),f315(x97672,x97674)))+~P1(f324(f324(f326(x97672),x97675),x97671))+~P1(f324(f324(f326(f870(x97672,x97672)),f324(f324(f259(x97672,x97672),f849(x97674,x97671,x97673,x97672)),x97675)),x97674)) % 181.55/181.55 [9768]E(x97681,f191(f871(x97682,a859)))+~P1(f324(f61(x97682),x97683))+~P1(f324(f61(x97682),x97681))+P1(f324(f324(f326(f870(f871(x97682,a859),f871(x97682,a859))),f324(f324(f259(f871(x97682,a859),f871(x97682,a859)),x97683),x97681)),f315(x97682,x97684)))+~P1(f324(f324(f326(x97682),x97685),x97681))+~P1(f324(f324(f326(f870(x97682,x97682)),f324(f324(f259(x97682,x97682),f576(x97684,x97681,x97683,x97682)),x97685)),x97684)) % 181.55/181.55 [9930]~P75(x99301)+~E(f324(f324(f6(x99305,x99301),x99302),x99306),x99304)+~P1(f324(f61(x99305),x99306))+P1(f324(f324(f326(x99305),f505(x99303,x99304,x99302,x99306,x99305,x99301)),x99306))+P1(f324(f324(f238(x99301),f324(x99302,x99303)),x99304))+~P1(f324(f324(f326(x99305),x99303),x99306)) % 181.55/181.55 [9977]~P75(x99771)+~E(f324(f324(f6(x99775,x99771),x99772),x99776),x99774)+~P1(f324(f61(x99775),x99776))+~P1(f324(f324(f326(x99775),x99773),x99776))+~P1(f324(f324(f238(x99771),f2(x99771)),f324(x99772,f505(x99773,x99774,x99772,x99776,x99775,x99771))))+P1(f324(f324(f238(x99771),f324(x99772,x99773)),x99774)) % 181.55/181.55 [10090]~E(x100905,x100908)+~E(x100904,x100907)+~P104(x100901)+~P72(x100902)+E(f324(f324(f6(x100901,x100902),x100903),f324(f294(x100901,x100904),x100905)),f324(f324(f6(x100901,x100902),x100906),f324(f294(x100901,x100907),x100908)))+P1(f324(f324(f238(x100901),x100904),f586(x100903,x100906,x100905,x100908,x100904,x100907,x100901,x100902))) % 181.55/181.55 [10106]~E(x101067,x101064)+~E(x101068,x101065)+~P104(x101061)+~P72(x101062)+~E(f324(x101063,f586(x101066,x101063,x101068,x101065,x101067,x101064,x101061,x101062)),f324(x101066,f586(x101066,x101063,x101068,x101065,x101067,x101064,x101061,x101062)))+E(f324(f324(f6(x101061,x101062),x101063),f324(f294(x101061,x101064),x101065)),f324(f324(f6(x101061,x101062),x101066),f324(f294(x101061,x101067),x101068))) % 181.55/181.55 [10108]~E(x101084,x101087)+~E(x101085,x101088)+~P104(x101081)+~P72(x101082)+E(f324(f324(f6(x101081,x101082),x101083),f324(f294(x101081,x101084),x101085)),f324(f324(f6(x101081,x101082),x101086),f324(f294(x101081,x101087),x101088)))+P1(f324(f324(f239(x101081),f586(x101083,x101086,x101085,x101088,x101084,x101087,x101081,x101082)),x101085)) % 181.55/181.55 [9774]~P9(x97745,x97749,x97746)+~P9(x97741,x977410,x97743)+~P15(x97741,x97745,f871(x97742,a859),x97743,x97746,x97748)+~P1(f324(f324(f326(x97745),x97747),x97749))+~P1(f324(f324(f326(x97741),x97744),x977410))+E(f324(f324(f41(x97741,f871(x97742,a859)),f324(f278(x97741,x97741,x97743),f324(f324(f302(x97741),x97744),f191(f871(x97741,a859))))),f324(f324(f8(f871(x97745,f871(x97742,a859)),f871(x97742,a859),x97741),f324(f41(x97745,f871(x97742,a859)),f324(f278(x97745,x97745,x97746),f324(f324(f302(x97745),x97747),f191(f871(x97745,a859)))))),x97748)),f324(f324(x97748,x97744),x97747)) % 181.55/181.55 [5549]~P105(x55493)+~P16(x55493,x55492)+~P16(x55493,x55491)+E(x55491,x55492)+~E(f324(f167(x55493),x55491),f324(f167(x55493),x55492))+~P1(f324(f131(x55493),x55492))+~P1(f324(f131(x55493),x55491)) % 181.55/181.55 [4908]~P124(x49082)+~P125(x49082)+~P139(x49082)+~P110(x49082)+~E(x49083,f2(x49082))+E(x49081,f2(a865))+E(f324(f324(f249(x49082),x49083),x49081),f2(x49082)) % 181.55/181.55 [9060]E(x90601,f2(a865))+~E(x90602,f324(f324(f81(a865),f324(f324(f82(a865),f324(f258(a865,a865),x90603)),x90601)),f324(f262(a865,a865),x90603)))+P1(f324(f47(x90602,x90601),x90603))+~P1(f324(f324(f238(a865),f324(f262(a865,a865),x90603)),f2(a865)))+~P1(f324(f324(f238(a865),f2(a865)),f324(f262(a865,a865),x90603)))+~P1(f324(f324(f239(a865),x90601),f324(f262(a865,a865),x90603)))+~P1(f324(f324(f239(a865),f324(f262(a865,a865),x90603)),x90601)) % 181.55/181.55 [9069]~E(f324(f258(a865,a865),x90693),f2(a865))+~E(x90691,f324(f324(f81(a865),f324(f324(f82(a865),f324(f258(a865,a865),x90693)),x90692)),f324(f262(a865,a865),x90693)))+P1(f324(f47(x90691,x90692),x90693))+~P1(f324(f324(f238(a865),f324(f262(a865,a865),x90693)),f2(a865)))+~P1(f324(f324(f238(a865),f2(a865)),f324(f262(a865,a865),x90693)))+~P1(f324(f324(f239(a865),x90692),f324(f262(a865,a865),x90693)))+~P1(f324(f324(f239(a865),f324(f262(a865,a865),x90693)),x90692)) % 181.55/181.55 [7912]~P66(x79122)+E(x79121,f191(f871(x79122,a859)))+E(x79123,f191(f871(x79122,a859)))+~P1(f324(f61(x79122),x79121))+~P1(f324(f61(x79122),x79123))+~E(f324(f324(f104(f871(x79122,a859)),x79123),x79121),f191(f871(x79122,a859)))+E(f324(f324(f82(x79122),f324(f63(x79122,f82(x79122)),x79123)),f324(f63(x79122,f82(x79122)),x79121)),f324(f63(x79122,f82(x79122)),f324(f324(f113(f871(x79122,a859)),x79123),x79121))) % 181.55/181.55 [7697]E(x76971,f2(a1))+E(f324(f324(f38(a1),x76972),x76971),x76973)+~P1(f324(f324(f238(a1),x76974),f2(a1)))+~E(x76972,f324(f324(f81(a1),f324(f324(f82(a1),x76971),x76973)),x76974))+~P1(f324(f324(f238(a1),f2(a1)),x76974))+~P1(f324(f324(f239(a1),x76974),x76971))+~P1(f324(f324(f239(a1),x76971),x76974)) % 181.55/181.55 [7704]E(f44(a1,x77042,x77041),x77043)+E(x77041,f2(a1))+~P1(f324(f324(f238(a1),x77043),f2(a1)))+~E(x77042,f324(f324(f81(a1),f324(f324(f82(a1),x77041),x77044)),x77043))+~P1(f324(f324(f238(a1),f2(a1)),x77043))+~P1(f324(f324(f239(a1),x77043),x77041))+~P1(f324(f324(f239(a1),x77041),x77043)) % 181.55/181.55 [7613]~P20(x76132,x76135,x76134)+E(x76131,f191(f871(x76132,a859)))+E(x76133,f191(f871(x76132,a859)))+~P1(f324(f61(x76132),x76131))+~P1(f324(f61(x76132),x76133))+~E(f324(f324(f104(f871(x76132,a859)),x76133),x76131),f191(f871(x76132,a859)))+E(f324(x76134,f324(f324(f113(f871(x76132,a859)),x76133),x76131)),f324(f324(x76135,f324(x76134,x76133)),f324(x76134,x76131))) % 181.55/181.55 [9304]~P27(x93043,x93041,x93045,x93044)+~P27(x93041,x93043,x93046,x93042)+E(f324(f37(x93041),x93042),f324(f37(x93043),x93044))+~P1(f324(f61(x93043),x93044))+~P1(f324(f61(x93041),x93042))+~P1(f324(f324(f238(f871(x93043,a859)),f324(f303(x93041,x93043,x93046),x93042)),x93044))+~P1(f324(f324(f238(f871(x93041,a859)),f324(f303(x93043,x93041,x93045),x93044)),x93042)) % 181.55/181.55 [9246]~P1(f324(f324(f239(a1),f324(f324(f81(a1),f324(f324(f82(a1),x92465),x92461)),x92466)),f2(a1)))+~E(f324(f324(f81(a1),f324(f324(f82(a1),x92463),x92462)),x92464),f324(f324(f81(a1),f324(f324(f82(a1),x92465),x92461)),x92466))+~P1(f324(f324(f238(a1),f2(a1)),x92466))+~P1(f324(f324(f239(a1),f2(a1)),x92465))+~P1(f324(f324(f238(a1),x92465),x92463))+~P1(f324(f324(f239(a1),x92464),x92463))+P1(f324(f324(f238(a1),x92461),x92462)) % 181.55/181.55 [9012]~E(f324(f324(f81(a1),f324(f324(f82(a1),x90123),x90121)),x90124),f324(f324(f81(a1),f324(f324(f82(a1),x90125),x90122)),x90126))+~P1(f324(f324(f238(a1),f2(a1)),x90124))+~P1(f324(f324(f239(a1),f2(a1)),x90125))+~P1(f324(f324(f238(a1),x90125),x90123))+~P1(f324(f324(f239(a1),x90126),x90125))+P1(f324(f324(f238(a1),x90121),x90122))+~P1(f324(f324(f238(a1),f2(a1)),f324(f324(f81(a1),f324(f324(f82(a1),x90125),x90122)),x90126))) % 181.55/181.55 [9189]~P128(x91891)+~E(f324(f324(f81(x91891),x91892),x91894),f79(x91891))+~P1(f324(f324(f238(x91891),x91895),x91896))+~P1(f324(f324(f238(x91891),x91893),x91896))+~P1(f324(f324(f238(x91891),f2(x91891)),x91894))+~P1(f324(f324(f238(x91891),f2(x91891)),x91892))+P1(f324(f324(f238(x91891),f324(f324(f81(x91891),f324(f324(f82(x91891),x91892),x91893)),f324(f324(f82(x91891),x91894),x91895))),x91896)) % 181.55/181.55 [9190]~P129(x91901)+~E(f324(f324(f81(x91901),x91902),x91904),f79(x91901))+~P1(f324(f324(f238(x91901),f2(x91901)),x91904))+~P1(f324(f324(f238(x91901),f2(x91901)),x91902))+~P1(f324(f324(f239(x91901),x91905),x91906))+~P1(f324(f324(f239(x91901),x91903),x91906))+P1(f324(f324(f239(x91901),f324(f324(f81(x91901),f324(f324(f82(x91901),x91902),x91903)),f324(f324(f82(x91901),x91904),x91905))),x91906)) % 181.55/181.55 [10021]~P9(x100217,x100216,x100215)+E(x100211,x100212)+~P14(x100217,f871(x100214,a859),x100215,x100213)+E(f324(x100213,f807(x100211,x100212,x100213,x100214,x100215,x100216,x100217)),f324(x100213,f800(x100211,x100212,x100213,x100214,x100215,x100216,x100217)))+~E(f324(f324(f41(x100217,f871(x100214,a859)),x100211),x100213),f324(f324(f41(x100217,f871(x100214,a859)),x100212),x100213))+~P1(f324(f324(f326(f871(x100217,a859)),x100212),f324(f324(f60(x100217),x100216),x100215)))+~P1(f324(f324(f326(f871(x100217,a859)),x100211),f324(f324(f60(x100217),x100216),x100215))) % 181.55/181.55 [10054]~P9(x100543,x100547,x100546)+E(x100541,x100542)+~P14(x100543,f871(x100545,a859),x100546,x100544)+~E(f324(f324(f41(x100543,f871(x100545,a859)),x100541),x100544),f324(f324(f41(x100543,f871(x100545,a859)),x100542),x100544))+P1(f324(f324(f326(x100543),f800(x100541,x100542,x100544,x100545,x100546,x100547,x100543)),x100547))+~P1(f324(f324(f326(f871(x100543,a859)),x100542),f324(f324(f60(x100543),x100547),x100546)))+~P1(f324(f324(f326(f871(x100543,a859)),x100541),f324(f324(f60(x100543),x100547),x100546))) % 181.55/181.55 [10055]~P9(x100553,x100557,x100556)+E(x100551,x100552)+~P14(x100553,f871(x100555,a859),x100556,x100554)+~E(f324(f324(f41(x100553,f871(x100555,a859)),x100551),x100554),f324(f324(f41(x100553,f871(x100555,a859)),x100552),x100554))+P1(f324(f324(f326(x100553),f807(x100551,x100552,x100554,x100555,x100556,x100557,x100553)),x100557))+~P1(f324(f324(f326(f871(x100553,a859)),x100552),f324(f324(f60(x100553),x100557),x100556)))+~P1(f324(f324(f326(f871(x100553,a859)),x100551),f324(f324(f60(x100553),x100557),x100556))) % 181.55/181.55 [10123]E(x101231,x101232)+~P9(x101233,x101236,x101237)+~P14(x101233,f871(x101234,a859),x101237,x101235)+~E(f324(f324(f41(x101233,f871(x101234,a859)),x101231),x101235),f324(f324(f41(x101233,f871(x101234,a859)),x101232),x101235))+~P1(f324(f324(f326(f870(x101233,x101233)),f324(f324(f259(x101233,x101233),f800(x101231,x101232,x101235,x101234,x101237,x101236,x101233)),f807(x101231,x101232,x101235,x101234,x101237,x101236,x101233))),x101237))+~P1(f324(f324(f326(f871(x101233,a859)),x101232),f324(f324(f60(x101233),x101236),x101237)))+~P1(f324(f324(f326(f871(x101233,a859)),x101231),f324(f324(f60(x101233),x101236),x101237))) % 181.55/181.55 [9011]~P9(x90111,x90117,x90114)+~E(x90115,x90116)+~P1(f324(f324(f326(x90111),x90113),x90116))+~P1(f324(f324(f326(x90111),x90112),x90115))+~P1(f324(f324(f326(f871(x90111,a859)),x90116),f324(f324(f60(x90111),x90117),x90114)))+~P1(f324(f324(f326(f871(x90111,a859)),x90115),f324(f324(f60(x90111),x90117),x90114)))+P1(f324(f324(f326(f870(x90111,x90111)),f324(f324(f259(x90111,x90111),x90112),x90113)),x90114)) % 181.55/181.55 [9151]E(x91511,x91512)+~P9(x91513,x91514,x91515)+~P1(f324(f324(f326(x91513),x91516),x91512))+~P1(f324(f324(f326(x91513),x91517),x91511))+~P1(f324(f324(f326(f871(x91513,a859)),x91512),f324(f324(f60(x91513),x91514),x91515)))+~P1(f324(f324(f326(f871(x91513,a859)),x91511),f324(f324(f60(x91513),x91514),x91515)))+~P1(f324(f324(f326(f870(x91513,x91513)),f324(f324(f259(x91513,x91513),x91517),x91516)),x91515)) % 181.55/181.55 [10142]~P9(x101429,x101428,x101427)+~P9(x101421,x1014211,x1014210)+~P15(x101421,x101429,f871(x101426,a859),x1014210,x101427,x101425)+P1(f324(f324(f326(x101421),f740(x101422,x101423,x101424,x101425,x101426,x101427,x101428,x101429,x1014210,x1014211,x101421)),x1014211))+~P1(f324(f324(f326(f871(x101429,a859)),x101423),f324(f324(f60(x101429),x101428),x101427)))+~P1(f324(f324(f326(f871(x101421,a859)),x101424),f324(f324(f60(x101421),x1014211),x1014210)))+P1(f324(f324(f326(f871(x101426,a859)),f324(f324(f41(x101421,f871(x101426,a859)),x101424),f324(f324(f8(f871(x101429,f871(x101426,a859)),f871(x101426,a859),x101421),f324(f41(x101429,f871(x101426,a859)),x101423)),x101425))),x101422)) % 181.55/181.55 [10143]~P9(x1014311,x1014310,x101439)+~P9(x101431,x101438,x101437)+~P15(x1014311,x101431,f871(x101436,a859),x101439,x101437,x101435)+P1(f324(f324(f326(x101431),f750(x101432,x101433,x101434,x101435,x101436,x101437,x101438,x101431,x101439,x1014310,x1014311)),x101438))+~P1(f324(f324(f326(f871(x1014311,a859)),x101434),f324(f324(f60(x1014311),x1014310),x101439)))+~P1(f324(f324(f326(f871(x101431,a859)),x101433),f324(f324(f60(x101431),x101438),x101437)))+P1(f324(f324(f326(f871(x101436,a859)),f324(f324(f41(x1014311,f871(x101436,a859)),x101434),f324(f324(f8(f871(x101431,f871(x101436,a859)),f871(x101436,a859),x1014311),f324(f41(x101431,f871(x101436,a859)),x101433)),x101435))),x101432)) % 181.55/181.55 [10144]~P9(x101442,x101448,x101449)+~P9(x101444,x1014410,x1014411)+~P15(x101442,x101444,f871(x101441,a859),x101449,x1014411,x101446)+~P1(f324(f324(f326(f871(x101442,a859)),x101443),f324(f324(f60(x101442),x101448),x101449)))+~P1(f324(f324(f326(f871(x101444,a859)),x101445),f324(f324(f60(x101444),x1014410),x1014411)))+~P1(f324(f324(f326(f871(x101441,a859)),f324(f324(x101446,f740(x101447,x101445,x101443,x101446,x101441,x1014411,x1014410,x101444,x101449,x101448,x101442)),f750(x101447,x101445,x101443,x101446,x101441,x1014411,x1014410,x101444,x101449,x101448,x101442))),x101447))+P1(f324(f324(f326(f871(x101441,a859)),f324(f324(f41(x101442,f871(x101441,a859)),x101443),f324(f324(f8(f871(x101444,f871(x101441,a859)),f871(x101441,a859),x101442),f324(f41(x101444,f871(x101441,a859)),x101445)),x101446))),x101447)) % 181.55/181.55 [9047]E(x90471,x90472)+~P105(x90474)+~P27(x90473,x90474,x90475,f324(f324(f113(f871(x90473,a859)),f324(f167(x90473),x90471)),f324(f167(x90473),x90472)))+~E(f324(f167(x90473),x90471),f324(f167(x90473),x90472))+~P16(x90474,f324(f324(f148(x90473,x90474),x90475),x90472))+~P16(x90474,f324(f324(f148(x90473,x90474),x90475),x90471))+~P1(f324(f131(x90474),f324(f324(f148(x90473,x90474),x90475),x90472)))+~P1(f324(f131(x90474),f324(f324(f148(x90473,x90474),x90475),x90471))) % 181.55/181.55 %EqnAxiom % 181.55/181.55 [1]E(x11,x11) % 181.55/181.55 [2]E(x22,x21)+~E(x21,x22) % 181.55/181.55 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 181.55/181.55 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 181.55/181.55 [5]~E(x51,x52)+E(f103(x51),f103(x52)) % 181.55/181.55 [6]~E(x61,x62)+E(f22(x61),f22(x62)) % 181.55/181.55 [7]~E(x71,x72)+E(f104(x71),f104(x72)) % 181.55/181.55 [8]~E(x81,x82)+E(f189(x81),f189(x82)) % 181.55/181.55 [9]~E(x91,x92)+E(f113(x91),f113(x92)) % 181.55/181.55 [10]~E(x101,x102)+E(f190(x101),f190(x102)) % 181.55/181.55 [11]~E(x111,x112)+E(f191(x111),f191(x112)) % 181.55/181.55 [12]~E(x121,x122)+E(f324(x121,x123),f324(x122,x123)) % 181.55/181.55 [13]~E(x131,x132)+E(f324(x133,x131),f324(x133,x132)) % 181.55/181.55 [14]~E(x141,x142)+E(f31(x141),f31(x142)) % 181.55/181.55 [15]~E(x151,x152)+E(f192(x151),f192(x152)) % 181.55/181.55 [16]~E(x161,x162)+E(f105(x161),f105(x162)) % 181.55/181.55 [17]~E(x171,x172)+E(f34(x171),f34(x172)) % 181.55/181.55 [18]~E(x181,x182)+E(f85(x181),f85(x182)) % 181.55/181.55 [19]~E(x191,x192)+E(f866(x191),f866(x192)) % 181.55/181.55 [20]~E(x201,x202)+E(f38(x201),f38(x202)) % 181.55/181.55 [21]~E(x211,x212)+E(f750(x211,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112),f750(x212,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112)) % 181.55/181.55 [22]~E(x221,x222)+E(f750(x223,x221,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f750(x223,x222,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212)) % 181.55/181.55 [23]~E(x231,x232)+E(f750(x233,x234,x231,x235,x236,x237,x238,x239,x2310,x2311,x2312),f750(x233,x234,x232,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 181.55/181.55 [24]~E(x241,x242)+E(f750(x243,x244,x245,x241,x246,x247,x248,x249,x2410,x2411,x2412),f750(x243,x244,x245,x242,x246,x247,x248,x249,x2410,x2411,x2412)) % 181.55/181.55 [25]~E(x251,x252)+E(f750(x253,x254,x255,x256,x251,x257,x258,x259,x2510,x2511,x2512),f750(x253,x254,x255,x256,x252,x257,x258,x259,x2510,x2511,x2512)) % 181.55/181.55 [26]~E(x261,x262)+E(f750(x263,x264,x265,x266,x267,x261,x268,x269,x2610,x2611,x2612),f750(x263,x264,x265,x266,x267,x262,x268,x269,x2610,x2611,x2612)) % 181.55/181.55 [27]~E(x271,x272)+E(f750(x273,x274,x275,x276,x277,x278,x271,x279,x2710,x2711,x2712),f750(x273,x274,x275,x276,x277,x278,x272,x279,x2710,x2711,x2712)) % 181.55/181.55 [28]~E(x281,x282)+E(f750(x283,x284,x285,x286,x287,x288,x289,x281,x2810,x2811,x2812),f750(x283,x284,x285,x286,x287,x288,x289,x282,x2810,x2811,x2812)) % 181.55/181.55 [29]~E(x291,x292)+E(f750(x293,x294,x295,x296,x297,x298,x299,x2910,x291,x2911,x2912),f750(x293,x294,x295,x296,x297,x298,x299,x2910,x292,x2911,x2912)) % 181.55/181.55 [30]~E(x301,x302)+E(f750(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x301,x3012),f750(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x302,x3012)) % 181.55/181.55 [31]~E(x311,x312)+E(f750(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x311),f750(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x312)) % 181.55/181.55 [32]~E(x321,x322)+E(f79(x321),f79(x322)) % 181.55/181.55 [33]~E(x331,x332)+E(f239(x331),f239(x332)) % 181.55/181.55 [34]~E(x341,x342)+E(f740(x341,x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412),f740(x342,x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412)) % 181.55/181.55 [35]~E(x351,x352)+E(f740(x353,x351,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f740(x353,x352,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512)) % 181.55/181.55 [36]~E(x361,x362)+E(f740(x363,x364,x361,x365,x366,x367,x368,x369,x3610,x3611,x3612),f740(x363,x364,x362,x365,x366,x367,x368,x369,x3610,x3611,x3612)) % 181.55/181.55 [37]~E(x371,x372)+E(f740(x373,x374,x375,x371,x376,x377,x378,x379,x3710,x3711,x3712),f740(x373,x374,x375,x372,x376,x377,x378,x379,x3710,x3711,x3712)) % 181.55/181.55 [38]~E(x381,x382)+E(f740(x383,x384,x385,x386,x381,x387,x388,x389,x3810,x3811,x3812),f740(x383,x384,x385,x386,x382,x387,x388,x389,x3810,x3811,x3812)) % 181.55/181.55 [39]~E(x391,x392)+E(f740(x393,x394,x395,x396,x397,x391,x398,x399,x3910,x3911,x3912),f740(x393,x394,x395,x396,x397,x392,x398,x399,x3910,x3911,x3912)) % 181.55/181.55 [40]~E(x401,x402)+E(f740(x403,x404,x405,x406,x407,x408,x401,x409,x4010,x4011,x4012),f740(x403,x404,x405,x406,x407,x408,x402,x409,x4010,x4011,x4012)) % 181.55/181.55 [41]~E(x411,x412)+E(f740(x413,x414,x415,x416,x417,x418,x419,x411,x4110,x4111,x4112),f740(x413,x414,x415,x416,x417,x418,x419,x412,x4110,x4111,x4112)) % 181.55/181.55 [42]~E(x421,x422)+E(f740(x423,x424,x425,x426,x427,x428,x429,x4210,x421,x4211,x4212),f740(x423,x424,x425,x426,x427,x428,x429,x4210,x422,x4211,x4212)) % 181.55/181.55 [43]~E(x431,x432)+E(f740(x433,x434,x435,x436,x437,x438,x439,x4310,x4311,x431,x4312),f740(x433,x434,x435,x436,x437,x438,x439,x4310,x4311,x432,x4312)) % 181.55/181.55 [44]~E(x441,x442)+E(f740(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412,x441),f740(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412,x442)) % 181.55/181.55 [45]~E(x451,x452)+E(f114(x451),f114(x452)) % 181.55/181.55 [46]~E(x461,x462)+E(f326(x461),f326(x462)) % 181.55/181.55 [47]~E(x471,x472)+E(f871(x471,x473),f871(x472,x473)) % 181.55/181.55 [48]~E(x481,x482)+E(f871(x483,x481),f871(x483,x482)) % 181.55/181.55 [49]~E(x491,x492)+E(f4(x491),f4(x492)) % 181.55/181.55 [50]~E(x501,x502)+E(f263(x501,x503,x504),f263(x502,x503,x504)) % 181.55/181.55 [51]~E(x511,x512)+E(f263(x513,x511,x514),f263(x513,x512,x514)) % 181.55/181.55 [52]~E(x521,x522)+E(f263(x523,x524,x521),f263(x523,x524,x522)) % 181.55/181.55 [53]~E(x531,x532)+E(f864(x531),f864(x532)) % 181.55/181.55 [54]~E(x541,x542)+E(f869(x541),f869(x542)) % 181.55/181.55 [55]~E(x551,x552)+E(f870(x551,x553),f870(x552,x553)) % 181.55/181.55 [56]~E(x561,x562)+E(f870(x563,x561),f870(x563,x562)) % 181.55/181.55 [57]~E(x571,x572)+E(f867(x571),f867(x572)) % 181.55/181.55 [58]~E(x581,x582)+E(f561(x581,x583,x584,x585),f561(x582,x583,x584,x585)) % 181.55/181.55 [59]~E(x591,x592)+E(f561(x593,x591,x594,x595),f561(x593,x592,x594,x595)) % 181.55/181.55 [60]~E(x601,x602)+E(f561(x603,x604,x601,x605),f561(x603,x604,x602,x605)) % 181.55/181.55 [61]~E(x611,x612)+E(f561(x613,x614,x615,x611),f561(x613,x614,x615,x612)) % 181.55/181.55 [62]~E(x621,x622)+E(f81(x621),f81(x622)) % 181.55/181.55 [63]~E(x631,x632)+E(f167(x631),f167(x632)) % 181.55/181.55 [64]~E(x641,x642)+E(f75(x641),f75(x642)) % 181.55/181.55 [65]~E(x651,x652)+E(f80(x651),f80(x652)) % 181.55/181.55 [66]~E(x661,x662)+E(f173(x661,x663),f173(x662,x663)) % 181.55/181.55 [67]~E(x671,x672)+E(f173(x673,x671),f173(x673,x672)) % 181.55/181.55 [68]~E(x681,x682)+E(f238(x681),f238(x682)) % 181.55/181.55 [69]~E(x691,x692)+E(f7(x691,x693,x694),f7(x692,x693,x694)) % 181.55/181.55 [70]~E(x701,x702)+E(f7(x703,x701,x704),f7(x703,x702,x704)) % 181.55/181.55 [71]~E(x711,x712)+E(f7(x713,x714,x711),f7(x713,x714,x712)) % 181.55/181.55 [72]~E(x721,x722)+E(f106(x721),f106(x722)) % 181.55/181.55 [73]~E(x731,x732)+E(f723(x731,x733,x734),f723(x732,x733,x734)) % 181.55/181.55 [74]~E(x741,x742)+E(f723(x743,x741,x744),f723(x743,x742,x744)) % 181.55/181.55 [75]~E(x751,x752)+E(f723(x753,x754,x751),f723(x753,x754,x752)) % 181.55/181.55 [76]~E(x761,x762)+E(f259(x761,x763),f259(x762,x763)) % 181.55/181.55 [77]~E(x771,x772)+E(f259(x773,x771),f259(x773,x772)) % 181.55/181.55 [78]~E(x781,x782)+E(f8(x781,x783,x784),f8(x782,x783,x784)) % 181.55/181.55 [79]~E(x791,x792)+E(f8(x793,x791,x794),f8(x793,x792,x794)) % 181.55/181.55 [80]~E(x801,x802)+E(f8(x803,x804,x801),f8(x803,x804,x802)) % 181.55/181.55 [81]~E(x811,x812)+E(f303(x811,x813,x814),f303(x812,x813,x814)) % 181.55/181.55 [82]~E(x821,x822)+E(f303(x823,x821,x824),f303(x823,x822,x824)) % 181.55/181.55 [83]~E(x831,x832)+E(f303(x833,x834,x831),f303(x833,x834,x832)) % 181.55/181.55 [84]~E(x841,x842)+E(f6(x841,x843),f6(x842,x843)) % 181.55/181.55 [85]~E(x851,x852)+E(f6(x853,x851),f6(x853,x852)) % 181.55/181.55 [86]~E(x861,x862)+E(f872(x861,x863),f872(x862,x863)) % 181.55/181.55 [87]~E(x871,x872)+E(f872(x873,x871),f872(x873,x872)) % 181.55/181.55 [88]~E(x881,x882)+E(f44(x881,x883,x884),f44(x882,x883,x884)) % 181.55/181.55 [89]~E(x891,x892)+E(f44(x893,x891,x894),f44(x893,x892,x894)) % 181.55/181.55 [90]~E(x901,x902)+E(f44(x903,x904,x901),f44(x903,x904,x902)) % 181.55/181.55 [91]~E(x911,x912)+E(f82(x911),f82(x912)) % 181.55/181.55 [92]~E(x921,x922)+E(f247(x921),f247(x922)) % 181.55/181.55 [93]~E(x931,x932)+E(f145(x931),f145(x932)) % 181.55/181.55 [94]~E(x941,x942)+E(f61(x941),f61(x942)) % 181.55/181.55 [95]~E(x951,x952)+E(f32(x951,x953),f32(x952,x953)) % 181.55/181.55 [96]~E(x961,x962)+E(f32(x963,x961),f32(x963,x962)) % 181.55/181.55 [97]~E(x971,x972)+E(f60(x971),f60(x972)) % 181.55/181.55 [98]~E(x981,x982)+E(f172(x981,x983,x984),f172(x982,x983,x984)) % 181.55/181.55 [99]~E(x991,x992)+E(f172(x993,x991,x994),f172(x993,x992,x994)) % 181.55/181.55 [100]~E(x1001,x1002)+E(f172(x1003,x1004,x1001),f172(x1003,x1004,x1002)) % 181.55/181.55 [101]~E(x1011,x1012)+E(f790(x1011),f790(x1012)) % 181.55/181.55 [102]~E(x1021,x1022)+E(f170(x1021),f170(x1022)) % 181.55/181.55 [103]~E(x1031,x1032)+E(f293(x1031),f293(x1032)) % 181.55/181.55 [104]~E(x1041,x1042)+E(f37(x1041),f37(x1042)) % 181.55/181.55 [105]~E(x1051,x1052)+E(f261(x1051,x1053),f261(x1052,x1053)) % 181.55/181.55 [106]~E(x1061,x1062)+E(f261(x1063,x1061),f261(x1063,x1062)) % 181.55/181.55 [107]~E(x1071,x1072)+E(f821(x1071,x1073,x1074,x1075),f821(x1072,x1073,x1074,x1075)) % 181.55/181.55 [108]~E(x1081,x1082)+E(f821(x1083,x1081,x1084,x1085),f821(x1083,x1082,x1084,x1085)) % 181.55/181.55 [109]~E(x1091,x1092)+E(f821(x1093,x1094,x1091,x1095),f821(x1093,x1094,x1092,x1095)) % 181.55/181.55 [110]~E(x1101,x1102)+E(f821(x1103,x1104,x1105,x1101),f821(x1103,x1104,x1105,x1102)) % 181.55/181.55 [111]~E(x1111,x1112)+E(f634(x1111,x1113,x1114),f634(x1112,x1113,x1114)) % 181.55/181.55 [112]~E(x1121,x1122)+E(f634(x1123,x1121,x1124),f634(x1123,x1122,x1124)) % 181.55/181.55 [113]~E(x1131,x1132)+E(f634(x1133,x1134,x1131),f634(x1133,x1134,x1132)) % 181.55/181.55 [114]~E(x1141,x1142)+E(f311(x1141,x1143,x1144,x1145),f311(x1142,x1143,x1144,x1145)) % 181.55/181.55 [115]~E(x1151,x1152)+E(f311(x1153,x1151,x1154,x1155),f311(x1153,x1152,x1154,x1155)) % 181.55/181.55 [116]~E(x1161,x1162)+E(f311(x1163,x1164,x1161,x1165),f311(x1163,x1164,x1162,x1165)) % 181.55/181.55 [117]~E(x1171,x1172)+E(f311(x1173,x1174,x1175,x1171),f311(x1173,x1174,x1175,x1172)) % 181.55/181.55 [118]~E(x1181,x1182)+E(f822(x1181,x1183,x1184,x1185),f822(x1182,x1183,x1184,x1185)) % 181.55/181.55 [119]~E(x1191,x1192)+E(f822(x1193,x1191,x1194,x1195),f822(x1193,x1192,x1194,x1195)) % 181.55/181.55 [120]~E(x1201,x1202)+E(f822(x1203,x1204,x1201,x1205),f822(x1203,x1204,x1202,x1205)) % 181.55/181.55 [121]~E(x1211,x1212)+E(f822(x1213,x1214,x1215,x1211),f822(x1213,x1214,x1215,x1212)) % 181.55/181.55 [122]~E(x1221,x1222)+E(f816(x1221,x1223,x1224,x1225,x1226,x1227),f816(x1222,x1223,x1224,x1225,x1226,x1227)) % 181.55/181.55 [123]~E(x1231,x1232)+E(f816(x1233,x1231,x1234,x1235,x1236,x1237),f816(x1233,x1232,x1234,x1235,x1236,x1237)) % 181.55/181.55 [124]~E(x1241,x1242)+E(f816(x1243,x1244,x1241,x1245,x1246,x1247),f816(x1243,x1244,x1242,x1245,x1246,x1247)) % 181.55/181.55 [125]~E(x1251,x1252)+E(f816(x1253,x1254,x1255,x1251,x1256,x1257),f816(x1253,x1254,x1255,x1252,x1256,x1257)) % 181.55/181.55 [126]~E(x1261,x1262)+E(f816(x1263,x1264,x1265,x1266,x1261,x1267),f816(x1263,x1264,x1265,x1266,x1262,x1267)) % 181.55/181.55 [127]~E(x1271,x1272)+E(f816(x1273,x1274,x1275,x1276,x1277,x1271),f816(x1273,x1274,x1275,x1276,x1277,x1272)) % 181.55/181.55 [128]~E(x1281,x1282)+E(f244(x1281),f244(x1282)) % 181.55/181.55 [129]~E(x1291,x1292)+E(f793(x1291,x1293,x1294),f793(x1292,x1293,x1294)) % 181.55/181.55 [130]~E(x1301,x1302)+E(f793(x1303,x1301,x1304),f793(x1303,x1302,x1304)) % 181.55/181.55 [131]~E(x1311,x1312)+E(f793(x1313,x1314,x1311),f793(x1313,x1314,x1312)) % 181.55/181.55 [132]~E(x1321,x1322)+E(f302(x1321),f302(x1322)) % 181.55/181.55 [133]~E(x1331,x1332)+E(f39(x1331,x1333),f39(x1332,x1333)) % 181.55/181.55 [134]~E(x1341,x1342)+E(f39(x1343,x1341),f39(x1343,x1342)) % 181.55/181.55 [135]~E(x1351,x1352)+E(f519(x1351,x1353,x1354),f519(x1352,x1353,x1354)) % 181.55/181.55 [136]~E(x1361,x1362)+E(f519(x1363,x1361,x1364),f519(x1363,x1362,x1364)) % 181.55/181.55 [137]~E(x1371,x1372)+E(f519(x1373,x1374,x1371),f519(x1373,x1374,x1372)) % 181.55/181.55 [138]~E(x1381,x1382)+E(f806(x1381,x1383,x1384),f806(x1382,x1383,x1384)) % 181.55/181.55 [139]~E(x1391,x1392)+E(f806(x1393,x1391,x1394),f806(x1393,x1392,x1394)) % 181.55/181.55 [140]~E(x1401,x1402)+E(f806(x1403,x1404,x1401),f806(x1403,x1404,x1402)) % 181.55/181.55 [141]~E(x1411,x1412)+E(f16(x1411,x1413),f16(x1412,x1413)) % 181.55/181.55 [142]~E(x1421,x1422)+E(f16(x1423,x1421),f16(x1423,x1422)) % 181.55/181.55 [143]~E(x1431,x1432)+E(f282(x1431),f282(x1432)) % 181.55/181.55 [144]~E(x1441,x1442)+E(f41(x1441,x1443),f41(x1442,x1443)) % 181.55/181.55 [145]~E(x1451,x1452)+E(f41(x1453,x1451),f41(x1453,x1452)) % 181.55/181.55 [146]~E(x1461,x1462)+E(f83(x1461,x1463),f83(x1462,x1463)) % 181.55/181.55 [147]~E(x1471,x1472)+E(f83(x1473,x1471),f83(x1473,x1472)) % 181.55/181.55 [148]~E(x1481,x1482)+E(f42(x1481,x1483),f42(x1482,x1483)) % 181.55/181.55 [149]~E(x1491,x1492)+E(f42(x1493,x1491),f42(x1493,x1492)) % 181.55/181.55 [150]~E(x1501,x1502)+E(f743(x1501,x1503,x1504),f743(x1502,x1503,x1504)) % 181.55/181.55 [151]~E(x1511,x1512)+E(f743(x1513,x1511,x1514),f743(x1513,x1512,x1514)) % 181.55/181.55 [152]~E(x1521,x1522)+E(f743(x1523,x1524,x1521),f743(x1523,x1524,x1522)) % 181.55/181.55 [153]~E(x1531,x1532)+E(f148(x1531,x1533),f148(x1532,x1533)) % 181.55/181.55 [154]~E(x1541,x1542)+E(f148(x1543,x1541),f148(x1543,x1542)) % 181.55/181.55 [155]~E(x1551,x1552)+E(f217(x1551),f217(x1552)) % 181.55/181.55 [156]~E(x1561,x1562)+E(f125(x1561,x1563,x1564),f125(x1562,x1563,x1564)) % 181.55/181.55 [157]~E(x1571,x1572)+E(f125(x1573,x1571,x1574),f125(x1573,x1572,x1574)) % 181.55/181.55 [158]~E(x1581,x1582)+E(f125(x1583,x1584,x1581),f125(x1583,x1584,x1582)) % 181.55/181.55 [159]~E(x1591,x1592)+E(f203(x1591),f203(x1592)) % 181.55/181.55 [160]~E(x1601,x1602)+E(f108(x1601),f108(x1602)) % 181.55/181.55 [161]~E(x1611,x1612)+E(f109(x1611),f109(x1612)) % 181.55/181.55 [162]~E(x1621,x1622)+E(f325(x1621),f325(x1622)) % 181.55/181.55 [163]~E(x1631,x1632)+E(f254(x1631,x1633,x1634),f254(x1632,x1633,x1634)) % 181.55/181.55 [164]~E(x1641,x1642)+E(f254(x1643,x1641,x1644),f254(x1643,x1642,x1644)) % 181.55/181.55 [165]~E(x1651,x1652)+E(f254(x1653,x1654,x1651),f254(x1653,x1654,x1652)) % 181.55/181.55 [166]~E(x1661,x1662)+E(f159(x1661),f159(x1662)) % 181.55/181.55 [167]~E(x1671,x1672)+E(f124(x1671),f124(x1672)) % 181.55/181.55 [168]~E(x1681,x1682)+E(f804(x1681,x1683,x1684),f804(x1682,x1683,x1684)) % 181.55/181.55 [169]~E(x1691,x1692)+E(f804(x1693,x1691,x1694),f804(x1693,x1692,x1694)) % 181.55/181.55 [170]~E(x1701,x1702)+E(f804(x1703,x1704,x1701),f804(x1703,x1704,x1702)) % 181.55/181.55 [171]~E(x1711,x1712)+E(f5(x1711),f5(x1712)) % 181.55/181.55 [172]~E(x1721,x1722)+E(f46(x1721,x1723),f46(x1722,x1723)) % 181.55/181.55 [173]~E(x1731,x1732)+E(f46(x1733,x1731),f46(x1733,x1732)) % 181.55/181.55 [174]~E(x1741,x1742)+E(f142(x1741,x1743,x1744),f142(x1742,x1743,x1744)) % 181.55/181.55 [175]~E(x1751,x1752)+E(f142(x1753,x1751,x1754),f142(x1753,x1752,x1754)) % 181.55/181.55 [176]~E(x1761,x1762)+E(f142(x1763,x1764,x1761),f142(x1763,x1764,x1762)) % 181.55/181.55 [177]~E(x1771,x1772)+E(f249(x1771),f249(x1772)) % 181.55/181.55 [178]~E(x1781,x1782)+E(f298(x1781,x1783,x1784),f298(x1782,x1783,x1784)) % 181.55/181.55 [179]~E(x1791,x1792)+E(f298(x1793,x1791,x1794),f298(x1793,x1792,x1794)) % 181.55/181.55 [180]~E(x1801,x1802)+E(f298(x1803,x1804,x1801),f298(x1803,x1804,x1802)) % 181.55/181.55 [181]~E(x1811,x1812)+E(f47(x1811,x1813),f47(x1812,x1813)) % 181.55/181.55 [182]~E(x1821,x1822)+E(f47(x1823,x1821),f47(x1823,x1822)) % 181.55/181.55 [183]~E(x1831,x1832)+E(f182(x1831,x1833,x1834,x1835,x1836),f182(x1832,x1833,x1834,x1835,x1836)) % 181.55/181.55 [184]~E(x1841,x1842)+E(f182(x1843,x1841,x1844,x1845,x1846),f182(x1843,x1842,x1844,x1845,x1846)) % 181.55/181.55 [185]~E(x1851,x1852)+E(f182(x1853,x1854,x1851,x1855,x1856),f182(x1853,x1854,x1852,x1855,x1856)) % 181.55/181.55 [186]~E(x1861,x1862)+E(f182(x1863,x1864,x1865,x1861,x1866),f182(x1863,x1864,x1865,x1862,x1866)) % 181.55/181.55 [187]~E(x1871,x1872)+E(f182(x1873,x1874,x1875,x1876,x1871),f182(x1873,x1874,x1875,x1876,x1872)) % 181.55/181.55 [188]~E(x1881,x1882)+E(f73(x1881,x1883,x1884,x1885),f73(x1882,x1883,x1884,x1885)) % 181.55/181.55 [189]~E(x1891,x1892)+E(f73(x1893,x1891,x1894,x1895),f73(x1893,x1892,x1894,x1895)) % 181.55/181.55 [190]~E(x1901,x1902)+E(f73(x1903,x1904,x1901,x1905),f73(x1903,x1904,x1902,x1905)) % 181.55/181.55 [191]~E(x1911,x1912)+E(f73(x1913,x1914,x1915,x1911),f73(x1913,x1914,x1915,x1912)) % 181.55/181.55 [192]~E(x1921,x1922)+E(f136(x1921,x1923,x1924,x1925),f136(x1922,x1923,x1924,x1925)) % 181.55/181.55 [193]~E(x1931,x1932)+E(f136(x1933,x1931,x1934,x1935),f136(x1933,x1932,x1934,x1935)) % 181.55/181.55 [194]~E(x1941,x1942)+E(f136(x1943,x1944,x1941,x1945),f136(x1943,x1944,x1942,x1945)) % 181.55/181.55 [195]~E(x1951,x1952)+E(f136(x1953,x1954,x1955,x1951),f136(x1953,x1954,x1955,x1952)) % 181.55/181.55 [196]~E(x1961,x1962)+E(f138(x1961,x1963),f138(x1962,x1963)) % 181.55/181.55 [197]~E(x1971,x1972)+E(f138(x1973,x1971),f138(x1973,x1972)) % 181.55/181.55 [198]~E(x1981,x1982)+E(f116(x1981),f116(x1982)) % 181.55/181.55 [199]~E(x1991,x1992)+E(f258(x1991,x1993),f258(x1992,x1993)) % 181.55/181.55 [200]~E(x2001,x2002)+E(f258(x2003,x2001),f258(x2003,x2002)) % 181.55/181.55 [201]~E(x2011,x2012)+E(f756(x2011,x2013),f756(x2012,x2013)) % 181.55/181.55 [202]~E(x2021,x2022)+E(f756(x2023,x2021),f756(x2023,x2022)) % 181.55/181.55 [203]~E(x2031,x2032)+E(f769(x2031,x2033,x2034,x2035,x2036),f769(x2032,x2033,x2034,x2035,x2036)) % 181.55/181.55 [204]~E(x2041,x2042)+E(f769(x2043,x2041,x2044,x2045,x2046),f769(x2043,x2042,x2044,x2045,x2046)) % 181.55/181.55 [205]~E(x2051,x2052)+E(f769(x2053,x2054,x2051,x2055,x2056),f769(x2053,x2054,x2052,x2055,x2056)) % 181.55/181.55 [206]~E(x2061,x2062)+E(f769(x2063,x2064,x2065,x2061,x2066),f769(x2063,x2064,x2065,x2062,x2066)) % 181.55/181.55 [207]~E(x2071,x2072)+E(f769(x2073,x2074,x2075,x2076,x2071),f769(x2073,x2074,x2075,x2076,x2072)) % 181.55/181.55 [208]~E(x2081,x2082)+E(f599(x2081,x2083),f599(x2082,x2083)) % 181.55/181.55 [209]~E(x2091,x2092)+E(f599(x2093,x2091),f599(x2093,x2092)) % 181.55/181.55 [210]~E(x2101,x2102)+E(f63(x2101,x2103),f63(x2102,x2103)) % 181.55/181.55 [211]~E(x2111,x2112)+E(f63(x2113,x2111),f63(x2113,x2112)) % 181.55/181.55 [212]~E(x2121,x2122)+E(f183(x2121,x2123,x2124,x2125),f183(x2122,x2123,x2124,x2125)) % 181.55/181.55 [213]~E(x2131,x2132)+E(f183(x2133,x2131,x2134,x2135),f183(x2133,x2132,x2134,x2135)) % 181.55/181.55 [214]~E(x2141,x2142)+E(f183(x2143,x2144,x2141,x2145),f183(x2143,x2144,x2142,x2145)) % 181.55/181.55 [215]~E(x2151,x2152)+E(f183(x2153,x2154,x2155,x2151),f183(x2153,x2154,x2155,x2152)) % 181.55/181.55 [216]~E(x2161,x2162)+E(f88(x2161),f88(x2162)) % 181.55/181.55 [217]~E(x2171,x2172)+E(f796(x2171,x2173,x2174,x2175),f796(x2172,x2173,x2174,x2175)) % 181.55/181.55 [218]~E(x2181,x2182)+E(f796(x2183,x2181,x2184,x2185),f796(x2183,x2182,x2184,x2185)) % 181.55/181.55 [219]~E(x2191,x2192)+E(f796(x2193,x2194,x2191,x2195),f796(x2193,x2194,x2192,x2195)) % 181.55/181.55 [220]~E(x2201,x2202)+E(f796(x2203,x2204,x2205,x2201),f796(x2203,x2204,x2205,x2202)) % 181.55/181.55 [221]~E(x2211,x2212)+E(f295(x2211,x2213,x2214),f295(x2212,x2213,x2214)) % 181.55/181.55 [222]~E(x2221,x2222)+E(f295(x2223,x2221,x2224),f295(x2223,x2222,x2224)) % 181.55/181.55 [223]~E(x2231,x2232)+E(f295(x2233,x2234,x2231),f295(x2233,x2234,x2232)) % 181.55/181.55 [224]~E(x2241,x2242)+E(f91(x2241,x2243),f91(x2242,x2243)) % 181.55/181.55 [225]~E(x2251,x2252)+E(f91(x2253,x2251),f91(x2253,x2252)) % 181.55/181.55 [226]~E(x2261,x2262)+E(f798(x2261,x2263,x2264,x2265),f798(x2262,x2263,x2264,x2265)) % 181.55/181.55 [227]~E(x2271,x2272)+E(f798(x2273,x2271,x2274,x2275),f798(x2273,x2272,x2274,x2275)) % 181.55/181.55 [228]~E(x2281,x2282)+E(f798(x2283,x2284,x2281,x2285),f798(x2283,x2284,x2282,x2285)) % 181.55/181.55 [229]~E(x2291,x2292)+E(f798(x2293,x2294,x2295,x2291),f798(x2293,x2294,x2295,x2292)) % 181.55/181.55 [230]~E(x2301,x2302)+E(f179(x2301,x2303,x2304),f179(x2302,x2303,x2304)) % 181.55/181.55 [231]~E(x2311,x2312)+E(f179(x2313,x2311,x2314),f179(x2313,x2312,x2314)) % 181.55/181.55 [232]~E(x2321,x2322)+E(f179(x2323,x2324,x2321),f179(x2323,x2324,x2322)) % 181.55/181.55 [233]~E(x2331,x2332)+E(f48(x2331,x2333),f48(x2332,x2333)) % 181.55/181.55 [234]~E(x2341,x2342)+E(f48(x2343,x2341),f48(x2343,x2342)) % 181.55/181.55 [235]~E(x2351,x2352)+E(f766(x2351,x2353,x2354,x2355),f766(x2352,x2353,x2354,x2355)) % 181.55/181.55 [236]~E(x2361,x2362)+E(f766(x2363,x2361,x2364,x2365),f766(x2363,x2362,x2364,x2365)) % 181.55/181.55 [237]~E(x2371,x2372)+E(f766(x2373,x2374,x2371,x2375),f766(x2373,x2374,x2372,x2375)) % 181.55/181.55 [238]~E(x2381,x2382)+E(f766(x2383,x2384,x2385,x2381),f766(x2383,x2384,x2385,x2382)) % 181.55/181.55 [239]~E(x2391,x2392)+E(f611(x2391,x2393,x2394,x2395,x2396),f611(x2392,x2393,x2394,x2395,x2396)) % 181.55/181.55 [240]~E(x2401,x2402)+E(f611(x2403,x2401,x2404,x2405,x2406),f611(x2403,x2402,x2404,x2405,x2406)) % 181.55/181.55 [241]~E(x2411,x2412)+E(f611(x2413,x2414,x2411,x2415,x2416),f611(x2413,x2414,x2412,x2415,x2416)) % 181.55/181.55 [242]~E(x2421,x2422)+E(f611(x2423,x2424,x2425,x2421,x2426),f611(x2423,x2424,x2425,x2422,x2426)) % 181.55/181.55 [243]~E(x2431,x2432)+E(f611(x2433,x2434,x2435,x2436,x2431),f611(x2433,x2434,x2435,x2436,x2432)) % 181.55/181.55 [244]~E(x2441,x2442)+E(f112(x2441),f112(x2442)) % 181.55/181.55 [245]~E(x2451,x2452)+E(f18(x2451,x2453,x2454),f18(x2452,x2453,x2454)) % 181.55/181.55 [246]~E(x2461,x2462)+E(f18(x2463,x2461,x2464),f18(x2463,x2462,x2464)) % 181.55/181.55 [247]~E(x2471,x2472)+E(f18(x2473,x2474,x2471),f18(x2473,x2474,x2472)) % 181.55/181.55 [248]~E(x2481,x2482)+E(f294(x2481,x2483),f294(x2482,x2483)) % 181.55/181.55 [249]~E(x2491,x2492)+E(f294(x2493,x2491),f294(x2493,x2492)) % 181.55/181.55 [250]~E(x2501,x2502)+E(f654(x2501,x2503,x2504,x2505),f654(x2502,x2503,x2504,x2505)) % 181.55/181.55 [251]~E(x2511,x2512)+E(f654(x2513,x2511,x2514,x2515),f654(x2513,x2512,x2514,x2515)) % 181.55/181.55 [252]~E(x2521,x2522)+E(f654(x2523,x2524,x2521,x2525),f654(x2523,x2524,x2522,x2525)) % 181.55/181.55 [253]~E(x2531,x2532)+E(f654(x2533,x2534,x2535,x2531),f654(x2533,x2534,x2535,x2532)) % 181.55/181.55 [254]~E(x2541,x2542)+E(f300(x2541,x2543),f300(x2542,x2543)) % 181.55/181.55 [255]~E(x2551,x2552)+E(f300(x2553,x2551),f300(x2553,x2552)) % 181.55/181.55 [256]~E(x2561,x2562)+E(f55(x2561),f55(x2562)) % 181.55/181.55 [257]~E(x2571,x2572)+E(f283(x2571,x2573),f283(x2572,x2573)) % 181.55/181.55 [258]~E(x2581,x2582)+E(f283(x2583,x2581),f283(x2583,x2582)) % 181.55/181.55 [259]~E(x2591,x2592)+E(f59(x2591,x2593,x2594,x2595),f59(x2592,x2593,x2594,x2595)) % 181.55/181.55 [260]~E(x2601,x2602)+E(f59(x2603,x2601,x2604,x2605),f59(x2603,x2602,x2604,x2605)) % 181.55/181.55 [261]~E(x2611,x2612)+E(f59(x2613,x2614,x2611,x2615),f59(x2613,x2614,x2612,x2615)) % 181.55/181.55 [262]~E(x2621,x2622)+E(f59(x2623,x2624,x2625,x2621),f59(x2623,x2624,x2625,x2622)) % 181.55/181.55 [263]~E(x2631,x2632)+E(f177(x2631,x2633),f177(x2632,x2633)) % 181.55/181.55 [264]~E(x2641,x2642)+E(f177(x2643,x2641),f177(x2643,x2642)) % 181.55/181.55 [265]~E(x2651,x2652)+E(f619(x2651,x2653,x2654,x2655,x2656),f619(x2652,x2653,x2654,x2655,x2656)) % 181.55/181.55 [266]~E(x2661,x2662)+E(f619(x2663,x2661,x2664,x2665,x2666),f619(x2663,x2662,x2664,x2665,x2666)) % 181.55/181.55 [267]~E(x2671,x2672)+E(f619(x2673,x2674,x2671,x2675,x2676),f619(x2673,x2674,x2672,x2675,x2676)) % 181.55/181.55 [268]~E(x2681,x2682)+E(f619(x2683,x2684,x2685,x2681,x2686),f619(x2683,x2684,x2685,x2682,x2686)) % 181.55/181.55 [269]~E(x2691,x2692)+E(f619(x2693,x2694,x2695,x2696,x2691),f619(x2693,x2694,x2695,x2696,x2692)) % 181.55/181.55 [270]~E(x2701,x2702)+E(f93(x2701),f93(x2702)) % 181.55/181.55 [271]~E(x2711,x2712)+E(f117(x2711,x2713),f117(x2712,x2713)) % 181.55/181.55 [272]~E(x2721,x2722)+E(f117(x2723,x2721),f117(x2723,x2722)) % 181.55/181.55 [273]~E(x2731,x2732)+E(f301(x2731),f301(x2732)) % 181.55/181.55 [274]~E(x2741,x2742)+E(f233(x2741),f233(x2742)) % 181.55/181.55 [275]~E(x2751,x2752)+E(f146(x2751,x2753),f146(x2752,x2753)) % 181.55/181.55 [276]~E(x2761,x2762)+E(f146(x2763,x2761),f146(x2763,x2762)) % 181.55/181.55 [277]~E(x2771,x2772)+E(f262(x2771,x2773),f262(x2772,x2773)) % 181.55/181.55 [278]~E(x2781,x2782)+E(f262(x2783,x2781),f262(x2783,x2782)) % 181.55/181.55 [279]~E(x2791,x2792)+E(f194(x2791),f194(x2792)) % 181.55/181.55 [280]~E(x2801,x2802)+E(f161(x2801,x2803,x2804),f161(x2802,x2803,x2804)) % 181.55/181.55 [281]~E(x2811,x2812)+E(f161(x2813,x2811,x2814),f161(x2813,x2812,x2814)) % 181.55/181.55 [282]~E(x2821,x2822)+E(f161(x2823,x2824,x2821),f161(x2823,x2824,x2822)) % 181.55/181.55 [283]~E(x2831,x2832)+E(f118(x2831),f118(x2832)) % 181.55/181.55 [284]~E(x2841,x2842)+E(f635(x2841,x2843,x2844,x2845,x2846,x2847,x2848,x2849),f635(x2842,x2843,x2844,x2845,x2846,x2847,x2848,x2849)) % 181.55/181.55 [285]~E(x2851,x2852)+E(f635(x2853,x2851,x2854,x2855,x2856,x2857,x2858,x2859),f635(x2853,x2852,x2854,x2855,x2856,x2857,x2858,x2859)) % 181.55/181.55 [286]~E(x2861,x2862)+E(f635(x2863,x2864,x2861,x2865,x2866,x2867,x2868,x2869),f635(x2863,x2864,x2862,x2865,x2866,x2867,x2868,x2869)) % 181.55/181.55 [287]~E(x2871,x2872)+E(f635(x2873,x2874,x2875,x2871,x2876,x2877,x2878,x2879),f635(x2873,x2874,x2875,x2872,x2876,x2877,x2878,x2879)) % 181.55/181.55 [288]~E(x2881,x2882)+E(f635(x2883,x2884,x2885,x2886,x2881,x2887,x2888,x2889),f635(x2883,x2884,x2885,x2886,x2882,x2887,x2888,x2889)) % 181.55/181.55 [289]~E(x2891,x2892)+E(f635(x2893,x2894,x2895,x2896,x2897,x2891,x2898,x2899),f635(x2893,x2894,x2895,x2896,x2897,x2892,x2898,x2899)) % 181.55/181.55 [290]~E(x2901,x2902)+E(f635(x2903,x2904,x2905,x2906,x2907,x2908,x2901,x2909),f635(x2903,x2904,x2905,x2906,x2907,x2908,x2902,x2909)) % 181.55/181.55 [291]~E(x2911,x2912)+E(f635(x2913,x2914,x2915,x2916,x2917,x2918,x2919,x2911),f635(x2913,x2914,x2915,x2916,x2917,x2918,x2919,x2912)) % 181.55/181.55 [292]~E(x2921,x2922)+E(f193(x2921,x2923,x2924,x2925),f193(x2922,x2923,x2924,x2925)) % 181.55/181.55 [293]~E(x2931,x2932)+E(f193(x2933,x2931,x2934,x2935),f193(x2933,x2932,x2934,x2935)) % 181.55/181.55 [294]~E(x2941,x2942)+E(f193(x2943,x2944,x2941,x2945),f193(x2943,x2944,x2942,x2945)) % 181.55/181.55 [295]~E(x2951,x2952)+E(f193(x2953,x2954,x2955,x2951),f193(x2953,x2954,x2955,x2952)) % 181.55/181.55 [296]~E(x2961,x2962)+E(f281(x2961,x2963,x2964),f281(x2962,x2963,x2964)) % 181.55/181.55 [297]~E(x2971,x2972)+E(f281(x2973,x2971,x2974),f281(x2973,x2972,x2974)) % 181.55/181.55 [298]~E(x2981,x2982)+E(f281(x2983,x2984,x2981),f281(x2983,x2984,x2982)) % 181.55/181.55 [299]~E(x2991,x2992)+E(f257(x2991,x2993),f257(x2992,x2993)) % 181.55/181.55 [300]~E(x3001,x3002)+E(f257(x3003,x3001),f257(x3003,x3002)) % 181.55/181.55 [301]~E(x3011,x3012)+E(f237(x3011),f237(x3012)) % 181.55/181.55 [302]~E(x3021,x3022)+E(f12(x3021,x3023,x3024),f12(x3022,x3023,x3024)) % 181.55/181.55 [303]~E(x3031,x3032)+E(f12(x3033,x3031,x3034),f12(x3033,x3032,x3034)) % 181.55/181.55 [304]~E(x3041,x3042)+E(f12(x3043,x3044,x3041),f12(x3043,x3044,x3042)) % 181.55/181.55 [305]~E(x3051,x3052)+E(f768(x3051,x3053,x3054,x3055,x3056),f768(x3052,x3053,x3054,x3055,x3056)) % 181.55/181.55 [306]~E(x3061,x3062)+E(f768(x3063,x3061,x3064,x3065,x3066),f768(x3063,x3062,x3064,x3065,x3066)) % 181.55/181.55 [307]~E(x3071,x3072)+E(f768(x3073,x3074,x3071,x3075,x3076),f768(x3073,x3074,x3072,x3075,x3076)) % 181.55/181.55 [308]~E(x3081,x3082)+E(f768(x3083,x3084,x3085,x3081,x3086),f768(x3083,x3084,x3085,x3082,x3086)) % 181.55/181.55 [309]~E(x3091,x3092)+E(f768(x3093,x3094,x3095,x3096,x3091),f768(x3093,x3094,x3095,x3096,x3092)) % 181.55/181.55 [310]~E(x3101,x3102)+E(f162(x3101),f162(x3102)) % 181.55/181.55 [311]~E(x3111,x3112)+E(f204(x3111,x3113),f204(x3112,x3113)) % 181.55/181.55 [312]~E(x3121,x3122)+E(f204(x3123,x3121),f204(x3123,x3122)) % 181.55/181.55 [313]~E(x3131,x3132)+E(f132(x3131),f132(x3132)) % 181.55/181.55 [314]~E(x3141,x3142)+E(f757(x3141,x3143,x3144,x3145),f757(x3142,x3143,x3144,x3145)) % 181.55/181.55 [315]~E(x3151,x3152)+E(f757(x3153,x3151,x3154,x3155),f757(x3153,x3152,x3154,x3155)) % 181.55/181.55 [316]~E(x3161,x3162)+E(f757(x3163,x3164,x3161,x3165),f757(x3163,x3164,x3162,x3165)) % 181.55/181.55 [317]~E(x3171,x3172)+E(f757(x3173,x3174,x3175,x3171),f757(x3173,x3174,x3175,x3172)) % 181.55/181.55 [318]~E(x3181,x3182)+E(f166(x3181),f166(x3182)) % 181.55/181.55 [319]~E(x3191,x3192)+E(f9(x3191,x3193),f9(x3192,x3193)) % 181.55/181.55 [320]~E(x3201,x3202)+E(f9(x3203,x3201),f9(x3203,x3202)) % 181.55/181.55 [321]~E(x3211,x3212)+E(f811(x3211),f811(x3212)) % 181.55/181.55 [322]~E(x3221,x3222)+E(f585(x3221,x3223,x3224,x3225),f585(x3222,x3223,x3224,x3225)) % 181.55/181.55 [323]~E(x3231,x3232)+E(f585(x3233,x3231,x3234,x3235),f585(x3233,x3232,x3234,x3235)) % 181.55/181.55 [324]~E(x3241,x3242)+E(f585(x3243,x3244,x3241,x3245),f585(x3243,x3244,x3242,x3245)) % 181.55/181.55 [325]~E(x3251,x3252)+E(f585(x3253,x3254,x3255,x3251),f585(x3253,x3254,x3255,x3252)) % 181.55/181.55 [326]~E(x3261,x3262)+E(f163(x3261),f163(x3262)) % 181.55/181.55 [327]~E(x3271,x3272)+E(f72(x3271,x3273),f72(x3272,x3273)) % 181.55/181.55 [328]~E(x3281,x3282)+E(f72(x3283,x3281),f72(x3283,x3282)) % 181.55/181.55 [329]~E(x3291,x3292)+E(f744(x3291,x3293,x3294,x3295),f744(x3292,x3293,x3294,x3295)) % 181.55/181.55 [330]~E(x3301,x3302)+E(f744(x3303,x3301,x3304,x3305),f744(x3303,x3302,x3304,x3305)) % 181.55/181.55 [331]~E(x3311,x3312)+E(f744(x3313,x3314,x3311,x3315),f744(x3313,x3314,x3312,x3315)) % 181.55/181.55 [332]~E(x3321,x3322)+E(f744(x3323,x3324,x3325,x3321),f744(x3323,x3324,x3325,x3322)) % 181.55/181.55 [333]~E(x3331,x3332)+E(f225(x3331,x3333),f225(x3332,x3333)) % 181.55/181.55 [334]~E(x3341,x3342)+E(f225(x3343,x3341),f225(x3343,x3342)) % 181.55/181.55 [335]~E(x3351,x3352)+E(f275(x3351,x3353),f275(x3352,x3353)) % 181.55/181.55 [336]~E(x3361,x3362)+E(f275(x3363,x3361),f275(x3363,x3362)) % 181.55/181.55 [337]~E(x3371,x3372)+E(f99(x3371),f99(x3372)) % 181.55/181.55 [338]~E(x3381,x3382)+E(f812(x3381,x3383,x3384),f812(x3382,x3383,x3384)) % 181.55/181.55 [339]~E(x3391,x3392)+E(f812(x3393,x3391,x3394),f812(x3393,x3392,x3394)) % 181.55/181.55 [340]~E(x3401,x3402)+E(f812(x3403,x3404,x3401),f812(x3403,x3404,x3402)) % 181.55/181.55 [341]~E(x3411,x3412)+E(f617(x3411,x3413,x3414,x3415,x3416),f617(x3412,x3413,x3414,x3415,x3416)) % 181.55/181.55 [342]~E(x3421,x3422)+E(f617(x3423,x3421,x3424,x3425,x3426),f617(x3423,x3422,x3424,x3425,x3426)) % 181.55/181.55 [343]~E(x3431,x3432)+E(f617(x3433,x3434,x3431,x3435,x3436),f617(x3433,x3434,x3432,x3435,x3436)) % 181.55/181.55 [344]~E(x3441,x3442)+E(f617(x3443,x3444,x3445,x3441,x3446),f617(x3443,x3444,x3445,x3442,x3446)) % 181.55/181.55 [345]~E(x3451,x3452)+E(f617(x3453,x3454,x3455,x3456,x3451),f617(x3453,x3454,x3455,x3456,x3452)) % 181.55/181.55 [346]~E(x3461,x3462)+E(f26(x3461,x3463),f26(x3462,x3463)) % 181.55/181.55 [347]~E(x3471,x3472)+E(f26(x3473,x3471),f26(x3473,x3472)) % 181.55/181.55 [348]~E(x3481,x3482)+E(f415(x3481),f415(x3482)) % 181.55/181.55 [349]~E(x3491,x3492)+E(f246(x3491),f246(x3492)) % 181.55/181.55 [350]~E(x3501,x3502)+E(f253(x3501,x3503,x3504),f253(x3502,x3503,x3504)) % 181.55/181.55 [351]~E(x3511,x3512)+E(f253(x3513,x3511,x3514),f253(x3513,x3512,x3514)) % 181.55/181.55 [352]~E(x3521,x3522)+E(f253(x3523,x3524,x3521),f253(x3523,x3524,x3522)) % 181.55/181.55 [353]~E(x3531,x3532)+E(f315(x3531,x3533),f315(x3532,x3533)) % 181.55/181.55 [354]~E(x3541,x3542)+E(f315(x3543,x3541),f315(x3543,x3542)) % 181.55/181.55 [355]~E(x3551,x3552)+E(f304(x3551,x3553,x3554),f304(x3552,x3553,x3554)) % 181.55/181.55 [356]~E(x3561,x3562)+E(f304(x3563,x3561,x3564),f304(x3563,x3562,x3564)) % 181.55/181.55 [357]~E(x3571,x3572)+E(f304(x3573,x3574,x3571),f304(x3573,x3574,x3572)) % 181.55/181.55 [358]~E(x3581,x3582)+E(f317(x3581,x3583),f317(x3582,x3583)) % 181.55/181.55 [359]~E(x3591,x3592)+E(f317(x3593,x3591),f317(x3593,x3592)) % 181.55/181.55 [360]~E(x3601,x3602)+E(f312(x3601,x3603),f312(x3602,x3603)) % 181.55/181.55 [361]~E(x3611,x3612)+E(f312(x3613,x3611),f312(x3613,x3612)) % 181.55/181.55 [362]~E(x3621,x3622)+E(f15(x3621,x3623),f15(x3622,x3623)) % 181.55/181.55 [363]~E(x3631,x3632)+E(f15(x3633,x3631),f15(x3633,x3632)) % 181.55/181.55 [364]~E(x3641,x3642)+E(f841(x3641),f841(x3642)) % 181.55/181.55 [365]~E(x3651,x3652)+E(f451(x3651,x3653,x3654,x3655),f451(x3652,x3653,x3654,x3655)) % 181.55/181.55 [366]~E(x3661,x3662)+E(f451(x3663,x3661,x3664,x3665),f451(x3663,x3662,x3664,x3665)) % 181.55/181.55 [367]~E(x3671,x3672)+E(f451(x3673,x3674,x3671,x3675),f451(x3673,x3674,x3672,x3675)) % 181.55/181.55 [368]~E(x3681,x3682)+E(f451(x3683,x3684,x3685,x3681),f451(x3683,x3684,x3685,x3682)) % 181.55/181.55 [369]~E(x3691,x3692)+E(f143(x3691,x3693,x3694,x3695,x3696),f143(x3692,x3693,x3694,x3695,x3696)) % 181.55/181.55 [370]~E(x3701,x3702)+E(f143(x3703,x3701,x3704,x3705,x3706),f143(x3703,x3702,x3704,x3705,x3706)) % 181.55/181.55 [371]~E(x3711,x3712)+E(f143(x3713,x3714,x3711,x3715,x3716),f143(x3713,x3714,x3712,x3715,x3716)) % 181.55/181.55 [372]~E(x3721,x3722)+E(f143(x3723,x3724,x3725,x3721,x3726),f143(x3723,x3724,x3725,x3722,x3726)) % 181.55/181.55 [373]~E(x3731,x3732)+E(f143(x3733,x3734,x3735,x3736,x3731),f143(x3733,x3734,x3735,x3736,x3732)) % 181.55/181.55 [374]~E(x3741,x3742)+E(f228(x3741,x3743,x3744),f228(x3742,x3743,x3744)) % 181.55/181.55 [375]~E(x3751,x3752)+E(f228(x3753,x3751,x3754),f228(x3753,x3752,x3754)) % 181.55/181.55 [376]~E(x3761,x3762)+E(f228(x3763,x3764,x3761),f228(x3763,x3764,x3762)) % 181.55/181.55 [377]~E(x3771,x3772)+E(f180(x3771,x3773,x3774,x3775),f180(x3772,x3773,x3774,x3775)) % 181.55/181.55 [378]~E(x3781,x3782)+E(f180(x3783,x3781,x3784,x3785),f180(x3783,x3782,x3784,x3785)) % 181.55/181.55 [379]~E(x3791,x3792)+E(f180(x3793,x3794,x3791,x3795),f180(x3793,x3794,x3792,x3795)) % 181.55/181.55 [380]~E(x3801,x3802)+E(f180(x3803,x3804,x3805,x3801),f180(x3803,x3804,x3805,x3802)) % 181.55/181.55 [381]~E(x3811,x3812)+E(f49(x3811,x3813),f49(x3812,x3813)) % 181.55/181.55 [382]~E(x3821,x3822)+E(f49(x3823,x3821),f49(x3823,x3822)) % 181.55/181.55 [383]~E(x3831,x3832)+E(f288(x3831,x3833,x3834,x3835),f288(x3832,x3833,x3834,x3835)) % 181.55/181.55 [384]~E(x3841,x3842)+E(f288(x3843,x3841,x3844,x3845),f288(x3843,x3842,x3844,x3845)) % 181.55/181.55 [385]~E(x3851,x3852)+E(f288(x3853,x3854,x3851,x3855),f288(x3853,x3854,x3852,x3855)) % 181.55/181.55 [386]~E(x3861,x3862)+E(f288(x3863,x3864,x3865,x3861),f288(x3863,x3864,x3865,x3862)) % 181.55/181.55 [387]~E(x3871,x3872)+E(f461(x3871,x3873,x3874,x3875),f461(x3872,x3873,x3874,x3875)) % 181.55/181.55 [388]~E(x3881,x3882)+E(f461(x3883,x3881,x3884,x3885),f461(x3883,x3882,x3884,x3885)) % 181.55/181.55 [389]~E(x3891,x3892)+E(f461(x3893,x3894,x3891,x3895),f461(x3893,x3894,x3892,x3895)) % 181.55/181.55 [390]~E(x3901,x3902)+E(f461(x3903,x3904,x3905,x3901),f461(x3903,x3904,x3905,x3902)) % 181.55/181.55 [391]~E(x3911,x3912)+E(f800(x3911,x3913,x3914,x3915,x3916,x3917,x3918),f800(x3912,x3913,x3914,x3915,x3916,x3917,x3918)) % 181.55/181.55 [392]~E(x3921,x3922)+E(f800(x3923,x3921,x3924,x3925,x3926,x3927,x3928),f800(x3923,x3922,x3924,x3925,x3926,x3927,x3928)) % 181.55/181.55 [393]~E(x3931,x3932)+E(f800(x3933,x3934,x3931,x3935,x3936,x3937,x3938),f800(x3933,x3934,x3932,x3935,x3936,x3937,x3938)) % 181.55/181.55 [394]~E(x3941,x3942)+E(f800(x3943,x3944,x3945,x3941,x3946,x3947,x3948),f800(x3943,x3944,x3945,x3942,x3946,x3947,x3948)) % 181.55/181.55 [395]~E(x3951,x3952)+E(f800(x3953,x3954,x3955,x3956,x3951,x3957,x3958),f800(x3953,x3954,x3955,x3956,x3952,x3957,x3958)) % 181.55/181.55 [396]~E(x3961,x3962)+E(f800(x3963,x3964,x3965,x3966,x3967,x3961,x3968),f800(x3963,x3964,x3965,x3966,x3967,x3962,x3968)) % 181.55/181.55 [397]~E(x3971,x3972)+E(f800(x3973,x3974,x3975,x3976,x3977,x3978,x3971),f800(x3973,x3974,x3975,x3976,x3977,x3978,x3972)) % 181.55/181.55 [398]~E(x3981,x3982)+E(f186(x3981,x3983,x3984,x3985),f186(x3982,x3983,x3984,x3985)) % 181.55/181.55 [399]~E(x3991,x3992)+E(f186(x3993,x3991,x3994,x3995),f186(x3993,x3992,x3994,x3995)) % 181.55/181.55 [400]~E(x4001,x4002)+E(f186(x4003,x4004,x4001,x4005),f186(x4003,x4004,x4002,x4005)) % 181.55/181.55 [401]~E(x4011,x4012)+E(f186(x4013,x4014,x4015,x4011),f186(x4013,x4014,x4015,x4012)) % 181.55/181.55 [402]~E(x4021,x4022)+E(f777(x4021,x4023,x4024),f777(x4022,x4023,x4024)) % 181.55/181.55 [403]~E(x4031,x4032)+E(f777(x4033,x4031,x4034),f777(x4033,x4032,x4034)) % 181.55/181.55 [404]~E(x4041,x4042)+E(f777(x4043,x4044,x4041),f777(x4043,x4044,x4042)) % 181.55/181.55 [405]~E(x4051,x4052)+E(f469(x4051,x4053),f469(x4052,x4053)) % 181.55/181.55 [406]~E(x4061,x4062)+E(f469(x4063,x4061),f469(x4063,x4062)) % 181.55/181.55 [407]~E(x4071,x4072)+E(f184(x4071,x4073),f184(x4072,x4073)) % 181.55/181.55 [408]~E(x4081,x4082)+E(f184(x4083,x4081),f184(x4083,x4082)) % 181.55/181.55 [409]~E(x4091,x4092)+E(f130(x4091,x4093),f130(x4092,x4093)) % 181.55/181.55 [410]~E(x4101,x4102)+E(f130(x4103,x4101),f130(x4103,x4102)) % 181.55/181.55 [411]~E(x4111,x4112)+E(f151(x4111,x4113),f151(x4112,x4113)) % 181.55/181.55 [412]~E(x4121,x4122)+E(f151(x4123,x4121),f151(x4123,x4122)) % 181.55/181.55 [413]~E(x4131,x4132)+E(f435(x4131,x4133,x4134,x4135),f435(x4132,x4133,x4134,x4135)) % 181.55/181.55 [414]~E(x4141,x4142)+E(f435(x4143,x4141,x4144,x4145),f435(x4143,x4142,x4144,x4145)) % 181.55/181.55 [415]~E(x4151,x4152)+E(f435(x4153,x4154,x4151,x4155),f435(x4153,x4154,x4152,x4155)) % 181.55/181.55 [416]~E(x4161,x4162)+E(f435(x4163,x4164,x4165,x4161),f435(x4163,x4164,x4165,x4162)) % 181.55/181.55 [417]~E(x4171,x4172)+E(f86(x4171,x4173),f86(x4172,x4173)) % 181.55/181.55 [418]~E(x4181,x4182)+E(f86(x4183,x4181),f86(x4183,x4182)) % 181.55/181.55 [419]~E(x4191,x4192)+E(f131(x4191),f131(x4192)) % 181.55/181.55 [420]~E(x4201,x4202)+E(f382(x4201,x4203,x4204),f382(x4202,x4203,x4204)) % 181.55/181.55 [421]~E(x4211,x4212)+E(f382(x4213,x4211,x4214),f382(x4213,x4212,x4214)) % 181.55/181.55 [422]~E(x4221,x4222)+E(f382(x4223,x4224,x4221),f382(x4223,x4224,x4222)) % 181.55/181.55 [423]~E(x4231,x4232)+E(f174(x4231,x4233),f174(x4232,x4233)) % 181.55/181.55 [424]~E(x4241,x4242)+E(f174(x4243,x4241),f174(x4243,x4242)) % 181.55/181.55 [425]~E(x4251,x4252)+E(f147(x4251,x4253),f147(x4252,x4253)) % 181.55/181.55 [426]~E(x4261,x4262)+E(f147(x4263,x4261),f147(x4263,x4262)) % 181.55/181.55 [427]~E(x4271,x4272)+E(f278(x4271,x4273,x4274),f278(x4272,x4273,x4274)) % 181.55/181.55 [428]~E(x4281,x4282)+E(f278(x4283,x4281,x4284),f278(x4283,x4282,x4284)) % 181.55/181.55 [429]~E(x4291,x4292)+E(f278(x4293,x4294,x4291),f278(x4293,x4294,x4292)) % 181.55/181.55 [430]~E(x4301,x4302)+E(f795(x4301,x4303,x4304),f795(x4302,x4303,x4304)) % 181.55/181.55 [431]~E(x4311,x4312)+E(f795(x4313,x4311,x4314),f795(x4313,x4312,x4314)) % 181.55/181.55 [432]~E(x4321,x4322)+E(f795(x4323,x4324,x4321),f795(x4323,x4324,x4322)) % 181.55/181.55 [433]~E(x4331,x4332)+E(f66(x4331,x4333,x4334,x4335,x4336),f66(x4332,x4333,x4334,x4335,x4336)) % 181.55/181.55 [434]~E(x4341,x4342)+E(f66(x4343,x4341,x4344,x4345,x4346),f66(x4343,x4342,x4344,x4345,x4346)) % 181.55/181.55 [435]~E(x4351,x4352)+E(f66(x4353,x4354,x4351,x4355,x4356),f66(x4353,x4354,x4352,x4355,x4356)) % 181.55/181.55 [436]~E(x4361,x4362)+E(f66(x4363,x4364,x4365,x4361,x4366),f66(x4363,x4364,x4365,x4362,x4366)) % 181.55/181.55 [437]~E(x4371,x4372)+E(f66(x4373,x4374,x4375,x4376,x4371),f66(x4373,x4374,x4375,x4376,x4372)) % 181.55/181.55 [438]~E(x4381,x4382)+E(f672(x4381,x4383,x4384,x4385,x4386),f672(x4382,x4383,x4384,x4385,x4386)) % 181.55/181.55 [439]~E(x4391,x4392)+E(f672(x4393,x4391,x4394,x4395,x4396),f672(x4393,x4392,x4394,x4395,x4396)) % 181.55/181.55 [440]~E(x4401,x4402)+E(f672(x4403,x4404,x4401,x4405,x4406),f672(x4403,x4404,x4402,x4405,x4406)) % 181.55/181.55 [441]~E(x4411,x4412)+E(f672(x4413,x4414,x4415,x4411,x4416),f672(x4413,x4414,x4415,x4412,x4416)) % 181.55/181.55 [442]~E(x4421,x4422)+E(f672(x4423,x4424,x4425,x4426,x4421),f672(x4423,x4424,x4425,x4426,x4422)) % 181.55/181.55 [443]~E(x4431,x4432)+E(f153(x4431,x4433),f153(x4432,x4433)) % 181.55/181.55 [444]~E(x4441,x4442)+E(f153(x4443,x4441),f153(x4443,x4442)) % 181.55/181.55 [445]~E(x4451,x4452)+E(f67(x4451,x4453,x4454),f67(x4452,x4453,x4454)) % 181.55/181.55 [446]~E(x4461,x4462)+E(f67(x4463,x4461,x4464),f67(x4463,x4462,x4464)) % 181.55/181.55 [447]~E(x4471,x4472)+E(f67(x4473,x4474,x4471),f67(x4473,x4474,x4472)) % 181.55/181.55 [448]~E(x4481,x4482)+E(f185(x4481,x4483,x4484),f185(x4482,x4483,x4484)) % 181.55/181.55 [449]~E(x4491,x4492)+E(f185(x4493,x4491,x4494),f185(x4493,x4492,x4494)) % 181.55/181.55 [450]~E(x4501,x4502)+E(f185(x4503,x4504,x4501),f185(x4503,x4504,x4502)) % 181.55/181.55 [451]~E(x4511,x4512)+E(f133(x4511,x4513),f133(x4512,x4513)) % 181.55/181.55 [452]~E(x4521,x4522)+E(f133(x4523,x4521),f133(x4523,x4522)) % 181.55/181.55 [453]~E(x4531,x4532)+E(f789(x4531,x4533,x4534),f789(x4532,x4533,x4534)) % 181.55/181.55 [454]~E(x4541,x4542)+E(f789(x4543,x4541,x4544),f789(x4543,x4542,x4544)) % 181.55/181.55 [455]~E(x4551,x4552)+E(f789(x4553,x4554,x4551),f789(x4553,x4554,x4552)) % 181.55/181.55 [456]~E(x4561,x4562)+E(f160(x4561),f160(x4562)) % 181.55/181.55 [457]~E(x4571,x4572)+E(f803(x4571,x4573,x4574),f803(x4572,x4573,x4574)) % 181.55/181.55 [458]~E(x4581,x4582)+E(f803(x4583,x4581,x4584),f803(x4583,x4582,x4584)) % 181.55/181.55 [459]~E(x4591,x4592)+E(f803(x4593,x4594,x4591),f803(x4593,x4594,x4592)) % 181.55/181.55 [460]~E(x4601,x4602)+E(f445(x4601,x4603),f445(x4602,x4603)) % 181.55/181.55 [461]~E(x4611,x4612)+E(f445(x4613,x4611),f445(x4613,x4612)) % 181.55/181.55 [462]~E(x4621,x4622)+E(f255(x4621,x4623),f255(x4622,x4623)) % 181.55/181.55 [463]~E(x4631,x4632)+E(f255(x4633,x4631),f255(x4633,x4632)) % 181.55/181.55 [464]~E(x4641,x4642)+E(f490(x4641,x4643,x4644,x4645),f490(x4642,x4643,x4644,x4645)) % 181.55/181.55 [465]~E(x4651,x4652)+E(f490(x4653,x4651,x4654,x4655),f490(x4653,x4652,x4654,x4655)) % 181.55/181.55 [466]~E(x4661,x4662)+E(f490(x4663,x4664,x4661,x4665),f490(x4663,x4664,x4662,x4665)) % 181.55/181.55 [467]~E(x4671,x4672)+E(f490(x4673,x4674,x4675,x4671),f490(x4673,x4674,x4675,x4672)) % 181.55/181.55 [468]~E(x4681,x4682)+E(f220(x4681,x4683),f220(x4682,x4683)) % 181.55/181.55 [469]~E(x4691,x4692)+E(f220(x4693,x4691),f220(x4693,x4692)) % 181.55/181.55 [470]~E(x4701,x4702)+E(f706(x4701,x4703,x4704),f706(x4702,x4703,x4704)) % 181.55/181.55 [471]~E(x4711,x4712)+E(f706(x4713,x4711,x4714),f706(x4713,x4712,x4714)) % 181.55/181.55 [472]~E(x4721,x4722)+E(f706(x4723,x4724,x4721),f706(x4723,x4724,x4722)) % 181.55/181.55 [473]~E(x4731,x4732)+E(f401(x4731,x4733,x4734),f401(x4732,x4733,x4734)) % 181.55/181.55 [474]~E(x4741,x4742)+E(f401(x4743,x4741,x4744),f401(x4743,x4742,x4744)) % 181.55/181.55 [475]~E(x4751,x4752)+E(f401(x4753,x4754,x4751),f401(x4753,x4754,x4752)) % 181.55/181.55 [476]~E(x4761,x4762)+E(f154(x4761,x4763),f154(x4762,x4763)) % 181.55/181.55 [477]~E(x4771,x4772)+E(f154(x4773,x4771),f154(x4773,x4772)) % 181.55/181.55 [478]~E(x4781,x4782)+E(f175(x4781,x4783),f175(x4782,x4783)) % 181.55/181.55 [479]~E(x4791,x4792)+E(f175(x4793,x4791),f175(x4793,x4792)) % 181.55/181.55 [480]~E(x4801,x4802)+E(f45(x4801,x4803),f45(x4802,x4803)) % 181.55/181.55 [481]~E(x4811,x4812)+E(f45(x4813,x4811),f45(x4813,x4812)) % 181.55/181.55 [482]~E(x4821,x4822)+E(f431(x4821,x4823,x4824,x4825,x4826),f431(x4822,x4823,x4824,x4825,x4826)) % 181.55/181.55 [483]~E(x4831,x4832)+E(f431(x4833,x4831,x4834,x4835,x4836),f431(x4833,x4832,x4834,x4835,x4836)) % 181.55/181.55 [484]~E(x4841,x4842)+E(f431(x4843,x4844,x4841,x4845,x4846),f431(x4843,x4844,x4842,x4845,x4846)) % 181.55/181.55 [485]~E(x4851,x4852)+E(f431(x4853,x4854,x4855,x4851,x4856),f431(x4853,x4854,x4855,x4852,x4856)) % 181.55/181.55 [486]~E(x4861,x4862)+E(f431(x4863,x4864,x4865,x4866,x4861),f431(x4863,x4864,x4865,x4866,x4862)) % 181.55/181.55 [487]~E(x4871,x4872)+E(f277(x4871),f277(x4872)) % 181.55/181.55 [488]~E(x4881,x4882)+E(f667(x4881,x4883),f667(x4882,x4883)) % 181.55/181.55 [489]~E(x4891,x4892)+E(f667(x4893,x4891),f667(x4893,x4892)) % 181.55/181.55 [490]~E(x4901,x4902)+E(f313(x4901,x4903),f313(x4902,x4903)) % 181.55/181.55 [491]~E(x4911,x4912)+E(f313(x4913,x4911),f313(x4913,x4912)) % 181.55/181.55 [492]~E(x4921,x4922)+E(f264(x4921,x4923,x4924,x4925,x4926,x4927),f264(x4922,x4923,x4924,x4925,x4926,x4927)) % 181.55/181.55 [493]~E(x4931,x4932)+E(f264(x4933,x4931,x4934,x4935,x4936,x4937),f264(x4933,x4932,x4934,x4935,x4936,x4937)) % 181.55/181.55 [494]~E(x4941,x4942)+E(f264(x4943,x4944,x4941,x4945,x4946,x4947),f264(x4943,x4944,x4942,x4945,x4946,x4947)) % 181.55/181.55 [495]~E(x4951,x4952)+E(f264(x4953,x4954,x4955,x4951,x4956,x4957),f264(x4953,x4954,x4955,x4952,x4956,x4957)) % 181.55/181.55 [496]~E(x4961,x4962)+E(f264(x4963,x4964,x4965,x4966,x4961,x4967),f264(x4963,x4964,x4965,x4966,x4962,x4967)) % 181.55/181.55 [497]~E(x4971,x4972)+E(f264(x4973,x4974,x4975,x4976,x4977,x4971),f264(x4973,x4974,x4975,x4976,x4977,x4972)) % 181.55/181.55 [498]~E(x4981,x4982)+E(f94(x4981,x4983,x4984,x4985),f94(x4982,x4983,x4984,x4985)) % 181.55/181.55 [499]~E(x4991,x4992)+E(f94(x4993,x4991,x4994,x4995),f94(x4993,x4992,x4994,x4995)) % 181.55/181.55 [500]~E(x5001,x5002)+E(f94(x5003,x5004,x5001,x5005),f94(x5003,x5004,x5002,x5005)) % 181.55/181.55 [501]~E(x5011,x5012)+E(f94(x5013,x5014,x5015,x5011),f94(x5013,x5014,x5015,x5012)) % 181.55/181.55 [502]~E(x5021,x5022)+E(f685(x5021,x5023,x5024),f685(x5022,x5023,x5024)) % 181.55/181.55 [503]~E(x5031,x5032)+E(f685(x5033,x5031,x5034),f685(x5033,x5032,x5034)) % 181.55/181.55 [504]~E(x5041,x5042)+E(f685(x5043,x5044,x5041),f685(x5043,x5044,x5042)) % 181.55/181.55 [505]~E(x5051,x5052)+E(f58(x5051),f58(x5052)) % 181.55/181.55 [506]~E(x5061,x5062)+E(f29(x5061,x5063,x5064),f29(x5062,x5063,x5064)) % 181.55/181.55 [507]~E(x5071,x5072)+E(f29(x5073,x5071,x5074),f29(x5073,x5072,x5074)) % 181.55/181.55 [508]~E(x5081,x5082)+E(f29(x5083,x5084,x5081),f29(x5083,x5084,x5082)) % 181.55/181.55 [509]~E(x5091,x5092)+E(f299(x5091),f299(x5092)) % 181.55/181.55 [510]~E(x5101,x5102)+E(f65(x5101,x5103,x5104),f65(x5102,x5103,x5104)) % 181.55/181.55 [511]~E(x5111,x5112)+E(f65(x5113,x5111,x5114),f65(x5113,x5112,x5114)) % 181.55/181.55 [512]~E(x5121,x5122)+E(f65(x5123,x5124,x5121),f65(x5123,x5124,x5122)) % 181.55/181.55 [513]~E(x5131,x5132)+E(f245(x5131),f245(x5132)) % 181.55/181.55 [514]~E(x5141,x5142)+E(f17(x5141,x5143,x5144,x5145),f17(x5142,x5143,x5144,x5145)) % 181.55/181.55 [515]~E(x5151,x5152)+E(f17(x5153,x5151,x5154,x5155),f17(x5153,x5152,x5154,x5155)) % 181.55/181.55 [516]~E(x5161,x5162)+E(f17(x5163,x5164,x5161,x5165),f17(x5163,x5164,x5162,x5165)) % 181.55/181.55 [517]~E(x5171,x5172)+E(f17(x5173,x5174,x5175,x5171),f17(x5173,x5174,x5175,x5172)) % 181.55/181.55 [518]~E(x5181,x5182)+E(f662(x5181,x5183,x5184,x5185),f662(x5182,x5183,x5184,x5185)) % 181.55/181.55 [519]~E(x5191,x5192)+E(f662(x5193,x5191,x5194,x5195),f662(x5193,x5192,x5194,x5195)) % 181.55/181.55 [520]~E(x5201,x5202)+E(f662(x5203,x5204,x5201,x5205),f662(x5203,x5204,x5202,x5205)) % 181.55/181.55 [521]~E(x5211,x5212)+E(f662(x5213,x5214,x5215,x5211),f662(x5213,x5214,x5215,x5212)) % 181.55/181.55 [522]~E(x5221,x5222)+E(f64(x5221,x5223,x5224),f64(x5222,x5223,x5224)) % 181.55/181.55 [523]~E(x5231,x5232)+E(f64(x5233,x5231,x5234),f64(x5233,x5232,x5234)) % 181.55/181.55 [524]~E(x5241,x5242)+E(f64(x5243,x5244,x5241),f64(x5243,x5244,x5242)) % 181.55/181.55 [525]~E(x5251,x5252)+E(f144(x5251,x5253,x5254,x5255),f144(x5252,x5253,x5254,x5255)) % 181.55/181.55 [526]~E(x5261,x5262)+E(f144(x5263,x5261,x5264,x5265),f144(x5263,x5262,x5264,x5265)) % 181.55/181.55 [527]~E(x5271,x5272)+E(f144(x5273,x5274,x5271,x5275),f144(x5273,x5274,x5272,x5275)) % 181.55/181.55 [528]~E(x5281,x5282)+E(f144(x5283,x5284,x5285,x5281),f144(x5283,x5284,x5285,x5282)) % 181.55/181.55 [529]~E(x5291,x5292)+E(f460(x5291,x5293),f460(x5292,x5293)) % 181.55/181.55 [530]~E(x5301,x5302)+E(f460(x5303,x5301),f460(x5303,x5302)) % 181.55/181.55 [531]~E(x5311,x5312)+E(f534(x5311,x5313,x5314),f534(x5312,x5313,x5314)) % 181.55/181.55 [532]~E(x5321,x5322)+E(f534(x5323,x5321,x5324),f534(x5323,x5322,x5324)) % 181.55/181.55 [533]~E(x5331,x5332)+E(f534(x5333,x5334,x5331),f534(x5333,x5334,x5332)) % 181.55/181.55 [534]~E(x5341,x5342)+E(f440(x5341,x5343),f440(x5342,x5343)) % 181.55/181.55 [535]~E(x5351,x5352)+E(f440(x5353,x5351),f440(x5353,x5352)) % 181.55/181.55 [536]~E(x5361,x5362)+E(f87(x5361,x5363),f87(x5362,x5363)) % 181.55/181.55 [537]~E(x5371,x5372)+E(f87(x5373,x5371),f87(x5373,x5372)) % 181.55/181.55 [538]~E(x5381,x5382)+E(f279(x5381,x5383),f279(x5382,x5383)) % 181.55/181.55 [539]~E(x5391,x5392)+E(f279(x5393,x5391),f279(x5393,x5392)) % 181.55/181.55 [540]~E(x5401,x5402)+E(f398(x5401,x5403,x5404),f398(x5402,x5403,x5404)) % 181.55/181.55 [541]~E(x5411,x5412)+E(f398(x5413,x5411,x5414),f398(x5413,x5412,x5414)) % 181.55/181.55 [542]~E(x5421,x5422)+E(f398(x5423,x5424,x5421),f398(x5423,x5424,x5422)) % 181.55/181.55 [543]~E(x5431,x5432)+E(f578(x5431,x5433,x5434),f578(x5432,x5433,x5434)) % 181.55/181.55 [544]~E(x5441,x5442)+E(f578(x5443,x5441,x5444),f578(x5443,x5442,x5444)) % 181.55/181.55 [545]~E(x5451,x5452)+E(f578(x5453,x5454,x5451),f578(x5453,x5454,x5452)) % 181.55/181.55 [546]~E(x5461,x5462)+E(f13(x5461,x5463),f13(x5462,x5463)) % 181.55/181.55 [547]~E(x5471,x5472)+E(f13(x5473,x5471),f13(x5473,x5472)) % 181.55/181.55 [548]~E(x5481,x5482)+E(f632(x5481,x5483,x5484),f632(x5482,x5483,x5484)) % 181.55/181.55 [549]~E(x5491,x5492)+E(f632(x5493,x5491,x5494),f632(x5493,x5492,x5494)) % 181.55/181.55 [550]~E(x5501,x5502)+E(f632(x5503,x5504,x5501),f632(x5503,x5504,x5502)) % 181.55/181.55 [551]~E(x5511,x5512)+E(f487(x5511,x5513),f487(x5512,x5513)) % 181.55/181.55 [552]~E(x5521,x5522)+E(f487(x5523,x5521),f487(x5523,x5522)) % 181.55/181.55 [553]~E(x5531,x5532)+E(f794(x5531,x5533,x5534),f794(x5532,x5533,x5534)) % 181.55/181.55 [554]~E(x5541,x5542)+E(f794(x5543,x5541,x5544),f794(x5543,x5542,x5544)) % 181.55/181.55 [555]~E(x5551,x5552)+E(f794(x5553,x5554,x5551),f794(x5553,x5554,x5552)) % 181.55/181.55 [556]~E(x5561,x5562)+E(f478(x5561,x5563,x5564,x5565,x5566,x5567,x5568),f478(x5562,x5563,x5564,x5565,x5566,x5567,x5568)) % 181.55/181.55 [557]~E(x5571,x5572)+E(f478(x5573,x5571,x5574,x5575,x5576,x5577,x5578),f478(x5573,x5572,x5574,x5575,x5576,x5577,x5578)) % 181.55/181.55 [558]~E(x5581,x5582)+E(f478(x5583,x5584,x5581,x5585,x5586,x5587,x5588),f478(x5583,x5584,x5582,x5585,x5586,x5587,x5588)) % 181.55/181.55 [559]~E(x5591,x5592)+E(f478(x5593,x5594,x5595,x5591,x5596,x5597,x5598),f478(x5593,x5594,x5595,x5592,x5596,x5597,x5598)) % 181.55/181.55 [560]~E(x5601,x5602)+E(f478(x5603,x5604,x5605,x5606,x5601,x5607,x5608),f478(x5603,x5604,x5605,x5606,x5602,x5607,x5608)) % 181.55/181.55 [561]~E(x5611,x5612)+E(f478(x5613,x5614,x5615,x5616,x5617,x5611,x5618),f478(x5613,x5614,x5615,x5616,x5617,x5612,x5618)) % 181.55/181.55 [562]~E(x5621,x5622)+E(f478(x5623,x5624,x5625,x5626,x5627,x5628,x5621),f478(x5623,x5624,x5625,x5626,x5627,x5628,x5622)) % 181.55/181.55 [563]~E(x5631,x5632)+E(f235(x5631,x5633,x5634,x5635),f235(x5632,x5633,x5634,x5635)) % 181.55/181.55 [564]~E(x5641,x5642)+E(f235(x5643,x5641,x5644,x5645),f235(x5643,x5642,x5644,x5645)) % 181.55/181.55 [565]~E(x5651,x5652)+E(f235(x5653,x5654,x5651,x5655),f235(x5653,x5654,x5652,x5655)) % 181.55/181.55 [566]~E(x5661,x5662)+E(f235(x5663,x5664,x5665,x5661),f235(x5663,x5664,x5665,x5662)) % 181.55/181.55 [567]~E(x5671,x5672)+E(f659(x5671,x5673,x5674,x5675),f659(x5672,x5673,x5674,x5675)) % 181.55/181.55 [568]~E(x5681,x5682)+E(f659(x5683,x5681,x5684,x5685),f659(x5683,x5682,x5684,x5685)) % 181.55/181.55 [569]~E(x5691,x5692)+E(f659(x5693,x5694,x5691,x5695),f659(x5693,x5694,x5692,x5695)) % 181.55/181.55 [570]~E(x5701,x5702)+E(f659(x5703,x5704,x5705,x5701),f659(x5703,x5704,x5705,x5702)) % 181.55/181.55 [571]~E(x5711,x5712)+E(f732(x5711,x5713,x5714),f732(x5712,x5713,x5714)) % 181.55/181.55 [572]~E(x5721,x5722)+E(f732(x5723,x5721,x5724),f732(x5723,x5722,x5724)) % 181.55/181.55 [573]~E(x5731,x5732)+E(f732(x5733,x5734,x5731),f732(x5733,x5734,x5732)) % 181.55/181.55 [574]~E(x5741,x5742)+E(f78(x5741,x5743,x5744,x5745),f78(x5742,x5743,x5744,x5745)) % 181.55/181.55 [575]~E(x5751,x5752)+E(f78(x5753,x5751,x5754,x5755),f78(x5753,x5752,x5754,x5755)) % 181.55/181.55 [576]~E(x5761,x5762)+E(f78(x5763,x5764,x5761,x5765),f78(x5763,x5764,x5762,x5765)) % 181.55/181.55 [577]~E(x5771,x5772)+E(f78(x5773,x5774,x5775,x5771),f78(x5773,x5774,x5775,x5772)) % 181.55/181.55 [578]~E(x5781,x5782)+E(f30(x5781,x5783,x5784),f30(x5782,x5783,x5784)) % 181.55/181.55 [579]~E(x5791,x5792)+E(f30(x5793,x5791,x5794),f30(x5793,x5792,x5794)) % 181.55/181.55 [580]~E(x5801,x5802)+E(f30(x5803,x5804,x5801),f30(x5803,x5804,x5802)) % 181.55/181.55 [581]~E(x5811,x5812)+E(f164(x5811,x5813,x5814),f164(x5812,x5813,x5814)) % 181.55/181.55 [582]~E(x5821,x5822)+E(f164(x5823,x5821,x5824),f164(x5823,x5822,x5824)) % 181.55/181.55 [583]~E(x5831,x5832)+E(f164(x5833,x5834,x5831),f164(x5833,x5834,x5832)) % 181.55/181.55 [584]~E(x5841,x5842)+E(f14(x5841,x5843),f14(x5842,x5843)) % 181.55/181.55 [585]~E(x5851,x5852)+E(f14(x5853,x5851),f14(x5853,x5852)) % 181.55/181.55 [586]~E(x5861,x5862)+E(f383(x5861,x5863,x5864),f383(x5862,x5863,x5864)) % 181.55/181.55 [587]~E(x5871,x5872)+E(f383(x5873,x5871,x5874),f383(x5873,x5872,x5874)) % 181.55/181.55 [588]~E(x5881,x5882)+E(f383(x5883,x5884,x5881),f383(x5883,x5884,x5882)) % 181.55/181.55 [589]~E(x5891,x5892)+E(f579(x5891,x5893,x5894,x5895,x5896,x5897),f579(x5892,x5893,x5894,x5895,x5896,x5897)) % 181.55/181.55 [590]~E(x5901,x5902)+E(f579(x5903,x5901,x5904,x5905,x5906,x5907),f579(x5903,x5902,x5904,x5905,x5906,x5907)) % 181.55/181.55 [591]~E(x5911,x5912)+E(f579(x5913,x5914,x5911,x5915,x5916,x5917),f579(x5913,x5914,x5912,x5915,x5916,x5917)) % 181.55/181.55 [592]~E(x5921,x5922)+E(f579(x5923,x5924,x5925,x5921,x5926,x5927),f579(x5923,x5924,x5925,x5922,x5926,x5927)) % 181.55/181.55 [593]~E(x5931,x5932)+E(f579(x5933,x5934,x5935,x5936,x5931,x5937),f579(x5933,x5934,x5935,x5936,x5932,x5937)) % 181.55/181.55 [594]~E(x5941,x5942)+E(f579(x5943,x5944,x5945,x5946,x5947,x5941),f579(x5943,x5944,x5945,x5946,x5947,x5942)) % 181.55/181.55 [595]~E(x5951,x5952)+E(f531(x5951,x5953,x5954,x5955),f531(x5952,x5953,x5954,x5955)) % 181.55/181.55 [596]~E(x5961,x5962)+E(f531(x5963,x5961,x5964,x5965),f531(x5963,x5962,x5964,x5965)) % 181.55/181.55 [597]~E(x5971,x5972)+E(f531(x5973,x5974,x5971,x5975),f531(x5973,x5974,x5972,x5975)) % 181.55/181.55 [598]~E(x5981,x5982)+E(f531(x5983,x5984,x5985,x5981),f531(x5983,x5984,x5985,x5982)) % 181.55/181.55 [599]~E(x5991,x5992)+E(f305(x5991,x5993),f305(x5992,x5993)) % 181.55/181.55 [600]~E(x6001,x6002)+E(f305(x6003,x6001),f305(x6003,x6002)) % 181.55/181.55 [601]~E(x6011,x6012)+E(f171(x6011,x6013,x6014),f171(x6012,x6013,x6014)) % 181.55/181.55 [602]~E(x6021,x6022)+E(f171(x6023,x6021,x6024),f171(x6023,x6022,x6024)) % 181.55/181.55 [603]~E(x6031,x6032)+E(f171(x6033,x6034,x6031),f171(x6033,x6034,x6032)) % 181.55/181.55 [604]~E(x6041,x6042)+E(f232(x6041,x6043),f232(x6042,x6043)) % 181.55/181.55 [605]~E(x6051,x6052)+E(f232(x6053,x6051),f232(x6053,x6052)) % 181.55/181.55 [606]~E(x6061,x6062)+E(f392(x6061,x6063,x6064),f392(x6062,x6063,x6064)) % 181.55/181.55 [607]~E(x6071,x6072)+E(f392(x6073,x6071,x6074),f392(x6073,x6072,x6074)) % 181.55/181.55 [608]~E(x6081,x6082)+E(f392(x6083,x6084,x6081),f392(x6083,x6084,x6082)) % 181.55/181.55 [609]~E(x6091,x6092)+E(f692(x6091,x6093,x6094),f692(x6092,x6093,x6094)) % 181.55/181.55 [610]~E(x6101,x6102)+E(f692(x6103,x6101,x6104),f692(x6103,x6102,x6104)) % 181.55/181.55 [611]~E(x6111,x6112)+E(f692(x6113,x6114,x6111),f692(x6113,x6114,x6112)) % 181.55/181.55 [612]~E(x6121,x6122)+E(f452(x6121,x6123,x6124,x6125),f452(x6122,x6123,x6124,x6125)) % 181.55/181.55 [613]~E(x6131,x6132)+E(f452(x6133,x6131,x6134,x6135),f452(x6133,x6132,x6134,x6135)) % 181.55/181.55 [614]~E(x6141,x6142)+E(f452(x6143,x6144,x6141,x6145),f452(x6143,x6144,x6142,x6145)) % 181.55/181.55 [615]~E(x6151,x6152)+E(f452(x6153,x6154,x6155,x6151),f452(x6153,x6154,x6155,x6152)) % 181.55/181.55 [616]~E(x6161,x6162)+E(f746(x6161,x6163,x6164,x6165,x6166),f746(x6162,x6163,x6164,x6165,x6166)) % 181.55/181.55 [617]~E(x6171,x6172)+E(f746(x6173,x6171,x6174,x6175,x6176),f746(x6173,x6172,x6174,x6175,x6176)) % 181.55/181.55 [618]~E(x6181,x6182)+E(f746(x6183,x6184,x6181,x6185,x6186),f746(x6183,x6184,x6182,x6185,x6186)) % 181.55/181.55 [619]~E(x6191,x6192)+E(f746(x6193,x6194,x6195,x6191,x6196),f746(x6193,x6194,x6195,x6192,x6196)) % 181.55/181.55 [620]~E(x6201,x6202)+E(f746(x6203,x6204,x6205,x6206,x6201),f746(x6203,x6204,x6205,x6206,x6202)) % 181.55/181.55 [621]~E(x6211,x6212)+E(f251(x6211,x6213,x6214),f251(x6212,x6213,x6214)) % 181.55/181.55 [622]~E(x6221,x6222)+E(f251(x6223,x6221,x6224),f251(x6223,x6222,x6224)) % 181.55/181.55 [623]~E(x6231,x6232)+E(f251(x6233,x6234,x6231),f251(x6233,x6234,x6232)) % 181.55/181.55 [624]~E(x6241,x6242)+E(f150(x6241,x6243,x6244,x6245),f150(x6242,x6243,x6244,x6245)) % 181.55/181.55 [625]~E(x6251,x6252)+E(f150(x6253,x6251,x6254,x6255),f150(x6253,x6252,x6254,x6255)) % 181.55/181.55 [626]~E(x6261,x6262)+E(f150(x6263,x6264,x6261,x6265),f150(x6263,x6264,x6262,x6265)) % 181.55/181.55 [627]~E(x6271,x6272)+E(f150(x6273,x6274,x6275,x6271),f150(x6273,x6274,x6275,x6272)) % 181.55/181.55 [628]~E(x6281,x6282)+E(f724(x6281,x6283,x6284),f724(x6282,x6283,x6284)) % 181.55/181.55 [629]~E(x6291,x6292)+E(f724(x6293,x6291,x6294),f724(x6293,x6292,x6294)) % 181.55/181.55 [630]~E(x6301,x6302)+E(f724(x6303,x6304,x6301),f724(x6303,x6304,x6302)) % 181.55/181.55 [631]~E(x6311,x6312)+E(f714(x6311,x6313,x6314,x6315,x6316),f714(x6312,x6313,x6314,x6315,x6316)) % 181.55/181.55 [632]~E(x6321,x6322)+E(f714(x6323,x6321,x6324,x6325,x6326),f714(x6323,x6322,x6324,x6325,x6326)) % 181.55/181.55 [633]~E(x6331,x6332)+E(f714(x6333,x6334,x6331,x6335,x6336),f714(x6333,x6334,x6332,x6335,x6336)) % 181.55/181.55 [634]~E(x6341,x6342)+E(f714(x6343,x6344,x6345,x6341,x6346),f714(x6343,x6344,x6345,x6342,x6346)) % 181.55/181.55 [635]~E(x6351,x6352)+E(f714(x6353,x6354,x6355,x6356,x6351),f714(x6353,x6354,x6355,x6356,x6352)) % 181.55/181.55 [636]~E(x6361,x6362)+E(f40(x6361,x6363),f40(x6362,x6363)) % 181.55/181.55 [637]~E(x6371,x6372)+E(f40(x6373,x6371),f40(x6373,x6372)) % 181.55/181.55 [638]~E(x6381,x6382)+E(f499(x6381,x6383,x6384,x6385,x6386,x6387),f499(x6382,x6383,x6384,x6385,x6386,x6387)) % 181.55/181.55 [639]~E(x6391,x6392)+E(f499(x6393,x6391,x6394,x6395,x6396,x6397),f499(x6393,x6392,x6394,x6395,x6396,x6397)) % 181.55/181.55 [640]~E(x6401,x6402)+E(f499(x6403,x6404,x6401,x6405,x6406,x6407),f499(x6403,x6404,x6402,x6405,x6406,x6407)) % 181.55/181.55 [641]~E(x6411,x6412)+E(f499(x6413,x6414,x6415,x6411,x6416,x6417),f499(x6413,x6414,x6415,x6412,x6416,x6417)) % 181.55/181.55 [642]~E(x6421,x6422)+E(f499(x6423,x6424,x6425,x6426,x6421,x6427),f499(x6423,x6424,x6425,x6426,x6422,x6427)) % 181.55/181.55 [643]~E(x6431,x6432)+E(f499(x6433,x6434,x6435,x6436,x6437,x6431),f499(x6433,x6434,x6435,x6436,x6437,x6432)) % 181.55/181.55 [644]~E(x6441,x6442)+E(f694(x6441,x6443,x6444,x6445,x6446),f694(x6442,x6443,x6444,x6445,x6446)) % 181.55/181.55 [645]~E(x6451,x6452)+E(f694(x6453,x6451,x6454,x6455,x6456),f694(x6453,x6452,x6454,x6455,x6456)) % 181.55/181.55 [646]~E(x6461,x6462)+E(f694(x6463,x6464,x6461,x6465,x6466),f694(x6463,x6464,x6462,x6465,x6466)) % 181.55/181.55 [647]~E(x6471,x6472)+E(f694(x6473,x6474,x6475,x6471,x6476),f694(x6473,x6474,x6475,x6472,x6476)) % 181.55/181.55 [648]~E(x6481,x6482)+E(f694(x6483,x6484,x6485,x6486,x6481),f694(x6483,x6484,x6485,x6486,x6482)) % 181.55/181.55 [649]~E(x6491,x6492)+E(f402(x6491,x6493,x6494),f402(x6492,x6493,x6494)) % 181.55/181.55 [650]~E(x6501,x6502)+E(f402(x6503,x6501,x6504),f402(x6503,x6502,x6504)) % 181.55/181.55 [651]~E(x6511,x6512)+E(f402(x6513,x6514,x6511),f402(x6513,x6514,x6512)) % 181.55/181.55 [652]~E(x6521,x6522)+E(f792(x6521,x6523,x6524),f792(x6522,x6523,x6524)) % 181.55/181.55 [653]~E(x6531,x6532)+E(f792(x6533,x6531,x6534),f792(x6533,x6532,x6534)) % 181.55/181.55 [654]~E(x6541,x6542)+E(f792(x6543,x6544,x6541),f792(x6543,x6544,x6542)) % 181.55/181.55 [655]~E(x6551,x6552)+E(f827(x6551,x6553,x6554),f827(x6552,x6553,x6554)) % 181.55/181.55 [656]~E(x6561,x6562)+E(f827(x6563,x6561,x6564),f827(x6563,x6562,x6564)) % 181.55/181.55 [657]~E(x6571,x6572)+E(f827(x6573,x6574,x6571),f827(x6573,x6574,x6572)) % 181.55/181.55 [658]~E(x6581,x6582)+E(f10(x6581,x6583),f10(x6582,x6583)) % 181.55/181.55 [659]~E(x6591,x6592)+E(f10(x6593,x6591),f10(x6593,x6592)) % 181.55/181.55 [660]~E(x6601,x6602)+E(f580(x6601,x6603,x6604),f580(x6602,x6603,x6604)) % 181.55/181.55 [661]~E(x6611,x6612)+E(f580(x6613,x6611,x6614),f580(x6613,x6612,x6614)) % 181.55/181.55 [662]~E(x6621,x6622)+E(f580(x6623,x6624,x6621),f580(x6623,x6624,x6622)) % 181.55/181.55 [663]~E(x6631,x6632)+E(f828(x6631,x6633,x6634,x6635,x6636,x6637),f828(x6632,x6633,x6634,x6635,x6636,x6637)) % 181.55/181.55 [664]~E(x6641,x6642)+E(f828(x6643,x6641,x6644,x6645,x6646,x6647),f828(x6643,x6642,x6644,x6645,x6646,x6647)) % 181.55/181.55 [665]~E(x6651,x6652)+E(f828(x6653,x6654,x6651,x6655,x6656,x6657),f828(x6653,x6654,x6652,x6655,x6656,x6657)) % 181.55/181.55 [666]~E(x6661,x6662)+E(f828(x6663,x6664,x6665,x6661,x6666,x6667),f828(x6663,x6664,x6665,x6662,x6666,x6667)) % 181.55/181.55 [667]~E(x6671,x6672)+E(f828(x6673,x6674,x6675,x6676,x6671,x6677),f828(x6673,x6674,x6675,x6676,x6672,x6677)) % 181.55/181.55 [668]~E(x6681,x6682)+E(f828(x6683,x6684,x6685,x6686,x6687,x6681),f828(x6683,x6684,x6685,x6686,x6687,x6682)) % 181.55/181.55 [669]~E(x6691,x6692)+E(f522(x6691,x6693),f522(x6692,x6693)) % 181.55/181.55 [670]~E(x6701,x6702)+E(f522(x6703,x6701),f522(x6703,x6702)) % 181.55/181.55 [671]~E(x6711,x6712)+E(f680(x6711,x6713),f680(x6712,x6713)) % 181.55/181.55 [672]~E(x6721,x6722)+E(f680(x6723,x6721),f680(x6723,x6722)) % 181.55/181.55 [673]~E(x6731,x6732)+E(f344(x6731,x6733,x6734,x6735,x6736),f344(x6732,x6733,x6734,x6735,x6736)) % 181.55/181.55 [674]~E(x6741,x6742)+E(f344(x6743,x6741,x6744,x6745,x6746),f344(x6743,x6742,x6744,x6745,x6746)) % 181.55/181.55 [675]~E(x6751,x6752)+E(f344(x6753,x6754,x6751,x6755,x6756),f344(x6753,x6754,x6752,x6755,x6756)) % 181.55/181.55 [676]~E(x6761,x6762)+E(f344(x6763,x6764,x6765,x6761,x6766),f344(x6763,x6764,x6765,x6762,x6766)) % 181.55/181.55 [677]~E(x6771,x6772)+E(f344(x6773,x6774,x6775,x6776,x6771),f344(x6773,x6774,x6775,x6776,x6772)) % 181.55/181.55 [678]~E(x6781,x6782)+E(f274(x6781,x6783,x6784),f274(x6782,x6783,x6784)) % 181.55/181.55 [679]~E(x6791,x6792)+E(f274(x6793,x6791,x6794),f274(x6793,x6792,x6794)) % 181.55/181.55 [680]~E(x6801,x6802)+E(f274(x6803,x6804,x6801),f274(x6803,x6804,x6802)) % 181.55/181.55 [681]~E(x6811,x6812)+E(f368(x6811,x6813),f368(x6812,x6813)) % 181.55/181.55 [682]~E(x6821,x6822)+E(f368(x6823,x6821),f368(x6823,x6822)) % 181.55/181.55 [683]~E(x6831,x6832)+E(f352(x6831,x6833,x6834),f352(x6832,x6833,x6834)) % 181.55/181.55 [684]~E(x6841,x6842)+E(f352(x6843,x6841,x6844),f352(x6843,x6842,x6844)) % 181.55/181.55 [685]~E(x6851,x6852)+E(f352(x6853,x6854,x6851),f352(x6853,x6854,x6852)) % 181.55/181.55 [686]~E(x6861,x6862)+E(f358(x6861,x6863),f358(x6862,x6863)) % 181.55/181.55 [687]~E(x6871,x6872)+E(f358(x6873,x6871),f358(x6873,x6872)) % 181.55/181.55 [688]~E(x6881,x6882)+E(f76(x6881,x6883,x6884,x6885,x6886),f76(x6882,x6883,x6884,x6885,x6886)) % 181.55/181.55 [689]~E(x6891,x6892)+E(f76(x6893,x6891,x6894,x6895,x6896),f76(x6893,x6892,x6894,x6895,x6896)) % 181.55/181.55 [690]~E(x6901,x6902)+E(f76(x6903,x6904,x6901,x6905,x6906),f76(x6903,x6904,x6902,x6905,x6906)) % 181.55/181.55 [691]~E(x6911,x6912)+E(f76(x6913,x6914,x6915,x6911,x6916),f76(x6913,x6914,x6915,x6912,x6916)) % 181.55/181.55 [692]~E(x6921,x6922)+E(f76(x6923,x6924,x6925,x6926,x6921),f76(x6923,x6924,x6925,x6926,x6922)) % 181.55/181.55 [693]~E(x6931,x6932)+E(f11(x6931,x6933,x6934),f11(x6932,x6933,x6934)) % 181.55/181.55 [694]~E(x6941,x6942)+E(f11(x6943,x6941,x6944),f11(x6943,x6942,x6944)) % 181.55/181.55 [695]~E(x6951,x6952)+E(f11(x6953,x6954,x6951),f11(x6953,x6954,x6952)) % 181.55/181.55 [696]~E(x6961,x6962)+E(f802(x6961,x6963,x6964),f802(x6962,x6963,x6964)) % 181.55/181.55 [697]~E(x6971,x6972)+E(f802(x6973,x6971,x6974),f802(x6973,x6972,x6974)) % 181.55/181.55 [698]~E(x6981,x6982)+E(f802(x6983,x6984,x6981),f802(x6983,x6984,x6982)) % 181.55/181.55 [699]~E(x6991,x6992)+E(f591(x6991,x6993,x6994,x6995,x6996),f591(x6992,x6993,x6994,x6995,x6996)) % 181.55/181.55 [700]~E(x7001,x7002)+E(f591(x7003,x7001,x7004,x7005,x7006),f591(x7003,x7002,x7004,x7005,x7006)) % 181.55/181.55 [701]~E(x7011,x7012)+E(f591(x7013,x7014,x7011,x7015,x7016),f591(x7013,x7014,x7012,x7015,x7016)) % 181.55/181.55 [702]~E(x7021,x7022)+E(f591(x7023,x7024,x7025,x7021,x7026),f591(x7023,x7024,x7025,x7022,x7026)) % 181.55/181.55 [703]~E(x7031,x7032)+E(f591(x7033,x7034,x7035,x7036,x7031),f591(x7033,x7034,x7035,x7036,x7032)) % 181.55/181.55 [704]~E(x7041,x7042)+E(f819(x7041,x7043,x7044,x7045),f819(x7042,x7043,x7044,x7045)) % 181.55/181.55 [705]~E(x7051,x7052)+E(f819(x7053,x7051,x7054,x7055),f819(x7053,x7052,x7054,x7055)) % 181.55/181.55 [706]~E(x7061,x7062)+E(f819(x7063,x7064,x7061,x7065),f819(x7063,x7064,x7062,x7065)) % 181.55/181.55 [707]~E(x7071,x7072)+E(f819(x7073,x7074,x7075,x7071),f819(x7073,x7074,x7075,x7072)) % 181.55/181.55 [708]~E(x7081,x7082)+E(f637(x7081,x7083,x7084),f637(x7082,x7083,x7084)) % 181.55/181.55 [709]~E(x7091,x7092)+E(f637(x7093,x7091,x7094),f637(x7093,x7092,x7094)) % 181.55/181.55 [710]~E(x7101,x7102)+E(f637(x7103,x7104,x7101),f637(x7103,x7104,x7102)) % 181.55/181.55 [711]~E(x7111,x7112)+E(f43(x7111),f43(x7112)) % 181.55/181.55 [712]~E(x7121,x7122)+E(f152(x7121,x7123),f152(x7122,x7123)) % 181.55/181.55 [713]~E(x7131,x7132)+E(f152(x7133,x7131),f152(x7133,x7132)) % 181.55/181.55 [714]~E(x7141,x7142)+E(f141(x7141,x7143),f141(x7142,x7143)) % 181.55/181.55 [715]~E(x7151,x7152)+E(f141(x7153,x7151),f141(x7153,x7152)) % 181.55/181.55 [716]~E(x7161,x7162)+E(f737(x7161,x7163),f737(x7162,x7163)) % 181.55/181.55 [717]~E(x7171,x7172)+E(f737(x7173,x7171),f737(x7173,x7172)) % 181.55/181.55 [718]~E(x7181,x7182)+E(f77(x7181,x7183,x7184,x7185,x7186),f77(x7182,x7183,x7184,x7185,x7186)) % 181.55/181.55 [719]~E(x7191,x7192)+E(f77(x7193,x7191,x7194,x7195,x7196),f77(x7193,x7192,x7194,x7195,x7196)) % 181.55/181.55 [720]~E(x7201,x7202)+E(f77(x7203,x7204,x7201,x7205,x7206),f77(x7203,x7204,x7202,x7205,x7206)) % 181.55/181.55 [721]~E(x7211,x7212)+E(f77(x7213,x7214,x7215,x7211,x7216),f77(x7213,x7214,x7215,x7212,x7216)) % 181.55/181.55 [722]~E(x7221,x7222)+E(f77(x7223,x7224,x7225,x7226,x7221),f77(x7223,x7224,x7225,x7226,x7222)) % 181.55/181.55 [723]~E(x7231,x7232)+E(f775(x7231,x7233,x7234,x7235,x7236,x7237,x7238),f775(x7232,x7233,x7234,x7235,x7236,x7237,x7238)) % 181.55/181.55 [724]~E(x7241,x7242)+E(f775(x7243,x7241,x7244,x7245,x7246,x7247,x7248),f775(x7243,x7242,x7244,x7245,x7246,x7247,x7248)) % 181.55/181.55 [725]~E(x7251,x7252)+E(f775(x7253,x7254,x7251,x7255,x7256,x7257,x7258),f775(x7253,x7254,x7252,x7255,x7256,x7257,x7258)) % 181.55/181.55 [726]~E(x7261,x7262)+E(f775(x7263,x7264,x7265,x7261,x7266,x7267,x7268),f775(x7263,x7264,x7265,x7262,x7266,x7267,x7268)) % 181.55/181.55 [727]~E(x7271,x7272)+E(f775(x7273,x7274,x7275,x7276,x7271,x7277,x7278),f775(x7273,x7274,x7275,x7276,x7272,x7277,x7278)) % 181.55/181.55 [728]~E(x7281,x7282)+E(f775(x7283,x7284,x7285,x7286,x7287,x7281,x7288),f775(x7283,x7284,x7285,x7286,x7287,x7282,x7288)) % 181.55/181.55 [729]~E(x7291,x7292)+E(f775(x7293,x7294,x7295,x7296,x7297,x7298,x7291),f775(x7293,x7294,x7295,x7296,x7297,x7298,x7292)) % 181.55/181.55 [730]~E(x7301,x7302)+E(f221(x7301,x7303),f221(x7302,x7303)) % 181.55/181.55 [731]~E(x7311,x7312)+E(f221(x7313,x7311),f221(x7313,x7312)) % 181.55/181.55 [732]~E(x7321,x7322)+E(f202(x7321,x7323,x7324,x7325),f202(x7322,x7323,x7324,x7325)) % 181.55/181.55 [733]~E(x7331,x7332)+E(f202(x7333,x7331,x7334,x7335),f202(x7333,x7332,x7334,x7335)) % 181.55/181.55 [734]~E(x7341,x7342)+E(f202(x7343,x7344,x7341,x7345),f202(x7343,x7344,x7342,x7345)) % 181.55/181.55 [735]~E(x7351,x7352)+E(f202(x7353,x7354,x7355,x7351),f202(x7353,x7354,x7355,x7352)) % 181.55/181.55 [736]~E(x7361,x7362)+E(f256(x7361,x7363),f256(x7362,x7363)) % 181.55/181.55 [737]~E(x7371,x7372)+E(f256(x7373,x7371),f256(x7373,x7372)) % 181.55/181.55 [738]~E(x7381,x7382)+E(f558(x7381,x7383,x7384),f558(x7382,x7383,x7384)) % 181.55/181.55 [739]~E(x7391,x7392)+E(f558(x7393,x7391,x7394),f558(x7393,x7392,x7394)) % 181.55/181.55 [740]~E(x7401,x7402)+E(f558(x7403,x7404,x7401),f558(x7403,x7404,x7402)) % 181.55/181.55 [741]~E(x7411,x7412)+E(f92(x7411),f92(x7412)) % 181.55/181.55 [742]~E(x7421,x7422)+E(f627(x7421,x7423,x7424,x7425,x7426),f627(x7422,x7423,x7424,x7425,x7426)) % 181.55/181.55 [743]~E(x7431,x7432)+E(f627(x7433,x7431,x7434,x7435,x7436),f627(x7433,x7432,x7434,x7435,x7436)) % 181.55/181.55 [744]~E(x7441,x7442)+E(f627(x7443,x7444,x7441,x7445,x7446),f627(x7443,x7444,x7442,x7445,x7446)) % 181.55/181.55 [745]~E(x7451,x7452)+E(f627(x7453,x7454,x7455,x7451,x7456),f627(x7453,x7454,x7455,x7452,x7456)) % 181.55/181.55 [746]~E(x7461,x7462)+E(f627(x7463,x7464,x7465,x7466,x7461),f627(x7463,x7464,x7465,x7466,x7462)) % 181.55/181.55 [747]~E(x7471,x7472)+E(f507(x7471,x7473,x7474,x7475,x7476),f507(x7472,x7473,x7474,x7475,x7476)) % 181.55/181.55 [748]~E(x7481,x7482)+E(f507(x7483,x7481,x7484,x7485,x7486),f507(x7483,x7482,x7484,x7485,x7486)) % 181.55/181.55 [749]~E(x7491,x7492)+E(f507(x7493,x7494,x7491,x7495,x7496),f507(x7493,x7494,x7492,x7495,x7496)) % 181.55/181.55 [750]~E(x7501,x7502)+E(f507(x7503,x7504,x7505,x7501,x7506),f507(x7503,x7504,x7505,x7502,x7506)) % 181.55/181.55 [751]~E(x7511,x7512)+E(f507(x7513,x7514,x7515,x7516,x7511),f507(x7513,x7514,x7515,x7516,x7512)) % 181.55/181.55 [752]~E(x7521,x7522)+E(f135(x7521),f135(x7522)) % 181.55/181.55 [753]~E(x7531,x7532)+E(f181(x7531,x7533,x7534),f181(x7532,x7533,x7534)) % 181.55/181.55 [754]~E(x7541,x7542)+E(f181(x7543,x7541,x7544),f181(x7543,x7542,x7544)) % 181.55/181.55 [755]~E(x7551,x7552)+E(f181(x7553,x7554,x7551),f181(x7553,x7554,x7552)) % 181.55/181.55 [756]~E(x7561,x7562)+E(f54(x7561,x7563,x7564),f54(x7562,x7563,x7564)) % 181.55/181.55 [757]~E(x7571,x7572)+E(f54(x7573,x7571,x7574),f54(x7573,x7572,x7574)) % 181.55/181.55 [758]~E(x7581,x7582)+E(f54(x7583,x7584,x7581),f54(x7583,x7584,x7582)) % 181.55/181.55 [759]~E(x7591,x7592)+E(f856(x7591,x7593),f856(x7592,x7593)) % 181.55/181.55 [760]~E(x7601,x7602)+E(f856(x7603,x7601),f856(x7603,x7602)) % 181.55/181.55 [761]~E(x7611,x7612)+E(f438(x7611,x7613,x7614,x7615),f438(x7612,x7613,x7614,x7615)) % 181.55/181.55 [762]~E(x7621,x7622)+E(f438(x7623,x7621,x7624,x7625),f438(x7623,x7622,x7624,x7625)) % 181.55/181.55 [763]~E(x7631,x7632)+E(f438(x7633,x7634,x7631,x7635),f438(x7633,x7634,x7632,x7635)) % 181.55/181.55 [764]~E(x7641,x7642)+E(f438(x7643,x7644,x7645,x7641),f438(x7643,x7644,x7645,x7642)) % 181.55/181.55 [765]~E(x7651,x7652)+E(f555(x7651,x7653),f555(x7652,x7653)) % 181.55/181.55 [766]~E(x7661,x7662)+E(f555(x7663,x7661),f555(x7663,x7662)) % 181.55/181.55 [767]~E(x7671,x7672)+E(f296(x7671),f296(x7672)) % 181.55/181.55 [768]~E(x7681,x7682)+E(f530(x7681,x7683,x7684),f530(x7682,x7683,x7684)) % 181.55/181.55 [769]~E(x7691,x7692)+E(f530(x7693,x7691,x7694),f530(x7693,x7692,x7694)) % 181.55/181.55 [770]~E(x7701,x7702)+E(f530(x7703,x7704,x7701),f530(x7703,x7704,x7702)) % 181.55/181.55 [771]~E(x7711,x7712)+E(f612(x7711,x7713,x7714,x7715,x7716),f612(x7712,x7713,x7714,x7715,x7716)) % 181.55/181.55 [772]~E(x7721,x7722)+E(f612(x7723,x7721,x7724,x7725,x7726),f612(x7723,x7722,x7724,x7725,x7726)) % 181.55/181.55 [773]~E(x7731,x7732)+E(f612(x7733,x7734,x7731,x7735,x7736),f612(x7733,x7734,x7732,x7735,x7736)) % 181.55/181.55 [774]~E(x7741,x7742)+E(f612(x7743,x7744,x7745,x7741,x7746),f612(x7743,x7744,x7745,x7742,x7746)) % 181.55/181.55 [775]~E(x7751,x7752)+E(f612(x7753,x7754,x7755,x7756,x7751),f612(x7753,x7754,x7755,x7756,x7752)) % 181.55/181.55 [776]~E(x7761,x7762)+E(f387(x7761,x7763,x7764),f387(x7762,x7763,x7764)) % 181.55/181.55 [777]~E(x7771,x7772)+E(f387(x7773,x7771,x7774),f387(x7773,x7772,x7774)) % 181.55/181.55 [778]~E(x7781,x7782)+E(f387(x7783,x7784,x7781),f387(x7783,x7784,x7782)) % 181.55/181.55 [779]~E(x7791,x7792)+E(f436(x7791,x7793,x7794,x7795),f436(x7792,x7793,x7794,x7795)) % 181.55/181.55 [780]~E(x7801,x7802)+E(f436(x7803,x7801,x7804,x7805),f436(x7803,x7802,x7804,x7805)) % 181.55/181.55 [781]~E(x7811,x7812)+E(f436(x7813,x7814,x7811,x7815),f436(x7813,x7814,x7812,x7815)) % 181.55/181.55 [782]~E(x7821,x7822)+E(f436(x7823,x7824,x7825,x7821),f436(x7823,x7824,x7825,x7822)) % 181.55/181.55 [783]~E(x7831,x7832)+E(f571(x7831,x7833,x7834,x7835,x7836,x7837),f571(x7832,x7833,x7834,x7835,x7836,x7837)) % 181.55/181.55 [784]~E(x7841,x7842)+E(f571(x7843,x7841,x7844,x7845,x7846,x7847),f571(x7843,x7842,x7844,x7845,x7846,x7847)) % 181.55/181.55 [785]~E(x7851,x7852)+E(f571(x7853,x7854,x7851,x7855,x7856,x7857),f571(x7853,x7854,x7852,x7855,x7856,x7857)) % 181.55/181.55 [786]~E(x7861,x7862)+E(f571(x7863,x7864,x7865,x7861,x7866,x7867),f571(x7863,x7864,x7865,x7862,x7866,x7867)) % 181.55/181.55 [787]~E(x7871,x7872)+E(f571(x7873,x7874,x7875,x7876,x7871,x7877),f571(x7873,x7874,x7875,x7876,x7872,x7877)) % 181.55/181.55 [788]~E(x7881,x7882)+E(f571(x7883,x7884,x7885,x7886,x7887,x7881),f571(x7883,x7884,x7885,x7886,x7887,x7882)) % 181.55/181.55 [789]~E(x7891,x7892)+E(f33(x7891,x7893),f33(x7892,x7893)) % 181.55/181.55 [790]~E(x7901,x7902)+E(f33(x7903,x7901),f33(x7903,x7902)) % 181.55/181.55 [791]~E(x7911,x7912)+E(f655(x7911,x7913,x7914,x7915,x7916,x7917),f655(x7912,x7913,x7914,x7915,x7916,x7917)) % 181.55/181.55 [792]~E(x7921,x7922)+E(f655(x7923,x7921,x7924,x7925,x7926,x7927),f655(x7923,x7922,x7924,x7925,x7926,x7927)) % 181.55/181.55 [793]~E(x7931,x7932)+E(f655(x7933,x7934,x7931,x7935,x7936,x7937),f655(x7933,x7934,x7932,x7935,x7936,x7937)) % 181.55/181.55 [794]~E(x7941,x7942)+E(f655(x7943,x7944,x7945,x7941,x7946,x7947),f655(x7943,x7944,x7945,x7942,x7946,x7947)) % 181.55/181.55 [795]~E(x7951,x7952)+E(f655(x7953,x7954,x7955,x7956,x7951,x7957),f655(x7953,x7954,x7955,x7956,x7952,x7957)) % 181.55/181.55 [796]~E(x7961,x7962)+E(f655(x7963,x7964,x7965,x7966,x7967,x7961),f655(x7963,x7964,x7965,x7966,x7967,x7962)) % 181.55/181.55 [797]~E(x7971,x7972)+E(f669(x7971,x7973,x7974),f669(x7972,x7973,x7974)) % 181.55/181.55 [798]~E(x7981,x7982)+E(f669(x7983,x7981,x7984),f669(x7983,x7982,x7984)) % 181.55/181.55 [799]~E(x7991,x7992)+E(f669(x7993,x7994,x7991),f669(x7993,x7994,x7992)) % 181.55/181.55 [800]~E(x8001,x8002)+E(f640(x8001,x8003,x8004),f640(x8002,x8003,x8004)) % 181.55/181.55 [801]~E(x8011,x8012)+E(f640(x8013,x8011,x8014),f640(x8013,x8012,x8014)) % 181.55/181.55 [802]~E(x8021,x8022)+E(f640(x8023,x8024,x8021),f640(x8023,x8024,x8022)) % 181.55/181.55 [803]~E(x8031,x8032)+E(f337(x8031,x8033,x8034),f337(x8032,x8033,x8034)) % 181.55/181.55 [804]~E(x8041,x8042)+E(f337(x8043,x8041,x8044),f337(x8043,x8042,x8044)) % 181.55/181.55 [805]~E(x8051,x8052)+E(f337(x8053,x8054,x8051),f337(x8053,x8054,x8052)) % 181.55/181.55 [806]~E(x8061,x8062)+E(f641(x8061,x8063,x8064,x8065),f641(x8062,x8063,x8064,x8065)) % 181.55/181.55 [807]~E(x8071,x8072)+E(f641(x8073,x8071,x8074,x8075),f641(x8073,x8072,x8074,x8075)) % 181.55/181.55 [808]~E(x8081,x8082)+E(f641(x8083,x8084,x8081,x8085),f641(x8083,x8084,x8082,x8085)) % 181.55/181.55 [809]~E(x8091,x8092)+E(f641(x8093,x8094,x8095,x8091),f641(x8093,x8094,x8095,x8092)) % 181.55/181.55 [810]~E(x8101,x8102)+E(f600(x8101,x8103,x8104),f600(x8102,x8103,x8104)) % 181.55/181.55 [811]~E(x8111,x8112)+E(f600(x8113,x8111,x8114),f600(x8113,x8112,x8114)) % 181.55/181.55 [812]~E(x8121,x8122)+E(f600(x8123,x8124,x8121),f600(x8123,x8124,x8122)) % 181.55/181.55 [813]~E(x8131,x8132)+E(f598(x8131,x8133,x8134),f598(x8132,x8133,x8134)) % 181.55/181.55 [814]~E(x8141,x8142)+E(f598(x8143,x8141,x8144),f598(x8143,x8142,x8144)) % 181.55/181.55 [815]~E(x8151,x8152)+E(f598(x8153,x8154,x8151),f598(x8153,x8154,x8152)) % 181.55/181.55 [816]~E(x8161,x8162)+E(f513(x8161,x8163,x8164,x8165,x8166),f513(x8162,x8163,x8164,x8165,x8166)) % 181.55/181.55 [817]~E(x8171,x8172)+E(f513(x8173,x8171,x8174,x8175,x8176),f513(x8173,x8172,x8174,x8175,x8176)) % 181.55/181.55 [818]~E(x8181,x8182)+E(f513(x8183,x8184,x8181,x8185,x8186),f513(x8183,x8184,x8182,x8185,x8186)) % 181.55/181.55 [819]~E(x8191,x8192)+E(f513(x8193,x8194,x8195,x8191,x8196),f513(x8193,x8194,x8195,x8192,x8196)) % 181.55/181.55 [820]~E(x8201,x8202)+E(f513(x8203,x8204,x8205,x8206,x8201),f513(x8203,x8204,x8205,x8206,x8202)) % 181.55/181.55 [821]~E(x8211,x8212)+E(f248(x8211,x8213,x8214),f248(x8212,x8213,x8214)) % 181.55/181.55 [822]~E(x8221,x8222)+E(f248(x8223,x8221,x8224),f248(x8223,x8222,x8224)) % 181.55/181.55 [823]~E(x8231,x8232)+E(f248(x8233,x8234,x8231),f248(x8233,x8234,x8232)) % 181.55/181.55 [824]~E(x8241,x8242)+E(f369(x8241,x8243,x8244),f369(x8242,x8243,x8244)) % 181.55/181.55 [825]~E(x8251,x8252)+E(f369(x8253,x8251,x8254),f369(x8253,x8252,x8254)) % 181.55/181.55 [826]~E(x8261,x8262)+E(f369(x8263,x8264,x8261),f369(x8263,x8264,x8262)) % 181.55/181.55 [827]~E(x8271,x8272)+E(f832(x8271,x8273,x8274,x8275,x8276),f832(x8272,x8273,x8274,x8275,x8276)) % 181.55/181.55 [828]~E(x8281,x8282)+E(f832(x8283,x8281,x8284,x8285,x8286),f832(x8283,x8282,x8284,x8285,x8286)) % 181.55/181.55 [829]~E(x8291,x8292)+E(f832(x8293,x8294,x8291,x8295,x8296),f832(x8293,x8294,x8292,x8295,x8296)) % 181.55/181.55 [830]~E(x8301,x8302)+E(f832(x8303,x8304,x8305,x8301,x8306),f832(x8303,x8304,x8305,x8302,x8306)) % 181.55/181.55 [831]~E(x8311,x8312)+E(f832(x8313,x8314,x8315,x8316,x8311),f832(x8313,x8314,x8315,x8316,x8312)) % 181.55/181.55 [832]~E(x8321,x8322)+E(f370(x8321,x8323,x8324),f370(x8322,x8323,x8324)) % 181.55/181.55 [833]~E(x8331,x8332)+E(f370(x8333,x8331,x8334),f370(x8333,x8332,x8334)) % 181.55/181.55 [834]~E(x8341,x8342)+E(f370(x8343,x8344,x8341),f370(x8343,x8344,x8342)) % 181.55/181.55 [835]~E(x8351,x8352)+E(f399(x8351,x8353,x8354),f399(x8352,x8353,x8354)) % 181.55/181.55 [836]~E(x8361,x8362)+E(f399(x8363,x8361,x8364),f399(x8363,x8362,x8364)) % 181.55/181.55 [837]~E(x8371,x8372)+E(f399(x8373,x8374,x8371),f399(x8373,x8374,x8372)) % 181.55/181.55 [838]~E(x8381,x8382)+E(f265(x8381,x8383,x8384,x8385),f265(x8382,x8383,x8384,x8385)) % 181.55/181.55 [839]~E(x8391,x8392)+E(f265(x8393,x8391,x8394,x8395),f265(x8393,x8392,x8394,x8395)) % 181.55/181.55 [840]~E(x8401,x8402)+E(f265(x8403,x8404,x8401,x8405),f265(x8403,x8404,x8402,x8405)) % 181.55/181.55 [841]~E(x8411,x8412)+E(f265(x8413,x8414,x8415,x8411),f265(x8413,x8414,x8415,x8412)) % 181.55/181.55 [842]~E(x8421,x8422)+E(f642(x8421,x8423,x8424,x8425),f642(x8422,x8423,x8424,x8425)) % 181.55/181.55 [843]~E(x8431,x8432)+E(f642(x8433,x8431,x8434,x8435),f642(x8433,x8432,x8434,x8435)) % 181.55/181.55 [844]~E(x8441,x8442)+E(f642(x8443,x8444,x8441,x8445),f642(x8443,x8444,x8442,x8445)) % 181.55/181.55 [845]~E(x8451,x8452)+E(f642(x8453,x8454,x8455,x8451),f642(x8453,x8454,x8455,x8452)) % 181.55/181.55 [846]~E(x8461,x8462)+E(f751(x8461,x8463,x8464,x8465),f751(x8462,x8463,x8464,x8465)) % 181.55/181.55 [847]~E(x8471,x8472)+E(f751(x8473,x8471,x8474,x8475),f751(x8473,x8472,x8474,x8475)) % 181.55/181.55 [848]~E(x8481,x8482)+E(f751(x8483,x8484,x8481,x8485),f751(x8483,x8484,x8482,x8485)) % 181.55/181.55 [849]~E(x8491,x8492)+E(f751(x8493,x8494,x8495,x8491),f751(x8493,x8494,x8495,x8492)) % 181.55/181.55 [850]~E(x8501,x8502)+E(f788(x8501,x8503,x8504),f788(x8502,x8503,x8504)) % 181.55/181.55 [851]~E(x8511,x8512)+E(f788(x8513,x8511,x8514),f788(x8513,x8512,x8514)) % 181.55/181.55 [852]~E(x8521,x8522)+E(f788(x8523,x8524,x8521),f788(x8523,x8524,x8522)) % 181.55/181.55 [853]~E(x8531,x8532)+E(f593(x8531,x8533,x8534,x8535,x8536),f593(x8532,x8533,x8534,x8535,x8536)) % 181.55/181.55 [854]~E(x8541,x8542)+E(f593(x8543,x8541,x8544,x8545,x8546),f593(x8543,x8542,x8544,x8545,x8546)) % 181.55/181.55 [855]~E(x8551,x8552)+E(f593(x8553,x8554,x8551,x8555,x8556),f593(x8553,x8554,x8552,x8555,x8556)) % 181.55/181.55 [856]~E(x8561,x8562)+E(f593(x8563,x8564,x8565,x8561,x8566),f593(x8563,x8564,x8565,x8562,x8566)) % 181.55/181.55 [857]~E(x8571,x8572)+E(f593(x8573,x8574,x8575,x8576,x8571),f593(x8573,x8574,x8575,x8576,x8572)) % 181.55/181.55 [858]~E(x8581,x8582)+E(f853(x8581,x8583,x8584,x8585,x8586,x8587,x8588),f853(x8582,x8583,x8584,x8585,x8586,x8587,x8588)) % 181.55/181.55 [859]~E(x8591,x8592)+E(f853(x8593,x8591,x8594,x8595,x8596,x8597,x8598),f853(x8593,x8592,x8594,x8595,x8596,x8597,x8598)) % 181.55/181.55 [860]~E(x8601,x8602)+E(f853(x8603,x8604,x8601,x8605,x8606,x8607,x8608),f853(x8603,x8604,x8602,x8605,x8606,x8607,x8608)) % 181.55/181.55 [861]~E(x8611,x8612)+E(f853(x8613,x8614,x8615,x8611,x8616,x8617,x8618),f853(x8613,x8614,x8615,x8612,x8616,x8617,x8618)) % 181.55/181.55 [862]~E(x8621,x8622)+E(f853(x8623,x8624,x8625,x8626,x8621,x8627,x8628),f853(x8623,x8624,x8625,x8626,x8622,x8627,x8628)) % 181.55/181.55 [863]~E(x8631,x8632)+E(f853(x8633,x8634,x8635,x8636,x8637,x8631,x8638),f853(x8633,x8634,x8635,x8636,x8637,x8632,x8638)) % 181.55/181.55 [864]~E(x8641,x8642)+E(f853(x8643,x8644,x8645,x8646,x8647,x8648,x8641),f853(x8643,x8644,x8645,x8646,x8647,x8648,x8642)) % 181.55/181.55 [865]~E(x8651,x8652)+E(f214(x8651,x8653,x8654,x8655),f214(x8652,x8653,x8654,x8655)) % 181.55/181.55 [866]~E(x8661,x8662)+E(f214(x8663,x8661,x8664,x8665),f214(x8663,x8662,x8664,x8665)) % 181.55/181.55 [867]~E(x8671,x8672)+E(f214(x8673,x8674,x8671,x8675),f214(x8673,x8674,x8672,x8675)) % 181.55/181.55 [868]~E(x8681,x8682)+E(f214(x8683,x8684,x8685,x8681),f214(x8683,x8684,x8685,x8682)) % 181.55/181.55 [869]~E(x8691,x8692)+E(f381(x8691,x8693,x8694,x8695),f381(x8692,x8693,x8694,x8695)) % 181.55/181.55 [870]~E(x8701,x8702)+E(f381(x8703,x8701,x8704,x8705),f381(x8703,x8702,x8704,x8705)) % 181.55/181.55 [871]~E(x8711,x8712)+E(f381(x8713,x8714,x8711,x8715),f381(x8713,x8714,x8712,x8715)) % 181.55/181.55 [872]~E(x8721,x8722)+E(f381(x8723,x8724,x8725,x8721),f381(x8723,x8724,x8725,x8722)) % 181.55/181.55 [873]~E(x8731,x8732)+E(f504(x8731,x8733,x8734,x8735,x8736,x8737),f504(x8732,x8733,x8734,x8735,x8736,x8737)) % 181.55/181.55 [874]~E(x8741,x8742)+E(f504(x8743,x8741,x8744,x8745,x8746,x8747),f504(x8743,x8742,x8744,x8745,x8746,x8747)) % 181.55/181.55 [875]~E(x8751,x8752)+E(f504(x8753,x8754,x8751,x8755,x8756,x8757),f504(x8753,x8754,x8752,x8755,x8756,x8757)) % 181.55/181.55 [876]~E(x8761,x8762)+E(f504(x8763,x8764,x8765,x8761,x8766,x8767),f504(x8763,x8764,x8765,x8762,x8766,x8767)) % 181.55/181.55 [877]~E(x8771,x8772)+E(f504(x8773,x8774,x8775,x8776,x8771,x8777),f504(x8773,x8774,x8775,x8776,x8772,x8777)) % 181.55/181.55 [878]~E(x8781,x8782)+E(f504(x8783,x8784,x8785,x8786,x8787,x8781),f504(x8783,x8784,x8785,x8786,x8787,x8782)) % 181.55/181.55 [879]~E(x8791,x8792)+E(f830(x8791,x8793,x8794,x8795),f830(x8792,x8793,x8794,x8795)) % 181.55/181.55 [880]~E(x8801,x8802)+E(f830(x8803,x8801,x8804,x8805),f830(x8803,x8802,x8804,x8805)) % 181.55/181.55 [881]~E(x8811,x8812)+E(f830(x8813,x8814,x8811,x8815),f830(x8813,x8814,x8812,x8815)) % 181.55/181.55 [882]~E(x8821,x8822)+E(f830(x8823,x8824,x8825,x8821),f830(x8823,x8824,x8825,x8822)) % 181.55/181.55 [883]~E(x8831,x8832)+E(f137(x8831,x8833),f137(x8832,x8833)) % 181.55/181.55 [884]~E(x8841,x8842)+E(f137(x8843,x8841),f137(x8843,x8842)) % 181.55/181.55 [885]~E(x8851,x8852)+E(f489(x8851,x8853,x8854),f489(x8852,x8853,x8854)) % 181.55/181.55 [886]~E(x8861,x8862)+E(f489(x8863,x8861,x8864),f489(x8863,x8862,x8864)) % 181.55/181.55 [887]~E(x8871,x8872)+E(f489(x8873,x8874,x8871),f489(x8873,x8874,x8872)) % 181.55/181.55 [888]~E(x8881,x8882)+E(f715(x8881,x8883),f715(x8882,x8883)) % 181.55/181.55 [889]~E(x8891,x8892)+E(f715(x8893,x8891),f715(x8893,x8892)) % 181.55/181.55 [890]~E(x8901,x8902)+E(f541(x8901,x8903,x8904),f541(x8902,x8903,x8904)) % 181.55/181.55 [891]~E(x8911,x8912)+E(f541(x8913,x8911,x8914),f541(x8913,x8912,x8914)) % 181.55/181.55 [892]~E(x8921,x8922)+E(f541(x8923,x8924,x8921),f541(x8923,x8924,x8922)) % 181.55/181.55 [893]~E(x8931,x8932)+E(f328(x8931,x8933,x8934,x8935),f328(x8932,x8933,x8934,x8935)) % 181.55/181.55 [894]~E(x8941,x8942)+E(f328(x8943,x8941,x8944,x8945),f328(x8943,x8942,x8944,x8945)) % 181.55/181.55 [895]~E(x8951,x8952)+E(f328(x8953,x8954,x8951,x8955),f328(x8953,x8954,x8952,x8955)) % 181.55/181.55 [896]~E(x8961,x8962)+E(f328(x8963,x8964,x8965,x8961),f328(x8963,x8964,x8965,x8962)) % 181.55/181.55 [897]~E(x8971,x8972)+E(f165(x8971,x8973,x8974),f165(x8972,x8973,x8974)) % 181.55/181.55 [898]~E(x8981,x8982)+E(f165(x8983,x8981,x8984),f165(x8983,x8982,x8984)) % 181.55/181.55 [899]~E(x8991,x8992)+E(f165(x8993,x8994,x8991),f165(x8993,x8994,x8992)) % 181.55/181.55 [900]~E(x9001,x9002)+E(f708(x9001,x9003,x9004,x9005,x9006),f708(x9002,x9003,x9004,x9005,x9006)) % 181.55/181.55 [901]~E(x9011,x9012)+E(f708(x9013,x9011,x9014,x9015,x9016),f708(x9013,x9012,x9014,x9015,x9016)) % 181.55/181.55 [902]~E(x9021,x9022)+E(f708(x9023,x9024,x9021,x9025,x9026),f708(x9023,x9024,x9022,x9025,x9026)) % 181.55/181.55 [903]~E(x9031,x9032)+E(f708(x9033,x9034,x9035,x9031,x9036),f708(x9033,x9034,x9035,x9032,x9036)) % 181.55/181.55 [904]~E(x9041,x9042)+E(f708(x9043,x9044,x9045,x9046,x9041),f708(x9043,x9044,x9045,x9046,x9042)) % 181.55/181.55 [905]~E(x9051,x9052)+E(f433(x9051,x9053,x9054,x9055),f433(x9052,x9053,x9054,x9055)) % 181.55/181.55 [906]~E(x9061,x9062)+E(f433(x9063,x9061,x9064,x9065),f433(x9063,x9062,x9064,x9065)) % 181.55/181.55 [907]~E(x9071,x9072)+E(f433(x9073,x9074,x9071,x9075),f433(x9073,x9074,x9072,x9075)) % 181.55/181.55 [908]~E(x9081,x9082)+E(f433(x9083,x9084,x9085,x9081),f433(x9083,x9084,x9085,x9082)) % 181.55/181.55 [909]~E(x9091,x9092)+E(f719(x9091,x9093,x9094,x9095),f719(x9092,x9093,x9094,x9095)) % 181.55/181.55 [910]~E(x9101,x9102)+E(f719(x9103,x9101,x9104,x9105),f719(x9103,x9102,x9104,x9105)) % 181.55/181.55 [911]~E(x9111,x9112)+E(f719(x9113,x9114,x9111,x9115),f719(x9113,x9114,x9112,x9115)) % 181.55/181.55 [912]~E(x9121,x9122)+E(f719(x9123,x9124,x9125,x9121),f719(x9123,x9124,x9125,x9122)) % 181.55/181.55 [913]~E(x9131,x9132)+E(f411(x9131),f411(x9132)) % 181.55/181.55 [914]~E(x9141,x9142)+E(f318(x9141,x9143,x9144),f318(x9142,x9143,x9144)) % 181.55/181.55 [915]~E(x9151,x9152)+E(f318(x9153,x9151,x9154),f318(x9153,x9152,x9154)) % 181.55/181.55 [916]~E(x9161,x9162)+E(f318(x9163,x9164,x9161),f318(x9163,x9164,x9162)) % 181.55/181.55 [917]~E(x9171,x9172)+E(f155(x9171,x9173),f155(x9172,x9173)) % 181.55/181.55 [918]~E(x9181,x9182)+E(f155(x9183,x9181),f155(x9183,x9182)) % 181.55/181.55 [919]~E(x9191,x9192)+E(f801(x9191,x9193,x9194,x9195),f801(x9192,x9193,x9194,x9195)) % 181.55/181.55 [920]~E(x9201,x9202)+E(f801(x9203,x9201,x9204,x9205),f801(x9203,x9202,x9204,x9205)) % 181.55/181.55 [921]~E(x9211,x9212)+E(f801(x9213,x9214,x9211,x9215),f801(x9213,x9214,x9212,x9215)) % 181.55/181.55 [922]~E(x9221,x9222)+E(f801(x9223,x9224,x9225,x9221),f801(x9223,x9224,x9225,x9222)) % 181.55/181.55 [923]~E(x9231,x9232)+E(f330(x9231,x9233,x9234),f330(x9232,x9233,x9234)) % 181.55/181.55 [924]~E(x9241,x9242)+E(f330(x9243,x9241,x9244),f330(x9243,x9242,x9244)) % 181.55/181.55 [925]~E(x9251,x9252)+E(f330(x9253,x9254,x9251),f330(x9253,x9254,x9252)) % 181.55/181.55 [926]~E(x9261,x9262)+E(f412(x9261,x9263,x9264),f412(x9262,x9263,x9264)) % 181.55/181.55 [927]~E(x9271,x9272)+E(f412(x9273,x9271,x9274),f412(x9273,x9272,x9274)) % 181.55/181.55 [928]~E(x9281,x9282)+E(f412(x9283,x9284,x9281),f412(x9283,x9284,x9282)) % 181.55/181.55 [929]~E(x9291,x9292)+E(f495(x9291,x9293,x9294,x9295,x9296),f495(x9292,x9293,x9294,x9295,x9296)) % 181.55/181.55 [930]~E(x9301,x9302)+E(f495(x9303,x9301,x9304,x9305,x9306),f495(x9303,x9302,x9304,x9305,x9306)) % 181.55/181.55 [931]~E(x9311,x9312)+E(f495(x9313,x9314,x9311,x9315,x9316),f495(x9313,x9314,x9312,x9315,x9316)) % 181.55/181.55 [932]~E(x9321,x9322)+E(f495(x9323,x9324,x9325,x9321,x9326),f495(x9323,x9324,x9325,x9322,x9326)) % 181.55/181.55 [933]~E(x9331,x9332)+E(f495(x9333,x9334,x9335,x9336,x9331),f495(x9333,x9334,x9335,x9336,x9332)) % 181.55/181.55 [934]~E(x9341,x9342)+E(f479(x9341,x9343,x9344),f479(x9342,x9343,x9344)) % 181.55/181.55 [935]~E(x9351,x9352)+E(f479(x9353,x9351,x9354),f479(x9353,x9352,x9354)) % 181.55/181.55 [936]~E(x9361,x9362)+E(f479(x9363,x9364,x9361),f479(x9363,x9364,x9362)) % 181.55/181.55 [937]~E(x9371,x9372)+E(f195(x9371,x9373),f195(x9372,x9373)) % 181.55/181.55 [938]~E(x9381,x9382)+E(f195(x9383,x9381),f195(x9383,x9382)) % 181.55/181.55 [939]~E(x9391,x9392)+E(f57(x9391),f57(x9392)) % 181.55/181.55 [940]~E(x9401,x9402)+E(f121(x9401,x9403),f121(x9402,x9403)) % 181.55/181.55 [941]~E(x9411,x9412)+E(f121(x9413,x9411),f121(x9413,x9412)) % 181.55/181.55 [942]~E(x9421,x9422)+E(f712(x9421,x9423,x9424,x9425),f712(x9422,x9423,x9424,x9425)) % 181.55/181.55 [943]~E(x9431,x9432)+E(f712(x9433,x9431,x9434,x9435),f712(x9433,x9432,x9434,x9435)) % 181.55/181.55 [944]~E(x9441,x9442)+E(f712(x9443,x9444,x9441,x9445),f712(x9443,x9444,x9442,x9445)) % 181.55/181.55 [945]~E(x9451,x9452)+E(f712(x9453,x9454,x9455,x9451),f712(x9453,x9454,x9455,x9452)) % 181.55/181.55 [946]~E(x9461,x9462)+E(f636(x9461,x9463,x9464),f636(x9462,x9463,x9464)) % 181.55/181.55 [947]~E(x9471,x9472)+E(f636(x9473,x9471,x9474),f636(x9473,x9472,x9474)) % 181.55/181.55 [948]~E(x9481,x9482)+E(f636(x9483,x9484,x9481),f636(x9483,x9484,x9482)) % 181.55/181.55 [949]~E(x9491,x9492)+E(f252(x9491,x9493),f252(x9492,x9493)) % 181.55/181.55 [950]~E(x9501,x9502)+E(f252(x9503,x9501),f252(x9503,x9502)) % 181.55/181.55 [951]~E(x9511,x9512)+E(f573(x9511,x9513),f573(x9512,x9513)) % 181.55/181.55 [952]~E(x9521,x9522)+E(f573(x9523,x9521),f573(x9523,x9522)) % 181.55/181.55 [953]~E(x9531,x9532)+E(f280(x9531,x9533),f280(x9532,x9533)) % 181.55/181.55 [954]~E(x9541,x9542)+E(f280(x9543,x9541),f280(x9543,x9542)) % 181.55/181.55 [955]~E(x9551,x9552)+E(f529(x9551,x9553,x9554),f529(x9552,x9553,x9554)) % 181.55/181.55 [956]~E(x9561,x9562)+E(f529(x9563,x9561,x9564),f529(x9563,x9562,x9564)) % 181.55/181.55 [957]~E(x9571,x9572)+E(f529(x9573,x9574,x9571),f529(x9573,x9574,x9572)) % 181.55/181.55 [958]~E(x9581,x9582)+E(f484(x9581,x9583,x9584,x9585,x9586,x9587),f484(x9582,x9583,x9584,x9585,x9586,x9587)) % 181.55/181.55 [959]~E(x9591,x9592)+E(f484(x9593,x9591,x9594,x9595,x9596,x9597),f484(x9593,x9592,x9594,x9595,x9596,x9597)) % 181.55/181.55 [960]~E(x9601,x9602)+E(f484(x9603,x9604,x9601,x9605,x9606,x9607),f484(x9603,x9604,x9602,x9605,x9606,x9607)) % 181.55/181.55 [961]~E(x9611,x9612)+E(f484(x9613,x9614,x9615,x9611,x9616,x9617),f484(x9613,x9614,x9615,x9612,x9616,x9617)) % 181.55/181.55 [962]~E(x9621,x9622)+E(f484(x9623,x9624,x9625,x9626,x9621,x9627),f484(x9623,x9624,x9625,x9626,x9622,x9627)) % 181.55/181.55 [963]~E(x9631,x9632)+E(f484(x9633,x9634,x9635,x9636,x9637,x9631),f484(x9633,x9634,x9635,x9636,x9637,x9632)) % 181.55/181.55 [964]~E(x9641,x9642)+E(f365(x9641,x9643,x9644),f365(x9642,x9643,x9644)) % 181.55/181.55 [965]~E(x9651,x9652)+E(f365(x9653,x9651,x9654),f365(x9653,x9652,x9654)) % 181.55/181.55 [966]~E(x9661,x9662)+E(f365(x9663,x9664,x9661),f365(x9663,x9664,x9662)) % 181.55/181.55 [967]~E(x9671,x9672)+E(f589(x9671,x9673,x9674,x9675,x9676),f589(x9672,x9673,x9674,x9675,x9676)) % 181.55/181.55 [968]~E(x9681,x9682)+E(f589(x9683,x9681,x9684,x9685,x9686),f589(x9683,x9682,x9684,x9685,x9686)) % 181.55/181.55 [969]~E(x9691,x9692)+E(f589(x9693,x9694,x9691,x9695,x9696),f589(x9693,x9694,x9692,x9695,x9696)) % 181.55/181.55 [970]~E(x9701,x9702)+E(f589(x9703,x9704,x9705,x9701,x9706),f589(x9703,x9704,x9705,x9702,x9706)) % 181.55/181.55 [971]~E(x9711,x9712)+E(f589(x9713,x9714,x9715,x9716,x9711),f589(x9713,x9714,x9715,x9716,x9712)) % 181.55/181.55 [972]~E(x9721,x9722)+E(f835(x9721,x9723,x9724,x9725,x9726),f835(x9722,x9723,x9724,x9725,x9726)) % 181.55/181.55 [973]~E(x9731,x9732)+E(f835(x9733,x9731,x9734,x9735,x9736),f835(x9733,x9732,x9734,x9735,x9736)) % 181.55/181.55 [974]~E(x9741,x9742)+E(f835(x9743,x9744,x9741,x9745,x9746),f835(x9743,x9744,x9742,x9745,x9746)) % 181.55/181.55 [975]~E(x9751,x9752)+E(f835(x9753,x9754,x9755,x9751,x9756),f835(x9753,x9754,x9755,x9752,x9756)) % 181.55/181.55 [976]~E(x9761,x9762)+E(f835(x9763,x9764,x9765,x9766,x9761),f835(x9763,x9764,x9765,x9766,x9762)) % 181.55/181.55 [977]~E(x9771,x9772)+E(f338(x9771,x9773),f338(x9772,x9773)) % 181.55/181.55 [978]~E(x9781,x9782)+E(f338(x9783,x9781),f338(x9783,x9782)) % 181.55/181.55 [979]~E(x9791,x9792)+E(f791(x9791,x9793,x9794),f791(x9792,x9793,x9794)) % 181.55/181.55 [980]~E(x9801,x9802)+E(f791(x9803,x9801,x9804),f791(x9803,x9802,x9804)) % 181.55/181.55 [981]~E(x9811,x9812)+E(f791(x9813,x9814,x9811),f791(x9813,x9814,x9812)) % 181.55/181.55 [982]~E(x9821,x9822)+E(f752(x9821,x9823,x9824,x9825,x9826),f752(x9822,x9823,x9824,x9825,x9826)) % 181.55/181.55 [983]~E(x9831,x9832)+E(f752(x9833,x9831,x9834,x9835,x9836),f752(x9833,x9832,x9834,x9835,x9836)) % 181.55/181.55 [984]~E(x9841,x9842)+E(f752(x9843,x9844,x9841,x9845,x9846),f752(x9843,x9844,x9842,x9845,x9846)) % 181.55/181.55 [985]~E(x9851,x9852)+E(f752(x9853,x9854,x9855,x9851,x9856),f752(x9853,x9854,x9855,x9852,x9856)) % 181.55/181.55 [986]~E(x9861,x9862)+E(f752(x9863,x9864,x9865,x9866,x9861),f752(x9863,x9864,x9865,x9866,x9862)) % 181.55/181.55 [987]~E(x9871,x9872)+E(f485(x9871,x9873,x9874,x9875,x9876,x9877),f485(x9872,x9873,x9874,x9875,x9876,x9877)) % 181.55/181.55 [988]~E(x9881,x9882)+E(f485(x9883,x9881,x9884,x9885,x9886,x9887),f485(x9883,x9882,x9884,x9885,x9886,x9887)) % 181.55/181.55 [989]~E(x9891,x9892)+E(f485(x9893,x9894,x9891,x9895,x9896,x9897),f485(x9893,x9894,x9892,x9895,x9896,x9897)) % 181.55/181.55 [990]~E(x9901,x9902)+E(f485(x9903,x9904,x9905,x9901,x9906,x9907),f485(x9903,x9904,x9905,x9902,x9906,x9907)) % 181.55/181.55 [991]~E(x9911,x9912)+E(f485(x9913,x9914,x9915,x9916,x9911,x9917),f485(x9913,x9914,x9915,x9916,x9912,x9917)) % 181.55/181.55 [992]~E(x9921,x9922)+E(f485(x9923,x9924,x9925,x9926,x9927,x9921),f485(x9923,x9924,x9925,x9926,x9927,x9922)) % 181.55/181.55 [993]~E(x9931,x9932)+E(f674(x9931,x9933,x9934,x9935,x9936),f674(x9932,x9933,x9934,x9935,x9936)) % 181.55/181.55 [994]~E(x9941,x9942)+E(f674(x9943,x9941,x9944,x9945,x9946),f674(x9943,x9942,x9944,x9945,x9946)) % 181.55/181.55 [995]~E(x9951,x9952)+E(f674(x9953,x9954,x9951,x9955,x9956),f674(x9953,x9954,x9952,x9955,x9956)) % 181.55/181.55 [996]~E(x9961,x9962)+E(f674(x9963,x9964,x9965,x9961,x9966),f674(x9963,x9964,x9965,x9962,x9966)) % 181.55/181.55 [997]~E(x9971,x9972)+E(f674(x9973,x9974,x9975,x9976,x9971),f674(x9973,x9974,x9975,x9976,x9972)) % 181.55/181.55 [998]~E(x9981,x9982)+E(f413(x9981,x9983,x9984),f413(x9982,x9983,x9984)) % 181.55/181.55 [999]~E(x9991,x9992)+E(f413(x9993,x9991,x9994),f413(x9993,x9992,x9994)) % 181.55/181.55 [1000]~E(x10001,x10002)+E(f413(x10003,x10004,x10001),f413(x10003,x10004,x10002)) % 181.55/181.55 [1001]~E(x10011,x10012)+E(f486(x10011,x10013),f486(x10012,x10013)) % 181.55/181.55 [1002]~E(x10021,x10022)+E(f486(x10023,x10021),f486(x10023,x10022)) % 181.55/181.55 [1003]~E(x10031,x10032)+E(f270(x10031,x10033),f270(x10032,x10033)) % 181.55/181.55 [1004]~E(x10041,x10042)+E(f270(x10043,x10041),f270(x10043,x10042)) % 181.55/181.55 [1005]~E(x10051,x10052)+E(f668(x10051,x10053),f668(x10052,x10053)) % 181.55/181.55 [1006]~E(x10061,x10062)+E(f668(x10063,x10061),f668(x10063,x10062)) % 181.55/181.55 [1007]~E(x10071,x10072)+E(f829(x10071,x10073,x10074),f829(x10072,x10073,x10074)) % 181.55/181.55 [1008]~E(x10081,x10082)+E(f829(x10083,x10081,x10084),f829(x10083,x10082,x10084)) % 181.55/181.55 [1009]~E(x10091,x10092)+E(f829(x10093,x10094,x10091),f829(x10093,x10094,x10092)) % 181.55/181.55 [1010]~E(x10101,x10102)+E(f335(x10101,x10103,x10104,x10105),f335(x10102,x10103,x10104,x10105)) % 181.55/181.55 [1011]~E(x10111,x10112)+E(f335(x10113,x10111,x10114,x10115),f335(x10113,x10112,x10114,x10115)) % 181.55/181.55 [1012]~E(x10121,x10122)+E(f335(x10123,x10124,x10121,x10125),f335(x10123,x10124,x10122,x10125)) % 181.55/181.55 [1013]~E(x10131,x10132)+E(f335(x10133,x10134,x10135,x10131),f335(x10133,x10134,x10135,x10132)) % 181.55/181.55 [1014]~E(x10141,x10142)+E(f423(x10141,x10143),f423(x10142,x10143)) % 181.55/181.55 [1015]~E(x10151,x10152)+E(f423(x10153,x10151),f423(x10153,x10152)) % 181.55/181.55 [1016]~E(x10161,x10162)+E(f784(x10161,x10163,x10164),f784(x10162,x10163,x10164)) % 181.55/181.55 [1017]~E(x10171,x10172)+E(f784(x10173,x10171,x10174),f784(x10173,x10172,x10174)) % 181.55/181.55 [1018]~E(x10181,x10182)+E(f784(x10183,x10184,x10181),f784(x10183,x10184,x10182)) % 181.55/181.55 [1019]~E(x10191,x10192)+E(f405(x10191),f405(x10192)) % 181.55/181.55 [1020]~E(x10201,x10202)+E(f676(x10201,x10203,x10204,x10205,x10206),f676(x10202,x10203,x10204,x10205,x10206)) % 181.55/181.55 [1021]~E(x10211,x10212)+E(f676(x10213,x10211,x10214,x10215,x10216),f676(x10213,x10212,x10214,x10215,x10216)) % 181.55/181.55 [1022]~E(x10221,x10222)+E(f676(x10223,x10224,x10221,x10225,x10226),f676(x10223,x10224,x10222,x10225,x10226)) % 181.55/181.55 [1023]~E(x10231,x10232)+E(f676(x10233,x10234,x10235,x10231,x10236),f676(x10233,x10234,x10235,x10232,x10236)) % 181.55/181.55 [1024]~E(x10241,x10242)+E(f676(x10243,x10244,x10245,x10246,x10241),f676(x10243,x10244,x10245,x10246,x10242)) % 181.55/181.55 [1025]~E(x10251,x10252)+E(f595(x10251,x10253,x10254),f595(x10252,x10253,x10254)) % 181.55/181.55 [1026]~E(x10261,x10262)+E(f595(x10263,x10261,x10264),f595(x10263,x10262,x10264)) % 181.55/181.55 [1027]~E(x10271,x10272)+E(f595(x10273,x10274,x10271),f595(x10273,x10274,x10272)) % 181.55/181.55 [1028]~E(x10281,x10282)+E(f643(x10281,x10283,x10284,x10285),f643(x10282,x10283,x10284,x10285)) % 181.55/181.55 [1029]~E(x10291,x10292)+E(f643(x10293,x10291,x10294,x10295),f643(x10293,x10292,x10294,x10295)) % 181.55/181.55 [1030]~E(x10301,x10302)+E(f643(x10303,x10304,x10301,x10305),f643(x10303,x10304,x10302,x10305)) % 181.55/181.55 [1031]~E(x10311,x10312)+E(f643(x10313,x10314,x10315,x10311),f643(x10313,x10314,x10315,x10312)) % 181.55/181.55 [1032]~E(x10321,x10322)+E(f707(x10321,x10323,x10324,x10325),f707(x10322,x10323,x10324,x10325)) % 181.55/181.55 [1033]~E(x10331,x10332)+E(f707(x10333,x10331,x10334,x10335),f707(x10333,x10332,x10334,x10335)) % 181.55/181.55 [1034]~E(x10341,x10342)+E(f707(x10343,x10344,x10341,x10345),f707(x10343,x10344,x10342,x10345)) % 181.55/181.55 [1035]~E(x10351,x10352)+E(f707(x10353,x10354,x10355,x10351),f707(x10353,x10354,x10355,x10352)) % 181.55/181.55 [1036]~E(x10361,x10362)+E(f336(x10361,x10363,x10364),f336(x10362,x10363,x10364)) % 181.55/181.55 [1037]~E(x10371,x10372)+E(f336(x10373,x10371,x10374),f336(x10373,x10372,x10374)) % 181.55/181.55 [1038]~E(x10381,x10382)+E(f336(x10383,x10384,x10381),f336(x10383,x10384,x10382)) % 181.55/181.55 [1039]~E(x10391,x10392)+E(f483(x10391,x10393,x10394),f483(x10392,x10393,x10394)) % 181.55/181.55 [1040]~E(x10401,x10402)+E(f483(x10403,x10401,x10404),f483(x10403,x10402,x10404)) % 181.55/181.55 [1041]~E(x10411,x10412)+E(f483(x10413,x10414,x10411),f483(x10413,x10414,x10412)) % 181.55/181.55 [1042]~E(x10421,x10422)+E(f691(x10421,x10423,x10424,x10425),f691(x10422,x10423,x10424,x10425)) % 181.55/181.55 [1043]~E(x10431,x10432)+E(f691(x10433,x10431,x10434,x10435),f691(x10433,x10432,x10434,x10435)) % 181.55/181.55 [1044]~E(x10441,x10442)+E(f691(x10443,x10444,x10441,x10445),f691(x10443,x10444,x10442,x10445)) % 181.55/181.55 [1045]~E(x10451,x10452)+E(f691(x10453,x10454,x10455,x10451),f691(x10453,x10454,x10455,x10452)) % 181.55/181.55 [1046]~E(x10461,x10462)+E(f444(x10461,x10463),f444(x10462,x10463)) % 181.55/181.55 [1047]~E(x10471,x10472)+E(f444(x10473,x10471),f444(x10473,x10472)) % 181.55/181.55 [1048]~E(x10481,x10482)+E(f817(x10481,x10483,x10484,x10485),f817(x10482,x10483,x10484,x10485)) % 181.55/181.55 [1049]~E(x10491,x10492)+E(f817(x10493,x10491,x10494,x10495),f817(x10493,x10492,x10494,x10495)) % 181.55/181.55 [1050]~E(x10501,x10502)+E(f817(x10503,x10504,x10501,x10505),f817(x10503,x10504,x10502,x10505)) % 181.55/181.55 [1051]~E(x10511,x10512)+E(f817(x10513,x10514,x10515,x10511),f817(x10513,x10514,x10515,x10512)) % 181.55/181.55 [1052]~E(x10521,x10522)+E(f544(x10521,x10523),f544(x10522,x10523)) % 181.55/181.55 [1053]~E(x10531,x10532)+E(f544(x10533,x10531),f544(x10533,x10532)) % 181.55/181.55 [1054]~E(x10541,x10542)+E(f814(x10541,x10543,x10544,x10545),f814(x10542,x10543,x10544,x10545)) % 181.55/181.55 [1055]~E(x10551,x10552)+E(f814(x10553,x10551,x10554,x10555),f814(x10553,x10552,x10554,x10555)) % 181.55/181.55 [1056]~E(x10561,x10562)+E(f814(x10563,x10564,x10561,x10565),f814(x10563,x10564,x10562,x10565)) % 181.55/181.55 [1057]~E(x10571,x10572)+E(f814(x10573,x10574,x10575,x10571),f814(x10573,x10574,x10575,x10572)) % 181.55/181.55 [1058]~E(x10581,x10582)+E(f839(x10581,x10583,x10584,x10585,x10586,x10587),f839(x10582,x10583,x10584,x10585,x10586,x10587)) % 181.55/181.55 [1059]~E(x10591,x10592)+E(f839(x10593,x10591,x10594,x10595,x10596,x10597),f839(x10593,x10592,x10594,x10595,x10596,x10597)) % 181.55/181.55 [1060]~E(x10601,x10602)+E(f839(x10603,x10604,x10601,x10605,x10606,x10607),f839(x10603,x10604,x10602,x10605,x10606,x10607)) % 181.55/181.55 [1061]~E(x10611,x10612)+E(f839(x10613,x10614,x10615,x10611,x10616,x10617),f839(x10613,x10614,x10615,x10612,x10616,x10617)) % 181.55/181.55 [1062]~E(x10621,x10622)+E(f839(x10623,x10624,x10625,x10626,x10621,x10627),f839(x10623,x10624,x10625,x10626,x10622,x10627)) % 181.55/181.55 [1063]~E(x10631,x10632)+E(f839(x10633,x10634,x10635,x10636,x10637,x10631),f839(x10633,x10634,x10635,x10636,x10637,x10632)) % 181.55/181.55 [1064]~E(x10641,x10642)+E(f386(x10641,x10643,x10644,x10645,x10646),f386(x10642,x10643,x10644,x10645,x10646)) % 181.55/181.55 [1065]~E(x10651,x10652)+E(f386(x10653,x10651,x10654,x10655,x10656),f386(x10653,x10652,x10654,x10655,x10656)) % 181.55/181.55 [1066]~E(x10661,x10662)+E(f386(x10663,x10664,x10661,x10665,x10666),f386(x10663,x10664,x10662,x10665,x10666)) % 181.55/181.55 [1067]~E(x10671,x10672)+E(f386(x10673,x10674,x10675,x10671,x10676),f386(x10673,x10674,x10675,x10672,x10676)) % 181.55/181.55 [1068]~E(x10681,x10682)+E(f386(x10683,x10684,x10685,x10686,x10681),f386(x10683,x10684,x10685,x10686,x10682)) % 181.55/181.55 [1069]~E(x10691,x10692)+E(f514(x10691,x10693,x10694),f514(x10692,x10693,x10694)) % 181.55/181.55 [1070]~E(x10701,x10702)+E(f514(x10703,x10701,x10704),f514(x10703,x10702,x10704)) % 181.55/181.55 [1071]~E(x10711,x10712)+E(f514(x10713,x10714,x10711),f514(x10713,x10714,x10712)) % 181.55/181.55 [1072]~E(x10721,x10722)+E(f652(x10721,x10723),f652(x10722,x10723)) % 181.55/181.55 [1073]~E(x10731,x10732)+E(f652(x10733,x10731),f652(x10733,x10732)) % 181.55/181.55 [1074]~E(x10741,x10742)+E(f127(x10741),f127(x10742)) % 181.55/181.55 [1075]~E(x10751,x10752)+E(f363(x10751,x10753,x10754),f363(x10752,x10753,x10754)) % 181.55/181.55 [1076]~E(x10761,x10762)+E(f363(x10763,x10761,x10764),f363(x10763,x10762,x10764)) % 181.55/181.55 [1077]~E(x10771,x10772)+E(f363(x10773,x10774,x10771),f363(x10773,x10774,x10772)) % 181.55/181.55 [1078]~E(x10781,x10782)+E(f462(x10781,x10783,x10784,x10785),f462(x10782,x10783,x10784,x10785)) % 181.55/181.55 [1079]~E(x10791,x10792)+E(f462(x10793,x10791,x10794,x10795),f462(x10793,x10792,x10794,x10795)) % 181.55/181.55 [1080]~E(x10801,x10802)+E(f462(x10803,x10804,x10801,x10805),f462(x10803,x10804,x10802,x10805)) % 181.55/181.55 [1081]~E(x10811,x10812)+E(f462(x10813,x10814,x10815,x10811),f462(x10813,x10814,x10815,x10812)) % 181.55/181.55 [1082]~E(x10821,x10822)+E(f134(x10821,x10823,x10824),f134(x10822,x10823,x10824)) % 181.55/181.55 [1083]~E(x10831,x10832)+E(f134(x10833,x10831,x10834),f134(x10833,x10832,x10834)) % 181.55/181.55 [1084]~E(x10841,x10842)+E(f134(x10843,x10844,x10841),f134(x10843,x10844,x10842)) % 181.55/181.55 [1085]~E(x10851,x10852)+E(f149(x10851,x10853,x10854),f149(x10852,x10853,x10854)) % 181.55/181.55 [1086]~E(x10861,x10862)+E(f149(x10863,x10861,x10864),f149(x10863,x10862,x10864)) % 181.55/181.55 [1087]~E(x10871,x10872)+E(f149(x10873,x10874,x10871),f149(x10873,x10874,x10872)) % 181.55/181.55 [1088]~E(x10881,x10882)+E(f511(x10881,x10883,x10884),f511(x10882,x10883,x10884)) % 181.55/181.55 [1089]~E(x10891,x10892)+E(f511(x10893,x10891,x10894),f511(x10893,x10892,x10894)) % 181.55/181.55 [1090]~E(x10901,x10902)+E(f511(x10903,x10904,x10901),f511(x10903,x10904,x10902)) % 181.55/181.55 [1091]~E(x10911,x10912)+E(f588(x10911,x10913),f588(x10912,x10913)) % 181.55/181.55 [1092]~E(x10921,x10922)+E(f588(x10923,x10921),f588(x10923,x10922)) % 181.55/181.55 [1093]~E(x10931,x10932)+E(f660(x10931,x10933,x10934,x10935),f660(x10932,x10933,x10934,x10935)) % 181.55/181.55 [1094]~E(x10941,x10942)+E(f660(x10943,x10941,x10944,x10945),f660(x10943,x10942,x10944,x10945)) % 181.55/181.55 [1095]~E(x10951,x10952)+E(f660(x10953,x10954,x10951,x10955),f660(x10953,x10954,x10952,x10955)) % 181.55/181.55 [1096]~E(x10961,x10962)+E(f660(x10963,x10964,x10965,x10961),f660(x10963,x10964,x10965,x10962)) % 181.55/181.55 [1097]~E(x10971,x10972)+E(f616(x10971,x10973,x10974,x10975,x10976),f616(x10972,x10973,x10974,x10975,x10976)) % 181.55/181.55 [1098]~E(x10981,x10982)+E(f616(x10983,x10981,x10984,x10985,x10986),f616(x10983,x10982,x10984,x10985,x10986)) % 181.55/181.55 [1099]~E(x10991,x10992)+E(f616(x10993,x10994,x10991,x10995,x10996),f616(x10993,x10994,x10992,x10995,x10996)) % 181.55/181.55 [1100]~E(x11001,x11002)+E(f616(x11003,x11004,x11005,x11001,x11006),f616(x11003,x11004,x11005,x11002,x11006)) % 181.55/181.55 [1101]~E(x11011,x11012)+E(f616(x11013,x11014,x11015,x11016,x11011),f616(x11013,x11014,x11015,x11016,x11012)) % 181.55/181.55 [1102]~E(x11021,x11022)+E(f570(x11021,x11023),f570(x11022,x11023)) % 181.55/181.55 [1103]~E(x11031,x11032)+E(f570(x11033,x11031),f570(x11033,x11032)) % 181.55/181.55 [1104]~E(x11041,x11042)+E(f366(x11041,x11043,x11044,x11045,x11046,x11047,x11048),f366(x11042,x11043,x11044,x11045,x11046,x11047,x11048)) % 181.55/181.55 [1105]~E(x11051,x11052)+E(f366(x11053,x11051,x11054,x11055,x11056,x11057,x11058),f366(x11053,x11052,x11054,x11055,x11056,x11057,x11058)) % 181.55/181.55 [1106]~E(x11061,x11062)+E(f366(x11063,x11064,x11061,x11065,x11066,x11067,x11068),f366(x11063,x11064,x11062,x11065,x11066,x11067,x11068)) % 181.55/181.55 [1107]~E(x11071,x11072)+E(f366(x11073,x11074,x11075,x11071,x11076,x11077,x11078),f366(x11073,x11074,x11075,x11072,x11076,x11077,x11078)) % 181.55/181.55 [1108]~E(x11081,x11082)+E(f366(x11083,x11084,x11085,x11086,x11081,x11087,x11088),f366(x11083,x11084,x11085,x11086,x11082,x11087,x11088)) % 181.55/181.55 [1109]~E(x11091,x11092)+E(f366(x11093,x11094,x11095,x11096,x11097,x11091,x11098),f366(x11093,x11094,x11095,x11096,x11097,x11092,x11098)) % 181.55/181.55 [1110]~E(x11101,x11102)+E(f366(x11103,x11104,x11105,x11106,x11107,x11108,x11101),f366(x11103,x11104,x11105,x11106,x11107,x11108,x11102)) % 181.55/181.55 [1111]~E(x11111,x11112)+E(f833(x11111,x11113,x11114,x11115,x11116),f833(x11112,x11113,x11114,x11115,x11116)) % 181.55/181.55 [1112]~E(x11121,x11122)+E(f833(x11123,x11121,x11124,x11125,x11126),f833(x11123,x11122,x11124,x11125,x11126)) % 181.55/181.55 [1113]~E(x11131,x11132)+E(f833(x11133,x11134,x11131,x11135,x11136),f833(x11133,x11134,x11132,x11135,x11136)) % 181.55/181.55 [1114]~E(x11141,x11142)+E(f833(x11143,x11144,x11145,x11141,x11146),f833(x11143,x11144,x11145,x11142,x11146)) % 181.55/181.55 [1115]~E(x11151,x11152)+E(f833(x11153,x11154,x11155,x11156,x11151),f833(x11153,x11154,x11155,x11156,x11152)) % 181.55/181.55 [1116]~E(x11161,x11162)+E(f273(x11161,x11163,x11164,x11165),f273(x11162,x11163,x11164,x11165)) % 181.55/181.55 [1117]~E(x11171,x11172)+E(f273(x11173,x11171,x11174,x11175),f273(x11173,x11172,x11174,x11175)) % 181.55/181.55 [1118]~E(x11181,x11182)+E(f273(x11183,x11184,x11181,x11185),f273(x11183,x11184,x11182,x11185)) % 181.55/181.55 [1119]~E(x11191,x11192)+E(f273(x11193,x11194,x11195,x11191),f273(x11193,x11194,x11195,x11192)) % 181.55/181.55 [1120]~E(x11201,x11202)+E(f648(x11201,x11203,x11204,x11205),f648(x11202,x11203,x11204,x11205)) % 181.55/181.55 [1121]~E(x11211,x11212)+E(f648(x11213,x11211,x11214,x11215),f648(x11213,x11212,x11214,x11215)) % 181.55/181.55 [1122]~E(x11221,x11222)+E(f648(x11223,x11224,x11221,x11225),f648(x11223,x11224,x11222,x11225)) % 181.55/181.55 [1123]~E(x11231,x11232)+E(f648(x11233,x11234,x11235,x11231),f648(x11233,x11234,x11235,x11232)) % 181.55/181.55 [1124]~E(x11241,x11242)+E(f407(x11241),f407(x11242)) % 181.55/181.55 [1125]~E(x11251,x11252)+E(f549(x11251,x11253,x11254,x11255),f549(x11252,x11253,x11254,x11255)) % 181.55/181.55 [1126]~E(x11261,x11262)+E(f549(x11263,x11261,x11264,x11265),f549(x11263,x11262,x11264,x11265)) % 181.55/181.55 [1127]~E(x11271,x11272)+E(f549(x11273,x11274,x11271,x11275),f549(x11273,x11274,x11272,x11275)) % 181.55/181.55 [1128]~E(x11281,x11282)+E(f549(x11283,x11284,x11285,x11281),f549(x11283,x11284,x11285,x11282)) % 181.55/181.55 [1129]~E(x11291,x11292)+E(f339(x11291,x11293),f339(x11292,x11293)) % 181.55/181.55 [1130]~E(x11301,x11302)+E(f339(x11303,x11301),f339(x11303,x11302)) % 181.55/181.55 [1131]~E(x11311,x11312)+E(f176(x11311),f176(x11312)) % 181.55/181.55 [1132]~E(x11321,x11322)+E(f350(x11321,x11323,x11324),f350(x11322,x11323,x11324)) % 181.55/181.55 [1133]~E(x11331,x11332)+E(f350(x11333,x11331,x11334),f350(x11333,x11332,x11334)) % 181.55/181.55 [1134]~E(x11341,x11342)+E(f350(x11343,x11344,x11341),f350(x11343,x11344,x11342)) % 181.55/181.55 [1135]~E(x11351,x11352)+E(f623(x11351,x11353,x11354,x11355),f623(x11352,x11353,x11354,x11355)) % 181.55/181.55 [1136]~E(x11361,x11362)+E(f623(x11363,x11361,x11364,x11365),f623(x11363,x11362,x11364,x11365)) % 181.55/181.55 [1137]~E(x11371,x11372)+E(f623(x11373,x11374,x11371,x11375),f623(x11373,x11374,x11372,x11375)) % 181.55/181.55 [1138]~E(x11381,x11382)+E(f623(x11383,x11384,x11385,x11381),f623(x11383,x11384,x11385,x11382)) % 181.55/181.55 [1139]~E(x11391,x11392)+E(f847(x11391,x11393,x11394,x11395),f847(x11392,x11393,x11394,x11395)) % 181.55/181.55 [1140]~E(x11401,x11402)+E(f847(x11403,x11401,x11404,x11405),f847(x11403,x11402,x11404,x11405)) % 181.55/181.55 [1141]~E(x11411,x11412)+E(f847(x11413,x11414,x11411,x11415),f847(x11413,x11414,x11412,x11415)) % 181.55/181.55 [1142]~E(x11421,x11422)+E(f847(x11423,x11424,x11425,x11421),f847(x11423,x11424,x11425,x11422)) % 181.55/181.55 [1143]~E(x11431,x11432)+E(f465(x11431,x11433,x11434,x11435,x11436,x11437,x11438),f465(x11432,x11433,x11434,x11435,x11436,x11437,x11438)) % 181.55/181.55 [1144]~E(x11441,x11442)+E(f465(x11443,x11441,x11444,x11445,x11446,x11447,x11448),f465(x11443,x11442,x11444,x11445,x11446,x11447,x11448)) % 181.55/181.55 [1145]~E(x11451,x11452)+E(f465(x11453,x11454,x11451,x11455,x11456,x11457,x11458),f465(x11453,x11454,x11452,x11455,x11456,x11457,x11458)) % 181.55/181.55 [1146]~E(x11461,x11462)+E(f465(x11463,x11464,x11465,x11461,x11466,x11467,x11468),f465(x11463,x11464,x11465,x11462,x11466,x11467,x11468)) % 181.55/181.55 [1147]~E(x11471,x11472)+E(f465(x11473,x11474,x11475,x11476,x11471,x11477,x11478),f465(x11473,x11474,x11475,x11476,x11472,x11477,x11478)) % 181.55/181.55 [1148]~E(x11481,x11482)+E(f465(x11483,x11484,x11485,x11486,x11487,x11481,x11488),f465(x11483,x11484,x11485,x11486,x11487,x11482,x11488)) % 181.55/181.55 [1149]~E(x11491,x11492)+E(f465(x11493,x11494,x11495,x11496,x11497,x11498,x11491),f465(x11493,x11494,x11495,x11496,x11497,x11498,x11492)) % 181.55/181.55 [1150]~E(x11501,x11502)+E(f297(x11501,x11503,x11504),f297(x11502,x11503,x11504)) % 181.55/181.55 [1151]~E(x11511,x11512)+E(f297(x11513,x11511,x11514),f297(x11513,x11512,x11514)) % 181.55/181.55 [1152]~E(x11521,x11522)+E(f297(x11523,x11524,x11521),f297(x11523,x11524,x11522)) % 181.55/181.55 [1153]~E(x11531,x11532)+E(f731(x11531,x11533),f731(x11532,x11533)) % 181.55/181.55 [1154]~E(x11541,x11542)+E(f731(x11543,x11541),f731(x11543,x11542)) % 181.55/181.55 [1155]~E(x11551,x11552)+E(f201(x11551,x11553,x11554,x11555),f201(x11552,x11553,x11554,x11555)) % 181.55/181.55 [1156]~E(x11561,x11562)+E(f201(x11563,x11561,x11564,x11565),f201(x11563,x11562,x11564,x11565)) % 181.55/181.55 [1157]~E(x11571,x11572)+E(f201(x11573,x11574,x11571,x11575),f201(x11573,x11574,x11572,x11575)) % 181.55/181.55 [1158]~E(x11581,x11582)+E(f201(x11583,x11584,x11585,x11581),f201(x11583,x11584,x11585,x11582)) % 181.55/181.55 [1159]~E(x11591,x11592)+E(f89(x11591),f89(x11592)) % 181.55/181.55 [1160]~E(x11601,x11602)+E(f621(x11601,x11603,x11604,x11605,x11606,x11607,x11608),f621(x11602,x11603,x11604,x11605,x11606,x11607,x11608)) % 181.55/181.55 [1161]~E(x11611,x11612)+E(f621(x11613,x11611,x11614,x11615,x11616,x11617,x11618),f621(x11613,x11612,x11614,x11615,x11616,x11617,x11618)) % 181.55/181.55 [1162]~E(x11621,x11622)+E(f621(x11623,x11624,x11621,x11625,x11626,x11627,x11628),f621(x11623,x11624,x11622,x11625,x11626,x11627,x11628)) % 181.55/181.55 [1163]~E(x11631,x11632)+E(f621(x11633,x11634,x11635,x11631,x11636,x11637,x11638),f621(x11633,x11634,x11635,x11632,x11636,x11637,x11638)) % 181.55/181.55 [1164]~E(x11641,x11642)+E(f621(x11643,x11644,x11645,x11646,x11641,x11647,x11648),f621(x11643,x11644,x11645,x11646,x11642,x11647,x11648)) % 181.55/181.55 [1165]~E(x11651,x11652)+E(f621(x11653,x11654,x11655,x11656,x11657,x11651,x11658),f621(x11653,x11654,x11655,x11656,x11657,x11652,x11658)) % 181.55/181.55 [1166]~E(x11661,x11662)+E(f621(x11663,x11664,x11665,x11666,x11667,x11668,x11661),f621(x11663,x11664,x11665,x11666,x11667,x11668,x11662)) % 181.55/181.55 [1167]~E(x11671,x11672)+E(f269(x11671),f269(x11672)) % 181.55/181.55 [1168]~E(x11681,x11682)+E(f341(x11681,x11683),f341(x11682,x11683)) % 181.55/181.55 [1169]~E(x11691,x11692)+E(f341(x11693,x11691),f341(x11693,x11692)) % 181.55/181.55 [1170]~E(x11701,x11702)+E(f168(x11701,x11703,x11704),f168(x11702,x11703,x11704)) % 181.55/181.55 [1171]~E(x11711,x11712)+E(f168(x11713,x11711,x11714),f168(x11713,x11712,x11714)) % 181.55/181.55 [1172]~E(x11721,x11722)+E(f168(x11723,x11724,x11721),f168(x11723,x11724,x11722)) % 181.55/181.55 [1173]~E(x11731,x11732)+E(f675(x11731,x11733,x11734,x11735,x11736),f675(x11732,x11733,x11734,x11735,x11736)) % 181.55/181.55 [1174]~E(x11741,x11742)+E(f675(x11743,x11741,x11744,x11745,x11746),f675(x11743,x11742,x11744,x11745,x11746)) % 181.55/181.55 [1175]~E(x11751,x11752)+E(f675(x11753,x11754,x11751,x11755,x11756),f675(x11753,x11754,x11752,x11755,x11756)) % 181.55/181.55 [1176]~E(x11761,x11762)+E(f675(x11763,x11764,x11765,x11761,x11766),f675(x11763,x11764,x11765,x11762,x11766)) % 181.55/181.55 [1177]~E(x11771,x11772)+E(f675(x11773,x11774,x11775,x11776,x11771),f675(x11773,x11774,x11775,x11776,x11772)) % 181.55/181.55 [1178]~E(x11781,x11782)+E(f698(x11781,x11783,x11784,x11785),f698(x11782,x11783,x11784,x11785)) % 181.55/181.55 [1179]~E(x11791,x11792)+E(f698(x11793,x11791,x11794,x11795),f698(x11793,x11792,x11794,x11795)) % 181.55/181.55 [1180]~E(x11801,x11802)+E(f698(x11803,x11804,x11801,x11805),f698(x11803,x11804,x11802,x11805)) % 181.55/181.55 [1181]~E(x11811,x11812)+E(f698(x11813,x11814,x11815,x11811),f698(x11813,x11814,x11815,x11812)) % 181.55/181.55 [1182]~E(x11821,x11822)+E(f851(x11821,x11823,x11824,x11825,x11826),f851(x11822,x11823,x11824,x11825,x11826)) % 181.55/181.55 [1183]~E(x11831,x11832)+E(f851(x11833,x11831,x11834,x11835,x11836),f851(x11833,x11832,x11834,x11835,x11836)) % 181.55/181.55 [1184]~E(x11841,x11842)+E(f851(x11843,x11844,x11841,x11845,x11846),f851(x11843,x11844,x11842,x11845,x11846)) % 181.55/181.55 [1185]~E(x11851,x11852)+E(f851(x11853,x11854,x11855,x11851,x11856),f851(x11853,x11854,x11855,x11852,x11856)) % 181.55/181.55 [1186]~E(x11861,x11862)+E(f851(x11863,x11864,x11865,x11866,x11861),f851(x11863,x11864,x11865,x11866,x11862)) % 181.55/181.55 [1187]~E(x11871,x11872)+E(f771(x11871,x11873,x11874,x11875,x11876),f771(x11872,x11873,x11874,x11875,x11876)) % 181.55/181.55 [1188]~E(x11881,x11882)+E(f771(x11883,x11881,x11884,x11885,x11886),f771(x11883,x11882,x11884,x11885,x11886)) % 181.55/181.55 [1189]~E(x11891,x11892)+E(f771(x11893,x11894,x11891,x11895,x11896),f771(x11893,x11894,x11892,x11895,x11896)) % 181.55/181.55 [1190]~E(x11901,x11902)+E(f771(x11903,x11904,x11905,x11901,x11906),f771(x11903,x11904,x11905,x11902,x11906)) % 181.55/181.55 [1191]~E(x11911,x11912)+E(f771(x11913,x11914,x11915,x11916,x11911),f771(x11913,x11914,x11915,x11916,x11912)) % 181.55/181.55 [1192]~E(x11921,x11922)+E(f139(x11921,x11923),f139(x11922,x11923)) % 181.55/181.55 [1193]~E(x11931,x11932)+E(f139(x11933,x11931),f139(x11933,x11932)) % 181.55/181.55 [1194]~E(x11941,x11942)+E(f772(x11941,x11943,x11944,x11945,x11946),f772(x11942,x11943,x11944,x11945,x11946)) % 181.55/181.55 [1195]~E(x11951,x11952)+E(f772(x11953,x11951,x11954,x11955,x11956),f772(x11953,x11952,x11954,x11955,x11956)) % 181.55/181.55 [1196]~E(x11961,x11962)+E(f772(x11963,x11964,x11961,x11965,x11966),f772(x11963,x11964,x11962,x11965,x11966)) % 181.55/181.55 [1197]~E(x11971,x11972)+E(f772(x11973,x11974,x11975,x11971,x11976),f772(x11973,x11974,x11975,x11972,x11976)) % 181.55/181.55 [1198]~E(x11981,x11982)+E(f772(x11983,x11984,x11985,x11986,x11981),f772(x11983,x11984,x11985,x11986,x11982)) % 181.55/181.55 [1199]~E(x11991,x11992)+E(f158(x11991,x11993,x11994,x11995),f158(x11992,x11993,x11994,x11995)) % 181.55/181.55 [1200]~E(x12001,x12002)+E(f158(x12003,x12001,x12004,x12005),f158(x12003,x12002,x12004,x12005)) % 181.55/181.55 [1201]~E(x12011,x12012)+E(f158(x12013,x12014,x12011,x12015),f158(x12013,x12014,x12012,x12015)) % 181.55/181.55 [1202]~E(x12021,x12022)+E(f158(x12023,x12024,x12025,x12021),f158(x12023,x12024,x12025,x12022)) % 181.55/181.55 [1203]~E(x12031,x12032)+E(f628(x12031,x12033,x12034,x12035,x12036,x12037,x12038),f628(x12032,x12033,x12034,x12035,x12036,x12037,x12038)) % 181.55/181.55 [1204]~E(x12041,x12042)+E(f628(x12043,x12041,x12044,x12045,x12046,x12047,x12048),f628(x12043,x12042,x12044,x12045,x12046,x12047,x12048)) % 181.55/181.55 [1205]~E(x12051,x12052)+E(f628(x12053,x12054,x12051,x12055,x12056,x12057,x12058),f628(x12053,x12054,x12052,x12055,x12056,x12057,x12058)) % 181.55/181.55 [1206]~E(x12061,x12062)+E(f628(x12063,x12064,x12065,x12061,x12066,x12067,x12068),f628(x12063,x12064,x12065,x12062,x12066,x12067,x12068)) % 181.55/181.55 [1207]~E(x12071,x12072)+E(f628(x12073,x12074,x12075,x12076,x12071,x12077,x12078),f628(x12073,x12074,x12075,x12076,x12072,x12077,x12078)) % 181.55/181.55 [1208]~E(x12081,x12082)+E(f628(x12083,x12084,x12085,x12086,x12087,x12081,x12088),f628(x12083,x12084,x12085,x12086,x12087,x12082,x12088)) % 181.55/181.55 [1209]~E(x12091,x12092)+E(f628(x12093,x12094,x12095,x12096,x12097,x12098,x12091),f628(x12093,x12094,x12095,x12096,x12097,x12098,x12092)) % 181.55/181.55 [1210]~E(x12101,x12102)+E(f836(x12101,x12103,x12104,x12105),f836(x12102,x12103,x12104,x12105)) % 181.55/181.55 [1211]~E(x12111,x12112)+E(f836(x12113,x12111,x12114,x12115),f836(x12113,x12112,x12114,x12115)) % 181.55/181.55 [1212]~E(x12121,x12122)+E(f836(x12123,x12124,x12121,x12125),f836(x12123,x12124,x12122,x12125)) % 181.55/181.55 [1213]~E(x12131,x12132)+E(f836(x12133,x12134,x12135,x12131),f836(x12133,x12134,x12135,x12132)) % 181.55/181.55 [1214]~E(x12141,x12142)+E(f120(x12141,x12143,x12144),f120(x12142,x12143,x12144)) % 181.55/181.55 [1215]~E(x12151,x12152)+E(f120(x12153,x12151,x12154),f120(x12153,x12152,x12154)) % 181.55/181.55 [1216]~E(x12161,x12162)+E(f120(x12163,x12164,x12161),f120(x12163,x12164,x12162)) % 181.55/181.55 [1217]~E(x12171,x12172)+E(f688(x12171,x12173,x12174,x12175,x12176),f688(x12172,x12173,x12174,x12175,x12176)) % 181.55/181.55 [1218]~E(x12181,x12182)+E(f688(x12183,x12181,x12184,x12185,x12186),f688(x12183,x12182,x12184,x12185,x12186)) % 181.55/181.55 [1219]~E(x12191,x12192)+E(f688(x12193,x12194,x12191,x12195,x12196),f688(x12193,x12194,x12192,x12195,x12196)) % 181.55/181.55 [1220]~E(x12201,x12202)+E(f688(x12203,x12204,x12205,x12201,x12206),f688(x12203,x12204,x12205,x12202,x12206)) % 181.55/181.55 [1221]~E(x12211,x12212)+E(f688(x12213,x12214,x12215,x12216,x12211),f688(x12213,x12214,x12215,x12216,x12212)) % 181.55/181.55 [1222]~E(x12221,x12222)+E(f525(x12221,x12223,x12224,x12225),f525(x12222,x12223,x12224,x12225)) % 181.55/181.55 [1223]~E(x12231,x12232)+E(f525(x12233,x12231,x12234,x12235),f525(x12233,x12232,x12234,x12235)) % 181.55/181.55 [1224]~E(x12241,x12242)+E(f525(x12243,x12244,x12241,x12245),f525(x12243,x12244,x12242,x12245)) % 181.55/181.55 [1225]~E(x12251,x12252)+E(f525(x12253,x12254,x12255,x12251),f525(x12253,x12254,x12255,x12252)) % 181.55/181.55 [1226]~E(x12261,x12262)+E(f797(x12261,x12263,x12264),f797(x12262,x12263,x12264)) % 181.55/181.55 [1227]~E(x12271,x12272)+E(f797(x12273,x12271,x12274),f797(x12273,x12272,x12274)) % 181.55/181.55 [1228]~E(x12281,x12282)+E(f797(x12283,x12284,x12281),f797(x12283,x12284,x12282)) % 181.55/181.55 [1229]~E(x12291,x12292)+E(f187(x12291),f187(x12292)) % 181.55/181.55 [1230]~E(x12301,x12302)+E(f395(x12301,x12303,x12304),f395(x12302,x12303,x12304)) % 181.55/181.55 [1231]~E(x12311,x12312)+E(f395(x12313,x12311,x12314),f395(x12313,x12312,x12314)) % 181.55/181.55 [1232]~E(x12321,x12322)+E(f395(x12323,x12324,x12321),f395(x12323,x12324,x12322)) % 181.55/181.55 [1233]~E(x12331,x12332)+E(f597(x12331,x12333,x12334),f597(x12332,x12333,x12334)) % 181.55/181.55 [1234]~E(x12341,x12342)+E(f597(x12343,x12341,x12344),f597(x12343,x12342,x12344)) % 181.55/181.55 [1235]~E(x12351,x12352)+E(f597(x12353,x12354,x12351),f597(x12353,x12354,x12352)) % 181.55/181.55 [1236]~E(x12361,x12362)+E(f391(x12361,x12363,x12364),f391(x12362,x12363,x12364)) % 181.55/181.55 [1237]~E(x12371,x12372)+E(f391(x12373,x12371,x12374),f391(x12373,x12372,x12374)) % 181.55/181.55 [1238]~E(x12381,x12382)+E(f391(x12383,x12384,x12381),f391(x12383,x12384,x12382)) % 181.55/181.55 [1239]~E(x12391,x12392)+E(f837(x12391,x12393,x12394,x12395),f837(x12392,x12393,x12394,x12395)) % 181.55/181.55 [1240]~E(x12401,x12402)+E(f837(x12403,x12401,x12404,x12405),f837(x12403,x12402,x12404,x12405)) % 181.55/181.55 [1241]~E(x12411,x12412)+E(f837(x12413,x12414,x12411,x12415),f837(x12413,x12414,x12412,x12415)) % 181.55/181.55 [1242]~E(x12421,x12422)+E(f837(x12423,x12424,x12425,x12421),f837(x12423,x12424,x12425,x12422)) % 181.55/181.55 [1243]~E(x12431,x12432)+E(f583(x12431),f583(x12432)) % 181.55/181.55 [1244]~E(x12441,x12442)+E(f503(x12441,x12443,x12444,x12445,x12446),f503(x12442,x12443,x12444,x12445,x12446)) % 181.55/181.55 [1245]~E(x12451,x12452)+E(f503(x12453,x12451,x12454,x12455,x12456),f503(x12453,x12452,x12454,x12455,x12456)) % 181.55/181.55 [1246]~E(x12461,x12462)+E(f503(x12463,x12464,x12461,x12465,x12466),f503(x12463,x12464,x12462,x12465,x12466)) % 181.55/181.55 [1247]~E(x12471,x12472)+E(f503(x12473,x12474,x12475,x12471,x12476),f503(x12473,x12474,x12475,x12472,x12476)) % 181.55/181.55 [1248]~E(x12481,x12482)+E(f503(x12483,x12484,x12485,x12486,x12481),f503(x12483,x12484,x12485,x12486,x12482)) % 181.55/181.55 [1249]~E(x12491,x12492)+E(f285(x12491,x12493,x12494),f285(x12492,x12493,x12494)) % 181.55/181.55 [1250]~E(x12501,x12502)+E(f285(x12503,x12501,x12504),f285(x12503,x12502,x12504)) % 181.55/181.55 [1251]~E(x12511,x12512)+E(f285(x12513,x12514,x12511),f285(x12513,x12514,x12512)) % 181.55/181.55 [1252]~E(x12521,x12522)+E(f505(x12521,x12523,x12524,x12525,x12526,x12527),f505(x12522,x12523,x12524,x12525,x12526,x12527)) % 181.55/181.55 [1253]~E(x12531,x12532)+E(f505(x12533,x12531,x12534,x12535,x12536,x12537),f505(x12533,x12532,x12534,x12535,x12536,x12537)) % 181.55/181.55 [1254]~E(x12541,x12542)+E(f505(x12543,x12544,x12541,x12545,x12546,x12547),f505(x12543,x12544,x12542,x12545,x12546,x12547)) % 181.55/181.55 [1255]~E(x12551,x12552)+E(f505(x12553,x12554,x12555,x12551,x12556,x12557),f505(x12553,x12554,x12555,x12552,x12556,x12557)) % 181.55/181.55 [1256]~E(x12561,x12562)+E(f505(x12563,x12564,x12565,x12566,x12561,x12567),f505(x12563,x12564,x12565,x12566,x12562,x12567)) % 181.55/181.55 [1257]~E(x12571,x12572)+E(f505(x12573,x12574,x12575,x12576,x12577,x12571),f505(x12573,x12574,x12575,x12576,x12577,x12572)) % 181.55/181.55 [1258]~E(x12581,x12582)+E(f493(x12581,x12583,x12584,x12585,x12586,x12587),f493(x12582,x12583,x12584,x12585,x12586,x12587)) % 181.55/181.55 [1259]~E(x12591,x12592)+E(f493(x12593,x12591,x12594,x12595,x12596,x12597),f493(x12593,x12592,x12594,x12595,x12596,x12597)) % 181.55/181.55 [1260]~E(x12601,x12602)+E(f493(x12603,x12604,x12601,x12605,x12606,x12607),f493(x12603,x12604,x12602,x12605,x12606,x12607)) % 181.55/181.55 [1261]~E(x12611,x12612)+E(f493(x12613,x12614,x12615,x12611,x12616,x12617),f493(x12613,x12614,x12615,x12612,x12616,x12617)) % 181.55/181.55 [1262]~E(x12621,x12622)+E(f493(x12623,x12624,x12625,x12626,x12621,x12627),f493(x12623,x12624,x12625,x12626,x12622,x12627)) % 181.55/181.55 [1263]~E(x12631,x12632)+E(f493(x12633,x12634,x12635,x12636,x12637,x12631),f493(x12633,x12634,x12635,x12636,x12637,x12632)) % 181.55/181.55 [1264]~E(x12641,x12642)+E(f373(x12641),f373(x12642)) % 181.55/181.55 [1265]~E(x12651,x12652)+E(f748(x12651,x12653),f748(x12652,x12653)) % 181.55/181.55 [1266]~E(x12661,x12662)+E(f748(x12663,x12661),f748(x12663,x12662)) % 181.55/181.55 [1267]~E(x12671,x12672)+E(f533(x12671,x12673,x12674,x12675),f533(x12672,x12673,x12674,x12675)) % 181.55/181.55 [1268]~E(x12681,x12682)+E(f533(x12683,x12681,x12684,x12685),f533(x12683,x12682,x12684,x12685)) % 181.55/181.55 [1269]~E(x12691,x12692)+E(f533(x12693,x12694,x12691,x12695),f533(x12693,x12694,x12692,x12695)) % 181.55/181.55 [1270]~E(x12701,x12702)+E(f533(x12703,x12704,x12705,x12701),f533(x12703,x12704,x12705,x12702)) % 181.55/181.55 [1271]~E(x12711,x12712)+E(f422(x12711,x12713,x12714),f422(x12712,x12713,x12714)) % 181.55/181.55 [1272]~E(x12721,x12722)+E(f422(x12723,x12721,x12724),f422(x12723,x12722,x12724)) % 181.55/181.55 [1273]~E(x12731,x12732)+E(f422(x12733,x12734,x12731),f422(x12733,x12734,x12732)) % 181.55/181.55 [1274]~E(x12741,x12742)+E(f610(x12741,x12743,x12744,x12745,x12746),f610(x12742,x12743,x12744,x12745,x12746)) % 181.55/181.55 [1275]~E(x12751,x12752)+E(f610(x12753,x12751,x12754,x12755,x12756),f610(x12753,x12752,x12754,x12755,x12756)) % 181.55/181.55 [1276]~E(x12761,x12762)+E(f610(x12763,x12764,x12761,x12765,x12766),f610(x12763,x12764,x12762,x12765,x12766)) % 181.55/181.55 [1277]~E(x12771,x12772)+E(f610(x12773,x12774,x12775,x12771,x12776),f610(x12773,x12774,x12775,x12772,x12776)) % 181.55/181.55 [1278]~E(x12781,x12782)+E(f610(x12783,x12784,x12785,x12786,x12781),f610(x12783,x12784,x12785,x12786,x12782)) % 181.55/181.55 [1279]~E(x12791,x12792)+E(f284(x12791,x12793),f284(x12792,x12793)) % 181.55/181.55 [1280]~E(x12801,x12802)+E(f284(x12803,x12801),f284(x12803,x12802)) % 181.55/181.55 [1281]~E(x12811,x12812)+E(f474(x12811,x12813,x12814,x12815,x12816),f474(x12812,x12813,x12814,x12815,x12816)) % 181.55/181.55 [1282]~E(x12821,x12822)+E(f474(x12823,x12821,x12824,x12825,x12826),f474(x12823,x12822,x12824,x12825,x12826)) % 181.55/181.55 [1283]~E(x12831,x12832)+E(f474(x12833,x12834,x12831,x12835,x12836),f474(x12833,x12834,x12832,x12835,x12836)) % 181.55/181.55 [1284]~E(x12841,x12842)+E(f474(x12843,x12844,x12845,x12841,x12846),f474(x12843,x12844,x12845,x12842,x12846)) % 181.55/181.55 [1285]~E(x12851,x12852)+E(f474(x12853,x12854,x12855,x12856,x12851),f474(x12853,x12854,x12855,x12856,x12852)) % 181.55/181.55 [1286]~E(x12861,x12862)+E(f663(x12861,x12863,x12864,x12865,x12866,x12867,x12868),f663(x12862,x12863,x12864,x12865,x12866,x12867,x12868)) % 181.55/181.55 [1287]~E(x12871,x12872)+E(f663(x12873,x12871,x12874,x12875,x12876,x12877,x12878),f663(x12873,x12872,x12874,x12875,x12876,x12877,x12878)) % 181.55/181.55 [1288]~E(x12881,x12882)+E(f663(x12883,x12884,x12881,x12885,x12886,x12887,x12888),f663(x12883,x12884,x12882,x12885,x12886,x12887,x12888)) % 181.55/181.55 [1289]~E(x12891,x12892)+E(f663(x12893,x12894,x12895,x12891,x12896,x12897,x12898),f663(x12893,x12894,x12895,x12892,x12896,x12897,x12898)) % 181.55/181.55 [1290]~E(x12901,x12902)+E(f663(x12903,x12904,x12905,x12906,x12901,x12907,x12908),f663(x12903,x12904,x12905,x12906,x12902,x12907,x12908)) % 181.55/181.55 [1291]~E(x12911,x12912)+E(f663(x12913,x12914,x12915,x12916,x12917,x12911,x12918),f663(x12913,x12914,x12915,x12916,x12917,x12912,x12918)) % 181.55/181.55 [1292]~E(x12921,x12922)+E(f663(x12923,x12924,x12925,x12926,x12927,x12928,x12921),f663(x12923,x12924,x12925,x12926,x12927,x12928,x12922)) % 181.55/181.55 [1293]~E(x12931,x12932)+E(f625(x12931,x12933,x12934,x12935,x12936),f625(x12932,x12933,x12934,x12935,x12936)) % 181.55/181.55 [1294]~E(x12941,x12942)+E(f625(x12943,x12941,x12944,x12945,x12946),f625(x12943,x12942,x12944,x12945,x12946)) % 181.55/181.55 [1295]~E(x12951,x12952)+E(f625(x12953,x12954,x12951,x12955,x12956),f625(x12953,x12954,x12952,x12955,x12956)) % 181.55/181.55 [1296]~E(x12961,x12962)+E(f625(x12963,x12964,x12965,x12961,x12966),f625(x12963,x12964,x12965,x12962,x12966)) % 181.55/181.55 [1297]~E(x12971,x12972)+E(f625(x12973,x12974,x12975,x12976,x12971),f625(x12973,x12974,x12975,x12976,x12972)) % 181.55/181.55 [1298]~E(x12981,x12982)+E(f346(x12981,x12983,x12984,x12985,x12986,x12987,x12988),f346(x12982,x12983,x12984,x12985,x12986,x12987,x12988)) % 181.55/181.55 [1299]~E(x12991,x12992)+E(f346(x12993,x12991,x12994,x12995,x12996,x12997,x12998),f346(x12993,x12992,x12994,x12995,x12996,x12997,x12998)) % 181.55/181.55 [1300]~E(x13001,x13002)+E(f346(x13003,x13004,x13001,x13005,x13006,x13007,x13008),f346(x13003,x13004,x13002,x13005,x13006,x13007,x13008)) % 181.55/181.55 [1301]~E(x13011,x13012)+E(f346(x13013,x13014,x13015,x13011,x13016,x13017,x13018),f346(x13013,x13014,x13015,x13012,x13016,x13017,x13018)) % 181.55/181.55 [1302]~E(x13021,x13022)+E(f346(x13023,x13024,x13025,x13026,x13021,x13027,x13028),f346(x13023,x13024,x13025,x13026,x13022,x13027,x13028)) % 181.55/181.55 [1303]~E(x13031,x13032)+E(f346(x13033,x13034,x13035,x13036,x13037,x13031,x13038),f346(x13033,x13034,x13035,x13036,x13037,x13032,x13038)) % 181.55/181.55 [1304]~E(x13041,x13042)+E(f346(x13043,x13044,x13045,x13046,x13047,x13048,x13041),f346(x13043,x13044,x13045,x13046,x13047,x13048,x13042)) % 181.55/181.55 [1305]~E(x13051,x13052)+E(f97(x13051,x13053,x13054,x13055),f97(x13052,x13053,x13054,x13055)) % 181.55/181.55 [1306]~E(x13061,x13062)+E(f97(x13063,x13061,x13064,x13065),f97(x13063,x13062,x13064,x13065)) % 181.55/181.55 [1307]~E(x13071,x13072)+E(f97(x13073,x13074,x13071,x13075),f97(x13073,x13074,x13072,x13075)) % 181.55/181.55 [1308]~E(x13081,x13082)+E(f97(x13083,x13084,x13085,x13081),f97(x13083,x13084,x13085,x13082)) % 181.55/181.55 [1309]~E(x13091,x13092)+E(f805(x13091,x13093,x13094),f805(x13092,x13093,x13094)) % 181.55/181.55 [1310]~E(x13101,x13102)+E(f805(x13103,x13101,x13104),f805(x13103,x13102,x13104)) % 181.55/181.55 [1311]~E(x13111,x13112)+E(f805(x13113,x13114,x13111),f805(x13113,x13114,x13112)) % 181.55/181.55 [1312]~E(x13121,x13122)+E(f738(x13121,x13123,x13124),f738(x13122,x13123,x13124)) % 181.55/181.55 [1313]~E(x13131,x13132)+E(f738(x13133,x13131,x13134),f738(x13133,x13132,x13134)) % 181.55/181.55 [1314]~E(x13141,x13142)+E(f738(x13143,x13144,x13141),f738(x13143,x13144,x13142)) % 181.55/181.55 [1315]~E(x13151,x13152)+E(f575(x13151,x13153,x13154),f575(x13152,x13153,x13154)) % 181.55/181.55 [1316]~E(x13161,x13162)+E(f575(x13163,x13161,x13164),f575(x13163,x13162,x13164)) % 181.55/181.55 [1317]~E(x13171,x13172)+E(f575(x13173,x13174,x13171),f575(x13173,x13174,x13172)) % 181.55/181.55 [1318]~E(x13181,x13182)+E(f722(x13181,x13183,x13184,x13185,x13186),f722(x13182,x13183,x13184,x13185,x13186)) % 181.55/181.55 [1319]~E(x13191,x13192)+E(f722(x13193,x13191,x13194,x13195,x13196),f722(x13193,x13192,x13194,x13195,x13196)) % 181.55/181.55 [1320]~E(x13201,x13202)+E(f722(x13203,x13204,x13201,x13205,x13206),f722(x13203,x13204,x13202,x13205,x13206)) % 181.55/181.55 [1321]~E(x13211,x13212)+E(f722(x13213,x13214,x13215,x13211,x13216),f722(x13213,x13214,x13215,x13212,x13216)) % 181.55/181.55 [1322]~E(x13221,x13222)+E(f722(x13223,x13224,x13225,x13226,x13221),f722(x13223,x13224,x13225,x13226,x13222)) % 181.55/181.55 [1323]~E(x13231,x13232)+E(f456(x13231,x13233,x13234,x13235),f456(x13232,x13233,x13234,x13235)) % 181.55/181.55 [1324]~E(x13241,x13242)+E(f456(x13243,x13241,x13244,x13245),f456(x13243,x13242,x13244,x13245)) % 181.55/181.55 [1325]~E(x13251,x13252)+E(f456(x13253,x13254,x13251,x13255),f456(x13253,x13254,x13252,x13255)) % 181.55/181.55 [1326]~E(x13261,x13262)+E(f456(x13263,x13264,x13265,x13261),f456(x13263,x13264,x13265,x13262)) % 181.55/181.55 [1327]~E(x13271,x13272)+E(f211(x13271,x13273,x13274,x13275),f211(x13272,x13273,x13274,x13275)) % 181.55/181.55 [1328]~E(x13281,x13282)+E(f211(x13283,x13281,x13284,x13285),f211(x13283,x13282,x13284,x13285)) % 181.55/181.55 [1329]~E(x13291,x13292)+E(f211(x13293,x13294,x13291,x13295),f211(x13293,x13294,x13292,x13295)) % 181.55/181.55 [1330]~E(x13301,x13302)+E(f211(x13303,x13304,x13305,x13301),f211(x13303,x13304,x13305,x13302)) % 181.55/181.55 [1331]~E(x13311,x13312)+E(f755(x13311,x13313),f755(x13312,x13313)) % 181.55/181.55 [1332]~E(x13321,x13322)+E(f755(x13323,x13321),f755(x13323,x13322)) % 181.55/181.55 [1333]~E(x13331,x13332)+E(f682(x13331,x13333,x13334),f682(x13332,x13333,x13334)) % 181.55/181.55 [1334]~E(x13341,x13342)+E(f682(x13343,x13341,x13344),f682(x13343,x13342,x13344)) % 181.55/181.55 [1335]~E(x13351,x13352)+E(f682(x13353,x13354,x13351),f682(x13353,x13354,x13352)) % 181.55/181.55 [1336]~E(x13361,x13362)+E(f272(x13361,x13363),f272(x13362,x13363)) % 181.55/181.55 [1337]~E(x13371,x13372)+E(f272(x13373,x13371),f272(x13373,x13372)) % 181.55/181.55 [1338]~E(x13381,x13382)+E(f205(x13381),f205(x13382)) % 181.55/181.55 [1339]~E(x13391,x13392)+E(f523(x13391,x13393,x13394),f523(x13392,x13393,x13394)) % 181.55/181.55 [1340]~E(x13401,x13402)+E(f523(x13403,x13401,x13404),f523(x13403,x13402,x13404)) % 181.55/181.55 [1341]~E(x13411,x13412)+E(f523(x13413,x13414,x13411),f523(x13413,x13414,x13412)) % 181.55/181.55 [1342]~E(x13421,x13422)+E(f845(x13421,x13423,x13424,x13425),f845(x13422,x13423,x13424,x13425)) % 181.55/181.55 [1343]~E(x13431,x13432)+E(f845(x13433,x13431,x13434,x13435),f845(x13433,x13432,x13434,x13435)) % 181.55/181.55 [1344]~E(x13441,x13442)+E(f845(x13443,x13444,x13441,x13445),f845(x13443,x13444,x13442,x13445)) % 181.55/181.55 [1345]~E(x13451,x13452)+E(f845(x13453,x13454,x13455,x13451),f845(x13453,x13454,x13455,x13452)) % 181.55/181.55 [1346]~E(x13461,x13462)+E(f717(x13461,x13463,x13464),f717(x13462,x13463,x13464)) % 181.55/181.55 [1347]~E(x13471,x13472)+E(f717(x13473,x13471,x13474),f717(x13473,x13472,x13474)) % 181.55/181.55 [1348]~E(x13481,x13482)+E(f717(x13483,x13484,x13481),f717(x13483,x13484,x13482)) % 181.55/181.55 [1349]~E(x13491,x13492)+E(f309(x13491),f309(x13492)) % 181.55/181.55 [1350]~E(x13501,x13502)+E(f509(x13501,x13503,x13504,x13505,x13506,x13507,x13508,x13509),f509(x13502,x13503,x13504,x13505,x13506,x13507,x13508,x13509)) % 181.55/181.55 [1351]~E(x13511,x13512)+E(f509(x13513,x13511,x13514,x13515,x13516,x13517,x13518,x13519),f509(x13513,x13512,x13514,x13515,x13516,x13517,x13518,x13519)) % 181.55/181.55 [1352]~E(x13521,x13522)+E(f509(x13523,x13524,x13521,x13525,x13526,x13527,x13528,x13529),f509(x13523,x13524,x13522,x13525,x13526,x13527,x13528,x13529)) % 181.55/181.55 [1353]~E(x13531,x13532)+E(f509(x13533,x13534,x13535,x13531,x13536,x13537,x13538,x13539),f509(x13533,x13534,x13535,x13532,x13536,x13537,x13538,x13539)) % 181.55/181.55 [1354]~E(x13541,x13542)+E(f509(x13543,x13544,x13545,x13546,x13541,x13547,x13548,x13549),f509(x13543,x13544,x13545,x13546,x13542,x13547,x13548,x13549)) % 181.55/181.55 [1355]~E(x13551,x13552)+E(f509(x13553,x13554,x13555,x13556,x13557,x13551,x13558,x13559),f509(x13553,x13554,x13555,x13556,x13557,x13552,x13558,x13559)) % 181.55/181.55 [1356]~E(x13561,x13562)+E(f509(x13563,x13564,x13565,x13566,x13567,x13568,x13561,x13569),f509(x13563,x13564,x13565,x13566,x13567,x13568,x13562,x13569)) % 181.55/181.55 [1357]~E(x13571,x13572)+E(f509(x13573,x13574,x13575,x13576,x13577,x13578,x13579,x13571),f509(x13573,x13574,x13575,x13576,x13577,x13578,x13579,x13572)) % 181.55/181.55 [1358]~E(x13581,x13582)+E(f210(x13581,x13583,x13584,x13585),f210(x13582,x13583,x13584,x13585)) % 181.55/181.55 [1359]~E(x13591,x13592)+E(f210(x13593,x13591,x13594,x13595),f210(x13593,x13592,x13594,x13595)) % 181.55/181.55 [1360]~E(x13601,x13602)+E(f210(x13603,x13604,x13601,x13605),f210(x13603,x13604,x13602,x13605)) % 181.55/181.55 [1361]~E(x13611,x13612)+E(f210(x13613,x13614,x13615,x13611),f210(x13613,x13614,x13615,x13612)) % 181.55/181.55 [1362]~E(x13621,x13622)+E(f826(x13621,x13623,x13624),f826(x13622,x13623,x13624)) % 181.55/181.55 [1363]~E(x13631,x13632)+E(f826(x13633,x13631,x13634),f826(x13633,x13632,x13634)) % 181.55/181.55 [1364]~E(x13641,x13642)+E(f826(x13643,x13644,x13641),f826(x13643,x13644,x13642)) % 181.55/181.55 [1365]~E(x13651,x13652)+E(f630(x13651,x13653,x13654),f630(x13652,x13653,x13654)) % 181.55/181.55 [1366]~E(x13661,x13662)+E(f630(x13663,x13661,x13664),f630(x13663,x13662,x13664)) % 181.55/181.55 [1367]~E(x13671,x13672)+E(f630(x13673,x13674,x13671),f630(x13673,x13674,x13672)) % 181.55/181.55 [1368]~E(x13681,x13682)+E(f52(x13681,x13683),f52(x13682,x13683)) % 181.55/181.55 [1369]~E(x13691,x13692)+E(f52(x13693,x13691),f52(x13693,x13692)) % 181.55/181.55 [1370]~E(x13701,x13702)+E(f774(x13701,x13703,x13704,x13705,x13706),f774(x13702,x13703,x13704,x13705,x13706)) % 181.55/181.55 [1371]~E(x13711,x13712)+E(f774(x13713,x13711,x13714,x13715,x13716),f774(x13713,x13712,x13714,x13715,x13716)) % 181.55/181.55 [1372]~E(x13721,x13722)+E(f774(x13723,x13724,x13721,x13725,x13726),f774(x13723,x13724,x13722,x13725,x13726)) % 181.55/181.55 [1373]~E(x13731,x13732)+E(f774(x13733,x13734,x13735,x13731,x13736),f774(x13733,x13734,x13735,x13732,x13736)) % 181.55/181.55 [1374]~E(x13741,x13742)+E(f774(x13743,x13744,x13745,x13746,x13741),f774(x13743,x13744,x13745,x13746,x13742)) % 181.55/181.55 [1375]~E(x13751,x13752)+E(f855(x13751,x13753,x13754),f855(x13752,x13753,x13754)) % 181.55/181.55 [1376]~E(x13761,x13762)+E(f855(x13763,x13761,x13764),f855(x13763,x13762,x13764)) % 181.55/181.55 [1377]~E(x13771,x13772)+E(f855(x13773,x13774,x13771),f855(x13773,x13774,x13772)) % 181.55/181.55 [1378]~E(x13781,x13782)+E(f497(x13781,x13783,x13784,x13785,x13786,x13787),f497(x13782,x13783,x13784,x13785,x13786,x13787)) % 181.55/181.55 [1379]~E(x13791,x13792)+E(f497(x13793,x13791,x13794,x13795,x13796,x13797),f497(x13793,x13792,x13794,x13795,x13796,x13797)) % 181.55/181.55 [1380]~E(x13801,x13802)+E(f497(x13803,x13804,x13801,x13805,x13806,x13807),f497(x13803,x13804,x13802,x13805,x13806,x13807)) % 181.55/181.55 [1381]~E(x13811,x13812)+E(f497(x13813,x13814,x13815,x13811,x13816,x13817),f497(x13813,x13814,x13815,x13812,x13816,x13817)) % 181.55/181.55 [1382]~E(x13821,x13822)+E(f497(x13823,x13824,x13825,x13826,x13821,x13827),f497(x13823,x13824,x13825,x13826,x13822,x13827)) % 181.55/181.55 [1383]~E(x13831,x13832)+E(f497(x13833,x13834,x13835,x13836,x13837,x13831),f497(x13833,x13834,x13835,x13836,x13837,x13832)) % 181.55/181.55 [1384]~E(x13841,x13842)+E(f216(x13841,x13843,x13844,x13845,x13846,x13847,x13848),f216(x13842,x13843,x13844,x13845,x13846,x13847,x13848)) % 181.55/181.55 [1385]~E(x13851,x13852)+E(f216(x13853,x13851,x13854,x13855,x13856,x13857,x13858),f216(x13853,x13852,x13854,x13855,x13856,x13857,x13858)) % 181.55/181.55 [1386]~E(x13861,x13862)+E(f216(x13863,x13864,x13861,x13865,x13866,x13867,x13868),f216(x13863,x13864,x13862,x13865,x13866,x13867,x13868)) % 181.55/181.55 [1387]~E(x13871,x13872)+E(f216(x13873,x13874,x13875,x13871,x13876,x13877,x13878),f216(x13873,x13874,x13875,x13872,x13876,x13877,x13878)) % 181.55/181.55 [1388]~E(x13881,x13882)+E(f216(x13883,x13884,x13885,x13886,x13881,x13887,x13888),f216(x13883,x13884,x13885,x13886,x13882,x13887,x13888)) % 181.55/181.55 [1389]~E(x13891,x13892)+E(f216(x13893,x13894,x13895,x13896,x13897,x13891,x13898),f216(x13893,x13894,x13895,x13896,x13897,x13892,x13898)) % 181.55/181.55 [1390]~E(x13901,x13902)+E(f216(x13903,x13904,x13905,x13906,x13907,x13908,x13901),f216(x13903,x13904,x13905,x13906,x13907,x13908,x13902)) % 181.55/181.55 [1391]~E(x13911,x13912)+E(f430(x13911,x13913,x13914,x13915,x13916),f430(x13912,x13913,x13914,x13915,x13916)) % 181.55/181.55 [1392]~E(x13921,x13922)+E(f430(x13923,x13921,x13924,x13925,x13926),f430(x13923,x13922,x13924,x13925,x13926)) % 181.55/181.55 [1393]~E(x13931,x13932)+E(f430(x13933,x13934,x13931,x13935,x13936),f430(x13933,x13934,x13932,x13935,x13936)) % 181.55/181.55 [1394]~E(x13941,x13942)+E(f430(x13943,x13944,x13945,x13941,x13946),f430(x13943,x13944,x13945,x13942,x13946)) % 181.55/181.55 [1395]~E(x13951,x13952)+E(f430(x13953,x13954,x13955,x13956,x13951),f430(x13953,x13954,x13955,x13956,x13952)) % 181.55/181.55 [1396]~E(x13961,x13962)+E(f767(x13961,x13963,x13964,x13965),f767(x13962,x13963,x13964,x13965)) % 181.55/181.55 [1397]~E(x13971,x13972)+E(f767(x13973,x13971,x13974,x13975),f767(x13973,x13972,x13974,x13975)) % 181.55/181.55 [1398]~E(x13981,x13982)+E(f767(x13983,x13984,x13981,x13985),f767(x13983,x13984,x13982,x13985)) % 181.55/181.55 [1399]~E(x13991,x13992)+E(f767(x13993,x13994,x13995,x13991),f767(x13993,x13994,x13995,x13992)) % 181.55/181.55 [1400]~E(x14001,x14002)+E(f453(x14001,x14003,x14004),f453(x14002,x14003,x14004)) % 181.55/181.55 [1401]~E(x14011,x14012)+E(f453(x14013,x14011,x14014),f453(x14013,x14012,x14014)) % 181.55/181.55 [1402]~E(x14021,x14022)+E(f453(x14023,x14024,x14021),f453(x14023,x14024,x14022)) % 181.55/181.55 [1403]~E(x14031,x14032)+E(f615(x14031,x14033,x14034,x14035,x14036),f615(x14032,x14033,x14034,x14035,x14036)) % 181.55/181.55 [1404]~E(x14041,x14042)+E(f615(x14043,x14041,x14044,x14045,x14046),f615(x14043,x14042,x14044,x14045,x14046)) % 181.55/181.55 [1405]~E(x14051,x14052)+E(f615(x14053,x14054,x14051,x14055,x14056),f615(x14053,x14054,x14052,x14055,x14056)) % 181.55/181.55 [1406]~E(x14061,x14062)+E(f615(x14063,x14064,x14065,x14061,x14066),f615(x14063,x14064,x14065,x14062,x14066)) % 181.55/181.55 [1407]~E(x14071,x14072)+E(f615(x14073,x14074,x14075,x14076,x14071),f615(x14073,x14074,x14075,x14076,x14072)) % 181.55/181.55 [1408]~E(x14081,x14082)+E(f696(x14081,x14083,x14084,x14085,x14086),f696(x14082,x14083,x14084,x14085,x14086)) % 181.55/181.55 [1409]~E(x14091,x14092)+E(f696(x14093,x14091,x14094,x14095,x14096),f696(x14093,x14092,x14094,x14095,x14096)) % 181.55/181.55 [1410]~E(x14101,x14102)+E(f696(x14103,x14104,x14101,x14105,x14106),f696(x14103,x14104,x14102,x14105,x14106)) % 181.55/181.55 [1411]~E(x14111,x14112)+E(f696(x14113,x14114,x14115,x14111,x14116),f696(x14113,x14114,x14115,x14112,x14116)) % 181.55/181.55 [1412]~E(x14121,x14122)+E(f696(x14123,x14124,x14125,x14126,x14121),f696(x14123,x14124,x14125,x14126,x14122)) % 181.55/181.55 [1413]~E(x14131,x14132)+E(f584(x14131,x14133,x14134,x14135),f584(x14132,x14133,x14134,x14135)) % 181.55/181.55 [1414]~E(x14141,x14142)+E(f584(x14143,x14141,x14144,x14145),f584(x14143,x14142,x14144,x14145)) % 181.55/181.55 [1415]~E(x14151,x14152)+E(f584(x14153,x14154,x14151,x14155),f584(x14153,x14154,x14152,x14155)) % 181.55/181.55 [1416]~E(x14161,x14162)+E(f584(x14163,x14164,x14165,x14161),f584(x14163,x14164,x14165,x14162)) % 181.55/181.55 [1417]~E(x14171,x14172)+E(f375(x14171,x14173),f375(x14172,x14173)) % 181.55/181.55 [1418]~E(x14181,x14182)+E(f375(x14183,x14181),f375(x14183,x14182)) % 181.55/181.55 [1419]~E(x14191,x14192)+E(f450(x14191,x14193,x14194,x14195),f450(x14192,x14193,x14194,x14195)) % 181.55/181.55 [1420]~E(x14201,x14202)+E(f450(x14203,x14201,x14204,x14205),f450(x14203,x14202,x14204,x14205)) % 181.55/181.55 [1421]~E(x14211,x14212)+E(f450(x14213,x14214,x14211,x14215),f450(x14213,x14214,x14212,x14215)) % 181.55/181.55 [1422]~E(x14221,x14222)+E(f450(x14223,x14224,x14225,x14221),f450(x14223,x14224,x14225,x14222)) % 181.55/181.55 [1423]~E(x14231,x14232)+E(f316(x14231,x14233,x14234,x14235),f316(x14232,x14233,x14234,x14235)) % 181.55/181.55 [1424]~E(x14241,x14242)+E(f316(x14243,x14241,x14244,x14245),f316(x14243,x14242,x14244,x14245)) % 181.55/181.55 [1425]~E(x14251,x14252)+E(f316(x14253,x14254,x14251,x14255),f316(x14253,x14254,x14252,x14255)) % 181.55/181.55 [1426]~E(x14261,x14262)+E(f316(x14263,x14264,x14265,x14261),f316(x14263,x14264,x14265,x14262)) % 181.55/181.55 [1427]~E(x14271,x14272)+E(f582(x14271,x14273,x14274,x14275,x14276,x14277,x14278,x14279),f582(x14272,x14273,x14274,x14275,x14276,x14277,x14278,x14279)) % 181.55/181.55 [1428]~E(x14281,x14282)+E(f582(x14283,x14281,x14284,x14285,x14286,x14287,x14288,x14289),f582(x14283,x14282,x14284,x14285,x14286,x14287,x14288,x14289)) % 181.55/181.55 [1429]~E(x14291,x14292)+E(f582(x14293,x14294,x14291,x14295,x14296,x14297,x14298,x14299),f582(x14293,x14294,x14292,x14295,x14296,x14297,x14298,x14299)) % 181.55/181.55 [1430]~E(x14301,x14302)+E(f582(x14303,x14304,x14305,x14301,x14306,x14307,x14308,x14309),f582(x14303,x14304,x14305,x14302,x14306,x14307,x14308,x14309)) % 181.55/181.55 [1431]~E(x14311,x14312)+E(f582(x14313,x14314,x14315,x14316,x14311,x14317,x14318,x14319),f582(x14313,x14314,x14315,x14316,x14312,x14317,x14318,x14319)) % 181.55/181.55 [1432]~E(x14321,x14322)+E(f582(x14323,x14324,x14325,x14326,x14327,x14321,x14328,x14329),f582(x14323,x14324,x14325,x14326,x14327,x14322,x14328,x14329)) % 181.55/181.55 [1433]~E(x14331,x14332)+E(f582(x14333,x14334,x14335,x14336,x14337,x14338,x14331,x14339),f582(x14333,x14334,x14335,x14336,x14337,x14338,x14332,x14339)) % 181.55/181.55 [1434]~E(x14341,x14342)+E(f582(x14343,x14344,x14345,x14346,x14347,x14348,x14349,x14341),f582(x14343,x14344,x14345,x14346,x14347,x14348,x14349,x14342)) % 181.55/181.55 [1435]~E(x14351,x14352)+E(f622(x14351,x14353,x14354),f622(x14352,x14353,x14354)) % 181.55/181.55 [1436]~E(x14361,x14362)+E(f622(x14363,x14361,x14364),f622(x14363,x14362,x14364)) % 181.55/181.55 [1437]~E(x14371,x14372)+E(f622(x14373,x14374,x14371),f622(x14373,x14374,x14372)) % 181.55/181.55 [1438]~E(x14381,x14382)+E(f639(x14381,x14383,x14384),f639(x14382,x14383,x14384)) % 181.55/181.55 [1439]~E(x14391,x14392)+E(f639(x14393,x14391,x14394),f639(x14393,x14392,x14394)) % 181.55/181.55 [1440]~E(x14401,x14402)+E(f639(x14403,x14404,x14401),f639(x14403,x14404,x14402)) % 181.55/181.55 [1441]~E(x14411,x14412)+E(f356(x14411,x14413,x14414,x14415,x14416,x14417,x14418),f356(x14412,x14413,x14414,x14415,x14416,x14417,x14418)) % 181.55/181.55 [1442]~E(x14421,x14422)+E(f356(x14423,x14421,x14424,x14425,x14426,x14427,x14428),f356(x14423,x14422,x14424,x14425,x14426,x14427,x14428)) % 181.55/181.55 [1443]~E(x14431,x14432)+E(f356(x14433,x14434,x14431,x14435,x14436,x14437,x14438),f356(x14433,x14434,x14432,x14435,x14436,x14437,x14438)) % 181.55/181.55 [1444]~E(x14441,x14442)+E(f356(x14443,x14444,x14445,x14441,x14446,x14447,x14448),f356(x14443,x14444,x14445,x14442,x14446,x14447,x14448)) % 181.55/181.55 [1445]~E(x14451,x14452)+E(f356(x14453,x14454,x14455,x14456,x14451,x14457,x14458),f356(x14453,x14454,x14455,x14456,x14452,x14457,x14458)) % 181.55/181.55 [1446]~E(x14461,x14462)+E(f356(x14463,x14464,x14465,x14466,x14467,x14461,x14468),f356(x14463,x14464,x14465,x14466,x14467,x14462,x14468)) % 181.55/181.55 [1447]~E(x14471,x14472)+E(f356(x14473,x14474,x14475,x14476,x14477,x14478,x14471),f356(x14473,x14474,x14475,x14476,x14477,x14478,x14472)) % 181.55/181.55 [1448]~E(x14481,x14482)+E(f223(x14481,x14483),f223(x14482,x14483)) % 181.55/181.55 [1449]~E(x14491,x14492)+E(f223(x14493,x14491),f223(x14493,x14492)) % 181.55/181.55 [1450]~E(x14501,x14502)+E(f606(x14501,x14503,x14504),f606(x14502,x14503,x14504)) % 181.55/181.55 [1451]~E(x14511,x14512)+E(f606(x14513,x14511,x14514),f606(x14513,x14512,x14514)) % 181.55/181.55 [1452]~E(x14521,x14522)+E(f606(x14523,x14524,x14521),f606(x14523,x14524,x14522)) % 181.55/181.55 [1453]~E(x14531,x14532)+E(f581(x14531,x14533,x14534),f581(x14532,x14533,x14534)) % 181.55/181.55 [1454]~E(x14541,x14542)+E(f581(x14543,x14541,x14544),f581(x14543,x14542,x14544)) % 181.55/181.55 [1455]~E(x14551,x14552)+E(f581(x14553,x14554,x14551),f581(x14553,x14554,x14552)) % 181.55/181.55 [1456]~E(x14561,x14562)+E(f657(x14561,x14563,x14564,x14565,x14566,x14567),f657(x14562,x14563,x14564,x14565,x14566,x14567)) % 181.55/181.55 [1457]~E(x14571,x14572)+E(f657(x14573,x14571,x14574,x14575,x14576,x14577),f657(x14573,x14572,x14574,x14575,x14576,x14577)) % 181.55/181.55 [1458]~E(x14581,x14582)+E(f657(x14583,x14584,x14581,x14585,x14586,x14587),f657(x14583,x14584,x14582,x14585,x14586,x14587)) % 181.55/181.55 [1459]~E(x14591,x14592)+E(f657(x14593,x14594,x14595,x14591,x14596,x14597),f657(x14593,x14594,x14595,x14592,x14596,x14597)) % 181.55/181.55 [1460]~E(x14601,x14602)+E(f657(x14603,x14604,x14605,x14606,x14601,x14607),f657(x14603,x14604,x14605,x14606,x14602,x14607)) % 181.55/181.55 [1461]~E(x14611,x14612)+E(f657(x14613,x14614,x14615,x14616,x14617,x14611),f657(x14613,x14614,x14615,x14616,x14617,x14612)) % 181.55/181.55 [1462]~E(x14621,x14622)+E(f234(x14621,x14623,x14624),f234(x14622,x14623,x14624)) % 181.55/181.55 [1463]~E(x14631,x14632)+E(f234(x14633,x14631,x14634),f234(x14633,x14632,x14634)) % 181.55/181.55 [1464]~E(x14641,x14642)+E(f234(x14643,x14644,x14641),f234(x14643,x14644,x14642)) % 181.55/181.55 [1465]~E(x14651,x14652)+E(f852(x14651,x14653,x14654,x14655,x14656),f852(x14652,x14653,x14654,x14655,x14656)) % 181.55/181.55 [1466]~E(x14661,x14662)+E(f852(x14663,x14661,x14664,x14665,x14666),f852(x14663,x14662,x14664,x14665,x14666)) % 181.55/181.55 [1467]~E(x14671,x14672)+E(f852(x14673,x14674,x14671,x14675,x14676),f852(x14673,x14674,x14672,x14675,x14676)) % 181.55/181.55 [1468]~E(x14681,x14682)+E(f852(x14683,x14684,x14685,x14681,x14686),f852(x14683,x14684,x14685,x14682,x14686)) % 181.55/181.55 [1469]~E(x14691,x14692)+E(f852(x14693,x14694,x14695,x14696,x14691),f852(x14693,x14694,x14695,x14696,x14692)) % 181.55/181.55 [1470]~E(x14701,x14702)+E(f207(x14701),f207(x14702)) % 181.55/181.55 [1471]~E(x14711,x14712)+E(f526(x14711,x14713,x14714),f526(x14712,x14713,x14714)) % 181.55/181.55 [1472]~E(x14721,x14722)+E(f526(x14723,x14721,x14724),f526(x14723,x14722,x14724)) % 181.55/181.55 [1473]~E(x14731,x14732)+E(f526(x14733,x14734,x14731),f526(x14733,x14734,x14732)) % 181.55/181.55 [1474]~E(x14741,x14742)+E(f95(x14741,x14743,x14744),f95(x14742,x14743,x14744)) % 181.55/181.55 [1475]~E(x14751,x14752)+E(f95(x14753,x14751,x14754),f95(x14753,x14752,x14754)) % 181.55/181.55 [1476]~E(x14761,x14762)+E(f95(x14763,x14764,x14761),f95(x14763,x14764,x14762)) % 181.55/181.55 [1477]~E(x14771,x14772)+E(f230(x14771,x14773,x14774),f230(x14772,x14773,x14774)) % 181.55/181.55 [1478]~E(x14781,x14782)+E(f230(x14783,x14781,x14784),f230(x14783,x14782,x14784)) % 181.55/181.55 [1479]~E(x14791,x14792)+E(f230(x14793,x14794,x14791),f230(x14793,x14794,x14792)) % 181.55/181.55 [1480]~E(x14801,x14802)+E(f434(x14801,x14803,x14804,x14805),f434(x14802,x14803,x14804,x14805)) % 181.55/181.55 [1481]~E(x14811,x14812)+E(f434(x14813,x14811,x14814,x14815),f434(x14813,x14812,x14814,x14815)) % 181.55/181.55 [1482]~E(x14821,x14822)+E(f434(x14823,x14824,x14821,x14825),f434(x14823,x14824,x14822,x14825)) % 181.55/181.55 [1483]~E(x14831,x14832)+E(f434(x14833,x14834,x14835,x14831),f434(x14833,x14834,x14835,x14832)) % 181.55/181.55 [1484]~E(x14841,x14842)+E(f850(x14841,x14843,x14844,x14845,x14846,x14847),f850(x14842,x14843,x14844,x14845,x14846,x14847)) % 181.55/181.55 [1485]~E(x14851,x14852)+E(f850(x14853,x14851,x14854,x14855,x14856,x14857),f850(x14853,x14852,x14854,x14855,x14856,x14857)) % 181.55/181.55 [1486]~E(x14861,x14862)+E(f850(x14863,x14864,x14861,x14865,x14866,x14867),f850(x14863,x14864,x14862,x14865,x14866,x14867)) % 181.55/181.55 [1487]~E(x14871,x14872)+E(f850(x14873,x14874,x14875,x14871,x14876,x14877),f850(x14873,x14874,x14875,x14872,x14876,x14877)) % 181.55/181.55 [1488]~E(x14881,x14882)+E(f850(x14883,x14884,x14885,x14886,x14881,x14887),f850(x14883,x14884,x14885,x14886,x14882,x14887)) % 181.55/181.55 [1489]~E(x14891,x14892)+E(f850(x14893,x14894,x14895,x14896,x14897,x14891),f850(x14893,x14894,x14895,x14896,x14897,x14892)) % 181.55/181.55 [1490]~E(x14901,x14902)+E(f842(x14901,x14903,x14904),f842(x14902,x14903,x14904)) % 181.55/181.55 [1491]~E(x14911,x14912)+E(f842(x14913,x14911,x14914),f842(x14913,x14912,x14914)) % 181.55/181.55 [1492]~E(x14921,x14922)+E(f842(x14923,x14924,x14921),f842(x14923,x14924,x14922)) % 181.55/181.55 [1493]~E(x14931,x14932)+E(f432(x14931,x14933),f432(x14932,x14933)) % 181.55/181.55 [1494]~E(x14941,x14942)+E(f432(x14943,x14941),f432(x14943,x14942)) % 181.55/181.55 [1495]~E(x14951,x14952)+E(f810(x14951,x14953,x14954,x14955,x14956,x14957,x14958),f810(x14952,x14953,x14954,x14955,x14956,x14957,x14958)) % 181.55/181.55 [1496]~E(x14961,x14962)+E(f810(x14963,x14961,x14964,x14965,x14966,x14967,x14968),f810(x14963,x14962,x14964,x14965,x14966,x14967,x14968)) % 181.55/181.55 [1497]~E(x14971,x14972)+E(f810(x14973,x14974,x14971,x14975,x14976,x14977,x14978),f810(x14973,x14974,x14972,x14975,x14976,x14977,x14978)) % 181.55/181.55 [1498]~E(x14981,x14982)+E(f810(x14983,x14984,x14985,x14981,x14986,x14987,x14988),f810(x14983,x14984,x14985,x14982,x14986,x14987,x14988)) % 181.55/181.55 [1499]~E(x14991,x14992)+E(f810(x14993,x14994,x14995,x14996,x14991,x14997,x14998),f810(x14993,x14994,x14995,x14996,x14992,x14997,x14998)) % 181.55/181.55 [1500]~E(x15001,x15002)+E(f810(x15003,x15004,x15005,x15006,x15007,x15001,x15008),f810(x15003,x15004,x15005,x15006,x15007,x15002,x15008)) % 181.55/181.55 [1501]~E(x15011,x15012)+E(f810(x15013,x15014,x15015,x15016,x15017,x15018,x15011),f810(x15013,x15014,x15015,x15016,x15017,x15018,x15012)) % 181.55/181.55 [1502]~E(x15021,x15022)+E(f689(x15021,x15023,x15024,x15025),f689(x15022,x15023,x15024,x15025)) % 181.55/181.55 [1503]~E(x15031,x15032)+E(f689(x15033,x15031,x15034,x15035),f689(x15033,x15032,x15034,x15035)) % 181.55/181.55 [1504]~E(x15041,x15042)+E(f689(x15043,x15044,x15041,x15045),f689(x15043,x15044,x15042,x15045)) % 181.55/181.55 [1505]~E(x15051,x15052)+E(f689(x15053,x15054,x15055,x15051),f689(x15053,x15054,x15055,x15052)) % 181.55/181.55 [1506]~E(x15061,x15062)+E(f651(x15061,x15063,x15064,x15065,x15066),f651(x15062,x15063,x15064,x15065,x15066)) % 181.55/181.55 [1507]~E(x15071,x15072)+E(f651(x15073,x15071,x15074,x15075,x15076),f651(x15073,x15072,x15074,x15075,x15076)) % 181.55/181.55 [1508]~E(x15081,x15082)+E(f651(x15083,x15084,x15081,x15085,x15086),f651(x15083,x15084,x15082,x15085,x15086)) % 181.55/181.55 [1509]~E(x15091,x15092)+E(f651(x15093,x15094,x15095,x15091,x15096),f651(x15093,x15094,x15095,x15092,x15096)) % 181.55/181.55 [1510]~E(x15101,x15102)+E(f651(x15103,x15104,x15105,x15106,x15101),f651(x15103,x15104,x15105,x15106,x15102)) % 181.55/181.55 [1511]~E(x15111,x15112)+E(f517(x15111,x15113,x15114,x15115),f517(x15112,x15113,x15114,x15115)) % 181.55/181.55 [1512]~E(x15121,x15122)+E(f517(x15123,x15121,x15124,x15125),f517(x15123,x15122,x15124,x15125)) % 181.55/181.55 [1513]~E(x15131,x15132)+E(f517(x15133,x15134,x15131,x15135),f517(x15133,x15134,x15132,x15135)) % 181.55/181.55 [1514]~E(x15141,x15142)+E(f517(x15143,x15144,x15145,x15141),f517(x15143,x15144,x15145,x15142)) % 181.55/181.55 [1515]~E(x15151,x15152)+E(f633(x15151,x15153,x15154),f633(x15152,x15153,x15154)) % 181.55/181.55 [1516]~E(x15161,x15162)+E(f633(x15163,x15161,x15164),f633(x15163,x15162,x15164)) % 181.55/181.55 [1517]~E(x15171,x15172)+E(f633(x15173,x15174,x15171),f633(x15173,x15174,x15172)) % 181.55/181.55 [1518]~E(x15181,x15182)+E(f260(x15181,x15183,x15184,x15185,x15186),f260(x15182,x15183,x15184,x15185,x15186)) % 181.55/181.55 [1519]~E(x15191,x15192)+E(f260(x15193,x15191,x15194,x15195,x15196),f260(x15193,x15192,x15194,x15195,x15196)) % 181.55/181.55 [1520]~E(x15201,x15202)+E(f260(x15203,x15204,x15201,x15205,x15206),f260(x15203,x15204,x15202,x15205,x15206)) % 181.55/181.55 [1521]~E(x15211,x15212)+E(f260(x15213,x15214,x15215,x15211,x15216),f260(x15213,x15214,x15215,x15212,x15216)) % 181.55/181.55 [1522]~E(x15221,x15222)+E(f260(x15223,x15224,x15225,x15226,x15221),f260(x15223,x15224,x15225,x15226,x15222)) % 181.55/181.55 [1523]~E(x15231,x15232)+E(f397(x15231,x15233,x15234,x15235),f397(x15232,x15233,x15234,x15235)) % 181.55/181.55 [1524]~E(x15241,x15242)+E(f397(x15243,x15241,x15244,x15245),f397(x15243,x15242,x15244,x15245)) % 181.55/181.55 [1525]~E(x15251,x15252)+E(f397(x15253,x15254,x15251,x15255),f397(x15253,x15254,x15252,x15255)) % 181.55/181.55 [1526]~E(x15261,x15262)+E(f397(x15263,x15264,x15265,x15261),f397(x15263,x15264,x15265,x15262)) % 181.55/181.55 [1527]~E(x15271,x15272)+E(f729(x15271,x15273),f729(x15272,x15273)) % 181.55/181.55 [1528]~E(x15281,x15282)+E(f729(x15283,x15281),f729(x15283,x15282)) % 181.55/181.55 [1529]~E(x15291,x15292)+E(f463(x15291,x15293,x15294,x15295),f463(x15292,x15293,x15294,x15295)) % 181.55/181.55 [1530]~E(x15301,x15302)+E(f463(x15303,x15301,x15304,x15305),f463(x15303,x15302,x15304,x15305)) % 181.55/181.55 [1531]~E(x15311,x15312)+E(f463(x15313,x15314,x15311,x15315),f463(x15313,x15314,x15312,x15315)) % 181.55/181.55 [1532]~E(x15321,x15322)+E(f463(x15323,x15324,x15325,x15321),f463(x15323,x15324,x15325,x15322)) % 181.55/181.55 [1533]~E(x15331,x15332)+E(f690(x15331,x15333,x15334,x15335),f690(x15332,x15333,x15334,x15335)) % 181.55/181.55 [1534]~E(x15341,x15342)+E(f690(x15343,x15341,x15344,x15345),f690(x15343,x15342,x15344,x15345)) % 181.55/181.55 [1535]~E(x15351,x15352)+E(f690(x15353,x15354,x15351,x15355),f690(x15353,x15354,x15352,x15355)) % 181.55/181.55 [1536]~E(x15361,x15362)+E(f690(x15363,x15364,x15365,x15361),f690(x15363,x15364,x15365,x15362)) % 181.55/181.55 [1537]~E(x15371,x15372)+E(f550(x15371,x15373,x15374,x15375),f550(x15372,x15373,x15374,x15375)) % 181.55/181.55 [1538]~E(x15381,x15382)+E(f550(x15383,x15381,x15384,x15385),f550(x15383,x15382,x15384,x15385)) % 181.55/181.55 [1539]~E(x15391,x15392)+E(f550(x15393,x15394,x15391,x15395),f550(x15393,x15394,x15392,x15395)) % 181.55/181.55 [1540]~E(x15401,x15402)+E(f550(x15403,x15404,x15405,x15401),f550(x15403,x15404,x15405,x15402)) % 181.55/181.55 [1541]~E(x15411,x15412)+E(f553(x15411,x15413,x15414),f553(x15412,x15413,x15414)) % 181.55/181.55 [1542]~E(x15421,x15422)+E(f553(x15423,x15421,x15424),f553(x15423,x15422,x15424)) % 181.55/181.55 [1543]~E(x15431,x15432)+E(f553(x15433,x15434,x15431),f553(x15433,x15434,x15432)) % 181.55/181.55 [1544]~E(x15441,x15442)+E(f353(x15441,x15443,x15444),f353(x15442,x15443,x15444)) % 181.55/181.55 [1545]~E(x15451,x15452)+E(f353(x15453,x15451,x15454),f353(x15453,x15452,x15454)) % 181.55/181.55 [1546]~E(x15461,x15462)+E(f353(x15463,x15464,x15461),f353(x15463,x15464,x15462)) % 181.55/181.55 [1547]~E(x15471,x15472)+E(f809(x15471,x15473,x15474,x15475,x15476),f809(x15472,x15473,x15474,x15475,x15476)) % 181.55/181.55 [1548]~E(x15481,x15482)+E(f809(x15483,x15481,x15484,x15485,x15486),f809(x15483,x15482,x15484,x15485,x15486)) % 181.55/181.55 [1549]~E(x15491,x15492)+E(f809(x15493,x15494,x15491,x15495,x15496),f809(x15493,x15494,x15492,x15495,x15496)) % 181.55/181.55 [1550]~E(x15501,x15502)+E(f809(x15503,x15504,x15505,x15501,x15506),f809(x15503,x15504,x15505,x15502,x15506)) % 181.55/181.55 [1551]~E(x15511,x15512)+E(f809(x15513,x15514,x15515,x15516,x15511),f809(x15513,x15514,x15515,x15516,x15512)) % 181.55/181.55 [1552]~E(x15521,x15522)+E(f345(x15521,x15523,x15524,x15525,x15526),f345(x15522,x15523,x15524,x15525,x15526)) % 181.55/181.55 [1553]~E(x15531,x15532)+E(f345(x15533,x15531,x15534,x15535,x15536),f345(x15533,x15532,x15534,x15535,x15536)) % 181.55/181.55 [1554]~E(x15541,x15542)+E(f345(x15543,x15544,x15541,x15545,x15546),f345(x15543,x15544,x15542,x15545,x15546)) % 181.55/181.55 [1555]~E(x15551,x15552)+E(f345(x15553,x15554,x15555,x15551,x15556),f345(x15553,x15554,x15555,x15552,x15556)) % 181.55/181.55 [1556]~E(x15561,x15562)+E(f345(x15563,x15564,x15565,x15566,x15561),f345(x15563,x15564,x15565,x15566,x15562)) % 181.55/181.55 [1557]~E(x15571,x15572)+E(f552(x15571,x15573,x15574),f552(x15572,x15573,x15574)) % 181.55/181.55 [1558]~E(x15581,x15582)+E(f552(x15583,x15581,x15584),f552(x15583,x15582,x15584)) % 181.55/181.55 [1559]~E(x15591,x15592)+E(f552(x15593,x15594,x15591),f552(x15593,x15594,x15592)) % 181.55/181.55 [1560]~E(x15601,x15602)+E(f604(x15601,x15603),f604(x15602,x15603)) % 181.55/181.55 [1561]~E(x15611,x15612)+E(f604(x15613,x15611),f604(x15613,x15612)) % 181.55/181.55 [1562]~E(x15621,x15622)+E(f447(x15621,x15623,x15624),f447(x15622,x15623,x15624)) % 181.55/181.55 [1563]~E(x15631,x15632)+E(f447(x15633,x15631,x15634),f447(x15633,x15632,x15634)) % 181.55/181.55 [1564]~E(x15641,x15642)+E(f447(x15643,x15644,x15641),f447(x15643,x15644,x15642)) % 181.55/181.55 [1565]~E(x15651,x15652)+E(f520(x15651,x15653,x15654),f520(x15652,x15653,x15654)) % 181.55/181.55 [1566]~E(x15661,x15662)+E(f520(x15663,x15661,x15664),f520(x15663,x15662,x15664)) % 181.55/181.55 [1567]~E(x15671,x15672)+E(f520(x15673,x15674,x15671),f520(x15673,x15674,x15672)) % 181.55/181.55 [1568]~E(x15681,x15682)+E(f762(x15681,x15683),f762(x15682,x15683)) % 181.55/181.55 [1569]~E(x15691,x15692)+E(f762(x15693,x15691),f762(x15693,x15692)) % 181.55/181.55 [1570]~E(x15701,x15702)+E(f518(x15701,x15703),f518(x15702,x15703)) % 181.55/181.55 [1571]~E(x15711,x15712)+E(f518(x15713,x15711),f518(x15713,x15712)) % 181.55/181.55 [1572]~E(x15721,x15722)+E(f307(x15721,x15723,x15724),f307(x15722,x15723,x15724)) % 181.55/181.55 [1573]~E(x15731,x15732)+E(f307(x15733,x15731,x15734),f307(x15733,x15732,x15734)) % 181.55/181.55 [1574]~E(x15741,x15742)+E(f307(x15743,x15744,x15741),f307(x15743,x15744,x15742)) % 181.55/181.55 [1575]~E(x15751,x15752)+E(f823(x15751,x15753),f823(x15752,x15753)) % 181.55/181.55 [1576]~E(x15761,x15762)+E(f823(x15763,x15761),f823(x15763,x15762)) % 181.55/181.55 [1577]~E(x15771,x15772)+E(f638(x15771,x15773,x15774),f638(x15772,x15773,x15774)) % 181.55/181.55 [1578]~E(x15781,x15782)+E(f638(x15783,x15781,x15784),f638(x15783,x15782,x15784)) % 181.55/181.55 [1579]~E(x15791,x15792)+E(f638(x15793,x15794,x15791),f638(x15793,x15794,x15792)) % 181.55/181.55 [1580]~E(x15801,x15802)+E(f449(x15801,x15803,x15804,x15805),f449(x15802,x15803,x15804,x15805)) % 181.55/181.55 [1581]~E(x15811,x15812)+E(f449(x15813,x15811,x15814,x15815),f449(x15813,x15812,x15814,x15815)) % 181.55/181.55 [1582]~E(x15821,x15822)+E(f449(x15823,x15824,x15821,x15825),f449(x15823,x15824,x15822,x15825)) % 181.55/181.55 [1583]~E(x15831,x15832)+E(f449(x15833,x15834,x15835,x15831),f449(x15833,x15834,x15835,x15832)) % 181.55/181.55 [1584]~E(x15841,x15842)+E(f703(x15841,x15843,x15844),f703(x15842,x15843,x15844)) % 181.55/181.55 [1585]~E(x15851,x15852)+E(f703(x15853,x15851,x15854),f703(x15853,x15852,x15854)) % 181.55/181.55 [1586]~E(x15861,x15862)+E(f703(x15863,x15864,x15861),f703(x15863,x15864,x15862)) % 181.55/181.55 [1587]~E(x15871,x15872)+E(f476(x15871,x15873,x15874),f476(x15872,x15873,x15874)) % 181.55/181.55 [1588]~E(x15881,x15882)+E(f476(x15883,x15881,x15884),f476(x15883,x15882,x15884)) % 181.55/181.55 [1589]~E(x15891,x15892)+E(f476(x15893,x15894,x15891),f476(x15893,x15894,x15892)) % 181.55/181.55 [1590]~E(x15901,x15902)+E(f286(x15901,x15903,x15904),f286(x15902,x15903,x15904)) % 181.55/181.55 [1591]~E(x15911,x15912)+E(f286(x15913,x15911,x15914),f286(x15913,x15912,x15914)) % 181.55/181.55 [1592]~E(x15921,x15922)+E(f286(x15923,x15924,x15921),f286(x15923,x15924,x15922)) % 181.55/181.55 [1593]~E(x15931,x15932)+E(f631(x15931,x15933,x15934,x15935,x15936),f631(x15932,x15933,x15934,x15935,x15936)) % 181.55/181.55 [1594]~E(x15941,x15942)+E(f631(x15943,x15941,x15944,x15945,x15946),f631(x15943,x15942,x15944,x15945,x15946)) % 181.55/181.55 [1595]~E(x15951,x15952)+E(f631(x15953,x15954,x15951,x15955,x15956),f631(x15953,x15954,x15952,x15955,x15956)) % 181.55/181.55 [1596]~E(x15961,x15962)+E(f631(x15963,x15964,x15965,x15961,x15966),f631(x15963,x15964,x15965,x15962,x15966)) % 181.55/181.55 [1597]~E(x15971,x15972)+E(f631(x15973,x15974,x15975,x15976,x15971),f631(x15973,x15974,x15975,x15976,x15972)) % 181.55/181.55 [1598]~E(x15981,x15982)+E(f624(x15981,x15983,x15984,x15985),f624(x15982,x15983,x15984,x15985)) % 181.55/181.55 [1599]~E(x15991,x15992)+E(f624(x15993,x15991,x15994,x15995),f624(x15993,x15992,x15994,x15995)) % 181.55/181.55 [1600]~E(x16001,x16002)+E(f624(x16003,x16004,x16001,x16005),f624(x16003,x16004,x16002,x16005)) % 181.55/181.55 [1601]~E(x16011,x16012)+E(f624(x16013,x16014,x16015,x16011),f624(x16013,x16014,x16015,x16012)) % 181.55/181.55 [1602]~E(x16021,x16022)+E(f645(x16021,x16023,x16024,x16025,x16026,x16027),f645(x16022,x16023,x16024,x16025,x16026,x16027)) % 181.55/181.55 [1603]~E(x16031,x16032)+E(f645(x16033,x16031,x16034,x16035,x16036,x16037),f645(x16033,x16032,x16034,x16035,x16036,x16037)) % 181.55/181.55 [1604]~E(x16041,x16042)+E(f645(x16043,x16044,x16041,x16045,x16046,x16047),f645(x16043,x16044,x16042,x16045,x16046,x16047)) % 181.55/181.55 [1605]~E(x16051,x16052)+E(f645(x16053,x16054,x16055,x16051,x16056,x16057),f645(x16053,x16054,x16055,x16052,x16056,x16057)) % 181.55/181.55 [1606]~E(x16061,x16062)+E(f645(x16063,x16064,x16065,x16066,x16061,x16067),f645(x16063,x16064,x16065,x16066,x16062,x16067)) % 181.55/181.55 [1607]~E(x16071,x16072)+E(f645(x16073,x16074,x16075,x16076,x16077,x16071),f645(x16073,x16074,x16075,x16076,x16077,x16072)) % 181.55/181.55 [1608]~E(x16081,x16082)+E(f734(x16081,x16083,x16084),f734(x16082,x16083,x16084)) % 181.55/181.55 [1609]~E(x16091,x16092)+E(f734(x16093,x16091,x16094),f734(x16093,x16092,x16094)) % 181.55/181.55 [1610]~E(x16101,x16102)+E(f734(x16103,x16104,x16101),f734(x16103,x16104,x16102)) % 181.55/181.55 [1611]~E(x16111,x16112)+E(f417(x16111),f417(x16112)) % 181.55/181.55 [1612]~E(x16121,x16122)+E(f292(x16121,x16123,x16124,x16125,x16126),f292(x16122,x16123,x16124,x16125,x16126)) % 181.55/181.55 [1613]~E(x16131,x16132)+E(f292(x16133,x16131,x16134,x16135,x16136),f292(x16133,x16132,x16134,x16135,x16136)) % 181.55/181.55 [1614]~E(x16141,x16142)+E(f292(x16143,x16144,x16141,x16145,x16146),f292(x16143,x16144,x16142,x16145,x16146)) % 181.55/181.55 [1615]~E(x16151,x16152)+E(f292(x16153,x16154,x16155,x16151,x16156),f292(x16153,x16154,x16155,x16152,x16156)) % 181.55/181.55 [1616]~E(x16161,x16162)+E(f292(x16163,x16164,x16165,x16166,x16161),f292(x16163,x16164,x16165,x16166,x16162)) % 181.55/181.55 [1617]~E(x16171,x16172)+E(f466(x16171,x16173,x16174,x16175),f466(x16172,x16173,x16174,x16175)) % 181.55/181.55 [1618]~E(x16181,x16182)+E(f466(x16183,x16181,x16184,x16185),f466(x16183,x16182,x16184,x16185)) % 181.55/181.55 [1619]~E(x16191,x16192)+E(f466(x16193,x16194,x16191,x16195),f466(x16193,x16194,x16192,x16195)) % 181.55/181.55 [1620]~E(x16201,x16202)+E(f466(x16203,x16204,x16205,x16201),f466(x16203,x16204,x16205,x16202)) % 181.55/181.55 [1621]~E(x16211,x16212)+E(f390(x16211,x16213,x16214,x16215,x16216,x16217,x16218,x16219),f390(x16212,x16213,x16214,x16215,x16216,x16217,x16218,x16219)) % 181.55/181.55 [1622]~E(x16221,x16222)+E(f390(x16223,x16221,x16224,x16225,x16226,x16227,x16228,x16229),f390(x16223,x16222,x16224,x16225,x16226,x16227,x16228,x16229)) % 181.55/181.55 [1623]~E(x16231,x16232)+E(f390(x16233,x16234,x16231,x16235,x16236,x16237,x16238,x16239),f390(x16233,x16234,x16232,x16235,x16236,x16237,x16238,x16239)) % 181.55/181.55 [1624]~E(x16241,x16242)+E(f390(x16243,x16244,x16245,x16241,x16246,x16247,x16248,x16249),f390(x16243,x16244,x16245,x16242,x16246,x16247,x16248,x16249)) % 181.55/181.55 [1625]~E(x16251,x16252)+E(f390(x16253,x16254,x16255,x16256,x16251,x16257,x16258,x16259),f390(x16253,x16254,x16255,x16256,x16252,x16257,x16258,x16259)) % 181.55/181.55 [1626]~E(x16261,x16262)+E(f390(x16263,x16264,x16265,x16266,x16267,x16261,x16268,x16269),f390(x16263,x16264,x16265,x16266,x16267,x16262,x16268,x16269)) % 181.55/181.55 [1627]~E(x16271,x16272)+E(f390(x16273,x16274,x16275,x16276,x16277,x16278,x16271,x16279),f390(x16273,x16274,x16275,x16276,x16277,x16278,x16272,x16279)) % 181.55/181.55 [1628]~E(x16281,x16282)+E(f390(x16283,x16284,x16285,x16286,x16287,x16288,x16289,x16281),f390(x16283,x16284,x16285,x16286,x16287,x16288,x16289,x16282)) % 181.55/181.55 [1629]~E(x16291,x16292)+E(f539(x16291,x16293,x16294,x16295,x16296),f539(x16292,x16293,x16294,x16295,x16296)) % 181.55/181.55 [1630]~E(x16301,x16302)+E(f539(x16303,x16301,x16304,x16305,x16306),f539(x16303,x16302,x16304,x16305,x16306)) % 181.55/181.55 [1631]~E(x16311,x16312)+E(f539(x16313,x16314,x16311,x16315,x16316),f539(x16313,x16314,x16312,x16315,x16316)) % 181.55/181.55 [1632]~E(x16321,x16322)+E(f539(x16323,x16324,x16325,x16321,x16326),f539(x16323,x16324,x16325,x16322,x16326)) % 181.55/181.55 [1633]~E(x16331,x16332)+E(f539(x16333,x16334,x16335,x16336,x16331),f539(x16333,x16334,x16335,x16336,x16332)) % 181.55/181.55 [1634]~E(x16341,x16342)+E(f379(x16341,x16343,x16344),f379(x16342,x16343,x16344)) % 181.55/181.55 [1635]~E(x16351,x16352)+E(f379(x16353,x16351,x16354),f379(x16353,x16352,x16354)) % 181.55/181.55 [1636]~E(x16361,x16362)+E(f379(x16363,x16364,x16361),f379(x16363,x16364,x16362)) % 181.55/181.55 [1637]~E(x16371,x16372)+E(f268(x16371,x16373),f268(x16372,x16373)) % 181.55/181.55 [1638]~E(x16381,x16382)+E(f268(x16383,x16381),f268(x16383,x16382)) % 181.55/181.55 [1639]~E(x16391,x16392)+E(f351(x16391,x16393,x16394),f351(x16392,x16393,x16394)) % 181.55/181.55 [1640]~E(x16401,x16402)+E(f351(x16403,x16401,x16404),f351(x16403,x16402,x16404)) % 181.55/181.55 [1641]~E(x16411,x16412)+E(f351(x16413,x16414,x16411),f351(x16413,x16414,x16412)) % 181.55/181.55 [1642]~E(x16421,x16422)+E(f686(x16421,x16423,x16424),f686(x16422,x16423,x16424)) % 181.55/181.55 [1643]~E(x16431,x16432)+E(f686(x16433,x16431,x16434),f686(x16433,x16432,x16434)) % 181.55/181.55 [1644]~E(x16441,x16442)+E(f686(x16443,x16444,x16441),f686(x16443,x16444,x16442)) % 181.55/181.55 [1645]~E(x16451,x16452)+E(f683(x16451,x16453,x16454),f683(x16452,x16453,x16454)) % 181.55/181.55 [1646]~E(x16461,x16462)+E(f683(x16463,x16461,x16464),f683(x16463,x16462,x16464)) % 181.55/181.55 [1647]~E(x16471,x16472)+E(f683(x16473,x16474,x16471),f683(x16473,x16474,x16472)) % 181.55/181.55 [1648]~E(x16481,x16482)+E(f443(x16481,x16483),f443(x16482,x16483)) % 181.55/181.55 [1649]~E(x16491,x16492)+E(f443(x16493,x16491),f443(x16493,x16492)) % 181.55/181.55 [1650]~E(x16501,x16502)+E(f760(x16501,x16503,x16504,x16505,x16506),f760(x16502,x16503,x16504,x16505,x16506)) % 181.55/181.55 [1651]~E(x16511,x16512)+E(f760(x16513,x16511,x16514,x16515,x16516),f760(x16513,x16512,x16514,x16515,x16516)) % 181.55/181.55 [1652]~E(x16521,x16522)+E(f760(x16523,x16524,x16521,x16525,x16526),f760(x16523,x16524,x16522,x16525,x16526)) % 181.55/181.55 [1653]~E(x16531,x16532)+E(f760(x16533,x16534,x16535,x16531,x16536),f760(x16533,x16534,x16535,x16532,x16536)) % 181.55/181.55 [1654]~E(x16541,x16542)+E(f760(x16543,x16544,x16545,x16546,x16541),f760(x16543,x16544,x16545,x16546,x16542)) % 181.55/181.55 [1655]~E(x16551,x16552)+E(f718(x16551,x16553),f718(x16552,x16553)) % 181.55/181.55 [1656]~E(x16561,x16562)+E(f718(x16563,x16561),f718(x16563,x16562)) % 181.55/181.55 [1657]~E(x16571,x16572)+E(f428(x16571,x16573,x16574),f428(x16572,x16573,x16574)) % 181.55/181.55 [1658]~E(x16581,x16582)+E(f428(x16583,x16581,x16584),f428(x16583,x16582,x16584)) % 181.55/181.55 [1659]~E(x16591,x16592)+E(f428(x16593,x16594,x16591),f428(x16593,x16594,x16592)) % 181.55/181.55 [1660]~E(x16601,x16602)+E(f364(x16601,x16603,x16604),f364(x16602,x16603,x16604)) % 181.55/181.55 [1661]~E(x16611,x16612)+E(f364(x16613,x16611,x16614),f364(x16613,x16612,x16614)) % 181.55/181.55 [1662]~E(x16621,x16622)+E(f364(x16623,x16624,x16621),f364(x16623,x16624,x16622)) % 181.55/181.55 [1663]~E(x16631,x16632)+E(f594(x16631,x16633,x16634),f594(x16632,x16633,x16634)) % 181.55/181.55 [1664]~E(x16641,x16642)+E(f594(x16643,x16641,x16644),f594(x16643,x16642,x16644)) % 181.55/181.55 [1665]~E(x16651,x16652)+E(f594(x16653,x16654,x16651),f594(x16653,x16654,x16652)) % 181.55/181.55 [1666]~E(x16661,x16662)+E(f467(x16661,x16663),f467(x16662,x16663)) % 181.55/181.55 [1667]~E(x16671,x16672)+E(f467(x16673,x16671),f467(x16673,x16672)) % 181.55/181.55 [1668]~E(x16681,x16682)+E(f496(x16681,x16683,x16684,x16685,x16686),f496(x16682,x16683,x16684,x16685,x16686)) % 181.55/181.55 [1669]~E(x16691,x16692)+E(f496(x16693,x16691,x16694,x16695,x16696),f496(x16693,x16692,x16694,x16695,x16696)) % 181.55/181.55 [1670]~E(x16701,x16702)+E(f496(x16703,x16704,x16701,x16705,x16706),f496(x16703,x16704,x16702,x16705,x16706)) % 181.55/181.55 [1671]~E(x16711,x16712)+E(f496(x16713,x16714,x16715,x16711,x16716),f496(x16713,x16714,x16715,x16712,x16716)) % 181.55/181.55 [1672]~E(x16721,x16722)+E(f496(x16723,x16724,x16725,x16726,x16721),f496(x16723,x16724,x16725,x16726,x16722)) % 181.55/181.55 [1673]~E(x16731,x16732)+E(f695(x16731,x16733,x16734,x16735,x16736),f695(x16732,x16733,x16734,x16735,x16736)) % 181.55/181.55 [1674]~E(x16741,x16742)+E(f695(x16743,x16741,x16744,x16745,x16746),f695(x16743,x16742,x16744,x16745,x16746)) % 181.55/181.55 [1675]~E(x16751,x16752)+E(f695(x16753,x16754,x16751,x16755,x16756),f695(x16753,x16754,x16752,x16755,x16756)) % 181.55/181.55 [1676]~E(x16761,x16762)+E(f695(x16763,x16764,x16765,x16761,x16766),f695(x16763,x16764,x16765,x16762,x16766)) % 181.55/181.55 [1677]~E(x16771,x16772)+E(f695(x16773,x16774,x16775,x16776,x16771),f695(x16773,x16774,x16775,x16776,x16772)) % 181.55/181.55 [1678]~E(x16781,x16782)+E(f735(x16781,x16783,x16784),f735(x16782,x16783,x16784)) % 181.55/181.55 [1679]~E(x16791,x16792)+E(f735(x16793,x16791,x16794),f735(x16793,x16792,x16794)) % 181.55/181.55 [1680]~E(x16801,x16802)+E(f735(x16803,x16804,x16801),f735(x16803,x16804,x16802)) % 181.55/181.55 [1681]~E(x16811,x16812)+E(f586(x16811,x16813,x16814,x16815,x16816,x16817,x16818,x16819),f586(x16812,x16813,x16814,x16815,x16816,x16817,x16818,x16819)) % 181.55/181.55 [1682]~E(x16821,x16822)+E(f586(x16823,x16821,x16824,x16825,x16826,x16827,x16828,x16829),f586(x16823,x16822,x16824,x16825,x16826,x16827,x16828,x16829)) % 181.55/181.55 [1683]~E(x16831,x16832)+E(f586(x16833,x16834,x16831,x16835,x16836,x16837,x16838,x16839),f586(x16833,x16834,x16832,x16835,x16836,x16837,x16838,x16839)) % 181.55/181.55 [1684]~E(x16841,x16842)+E(f586(x16843,x16844,x16845,x16841,x16846,x16847,x16848,x16849),f586(x16843,x16844,x16845,x16842,x16846,x16847,x16848,x16849)) % 181.55/181.55 [1685]~E(x16851,x16852)+E(f586(x16853,x16854,x16855,x16856,x16851,x16857,x16858,x16859),f586(x16853,x16854,x16855,x16856,x16852,x16857,x16858,x16859)) % 181.55/181.55 [1686]~E(x16861,x16862)+E(f586(x16863,x16864,x16865,x16866,x16867,x16861,x16868,x16869),f586(x16863,x16864,x16865,x16866,x16867,x16862,x16868,x16869)) % 181.55/181.55 [1687]~E(x16871,x16872)+E(f586(x16873,x16874,x16875,x16876,x16877,x16878,x16871,x16879),f586(x16873,x16874,x16875,x16876,x16877,x16878,x16872,x16879)) % 181.55/181.55 [1688]~E(x16881,x16882)+E(f586(x16883,x16884,x16885,x16886,x16887,x16888,x16889,x16881),f586(x16883,x16884,x16885,x16886,x16887,x16888,x16889,x16882)) % 181.55/181.55 [1689]~E(x16891,x16892)+E(f126(x16891),f126(x16892)) % 181.55/181.55 [1690]~E(x16901,x16902)+E(f754(x16901,x16903),f754(x16902,x16903)) % 181.55/181.55 [1691]~E(x16911,x16912)+E(f754(x16913,x16911),f754(x16913,x16912)) % 181.55/181.55 [1692]~E(x16921,x16922)+E(f406(x16921),f406(x16922)) % 181.55/181.55 [1693]~E(x16931,x16932)+E(f53(x16931,x16933),f53(x16932,x16933)) % 181.55/181.55 [1694]~E(x16941,x16942)+E(f53(x16943,x16941),f53(x16943,x16942)) % 181.55/181.55 [1695]~E(x16951,x16952)+E(f577(x16951,x16953,x16954,x16955,x16956),f577(x16952,x16953,x16954,x16955,x16956)) % 181.55/181.55 [1696]~E(x16961,x16962)+E(f577(x16963,x16961,x16964,x16965,x16966),f577(x16963,x16962,x16964,x16965,x16966)) % 181.55/181.55 [1697]~E(x16971,x16972)+E(f577(x16973,x16974,x16971,x16975,x16976),f577(x16973,x16974,x16972,x16975,x16976)) % 181.55/181.55 [1698]~E(x16981,x16982)+E(f577(x16983,x16984,x16985,x16981,x16986),f577(x16983,x16984,x16985,x16982,x16986)) % 181.55/181.55 [1699]~E(x16991,x16992)+E(f577(x16993,x16994,x16995,x16996,x16991),f577(x16993,x16994,x16995,x16996,x16992)) % 181.55/181.55 [1700]~E(x17001,x17002)+E(f200(x17001,x17003,x17004,x17005),f200(x17002,x17003,x17004,x17005)) % 181.55/181.55 [1701]~E(x17011,x17012)+E(f200(x17013,x17011,x17014,x17015),f200(x17013,x17012,x17014,x17015)) % 181.55/181.55 [1702]~E(x17021,x17022)+E(f200(x17023,x17024,x17021,x17025),f200(x17023,x17024,x17022,x17025)) % 181.55/181.55 [1703]~E(x17031,x17032)+E(f200(x17033,x17034,x17035,x17031),f200(x17033,x17034,x17035,x17032)) % 181.55/181.55 [1704]~E(x17041,x17042)+E(f362(x17041,x17043),f362(x17042,x17043)) % 181.55/181.55 [1705]~E(x17051,x17052)+E(f362(x17053,x17051),f362(x17053,x17052)) % 181.55/181.55 [1706]~E(x17061,x17062)+E(f471(x17061,x17063,x17064,x17065),f471(x17062,x17063,x17064,x17065)) % 181.55/181.55 [1707]~E(x17071,x17072)+E(f471(x17073,x17071,x17074,x17075),f471(x17073,x17072,x17074,x17075)) % 181.55/181.55 [1708]~E(x17081,x17082)+E(f471(x17083,x17084,x17081,x17085),f471(x17083,x17084,x17082,x17085)) % 181.55/181.55 [1709]~E(x17091,x17092)+E(f471(x17093,x17094,x17095,x17091),f471(x17093,x17094,x17095,x17092)) % 181.55/181.55 [1710]~E(x17101,x17102)+E(f421(x17101,x17103,x17104),f421(x17102,x17103,x17104)) % 181.55/181.55 [1711]~E(x17111,x17112)+E(f421(x17113,x17111,x17114),f421(x17113,x17112,x17114)) % 181.55/181.55 [1712]~E(x17121,x17122)+E(f421(x17123,x17124,x17121),f421(x17123,x17124,x17122)) % 181.55/181.55 [1713]~E(x17131,x17132)+E(f267(x17131,x17133,x17134,x17135,x17136),f267(x17132,x17133,x17134,x17135,x17136)) % 181.55/181.55 [1714]~E(x17141,x17142)+E(f267(x17143,x17141,x17144,x17145,x17146),f267(x17143,x17142,x17144,x17145,x17146)) % 181.55/181.55 [1715]~E(x17151,x17152)+E(f267(x17153,x17154,x17151,x17155,x17156),f267(x17153,x17154,x17152,x17155,x17156)) % 181.55/181.55 [1716]~E(x17161,x17162)+E(f267(x17163,x17164,x17165,x17161,x17166),f267(x17163,x17164,x17165,x17162,x17166)) % 181.55/181.55 [1717]~E(x17171,x17172)+E(f267(x17173,x17174,x17175,x17176,x17171),f267(x17173,x17174,x17175,x17176,x17172)) % 181.55/181.55 [1718]~E(x17181,x17182)+E(f758(x17181,x17183,x17184,x17185,x17186,x17187,x17188,x17189),f758(x17182,x17183,x17184,x17185,x17186,x17187,x17188,x17189)) % 181.55/181.55 [1719]~E(x17191,x17192)+E(f758(x17193,x17191,x17194,x17195,x17196,x17197,x17198,x17199),f758(x17193,x17192,x17194,x17195,x17196,x17197,x17198,x17199)) % 181.55/181.55 [1720]~E(x17201,x17202)+E(f758(x17203,x17204,x17201,x17205,x17206,x17207,x17208,x17209),f758(x17203,x17204,x17202,x17205,x17206,x17207,x17208,x17209)) % 181.55/181.55 [1721]~E(x17211,x17212)+E(f758(x17213,x17214,x17215,x17211,x17216,x17217,x17218,x17219),f758(x17213,x17214,x17215,x17212,x17216,x17217,x17218,x17219)) % 181.55/181.55 [1722]~E(x17221,x17222)+E(f758(x17223,x17224,x17225,x17226,x17221,x17227,x17228,x17229),f758(x17223,x17224,x17225,x17226,x17222,x17227,x17228,x17229)) % 181.55/181.55 [1723]~E(x17231,x17232)+E(f758(x17233,x17234,x17235,x17236,x17237,x17231,x17238,x17239),f758(x17233,x17234,x17235,x17236,x17237,x17232,x17238,x17239)) % 181.55/181.55 [1724]~E(x17241,x17242)+E(f758(x17243,x17244,x17245,x17246,x17247,x17248,x17241,x17249),f758(x17243,x17244,x17245,x17246,x17247,x17248,x17242,x17249)) % 181.55/181.55 [1725]~E(x17251,x17252)+E(f758(x17253,x17254,x17255,x17256,x17257,x17258,x17259,x17251),f758(x17253,x17254,x17255,x17256,x17257,x17258,x17259,x17252)) % 181.55/181.55 [1726]~E(x17261,x17262)+E(f512(x17261,x17263,x17264),f512(x17262,x17263,x17264)) % 181.55/181.55 [1727]~E(x17271,x17272)+E(f512(x17273,x17271,x17274),f512(x17273,x17272,x17274)) % 181.55/181.55 [1728]~E(x17281,x17282)+E(f512(x17283,x17284,x17281),f512(x17283,x17284,x17282)) % 181.55/181.55 [1729]~E(x17291,x17292)+E(f562(x17291,x17293,x17294,x17295),f562(x17292,x17293,x17294,x17295)) % 181.55/181.55 [1730]~E(x17301,x17302)+E(f562(x17303,x17301,x17304,x17305),f562(x17303,x17302,x17304,x17305)) % 181.55/181.55 [1731]~E(x17311,x17312)+E(f562(x17313,x17314,x17311,x17315),f562(x17313,x17314,x17312,x17315)) % 181.55/181.55 [1732]~E(x17321,x17322)+E(f562(x17323,x17324,x17325,x17321),f562(x17323,x17324,x17325,x17322)) % 181.55/181.55 [1733]~E(x17331,x17332)+E(f548(x17331,x17333,x17334,x17335),f548(x17332,x17333,x17334,x17335)) % 181.55/181.55 [1734]~E(x17341,x17342)+E(f548(x17343,x17341,x17344,x17345),f548(x17343,x17342,x17344,x17345)) % 181.55/181.55 [1735]~E(x17351,x17352)+E(f548(x17353,x17354,x17351,x17355),f548(x17353,x17354,x17352,x17355)) % 181.55/181.55 [1736]~E(x17361,x17362)+E(f548(x17363,x17364,x17365,x17361),f548(x17363,x17364,x17365,x17362)) % 181.55/181.55 [1737]~E(x17371,x17372)+E(f783(x17371,x17373,x17374),f783(x17372,x17373,x17374)) % 181.55/181.55 [1738]~E(x17381,x17382)+E(f783(x17383,x17381,x17384),f783(x17383,x17382,x17384)) % 181.55/181.55 [1739]~E(x17391,x17392)+E(f783(x17393,x17394,x17391),f783(x17393,x17394,x17392)) % 181.55/181.55 [1740]~E(x17401,x17402)+E(f494(x17401,x17403,x17404,x17405,x17406),f494(x17402,x17403,x17404,x17405,x17406)) % 181.55/181.55 [1741]~E(x17411,x17412)+E(f494(x17413,x17411,x17414,x17415,x17416),f494(x17413,x17412,x17414,x17415,x17416)) % 181.55/181.55 [1742]~E(x17421,x17422)+E(f494(x17423,x17424,x17421,x17425,x17426),f494(x17423,x17424,x17422,x17425,x17426)) % 181.55/181.55 [1743]~E(x17431,x17432)+E(f494(x17433,x17434,x17435,x17431,x17436),f494(x17433,x17434,x17435,x17432,x17436)) % 181.55/181.55 [1744]~E(x17441,x17442)+E(f494(x17443,x17444,x17445,x17446,x17441),f494(x17443,x17444,x17445,x17446,x17442)) % 181.55/181.55 [1745]~E(x17451,x17452)+E(f426(x17451,x17453,x17454),f426(x17452,x17453,x17454)) % 181.55/181.55 [1746]~E(x17461,x17462)+E(f426(x17463,x17461,x17464),f426(x17463,x17462,x17464)) % 181.55/181.55 [1747]~E(x17471,x17472)+E(f426(x17473,x17474,x17471),f426(x17473,x17474,x17472)) % 181.55/181.55 [1748]~E(x17481,x17482)+E(f457(x17481,x17483,x17484,x17485),f457(x17482,x17483,x17484,x17485)) % 181.55/181.55 [1749]~E(x17491,x17492)+E(f457(x17493,x17491,x17494,x17495),f457(x17493,x17492,x17494,x17495)) % 181.55/181.55 [1750]~E(x17501,x17502)+E(f457(x17503,x17504,x17501,x17505),f457(x17503,x17504,x17502,x17505)) % 181.55/181.55 [1751]~E(x17511,x17512)+E(f457(x17513,x17514,x17515,x17511),f457(x17513,x17514,x17515,x17512)) % 181.55/181.55 [1752]~E(x17521,x17522)+E(f728(x17521,x17523,x17524,x17525,x17526),f728(x17522,x17523,x17524,x17525,x17526)) % 181.55/181.55 [1753]~E(x17531,x17532)+E(f728(x17533,x17531,x17534,x17535,x17536),f728(x17533,x17532,x17534,x17535,x17536)) % 181.55/181.55 [1754]~E(x17541,x17542)+E(f728(x17543,x17544,x17541,x17545,x17546),f728(x17543,x17544,x17542,x17545,x17546)) % 181.55/181.55 [1755]~E(x17551,x17552)+E(f728(x17553,x17554,x17555,x17551,x17556),f728(x17553,x17554,x17555,x17552,x17556)) % 181.55/181.55 [1756]~E(x17561,x17562)+E(f728(x17563,x17564,x17565,x17566,x17561),f728(x17563,x17564,x17565,x17566,x17562)) % 181.55/181.55 [1757]~E(x17571,x17572)+E(f609(x17571,x17573,x17574,x17575),f609(x17572,x17573,x17574,x17575)) % 181.55/181.55 [1758]~E(x17581,x17582)+E(f609(x17583,x17581,x17584,x17585),f609(x17583,x17582,x17584,x17585)) % 181.55/181.55 [1759]~E(x17591,x17592)+E(f609(x17593,x17594,x17591,x17595),f609(x17593,x17594,x17592,x17595)) % 181.55/181.55 [1760]~E(x17601,x17602)+E(f609(x17603,x17604,x17605,x17601),f609(x17603,x17604,x17605,x17602)) % 181.55/181.55 [1761]~E(x17611,x17612)+E(f807(x17611,x17613,x17614,x17615,x17616,x17617,x17618),f807(x17612,x17613,x17614,x17615,x17616,x17617,x17618)) % 181.55/181.55 [1762]~E(x17621,x17622)+E(f807(x17623,x17621,x17624,x17625,x17626,x17627,x17628),f807(x17623,x17622,x17624,x17625,x17626,x17627,x17628)) % 181.55/181.55 [1763]~E(x17631,x17632)+E(f807(x17633,x17634,x17631,x17635,x17636,x17637,x17638),f807(x17633,x17634,x17632,x17635,x17636,x17637,x17638)) % 181.55/181.55 [1764]~E(x17641,x17642)+E(f807(x17643,x17644,x17645,x17641,x17646,x17647,x17648),f807(x17643,x17644,x17645,x17642,x17646,x17647,x17648)) % 181.55/181.55 [1765]~E(x17651,x17652)+E(f807(x17653,x17654,x17655,x17656,x17651,x17657,x17658),f807(x17653,x17654,x17655,x17656,x17652,x17657,x17658)) % 181.55/181.55 [1766]~E(x17661,x17662)+E(f807(x17663,x17664,x17665,x17666,x17667,x17661,x17668),f807(x17663,x17664,x17665,x17666,x17667,x17662,x17668)) % 181.55/181.55 [1767]~E(x17671,x17672)+E(f807(x17673,x17674,x17675,x17676,x17677,x17678,x17671),f807(x17673,x17674,x17675,x17676,x17677,x17678,x17672)) % 181.55/181.55 [1768]~E(x17681,x17682)+E(f361(x17681,x17683),f361(x17682,x17683)) % 181.55/181.55 [1769]~E(x17691,x17692)+E(f361(x17693,x17691),f361(x17693,x17692)) % 181.55/181.55 [1770]~E(x17701,x17702)+E(f157(x17701,x17703,x17704,x17705),f157(x17702,x17703,x17704,x17705)) % 181.55/181.55 [1771]~E(x17711,x17712)+E(f157(x17713,x17711,x17714,x17715),f157(x17713,x17712,x17714,x17715)) % 181.55/181.55 [1772]~E(x17721,x17722)+E(f157(x17723,x17724,x17721,x17725),f157(x17723,x17724,x17722,x17725)) % 181.55/181.55 [1773]~E(x17731,x17732)+E(f157(x17733,x17734,x17735,x17731),f157(x17733,x17734,x17735,x17732)) % 181.55/181.55 [1774]~E(x17741,x17742)+E(f687(x17741,x17743,x17744,x17745),f687(x17742,x17743,x17744,x17745)) % 181.55/181.55 [1775]~E(x17751,x17752)+E(f687(x17753,x17751,x17754,x17755),f687(x17753,x17752,x17754,x17755)) % 181.55/181.55 [1776]~E(x17761,x17762)+E(f687(x17763,x17764,x17761,x17765),f687(x17763,x17764,x17762,x17765)) % 181.55/181.55 [1777]~E(x17771,x17772)+E(f687(x17773,x17774,x17775,x17771),f687(x17773,x17774,x17775,x17772)) % 181.55/181.55 [1778]~E(x17781,x17782)+E(f250(x17781,x17783,x17784),f250(x17782,x17783,x17784)) % 181.55/181.55 [1779]~E(x17791,x17792)+E(f250(x17793,x17791,x17794),f250(x17793,x17792,x17794)) % 181.55/181.55 [1780]~E(x17801,x17802)+E(f250(x17803,x17804,x17801),f250(x17803,x17804,x17802)) % 181.55/181.55 [1781]~E(x17811,x17812)+E(f508(x17811,x17813,x17814,x17815,x17816),f508(x17812,x17813,x17814,x17815,x17816)) % 181.55/181.55 [1782]~E(x17821,x17822)+E(f508(x17823,x17821,x17824,x17825,x17826),f508(x17823,x17822,x17824,x17825,x17826)) % 181.55/181.55 [1783]~E(x17831,x17832)+E(f508(x17833,x17834,x17831,x17835,x17836),f508(x17833,x17834,x17832,x17835,x17836)) % 181.55/181.55 [1784]~E(x17841,x17842)+E(f508(x17843,x17844,x17845,x17841,x17846),f508(x17843,x17844,x17845,x17842,x17846)) % 181.55/181.55 [1785]~E(x17851,x17852)+E(f508(x17853,x17854,x17855,x17856,x17851),f508(x17853,x17854,x17855,x17856,x17852)) % 181.55/181.55 [1786]~E(x17861,x17862)+E(f416(x17861),f416(x17862)) % 181.55/181.55 [1787]~E(x17871,x17872)+E(f332(x17871,x17873),f332(x17872,x17873)) % 181.55/181.55 [1788]~E(x17881,x17882)+E(f332(x17883,x17881),f332(x17883,x17882)) % 181.55/181.55 [1789]~E(x17891,x17892)+E(f569(x17891,x17893,x17894),f569(x17892,x17893,x17894)) % 181.55/181.55 [1790]~E(x17901,x17902)+E(f569(x17903,x17901,x17904),f569(x17903,x17902,x17904)) % 181.55/181.55 [1791]~E(x17911,x17912)+E(f569(x17913,x17914,x17911),f569(x17913,x17914,x17912)) % 181.55/181.55 [1792]~E(x17921,x17922)+E(f726(x17921,x17923),f726(x17922,x17923)) % 181.55/181.55 [1793]~E(x17931,x17932)+E(f726(x17933,x17931),f726(x17933,x17932)) % 181.55/181.55 [1794]~E(x17941,x17942)+E(f360(x17941,x17943),f360(x17942,x17943)) % 181.55/181.55 [1795]~E(x17951,x17952)+E(f360(x17953,x17951),f360(x17953,x17952)) % 181.55/181.55 [1796]~E(x17961,x17962)+E(f197(x17961,x17963),f197(x17962,x17963)) % 181.55/181.55 [1797]~E(x17971,x17972)+E(f197(x17973,x17971),f197(x17973,x17972)) % 181.55/181.55 [1798]~E(x17981,x17982)+E(f650(x17981,x17983,x17984),f650(x17982,x17983,x17984)) % 181.55/181.55 [1799]~E(x17991,x17992)+E(f650(x17993,x17991,x17994),f650(x17993,x17992,x17994)) % 181.55/181.55 [1800]~E(x18001,x18002)+E(f650(x18003,x18004,x18001),f650(x18003,x18004,x18002)) % 181.55/181.55 [1801]~E(x18011,x18012)+E(f122(x18011,x18013,x18014,x18015),f122(x18012,x18013,x18014,x18015)) % 181.55/181.55 [1802]~E(x18021,x18022)+E(f122(x18023,x18021,x18024,x18025),f122(x18023,x18022,x18024,x18025)) % 181.55/181.55 [1803]~E(x18031,x18032)+E(f122(x18033,x18034,x18031,x18035),f122(x18033,x18034,x18032,x18035)) % 181.55/181.55 [1804]~E(x18041,x18042)+E(f122(x18043,x18044,x18045,x18041),f122(x18043,x18044,x18045,x18042)) % 181.55/181.55 [1805]~E(x18051,x18052)+E(f480(x18051,x18053,x18054,x18055),f480(x18052,x18053,x18054,x18055)) % 181.55/181.55 [1806]~E(x18061,x18062)+E(f480(x18063,x18061,x18064,x18065),f480(x18063,x18062,x18064,x18065)) % 181.55/181.55 [1807]~E(x18071,x18072)+E(f480(x18073,x18074,x18071,x18075),f480(x18073,x18074,x18072,x18075)) % 181.55/181.55 [1808]~E(x18081,x18082)+E(f480(x18083,x18084,x18085,x18081),f480(x18083,x18084,x18085,x18082)) % 181.55/181.55 [1809]~E(x18091,x18092)+E(f547(x18091,x18093,x18094),f547(x18092,x18093,x18094)) % 181.55/181.55 [1810]~E(x18101,x18102)+E(f547(x18103,x18101,x18104),f547(x18103,x18102,x18104)) % 181.55/181.55 [1811]~E(x18111,x18112)+E(f547(x18113,x18114,x18111),f547(x18113,x18114,x18112)) % 181.55/181.55 [1812]~E(x18121,x18122)+E(f846(x18121,x18123,x18124,x18125),f846(x18122,x18123,x18124,x18125)) % 181.55/181.55 [1813]~E(x18131,x18132)+E(f846(x18133,x18131,x18134,x18135),f846(x18133,x18132,x18134,x18135)) % 181.55/181.55 [1814]~E(x18141,x18142)+E(f846(x18143,x18144,x18141,x18145),f846(x18143,x18144,x18142,x18145)) % 181.55/181.55 [1815]~E(x18151,x18152)+E(f846(x18153,x18154,x18155,x18151),f846(x18153,x18154,x18155,x18152)) % 181.55/181.55 [1816]~E(x18161,x18162)+E(f140(x18161,x18163),f140(x18162,x18163)) % 181.55/181.55 [1817]~E(x18171,x18172)+E(f140(x18173,x18171),f140(x18173,x18172)) % 181.55/181.55 [1818]~E(x18181,x18182)+E(f219(x18181,x18183),f219(x18182,x18183)) % 181.55/181.55 [1819]~E(x18191,x18192)+E(f219(x18193,x18191),f219(x18193,x18192)) % 181.55/181.55 [1820]~E(x18201,x18202)+E(f506(x18201,x18203,x18204,x18205,x18206),f506(x18202,x18203,x18204,x18205,x18206)) % 181.55/181.55 [1821]~E(x18211,x18212)+E(f506(x18213,x18211,x18214,x18215,x18216),f506(x18213,x18212,x18214,x18215,x18216)) % 181.55/181.55 [1822]~E(x18221,x18222)+E(f506(x18223,x18224,x18221,x18225,x18226),f506(x18223,x18224,x18222,x18225,x18226)) % 181.55/181.55 [1823]~E(x18231,x18232)+E(f506(x18233,x18234,x18235,x18231,x18236),f506(x18233,x18234,x18235,x18232,x18236)) % 181.55/181.55 [1824]~E(x18241,x18242)+E(f506(x18243,x18244,x18245,x18246,x18241),f506(x18243,x18244,x18245,x18246,x18242)) % 181.55/181.55 [1825]~E(x18251,x18252)+E(f596(x18251,x18253,x18254,x18255,x18256),f596(x18252,x18253,x18254,x18255,x18256)) % 181.55/181.55 [1826]~E(x18261,x18262)+E(f596(x18263,x18261,x18264,x18265,x18266),f596(x18263,x18262,x18264,x18265,x18266)) % 181.55/181.55 [1827]~E(x18271,x18272)+E(f596(x18273,x18274,x18271,x18275,x18276),f596(x18273,x18274,x18272,x18275,x18276)) % 181.55/181.55 [1828]~E(x18281,x18282)+E(f596(x18283,x18284,x18285,x18281,x18286),f596(x18283,x18284,x18285,x18282,x18286)) % 181.55/181.55 [1829]~E(x18291,x18292)+E(f596(x18293,x18294,x18295,x18296,x18291),f596(x18293,x18294,x18295,x18296,x18292)) % 181.55/181.55 [1830]~E(x18301,x18302)+E(f780(x18301,x18303,x18304),f780(x18302,x18303,x18304)) % 181.55/181.55 [1831]~E(x18311,x18312)+E(f780(x18313,x18311,x18314),f780(x18313,x18312,x18314)) % 181.55/181.55 [1832]~E(x18321,x18322)+E(f780(x18323,x18324,x18321),f780(x18323,x18324,x18322)) % 181.55/181.55 [1833]~E(x18331,x18332)+E(f720(x18331,x18333,x18334),f720(x18332,x18333,x18334)) % 181.55/181.55 [1834]~E(x18341,x18342)+E(f720(x18343,x18341,x18344),f720(x18343,x18342,x18344)) % 181.55/181.55 [1835]~E(x18351,x18352)+E(f720(x18353,x18354,x18351),f720(x18353,x18354,x18352)) % 181.55/181.55 [1836]~E(x18361,x18362)+E(f747(x18361,x18363),f747(x18362,x18363)) % 181.55/181.55 [1837]~E(x18371,x18372)+E(f747(x18373,x18371),f747(x18373,x18372)) % 181.55/181.55 [1838]~E(x18381,x18382)+E(f678(x18381,x18383,x18384),f678(x18382,x18383,x18384)) % 181.55/181.55 [1839]~E(x18391,x18392)+E(f678(x18393,x18391,x18394),f678(x18393,x18392,x18394)) % 181.55/181.55 [1840]~E(x18401,x18402)+E(f678(x18403,x18404,x18401),f678(x18403,x18404,x18402)) % 181.55/181.55 [1841]~E(x18411,x18412)+E(f556(x18411,x18413),f556(x18412,x18413)) % 181.55/181.55 [1842]~E(x18421,x18422)+E(f556(x18423,x18421),f556(x18423,x18422)) % 181.55/181.55 [1843]~E(x18431,x18432)+E(f574(x18431,x18433,x18434,x18435),f574(x18432,x18433,x18434,x18435)) % 181.55/181.55 [1844]~E(x18441,x18442)+E(f574(x18443,x18441,x18444,x18445),f574(x18443,x18442,x18444,x18445)) % 181.55/181.55 [1845]~E(x18451,x18452)+E(f574(x18453,x18454,x18451,x18455),f574(x18453,x18454,x18452,x18455)) % 181.55/181.55 [1846]~E(x18461,x18462)+E(f574(x18463,x18464,x18465,x18461),f574(x18463,x18464,x18465,x18462)) % 181.55/181.55 [1847]~E(x18471,x18472)+E(f620(x18471,x18473,x18474,x18475,x18476),f620(x18472,x18473,x18474,x18475,x18476)) % 181.55/181.55 [1848]~E(x18481,x18482)+E(f620(x18483,x18481,x18484,x18485,x18486),f620(x18483,x18482,x18484,x18485,x18486)) % 181.55/181.55 [1849]~E(x18491,x18492)+E(f620(x18493,x18494,x18491,x18495,x18496),f620(x18493,x18494,x18492,x18495,x18496)) % 181.55/181.55 [1850]~E(x18501,x18502)+E(f620(x18503,x18504,x18505,x18501,x18506),f620(x18503,x18504,x18505,x18502,x18506)) % 181.55/181.55 [1851]~E(x18511,x18512)+E(f620(x18513,x18514,x18515,x18516,x18511),f620(x18513,x18514,x18515,x18516,x18512)) % 181.55/181.55 [1852]~E(x18521,x18522)+E(f169(x18521,x18523,x18524),f169(x18522,x18523,x18524)) % 181.55/181.55 [1853]~E(x18531,x18532)+E(f169(x18533,x18531,x18534),f169(x18533,x18532,x18534)) % 181.55/181.55 [1854]~E(x18541,x18542)+E(f169(x18543,x18544,x18541),f169(x18543,x18544,x18542)) % 181.55/181.55 [1855]~E(x18551,x18552)+E(f808(x18551,x18553),f808(x18552,x18553)) % 181.55/181.55 [1856]~E(x18561,x18562)+E(f808(x18563,x18561),f808(x18563,x18562)) % 181.55/181.55 [1857]~E(x18571,x18572)+E(f745(x18571,x18573,x18574,x18575),f745(x18572,x18573,x18574,x18575)) % 181.55/181.55 [1858]~E(x18581,x18582)+E(f745(x18583,x18581,x18584,x18585),f745(x18583,x18582,x18584,x18585)) % 181.55/181.55 [1859]~E(x18591,x18592)+E(f745(x18593,x18594,x18591,x18595),f745(x18593,x18594,x18592,x18595)) % 181.55/181.55 [1860]~E(x18601,x18602)+E(f745(x18603,x18604,x18605,x18601),f745(x18603,x18604,x18605,x18602)) % 181.55/181.55 [1861]~E(x18611,x18612)+E(f156(x18611,x18613),f156(x18612,x18613)) % 181.55/181.55 [1862]~E(x18621,x18622)+E(f156(x18623,x18621),f156(x18623,x18622)) % 181.55/181.55 [1863]~E(x18631,x18632)+E(f475(x18631,x18633,x18634,x18635,x18636),f475(x18632,x18633,x18634,x18635,x18636)) % 181.55/181.55 [1864]~E(x18641,x18642)+E(f475(x18643,x18641,x18644,x18645,x18646),f475(x18643,x18642,x18644,x18645,x18646)) % 181.55/181.55 [1865]~E(x18651,x18652)+E(f475(x18653,x18654,x18651,x18655,x18656),f475(x18653,x18654,x18652,x18655,x18656)) % 181.55/181.55 [1866]~E(x18661,x18662)+E(f475(x18663,x18664,x18665,x18661,x18666),f475(x18663,x18664,x18665,x18662,x18666)) % 181.55/181.55 [1867]~E(x18671,x18672)+E(f475(x18673,x18674,x18675,x18676,x18671),f475(x18673,x18674,x18675,x18676,x18672)) % 181.55/181.55 [1868]~E(x18681,x18682)+E(f551(x18681,x18683,x18684),f551(x18682,x18683,x18684)) % 181.55/181.55 [1869]~E(x18691,x18692)+E(f551(x18693,x18691,x18694),f551(x18693,x18692,x18694)) % 181.55/181.55 [1870]~E(x18701,x18702)+E(f551(x18703,x18704,x18701),f551(x18703,x18704,x18702)) % 181.55/181.55 [1871]~E(x18711,x18712)+E(f213(x18711),f213(x18712)) % 181.55/181.55 [1872]~E(x18721,x18722)+E(f439(x18721,x18723,x18724,x18725),f439(x18722,x18723,x18724,x18725)) % 181.55/181.55 [1873]~E(x18731,x18732)+E(f439(x18733,x18731,x18734,x18735),f439(x18733,x18732,x18734,x18735)) % 181.55/181.55 [1874]~E(x18741,x18742)+E(f439(x18743,x18744,x18741,x18745),f439(x18743,x18744,x18742,x18745)) % 181.55/181.55 [1875]~E(x18751,x18752)+E(f439(x18753,x18754,x18755,x18751),f439(x18753,x18754,x18755,x18752)) % 181.55/181.55 [1876]~E(x18761,x18762)+E(f605(x18761,x18763,x18764),f605(x18762,x18763,x18764)) % 181.55/181.55 [1877]~E(x18771,x18772)+E(f605(x18773,x18771,x18774),f605(x18773,x18772,x18774)) % 181.55/181.55 [1878]~E(x18781,x18782)+E(f605(x18783,x18784,x18781),f605(x18783,x18784,x18782)) % 181.55/181.55 [1879]~E(x18791,x18792)+E(f357(x18791,x18793),f357(x18792,x18793)) % 181.55/181.55 [1880]~E(x18801,x18802)+E(f357(x18803,x18801),f357(x18803,x18802)) % 181.55/181.55 [1881]~E(x18811,x18812)+E(f488(x18811,x18813,x18814),f488(x18812,x18813,x18814)) % 181.55/181.55 [1882]~E(x18821,x18822)+E(f488(x18823,x18821,x18824),f488(x18823,x18822,x18824)) % 181.55/181.55 [1883]~E(x18831,x18832)+E(f488(x18833,x18834,x18831),f488(x18833,x18834,x18832)) % 181.55/181.55 [1884]~E(x18841,x18842)+E(f749(x18841,x18843,x18844,x18845),f749(x18842,x18843,x18844,x18845)) % 181.55/181.55 [1885]~E(x18851,x18852)+E(f749(x18853,x18851,x18854,x18855),f749(x18853,x18852,x18854,x18855)) % 181.55/181.55 [1886]~E(x18861,x18862)+E(f749(x18863,x18864,x18861,x18865),f749(x18863,x18864,x18862,x18865)) % 181.55/181.55 [1887]~E(x18871,x18872)+E(f749(x18873,x18874,x18875,x18871),f749(x18873,x18874,x18875,x18872)) % 181.55/181.55 [1888]~E(x18881,x18882)+E(f347(x18881,x18883,x18884,x18885),f347(x18882,x18883,x18884,x18885)) % 181.55/181.55 [1889]~E(x18891,x18892)+E(f347(x18893,x18891,x18894,x18895),f347(x18893,x18892,x18894,x18895)) % 181.55/181.55 [1890]~E(x18901,x18902)+E(f347(x18903,x18904,x18901,x18905),f347(x18903,x18904,x18902,x18905)) % 181.55/181.55 [1891]~E(x18911,x18912)+E(f347(x18913,x18914,x18915,x18911),f347(x18913,x18914,x18915,x18912)) % 181.55/181.55 [1892]~E(x18921,x18922)+E(f515(x18921,x18923,x18924,x18925,x18926),f515(x18922,x18923,x18924,x18925,x18926)) % 181.55/181.55 [1893]~E(x18931,x18932)+E(f515(x18933,x18931,x18934,x18935,x18936),f515(x18933,x18932,x18934,x18935,x18936)) % 181.55/181.55 [1894]~E(x18941,x18942)+E(f515(x18943,x18944,x18941,x18945,x18946),f515(x18943,x18944,x18942,x18945,x18946)) % 181.55/181.55 [1895]~E(x18951,x18952)+E(f515(x18953,x18954,x18955,x18951,x18956),f515(x18953,x18954,x18955,x18952,x18956)) % 181.55/181.55 [1896]~E(x18961,x18962)+E(f515(x18963,x18964,x18965,x18966,x18961),f515(x18963,x18964,x18965,x18966,x18962)) % 181.55/181.55 [1897]~E(x18971,x18972)+E(f429(x18971,x18973,x18974,x18975,x18976),f429(x18972,x18973,x18974,x18975,x18976)) % 181.55/181.55 [1898]~E(x18981,x18982)+E(f429(x18983,x18981,x18984,x18985,x18986),f429(x18983,x18982,x18984,x18985,x18986)) % 181.55/181.55 [1899]~E(x18991,x18992)+E(f429(x18993,x18994,x18991,x18995,x18996),f429(x18993,x18994,x18992,x18995,x18996)) % 181.55/181.55 [1900]~E(x19001,x19002)+E(f429(x19003,x19004,x19005,x19001,x19006),f429(x19003,x19004,x19005,x19002,x19006)) % 181.55/181.55 [1901]~E(x19011,x19012)+E(f429(x19013,x19014,x19015,x19016,x19011),f429(x19013,x19014,x19015,x19016,x19012)) % 181.55/181.55 [1902]~E(x19021,x19022)+E(f409(x19021),f409(x19022)) % 181.55/181.55 [1903]~E(x19031,x19032)+E(f62(x19031,x19033,x19034),f62(x19032,x19033,x19034)) % 181.55/181.55 [1904]~E(x19041,x19042)+E(f62(x19043,x19041,x19044),f62(x19043,x19042,x19044)) % 181.55/181.55 [1905]~E(x19051,x19052)+E(f62(x19053,x19054,x19051),f62(x19053,x19054,x19052)) % 181.55/181.55 [1906]~E(x19061,x19062)+E(f540(x19061,x19063,x19064),f540(x19062,x19063,x19064)) % 181.55/181.55 [1907]~E(x19071,x19072)+E(f540(x19073,x19071,x19074),f540(x19073,x19072,x19074)) % 181.55/181.55 [1908]~E(x19081,x19082)+E(f540(x19083,x19084,x19081),f540(x19083,x19084,x19082)) % 181.55/181.55 [1909]~E(x19091,x19092)+E(f419(x19091,x19093,x19094,x19095,x19096),f419(x19092,x19093,x19094,x19095,x19096)) % 181.55/181.55 [1910]~E(x19101,x19102)+E(f419(x19103,x19101,x19104,x19105,x19106),f419(x19103,x19102,x19104,x19105,x19106)) % 181.55/181.55 [1911]~E(x19111,x19112)+E(f419(x19113,x19114,x19111,x19115,x19116),f419(x19113,x19114,x19112,x19115,x19116)) % 181.55/181.55 [1912]~E(x19121,x19122)+E(f419(x19123,x19124,x19125,x19121,x19126),f419(x19123,x19124,x19125,x19122,x19126)) % 181.55/181.55 [1913]~E(x19131,x19132)+E(f419(x19133,x19134,x19135,x19136,x19131),f419(x19133,x19134,x19135,x19136,x19132)) % 181.55/181.55 [1914]~E(x19141,x19142)+E(f96(x19141,x19143,x19144),f96(x19142,x19143,x19144)) % 181.55/181.55 [1915]~E(x19151,x19152)+E(f96(x19153,x19151,x19154),f96(x19153,x19152,x19154)) % 181.55/181.55 [1916]~E(x19161,x19162)+E(f96(x19163,x19164,x19161),f96(x19163,x19164,x19162)) % 181.55/181.55 [1917]~E(x19171,x19172)+E(f545(x19171,x19173),f545(x19172,x19173)) % 181.55/181.55 [1918]~E(x19181,x19182)+E(f545(x19183,x19181),f545(x19183,x19182)) % 181.55/181.55 [1919]~E(x19191,x19192)+E(f414(x19191,x19193),f414(x19192,x19193)) % 181.55/181.55 [1920]~E(x19201,x19202)+E(f414(x19203,x19201),f414(x19203,x19202)) % 181.55/181.55 [1921]~E(x19211,x19212)+E(f454(x19211,x19213,x19214),f454(x19212,x19213,x19214)) % 181.55/181.55 [1922]~E(x19221,x19222)+E(f454(x19223,x19221,x19224),f454(x19223,x19222,x19224)) % 181.55/181.55 [1923]~E(x19231,x19232)+E(f454(x19233,x19234,x19231),f454(x19233,x19234,x19232)) % 181.55/181.55 [1924]~E(x19241,x19242)+E(f770(x19241,x19243,x19244,x19245,x19246),f770(x19242,x19243,x19244,x19245,x19246)) % 181.55/181.55 [1925]~E(x19251,x19252)+E(f770(x19253,x19251,x19254,x19255,x19256),f770(x19253,x19252,x19254,x19255,x19256)) % 181.55/181.55 [1926]~E(x19261,x19262)+E(f770(x19263,x19264,x19261,x19265,x19266),f770(x19263,x19264,x19262,x19265,x19266)) % 181.55/181.55 [1927]~E(x19271,x19272)+E(f770(x19273,x19274,x19275,x19271,x19276),f770(x19273,x19274,x19275,x19272,x19276)) % 181.55/181.55 [1928]~E(x19281,x19282)+E(f770(x19283,x19284,x19285,x19286,x19281),f770(x19283,x19284,x19285,x19286,x19282)) % 181.55/181.55 [1929]~E(x19291,x19292)+E(f393(x19291,x19293,x19294),f393(x19292,x19293,x19294)) % 181.55/181.55 [1930]~E(x19301,x19302)+E(f393(x19303,x19301,x19304),f393(x19303,x19302,x19304)) % 181.55/181.55 [1931]~E(x19311,x19312)+E(f393(x19313,x19314,x19311),f393(x19313,x19314,x19312)) % 181.55/181.55 [1932]~E(x19321,x19322)+E(f468(x19321,x19323),f468(x19322,x19323)) % 181.55/181.55 [1933]~E(x19331,x19332)+E(f468(x19333,x19331),f468(x19333,x19332)) % 181.55/181.55 [1934]~E(x19341,x19342)+E(f543(x19341),f543(x19342)) % 181.55/181.55 [1935]~E(x19351,x19352)+E(f563(x19351,x19353,x19354,x19355,x19356,x19357),f563(x19352,x19353,x19354,x19355,x19356,x19357)) % 181.55/181.55 [1936]~E(x19361,x19362)+E(f563(x19363,x19361,x19364,x19365,x19366,x19367),f563(x19363,x19362,x19364,x19365,x19366,x19367)) % 181.55/181.55 [1937]~E(x19371,x19372)+E(f563(x19373,x19374,x19371,x19375,x19376,x19377),f563(x19373,x19374,x19372,x19375,x19376,x19377)) % 181.55/181.55 [1938]~E(x19381,x19382)+E(f563(x19383,x19384,x19385,x19381,x19386,x19387),f563(x19383,x19384,x19385,x19382,x19386,x19387)) % 181.55/181.55 [1939]~E(x19391,x19392)+E(f563(x19393,x19394,x19395,x19396,x19391,x19397),f563(x19393,x19394,x19395,x19396,x19392,x19397)) % 181.55/181.55 [1940]~E(x19401,x19402)+E(f563(x19403,x19404,x19405,x19406,x19407,x19401),f563(x19403,x19404,x19405,x19406,x19407,x19402)) % 181.55/181.55 [1941]~E(x19411,x19412)+E(f787(x19411,x19413),f787(x19412,x19413)) % 181.55/181.55 [1942]~E(x19421,x19422)+E(f787(x19423,x19421),f787(x19423,x19422)) % 181.55/181.55 [1943]~E(x19431,x19432)+E(f854(x19431,x19433,x19434,x19435),f854(x19432,x19433,x19434,x19435)) % 181.55/181.55 [1944]~E(x19441,x19442)+E(f854(x19443,x19441,x19444,x19445),f854(x19443,x19442,x19444,x19445)) % 181.55/181.55 [1945]~E(x19451,x19452)+E(f854(x19453,x19454,x19451,x19455),f854(x19453,x19454,x19452,x19455)) % 181.55/181.55 [1946]~E(x19461,x19462)+E(f854(x19463,x19464,x19465,x19461),f854(x19463,x19464,x19465,x19462)) % 181.55/181.55 [1947]~E(x19471,x19472)+E(f448(x19471,x19473),f448(x19472,x19473)) % 181.55/181.55 [1948]~E(x19481,x19482)+E(f448(x19483,x19481),f448(x19483,x19482)) % 181.55/181.55 [1949]~E(x19491,x19492)+E(f385(x19491,x19493,x19494,x19495,x19496),f385(x19492,x19493,x19494,x19495,x19496)) % 181.55/181.55 [1950]~E(x19501,x19502)+E(f385(x19503,x19501,x19504,x19505,x19506),f385(x19503,x19502,x19504,x19505,x19506)) % 181.55/181.55 [1951]~E(x19511,x19512)+E(f385(x19513,x19514,x19511,x19515,x19516),f385(x19513,x19514,x19512,x19515,x19516)) % 181.55/181.55 [1952]~E(x19521,x19522)+E(f385(x19523,x19524,x19525,x19521,x19526),f385(x19523,x19524,x19525,x19522,x19526)) % 181.55/181.55 [1953]~E(x19531,x19532)+E(f385(x19533,x19534,x19535,x19536,x19531),f385(x19533,x19534,x19535,x19536,x19532)) % 181.55/181.55 [1954]~E(x19541,x19542)+E(f236(x19541,x19543,x19544,x19545,x19546),f236(x19542,x19543,x19544,x19545,x19546)) % 181.55/181.55 [1955]~E(x19551,x19552)+E(f236(x19553,x19551,x19554,x19555,x19556),f236(x19553,x19552,x19554,x19555,x19556)) % 181.55/181.55 [1956]~E(x19561,x19562)+E(f236(x19563,x19564,x19561,x19565,x19566),f236(x19563,x19564,x19562,x19565,x19566)) % 181.55/181.55 [1957]~E(x19571,x19572)+E(f236(x19573,x19574,x19575,x19571,x19576),f236(x19573,x19574,x19575,x19572,x19576)) % 181.55/181.55 [1958]~E(x19581,x19582)+E(f236(x19583,x19584,x19585,x19586,x19581),f236(x19583,x19584,x19585,x19586,x19582)) % 181.55/181.55 [1959]~E(x19591,x19592)+E(f306(x19591,x19593,x19594),f306(x19592,x19593,x19594)) % 181.55/181.55 [1960]~E(x19601,x19602)+E(f306(x19603,x19601,x19604),f306(x19603,x19602,x19604)) % 181.55/181.55 [1961]~E(x19611,x19612)+E(f306(x19613,x19614,x19611),f306(x19613,x19614,x19612)) % 181.55/181.55 [1962]~E(x19621,x19622)+E(f458(x19621,x19623,x19624),f458(x19622,x19623,x19624)) % 181.55/181.55 [1963]~E(x19631,x19632)+E(f458(x19633,x19631,x19634),f458(x19633,x19632,x19634)) % 181.55/181.55 [1964]~E(x19641,x19642)+E(f458(x19643,x19644,x19641),f458(x19643,x19644,x19642)) % 181.55/181.55 [1965]~E(x19651,x19652)+E(f647(x19651,x19653,x19654,x19655),f647(x19652,x19653,x19654,x19655)) % 181.55/181.55 [1966]~E(x19661,x19662)+E(f647(x19663,x19661,x19664,x19665),f647(x19663,x19662,x19664,x19665)) % 181.55/181.55 [1967]~E(x19671,x19672)+E(f647(x19673,x19674,x19671,x19675),f647(x19673,x19674,x19672,x19675)) % 181.55/181.55 [1968]~E(x19681,x19682)+E(f647(x19683,x19684,x19685,x19681),f647(x19683,x19684,x19685,x19682)) % 181.55/181.55 [1969]~E(x19691,x19692)+E(f524(x19691,x19693,x19694),f524(x19692,x19693,x19694)) % 181.55/181.55 [1970]~E(x19701,x19702)+E(f524(x19703,x19701,x19704),f524(x19703,x19702,x19704)) % 181.55/181.55 [1971]~E(x19711,x19712)+E(f524(x19713,x19714,x19711),f524(x19713,x19714,x19712)) % 181.55/181.55 [1972]~E(x19721,x19722)+E(f532(x19721,x19723,x19724,x19725),f532(x19722,x19723,x19724,x19725)) % 181.55/181.55 [1973]~E(x19731,x19732)+E(f532(x19733,x19731,x19734,x19735),f532(x19733,x19732,x19734,x19735)) % 181.55/181.55 [1974]~E(x19741,x19742)+E(f532(x19743,x19744,x19741,x19745),f532(x19743,x19744,x19742,x19745)) % 181.55/181.55 [1975]~E(x19751,x19752)+E(f532(x19753,x19754,x19755,x19751),f532(x19753,x19754,x19755,x19752)) % 181.55/181.55 [1976]~E(x19761,x19762)+E(f781(x19761,x19763,x19764),f781(x19762,x19763,x19764)) % 181.55/181.55 [1977]~E(x19771,x19772)+E(f781(x19773,x19771,x19774),f781(x19773,x19772,x19774)) % 181.55/181.55 [1978]~E(x19781,x19782)+E(f781(x19783,x19784,x19781),f781(x19783,x19784,x19782)) % 181.55/181.55 [1979]~E(x19791,x19792)+E(f818(x19791,x19793,x19794,x19795,x19796),f818(x19792,x19793,x19794,x19795,x19796)) % 181.55/181.55 [1980]~E(x19801,x19802)+E(f818(x19803,x19801,x19804,x19805,x19806),f818(x19803,x19802,x19804,x19805,x19806)) % 181.55/181.55 [1981]~E(x19811,x19812)+E(f818(x19813,x19814,x19811,x19815,x19816),f818(x19813,x19814,x19812,x19815,x19816)) % 181.55/181.55 [1982]~E(x19821,x19822)+E(f818(x19823,x19824,x19825,x19821,x19826),f818(x19823,x19824,x19825,x19822,x19826)) % 181.55/181.55 [1983]~E(x19831,x19832)+E(f818(x19833,x19834,x19835,x19836,x19831),f818(x19833,x19834,x19835,x19836,x19832)) % 181.55/181.55 [1984]~E(x19841,x19842)+E(f834(x19841,x19843,x19844,x19845,x19846),f834(x19842,x19843,x19844,x19845,x19846)) % 181.55/181.55 [1985]~E(x19851,x19852)+E(f834(x19853,x19851,x19854,x19855,x19856),f834(x19853,x19852,x19854,x19855,x19856)) % 181.55/181.55 [1986]~E(x19861,x19862)+E(f834(x19863,x19864,x19861,x19865,x19866),f834(x19863,x19864,x19862,x19865,x19866)) % 181.55/181.55 [1987]~E(x19871,x19872)+E(f834(x19873,x19874,x19875,x19871,x19876),f834(x19873,x19874,x19875,x19872,x19876)) % 181.55/181.55 [1988]~E(x19881,x19882)+E(f834(x19883,x19884,x19885,x19886,x19881),f834(x19883,x19884,x19885,x19886,x19882)) % 181.55/181.55 [1989]~E(x19891,x19892)+E(f670(x19891,x19893,x19894),f670(x19892,x19893,x19894)) % 181.55/181.55 [1990]~E(x19901,x19902)+E(f670(x19903,x19901,x19904),f670(x19903,x19902,x19904)) % 181.55/181.55 [1991]~E(x19911,x19912)+E(f670(x19913,x19914,x19911),f670(x19913,x19914,x19912)) % 181.55/181.55 [1992]~E(x19921,x19922)+E(f470(x19921,x19923,x19924,x19925),f470(x19922,x19923,x19924,x19925)) % 181.55/181.55 [1993]~E(x19931,x19932)+E(f470(x19933,x19931,x19934,x19935),f470(x19933,x19932,x19934,x19935)) % 181.55/181.55 [1994]~E(x19941,x19942)+E(f470(x19943,x19944,x19941,x19945),f470(x19943,x19944,x19942,x19945)) % 181.55/181.55 [1995]~E(x19951,x19952)+E(f470(x19953,x19954,x19955,x19951),f470(x19953,x19954,x19955,x19952)) % 181.55/181.55 [1996]~E(x19961,x19962)+E(f824(x19961,x19963),f824(x19962,x19963)) % 181.55/181.55 [1997]~E(x19971,x19972)+E(f824(x19973,x19971),f824(x19973,x19972)) % 181.55/181.55 [1998]~E(x19981,x19982)+E(f521(x19981,x19983,x19984,x19985),f521(x19982,x19983,x19984,x19985)) % 181.55/181.55 [1999]~E(x19991,x19992)+E(f521(x19993,x19991,x19994,x19995),f521(x19993,x19992,x19994,x19995)) % 181.55/181.55 [2000]~E(x20001,x20002)+E(f521(x20003,x20004,x20001,x20005),f521(x20003,x20004,x20002,x20005)) % 181.55/181.55 [2001]~E(x20011,x20012)+E(f521(x20013,x20014,x20015,x20011),f521(x20013,x20014,x20015,x20012)) % 181.55/181.55 [2002]~E(x20021,x20022)+E(f727(x20021,x20023),f727(x20022,x20023)) % 181.55/181.55 [2003]~E(x20031,x20032)+E(f727(x20033,x20031),f727(x20033,x20032)) % 181.55/181.55 [2004]~E(x20041,x20042)+E(f693(x20041,x20043,x20044,x20045,x20046),f693(x20042,x20043,x20044,x20045,x20046)) % 181.55/181.55 [2005]~E(x20051,x20052)+E(f693(x20053,x20051,x20054,x20055,x20056),f693(x20053,x20052,x20054,x20055,x20056)) % 181.55/181.55 [2006]~E(x20061,x20062)+E(f693(x20063,x20064,x20061,x20065,x20066),f693(x20063,x20064,x20062,x20065,x20066)) % 181.55/181.55 [2007]~E(x20071,x20072)+E(f693(x20073,x20074,x20075,x20071,x20076),f693(x20073,x20074,x20075,x20072,x20076)) % 181.55/181.55 [2008]~E(x20081,x20082)+E(f693(x20083,x20084,x20085,x20086,x20081),f693(x20083,x20084,x20085,x20086,x20082)) % 181.55/181.55 [2009]~E(x20091,x20092)+E(f359(x20091,x20093),f359(x20092,x20093)) % 181.55/181.55 [2010]~E(x20101,x20102)+E(f359(x20103,x20101),f359(x20103,x20102)) % 181.55/181.55 [2011]~E(x20111,x20112)+E(f815(x20111,x20113,x20114,x20115),f815(x20112,x20113,x20114,x20115)) % 181.55/181.55 [2012]~E(x20121,x20122)+E(f815(x20123,x20121,x20124,x20125),f815(x20123,x20122,x20124,x20125)) % 181.55/181.55 [2013]~E(x20131,x20132)+E(f815(x20133,x20134,x20131,x20135),f815(x20133,x20134,x20132,x20135)) % 181.55/181.55 [2014]~E(x20141,x20142)+E(f815(x20143,x20144,x20145,x20141),f815(x20143,x20144,x20145,x20142)) % 181.55/181.55 [2015]~E(x20151,x20152)+E(f206(x20151,x20153),f206(x20152,x20153)) % 181.55/181.55 [2016]~E(x20161,x20162)+E(f206(x20163,x20161),f206(x20163,x20162)) % 181.55/181.55 [2017]~E(x20171,x20172)+E(f711(x20171,x20173,x20174),f711(x20172,x20173,x20174)) % 181.55/181.55 [2018]~E(x20181,x20182)+E(f711(x20183,x20181,x20184),f711(x20183,x20182,x20184)) % 181.55/181.55 [2019]~E(x20191,x20192)+E(f711(x20193,x20194,x20191),f711(x20193,x20194,x20192)) % 181.55/181.55 [2020]~E(x20201,x20202)+E(f289(x20201,x20203,x20204,x20205,x20206),f289(x20202,x20203,x20204,x20205,x20206)) % 181.55/181.55 [2021]~E(x20211,x20212)+E(f289(x20213,x20211,x20214,x20215,x20216),f289(x20213,x20212,x20214,x20215,x20216)) % 181.55/181.55 [2022]~E(x20221,x20222)+E(f289(x20223,x20224,x20221,x20225,x20226),f289(x20223,x20224,x20222,x20225,x20226)) % 181.55/181.55 [2023]~E(x20231,x20232)+E(f289(x20233,x20234,x20235,x20231,x20236),f289(x20233,x20234,x20235,x20232,x20236)) % 181.55/181.55 [2024]~E(x20241,x20242)+E(f289(x20243,x20244,x20245,x20246,x20241),f289(x20243,x20244,x20245,x20246,x20242)) % 181.55/181.55 [2025]~E(x20251,x20252)+E(f498(x20251,x20253,x20254,x20255,x20256,x20257),f498(x20252,x20253,x20254,x20255,x20256,x20257)) % 181.55/181.55 [2026]~E(x20261,x20262)+E(f498(x20263,x20261,x20264,x20265,x20266,x20267),f498(x20263,x20262,x20264,x20265,x20266,x20267)) % 181.55/181.55 [2027]~E(x20271,x20272)+E(f498(x20273,x20274,x20271,x20275,x20276,x20277),f498(x20273,x20274,x20272,x20275,x20276,x20277)) % 181.55/181.55 [2028]~E(x20281,x20282)+E(f498(x20283,x20284,x20285,x20281,x20286,x20287),f498(x20283,x20284,x20285,x20282,x20286,x20287)) % 181.55/181.55 [2029]~E(x20291,x20292)+E(f498(x20293,x20294,x20295,x20296,x20291,x20297),f498(x20293,x20294,x20295,x20296,x20292,x20297)) % 181.55/181.55 [2030]~E(x20301,x20302)+E(f498(x20303,x20304,x20305,x20306,x20307,x20301),f498(x20303,x20304,x20305,x20306,x20307,x20302)) % 181.55/181.55 [2031]~E(x20311,x20312)+E(f592(x20311,x20313,x20314,x20315,x20316),f592(x20312,x20313,x20314,x20315,x20316)) % 181.55/181.55 [2032]~E(x20321,x20322)+E(f592(x20323,x20321,x20324,x20325,x20326),f592(x20323,x20322,x20324,x20325,x20326)) % 181.55/181.55 [2033]~E(x20331,x20332)+E(f592(x20333,x20334,x20331,x20335,x20336),f592(x20333,x20334,x20332,x20335,x20336)) % 181.55/181.55 [2034]~E(x20341,x20342)+E(f592(x20343,x20344,x20345,x20341,x20346),f592(x20343,x20344,x20345,x20342,x20346)) % 181.55/181.55 [2035]~E(x20351,x20352)+E(f592(x20353,x20354,x20355,x20356,x20351),f592(x20353,x20354,x20355,x20356,x20352)) % 181.55/181.55 [2036]~E(x20361,x20362)+E(f567(x20361),f567(x20362)) % 181.55/181.55 [2037]~E(x20371,x20372)+E(f376(x20371,x20373),f376(x20372,x20373)) % 181.55/181.55 [2038]~E(x20381,x20382)+E(f376(x20383,x20381),f376(x20383,x20382)) % 181.55/181.55 [2039]~E(x20391,x20392)+E(f123(x20391),f123(x20392)) % 181.55/181.55 [2040]~E(x20401,x20402)+E(f572(x20401,x20403,x20404),f572(x20402,x20403,x20404)) % 181.55/181.55 [2041]~E(x20411,x20412)+E(f572(x20413,x20411,x20414),f572(x20413,x20412,x20414)) % 181.55/181.55 [2042]~E(x20421,x20422)+E(f572(x20423,x20424,x20421),f572(x20423,x20424,x20422)) % 181.55/181.55 [2043]~E(x20431,x20432)+E(f614(x20431,x20433,x20434,x20435),f614(x20432,x20433,x20434,x20435)) % 181.55/181.55 [2044]~E(x20441,x20442)+E(f614(x20443,x20441,x20444,x20445),f614(x20443,x20442,x20444,x20445)) % 181.55/181.55 [2045]~E(x20451,x20452)+E(f614(x20453,x20454,x20451,x20455),f614(x20453,x20454,x20452,x20455)) % 181.55/181.55 [2046]~E(x20461,x20462)+E(f614(x20463,x20464,x20465,x20461),f614(x20463,x20464,x20465,x20462)) % 181.55/181.55 [2047]~E(x20471,x20472)+E(f710(x20471,x20473,x20474),f710(x20472,x20473,x20474)) % 181.55/181.55 [2048]~E(x20481,x20482)+E(f710(x20483,x20481,x20484),f710(x20483,x20482,x20484)) % 181.55/181.55 [2049]~E(x20491,x20492)+E(f710(x20493,x20494,x20491),f710(x20493,x20494,x20492)) % 181.55/181.55 [2050]~E(x20501,x20502)+E(f500(x20501,x20503,x20504,x20505,x20506),f500(x20502,x20503,x20504,x20505,x20506)) % 181.55/181.55 [2051]~E(x20511,x20512)+E(f500(x20513,x20511,x20514,x20515,x20516),f500(x20513,x20512,x20514,x20515,x20516)) % 181.55/181.55 [2052]~E(x20521,x20522)+E(f500(x20523,x20524,x20521,x20525,x20526),f500(x20523,x20524,x20522,x20525,x20526)) % 181.55/181.55 [2053]~E(x20531,x20532)+E(f500(x20533,x20534,x20535,x20531,x20536),f500(x20533,x20534,x20535,x20532,x20536)) % 181.55/181.55 [2054]~E(x20541,x20542)+E(f500(x20543,x20544,x20545,x20546,x20541),f500(x20543,x20544,x20545,x20546,x20542)) % 181.55/181.55 [2055]~E(x20551,x20552)+E(f782(x20551,x20553,x20554),f782(x20552,x20553,x20554)) % 181.55/181.55 [2056]~E(x20561,x20562)+E(f782(x20563,x20561,x20564),f782(x20563,x20562,x20564)) % 181.55/181.55 [2057]~E(x20571,x20572)+E(f782(x20573,x20574,x20571),f782(x20573,x20574,x20572)) % 181.55/181.55 [2058]~E(x20581,x20582)+E(f564(x20581,x20583,x20584,x20585,x20586,x20587),f564(x20582,x20583,x20584,x20585,x20586,x20587)) % 181.55/181.55 [2059]~E(x20591,x20592)+E(f564(x20593,x20591,x20594,x20595,x20596,x20597),f564(x20593,x20592,x20594,x20595,x20596,x20597)) % 181.55/181.55 [2060]~E(x20601,x20602)+E(f564(x20603,x20604,x20601,x20605,x20606,x20607),f564(x20603,x20604,x20602,x20605,x20606,x20607)) % 181.55/181.55 [2061]~E(x20611,x20612)+E(f564(x20613,x20614,x20615,x20611,x20616,x20617),f564(x20613,x20614,x20615,x20612,x20616,x20617)) % 181.55/181.55 [2062]~E(x20621,x20622)+E(f564(x20623,x20624,x20625,x20626,x20621,x20627),f564(x20623,x20624,x20625,x20626,x20622,x20627)) % 181.55/181.55 [2063]~E(x20631,x20632)+E(f564(x20633,x20634,x20635,x20636,x20637,x20631),f564(x20633,x20634,x20635,x20636,x20637,x20632)) % 181.55/181.55 [2064]~E(x20641,x20642)+E(f240(x20641,x20643),f240(x20642,x20643)) % 181.55/181.55 [2065]~E(x20651,x20652)+E(f240(x20653,x20651),f240(x20653,x20652)) % 181.55/181.55 [2066]~E(x20661,x20662)+E(f459(x20661,x20663,x20664),f459(x20662,x20663,x20664)) % 181.55/181.55 [2067]~E(x20671,x20672)+E(f459(x20673,x20671,x20674),f459(x20673,x20672,x20674)) % 181.55/181.55 [2068]~E(x20681,x20682)+E(f459(x20683,x20684,x20681),f459(x20683,x20684,x20682)) % 181.55/181.55 [2069]~E(x20691,x20692)+E(f437(x20691,x20693,x20694,x20695),f437(x20692,x20693,x20694,x20695)) % 181.55/181.55 [2070]~E(x20701,x20702)+E(f437(x20703,x20701,x20704,x20705),f437(x20703,x20702,x20704,x20705)) % 181.55/181.55 [2071]~E(x20711,x20712)+E(f437(x20713,x20714,x20711,x20715),f437(x20713,x20714,x20712,x20715)) % 181.55/181.55 [2072]~E(x20721,x20722)+E(f437(x20723,x20724,x20725,x20721),f437(x20723,x20724,x20725,x20722)) % 181.55/181.55 [2073]~E(x20731,x20732)+E(f608(x20731,x20733),f608(x20732,x20733)) % 181.55/181.55 [2074]~E(x20741,x20742)+E(f608(x20743,x20741),f608(x20743,x20742)) % 181.55/181.55 [2075]~E(x20751,x20752)+E(f730(x20751,x20753),f730(x20752,x20753)) % 181.55/181.55 [2076]~E(x20761,x20762)+E(f730(x20763,x20761),f730(x20763,x20762)) % 181.55/181.55 [2077]~E(x20771,x20772)+E(f546(x20771,x20773),f546(x20772,x20773)) % 181.55/181.55 [2078]~E(x20781,x20782)+E(f546(x20783,x20781),f546(x20783,x20782)) % 181.55/181.55 [2079]~E(x20791,x20792)+E(f481(x20791,x20793,x20794,x20795),f481(x20792,x20793,x20794,x20795)) % 181.55/181.55 [2080]~E(x20801,x20802)+E(f481(x20803,x20801,x20804,x20805),f481(x20803,x20802,x20804,x20805)) % 181.55/181.55 [2081]~E(x20811,x20812)+E(f481(x20813,x20814,x20811,x20815),f481(x20813,x20814,x20812,x20815)) % 181.55/181.55 [2082]~E(x20821,x20822)+E(f481(x20823,x20824,x20825,x20821),f481(x20823,x20824,x20825,x20822)) % 181.55/181.55 [2083]~E(x20831,x20832)+E(f661(x20831,x20833,x20834,x20835,x20836),f661(x20832,x20833,x20834,x20835,x20836)) % 181.55/181.55 [2084]~E(x20841,x20842)+E(f661(x20843,x20841,x20844,x20845,x20846),f661(x20843,x20842,x20844,x20845,x20846)) % 181.55/181.55 [2085]~E(x20851,x20852)+E(f661(x20853,x20854,x20851,x20855,x20856),f661(x20853,x20854,x20852,x20855,x20856)) % 181.55/181.55 [2086]~E(x20861,x20862)+E(f661(x20863,x20864,x20865,x20861,x20866),f661(x20863,x20864,x20865,x20862,x20866)) % 181.55/181.55 [2087]~E(x20871,x20872)+E(f661(x20873,x20874,x20875,x20876,x20871),f661(x20873,x20874,x20875,x20876,x20872)) % 181.55/181.55 [2088]~E(x20881,x20882)+E(f741(x20881,x20883,x20884),f741(x20882,x20883,x20884)) % 181.55/181.55 [2089]~E(x20891,x20892)+E(f741(x20893,x20891,x20894),f741(x20893,x20892,x20894)) % 181.55/181.55 [2090]~E(x20901,x20902)+E(f741(x20903,x20904,x20901),f741(x20903,x20904,x20902)) % 181.55/181.55 [2091]~E(x20911,x20912)+E(f371(x20911,x20913,x20914),f371(x20912,x20913,x20914)) % 181.55/181.55 [2092]~E(x20921,x20922)+E(f371(x20923,x20921,x20924),f371(x20923,x20922,x20924)) % 181.55/181.55 [2093]~E(x20931,x20932)+E(f371(x20933,x20934,x20931),f371(x20933,x20934,x20932)) % 181.55/181.55 [2094]~E(x20941,x20942)+E(f753(x20941,x20943,x20944,x20945,x20946),f753(x20942,x20943,x20944,x20945,x20946)) % 181.55/181.55 [2095]~E(x20951,x20952)+E(f753(x20953,x20951,x20954,x20955,x20956),f753(x20953,x20952,x20954,x20955,x20956)) % 181.55/181.55 [2096]~E(x20961,x20962)+E(f753(x20963,x20964,x20961,x20965,x20966),f753(x20963,x20964,x20962,x20965,x20966)) % 181.55/181.55 [2097]~E(x20971,x20972)+E(f753(x20973,x20974,x20975,x20971,x20976),f753(x20973,x20974,x20975,x20972,x20976)) % 181.55/181.55 [2098]~E(x20981,x20982)+E(f753(x20983,x20984,x20985,x20986,x20981),f753(x20983,x20984,x20985,x20986,x20982)) % 181.55/181.55 [2099]~E(x20991,x20992)+E(f820(x20991,x20993,x20994,x20995),f820(x20992,x20993,x20994,x20995)) % 181.55/181.55 [2100]~E(x21001,x21002)+E(f820(x21003,x21001,x21004,x21005),f820(x21003,x21002,x21004,x21005)) % 181.55/181.55 [2101]~E(x21011,x21012)+E(f820(x21013,x21014,x21011,x21015),f820(x21013,x21014,x21012,x21015)) % 181.55/181.55 [2102]~E(x21021,x21022)+E(f820(x21023,x21024,x21025,x21021),f820(x21023,x21024,x21025,x21022)) % 181.55/181.55 [2103]~E(x21031,x21032)+E(f664(x21031,x21033,x21034,x21035,x21036),f664(x21032,x21033,x21034,x21035,x21036)) % 181.55/181.55 [2104]~E(x21041,x21042)+E(f664(x21043,x21041,x21044,x21045,x21046),f664(x21043,x21042,x21044,x21045,x21046)) % 181.55/181.55 [2105]~E(x21051,x21052)+E(f664(x21053,x21054,x21051,x21055,x21056),f664(x21053,x21054,x21052,x21055,x21056)) % 181.55/181.55 [2106]~E(x21061,x21062)+E(f664(x21063,x21064,x21065,x21061,x21066),f664(x21063,x21064,x21065,x21062,x21066)) % 181.55/181.55 [2107]~E(x21071,x21072)+E(f664(x21073,x21074,x21075,x21076,x21071),f664(x21073,x21074,x21075,x21076,x21072)) % 181.55/181.55 [2108]~E(x21081,x21082)+E(f408(x21081,x21083,x21084,x21085),f408(x21082,x21083,x21084,x21085)) % 181.55/181.55 [2109]~E(x21091,x21092)+E(f408(x21093,x21091,x21094,x21095),f408(x21093,x21092,x21094,x21095)) % 181.55/181.55 [2110]~E(x21101,x21102)+E(f408(x21103,x21104,x21101,x21105),f408(x21103,x21104,x21102,x21105)) % 181.55/181.55 [2111]~E(x21111,x21112)+E(f408(x21113,x21114,x21115,x21111),f408(x21113,x21114,x21115,x21112)) % 181.55/181.55 [2112]~E(x21121,x21122)+E(f491(x21121,x21123,x21124,x21125),f491(x21122,x21123,x21124,x21125)) % 181.55/181.55 [2113]~E(x21131,x21132)+E(f491(x21133,x21131,x21134,x21135),f491(x21133,x21132,x21134,x21135)) % 181.55/181.55 [2114]~E(x21141,x21142)+E(f491(x21143,x21144,x21141,x21145),f491(x21143,x21144,x21142,x21145)) % 181.55/181.55 [2115]~E(x21151,x21152)+E(f491(x21153,x21154,x21155,x21151),f491(x21153,x21154,x21155,x21152)) % 181.55/181.55 [2116]~E(x21161,x21162)+E(f241(x21161,x21163),f241(x21162,x21163)) % 181.55/181.55 [2117]~E(x21171,x21172)+E(f241(x21173,x21171),f241(x21173,x21172)) % 181.55/181.55 [2118]~E(x21181,x21182)+E(f396(x21181,x21183,x21184),f396(x21182,x21183,x21184)) % 181.55/181.55 [2119]~E(x21191,x21192)+E(f396(x21193,x21191,x21194),f396(x21193,x21192,x21194)) % 181.55/181.55 [2120]~E(x21201,x21202)+E(f396(x21203,x21204,x21201),f396(x21203,x21204,x21202)) % 181.55/181.55 [2121]~E(x21211,x21212)+E(f779(x21211,x21213,x21214),f779(x21212,x21213,x21214)) % 181.55/181.55 [2122]~E(x21221,x21222)+E(f779(x21223,x21221,x21224),f779(x21223,x21222,x21224)) % 181.55/181.55 [2123]~E(x21231,x21232)+E(f779(x21233,x21234,x21231),f779(x21233,x21234,x21232)) % 181.55/181.55 [2124]~E(x21241,x21242)+E(f613(x21241,x21243,x21244,x21245),f613(x21242,x21243,x21244,x21245)) % 181.55/181.55 [2125]~E(x21251,x21252)+E(f613(x21253,x21251,x21254,x21255),f613(x21253,x21252,x21254,x21255)) % 181.55/181.55 [2126]~E(x21261,x21262)+E(f613(x21263,x21264,x21261,x21265),f613(x21263,x21264,x21262,x21265)) % 181.55/181.55 [2127]~E(x21271,x21272)+E(f613(x21273,x21274,x21275,x21271),f613(x21273,x21274,x21275,x21272)) % 181.55/181.55 [2128]~E(x21281,x21282)+E(f761(x21281,x21283,x21284,x21285,x21286,x21287,x21288),f761(x21282,x21283,x21284,x21285,x21286,x21287,x21288)) % 181.55/181.55 [2129]~E(x21291,x21292)+E(f761(x21293,x21291,x21294,x21295,x21296,x21297,x21298),f761(x21293,x21292,x21294,x21295,x21296,x21297,x21298)) % 181.55/181.55 [2130]~E(x21301,x21302)+E(f761(x21303,x21304,x21301,x21305,x21306,x21307,x21308),f761(x21303,x21304,x21302,x21305,x21306,x21307,x21308)) % 181.55/181.55 [2131]~E(x21311,x21312)+E(f761(x21313,x21314,x21315,x21311,x21316,x21317,x21318),f761(x21313,x21314,x21315,x21312,x21316,x21317,x21318)) % 181.55/181.55 [2132]~E(x21321,x21322)+E(f761(x21323,x21324,x21325,x21326,x21321,x21327,x21328),f761(x21323,x21324,x21325,x21326,x21322,x21327,x21328)) % 181.55/181.55 [2133]~E(x21331,x21332)+E(f761(x21333,x21334,x21335,x21336,x21337,x21331,x21338),f761(x21333,x21334,x21335,x21336,x21337,x21332,x21338)) % 181.55/181.55 [2134]~E(x21341,x21342)+E(f761(x21343,x21344,x21345,x21346,x21347,x21348,x21341),f761(x21343,x21344,x21345,x21346,x21347,x21348,x21342)) % 181.55/181.55 [2135]~E(x21351,x21352)+E(f231(x21351,x21353,x21354,x21355),f231(x21352,x21353,x21354,x21355)) % 181.55/181.55 [2136]~E(x21361,x21362)+E(f231(x21363,x21361,x21364,x21365),f231(x21363,x21362,x21364,x21365)) % 181.55/181.55 [2137]~E(x21371,x21372)+E(f231(x21373,x21374,x21371,x21375),f231(x21373,x21374,x21372,x21375)) % 181.55/181.55 [2138]~E(x21381,x21382)+E(f231(x21383,x21384,x21385,x21381),f231(x21383,x21384,x21385,x21382)) % 181.55/181.55 [2139]~E(x21391,x21392)+E(f331(x21391),f331(x21392)) % 181.55/181.55 [2140]~E(x21401,x21402)+E(f759(x21401,x21403,x21404,x21405),f759(x21402,x21403,x21404,x21405)) % 181.55/181.55 [2141]~E(x21411,x21412)+E(f759(x21413,x21411,x21414,x21415),f759(x21413,x21412,x21414,x21415)) % 181.55/181.55 [2142]~E(x21421,x21422)+E(f759(x21423,x21424,x21421,x21425),f759(x21423,x21424,x21422,x21425)) % 181.55/181.55 [2143]~E(x21431,x21432)+E(f759(x21433,x21434,x21435,x21431),f759(x21433,x21434,x21435,x21432)) % 181.55/181.55 [2144]~E(x21441,x21442)+E(f473(x21441,x21443,x21444,x21445),f473(x21442,x21443,x21444,x21445)) % 181.55/181.55 [2145]~E(x21451,x21452)+E(f473(x21453,x21451,x21454,x21455),f473(x21453,x21452,x21454,x21455)) % 181.55/181.55 [2146]~E(x21461,x21462)+E(f473(x21463,x21464,x21461,x21465),f473(x21463,x21464,x21462,x21465)) % 181.55/181.55 [2147]~E(x21471,x21472)+E(f473(x21473,x21474,x21475,x21471),f473(x21473,x21474,x21475,x21472)) % 181.55/181.55 [2148]~E(x21481,x21482)+E(f464(x21481,x21483,x21484,x21485),f464(x21482,x21483,x21484,x21485)) % 181.55/181.55 [2149]~E(x21491,x21492)+E(f464(x21493,x21491,x21494,x21495),f464(x21493,x21492,x21494,x21495)) % 181.55/181.55 [2150]~E(x21501,x21502)+E(f464(x21503,x21504,x21501,x21505),f464(x21503,x21504,x21502,x21505)) % 181.55/181.55 [2151]~E(x21511,x21512)+E(f464(x21513,x21514,x21515,x21511),f464(x21513,x21514,x21515,x21512)) % 181.55/181.55 [2152]~E(x21521,x21522)+E(f446(x21521,x21523,x21524),f446(x21522,x21523,x21524)) % 181.55/181.55 [2153]~E(x21531,x21532)+E(f446(x21533,x21531,x21534),f446(x21533,x21532,x21534)) % 181.55/181.55 [2154]~E(x21541,x21542)+E(f446(x21543,x21544,x21541),f446(x21543,x21544,x21542)) % 181.55/181.55 [2155]~E(x21551,x21552)+E(f665(x21551,x21553,x21554,x21555,x21556,x21557),f665(x21552,x21553,x21554,x21555,x21556,x21557)) % 181.55/181.55 [2156]~E(x21561,x21562)+E(f665(x21563,x21561,x21564,x21565,x21566,x21567),f665(x21563,x21562,x21564,x21565,x21566,x21567)) % 181.55/181.55 [2157]~E(x21571,x21572)+E(f665(x21573,x21574,x21571,x21575,x21576,x21577),f665(x21573,x21574,x21572,x21575,x21576,x21577)) % 181.55/181.55 [2158]~E(x21581,x21582)+E(f665(x21583,x21584,x21585,x21581,x21586,x21587),f665(x21583,x21584,x21585,x21582,x21586,x21587)) % 181.55/181.55 [2159]~E(x21591,x21592)+E(f665(x21593,x21594,x21595,x21596,x21591,x21597),f665(x21593,x21594,x21595,x21596,x21592,x21597)) % 181.55/181.55 [2160]~E(x21601,x21602)+E(f665(x21603,x21604,x21605,x21606,x21607,x21601),f665(x21603,x21604,x21605,x21606,x21607,x21602)) % 181.55/181.55 [2161]~E(x21611,x21612)+E(f838(x21611,x21613,x21614,x21615),f838(x21612,x21613,x21614,x21615)) % 181.55/181.55 [2162]~E(x21621,x21622)+E(f838(x21623,x21621,x21624,x21625),f838(x21623,x21622,x21624,x21625)) % 181.55/181.55 [2163]~E(x21631,x21632)+E(f838(x21633,x21634,x21631,x21635),f838(x21633,x21634,x21632,x21635)) % 181.55/181.55 [2164]~E(x21641,x21642)+E(f838(x21643,x21644,x21645,x21641),f838(x21643,x21644,x21645,x21642)) % 181.55/181.55 [2165]~E(x21651,x21652)+E(f671(x21651,x21653,x21654,x21655),f671(x21652,x21653,x21654,x21655)) % 181.55/181.55 [2166]~E(x21661,x21662)+E(f671(x21663,x21661,x21664,x21665),f671(x21663,x21662,x21664,x21665)) % 181.55/181.55 [2167]~E(x21671,x21672)+E(f671(x21673,x21674,x21671,x21675),f671(x21673,x21674,x21672,x21675)) % 181.55/181.55 [2168]~E(x21681,x21682)+E(f671(x21683,x21684,x21685,x21681),f671(x21683,x21684,x21685,x21682)) % 181.55/181.55 [2169]~E(x21691,x21692)+E(f276(x21691,x21693,x21694,x21695),f276(x21692,x21693,x21694,x21695)) % 181.55/181.55 [2170]~E(x21701,x21702)+E(f276(x21703,x21701,x21704,x21705),f276(x21703,x21702,x21704,x21705)) % 181.55/181.55 [2171]~E(x21711,x21712)+E(f276(x21713,x21714,x21711,x21715),f276(x21713,x21714,x21712,x21715)) % 181.55/181.55 [2172]~E(x21721,x21722)+E(f276(x21723,x21724,x21725,x21721),f276(x21723,x21724,x21725,x21722)) % 181.55/181.55 [2173]~E(x21731,x21732)+E(f372(x21731,x21733,x21734),f372(x21732,x21733,x21734)) % 181.55/181.55 [2174]~E(x21741,x21742)+E(f372(x21743,x21741,x21744),f372(x21743,x21742,x21744)) % 181.55/181.55 [2175]~E(x21751,x21752)+E(f372(x21753,x21754,x21751),f372(x21753,x21754,x21752)) % 181.55/181.55 [2176]~E(x21761,x21762)+E(f367(x21761,x21763,x21764),f367(x21762,x21763,x21764)) % 181.55/181.55 [2177]~E(x21771,x21772)+E(f367(x21773,x21771,x21774),f367(x21773,x21772,x21774)) % 181.55/181.55 [2178]~E(x21781,x21782)+E(f367(x21783,x21784,x21781),f367(x21783,x21784,x21782)) % 181.55/181.55 [2179]~E(x21791,x21792)+E(f697(x21791,x21793,x21794,x21795),f697(x21792,x21793,x21794,x21795)) % 181.55/181.55 [2180]~E(x21801,x21802)+E(f697(x21803,x21801,x21804,x21805),f697(x21803,x21802,x21804,x21805)) % 181.55/181.55 [2181]~E(x21811,x21812)+E(f697(x21813,x21814,x21811,x21815),f697(x21813,x21814,x21812,x21815)) % 181.55/181.55 [2182]~E(x21821,x21822)+E(f697(x21823,x21824,x21825,x21821),f697(x21823,x21824,x21825,x21822)) % 181.55/181.55 [2183]~E(x21831,x21832)+E(f482(x21831,x21833,x21834),f482(x21832,x21833,x21834)) % 181.55/181.55 [2184]~E(x21841,x21842)+E(f482(x21843,x21841,x21844),f482(x21843,x21842,x21844)) % 181.55/181.55 [2185]~E(x21851,x21852)+E(f482(x21853,x21854,x21851),f482(x21853,x21854,x21852)) % 181.55/181.55 [2186]~E(x21861,x21862)+E(f348(x21861,x21863,x21864),f348(x21862,x21863,x21864)) % 181.55/181.55 [2187]~E(x21871,x21872)+E(f348(x21873,x21871,x21874),f348(x21873,x21872,x21874)) % 181.55/181.55 [2188]~E(x21881,x21882)+E(f348(x21883,x21884,x21881),f348(x21883,x21884,x21882)) % 181.55/181.55 [2189]~E(x21891,x21892)+E(f701(x21891,x21893,x21894,x21895),f701(x21892,x21893,x21894,x21895)) % 181.55/181.55 [2190]~E(x21901,x21902)+E(f701(x21903,x21901,x21904,x21905),f701(x21903,x21902,x21904,x21905)) % 181.55/181.55 [2191]~E(x21911,x21912)+E(f701(x21913,x21914,x21911,x21915),f701(x21913,x21914,x21912,x21915)) % 181.55/181.55 [2192]~E(x21921,x21922)+E(f701(x21923,x21924,x21925,x21921),f701(x21923,x21924,x21925,x21922)) % 181.55/181.55 [2193]~E(x21931,x21932)+E(f679(x21931,x21933,x21934),f679(x21932,x21933,x21934)) % 181.55/181.55 [2194]~E(x21941,x21942)+E(f679(x21943,x21941,x21944),f679(x21943,x21942,x21944)) % 181.55/181.55 [2195]~E(x21951,x21952)+E(f679(x21953,x21954,x21951),f679(x21953,x21954,x21952)) % 181.55/181.55 [2196]~E(x21961,x21962)+E(f535(x21961,x21963),f535(x21962,x21963)) % 181.55/181.55 [2197]~E(x21971,x21972)+E(f535(x21973,x21971),f535(x21973,x21972)) % 181.55/181.55 [2198]~E(x21981,x21982)+E(f656(x21981,x21983,x21984,x21985,x21986,x21987),f656(x21982,x21983,x21984,x21985,x21986,x21987)) % 181.55/181.55 [2199]~E(x21991,x21992)+E(f656(x21993,x21991,x21994,x21995,x21996,x21997),f656(x21993,x21992,x21994,x21995,x21996,x21997)) % 181.55/181.55 [2200]~E(x22001,x22002)+E(f656(x22003,x22004,x22001,x22005,x22006,x22007),f656(x22003,x22004,x22002,x22005,x22006,x22007)) % 181.55/181.55 [2201]~E(x22011,x22012)+E(f656(x22013,x22014,x22015,x22011,x22016,x22017),f656(x22013,x22014,x22015,x22012,x22016,x22017)) % 181.55/181.55 [2202]~E(x22021,x22022)+E(f656(x22023,x22024,x22025,x22026,x22021,x22027),f656(x22023,x22024,x22025,x22026,x22022,x22027)) % 181.55/181.55 [2203]~E(x22031,x22032)+E(f656(x22033,x22034,x22035,x22036,x22037,x22031),f656(x22033,x22034,x22035,x22036,x22037,x22032)) % 181.55/181.55 [2204]~E(x22041,x22042)+E(f129(x22041,x22043,x22044,x22045,x22046),f129(x22042,x22043,x22044,x22045,x22046)) % 181.55/181.55 [2205]~E(x22051,x22052)+E(f129(x22053,x22051,x22054,x22055,x22056),f129(x22053,x22052,x22054,x22055,x22056)) % 181.55/181.55 [2206]~E(x22061,x22062)+E(f129(x22063,x22064,x22061,x22065,x22066),f129(x22063,x22064,x22062,x22065,x22066)) % 181.55/181.55 [2207]~E(x22071,x22072)+E(f129(x22073,x22074,x22075,x22071,x22076),f129(x22073,x22074,x22075,x22072,x22076)) % 181.55/181.55 [2208]~E(x22081,x22082)+E(f129(x22083,x22084,x22085,x22086,x22081),f129(x22083,x22084,x22085,x22086,x22082)) % 181.55/181.55 [2209]~E(x22091,x22092)+E(f786(x22091,x22093,x22094,x22095),f786(x22092,x22093,x22094,x22095)) % 181.55/181.55 [2210]~E(x22101,x22102)+E(f786(x22103,x22101,x22104,x22105),f786(x22103,x22102,x22104,x22105)) % 181.55/181.55 [2211]~E(x22111,x22112)+E(f786(x22113,x22114,x22111,x22115),f786(x22113,x22114,x22112,x22115)) % 181.55/181.55 [2212]~E(x22121,x22122)+E(f786(x22123,x22124,x22125,x22121),f786(x22123,x22124,x22125,x22122)) % 181.55/181.55 [2213]~E(x22131,x22132)+E(f98(x22131,x22133,x22134,x22135),f98(x22132,x22133,x22134,x22135)) % 181.55/181.55 [2214]~E(x22141,x22142)+E(f98(x22143,x22141,x22144,x22145),f98(x22143,x22142,x22144,x22145)) % 181.55/181.55 [2215]~E(x22151,x22152)+E(f98(x22153,x22154,x22151,x22155),f98(x22153,x22154,x22152,x22155)) % 181.55/181.55 [2216]~E(x22161,x22162)+E(f98(x22163,x22164,x22165,x22161),f98(x22163,x22164,x22165,x22162)) % 181.55/181.55 [2217]~E(x22171,x22172)+E(f590(x22171,x22173,x22174),f590(x22172,x22173,x22174)) % 181.55/181.55 [2218]~E(x22181,x22182)+E(f590(x22183,x22181,x22184),f590(x22183,x22182,x22184)) % 181.55/181.55 [2219]~E(x22191,x22192)+E(f590(x22193,x22194,x22191),f590(x22193,x22194,x22192)) % 181.55/181.55 [2220]~E(x22201,x22202)+E(f527(x22201,x22203,x22204),f527(x22202,x22203,x22204)) % 181.55/181.55 [2221]~E(x22211,x22212)+E(f527(x22213,x22211,x22214),f527(x22213,x22212,x22214)) % 181.55/181.55 [2222]~E(x22221,x22222)+E(f527(x22223,x22224,x22221),f527(x22223,x22224,x22222)) % 181.55/181.55 [2223]~E(x22231,x22232)+E(f725(x22231,x22233,x22234),f725(x22232,x22233,x22234)) % 181.55/181.55 [2224]~E(x22241,x22242)+E(f725(x22243,x22241,x22244),f725(x22243,x22242,x22244)) % 181.55/181.55 [2225]~E(x22251,x22252)+E(f725(x22253,x22254,x22251),f725(x22253,x22254,x22252)) % 181.55/181.55 [2226]~E(x22261,x22262)+E(f128(x22261,x22263),f128(x22262,x22263)) % 181.55/181.55 [2227]~E(x22271,x22272)+E(f128(x22273,x22271),f128(x22273,x22272)) % 181.55/181.55 [2228]~E(x22281,x22282)+E(f287(x22281,x22283,x22284),f287(x22282,x22283,x22284)) % 181.55/181.55 [2229]~E(x22291,x22292)+E(f287(x22293,x22291,x22294),f287(x22293,x22292,x22294)) % 181.55/181.55 [2230]~E(x22301,x22302)+E(f287(x22303,x22304,x22301),f287(x22303,x22304,x22302)) % 181.55/181.55 [2231]~E(x22311,x22312)+E(f492(x22311,x22313,x22314,x22315,x22316,x22317),f492(x22312,x22313,x22314,x22315,x22316,x22317)) % 181.55/181.55 [2232]~E(x22321,x22322)+E(f492(x22323,x22321,x22324,x22325,x22326,x22327),f492(x22323,x22322,x22324,x22325,x22326,x22327)) % 181.55/181.55 [2233]~E(x22331,x22332)+E(f492(x22333,x22334,x22331,x22335,x22336,x22337),f492(x22333,x22334,x22332,x22335,x22336,x22337)) % 181.55/181.55 [2234]~E(x22341,x22342)+E(f492(x22343,x22344,x22345,x22341,x22346,x22347),f492(x22343,x22344,x22345,x22342,x22346,x22347)) % 181.55/181.55 [2235]~E(x22351,x22352)+E(f492(x22353,x22354,x22355,x22356,x22351,x22357),f492(x22353,x22354,x22355,x22356,x22352,x22357)) % 181.55/181.55 [2236]~E(x22361,x22362)+E(f492(x22363,x22364,x22365,x22366,x22367,x22361),f492(x22363,x22364,x22365,x22366,x22367,x22362)) % 181.55/181.55 [2237]~E(x22371,x22372)+E(f537(x22371,x22373,x22374),f537(x22372,x22373,x22374)) % 181.55/181.55 [2238]~E(x22381,x22382)+E(f537(x22383,x22381,x22384),f537(x22383,x22382,x22384)) % 181.55/181.55 [2239]~E(x22391,x22392)+E(f537(x22393,x22394,x22391),f537(x22393,x22394,x22392)) % 181.55/181.55 [2240]~E(x22401,x22402)+E(f702(x22401,x22403,x22404,x22405,x22406),f702(x22402,x22403,x22404,x22405,x22406)) % 181.55/181.55 [2241]~E(x22411,x22412)+E(f702(x22413,x22411,x22414,x22415,x22416),f702(x22413,x22412,x22414,x22415,x22416)) % 181.55/181.55 [2242]~E(x22421,x22422)+E(f702(x22423,x22424,x22421,x22425,x22426),f702(x22423,x22424,x22422,x22425,x22426)) % 181.55/181.55 [2243]~E(x22431,x22432)+E(f702(x22433,x22434,x22435,x22431,x22436),f702(x22433,x22434,x22435,x22432,x22436)) % 181.55/181.55 [2244]~E(x22441,x22442)+E(f702(x22443,x22444,x22445,x22446,x22441),f702(x22443,x22444,x22445,x22446,x22442)) % 181.55/181.55 [2245]~E(x22451,x22452)+E(f389(x22451,x22453,x22454,x22455,x22456),f389(x22452,x22453,x22454,x22455,x22456)) % 181.55/181.55 [2246]~E(x22461,x22462)+E(f389(x22463,x22461,x22464,x22465,x22466),f389(x22463,x22462,x22464,x22465,x22466)) % 181.55/181.55 [2247]~E(x22471,x22472)+E(f389(x22473,x22474,x22471,x22475,x22476),f389(x22473,x22474,x22472,x22475,x22476)) % 181.55/181.55 [2248]~E(x22481,x22482)+E(f389(x22483,x22484,x22485,x22481,x22486),f389(x22483,x22484,x22485,x22482,x22486)) % 181.55/181.55 [2249]~E(x22491,x22492)+E(f389(x22493,x22494,x22495,x22496,x22491),f389(x22493,x22494,x22495,x22496,x22492)) % 181.55/181.55 [2250]~E(x22501,x22502)+E(f603(x22501,x22503),f603(x22502,x22503)) % 181.55/181.55 [2251]~E(x22511,x22512)+E(f603(x22513,x22511),f603(x22513,x22512)) % 181.55/181.55 [2252]~E(x22521,x22522)+E(f227(x22521,x22523,x22524,x22525),f227(x22522,x22523,x22524,x22525)) % 181.55/181.55 [2253]~E(x22531,x22532)+E(f227(x22533,x22531,x22534,x22535),f227(x22533,x22532,x22534,x22535)) % 181.55/181.55 [2254]~E(x22541,x22542)+E(f227(x22543,x22544,x22541,x22545),f227(x22543,x22544,x22542,x22545)) % 181.55/181.55 [2255]~E(x22551,x22552)+E(f227(x22553,x22554,x22555,x22551),f227(x22553,x22554,x22555,x22552)) % 181.55/181.55 [2256]~E(x22561,x22562)+E(f340(x22561,x22563),f340(x22562,x22563)) % 181.55/181.55 [2257]~E(x22571,x22572)+E(f340(x22573,x22571),f340(x22573,x22572)) % 181.55/181.55 [2258]~E(x22581,x22582)+E(f455(x22581,x22583,x22584,x22585),f455(x22582,x22583,x22584,x22585)) % 181.55/181.55 [2259]~E(x22591,x22592)+E(f455(x22593,x22591,x22594,x22595),f455(x22593,x22592,x22594,x22595)) % 181.55/181.55 [2260]~E(x22601,x22602)+E(f455(x22603,x22604,x22601,x22605),f455(x22603,x22604,x22602,x22605)) % 181.55/181.55 [2261]~E(x22611,x22612)+E(f455(x22613,x22614,x22615,x22611),f455(x22613,x22614,x22615,x22612)) % 181.55/181.55 [2262]~E(x22621,x22622)+E(f763(x22621,x22623,x22624),f763(x22622,x22623,x22624)) % 181.55/181.55 [2263]~E(x22631,x22632)+E(f763(x22633,x22631,x22634),f763(x22633,x22632,x22634)) % 181.55/181.55 [2264]~E(x22641,x22642)+E(f763(x22643,x22644,x22641),f763(x22643,x22644,x22642)) % 181.55/181.55 [2265]~E(x22651,x22652)+E(f831(x22651,x22653,x22654,x22655,x22656),f831(x22652,x22653,x22654,x22655,x22656)) % 181.55/181.55 [2266]~E(x22661,x22662)+E(f831(x22663,x22661,x22664,x22665,x22666),f831(x22663,x22662,x22664,x22665,x22666)) % 181.55/181.55 [2267]~E(x22671,x22672)+E(f831(x22673,x22674,x22671,x22675,x22676),f831(x22673,x22674,x22672,x22675,x22676)) % 181.55/181.55 [2268]~E(x22681,x22682)+E(f831(x22683,x22684,x22685,x22681,x22686),f831(x22683,x22684,x22685,x22682,x22686)) % 181.55/181.55 [2269]~E(x22691,x22692)+E(f831(x22693,x22694,x22695,x22696,x22691),f831(x22693,x22694,x22695,x22696,x22692)) % 181.55/181.55 [2270]~E(x22701,x22702)+E(f736(x22701,x22703),f736(x22702,x22703)) % 181.55/181.55 [2271]~E(x22711,x22712)+E(f736(x22713,x22711),f736(x22713,x22712)) % 181.55/181.55 [2272]~E(x22721,x22722)+E(f384(x22721,x22723,x22724),f384(x22722,x22723,x22724)) % 181.55/181.55 [2273]~E(x22731,x22732)+E(f384(x22733,x22731,x22734),f384(x22733,x22732,x22734)) % 181.55/181.55 [2274]~E(x22741,x22742)+E(f384(x22743,x22744,x22741),f384(x22743,x22744,x22742)) % 181.55/181.55 [2275]~E(x22751,x22752)+E(f198(x22751,x22753,x22754,x22755),f198(x22752,x22753,x22754,x22755)) % 181.55/181.55 [2276]~E(x22761,x22762)+E(f198(x22763,x22761,x22764,x22765),f198(x22763,x22762,x22764,x22765)) % 181.55/181.55 [2277]~E(x22771,x22772)+E(f198(x22773,x22774,x22771,x22775),f198(x22773,x22774,x22772,x22775)) % 181.55/181.55 [2278]~E(x22781,x22782)+E(f198(x22783,x22784,x22785,x22781),f198(x22783,x22784,x22785,x22782)) % 181.55/181.55 [2279]~E(x22791,x22792)+E(f709(x22791,x22793,x22794,x22795),f709(x22792,x22793,x22794,x22795)) % 181.55/181.55 [2280]~E(x22801,x22802)+E(f709(x22803,x22801,x22804,x22805),f709(x22803,x22802,x22804,x22805)) % 181.55/181.55 [2281]~E(x22811,x22812)+E(f709(x22813,x22814,x22811,x22815),f709(x22813,x22814,x22812,x22815)) % 181.55/181.55 [2282]~E(x22821,x22822)+E(f709(x22823,x22824,x22825,x22821),f709(x22823,x22824,x22825,x22822)) % 181.55/181.55 [2283]~E(x22831,x22832)+E(f290(x22831,x22833,x22834),f290(x22832,x22833,x22834)) % 181.55/181.55 [2284]~E(x22841,x22842)+E(f290(x22843,x22841,x22844),f290(x22843,x22842,x22844)) % 181.55/181.55 [2285]~E(x22851,x22852)+E(f290(x22853,x22854,x22851),f290(x22853,x22854,x22852)) % 181.55/181.55 [2286]~E(x22861,x22862)+E(f554(x22861,x22863,x22864),f554(x22862,x22863,x22864)) % 181.55/181.55 [2287]~E(x22871,x22872)+E(f554(x22873,x22871,x22874),f554(x22873,x22872,x22874)) % 181.55/181.55 [2288]~E(x22881,x22882)+E(f554(x22883,x22884,x22881),f554(x22883,x22884,x22882)) % 181.55/181.55 [2289]~E(x22891,x22892)+E(f776(x22891,x22893,x22894,x22895),f776(x22892,x22893,x22894,x22895)) % 181.55/181.55 [2290]~E(x22901,x22902)+E(f776(x22903,x22901,x22904,x22905),f776(x22903,x22902,x22904,x22905)) % 181.55/181.55 [2291]~E(x22911,x22912)+E(f776(x22913,x22914,x22911,x22915),f776(x22913,x22914,x22912,x22915)) % 181.55/181.55 [2292]~E(x22921,x22922)+E(f776(x22923,x22924,x22925,x22921),f776(x22923,x22924,x22925,x22922)) % 181.55/181.55 [2293]~E(x22931,x22932)+E(f765(x22931,x22933,x22934),f765(x22932,x22933,x22934)) % 181.55/181.55 [2294]~E(x22941,x22942)+E(f765(x22943,x22941,x22944),f765(x22943,x22942,x22944)) % 181.55/181.55 [2295]~E(x22951,x22952)+E(f765(x22953,x22954,x22951),f765(x22953,x22954,x22952)) % 181.55/181.55 [2296]~E(x22961,x22962)+E(f658(x22961,x22963,x22964,x22965,x22966),f658(x22962,x22963,x22964,x22965,x22966)) % 181.55/181.55 [2297]~E(x22971,x22972)+E(f658(x22973,x22971,x22974,x22975,x22976),f658(x22973,x22972,x22974,x22975,x22976)) % 181.55/181.55 [2298]~E(x22981,x22982)+E(f658(x22983,x22984,x22981,x22985,x22986),f658(x22983,x22984,x22982,x22985,x22986)) % 181.55/181.55 [2299]~E(x22991,x22992)+E(f658(x22993,x22994,x22995,x22991,x22996),f658(x22993,x22994,x22995,x22992,x22996)) % 181.55/181.55 [2300]~E(x23001,x23002)+E(f658(x23003,x23004,x23005,x23006,x23001),f658(x23003,x23004,x23005,x23006,x23002)) % 181.55/181.55 [2301]~E(x23011,x23012)+E(f799(x23011,x23013),f799(x23012,x23013)) % 181.55/181.55 [2302]~E(x23021,x23022)+E(f799(x23023,x23021),f799(x23023,x23022)) % 181.55/181.55 [2303]~E(x23031,x23032)+E(f840(x23031,x23033),f840(x23032,x23033)) % 181.55/181.55 [2304]~E(x23041,x23042)+E(f840(x23043,x23041),f840(x23043,x23042)) % 181.55/181.55 [2305]~E(x23051,x23052)+E(f291(x23051,x23053,x23054,x23055),f291(x23052,x23053,x23054,x23055)) % 181.55/181.55 [2306]~E(x23061,x23062)+E(f291(x23063,x23061,x23064,x23065),f291(x23063,x23062,x23064,x23065)) % 181.55/181.55 [2307]~E(x23071,x23072)+E(f291(x23073,x23074,x23071,x23075),f291(x23073,x23074,x23072,x23075)) % 181.55/181.55 [2308]~E(x23081,x23082)+E(f291(x23083,x23084,x23085,x23081),f291(x23083,x23084,x23085,x23082)) % 181.55/181.55 [2309]~E(x23091,x23092)+E(f705(x23091,x23093,x23094),f705(x23092,x23093,x23094)) % 181.55/181.55 [2310]~E(x23101,x23102)+E(f705(x23103,x23101,x23104),f705(x23103,x23102,x23104)) % 181.55/181.55 [2311]~E(x23111,x23112)+E(f705(x23113,x23114,x23111),f705(x23113,x23114,x23112)) % 181.55/181.55 [2312]~E(x23121,x23122)+E(f472(x23121,x23123,x23124,x23125),f472(x23122,x23123,x23124,x23125)) % 181.55/181.55 [2313]~E(x23131,x23132)+E(f472(x23133,x23131,x23134,x23135),f472(x23133,x23132,x23134,x23135)) % 181.55/181.55 [2314]~E(x23141,x23142)+E(f472(x23143,x23144,x23141,x23145),f472(x23143,x23144,x23142,x23145)) % 181.55/181.55 [2315]~E(x23151,x23152)+E(f472(x23153,x23154,x23155,x23151),f472(x23153,x23154,x23155,x23152)) % 181.55/181.55 [2316]~E(x23161,x23162)+E(f733(x23161,x23163,x23164),f733(x23162,x23163,x23164)) % 181.55/181.55 [2317]~E(x23171,x23172)+E(f733(x23173,x23171,x23174),f733(x23173,x23172,x23174)) % 181.55/181.55 [2318]~E(x23181,x23182)+E(f733(x23183,x23184,x23181),f733(x23183,x23184,x23182)) % 181.55/181.55 [2319]~E(x23191,x23192)+E(f566(x23191,x23193,x23194,x23195,x23196,x23197),f566(x23192,x23193,x23194,x23195,x23196,x23197)) % 181.55/181.55 [2320]~E(x23201,x23202)+E(f566(x23203,x23201,x23204,x23205,x23206,x23207),f566(x23203,x23202,x23204,x23205,x23206,x23207)) % 181.55/181.55 [2321]~E(x23211,x23212)+E(f566(x23213,x23214,x23211,x23215,x23216,x23217),f566(x23213,x23214,x23212,x23215,x23216,x23217)) % 181.55/181.55 [2322]~E(x23221,x23222)+E(f566(x23223,x23224,x23225,x23221,x23226,x23227),f566(x23223,x23224,x23225,x23222,x23226,x23227)) % 181.55/181.55 [2323]~E(x23231,x23232)+E(f566(x23233,x23234,x23235,x23236,x23231,x23237),f566(x23233,x23234,x23235,x23236,x23232,x23237)) % 181.55/181.55 [2324]~E(x23241,x23242)+E(f566(x23243,x23244,x23245,x23246,x23247,x23241),f566(x23243,x23244,x23245,x23246,x23247,x23242)) % 181.55/181.55 [2325]~E(x23251,x23252)+E(f653(x23251,x23253,x23254,x23255),f653(x23252,x23253,x23254,x23255)) % 181.55/181.55 [2326]~E(x23261,x23262)+E(f653(x23263,x23261,x23264,x23265),f653(x23263,x23262,x23264,x23265)) % 181.55/181.55 [2327]~E(x23271,x23272)+E(f653(x23273,x23274,x23271,x23275),f653(x23273,x23274,x23272,x23275)) % 181.55/181.55 [2328]~E(x23281,x23282)+E(f653(x23283,x23284,x23285,x23281),f653(x23283,x23284,x23285,x23282)) % 181.55/181.55 [2329]~E(x23291,x23292)+E(f629(x23291,x23293,x23294),f629(x23292,x23293,x23294)) % 181.55/181.55 [2330]~E(x23301,x23302)+E(f629(x23303,x23301,x23304),f629(x23303,x23302,x23304)) % 181.55/181.55 [2331]~E(x23311,x23312)+E(f629(x23313,x23314,x23311),f629(x23313,x23314,x23312)) % 181.55/181.55 [2332]~E(x23321,x23322)+E(f410(x23321),f410(x23322)) % 181.55/181.55 [2333]~E(x23331,x23332)+E(f644(x23331,x23333,x23334,x23335,x23336),f644(x23332,x23333,x23334,x23335,x23336)) % 181.55/181.55 [2334]~E(x23341,x23342)+E(f644(x23343,x23341,x23344,x23345,x23346),f644(x23343,x23342,x23344,x23345,x23346)) % 181.55/181.55 [2335]~E(x23351,x23352)+E(f644(x23353,x23354,x23351,x23355,x23356),f644(x23353,x23354,x23352,x23355,x23356)) % 181.55/181.55 [2336]~E(x23361,x23362)+E(f644(x23363,x23364,x23365,x23361,x23366),f644(x23363,x23364,x23365,x23362,x23366)) % 181.55/181.55 [2337]~E(x23371,x23372)+E(f644(x23373,x23374,x23375,x23376,x23371),f644(x23373,x23374,x23375,x23376,x23372)) % 181.55/181.55 [2338]~E(x23381,x23382)+E(f557(x23381,x23383),f557(x23382,x23383)) % 181.55/181.55 [2339]~E(x23391,x23392)+E(f557(x23393,x23391),f557(x23393,x23392)) % 181.55/181.55 [2340]~E(x23401,x23402)+E(f721(x23401,x23403),f721(x23402,x23403)) % 181.55/181.55 [2341]~E(x23411,x23412)+E(f721(x23413,x23411),f721(x23413,x23412)) % 181.55/181.55 [2342]~E(x23421,x23422)+E(f442(x23421,x23423),f442(x23422,x23423)) % 181.55/181.55 [2343]~E(x23431,x23432)+E(f442(x23433,x23431),f442(x23433,x23432)) % 181.55/181.55 [2344]~E(x23441,x23442)+E(f713(x23441,x23443,x23444,x23445),f713(x23442,x23443,x23444,x23445)) % 181.55/181.55 [2345]~E(x23451,x23452)+E(f713(x23453,x23451,x23454,x23455),f713(x23453,x23452,x23454,x23455)) % 181.55/181.55 [2346]~E(x23461,x23462)+E(f713(x23463,x23464,x23461,x23465),f713(x23463,x23464,x23462,x23465)) % 181.55/181.55 [2347]~E(x23471,x23472)+E(f713(x23473,x23474,x23475,x23471),f713(x23473,x23474,x23475,x23472)) % 181.55/181.55 [2348]~E(x23481,x23482)+E(f739(x23481,x23483,x23484),f739(x23482,x23483,x23484)) % 181.55/181.55 [2349]~E(x23491,x23492)+E(f739(x23493,x23491,x23494),f739(x23493,x23492,x23494)) % 181.55/181.55 [2350]~E(x23501,x23502)+E(f739(x23503,x23504,x23501),f739(x23503,x23504,x23502)) % 181.55/181.55 [2351]~E(x23511,x23512)+E(f119(x23511,x23513,x23514,x23515),f119(x23512,x23513,x23514,x23515)) % 181.55/181.55 [2352]~E(x23521,x23522)+E(f119(x23523,x23521,x23524,x23525),f119(x23523,x23522,x23524,x23525)) % 181.55/181.55 [2353]~E(x23531,x23532)+E(f119(x23533,x23534,x23531,x23535),f119(x23533,x23534,x23532,x23535)) % 181.55/181.55 [2354]~E(x23541,x23542)+E(f119(x23543,x23544,x23545,x23541),f119(x23543,x23544,x23545,x23542)) % 181.55/181.55 [2355]~E(x23551,x23552)+E(f342(x23551,x23553,x23554),f342(x23552,x23553,x23554)) % 181.55/181.55 [2356]~E(x23561,x23562)+E(f342(x23563,x23561,x23564),f342(x23563,x23562,x23564)) % 181.55/181.55 [2357]~E(x23571,x23572)+E(f342(x23573,x23574,x23571),f342(x23573,x23574,x23572)) % 181.55/181.55 [2358]~E(x23581,x23582)+E(f212(x23581,x23583,x23584,x23585,x23586,x23587,x23588),f212(x23582,x23583,x23584,x23585,x23586,x23587,x23588)) % 181.55/181.55 [2359]~E(x23591,x23592)+E(f212(x23593,x23591,x23594,x23595,x23596,x23597,x23598),f212(x23593,x23592,x23594,x23595,x23596,x23597,x23598)) % 181.55/181.55 [2360]~E(x23601,x23602)+E(f212(x23603,x23604,x23601,x23605,x23606,x23607,x23608),f212(x23603,x23604,x23602,x23605,x23606,x23607,x23608)) % 181.55/181.55 [2361]~E(x23611,x23612)+E(f212(x23613,x23614,x23615,x23611,x23616,x23617,x23618),f212(x23613,x23614,x23615,x23612,x23616,x23617,x23618)) % 181.55/181.55 [2362]~E(x23621,x23622)+E(f212(x23623,x23624,x23625,x23626,x23621,x23627,x23628),f212(x23623,x23624,x23625,x23626,x23622,x23627,x23628)) % 181.55/181.55 [2363]~E(x23631,x23632)+E(f212(x23633,x23634,x23635,x23636,x23637,x23631,x23638),f212(x23633,x23634,x23635,x23636,x23637,x23632,x23638)) % 181.55/181.55 [2364]~E(x23641,x23642)+E(f212(x23643,x23644,x23645,x23646,x23647,x23648,x23641),f212(x23643,x23644,x23645,x23646,x23647,x23648,x23642)) % 181.55/181.55 [2365]~E(x23651,x23652)+E(f418(x23651,x23653),f418(x23652,x23653)) % 181.55/181.55 [2366]~E(x23661,x23662)+E(f418(x23663,x23661),f418(x23663,x23662)) % 181.55/181.55 [2367]~E(x23671,x23672)+E(f700(x23671,x23673,x23674,x23675),f700(x23672,x23673,x23674,x23675)) % 181.55/181.55 [2368]~E(x23681,x23682)+E(f700(x23683,x23681,x23684,x23685),f700(x23683,x23682,x23684,x23685)) % 181.55/181.55 [2369]~E(x23691,x23692)+E(f700(x23693,x23694,x23691,x23695),f700(x23693,x23694,x23692,x23695)) % 181.55/181.55 [2370]~E(x23701,x23702)+E(f700(x23703,x23704,x23705,x23701),f700(x23703,x23704,x23705,x23702)) % 181.55/181.55 [2371]~E(x23711,x23712)+E(f74(x23711,x23713),f74(x23712,x23713)) % 181.55/181.55 [2372]~E(x23721,x23722)+E(f74(x23723,x23721),f74(x23723,x23722)) % 181.55/181.55 [2373]~E(x23731,x23732)+E(f477(x23731,x23733,x23734,x23735),f477(x23732,x23733,x23734,x23735)) % 181.55/181.55 [2374]~E(x23741,x23742)+E(f477(x23743,x23741,x23744,x23745),f477(x23743,x23742,x23744,x23745)) % 181.55/181.55 [2375]~E(x23751,x23752)+E(f477(x23753,x23754,x23751,x23755),f477(x23753,x23754,x23752,x23755)) % 181.55/181.55 [2376]~E(x23761,x23762)+E(f477(x23763,x23764,x23765,x23761),f477(x23763,x23764,x23765,x23762)) % 181.55/181.55 [2377]~E(x23771,x23772)+E(f271(x23771,x23773),f271(x23772,x23773)) % 181.55/181.55 [2378]~E(x23781,x23782)+E(f271(x23783,x23781),f271(x23783,x23782)) % 181.55/181.55 [2379]~E(x23791,x23792)+E(f226(x23791,x23793,x23794),f226(x23792,x23793,x23794)) % 181.55/181.55 [2380]~E(x23801,x23802)+E(f226(x23803,x23801,x23804),f226(x23803,x23802,x23804)) % 181.55/181.55 [2381]~E(x23811,x23812)+E(f226(x23813,x23814,x23811),f226(x23813,x23814,x23812)) % 181.55/181.55 [2382]~E(x23821,x23822)+E(f778(x23821,x23823,x23824),f778(x23822,x23823,x23824)) % 181.55/181.55 [2383]~E(x23831,x23832)+E(f778(x23833,x23831,x23834),f778(x23833,x23832,x23834)) % 181.55/181.55 [2384]~E(x23841,x23842)+E(f778(x23843,x23844,x23841),f778(x23843,x23844,x23842)) % 181.55/181.55 [2385]~E(x23851,x23852)+E(f773(x23851,x23853,x23854,x23855,x23856,x23857,x23858),f773(x23852,x23853,x23854,x23855,x23856,x23857,x23858)) % 181.55/181.55 [2386]~E(x23861,x23862)+E(f773(x23863,x23861,x23864,x23865,x23866,x23867,x23868),f773(x23863,x23862,x23864,x23865,x23866,x23867,x23868)) % 181.55/181.55 [2387]~E(x23871,x23872)+E(f773(x23873,x23874,x23871,x23875,x23876,x23877,x23878),f773(x23873,x23874,x23872,x23875,x23876,x23877,x23878)) % 181.55/181.55 [2388]~E(x23881,x23882)+E(f773(x23883,x23884,x23885,x23881,x23886,x23887,x23888),f773(x23883,x23884,x23885,x23882,x23886,x23887,x23888)) % 181.55/181.55 [2389]~E(x23891,x23892)+E(f773(x23893,x23894,x23895,x23896,x23891,x23897,x23898),f773(x23893,x23894,x23895,x23896,x23892,x23897,x23898)) % 181.55/181.55 [2390]~E(x23901,x23902)+E(f773(x23903,x23904,x23905,x23906,x23907,x23901,x23908),f773(x23903,x23904,x23905,x23906,x23907,x23902,x23908)) % 181.55/181.55 [2391]~E(x23911,x23912)+E(f773(x23913,x23914,x23915,x23916,x23917,x23918,x23911),f773(x23913,x23914,x23915,x23916,x23917,x23918,x23912)) % 181.55/181.55 [2392]~E(x23921,x23922)+E(f684(x23921,x23923),f684(x23922,x23923)) % 181.55/181.55 [2393]~E(x23931,x23932)+E(f684(x23933,x23931),f684(x23933,x23932)) % 181.55/181.55 [2394]~E(x23941,x23942)+E(f601(x23941,x23943),f601(x23942,x23943)) % 181.55/181.55 [2395]~E(x23951,x23952)+E(f601(x23953,x23951),f601(x23953,x23952)) % 181.55/181.55 [2396]~E(x23961,x23962)+E(f333(x23961,x23963,x23964),f333(x23962,x23963,x23964)) % 181.55/181.55 [2397]~E(x23971,x23972)+E(f333(x23973,x23971,x23974),f333(x23973,x23972,x23974)) % 181.55/181.55 [2398]~E(x23981,x23982)+E(f333(x23983,x23984,x23981),f333(x23983,x23984,x23982)) % 181.55/181.55 [2399]~E(x23991,x23992)+E(f849(x23991,x23993,x23994,x23995),f849(x23992,x23993,x23994,x23995)) % 181.55/181.55 [2400]~E(x24001,x24002)+E(f849(x24003,x24001,x24004,x24005),f849(x24003,x24002,x24004,x24005)) % 181.55/181.55 [2401]~E(x24011,x24012)+E(f849(x24013,x24014,x24011,x24015),f849(x24013,x24014,x24012,x24015)) % 181.55/181.55 [2402]~E(x24021,x24022)+E(f849(x24023,x24024,x24025,x24021),f849(x24023,x24024,x24025,x24022)) % 181.55/181.55 [2403]~E(x24031,x24032)+E(f400(x24031,x24033,x24034),f400(x24032,x24033,x24034)) % 181.55/181.55 [2404]~E(x24041,x24042)+E(f400(x24043,x24041,x24044),f400(x24043,x24042,x24044)) % 181.55/181.55 [2405]~E(x24051,x24052)+E(f400(x24053,x24054,x24051),f400(x24053,x24054,x24052)) % 181.55/181.55 [2406]~E(x24061,x24062)+E(f618(x24061,x24063,x24064,x24065,x24066),f618(x24062,x24063,x24064,x24065,x24066)) % 181.55/181.55 [2407]~E(x24071,x24072)+E(f618(x24073,x24071,x24074,x24075,x24076),f618(x24073,x24072,x24074,x24075,x24076)) % 181.55/181.55 [2408]~E(x24081,x24082)+E(f618(x24083,x24084,x24081,x24085,x24086),f618(x24083,x24084,x24082,x24085,x24086)) % 181.55/181.55 [2409]~E(x24091,x24092)+E(f618(x24093,x24094,x24095,x24091,x24096),f618(x24093,x24094,x24095,x24092,x24096)) % 181.55/181.55 [2410]~E(x24101,x24102)+E(f618(x24103,x24104,x24105,x24106,x24101),f618(x24103,x24104,x24105,x24106,x24102)) % 181.55/181.55 [2411]~E(x24111,x24112)+E(f441(x24111,x24113),f441(x24112,x24113)) % 181.55/181.55 [2412]~E(x24121,x24122)+E(f441(x24123,x24121),f441(x24123,x24122)) % 181.55/181.55 [2413]~E(x24131,x24132)+E(f501(x24131,x24133,x24134,x24135,x24136),f501(x24132,x24133,x24134,x24135,x24136)) % 181.55/181.55 [2414]~E(x24141,x24142)+E(f501(x24143,x24141,x24144,x24145,x24146),f501(x24143,x24142,x24144,x24145,x24146)) % 181.55/181.55 [2415]~E(x24151,x24152)+E(f501(x24153,x24154,x24151,x24155,x24156),f501(x24153,x24154,x24152,x24155,x24156)) % 181.55/181.55 [2416]~E(x24161,x24162)+E(f501(x24163,x24164,x24165,x24161,x24166),f501(x24163,x24164,x24165,x24162,x24166)) % 181.55/181.55 [2417]~E(x24171,x24172)+E(f501(x24173,x24174,x24175,x24176,x24171),f501(x24173,x24174,x24175,x24176,x24172)) % 181.55/181.55 [2418]~E(x24181,x24182)+E(f425(x24181),f425(x24182)) % 181.55/181.55 [2419]~E(x24191,x24192)+E(f510(x24191,x24193,x24194,x24195,x24196,x24197,x24198,x24199),f510(x24192,x24193,x24194,x24195,x24196,x24197,x24198,x24199)) % 181.55/181.55 [2420]~E(x24201,x24202)+E(f510(x24203,x24201,x24204,x24205,x24206,x24207,x24208,x24209),f510(x24203,x24202,x24204,x24205,x24206,x24207,x24208,x24209)) % 181.55/181.55 [2421]~E(x24211,x24212)+E(f510(x24213,x24214,x24211,x24215,x24216,x24217,x24218,x24219),f510(x24213,x24214,x24212,x24215,x24216,x24217,x24218,x24219)) % 181.55/181.55 [2422]~E(x24221,x24222)+E(f510(x24223,x24224,x24225,x24221,x24226,x24227,x24228,x24229),f510(x24223,x24224,x24225,x24222,x24226,x24227,x24228,x24229)) % 181.55/181.55 [2423]~E(x24231,x24232)+E(f510(x24233,x24234,x24235,x24236,x24231,x24237,x24238,x24239),f510(x24233,x24234,x24235,x24236,x24232,x24237,x24238,x24239)) % 181.55/181.55 [2424]~E(x24241,x24242)+E(f510(x24243,x24244,x24245,x24246,x24247,x24241,x24248,x24249),f510(x24243,x24244,x24245,x24246,x24247,x24242,x24248,x24249)) % 181.55/181.55 [2425]~E(x24251,x24252)+E(f510(x24253,x24254,x24255,x24256,x24257,x24258,x24251,x24259),f510(x24253,x24254,x24255,x24256,x24257,x24258,x24252,x24259)) % 181.55/181.55 [2426]~E(x24261,x24262)+E(f510(x24263,x24264,x24265,x24266,x24267,x24268,x24269,x24261),f510(x24263,x24264,x24265,x24266,x24267,x24268,x24269,x24262)) % 181.55/181.55 [2427]~E(x24271,x24272)+E(f843(x24271,x24273),f843(x24272,x24273)) % 181.55/181.55 [2428]~E(x24281,x24282)+E(f843(x24283,x24281),f843(x24283,x24282)) % 181.55/181.55 [2429]~E(x24291,x24292)+E(f646(x24291,x24293,x24294,x24295,x24296,x24297,x24298),f646(x24292,x24293,x24294,x24295,x24296,x24297,x24298)) % 181.55/181.55 [2430]~E(x24301,x24302)+E(f646(x24303,x24301,x24304,x24305,x24306,x24307,x24308),f646(x24303,x24302,x24304,x24305,x24306,x24307,x24308)) % 181.55/181.55 [2431]~E(x24311,x24312)+E(f646(x24313,x24314,x24311,x24315,x24316,x24317,x24318),f646(x24313,x24314,x24312,x24315,x24316,x24317,x24318)) % 181.55/181.55 [2432]~E(x24321,x24322)+E(f646(x24323,x24324,x24325,x24321,x24326,x24327,x24328),f646(x24323,x24324,x24325,x24322,x24326,x24327,x24328)) % 181.55/181.55 [2433]~E(x24331,x24332)+E(f646(x24333,x24334,x24335,x24336,x24331,x24337,x24338),f646(x24333,x24334,x24335,x24336,x24332,x24337,x24338)) % 181.55/181.55 [2434]~E(x24341,x24342)+E(f646(x24343,x24344,x24345,x24346,x24347,x24341,x24348),f646(x24343,x24344,x24345,x24346,x24347,x24342,x24348)) % 181.55/181.55 [2435]~E(x24351,x24352)+E(f646(x24353,x24354,x24355,x24356,x24357,x24358,x24351),f646(x24353,x24354,x24355,x24356,x24357,x24358,x24352)) % 181.55/181.55 [2436]~E(x24361,x24362)+E(f536(x24361),f536(x24362)) % 181.55/181.55 [2437]~E(x24371,x24372)+E(f785(x24371,x24373,x24374),f785(x24372,x24373,x24374)) % 181.55/181.55 [2438]~E(x24381,x24382)+E(f785(x24383,x24381,x24384),f785(x24383,x24382,x24384)) % 181.55/181.55 [2439]~E(x24391,x24392)+E(f785(x24393,x24394,x24391),f785(x24393,x24394,x24392)) % 181.55/181.55 [2440]~E(x24401,x24402)+E(f403(x24401,x24403,x24404),f403(x24402,x24403,x24404)) % 181.55/181.55 [2441]~E(x24411,x24412)+E(f403(x24413,x24411,x24414),f403(x24413,x24412,x24414)) % 181.55/181.55 [2442]~E(x24421,x24422)+E(f403(x24423,x24424,x24421),f403(x24423,x24424,x24422)) % 181.55/181.55 [2443]~E(x24431,x24432)+E(f857(x24431,x24433),f857(x24432,x24433)) % 181.55/181.55 [2444]~E(x24441,x24442)+E(f857(x24443,x24441),f857(x24443,x24442)) % 181.55/181.55 [2445]~E(x24451,x24452)+E(f354(x24451,x24453),f354(x24452,x24453)) % 181.55/181.55 [2446]~E(x24461,x24462)+E(f354(x24463,x24461),f354(x24463,x24462)) % 181.55/181.55 [2447]~E(x24471,x24472)+E(f568(x24471,x24473),f568(x24472,x24473)) % 181.55/181.55 [2448]~E(x24481,x24482)+E(f568(x24483,x24481),f568(x24483,x24482)) % 181.55/181.55 [2449]~E(x24491,x24492)+E(f576(x24491,x24493,x24494,x24495),f576(x24492,x24493,x24494,x24495)) % 181.55/181.55 [2450]~E(x24501,x24502)+E(f576(x24503,x24501,x24504,x24505),f576(x24503,x24502,x24504,x24505)) % 181.55/181.55 [2451]~E(x24511,x24512)+E(f576(x24513,x24514,x24511,x24515),f576(x24513,x24514,x24512,x24515)) % 181.55/181.55 [2452]~E(x24521,x24522)+E(f576(x24523,x24524,x24525,x24521),f576(x24523,x24524,x24525,x24522)) % 181.55/181.55 [2453]~E(x24531,x24532)+E(f215(x24531,x24533,x24534,x24535),f215(x24532,x24533,x24534,x24535)) % 181.55/181.55 [2454]~E(x24541,x24542)+E(f215(x24543,x24541,x24544,x24545),f215(x24543,x24542,x24544,x24545)) % 181.55/181.55 [2455]~E(x24551,x24552)+E(f215(x24553,x24554,x24551,x24555),f215(x24553,x24554,x24552,x24555)) % 181.55/181.55 [2456]~E(x24561,x24562)+E(f215(x24563,x24564,x24565,x24561),f215(x24563,x24564,x24565,x24562)) % 181.55/181.55 [2457]~E(x24571,x24572)+E(f528(x24571,x24573,x24574,x24575),f528(x24572,x24573,x24574,x24575)) % 181.55/181.55 [2458]~E(x24581,x24582)+E(f528(x24583,x24581,x24584,x24585),f528(x24583,x24582,x24584,x24585)) % 181.55/181.55 [2459]~E(x24591,x24592)+E(f528(x24593,x24594,x24591,x24595),f528(x24593,x24594,x24592,x24595)) % 181.55/181.55 [2460]~E(x24601,x24602)+E(f528(x24603,x24604,x24605,x24601),f528(x24603,x24604,x24605,x24602)) % 181.55/181.55 [2461]~E(x24611,x24612)+E(f559(x24611,x24613,x24614),f559(x24612,x24613,x24614)) % 181.55/181.55 [2462]~E(x24621,x24622)+E(f559(x24623,x24621,x24624),f559(x24623,x24622,x24624)) % 181.55/181.55 [2463]~E(x24631,x24632)+E(f559(x24633,x24634,x24631),f559(x24633,x24634,x24632)) % 181.55/181.55 [2464]~E(x24641,x24642)+E(f681(x24641,x24643,x24644),f681(x24642,x24643,x24644)) % 181.55/181.55 [2465]~E(x24651,x24652)+E(f681(x24653,x24651,x24654),f681(x24653,x24652,x24654)) % 181.55/181.55 [2466]~E(x24661,x24662)+E(f681(x24663,x24664,x24661),f681(x24663,x24664,x24662)) % 181.55/181.55 [2467]~E(x24671,x24672)+E(f516(x24671,x24673,x24674,x24675,x24676),f516(x24672,x24673,x24674,x24675,x24676)) % 181.55/181.55 [2468]~E(x24681,x24682)+E(f516(x24683,x24681,x24684,x24685,x24686),f516(x24683,x24682,x24684,x24685,x24686)) % 181.55/181.55 [2469]~E(x24691,x24692)+E(f516(x24693,x24694,x24691,x24695,x24696),f516(x24693,x24694,x24692,x24695,x24696)) % 181.55/181.55 [2470]~E(x24701,x24702)+E(f516(x24703,x24704,x24705,x24701,x24706),f516(x24703,x24704,x24705,x24702,x24706)) % 181.55/181.55 [2471]~E(x24711,x24712)+E(f516(x24713,x24714,x24715,x24716,x24711),f516(x24713,x24714,x24715,x24716,x24712)) % 181.55/181.55 [2472]~E(x24721,x24722)+E(f329(x24721),f329(x24722)) % 181.55/181.55 [2473]~E(x24731,x24732)+E(f626(x24731,x24733,x24734,x24735,x24736),f626(x24732,x24733,x24734,x24735,x24736)) % 181.55/181.55 [2474]~E(x24741,x24742)+E(f626(x24743,x24741,x24744,x24745,x24746),f626(x24743,x24742,x24744,x24745,x24746)) % 181.55/181.55 [2475]~E(x24751,x24752)+E(f626(x24753,x24754,x24751,x24755,x24756),f626(x24753,x24754,x24752,x24755,x24756)) % 181.55/181.55 [2476]~E(x24761,x24762)+E(f626(x24763,x24764,x24765,x24761,x24766),f626(x24763,x24764,x24765,x24762,x24766)) % 181.55/181.55 [2477]~E(x24771,x24772)+E(f626(x24773,x24774,x24775,x24776,x24771),f626(x24773,x24774,x24775,x24776,x24772)) % 181.55/181.55 [2478]~E(x24781,x24782)+E(f673(x24781,x24783,x24784,x24785,x24786),f673(x24782,x24783,x24784,x24785,x24786)) % 181.55/181.55 [2479]~E(x24791,x24792)+E(f673(x24793,x24791,x24794,x24795,x24796),f673(x24793,x24792,x24794,x24795,x24796)) % 181.55/181.55 [2480]~E(x24801,x24802)+E(f673(x24803,x24804,x24801,x24805,x24806),f673(x24803,x24804,x24802,x24805,x24806)) % 181.55/181.55 [2481]~E(x24811,x24812)+E(f673(x24813,x24814,x24815,x24811,x24816),f673(x24813,x24814,x24815,x24812,x24816)) % 181.55/181.55 [2482]~E(x24821,x24822)+E(f673(x24823,x24824,x24825,x24826,x24821),f673(x24823,x24824,x24825,x24826,x24822)) % 181.55/181.55 [2483]~E(x24831,x24832)+E(f334(x24831,x24833),f334(x24832,x24833)) % 181.55/181.55 [2484]~E(x24841,x24842)+E(f334(x24843,x24841),f334(x24843,x24842)) % 181.55/181.55 [2485]~E(x24851,x24852)+E(f378(x24851,x24853,x24854,x24855),f378(x24852,x24853,x24854,x24855)) % 181.55/181.55 [2486]~E(x24861,x24862)+E(f378(x24863,x24861,x24864,x24865),f378(x24863,x24862,x24864,x24865)) % 181.55/181.55 [2487]~E(x24871,x24872)+E(f378(x24873,x24874,x24871,x24875),f378(x24873,x24874,x24872,x24875)) % 181.55/181.55 [2488]~E(x24881,x24882)+E(f378(x24883,x24884,x24885,x24881),f378(x24883,x24884,x24885,x24882)) % 181.55/181.55 [2489]~E(x24891,x24892)+E(f349(x24891,x24893,x24894),f349(x24892,x24893,x24894)) % 181.55/181.55 [2490]~E(x24901,x24902)+E(f349(x24903,x24901,x24904),f349(x24903,x24902,x24904)) % 181.55/181.55 [2491]~E(x24911,x24912)+E(f349(x24913,x24914,x24911),f349(x24913,x24914,x24912)) % 181.55/181.55 [2492]~E(x24921,x24922)+E(f538(x24921,x24923),f538(x24922,x24923)) % 181.55/181.55 [2493]~E(x24931,x24932)+E(f538(x24933,x24931),f538(x24933,x24932)) % 181.55/181.55 [2494]~E(x24941,x24942)+E(f380(x24941,x24943,x24944),f380(x24942,x24943,x24944)) % 181.55/181.55 [2495]~E(x24951,x24952)+E(f380(x24953,x24951,x24954),f380(x24953,x24952,x24954)) % 181.55/181.55 [2496]~E(x24961,x24962)+E(f380(x24963,x24964,x24961),f380(x24963,x24964,x24962)) % 181.55/181.55 [2497]~E(x24971,x24972)+E(f394(x24971,x24973,x24974),f394(x24972,x24973,x24974)) % 181.55/181.55 [2498]~E(x24981,x24982)+E(f394(x24983,x24981,x24984),f394(x24983,x24982,x24984)) % 181.55/181.55 [2499]~E(x24991,x24992)+E(f394(x24993,x24994,x24991),f394(x24993,x24994,x24992)) % 181.55/181.55 [2500]~E(x25001,x25002)+E(f404(x25001,x25003,x25004),f404(x25002,x25003,x25004)) % 181.55/181.55 [2501]~E(x25011,x25012)+E(f404(x25013,x25011,x25014),f404(x25013,x25012,x25014)) % 181.55/181.55 [2502]~E(x25021,x25022)+E(f404(x25023,x25024,x25021),f404(x25023,x25024,x25022)) % 181.55/181.55 [2503]~E(x25031,x25032)+E(f374(x25031,x25033),f374(x25032,x25033)) % 181.55/181.55 [2504]~E(x25041,x25042)+E(f374(x25043,x25041),f374(x25043,x25042)) % 181.55/181.55 [2505]~E(x25051,x25052)+E(f848(x25051,x25053,x25054,x25055),f848(x25052,x25053,x25054,x25055)) % 181.55/181.55 [2506]~E(x25061,x25062)+E(f848(x25063,x25061,x25064,x25065),f848(x25063,x25062,x25064,x25065)) % 181.55/181.55 [2507]~E(x25071,x25072)+E(f848(x25073,x25074,x25071,x25075),f848(x25073,x25074,x25072,x25075)) % 181.55/181.55 [2508]~E(x25081,x25082)+E(f848(x25083,x25084,x25085,x25081),f848(x25083,x25084,x25085,x25082)) % 181.55/181.55 [2509]~E(x25091,x25092)+E(f825(x25091),f825(x25092)) % 181.55/181.55 [2510]~E(x25101,x25102)+E(f764(x25101,x25103,x25104),f764(x25102,x25103,x25104)) % 181.55/181.55 [2511]~E(x25111,x25112)+E(f764(x25113,x25111,x25114),f764(x25113,x25112,x25114)) % 181.55/181.55 [2512]~E(x25121,x25122)+E(f764(x25123,x25124,x25121),f764(x25123,x25124,x25122)) % 181.55/181.55 [2513]~E(x25131,x25132)+E(f699(x25131,x25133,x25134,x25135,x25136),f699(x25132,x25133,x25134,x25135,x25136)) % 181.55/181.55 [2514]~E(x25141,x25142)+E(f699(x25143,x25141,x25144,x25145,x25146),f699(x25143,x25142,x25144,x25145,x25146)) % 181.55/181.55 [2515]~E(x25151,x25152)+E(f699(x25153,x25154,x25151,x25155,x25156),f699(x25153,x25154,x25152,x25155,x25156)) % 181.55/181.55 [2516]~E(x25161,x25162)+E(f699(x25163,x25164,x25165,x25161,x25166),f699(x25163,x25164,x25165,x25162,x25166)) % 181.55/181.55 [2517]~E(x25171,x25172)+E(f699(x25173,x25174,x25175,x25176,x25171),f699(x25173,x25174,x25175,x25176,x25172)) % 181.55/181.55 [2518]~E(x25181,x25182)+E(f343(x25181,x25183,x25184),f343(x25182,x25183,x25184)) % 181.55/181.55 [2519]~E(x25191,x25192)+E(f343(x25193,x25191,x25194),f343(x25193,x25192,x25194)) % 181.55/181.55 [2520]~E(x25201,x25202)+E(f343(x25203,x25204,x25201),f343(x25203,x25204,x25202)) % 181.55/181.55 [2521]~E(x25211,x25212)+E(f565(x25211,x25213,x25214,x25215,x25216,x25217),f565(x25212,x25213,x25214,x25215,x25216,x25217)) % 181.55/181.55 [2522]~E(x25221,x25222)+E(f565(x25223,x25221,x25224,x25225,x25226,x25227),f565(x25223,x25222,x25224,x25225,x25226,x25227)) % 181.55/181.55 [2523]~E(x25231,x25232)+E(f565(x25233,x25234,x25231,x25235,x25236,x25237),f565(x25233,x25234,x25232,x25235,x25236,x25237)) % 181.55/181.55 [2524]~E(x25241,x25242)+E(f565(x25243,x25244,x25245,x25241,x25246,x25247),f565(x25243,x25244,x25245,x25242,x25246,x25247)) % 181.55/181.55 [2525]~E(x25251,x25252)+E(f565(x25253,x25254,x25255,x25256,x25251,x25257),f565(x25253,x25254,x25255,x25256,x25252,x25257)) % 181.55/181.55 [2526]~E(x25261,x25262)+E(f565(x25263,x25264,x25265,x25266,x25267,x25261),f565(x25263,x25264,x25265,x25266,x25267,x25262)) % 181.55/181.55 [2527]~E(x25271,x25272)+E(f844(x25271,x25273),f844(x25272,x25273)) % 181.55/181.55 [2528]~E(x25281,x25282)+E(f844(x25283,x25281),f844(x25283,x25282)) % 181.55/181.55 [2529]~E(x25291,x25292)+E(f607(x25291,x25293,x25294),f607(x25292,x25293,x25294)) % 181.55/181.55 [2530]~E(x25301,x25302)+E(f607(x25303,x25301,x25304),f607(x25303,x25302,x25304)) % 181.55/181.55 [2531]~E(x25311,x25312)+E(f607(x25313,x25314,x25311),f607(x25313,x25314,x25312)) % 181.55/181.55 [2532]~E(x25321,x25322)+E(f209(x25321),f209(x25322)) % 181.55/181.55 [2533]~E(x25331,x25332)+E(f377(x25331,x25333,x25334),f377(x25332,x25333,x25334)) % 181.55/181.55 [2534]~E(x25341,x25342)+E(f377(x25343,x25341,x25344),f377(x25343,x25342,x25344)) % 181.55/181.55 [2535]~E(x25351,x25352)+E(f377(x25353,x25354,x25351),f377(x25353,x25354,x25352)) % 181.55/181.55 [2536]~E(x25361,x25362)+E(f355(x25361,x25363),f355(x25362,x25363)) % 181.55/181.55 [2537]~E(x25371,x25372)+E(f355(x25373,x25371),f355(x25373,x25372)) % 181.55/181.55 [2538]~E(x25381,x25382)+E(f587(x25381,x25383,x25384),f587(x25382,x25383,x25384)) % 181.55/181.55 [2539]~E(x25391,x25392)+E(f587(x25393,x25391,x25394),f587(x25393,x25392,x25394)) % 181.55/181.55 [2540]~E(x25401,x25402)+E(f587(x25403,x25404,x25401),f587(x25403,x25404,x25402)) % 181.55/181.55 [2541]~E(x25411,x25412)+E(f502(x25411,x25413,x25414),f502(x25412,x25413,x25414)) % 181.55/181.55 [2542]~E(x25421,x25422)+E(f502(x25423,x25421,x25424),f502(x25423,x25422,x25424)) % 181.55/181.55 [2543]~E(x25431,x25432)+E(f502(x25433,x25434,x25431),f502(x25433,x25434,x25432)) % 181.55/181.55 [2544]~E(x25441,x25442)+E(f424(x25441),f424(x25442)) % 181.55/181.55 [2545]~E(x25451,x25452)+E(f420(x25451,x25453),f420(x25452,x25453)) % 181.55/181.55 [2546]~E(x25461,x25462)+E(f420(x25463,x25461),f420(x25463,x25462)) % 181.55/181.55 [2547]~E(x25471,x25472)+E(f542(x25471,x25473,x25474,x25475),f542(x25472,x25473,x25474,x25475)) % 181.55/181.55 [2548]~E(x25481,x25482)+E(f542(x25483,x25481,x25484,x25485),f542(x25483,x25482,x25484,x25485)) % 181.55/181.55 [2549]~E(x25491,x25492)+E(f542(x25493,x25494,x25491,x25495),f542(x25493,x25494,x25492,x25495)) % 181.55/181.55 [2550]~E(x25501,x25502)+E(f542(x25503,x25504,x25505,x25501),f542(x25503,x25504,x25505,x25502)) % 181.55/181.55 [2551]~E(x25511,x25512)+E(f649(x25511,x25513,x25514),f649(x25512,x25513,x25514)) % 181.55/181.55 [2552]~E(x25521,x25522)+E(f649(x25523,x25521,x25524),f649(x25523,x25522,x25524)) % 181.55/181.55 [2553]~E(x25531,x25532)+E(f649(x25533,x25534,x25531),f649(x25533,x25534,x25532)) % 181.55/181.55 [2554]~E(x25541,x25542)+E(f266(x25541,x25543,x25544,x25545,x25546),f266(x25542,x25543,x25544,x25545,x25546)) % 181.55/181.55 [2555]~E(x25551,x25552)+E(f266(x25553,x25551,x25554,x25555,x25556),f266(x25553,x25552,x25554,x25555,x25556)) % 181.55/181.55 [2556]~E(x25561,x25562)+E(f266(x25563,x25564,x25561,x25565,x25566),f266(x25563,x25564,x25562,x25565,x25566)) % 181.55/181.55 [2557]~E(x25571,x25572)+E(f266(x25573,x25574,x25575,x25571,x25576),f266(x25573,x25574,x25575,x25572,x25576)) % 181.55/181.55 [2558]~E(x25581,x25582)+E(f266(x25583,x25584,x25585,x25586,x25581),f266(x25583,x25584,x25585,x25586,x25582)) % 181.55/181.55 [2559]~E(x25591,x25592)+E(f813(x25591,x25593,x25594),f813(x25592,x25593,x25594)) % 181.55/181.55 [2560]~E(x25601,x25602)+E(f813(x25603,x25601,x25604),f813(x25603,x25602,x25604)) % 181.55/181.55 [2561]~E(x25611,x25612)+E(f813(x25613,x25614,x25611),f813(x25613,x25614,x25612)) % 181.55/181.55 [2562]~E(x25621,x25622)+E(f208(x25621,x25623),f208(x25622,x25623)) % 181.55/181.55 [2563]~E(x25631,x25632)+E(f208(x25633,x25631),f208(x25633,x25632)) % 181.55/181.55 [2564]~E(x25641,x25642)+E(f704(x25641,x25643,x25644,x25645),f704(x25642,x25643,x25644,x25645)) % 181.55/181.55 [2565]~E(x25651,x25652)+E(f704(x25653,x25651,x25654,x25655),f704(x25653,x25652,x25654,x25655)) % 181.55/181.55 [2566]~E(x25661,x25662)+E(f704(x25663,x25664,x25661,x25665),f704(x25663,x25664,x25662,x25665)) % 181.55/181.55 [2567]~E(x25671,x25672)+E(f704(x25673,x25674,x25675,x25671),f704(x25673,x25674,x25675,x25672)) % 181.55/181.55 [2568]~E(x25681,x25682)+E(f427(x25681,x25683,x25684),f427(x25682,x25683,x25684)) % 181.55/181.55 [2569]~E(x25691,x25692)+E(f427(x25693,x25691,x25694),f427(x25693,x25692,x25694)) % 181.55/181.55 [2570]~E(x25701,x25702)+E(f427(x25703,x25704,x25701),f427(x25703,x25704,x25702)) % 181.55/181.55 [2571]~E(x25711,x25712)+E(f602(x25711,x25713),f602(x25712,x25713)) % 181.55/181.55 [2572]~E(x25721,x25722)+E(f602(x25723,x25721),f602(x25723,x25722)) % 181.55/181.55 [2573]~E(x25731,x25732)+E(f560(x25731,x25733,x25734),f560(x25732,x25733,x25734)) % 181.55/181.55 [2574]~E(x25741,x25742)+E(f560(x25743,x25741,x25744),f560(x25743,x25742,x25744)) % 181.55/181.55 [2575]~E(x25751,x25752)+E(f560(x25753,x25754,x25751),f560(x25753,x25754,x25752)) % 181.55/181.55 [2576]~E(x25761,x25762)+E(f21(x25761,x25763),f21(x25762,x25763)) % 181.55/181.55 [2577]~E(x25771,x25772)+E(f21(x25773,x25771),f21(x25773,x25772)) % 181.55/181.55 [2578]~E(x25781,x25782)+E(f677(x25781,x25783,x25784,x25785,x25786),f677(x25782,x25783,x25784,x25785,x25786)) % 181.55/181.55 [2579]~E(x25791,x25792)+E(f677(x25793,x25791,x25794,x25795,x25796),f677(x25793,x25792,x25794,x25795,x25796)) % 181.55/181.55 [2580]~E(x25801,x25802)+E(f677(x25803,x25804,x25801,x25805,x25806),f677(x25803,x25804,x25802,x25805,x25806)) % 181.55/181.55 [2581]~E(x25811,x25812)+E(f677(x25813,x25814,x25815,x25811,x25816),f677(x25813,x25814,x25815,x25812,x25816)) % 181.55/181.55 [2582]~E(x25821,x25822)+E(f677(x25823,x25824,x25825,x25826,x25821),f677(x25823,x25824,x25825,x25826,x25822)) % 181.55/181.55 [2583]~E(x25831,x25832)+E(f742(x25831,x25833,x25834,x25835),f742(x25832,x25833,x25834,x25835)) % 181.55/181.55 [2584]~E(x25841,x25842)+E(f742(x25843,x25841,x25844,x25845),f742(x25843,x25842,x25844,x25845)) % 181.55/181.55 [2585]~E(x25851,x25852)+E(f742(x25853,x25854,x25851,x25855),f742(x25853,x25854,x25852,x25855)) % 181.55/181.55 [2586]~E(x25861,x25862)+E(f742(x25863,x25864,x25865,x25861),f742(x25863,x25864,x25865,x25862)) % 181.55/181.55 [2587]~E(x25871,x25872)+E(f716(x25871,x25873),f716(x25872,x25873)) % 181.55/181.55 [2588]~E(x25881,x25882)+E(f716(x25883,x25881),f716(x25883,x25882)) % 181.55/181.55 [2589]~E(x25891,x25892)+E(f666(x25891,x25893),f666(x25892,x25893)) % 181.55/181.55 [2590]~E(x25901,x25902)+E(f666(x25903,x25901),f666(x25903,x25902)) % 181.55/181.55 [2591]~E(x25911,x25912)+E(f388(x25911,x25913,x25914,x25915),f388(x25912,x25913,x25914,x25915)) % 181.55/181.55 [2592]~E(x25921,x25922)+E(f388(x25923,x25921,x25924,x25925),f388(x25923,x25922,x25924,x25925)) % 181.55/181.55 [2593]~E(x25931,x25932)+E(f388(x25933,x25934,x25931,x25935),f388(x25933,x25934,x25932,x25935)) % 181.55/181.55 [2594]~E(x25941,x25942)+E(f388(x25943,x25944,x25945,x25941),f388(x25943,x25944,x25945,x25942)) % 181.55/181.55 [2595]~E(x25951,x25952)+E(f308(x25951,x25953,x25954),f308(x25952,x25953,x25954)) % 181.55/181.55 [2596]~E(x25961,x25962)+E(f308(x25963,x25961,x25964),f308(x25963,x25962,x25964)) % 181.55/181.55 [2597]~E(x25971,x25972)+E(f308(x25973,x25974,x25971),f308(x25973,x25974,x25972)) % 181.55/181.55 [2598]~P1(x25981)+P1(x25982)+~E(x25981,x25982) % 181.55/181.55 [2599]~P2(x25991)+P2(x25992)+~E(x25991,x25992) % 181.55/181.55 [2600]~P105(x26001)+P105(x26002)+~E(x26001,x26002) % 181.55/181.55 [2601]~P3(x26011)+P3(x26012)+~E(x26011,x26012) % 181.55/181.55 [2602]P27(x26022,x26023,x26024,x26025)+~E(x26021,x26022)+~P27(x26021,x26023,x26024,x26025) % 181.55/181.55 [2603]P27(x26033,x26032,x26034,x26035)+~E(x26031,x26032)+~P27(x26033,x26031,x26034,x26035) % 181.55/181.55 [2604]P27(x26043,x26044,x26042,x26045)+~E(x26041,x26042)+~P27(x26043,x26044,x26041,x26045) % 181.55/181.55 [2605]P27(x26053,x26054,x26055,x26052)+~E(x26051,x26052)+~P27(x26053,x26054,x26055,x26051) % 181.55/181.55 [2606]P144(x26062,x26063,x26064)+~E(x26061,x26062)+~P144(x26061,x26063,x26064) % 181.55/181.55 [2607]P144(x26073,x26072,x26074)+~E(x26071,x26072)+~P144(x26073,x26071,x26074) % 181.55/181.55 [2608]P144(x26083,x26084,x26082)+~E(x26081,x26082)+~P144(x26083,x26084,x26081) % 181.55/181.55 [2609]P143(x26092,x26093,x26094)+~E(x26091,x26092)+~P143(x26091,x26093,x26094) % 181.55/181.55 [2610]P143(x26103,x26102,x26104)+~E(x26101,x26102)+~P143(x26103,x26101,x26104) % 181.55/181.55 [2611]P143(x26113,x26114,x26112)+~E(x26111,x26112)+~P143(x26113,x26114,x26111) % 181.55/181.55 [2612]~P103(x26121)+P103(x26122)+~E(x26121,x26122) % 181.55/181.55 [2613]~P92(x26131)+P92(x26132)+~E(x26131,x26132) % 181.55/181.55 [2614]~P74(x26141)+P74(x26142)+~E(x26141,x26142) % 181.55/181.55 [2615]~P75(x26151)+P75(x26152)+~E(x26151,x26152) % 181.55/181.55 [2616]~P107(x26161)+P107(x26162)+~E(x26161,x26162) % 181.55/181.55 [2617]~P104(x26171)+P104(x26172)+~E(x26171,x26172) % 181.55/181.55 [2618]~P64(x26181)+P64(x26182)+~E(x26181,x26182) % 181.55/181.55 [2619]~P117(x26191)+P117(x26192)+~E(x26191,x26192) % 181.55/181.55 [2620]P16(x26202,x26203)+~E(x26201,x26202)+~P16(x26201,x26203) % 181.55/181.55 [2621]P16(x26213,x26212)+~E(x26211,x26212)+~P16(x26213,x26211) % 181.55/181.55 [2622]~P98(x26221)+P98(x26222)+~E(x26221,x26222) % 181.55/181.55 [2623]~P63(x26231)+P63(x26232)+~E(x26231,x26232) % 181.55/181.55 [2624]~P112(x26241)+P112(x26242)+~E(x26241,x26242) % 181.55/181.55 [2625]~P106(x26251)+P106(x26252)+~E(x26251,x26252) % 181.55/181.55 [2626]~P65(x26261)+P65(x26262)+~E(x26261,x26262) % 181.55/181.55 [2627]~P81(x26271)+P81(x26272)+~E(x26271,x26272) % 181.55/181.55 [2628]~P93(x26281)+P93(x26282)+~E(x26281,x26282) % 181.55/181.55 [2629]P52(x26292,x26293,x26294)+~E(x26291,x26292)+~P52(x26291,x26293,x26294) % 181.55/181.55 [2630]P52(x26303,x26302,x26304)+~E(x26301,x26302)+~P52(x26303,x26301,x26304) % 181.55/181.55 [2631]P52(x26313,x26314,x26312)+~E(x26311,x26312)+~P52(x26313,x26314,x26311) % 181.55/181.55 [2632]~P79(x26321)+P79(x26322)+~E(x26321,x26322) % 181.55/181.55 [2633]~P80(x26331)+P80(x26332)+~E(x26331,x26332) % 181.55/181.55 [2634]P39(x26342,x26343)+~E(x26341,x26342)+~P39(x26341,x26343) % 181.55/181.55 [2635]P39(x26353,x26352)+~E(x26351,x26352)+~P39(x26353,x26351) % 181.55/181.55 [2636]~P4(x26361)+P4(x26362)+~E(x26361,x26362) % 181.55/181.55 [2637]~P5(x26371)+P5(x26372)+~E(x26371,x26372) % 181.55/181.55 [2638]~P6(x26381)+P6(x26382)+~E(x26381,x26382) % 181.55/181.55 [2639]~P94(x26391)+P94(x26392)+~E(x26391,x26392) % 181.55/181.55 [2640]~P120(x26401)+P120(x26402)+~E(x26401,x26402) % 181.55/181.55 [2641]~P121(x26411)+P121(x26412)+~E(x26411,x26412) % 181.55/181.55 [2642]~P99(x26421)+P99(x26422)+~E(x26421,x26422) % 181.55/181.55 [2643]P37(x26432,x26433,x26434)+~E(x26431,x26432)+~P37(x26431,x26433,x26434) % 181.55/181.55 [2644]P37(x26443,x26442,x26444)+~E(x26441,x26442)+~P37(x26443,x26441,x26444) % 181.55/181.55 [2645]P37(x26453,x26454,x26452)+~E(x26451,x26452)+~P37(x26453,x26454,x26451) % 181.55/181.55 [2646]P32(x26462,x26463)+~E(x26461,x26462)+~P32(x26461,x26463) % 181.55/181.55 [2647]P32(x26473,x26472)+~E(x26471,x26472)+~P32(x26473,x26471) % 181.55/181.55 [2648]~P95(x26481)+P95(x26482)+~E(x26481,x26482) % 181.55/181.55 [2649]~P97(x26491)+P97(x26492)+~E(x26491,x26492) % 181.55/181.55 [2650]~P100(x26501)+P100(x26502)+~E(x26501,x26502) % 181.55/181.55 [2651]~P123(x26511)+P123(x26512)+~E(x26511,x26512) % 181.55/181.55 [2652]P36(x26522,x26523,x26524,x26525,x26526)+~E(x26521,x26522)+~P36(x26521,x26523,x26524,x26525,x26526) % 181.55/181.55 [2653]P36(x26533,x26532,x26534,x26535,x26536)+~E(x26531,x26532)+~P36(x26533,x26531,x26534,x26535,x26536) % 181.55/181.55 [2654]P36(x26543,x26544,x26542,x26545,x26546)+~E(x26541,x26542)+~P36(x26543,x26544,x26541,x26545,x26546) % 181.55/181.55 [2655]P36(x26553,x26554,x26555,x26552,x26556)+~E(x26551,x26552)+~P36(x26553,x26554,x26555,x26551,x26556) % 181.55/181.55 [2656]P36(x26563,x26564,x26565,x26566,x26562)+~E(x26561,x26562)+~P36(x26563,x26564,x26565,x26566,x26561) % 181.55/181.55 [2657]~P116(x26571)+P116(x26572)+~E(x26571,x26572) % 181.55/181.55 [2658]P33(x26582,x26583,x26584)+~E(x26581,x26582)+~P33(x26581,x26583,x26584) % 181.55/181.55 [2659]P33(x26593,x26592,x26594)+~E(x26591,x26592)+~P33(x26593,x26591,x26594) % 181.55/181.55 [2660]P33(x26603,x26604,x26602)+~E(x26601,x26602)+~P33(x26603,x26604,x26601) % 181.55/181.55 [2661]~P132(x26611)+P132(x26612)+~E(x26611,x26612) % 181.55/181.55 [2662]~P66(x26621)+P66(x26622)+~E(x26621,x26622) % 181.55/181.55 [2663]P35(x26632,x26633,x26634)+~E(x26631,x26632)+~P35(x26631,x26633,x26634) % 181.55/181.55 [2664]P35(x26643,x26642,x26644)+~E(x26641,x26642)+~P35(x26643,x26641,x26644) % 181.55/181.55 [2665]P35(x26653,x26654,x26652)+~E(x26651,x26652)+~P35(x26653,x26654,x26651) % 181.55/181.55 [2666]P9(x26662,x26663,x26664)+~E(x26661,x26662)+~P9(x26661,x26663,x26664) % 181.55/181.55 [2667]P9(x26673,x26672,x26674)+~E(x26671,x26672)+~P9(x26673,x26671,x26674) % 181.55/181.55 [2668]P9(x26683,x26684,x26682)+~E(x26681,x26682)+~P9(x26683,x26684,x26681) % 181.55/181.55 [2669]~P108(x26691)+P108(x26692)+~E(x26691,x26692) % 181.55/181.55 [2670]P26(x26702,x26703,x26704)+~E(x26701,x26702)+~P26(x26701,x26703,x26704) % 181.55/181.55 [2671]P26(x26713,x26712,x26714)+~E(x26711,x26712)+~P26(x26713,x26711,x26714) % 181.55/181.55 [2672]P26(x26723,x26724,x26722)+~E(x26721,x26722)+~P26(x26723,x26724,x26721) % 181.55/181.55 [2673]~P58(x26731)+P58(x26732)+~E(x26731,x26732) % 181.55/181.55 [2674]P17(x26742,x26743,x26744)+~E(x26741,x26742)+~P17(x26741,x26743,x26744) % 181.55/181.55 [2675]P17(x26753,x26752,x26754)+~E(x26751,x26752)+~P17(x26753,x26751,x26754) % 181.55/181.55 [2676]P17(x26763,x26764,x26762)+~E(x26761,x26762)+~P17(x26763,x26764,x26761) % 181.55/181.55 [2677]~P61(x26771)+P61(x26772)+~E(x26771,x26772) % 181.55/181.55 [2678]~P76(x26781)+P76(x26782)+~E(x26781,x26782) % 181.55/181.55 [2679]P53(x26792,x26793,x26794)+~E(x26791,x26792)+~P53(x26791,x26793,x26794) % 181.55/181.55 [2680]P53(x26803,x26802,x26804)+~E(x26801,x26802)+~P53(x26803,x26801,x26804) % 181.55/181.55 [2681]P53(x26813,x26814,x26812)+~E(x26811,x26812)+~P53(x26813,x26814,x26811) % 181.55/181.55 [2682]~P90(x26821)+P90(x26822)+~E(x26821,x26822) % 181.55/181.55 [2683]~P77(x26831)+P77(x26832)+~E(x26831,x26832) % 181.55/181.55 [2684]P18(x26842,x26843,x26844)+~E(x26841,x26842)+~P18(x26841,x26843,x26844) % 181.55/181.55 [2685]P18(x26853,x26852,x26854)+~E(x26851,x26852)+~P18(x26853,x26851,x26854) % 181.55/181.55 [2686]P18(x26863,x26864,x26862)+~E(x26861,x26862)+~P18(x26863,x26864,x26861) % 181.55/181.55 [2687]P28(x26872,x26873,x26874,x26875,x26876)+~E(x26871,x26872)+~P28(x26871,x26873,x26874,x26875,x26876) % 181.55/181.55 [2688]P28(x26883,x26882,x26884,x26885,x26886)+~E(x26881,x26882)+~P28(x26883,x26881,x26884,x26885,x26886) % 181.55/181.55 [2689]P28(x26893,x26894,x26892,x26895,x26896)+~E(x26891,x26892)+~P28(x26893,x26894,x26891,x26895,x26896) % 181.55/181.55 [2690]P28(x26903,x26904,x26905,x26902,x26906)+~E(x26901,x26902)+~P28(x26903,x26904,x26905,x26901,x26906) % 181.55/181.55 [2691]P28(x26913,x26914,x26915,x26916,x26912)+~E(x26911,x26912)+~P28(x26913,x26914,x26915,x26916,x26911) % 181.55/181.55 [2692]~P68(x26921)+P68(x26922)+~E(x26921,x26922) % 181.55/181.55 [2693]P41(x26932,x26933,x26934)+~E(x26931,x26932)+~P41(x26931,x26933,x26934) % 181.55/181.55 [2694]P41(x26943,x26942,x26944)+~E(x26941,x26942)+~P41(x26943,x26941,x26944) % 181.55/181.55 [2695]P41(x26953,x26954,x26952)+~E(x26951,x26952)+~P41(x26953,x26954,x26951) % 181.55/181.55 [2696]~P122(x26961)+P122(x26962)+~E(x26961,x26962) % 181.55/181.56 [2697]~P83(x26971)+P83(x26972)+~E(x26971,x26972) % 181.55/181.56 [2698]P14(x26982,x26983,x26984,x26985)+~E(x26981,x26982)+~P14(x26981,x26983,x26984,x26985) % 181.55/181.56 [2699]P14(x26993,x26992,x26994,x26995)+~E(x26991,x26992)+~P14(x26993,x26991,x26994,x26995) % 181.55/181.56 [2700]P14(x27003,x27004,x27002,x27005)+~E(x27001,x27002)+~P14(x27003,x27004,x27001,x27005) % 181.55/181.56 [2701]P14(x27013,x27014,x27015,x27012)+~E(x27011,x27012)+~P14(x27013,x27014,x27015,x27011) % 181.55/181.56 [2702]~P135(x27021)+P135(x27022)+~E(x27021,x27022) % 181.55/181.56 [2703]~P134(x27031)+P134(x27032)+~E(x27031,x27032) % 181.55/181.56 [2704]~P109(x27041)+P109(x27042)+~E(x27041,x27042) % 181.55/181.56 [2705]P22(x27052,x27053,x27054,x27055)+~E(x27051,x27052)+~P22(x27051,x27053,x27054,x27055) % 181.55/181.56 [2706]P22(x27063,x27062,x27064,x27065)+~E(x27061,x27062)+~P22(x27063,x27061,x27064,x27065) % 181.55/181.56 [2707]P22(x27073,x27074,x27072,x27075)+~E(x27071,x27072)+~P22(x27073,x27074,x27071,x27075) % 181.55/181.56 [2708]P22(x27083,x27084,x27085,x27082)+~E(x27081,x27082)+~P22(x27083,x27084,x27085,x27081) % 181.55/181.56 [2709]P8(x27092,x27093)+~E(x27091,x27092)+~P8(x27091,x27093) % 181.55/181.56 [2710]P8(x27103,x27102)+~E(x27101,x27102)+~P8(x27103,x27101) % 181.55/181.56 [2711]~P72(x27111)+P72(x27112)+~E(x27111,x27112) % 181.55/181.56 [2712]~P136(x27121)+P136(x27122)+~E(x27121,x27122) % 181.55/181.56 [2713]~P62(x27131)+P62(x27132)+~E(x27131,x27132) % 181.55/181.56 [2714]~P69(x27141)+P69(x27142)+~E(x27141,x27142) % 181.55/181.56 [2715]~P140(x27151)+P140(x27152)+~E(x27151,x27152) % 181.55/181.56 [2716]~P110(x27161)+P110(x27162)+~E(x27161,x27162) % 181.55/181.56 [2717]~P70(x27171)+P70(x27172)+~E(x27171,x27172) % 181.55/181.56 [2718]P50(x27182,x27183)+~E(x27181,x27182)+~P50(x27181,x27183) % 181.55/181.56 [2719]P50(x27193,x27192)+~E(x27191,x27192)+~P50(x27193,x27191) % 181.55/181.56 [2720]~P114(x27201)+P114(x27202)+~E(x27201,x27202) % 181.55/181.56 [2721]~P67(x27211)+P67(x27212)+~E(x27211,x27212) % 181.55/181.56 [2722]~P40(x27221)+P40(x27222)+~E(x27221,x27222) % 181.55/181.56 [2723]~P60(x27231)+P60(x27232)+~E(x27231,x27232) % 181.55/181.56 [2724]~P82(x27241)+P82(x27242)+~E(x27241,x27242) % 181.55/181.56 [2725]~P59(x27251)+P59(x27252)+~E(x27251,x27252) % 181.55/181.56 [2726]~P91(x27261)+P91(x27262)+~E(x27261,x27262) % 181.55/181.56 [2727]~P141(x27271)+P141(x27272)+~E(x27271,x27272) % 181.55/181.56 [2728]~P7(x27281)+P7(x27282)+~E(x27281,x27282) % 181.55/181.56 [2729]~P125(x27291)+P125(x27292)+~E(x27291,x27292) % 181.55/181.56 [2730]~P84(x27301)+P84(x27302)+~E(x27301,x27302) % 181.55/181.56 [2731]~P126(x27311)+P126(x27312)+~E(x27311,x27312) % 181.55/181.56 [2732]P31(x27322,x27323,x27324)+~E(x27321,x27322)+~P31(x27321,x27323,x27324) % 181.55/181.56 [2733]P31(x27333,x27332,x27334)+~E(x27331,x27332)+~P31(x27333,x27331,x27334) % 181.55/181.56 [2734]P31(x27343,x27344,x27342)+~E(x27341,x27342)+~P31(x27343,x27344,x27341) % 181.55/181.56 [2735]~P137(x27351)+P137(x27352)+~E(x27351,x27352) % 181.55/181.56 [2736]P30(x27362,x27363,x27364)+~E(x27361,x27362)+~P30(x27361,x27363,x27364) % 181.55/181.56 [2737]P30(x27373,x27372,x27374)+~E(x27371,x27372)+~P30(x27373,x27371,x27374) % 181.55/181.56 [2738]P30(x27383,x27384,x27382)+~E(x27381,x27382)+~P30(x27383,x27384,x27381) % 181.55/181.56 [2739]~P46(x27391)+P46(x27392)+~E(x27391,x27392) % 181.55/181.56 [2740]~P113(x27401)+P113(x27402)+~E(x27401,x27402) % 181.55/181.56 [2741]P54(x27412,x27413,x27414,x27415,x27416)+~E(x27411,x27412)+~P54(x27411,x27413,x27414,x27415,x27416) % 181.55/181.56 [2742]P54(x27423,x27422,x27424,x27425,x27426)+~E(x27421,x27422)+~P54(x27423,x27421,x27424,x27425,x27426) % 181.55/181.56 [2743]P54(x27433,x27434,x27432,x27435,x27436)+~E(x27431,x27432)+~P54(x27433,x27434,x27431,x27435,x27436) % 181.55/181.56 [2744]P54(x27443,x27444,x27445,x27442,x27446)+~E(x27441,x27442)+~P54(x27443,x27444,x27445,x27441,x27446) % 181.55/181.56 [2745]P54(x27453,x27454,x27455,x27456,x27452)+~E(x27451,x27452)+~P54(x27453,x27454,x27455,x27456,x27451) % 181.55/181.56 [2746]~P78(x27461)+P78(x27462)+~E(x27461,x27462) % 181.55/181.56 [2747]P34(x27472,x27473,x27474,x27475)+~E(x27471,x27472)+~P34(x27471,x27473,x27474,x27475) % 181.55/181.56 [2748]P34(x27483,x27482,x27484,x27485)+~E(x27481,x27482)+~P34(x27483,x27481,x27484,x27485) % 181.55/181.56 [2749]P34(x27493,x27494,x27492,x27495)+~E(x27491,x27492)+~P34(x27493,x27494,x27491,x27495) % 181.55/181.56 [2750]P34(x27503,x27504,x27505,x27502)+~E(x27501,x27502)+~P34(x27503,x27504,x27505,x27501) % 181.55/181.56 [2751]~P73(x27511)+P73(x27512)+~E(x27511,x27512) % 181.55/181.56 [2752]P55(x27522,x27523)+~E(x27521,x27522)+~P55(x27521,x27523) % 181.55/181.56 [2753]P55(x27533,x27532)+~E(x27531,x27532)+~P55(x27533,x27531) % 181.55/181.56 [2754]~P115(x27541)+P115(x27542)+~E(x27541,x27542) % 181.55/181.56 [2755]~P124(x27551)+P124(x27552)+~E(x27551,x27552) % 181.55/181.56 [2756]~P88(x27561)+P88(x27562)+~E(x27561,x27562) % 181.55/181.56 [2757]~P89(x27571)+P89(x27572)+~E(x27571,x27572) % 181.55/181.56 [2758]P11(x27582,x27583,x27584,x27585,x27586)+~E(x27581,x27582)+~P11(x27581,x27583,x27584,x27585,x27586) % 181.55/181.56 [2759]P11(x27593,x27592,x27594,x27595,x27596)+~E(x27591,x27592)+~P11(x27593,x27591,x27594,x27595,x27596) % 181.55/181.56 [2760]P11(x27603,x27604,x27602,x27605,x27606)+~E(x27601,x27602)+~P11(x27603,x27604,x27601,x27605,x27606) % 181.55/181.56 [2761]P11(x27613,x27614,x27615,x27612,x27616)+~E(x27611,x27612)+~P11(x27613,x27614,x27615,x27611,x27616) % 181.55/181.56 [2762]P11(x27623,x27624,x27625,x27626,x27622)+~E(x27621,x27622)+~P11(x27623,x27624,x27625,x27626,x27621) % 181.55/181.56 [2763]P29(x27632,x27633)+~E(x27631,x27632)+~P29(x27631,x27633) % 181.55/181.56 [2764]P29(x27643,x27642)+~E(x27641,x27642)+~P29(x27643,x27641) % 181.55/181.56 [2765]~P139(x27651)+P139(x27652)+~E(x27651,x27652) % 181.55/181.56 [2766]P21(x27662,x27663,x27664,x27665)+~E(x27661,x27662)+~P21(x27661,x27663,x27664,x27665) % 181.55/181.56 [2767]P21(x27673,x27672,x27674,x27675)+~E(x27671,x27672)+~P21(x27673,x27671,x27674,x27675) % 181.55/181.56 [2768]P21(x27683,x27684,x27682,x27685)+~E(x27681,x27682)+~P21(x27683,x27684,x27681,x27685) % 181.55/181.56 [2769]P21(x27693,x27694,x27695,x27692)+~E(x27691,x27692)+~P21(x27693,x27694,x27695,x27691) % 181.55/181.56 [2770]P48(x27702,x27703,x27704)+~E(x27701,x27702)+~P48(x27701,x27703,x27704) % 181.55/181.56 [2771]P48(x27713,x27712,x27714)+~E(x27711,x27712)+~P48(x27713,x27711,x27714) % 181.55/181.56 [2772]P48(x27723,x27724,x27722)+~E(x27721,x27722)+~P48(x27723,x27724,x27721) % 181.55/181.56 [2773]P43(x27732,x27733)+~E(x27731,x27732)+~P43(x27731,x27733) % 181.55/181.56 [2774]P43(x27743,x27742)+~E(x27741,x27742)+~P43(x27743,x27741) % 181.55/181.56 [2775]P12(x27752,x27753,x27754)+~E(x27751,x27752)+~P12(x27751,x27753,x27754) % 181.55/181.56 [2776]P12(x27763,x27762,x27764)+~E(x27761,x27762)+~P12(x27763,x27761,x27764) % 181.55/181.56 [2777]P12(x27773,x27774,x27772)+~E(x27771,x27772)+~P12(x27773,x27774,x27771) % 181.55/181.56 [2778]~P133(x27781)+P133(x27782)+~E(x27781,x27782) % 181.55/181.56 [2779]P44(x27792,x27793,x27794,x27795,x27796,x27797)+~E(x27791,x27792)+~P44(x27791,x27793,x27794,x27795,x27796,x27797) % 181.55/181.56 [2780]P44(x27803,x27802,x27804,x27805,x27806,x27807)+~E(x27801,x27802)+~P44(x27803,x27801,x27804,x27805,x27806,x27807) % 181.55/181.56 [2781]P44(x27813,x27814,x27812,x27815,x27816,x27817)+~E(x27811,x27812)+~P44(x27813,x27814,x27811,x27815,x27816,x27817) % 181.55/181.56 [2782]P44(x27823,x27824,x27825,x27822,x27826,x27827)+~E(x27821,x27822)+~P44(x27823,x27824,x27825,x27821,x27826,x27827) % 181.55/181.56 [2783]P44(x27833,x27834,x27835,x27836,x27832,x27837)+~E(x27831,x27832)+~P44(x27833,x27834,x27835,x27836,x27831,x27837) % 181.55/181.56 [2784]P44(x27843,x27844,x27845,x27846,x27847,x27842)+~E(x27841,x27842)+~P44(x27843,x27844,x27845,x27846,x27847,x27841) % 181.55/181.56 [2785]~P101(x27851)+P101(x27852)+~E(x27851,x27852) % 181.55/181.56 [2786]~P138(x27861)+P138(x27862)+~E(x27861,x27862) % 181.55/181.56 [2787]~P130(x27871)+P130(x27872)+~E(x27871,x27872) % 181.55/181.56 [2788]P56(x27882,x27883,x27884,x27885)+~E(x27881,x27882)+~P56(x27881,x27883,x27884,x27885) % 181.55/181.56 [2789]P56(x27893,x27892,x27894,x27895)+~E(x27891,x27892)+~P56(x27893,x27891,x27894,x27895) % 181.55/181.56 [2790]P56(x27903,x27904,x27902,x27905)+~E(x27901,x27902)+~P56(x27903,x27904,x27901,x27905) % 181.55/181.56 [2791]P56(x27913,x27914,x27915,x27912)+~E(x27911,x27912)+~P56(x27913,x27914,x27915,x27911) % 181.55/181.56 [2792]P13(x27922,x27923,x27924)+~E(x27921,x27922)+~P13(x27921,x27923,x27924) % 181.55/181.56 [2793]P13(x27933,x27932,x27934)+~E(x27931,x27932)+~P13(x27933,x27931,x27934) % 181.55/181.56 [2794]P13(x27943,x27944,x27942)+~E(x27941,x27942)+~P13(x27943,x27944,x27941) % 181.55/181.56 [2795]P45(x27952,x27953)+~E(x27951,x27952)+~P45(x27951,x27953) % 181.55/181.56 [2796]P45(x27963,x27962)+~E(x27961,x27962)+~P45(x27963,x27961) % 181.55/181.56 [2797]~P85(x27971)+P85(x27972)+~E(x27971,x27972) % 181.55/181.56 [2798]P57(x27982,x27983)+~E(x27981,x27982)+~P57(x27981,x27983) % 181.55/181.56 [2799]P57(x27993,x27992)+~E(x27991,x27992)+~P57(x27993,x27991) % 181.55/181.56 [2800]P20(x28002,x28003,x28004)+~E(x28001,x28002)+~P20(x28001,x28003,x28004) % 181.55/181.56 [2801]P20(x28013,x28012,x28014)+~E(x28011,x28012)+~P20(x28013,x28011,x28014) % 181.55/181.56 [2802]P20(x28023,x28024,x28022)+~E(x28021,x28022)+~P20(x28023,x28024,x28021) % 181.55/181.56 [2803]~P142(x28031)+P142(x28032)+~E(x28031,x28032) % 181.55/181.56 [2804]~P129(x28041)+P129(x28042)+~E(x28041,x28042) % 181.55/181.56 [2805]P25(x28052,x28053,x28054,x28055,x28056,x28057)+~E(x28051,x28052)+~P25(x28051,x28053,x28054,x28055,x28056,x28057) % 181.55/181.56 [2806]P25(x28063,x28062,x28064,x28065,x28066,x28067)+~E(x28061,x28062)+~P25(x28063,x28061,x28064,x28065,x28066,x28067) % 181.55/181.56 [2807]P25(x28073,x28074,x28072,x28075,x28076,x28077)+~E(x28071,x28072)+~P25(x28073,x28074,x28071,x28075,x28076,x28077) % 181.55/181.56 [2808]P25(x28083,x28084,x28085,x28082,x28086,x28087)+~E(x28081,x28082)+~P25(x28083,x28084,x28085,x28081,x28086,x28087) % 181.55/181.56 [2809]P25(x28093,x28094,x28095,x28096,x28092,x28097)+~E(x28091,x28092)+~P25(x28093,x28094,x28095,x28096,x28091,x28097) % 181.55/181.56 [2810]P25(x28103,x28104,x28105,x28106,x28107,x28102)+~E(x28101,x28102)+~P25(x28103,x28104,x28105,x28106,x28107,x28101) % 181.55/181.56 [2811]P19(x28112,x28113,x28114)+~E(x28111,x28112)+~P19(x28111,x28113,x28114) % 181.55/181.56 [2812]P19(x28123,x28122,x28124)+~E(x28121,x28122)+~P19(x28123,x28121,x28124) % 181.55/181.56 [2813]P19(x28133,x28134,x28132)+~E(x28131,x28132)+~P19(x28133,x28134,x28131) % 181.55/181.56 [2814]~P96(x28141)+P96(x28142)+~E(x28141,x28142) % 181.55/181.56 [2815]P15(x28152,x28153,x28154,x28155,x28156,x28157)+~E(x28151,x28152)+~P15(x28151,x28153,x28154,x28155,x28156,x28157) % 181.55/181.56 [2816]P15(x28163,x28162,x28164,x28165,x28166,x28167)+~E(x28161,x28162)+~P15(x28163,x28161,x28164,x28165,x28166,x28167) % 181.55/181.56 [2817]P15(x28173,x28174,x28172,x28175,x28176,x28177)+~E(x28171,x28172)+~P15(x28173,x28174,x28171,x28175,x28176,x28177) % 181.55/181.56 [2818]P15(x28183,x28184,x28185,x28182,x28186,x28187)+~E(x28181,x28182)+~P15(x28183,x28184,x28185,x28181,x28186,x28187) % 181.55/181.56 [2819]P15(x28193,x28194,x28195,x28196,x28192,x28197)+~E(x28191,x28192)+~P15(x28193,x28194,x28195,x28196,x28191,x28197) % 181.55/181.56 [2820]P15(x28203,x28204,x28205,x28206,x28207,x28202)+~E(x28201,x28202)+~P15(x28203,x28204,x28205,x28206,x28207,x28201) % 181.55/181.56 [2821]P24(x28212,x28213,x28214,x28215,x28216,x28217)+~E(x28211,x28212)+~P24(x28211,x28213,x28214,x28215,x28216,x28217) % 181.55/181.56 [2822]P24(x28223,x28222,x28224,x28225,x28226,x28227)+~E(x28221,x28222)+~P24(x28223,x28221,x28224,x28225,x28226,x28227) % 181.55/181.56 [2823]P24(x28233,x28234,x28232,x28235,x28236,x28237)+~E(x28231,x28232)+~P24(x28233,x28234,x28231,x28235,x28236,x28237) % 181.55/181.56 [2824]P24(x28243,x28244,x28245,x28242,x28246,x28247)+~E(x28241,x28242)+~P24(x28243,x28244,x28245,x28241,x28246,x28247) % 181.55/181.56 [2825]P24(x28253,x28254,x28255,x28256,x28252,x28257)+~E(x28251,x28252)+~P24(x28253,x28254,x28255,x28256,x28251,x28257) % 181.55/181.56 [2826]P24(x28263,x28264,x28265,x28266,x28267,x28262)+~E(x28261,x28262)+~P24(x28263,x28264,x28265,x28266,x28267,x28261) % 181.55/181.56 [2827]~P86(x28271)+P86(x28272)+~E(x28271,x28272) % 181.55/181.56 [2828]~P131(x28281)+P131(x28282)+~E(x28281,x28282) % 181.55/181.56 [2829]P51(x28292,x28293,x28294,x28295)+~E(x28291,x28292)+~P51(x28291,x28293,x28294,x28295) % 181.55/181.56 [2830]P51(x28303,x28302,x28304,x28305)+~E(x28301,x28302)+~P51(x28303,x28301,x28304,x28305) % 181.55/181.56 [2831]P51(x28313,x28314,x28312,x28315)+~E(x28311,x28312)+~P51(x28313,x28314,x28311,x28315) % 181.55/181.56 [2832]P51(x28323,x28324,x28325,x28322)+~E(x28321,x28322)+~P51(x28323,x28324,x28325,x28321) % 181.55/181.56 [2833]~P102(x28331)+P102(x28332)+~E(x28331,x28332) % 181.55/181.56 [2834]~P128(x28341)+P128(x28342)+~E(x28341,x28342) % 181.55/181.56 [2835]P10(x28352,x28353,x28354)+~E(x28351,x28352)+~P10(x28351,x28353,x28354) % 181.55/181.56 [2836]P10(x28363,x28362,x28364)+~E(x28361,x28362)+~P10(x28363,x28361,x28364) % 181.55/181.56 [2837]P10(x28373,x28374,x28372)+~E(x28371,x28372)+~P10(x28373,x28374,x28371) % 181.55/181.56 [2838]~P118(x28381)+P118(x28382)+~E(x28381,x28382) % 181.55/181.56 [2839]~P71(x28391)+P71(x28392)+~E(x28391,x28392) % 181.55/181.56 [2840]~P111(x28401)+P111(x28402)+~E(x28401,x28402) % 181.55/181.56 [2841]P23(x28412,x28413,x28414,x28415,x28416)+~E(x28411,x28412)+~P23(x28411,x28413,x28414,x28415,x28416) % 181.55/181.56 [2842]P23(x28423,x28422,x28424,x28425,x28426)+~E(x28421,x28422)+~P23(x28423,x28421,x28424,x28425,x28426) % 181.55/181.56 [2843]P23(x28433,x28434,x28432,x28435,x28436)+~E(x28431,x28432)+~P23(x28433,x28434,x28431,x28435,x28436) % 181.55/181.56 [2844]P23(x28443,x28444,x28445,x28442,x28446)+~E(x28441,x28442)+~P23(x28443,x28444,x28445,x28441,x28446) % 181.55/181.56 [2845]P23(x28453,x28454,x28455,x28456,x28452)+~E(x28451,x28452)+~P23(x28453,x28454,x28455,x28456,x28451) % 181.55/181.56 [2846]~P87(x28461)+P87(x28462)+~E(x28461,x28462) % 181.55/181.56 [2847]P42(x28472,x28473,x28474,x28475)+~E(x28471,x28472)+~P42(x28471,x28473,x28474,x28475) % 181.55/181.56 [2848]P42(x28483,x28482,x28484,x28485)+~E(x28481,x28482)+~P42(x28483,x28481,x28484,x28485) % 181.55/181.56 [2849]P42(x28493,x28494,x28492,x28495)+~E(x28491,x28492)+~P42(x28493,x28494,x28491,x28495) % 181.55/181.56 [2850]P42(x28503,x28504,x28505,x28502)+~E(x28501,x28502)+~P42(x28503,x28504,x28505,x28501) % 181.55/181.56 [2851]~P127(x28511)+P127(x28512)+~E(x28511,x28512) % 181.55/181.56 [2852]~P38(x28521)+P38(x28522)+~E(x28521,x28522) % 181.55/181.56 [2853]P47(x28532,x28533)+~E(x28531,x28532)+~P47(x28531,x28533) % 181.55/181.56 [2854]P47(x28543,x28542)+~E(x28541,x28542)+~P47(x28543,x28541) % 181.55/181.56 [2855]P49(x28552,x28553,x28554)+~E(x28551,x28552)+~P49(x28551,x28553,x28554) % 181.55/181.56 [2856]P49(x28563,x28562,x28564)+~E(x28561,x28562)+~P49(x28563,x28561,x28564) % 181.55/181.56 [2857]P49(x28573,x28574,x28572)+~E(x28571,x28572)+~P49(x28573,x28574,x28571) % 181.55/181.56 [2858]~P119(x28581)+P119(x28582)+~E(x28581,x28582) % 181.55/181.56 % 181.55/181.56 %------------------------------------------- % 181.73/181.61 cnf(10146,plain, % 181.73/181.61 (E(f76(x101461,x101462,x101463,x101463,x101464),x101464)), % 181.73/181.61 inference(rename_variables,[],[3926])). % 181.73/181.61 cnf(10149,plain, % 181.73/181.61 (~E(f324(a115,x101491),x101491)), % 181.73/181.61 inference(rename_variables,[],[4449])). % 181.73/181.61 cnf(10152,plain, % 181.73/181.61 (E(f76(x101521,x101522,x101523,x101523,x101524),x101524)), % 181.73/181.61 inference(rename_variables,[],[3926])). % 181.73/181.61 cnf(10159,plain, % 181.73/181.61 (~E(f324(a115,x101591),x101591)), % 181.73/181.61 inference(rename_variables,[],[4449])). % 181.73/181.61 cnf(10166,plain, % 181.73/181.61 (E(f324(f192(f866(x101661)),f165(x101661,x101662,x101663)),x101662)), % 181.73/181.61 inference(rename_variables,[],[3336])). % 181.73/181.61 cnf(10173,plain, % 181.73/181.61 (~E(f324(a115,x101731),x101731)), % 181.73/181.61 inference(rename_variables,[],[4449])). % 181.73/181.61 cnf(10178,plain, % 181.73/181.61 (~P1(f324(f62(x101781,x101782,f191(f871(x101781,a859))),x101783))), % 181.73/181.61 inference(rename_variables,[],[4546])). % 181.73/181.61 cnf(10181,plain, % 181.73/181.61 (~P1(f324(f62(x101811,x101812,f191(f871(x101811,a859))),x101813))), % 181.73/181.61 inference(rename_variables,[],[4546])). % 181.73/181.61 cnf(10184,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),x101841),f2(a865)))), % 181.73/181.61 inference(rename_variables,[],[4526])). % 181.73/181.61 cnf(10187,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),x101871),f2(a865)))), % 181.73/181.61 inference(rename_variables,[],[4526])). % 181.73/181.61 cnf(10204,plain, % 181.73/181.61 (~P1(f324(f324(f238(a865),f324(a115,x102041)),x102041))), % 181.73/181.61 inference(rename_variables,[],[4531])). % 181.73/181.61 cnf(10207,plain, % 181.73/181.61 (~E(f324(f324(f145(x102071),x102072),x102073),x102073)), % 181.73/181.61 inference(rename_variables,[],[4482])). % 181.73/181.61 cnf(10213,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),x102131),f2(a865)))), % 181.73/181.61 inference(rename_variables,[],[4526])). % 181.73/181.61 cnf(10216,plain, % 181.73/181.61 (E(f76(x102161,x102162,x102163,x102163,x102164),x102164)), % 181.73/181.61 inference(rename_variables,[],[3926])). % 181.73/181.61 cnf(10219,plain, % 181.73/181.61 (E(f76(x102191,x102192,x102193,x102193,x102194),x102194)), % 181.73/181.61 inference(rename_variables,[],[3926])). % 181.73/181.61 cnf(10226,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x102261),x102262)),x102262))), % 181.73/181.61 inference(rename_variables,[],[4548])). % 181.73/181.61 cnf(10229,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x102291),x102292)),x102292))), % 181.73/181.61 inference(rename_variables,[],[4548])). % 181.73/181.61 cnf(10236,plain, % 181.73/181.61 (~E(x102361,f324(a115,x102361))), % 181.73/181.61 inference(scs_inference,[],[3926,10146,10152,10216,4449,10149,10159,3336,3103,3162,3128,3109,4482,3337,3252,4526,10184,10187,4523,4477,4531,4095,4529,3242,4513,4546,10178,4550,4548,10226,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145])). % 181.73/181.61 cnf(10250,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),x102501),x102501))), % 181.73/181.61 inference(rename_variables,[],[4522])). % 181.73/181.61 cnf(10253,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),f44(a865,x102531,x102532)),x102531))), % 181.73/181.61 inference(rename_variables,[],[3723])). % 181.73/181.61 cnf(10274,plain, % 181.73/181.61 (E(f324(f37(a865),f324(f245(a865),x102741)),x102741)), % 181.73/181.61 inference(rename_variables,[],[3160])). % 181.73/181.61 cnf(10282,plain, % 181.73/181.61 (~E(f324(a115,x102821),x102821)), % 181.73/181.61 inference(rename_variables,[],[4449])). % 181.73/181.61 cnf(10285,plain, % 181.73/181.61 (~E(f324(a115,x102851),x102851)), % 181.73/181.61 inference(rename_variables,[],[4449])). % 181.73/181.61 cnf(10288,plain, % 181.73/181.61 (~E(f324(a115,x102881),x102881)), % 181.73/181.61 inference(rename_variables,[],[4449])). % 181.73/181.61 cnf(10293,plain, % 181.73/181.61 (P1(f324(f324(f239(a865),x102931),f324(a115,x102931)))), % 181.73/181.61 inference(rename_variables,[],[3337])). % 181.73/181.61 cnf(10302,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),x103021),x103021))), % 181.73/181.61 inference(rename_variables,[],[3268])). % 181.73/181.61 cnf(10309,plain, % 181.73/181.61 (E(f76(x103091,x103092,x103093,x103093,x103094),x103094)), % 181.73/181.61 inference(rename_variables,[],[3926])). % 181.73/181.61 cnf(10312,plain, % 181.73/181.61 (E(f76(x103121,x103122,x103123,x103123,x103124),x103124)), % 181.73/181.61 inference(rename_variables,[],[3926])). % 181.73/181.61 cnf(10331,plain, % 181.73/181.61 (P1(f324(f324(f238(a1),x103311),x103311))), % 181.73/181.61 inference(rename_variables,[],[3269])). % 181.73/181.61 cnf(10340,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),x103401),x103401))), % 181.73/181.61 inference(rename_variables,[],[4522])). % 181.73/181.61 cnf(10345,plain, % 181.73/181.61 (~E(f324(f324(f324(f72(x103451,f869(x103452)),x103453),x103454),f324(f233(x103452),x103455)),f324(f16(f869(x103452),x103451),f203(x103452)))), % 181.73/181.61 inference(rename_variables,[],[4543])). % 181.73/181.61 cnf(10349,plain, % 181.73/181.61 (E(f324(f324(f81(a865),x103491),f332(x103491,x103491)),x103491)), % 181.73/181.61 inference(scs_inference,[],[3926,10146,10152,10216,10219,10309,4449,10149,10159,10173,10282,10285,3336,3103,3162,3128,3109,3197,4543,4482,3160,4051,4555,3180,3337,10293,3252,4526,10184,10187,3705,3852,3298,3271,4523,4477,4004,3268,10302,3269,3270,4522,10250,3363,3785,3723,10253,4531,10204,4095,4529,4512,3242,4513,4517,4546,10178,4550,3745,4548,10226,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427])). % 181.73/181.61 cnf(10372,plain, % 181.73/181.61 (~E(f324(f324(f145(x103721),x103722),x103723),x103723)), % 181.73/181.61 inference(rename_variables,[],[4482])). % 181.73/181.61 cnf(10375,plain, % 181.73/181.61 (~E(f324(a25,x103751),f33(x103752,x103753))), % 181.73/181.61 inference(rename_variables,[],[4467])). % 181.73/181.61 cnf(10386,plain, % 181.73/181.61 (P1(f324(f324(f238(a1),x103861),x103861))), % 181.73/181.61 inference(rename_variables,[],[3269])). % 181.73/181.61 cnf(10391,plain, % 181.73/181.61 (~E(f324(a115,x103911),x103911)), % 181.73/181.61 inference(rename_variables,[],[4449])). % 181.73/181.61 cnf(10398,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),x103981),x103981))), % 181.73/181.61 inference(rename_variables,[],[3268])). % 181.73/181.61 cnf(10411,plain, % 181.73/181.61 (P1(f324(f324(f239(a865),x104111),f324(a115,x104111)))), % 181.73/181.61 inference(rename_variables,[],[3337])). % 181.73/181.61 cnf(10416,plain, % 181.73/181.61 (E(f324(f324(f124(x104161),f116(x104161)),x104162),x104162)), % 181.73/181.61 inference(rename_variables,[],[3220])). % 181.73/181.61 cnf(10434,plain, % 181.73/181.61 (~P1(f324(f62(x104341,x104342,f191(f871(x104341,a859))),x104343))), % 181.73/181.61 inference(rename_variables,[],[4546])). % 181.73/181.61 cnf(10453,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),x104531),x104531))), % 181.73/181.61 inference(rename_variables,[],[4522])). % 181.73/181.61 cnf(10468,plain, % 181.73/181.61 (~E(f324(a25,x104681),f33(x104682,x104683))), % 181.73/181.61 inference(rename_variables,[],[4467])). % 181.73/181.61 cnf(10477,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),x104771),x104771))), % 181.73/181.61 inference(rename_variables,[],[4522])). % 181.73/181.61 cnf(10482,plain, % 181.73/181.61 (P1(f324(f324(f239(a865),x104821),f324(a115,x104821)))), % 181.73/181.61 inference(rename_variables,[],[3337])). % 181.73/181.61 cnf(10485,plain, % 181.73/181.61 (~P1(f324(f62(x104851,x104852,f191(f871(x104851,a859))),x104853))), % 181.73/181.61 inference(rename_variables,[],[4546])). % 181.73/181.61 cnf(10488,plain, % 181.73/181.61 (~P1(f324(f62(x104881,x104882,f191(f871(x104881,a859))),x104883))), % 181.73/181.61 inference(rename_variables,[],[4546])). % 181.73/181.61 cnf(10493,plain, % 181.73/181.61 (~P1(f324(f62(x104931,x104932,f191(f871(x104931,a859))),x104933))), % 181.73/181.61 inference(rename_variables,[],[4546])). % 181.73/181.61 cnf(10504,plain, % 181.73/181.61 (~E(f324(a115,x105041),x105041)), % 181.73/181.61 inference(rename_variables,[],[4449])). % 181.73/181.61 cnf(10529,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),x105291),x105291))), % 181.73/181.61 inference(rename_variables,[],[3268])). % 181.73/181.61 cnf(10532,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),x105321),f324(f324(f82(a865),x105321),x105321)))), % 181.73/181.61 inference(rename_variables,[],[3535])). % 181.73/181.61 cnf(10535,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),x105351),f324(f324(f82(a865),x105351),x105351)))), % 181.73/181.61 inference(rename_variables,[],[3535])). % 181.73/181.61 cnf(10538,plain, % 181.73/181.61 (P1(f324(f324(f239(a865),x105381),f324(a115,f324(f324(f81(a865),x105382),x105381))))), % 181.73/181.61 inference(rename_variables,[],[3716])). % 181.73/181.61 cnf(10543,plain, % 181.73/181.61 (P1(f324(f324(f239(a865),x105431),f324(a115,x105431)))), % 181.73/181.61 inference(rename_variables,[],[3337])). % 181.73/181.61 cnf(10546,plain, % 181.73/181.61 (P1(f324(f324(f239(a865),x105461),f324(a115,x105461)))), % 181.73/181.61 inference(rename_variables,[],[3337])). % 181.73/181.61 cnf(10549,plain, % 181.73/181.61 (P1(f324(f324(f326(x105491),x105492),f247(f871(x105491,a859))))), % 181.73/181.61 inference(rename_variables,[],[3426])). % 181.73/181.61 cnf(10564,plain, % 181.73/181.61 (~P1(f324(f324(f238(a865),f324(a115,x105641)),x105641))), % 181.73/181.61 inference(rename_variables,[],[4531])). % 181.73/181.61 cnf(10567,plain, % 181.73/181.61 (~P1(f324(f324(f238(a865),f324(a115,x105671)),x105671))), % 181.73/181.61 inference(rename_variables,[],[4531])). % 181.73/181.61 cnf(10570,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x105701),x105702)),x105702))), % 181.73/181.61 inference(rename_variables,[],[4548])). % 181.73/181.61 cnf(10573,plain, % 181.73/181.61 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x105731),x105732)),x105732))), % 181.73/181.61 inference(rename_variables,[],[4548])). % 181.73/181.61 cnf(10576,plain, % 181.73/181.61 (P1(f324(f247(f871(x105761,a859)),x105762))), % 181.73/181.61 inference(rename_variables,[],[3330])). % 181.73/181.61 cnf(10579,plain, % 181.73/181.61 (E(f324(f37(a865),f324(f245(a865),x105791)),x105791)), % 181.73/181.61 inference(rename_variables,[],[3160])). % 181.73/181.61 cnf(10582,plain, % 181.73/181.61 (P1(f324(f324(f239(a865),x105821),f324(a115,x105821)))), % 181.73/181.61 inference(rename_variables,[],[3337])). % 181.73/181.61 cnf(10589,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),x105891),x105891))), % 181.73/181.61 inference(rename_variables,[],[3268])). % 181.73/181.61 cnf(10594,plain, % 181.73/181.61 (P1(f324(f324(f238(a1),x105941),x105941))), % 181.73/181.61 inference(rename_variables,[],[3269])). % 181.73/181.61 cnf(10603,plain, % 181.73/181.61 (E(f76(x106031,x106032,x106033,x106033,x106034),x106034)), % 181.73/181.61 inference(rename_variables,[],[3926])). % 181.73/181.61 cnf(10606,plain, % 181.73/181.61 (P1(f324(f247(f871(x106061,a859)),x106062))), % 181.73/181.61 inference(rename_variables,[],[3330])). % 181.73/181.61 cnf(10609,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),f2(a865)),x106091))), % 181.73/181.61 inference(rename_variables,[],[3290])). % 181.73/181.61 cnf(10612,plain, % 181.73/181.61 (P1(f324(f324(f238(f871(x106121,a859)),f191(f871(x106121,a859))),x106122))), % 181.73/181.61 inference(rename_variables,[],[3714])). % 181.73/181.61 cnf(10615,plain, % 181.73/181.61 (P1(f324(f247(f871(x106151,a859)),x106152))), % 181.73/181.61 inference(rename_variables,[],[3330])). % 181.73/181.61 cnf(10618,plain, % 181.73/181.61 (P1(f324(f324(f238(a865),x106181),f324(f324(f82(a865),x106181),x106181)))), % 181.73/181.61 inference(rename_variables,[],[3535])). % 181.73/181.61 cnf(10623,plain, % 181.73/181.61 (E(f76(x106231,x106232,x106233,x106233,x106234),x106234)), % 181.73/181.61 inference(rename_variables,[],[3926])). % 181.73/181.61 cnf(10627,plain, % 181.73/181.61 (~P1(f324(f324(f238(a865),f324(a115,f324(a115,f324(f324(f81(a865),x106271),x106272)))),f324(a115,x106272)))), % 181.73/181.61 inference(scs_inference,[],[3926,10146,10152,10216,10219,10309,10312,10603,4449,10149,10159,10173,10282,10285,10288,10391,4467,10375,3336,3103,3162,3128,3109,3197,3220,10416,4543,4482,10207,3160,10274,4051,4555,3180,3629,3570,3337,10293,10411,10482,10543,10546,10582,3718,3252,4526,10184,10187,10213,4538,3705,3479,3852,3296,3298,3271,4523,4477,4004,3268,10302,10398,10529,3269,10331,10386,3270,4522,10250,10340,10453,3426,3330,10576,10606,3363,3785,3723,10253,4531,10204,10564,3290,4095,4529,4512,3242,3247,4514,4513,4517,4546,10178,10181,10434,10485,10488,4553,3714,3535,10532,10535,4550,3745,4548,10226,10229,10570,3716,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304])). % 181.73/181.62 cnf(10660,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x106601),x106601))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(10671,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x106711,f871(x106712,a859))),x106713),x106714))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(10680,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x106801),f324(a115,x106801)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(10682,plain, % 181.73/181.62 (P1(f324(f324(f239(a1),f324(f324(f22(a1),x106821),f79(a1))),x106821))), % 181.73/181.62 inference(scs_inference,[],[3926,10146,10152,10216,10219,10309,10312,10603,4449,10149,10159,10173,10282,10285,10288,10391,4467,10375,3336,3103,3162,3128,3109,3197,3220,10416,4543,4482,10207,3160,10274,4051,3903,4555,3180,3629,3570,3337,10293,10411,10482,10543,10546,10582,3718,3252,4526,10184,10187,10213,4538,3705,3479,3852,3296,3298,3271,4523,4477,4004,3268,10302,10398,10529,10589,10660,3269,10331,10386,10594,3270,4522,10250,10340,10453,3426,4534,3330,10576,10606,3363,3785,3723,10253,4531,10204,10564,10567,3290,4095,4529,4512,4515,3242,3247,4514,4513,4517,4546,10178,10181,10434,10485,10488,4553,3714,3535,10532,10535,4550,4551,3745,4548,10226,10229,10570,3716,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565])). % 181.73/181.62 cnf(10683,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x106831),x106831))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(10688,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x106881),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(10701,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x107011),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(10704,plain, % 181.73/181.62 (~P1(f324(f324(f239(f871(x107041,a859)),x107042),f191(f871(x107041,a859))))), % 181.73/181.62 inference(rename_variables,[],[4544])). % 181.73/181.62 cnf(10707,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x107071),x107071))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(10710,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x107101),x107101))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(10725,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x107251),x107251))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(10734,plain, % 181.73/181.62 (~P1(f324(f324(f326(x107341),x107342),f191(f871(x107341,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(10743,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x107431),x107431))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(10746,plain, % 181.73/181.62 (~P1(f324(f324(f326(x107461),x107462),f191(f871(x107461,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(10749,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x107491,a859)),f324(f303(x107492,x107491,x107493),f324(f304(x107492,x107491,x107493),x107494))),x107494))), % 181.73/181.62 inference(rename_variables,[],[4155])). % 181.73/181.62 cnf(10756,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x107561,a859)),f324(f167(x107561),f324(f130(x107561,x107562),x107563))),f324(f167(x107561),x107563)))), % 181.73/181.62 inference(rename_variables,[],[3913])). % 181.73/181.62 cnf(10759,plain, % 181.73/181.62 (E(f324(f303(x107591,x107591,f5(x107591)),x107592),x107592)), % 181.73/181.62 inference(rename_variables,[],[3326])). % 181.73/181.62 cnf(10764,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x107641))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(10767,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x107671),x107671))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(10770,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x107701),x107701))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(10773,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x107731,f871(x107732,a859))),x107733),x107734))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(10780,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x107801),x107801))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(10791,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x107911),f324(f324(f82(a865),x107911),x107911)))), % 181.73/181.62 inference(rename_variables,[],[3535])). % 181.73/181.62 cnf(10797,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x107971),f324(a115,f324(f324(f81(a865),x107972),x107971))))), % 181.73/181.62 inference(rename_variables,[],[3716])). % 181.73/181.62 cnf(10804,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x108041),x108041))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(10807,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x108071),x108071))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(10810,plain, % 181.73/181.62 (~E(f324(a115,x108101),x108101)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(10815,plain, % 181.73/181.62 (P1(f324(f324(f326(x108151),x108152),f247(f871(x108151,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(10820,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x108201),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(10835,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x108351))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(10842,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x108421),x108421))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(10851,plain, % 181.73/181.62 (~P1(f324(f324(f326(x108511),x108512),f191(f871(x108511,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(10855,plain, % 181.73/181.62 (E(f324(f324(f104(f871(x108551,a859)),f324(f324(f104(f871(x108551,a859)),x108552),f324(f80(f871(x108551,a859)),x108553))),x108553),f191(f871(x108551,a859)))), % 181.73/181.62 inference(scs_inference,[],[3926,10146,10152,10216,10219,10309,10312,10603,4449,10149,10159,10173,10282,10285,10288,10391,10504,4467,10375,3336,3103,3162,3128,3109,3326,3197,3220,10416,4543,4482,10207,3160,10274,4051,3903,4555,3180,3471,3629,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,3718,3252,4526,10184,10187,10213,10688,10701,4538,3705,3479,3852,3296,3298,3271,4523,4477,4015,3913,10756,3630,4004,4544,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,3269,10331,10386,10594,10683,3270,4522,10250,10340,10453,10477,10725,10770,3426,10549,10815,4534,10734,10746,3330,10576,10606,3363,3785,3723,10253,4531,10204,10564,10567,3290,10609,10764,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,4546,10178,10181,10434,10485,10488,4553,3714,3535,10532,10535,10618,10791,4550,4551,10671,4155,3745,4548,10226,10229,10570,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701])). % 181.73/181.62 cnf(10859,plain, % 181.73/181.62 (P1(f324(f324(f326(x108591),x108592),f247(f871(x108591,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(10862,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x108621),f866(x108621))),f324(f324(f259(f866(x108621),f866(x108621)),x108622),f116(x108621))),f139(x108621,x108623)))), % 181.73/181.62 inference(rename_variables,[],[4555])). % 181.73/181.62 cnf(10868,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(x108681,x108681)),x108682),f256(x108681,f191(f871(x108681,a859)))))), % 181.73/181.62 inference(scs_inference,[],[3926,10146,10152,10216,10219,10309,10312,10603,4449,10149,10159,10173,10282,10285,10288,10391,10504,4467,10375,3336,3103,3162,3128,3109,3326,3197,3220,10416,4543,4482,10207,3160,10274,4051,3903,4555,3180,3471,3629,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,3718,3252,4526,10184,10187,10213,10688,10701,4538,3705,3479,3852,3296,3298,3271,4523,4477,4015,3913,10756,3630,4004,4544,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,3269,10331,10386,10594,10683,3270,4522,10250,10340,10453,10477,10725,10770,3426,10549,10815,4534,10734,10746,10851,3330,10576,10606,3363,3785,3723,10253,4531,10204,10564,10567,3290,10609,10764,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,4546,10178,10181,10434,10485,10488,4553,3714,3535,10532,10535,10618,10791,4550,4551,10671,4155,3745,4548,10226,10229,10570,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840])). % 181.73/181.62 cnf(10869,plain, % 181.73/181.62 (~P1(f324(f324(f326(x108691),x108692),f191(f871(x108691,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(10871,plain, % 181.73/181.62 (~P1(f324(f324(f326(x108711),x108712),f324(f304(x108711,x108713,x108714),f191(f871(x108713,a859)))))), % 181.73/181.62 inference(scs_inference,[],[3926,10146,10152,10216,10219,10309,10312,10603,4449,10149,10159,10173,10282,10285,10288,10391,10504,4467,10375,3336,3103,3162,3128,3109,3326,3197,3220,10416,4543,4482,10207,3160,10274,4051,3903,4555,3180,3471,3629,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,3718,3252,4526,10184,10187,10213,10688,10701,4538,3705,3479,3852,3296,3298,3271,4523,4477,4015,3913,10756,3630,4004,4544,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,3269,10331,10386,10594,10683,3270,4522,10250,10340,10453,10477,10725,10770,3426,10549,10815,4534,10734,10746,10851,10869,3330,10576,10606,3363,3785,3723,10253,4531,10204,10564,10567,3290,10609,10764,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,4546,10178,10181,10434,10485,10488,4553,3714,3535,10532,10535,10618,10791,4550,4551,10671,4155,3745,4548,10226,10229,10570,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876])). % 181.73/181.62 cnf(10872,plain, % 181.73/181.62 (~P1(f324(f324(f326(x108721),x108722),f191(f871(x108721,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(10875,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x108751,a859)),x108752),f324(f324(f302(x108751),x108753),x108752)))), % 181.73/181.62 inference(rename_variables,[],[3712])). % 181.73/181.62 cnf(10878,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x108781),x108781))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(10881,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x108811,a859)),x108812),f324(f324(f302(x108811),x108813),x108812)))), % 181.73/181.62 inference(rename_variables,[],[3712])). % 181.73/181.62 cnf(10884,plain, % 181.73/181.62 (E(f324(f303(x108841,x108841,f5(x108841)),x108842),x108842)), % 181.73/181.62 inference(rename_variables,[],[3326])). % 181.73/181.62 cnf(10887,plain, % 181.73/181.62 (E(f76(x108871,x108872,x108873,x108873,x108874),x108874)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(10890,plain, % 181.73/181.62 (E(f76(x108901,x108902,x108903,x108903,x108904),x108904)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(10903,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x109031,a859)),x109032),f324(f324(f302(x109031),x109033),x109032)))), % 181.73/181.62 inference(rename_variables,[],[3712])). % 181.73/181.62 cnf(10916,plain, % 181.73/181.62 (~E(f324(a25,x109161),f33(x109162,x109163))), % 181.73/181.62 inference(rename_variables,[],[4467])). % 181.73/181.62 cnf(10919,plain, % 181.73/181.62 (~P1(f324(f62(x109191,x109192,f191(f871(x109191,a859))),x109193))), % 181.73/181.62 inference(rename_variables,[],[4546])). % 181.73/181.62 cnf(10932,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x109321),f324(a115,x109321)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(10942,plain, % 181.73/181.62 (~E(f324(f303(x109421,f871(x109421,a859),x109422),x109423),f324(f301(x109421),x109423))), % 181.73/181.62 inference(rename_variables,[],[4532])). % 181.73/181.62 cnf(10945,plain, % 181.73/181.62 (~P1(f324(f324(f326(x109451),x109452),f191(f871(x109451,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(10948,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x109481,x109481)),f324(f324(f259(x109481,x109481),x109482),x109482)),f300(x109481,x109483)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(10951,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x109511,a859)),f324(f167(x109511),f171(x109511,x109512,x109513))),f324(f167(x109511),x109512)))), % 181.73/181.62 inference(rename_variables,[],[3967])). % 181.73/181.62 cnf(10954,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x109541,a859)),x109542),f247(f871(x109541,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(10970,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x109701,a859)),f191(f871(x109701,a859))),x109702))), % 181.73/181.62 inference(rename_variables,[],[3714])). % 181.73/181.62 cnf(10981,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x109811),f866(x109811))),f324(f324(f259(f866(x109811),f866(x109811)),x109812),f116(x109811))),f141(x109811,x109813)))), % 181.73/181.62 inference(rename_variables,[],[4556])). % 181.73/181.62 cnf(10992,plain, % 181.73/181.62 (~E(f324(a115,x109921),x109921)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(10995,plain, % 181.73/181.62 (~E(f324(a115,x109951),x109951)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11005,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x110051,a859)),x110052),x110052))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(11012,plain, % 181.73/181.62 (~E(f324(a115,x110121),x110121)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11015,plain, % 181.73/181.62 (~E(f324(a115,x110151),x110151)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11020,plain, % 181.73/181.62 (P27(x110201,x110201,f5(x110201),x110202)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(11025,plain, % 181.73/181.62 (~E(f324(f303(x110251,f871(x110251,a859),x110252),x110253),f324(f301(x110251),x110253))), % 181.73/181.62 inference(rename_variables,[],[4532])). % 181.73/181.62 cnf(11030,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x110301,a859)),x110302),f247(f871(x110301,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(11046,plain, % 181.73/181.62 (~P1(f324(f324(f326(x110461),x110462),f191(f871(x110461,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11049,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x110491)),x110491))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11054,plain, % 181.73/181.62 (~P1(f324(f324(f326(x110541),x110542),f191(f871(x110541,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11067,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x110671)),x110671))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11070,plain, % 181.73/181.62 (~P1(f324(f324(f326(x110701),x110702),f191(f871(x110701,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11082,plain, % 181.73/181.62 (E(f324(x110821,f661(f324(x110821,x110822),f324(f233(x110823),x110822),x110821,x110824,x110823)),f324(x110821,x110822))), % 181.73/181.62 inference(scs_inference,[],[3509,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,4467,10375,10468,10916,3725,3336,3103,3162,3128,3109,3326,10759,3197,3220,10416,3373,4543,3901,4482,10207,4532,10942,3374,3160,10274,4051,3903,10948,4555,10862,4556,3180,3471,3629,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,10932,3718,3252,4526,10184,10187,10213,10688,10701,10820,4538,3705,3479,3852,3296,3298,3271,4523,4477,4015,3913,10756,3967,3630,4004,3648,10954,4544,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,3269,10331,10386,10594,10683,3270,4522,10250,10340,10453,10477,10725,10770,3426,10549,10815,10859,4534,10734,10746,10851,10869,10872,10945,11046,11054,3330,10576,10606,3363,3785,3723,10253,4531,10204,10564,10567,11049,3290,10609,10764,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,4546,10178,10181,10434,10485,10488,10493,4553,3869,3712,10875,10881,3567,3714,10612,3535,10532,10535,10618,10791,4550,4551,10671,4155,3745,4548,10226,10229,10570,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843])). % 181.73/181.62 cnf(11091,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x110911,x110911)),f324(f324(f259(x110911,x110911),x110912),x110912)),f300(x110911,x110913)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(11096,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x110961),f866(x110961))),f324(f324(f259(f866(x110961),f866(x110961)),x110962),f116(x110961))),f139(x110961,x110963)))), % 181.73/181.62 inference(rename_variables,[],[4555])). % 181.73/181.62 cnf(11099,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x110991),f866(x110991))),f324(f324(f259(f866(x110991),f866(x110991)),x110992),f116(x110991))),f141(x110991,x110993)))), % 181.73/181.62 inference(rename_variables,[],[4556])). % 181.73/181.62 cnf(11102,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x111021),f866(x111021))),f324(f324(f259(f866(x111021),f866(x111021)),x111022),f116(x111021))),f151(x111021,x111023)))), % 181.73/181.62 inference(rename_variables,[],[4557])). % 181.73/181.62 cnf(11107,plain, % 181.73/181.62 (~P1(f324(f324(f239(f871(x111071,a859)),x111072),f191(f871(x111071,a859))))), % 181.73/181.62 inference(rename_variables,[],[4544])). % 181.73/181.62 cnf(11110,plain, % 181.73/181.62 (~P1(f324(f324(f326(x111101),x111102),f191(f871(x111101,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11117,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x111171,a859)),x111172),f247(f871(x111171,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(11128,plain, % 181.73/181.62 (~P1(f324(f324(f326(x111281),x111282),f191(f871(x111281,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11131,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(x111311,x111311)),f324(f324(f259(x111311,x111311),x111312),x111313)),f147(x111311,f116(f871(x111311,a865)))))), % 181.73/181.62 inference(rename_variables,[],[4553])). % 181.73/181.62 cnf(11134,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x111341,a859)),x111342),x111342))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(11137,plain, % 181.73/181.62 (~P1(f324(f324(f326(x111371),x111372),f191(f871(x111371,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11140,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x111401,a859)),f191(f871(x111401,a859))),x111402))), % 181.73/181.62 inference(rename_variables,[],[3714])). % 181.73/181.62 cnf(11143,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x111431,x111431)),f324(f324(f259(x111431,x111431),x111432),x111432)),f300(x111431,x111433)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(11154,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x111541),f866(x111541))),f324(f324(f259(f866(x111541),f866(x111541)),x111542),f116(x111541))),f151(x111541,x111543)))), % 181.73/181.62 inference(rename_variables,[],[4557])). % 181.73/181.62 cnf(11157,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x111571),f866(x111571))),f324(f324(f259(f866(x111571),f866(x111571)),f116(x111571)),x111572)),f139(x111571,x111573)))), % 181.73/181.62 inference(rename_variables,[],[4558])). % 181.73/181.62 cnf(11165,plain, % 181.73/181.62 (P1(f324(f324(f326(x111651),x111652),f247(f871(x111651,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(11170,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x111701,a859)),f191(f871(x111701,a859))),x111702))), % 181.73/181.62 inference(rename_variables,[],[3714])). % 181.73/181.62 cnf(11173,plain, % 181.73/181.62 (~P1(f324(f324(f326(x111731),x111732),f191(f871(x111731,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11176,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x111761,a859)),x111762),f247(f871(x111761,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(11183,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x111831,a859)),f191(f871(x111831,a859))),x111832))), % 181.73/181.62 inference(rename_variables,[],[3714])). % 181.73/181.62 cnf(11198,plain, % 181.73/181.62 (P1(f324(f247(f871(x111981,a859)),x111982))), % 181.73/181.62 inference(rename_variables,[],[3330])). % 181.73/181.62 cnf(11206,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x112061),f866(x112061))),f324(f324(f259(f866(x112061),f866(x112061)),x112062),f116(x112061))),f139(x112061,x112063)))), % 181.73/181.62 inference(rename_variables,[],[4555])). % 181.73/181.62 cnf(11209,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x112091),f866(x112091))),f324(f324(f259(f866(x112091),f866(x112091)),x112092),f116(x112091))),f141(x112091,x112093)))), % 181.73/181.62 inference(rename_variables,[],[4556])). % 181.73/181.62 cnf(11212,plain, % 181.73/181.62 (~E(f324(f324(f145(x112121),x112122),x112123),x112123)), % 181.73/181.62 inference(rename_variables,[],[4482])). % 181.73/181.62 cnf(11215,plain, % 181.73/181.62 (~E(f324(a115,x112151),x112151)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11218,plain, % 181.73/181.62 (~P1(f324(f324(f326(x112181),x112182),f191(f871(x112181,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11223,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(f866(x112231),f866(x112231))),f324(f324(f259(f866(x112231),f866(x112231)),x112232),x112232)),f152(x112231,f300(x112231,x112233))))), % 181.73/181.62 inference(rename_variables,[],[4045])). % 181.73/181.62 cnf(11228,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x112281),f866(x112281))),f324(f324(f259(f866(x112281),f866(x112281)),x112282),f116(x112281))),f139(x112281,x112283)))), % 181.73/181.62 inference(rename_variables,[],[4555])). % 181.73/181.62 cnf(11238,plain, % 181.73/181.62 (~P1(f324(f324(f326(x112381),x112382),f191(f871(x112381,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11241,plain, % 181.73/181.62 (~P1(f324(f324(f326(x112411),x112412),f191(f871(x112411,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11244,plain, % 181.73/181.62 (~P1(f324(f324(f326(x112441),x112442),f191(f871(x112441,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11247,plain, % 181.73/181.62 (P1(f324(f324(f326(x112471),x112472),f247(f871(x112471,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(11250,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x112501),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(11255,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(x112551,x112551)),f324(f324(f259(x112551,x112551),x112552),x112553)),f147(x112551,f116(f871(x112551,a865)))))), % 181.73/181.62 inference(rename_variables,[],[4553])). % 181.73/181.62 cnf(11258,plain, % 181.73/181.62 (~E(f324(f303(x112581,f871(x112581,a859),x112582),x112583),f324(f301(x112581),x112583))), % 181.73/181.62 inference(rename_variables,[],[4532])). % 181.73/181.62 cnf(11261,plain, % 181.73/181.62 (~E(f324(f303(x112611,f871(x112611,a859),x112612),x112613),f324(f301(x112611),x112613))), % 181.73/181.62 inference(rename_variables,[],[4532])). % 181.73/181.62 cnf(11266,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x112661),f866(x112661))),f324(f324(f259(f866(x112661),f866(x112661)),x112662),f116(x112661))),f139(x112661,x112663)))), % 181.73/181.62 inference(rename_variables,[],[4555])). % 181.73/181.62 cnf(11272,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x112721),f866(x112721))),f324(f324(f259(f866(x112721),f866(x112721)),x112722),f116(x112721))),f139(x112721,x112723)))), % 181.73/181.62 inference(rename_variables,[],[4555])). % 181.73/181.62 cnf(11275,plain, % 181.73/181.62 (~P1(f324(f324(f326(x112751),x112752),f191(f871(x112751,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11279,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x112791,x112792)),f324(f324(f259(x112791,x112792),f324(x112793,x112794)),f324(x112795,x112794))),f324(f303(f870(x112796,x112796),f870(x112791,x112792),f264(x112796,x112791,x112796,x112792,x112793,x112795)),f300(x112796,x112797))))), % 181.73/181.62 inference(scs_inference,[],[3509,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,4467,10375,10468,10916,3725,3336,3103,3162,3128,3109,3326,10759,3197,3220,10416,3373,4543,3901,4482,10207,10372,4532,10942,11025,11258,3374,3160,10274,4051,3903,10948,11091,11143,4555,10862,11096,11206,11228,11266,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,3629,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,10932,3718,3252,4526,10184,10187,10213,10688,10701,10820,4538,3705,3479,3852,3296,3298,3271,4523,4477,4045,11223,4015,3913,10756,3967,3630,4004,3648,10954,11030,11117,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,3269,10331,10386,10594,10683,3270,4522,10250,10340,10453,10477,10725,10770,3426,10549,10815,10859,11165,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,3330,10576,10606,10615,3363,3785,3723,10253,4531,10204,10564,10567,11049,3290,10609,10764,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,4546,10178,10181,10434,10485,10488,10493,4553,11131,3869,3712,10875,10881,3567,11005,3714,10612,10970,11140,11170,3535,10532,10535,10618,10791,4550,4551,10671,4155,4056,3745,4548,10226,10229,10570,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997])). % 181.73/181.62 cnf(11282,plain, % 181.73/181.62 (~P1(f324(f324(f326(x112821),x112822),f191(f871(x112821,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11285,plain, % 181.73/181.62 (~P1(f324(f324(f326(x112851),x112852),f191(f871(x112851,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11288,plain, % 181.73/181.62 (P1(f324(f324(f326(x112881),f324(x112882,x112883)),f324(f303(x112884,x112881,x112882),f247(f871(x112884,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(11291,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(x112911,x112911)),f324(f324(f259(x112911,x112911),x112912),x112913)),f147(x112911,f116(f871(x112911,a865)))))), % 181.73/181.62 inference(rename_variables,[],[4553])). % 181.73/181.62 cnf(11297,plain, % 181.73/181.62 (E(f76(x112971,x112972,x112973,x112973,x112974),x112974)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11300,plain, % 181.73/181.62 (E(f76(x113001,x113002,x113003,x113003,x113004),x113004)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11303,plain, % 181.73/181.62 (~E(f324(a115,x113031),x113031)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11310,plain, % 181.73/181.62 (~E(f324(a115,x113101),x113101)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11315,plain, % 181.73/181.62 (E(f76(x113151,x113152,x113153,x113153,x113154),x113154)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11318,plain, % 181.73/181.62 (E(f76(x113181,x113182,x113183,x113183,x113184),x113184)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11324,plain, % 181.73/181.62 (~E(f324(a115,x113241),x113241)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11331,plain, % 181.73/181.62 (~E(f324(f324(f81(a1),x113311),x113311),a100)), % 181.73/181.62 inference(rename_variables,[],[4480])). % 181.73/181.62 cnf(11340,plain, % 181.73/181.62 (E(f324(f324(f22(a865),f2(a865)),x113401),f2(a865))), % 181.73/181.62 inference(rename_variables,[],[3181])). % 181.73/181.62 cnf(11343,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x113431),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(11350,plain, % 181.73/181.62 (E(f324(f324(f81(a1),f324(f324(f82(a1),x113501),f324(f324(f38(a1),x113502),x113501))),f44(a1,x113502,x113501)),x113502)), % 181.73/181.62 inference(rename_variables,[],[3817])). % 181.73/181.62 cnf(11366,plain, % 181.73/181.62 (E(f76(x113661,x113662,x113663,x113663,x113664),x113664)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11369,plain, % 181.73/181.62 (E(f76(x113691,x113692,x113693,x113693,x113694),x113694)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11372,plain, % 181.73/181.62 (E(f76(x113721,x113722,x113723,x113723,x113724),x113724)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11375,plain, % 181.73/181.62 (E(f76(x113751,x113752,x113753,x113753,x113754),x113754)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11378,plain, % 181.73/181.62 (~E(f324(a115,x113781),x113781)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11381,plain, % 181.73/181.62 (~E(f324(a115,x113811),x113811)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11385,plain, % 181.73/181.62 (E(f76(x113851,x113852,x113853,x113853,x113854),x113854)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11408,plain, % 181.73/181.62 (~P1(f324(f62(x114081,x114082,f191(f871(x114081,a859))),x114083))), % 181.73/181.62 inference(rename_variables,[],[4546])). % 181.73/181.62 cnf(11411,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x114111,f871(x114112,a859))),x114113),x114114))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(11414,plain, % 181.73/181.62 (P1(f324(f324(f326(x114141),x114142),f247(f871(x114141,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(11422,plain, % 181.73/181.62 (E(f76(x114221,x114222,x114223,x114223,x114224),x114224)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11427,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x114271),x114271))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11434,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x114341),x114341))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11435,plain, % 181.73/181.62 (E(f76(x114351,x114352,x114353,x114353,x114354),x114354)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11440,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x114401,f871(x114402,a859))),x114403),x114404))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(11451,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x114511),x114512)),x114512))), % 181.73/181.62 inference(rename_variables,[],[4548])). % 181.73/181.62 cnf(11454,plain, % 181.73/181.62 (~P1(f324(f324(f239(a1),f324(f103(a1),x114541)),f2(a1)))), % 181.73/181.62 inference(rename_variables,[],[4538])). % 181.73/181.62 cnf(11465,plain, % 181.73/181.62 (E(f76(x114651,x114652,x114653,x114653,x114654),x114654)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11468,plain, % 181.73/181.62 (E(f76(x114681,x114682,x114683,x114683,x114684),x114684)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11470,plain, % 181.73/181.62 (~E(f324(f324(f104(a865),f324(a115,x114701)),x114701),f324(a115,x114701))), % 181.73/181.62 inference(scs_inference,[],[3509,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,4467,10375,10468,10916,2871,2878,2882,2883,2886,2889,2893,2896,2913,2920,2931,2932,2933,2961,2965,3006,3022,3031,3038,3045,3060,4445,3725,3336,3103,3817,11350,3162,3128,3109,3326,10759,3197,3220,10416,3373,4543,3901,4482,10207,10372,4532,10942,11025,11258,11261,3374,3159,3160,10274,10579,3080,3181,11340,4051,3903,10948,11091,11143,4555,10862,11096,11206,11228,11266,11272,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,3629,4480,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,10932,3718,3252,4526,10184,10187,10213,10688,10701,10820,11250,11343,4538,3705,3479,3852,3296,3298,3271,4523,4477,3463,4539,4045,11223,3591,4015,3913,10756,3967,3630,4004,3648,10954,11030,11117,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,3269,10331,10386,10594,10683,10807,3270,4522,10250,10340,10453,10477,10725,10770,3426,10549,10815,10859,11165,11247,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,3330,10576,10606,10615,3363,3785,3723,10253,4531,10204,10564,10567,11049,11067,3290,10609,10764,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,4546,10178,10181,10434,10485,10488,10493,10919,4553,11131,11255,3869,3712,10875,10881,3567,11005,3714,10612,10970,11140,11170,3535,10532,10535,10618,10791,4550,4540,4551,10671,10773,11411,4155,4056,3745,4548,10226,10229,10570,10573,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997,10068,10069,10122,10136,2,12,13,4583,4584,4602,4633,4634,4636,4663,4671,4672,4683,4732,4734,4764,4778,4807,4901,4902,4916,4935,4991,4992,4995,4996,4998,5000,5001,5012,5013,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5086,5094,5097,5104,5160,5166,5167,5173,5201,5212,5218,5233,5253,5260,5261,5262,5271,5280,5287,5289,5290,5296,5303,5304,5317,5318,5319,5320,5322,5323,5328])). % 181.73/181.62 cnf(11479,plain, % 181.73/181.62 (E(f76(x114791,x114792,x114793,x114793,x114794),x114794)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11484,plain, % 181.73/181.62 (E(f76(x114841,x114842,x114843,x114843,x114844),x114844)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11487,plain, % 181.73/181.62 (~P1(f324(f324(f239(a1),f324(f103(a1),x114871)),f2(a1)))), % 181.73/181.62 inference(rename_variables,[],[4538])). % 181.73/181.62 cnf(11490,plain, % 181.73/181.62 (E(f76(x114901,x114902,x114903,x114903,x114904),x114904)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11493,plain, % 181.73/181.62 (~E(f324(a115,x114931),x114931)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11496,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x114961),x114961))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11503,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x115031),x115031))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11524,plain, % 181.73/181.62 (~P1(f324(f324(f239(a1),f324(f103(a1),x115241)),f2(a1)))), % 181.73/181.62 inference(rename_variables,[],[4538])). % 181.73/181.62 cnf(11539,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x115391)),x115391))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11540,plain, % 181.73/181.62 (~E(f324(a115,x115401),x115401)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11550,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x115501),x115502)),x115501))), % 181.73/181.62 inference(rename_variables,[],[4549])). % 181.73/181.62 cnf(11553,plain, % 181.73/181.62 (~P1(f324(f324(f239(a1),f324(f103(a1),x115531)),f2(a1)))), % 181.73/181.62 inference(rename_variables,[],[4538])). % 181.73/181.62 cnf(11556,plain, % 181.73/181.62 (~E(f324(a115,x115561),x115561)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11569,plain, % 181.73/181.62 (P1(f324(f324(f326(x115691),x115692),f324(f324(f302(x115691),x115692),x115693)))), % 181.73/181.62 inference(rename_variables,[],[3581])). % 181.73/181.62 cnf(11570,plain, % 181.73/181.62 (~P1(f324(f324(f238(a1),f2(a1)),f324(f80(a1),f324(f103(a1),f324(a115,x115701)))))), % 181.73/181.62 inference(rename_variables,[],[4550])). % 181.73/181.62 cnf(11573,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),f324(f324(f22(a865),x115731),x115732)),f324(a115,x115731)))), % 181.73/181.62 inference(rename_variables,[],[3718])). % 181.73/181.62 cnf(11576,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f44(a865,x115761,x115762)),x115761))), % 181.73/181.62 inference(rename_variables,[],[3723])). % 181.73/181.62 cnf(11582,plain, % 181.73/181.62 (E(f324(f324(f124(x115821),x115822),f116(x115821)),x115822)), % 181.73/181.62 inference(rename_variables,[],[3198])). % 181.73/181.62 cnf(11585,plain, % 181.73/181.62 (E(f76(x115851,x115852,x115853,x115853,x115854),x115854)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11588,plain, % 181.73/181.62 (E(f76(x115881,x115882,x115883,x115883,x115884),x115884)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11591,plain, % 181.73/181.62 (E(f76(x115911,x115912,x115913,x115913,x115914),x115914)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11594,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x115941)),x115941))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11595,plain, % 181.73/181.62 (E(f76(x115951,x115952,x115953,x115953,x115954),x115954)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11604,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x116041),x116041))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11605,plain, % 181.73/181.62 (E(f76(x116051,x116052,x116053,x116053,x116054),x116054)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11608,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f44(a865,x116081,x116082)),x116081))), % 181.73/181.62 inference(rename_variables,[],[3723])). % 181.73/181.62 cnf(11609,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x116091))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(11611,plain, % 181.73/181.62 (~P1(f324(f324(f238(a1),f79(a1)),f2(a1)))), % 181.73/181.62 inference(scs_inference,[],[3509,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,4467,10375,10468,10916,2870,2871,2878,2879,2882,2883,2886,2889,2893,2896,2897,2901,2902,2913,2920,2931,2932,2933,2961,2965,3006,3022,3029,3031,3038,3045,3060,4445,3310,3198,11582,3725,3336,3103,3817,11350,3162,3128,3122,3109,3110,3326,10759,3197,3220,10416,3373,4543,3901,4482,10207,10372,4532,10942,11025,11258,11261,3374,3159,3160,10274,10579,3431,3080,3181,11340,4051,3903,10948,11091,11143,4555,10862,11096,11206,11228,11266,11272,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,3629,4338,4339,4480,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,10932,3718,3252,4526,10184,10187,10213,10688,10701,10820,11250,11343,4538,11454,11487,11524,3705,3479,3852,3296,3298,3271,4523,4477,3463,4539,4045,11223,3591,4015,3913,10756,3967,3630,4004,3648,10954,11030,11117,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,3269,10331,10386,10594,10683,10807,11427,3270,4522,10250,10340,10453,10477,10725,10770,10780,11503,3426,10549,10815,10859,11165,11247,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,3330,10576,10606,10615,3369,3363,3785,3723,10253,11576,4531,10204,10564,10567,11049,11067,11539,3290,10609,10764,10835,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,3581,4546,10178,10181,10434,10485,10488,10493,10919,4553,11131,11255,3869,3712,10875,10881,3567,11005,3714,10612,10970,11140,11170,3535,10532,10535,10618,10791,4550,4540,4551,10671,10773,11411,4155,4056,3745,4548,10226,10229,10570,10573,4549,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997,10068,10069,10122,10136,2,12,13,4583,4584,4602,4633,4634,4636,4663,4671,4672,4683,4732,4734,4764,4778,4807,4901,4902,4916,4935,4991,4992,4995,4996,4998,5000,5001,5012,5013,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5086,5094,5097,5104,5160,5166,5167,5173,5201,5212,5218,5233,5253,5260,5261,5262,5271,5280,5287,5289,5290,5296,5303,5304,5317,5318,5319,5320,5322,5323,5328,5329,5330,5331,5362,5363,5364,5372,5373,5374,5375,5418,5423,5425,5461,5463,5464,5466,5467,5469,5470,5472,5481,5486,5488,5489,5490,5491,5492,5493,5500,5510,5513,5524,5540,5541,5544,5553,5555,5556,5557,5582,5592,5608,5609,5619,5620,5622,5624,5629,5664,5669,5671,5729,5763,5764])). % 181.73/181.62 cnf(11626,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x116261),x116261))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11629,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x116291),x116291))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11632,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x116321),x116321))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11635,plain, % 181.73/181.62 (P1(f324(f324(f326(x116351),f324(x116352,x116353)),f324(f303(x116354,x116351,x116352),f247(f871(x116354,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(11636,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x116361)),x116361))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11639,plain, % 181.73/181.62 (P1(f324(f324(f326(x116391),f324(x116392,x116393)),f324(f303(x116394,x116391,x116392),f247(f871(x116394,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(11640,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x116401),x116402)),x116402))), % 181.73/181.62 inference(rename_variables,[],[4548])). % 181.73/181.62 cnf(11645,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x116451),x116452)),x116451))), % 181.73/181.62 inference(rename_variables,[],[4549])). % 181.73/181.62 cnf(11648,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x116481),x116481))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11651,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x116511),x116511))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11657,plain, % 181.73/181.62 (~P37(x116571,x116572,f116(x116571))), % 181.73/181.62 inference(rename_variables,[],[4491])). % 181.73/181.62 cnf(11660,plain, % 181.73/181.62 (P1(f324(f324(f326(x116601),x116602),f247(f871(x116601,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(11661,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x116611)),x116611))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11664,plain, % 181.73/181.62 (~P1(f324(f62(x116641,x116642,f191(f871(x116641,a859))),x116643))), % 181.73/181.62 inference(rename_variables,[],[4546])). % 181.73/181.62 cnf(11677,plain, % 181.73/181.62 (~P1(f324(f324(f326(x116771),x116772),f191(f871(x116771,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11680,plain, % 181.73/181.62 (E(f324(f324(f16(x116801,x116802),x116803),x116804),x116803)), % 181.73/181.62 inference(rename_variables,[],[3259])). % 181.73/181.62 cnf(11683,plain, % 181.73/181.62 (E(f324(f324(f16(x116831,x116832),x116833),x116834),x116833)), % 181.73/181.62 inference(rename_variables,[],[3259])). % 181.73/181.62 cnf(11695,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),f2(a865)),f324(a115,x116951)))), % 181.73/181.62 inference(rename_variables,[],[3349])). % 181.73/181.62 cnf(11698,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x116981),x116981))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11699,plain, % 181.73/181.62 (E(f76(x116991,x116992,x116993,x116993,x116994),x116994)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11702,plain, % 181.73/181.62 (P1(f324(f324(f326(x117021),f324(x117022,x117023)),f324(f303(x117024,x117021,x117022),f247(f871(x117024,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(11705,plain, % 181.73/181.62 (P1(f324(f61(x117051),f324(f167(x117051),x117052)))), % 181.73/181.62 inference(rename_variables,[],[3309])). % 181.73/181.62 cnf(11708,plain, % 181.73/181.62 (P1(f324(f61(x117081),f324(f167(x117081),x117082)))), % 181.73/181.62 inference(rename_variables,[],[3309])). % 181.73/181.62 cnf(11711,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),f324(f80(a1),f324(f103(a1),x117111))),f324(f103(a1),x117112)))), % 181.73/181.62 inference(rename_variables,[],[3746])). % 181.73/181.62 cnf(11714,plain, % 181.73/181.62 (~P1(f324(f324(f326(x117141),x117142),f191(f871(x117141,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11728,plain, % 181.73/181.62 (~P1(f324(f324(f326(a865),f2(a865)),f324(f296(a865),x117281)))), % 181.73/181.62 inference(scs_inference,[],[3509,4490,4491,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,11605,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,4467,10375,10468,10916,2870,2871,2875,2878,2879,2882,2883,2886,2889,2891,2893,2896,2897,2901,2902,2913,2920,2931,2932,2933,2961,2965,3006,3022,3029,3031,3038,3045,3060,4445,3310,3198,11582,3725,3336,3103,3817,11350,3162,3128,3122,3109,3110,3326,10759,3197,3220,10416,3373,4543,3901,4482,10207,10372,3259,11680,4532,10942,11025,11258,11261,3374,3159,3160,10274,10579,3431,3080,3181,11340,4051,3903,10948,11091,11143,4555,10862,11096,11206,11228,11266,11272,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,3629,4338,4339,4480,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,10932,3718,11573,3252,3349,4526,10184,10187,10213,10688,10701,10820,11250,11343,4538,11454,11487,11524,3705,3479,3852,3296,3298,3271,4523,4477,3463,4539,4045,11223,3591,3309,11705,4015,3913,10756,3967,3630,4004,3648,10954,11030,11117,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,11434,11651,3269,10331,10386,10594,10683,10807,11427,3270,3345,4522,10250,10340,10453,10477,10725,10770,10780,11503,11604,11626,11629,11632,3426,10549,10815,10859,11165,11247,11414,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,11285,11677,3330,10576,10606,10615,3369,3363,3785,3723,10253,11576,4531,10204,10564,10567,11049,11067,11539,11594,11636,11661,3290,10609,10764,10835,3746,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,3581,4546,10178,10181,10434,10485,10488,10493,10919,11408,4553,11131,11255,3981,3869,11288,11635,11639,3712,10875,10881,3567,11005,3714,10612,10970,11140,11170,3535,10532,10535,10618,10791,4550,11570,4540,4551,10671,10773,11411,4155,4056,3745,3692,4548,10226,10229,10570,10573,11451,4549,11550,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997,10068,10069,10122,10136,2,12,13,4583,4584,4602,4633,4634,4636,4663,4671,4672,4683,4732,4734,4764,4778,4807,4901,4902,4916,4935,4991,4992,4995,4996,4998,5000,5001,5012,5013,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5086,5094,5097,5104,5160,5166,5167,5173,5201,5212,5218,5233,5253,5260,5261,5262,5271,5280,5287,5289,5290,5296,5303,5304,5317,5318,5319,5320,5322,5323,5328,5329,5330,5331,5362,5363,5364,5372,5373,5374,5375,5418,5423,5425,5461,5463,5464,5466,5467,5469,5470,5472,5481,5486,5488,5489,5490,5491,5492,5493,5500,5510,5513,5524,5540,5541,5544,5553,5555,5556,5557,5582,5592,5608,5609,5619,5620,5622,5624,5629,5664,5669,5671,5729,5763,5764,5768,5774,5777,5778,5779,5780,5786,5797,5798,5800,5801,5809,5830,5859,5875,5878,5879,5881,5890,5907,5911,5914,5915,5916,5931,5941,5942,5970,5971,5975,5995,5998,6002,6021,6025,6026,6051,6054,6062,6070,6076,6080,6087,6088,6089])). % 181.73/181.62 cnf(11730,plain, % 181.73/181.62 (~P1(f324(f324(f326(a865),x117301),f324(f245(a865),f2(a865))))), % 181.73/181.62 inference(scs_inference,[],[3509,4490,4491,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,11605,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,4467,10375,10468,10916,2870,2871,2875,2878,2879,2882,2883,2886,2889,2891,2893,2896,2897,2901,2902,2913,2920,2931,2932,2933,2961,2965,3006,3022,3029,3031,3038,3045,3060,4445,3310,3198,11582,3725,3336,3103,3817,11350,3162,3128,3122,3109,3110,3326,10759,3197,3220,10416,3373,4543,3901,4482,10207,10372,3259,11680,4532,10942,11025,11258,11261,3374,3159,3160,10274,10579,3431,3080,3181,11340,4051,3903,10948,11091,11143,4555,10862,11096,11206,11228,11266,11272,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,3629,4338,4339,4480,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,10932,3718,11573,3252,3349,4526,10184,10187,10213,10688,10701,10820,11250,11343,4538,11454,11487,11524,3705,3479,3852,3296,3298,3271,4523,4477,3463,4539,4045,11223,3591,3309,11705,4015,3913,10756,3967,3630,4004,3648,10954,11030,11117,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,11434,11651,3269,10331,10386,10594,10683,10807,11427,3270,3345,4522,10250,10340,10453,10477,10725,10770,10780,11503,11604,11626,11629,11632,3426,10549,10815,10859,11165,11247,11414,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,11285,11677,3330,10576,10606,10615,3369,3363,3785,3723,10253,11576,4531,10204,10564,10567,11049,11067,11539,11594,11636,11661,3290,10609,10764,10835,3746,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,3581,4546,10178,10181,10434,10485,10488,10493,10919,11408,4553,11131,11255,3981,3869,11288,11635,11639,3712,10875,10881,3567,11005,3714,10612,10970,11140,11170,3535,10532,10535,10618,10791,4550,11570,4540,4551,10671,10773,11411,4155,4056,3745,3692,4548,10226,10229,10570,10573,11451,4549,11550,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997,10068,10069,10122,10136,2,12,13,4583,4584,4602,4633,4634,4636,4663,4671,4672,4683,4732,4734,4764,4778,4807,4901,4902,4916,4935,4991,4992,4995,4996,4998,5000,5001,5012,5013,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5086,5094,5097,5104,5160,5166,5167,5173,5201,5212,5218,5233,5253,5260,5261,5262,5271,5280,5287,5289,5290,5296,5303,5304,5317,5318,5319,5320,5322,5323,5328,5329,5330,5331,5362,5363,5364,5372,5373,5374,5375,5418,5423,5425,5461,5463,5464,5466,5467,5469,5470,5472,5481,5486,5488,5489,5490,5491,5492,5493,5500,5510,5513,5524,5540,5541,5544,5553,5555,5556,5557,5582,5592,5608,5609,5619,5620,5622,5624,5629,5664,5669,5671,5729,5763,5764,5768,5774,5777,5778,5779,5780,5786,5797,5798,5800,5801,5809,5830,5859,5875,5878,5879,5881,5890,5907,5911,5914,5915,5916,5931,5941,5942,5970,5971,5975,5995,5998,6002,6021,6025,6026,6051,6054,6062,6070,6076,6080,6087,6088,6089,6090])). % 181.73/181.62 cnf(11733,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x117331),x117331))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11734,plain, % 181.73/181.62 (E(f76(x117341,x117342,x117343,x117343,x117344),x117344)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(11737,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x117371),x117371))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11746,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x117461),x117461))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11749,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x117491),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(11754,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x117541),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(11761,plain, % 181.73/181.62 (P1(f324(f247(f871(x117611,a859)),x117612))), % 181.73/181.62 inference(rename_variables,[],[3330])). % 181.73/181.62 cnf(11766,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x117661))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(11767,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x117671)),x117671))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11770,plain, % 181.73/181.62 (~P1(f324(f62(x117701,x117702,f191(f871(x117701,a859))),x117703))), % 181.73/181.62 inference(rename_variables,[],[4546])). % 181.73/181.62 cnf(11776,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x117761),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(11777,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x117771),f324(a115,x117771)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(11793,plain, % 181.73/181.62 (P1(f324(f324(f239(a1),f324(f80(a1),f79(a1))),f2(a1)))), % 181.73/181.62 inference(scs_inference,[],[3509,4490,4491,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,11605,11699,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,4467,10375,10468,10916,2870,2871,2875,2878,2879,2882,2883,2885,2886,2889,2891,2893,2896,2897,2901,2902,2913,2920,2923,2931,2932,2933,2961,2965,3006,3021,3022,3029,3031,3038,3045,3060,4445,3310,3198,11582,3725,3336,3103,3817,11350,3162,3128,3122,3109,3110,3326,10759,3197,3220,10416,3373,4543,3901,4482,10207,10372,3259,11680,4532,10942,11025,11258,11261,3374,3159,3160,10274,10579,3431,3080,3181,11340,4051,3903,10948,11091,11143,4555,10862,11096,11206,11228,11266,11272,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,3629,4338,4339,4480,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,10932,3718,11573,3252,3349,4526,10184,10187,10213,10688,10701,10820,11250,11343,11749,11754,4538,11454,11487,11524,11553,3705,3479,3852,3296,3298,3271,4523,4477,3463,4539,4045,11223,3591,3309,11705,4015,3913,10756,3967,3630,4004,3648,10954,11030,11117,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,11434,11651,3269,10331,10386,10594,10683,10807,11427,11496,11733,11737,3270,3345,4522,10250,10340,10453,10477,10725,10770,10780,11503,11604,11626,11629,11632,3426,10549,10815,10859,11165,11247,11414,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,11285,11677,3330,10576,10606,10615,11198,3369,3363,3785,3723,10253,11576,11608,4531,10204,10564,10567,11049,11067,11539,11594,11636,11661,3290,10609,10764,10835,11609,3746,4095,4529,3793,4512,4515,3242,3247,4514,4513,4517,3581,4546,10178,10181,10434,10485,10488,10493,10919,11408,11664,11770,4553,11131,11255,3981,3869,11288,11635,11639,3712,10875,10881,3567,11005,3714,10612,10970,11140,11170,3535,10532,10535,10618,10791,4550,11570,4540,4551,10671,10773,11411,4155,4056,3745,3692,4548,10226,10229,10570,10573,11451,4549,11550,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997,10068,10069,10122,10136,2,12,13,4583,4584,4602,4633,4634,4636,4663,4671,4672,4683,4732,4734,4764,4778,4807,4901,4902,4916,4935,4991,4992,4995,4996,4998,5000,5001,5012,5013,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5086,5094,5097,5104,5160,5166,5167,5173,5201,5212,5218,5233,5253,5260,5261,5262,5271,5280,5287,5289,5290,5296,5303,5304,5317,5318,5319,5320,5322,5323,5328,5329,5330,5331,5362,5363,5364,5372,5373,5374,5375,5418,5423,5425,5461,5463,5464,5466,5467,5469,5470,5472,5481,5486,5488,5489,5490,5491,5492,5493,5500,5510,5513,5524,5540,5541,5544,5553,5555,5556,5557,5582,5592,5608,5609,5619,5620,5622,5624,5629,5664,5669,5671,5729,5763,5764,5768,5774,5777,5778,5779,5780,5786,5797,5798,5800,5801,5809,5830,5859,5875,5878,5879,5881,5890,5907,5911,5914,5915,5916,5931,5941,5942,5970,5971,5975,5995,5998,6002,6021,6025,6026,6051,6054,6062,6070,6076,6080,6087,6088,6089,6090,6123,6138,6191,6226,6228,6249,6250,6255,6259,6260,6263,6269,6278,6293,6313,6314,6317,6320,6330,6345,6366,6372,6374,6389,6390])). % 181.73/181.62 cnf(11796,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x117961)),x117961))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11799,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x117991)),x117991))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11802,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x118021)),x118021))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11805,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x118051)),x118051))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(11808,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x118081),x118081))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11811,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x118111),x118111))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11814,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x118141),x118141))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11817,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x118171),x118171))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11835,plain, % 181.73/181.62 (E(f324(f192(f866(x118351)),f165(x118351,x118352,x118353)),x118352)), % 181.73/181.62 inference(rename_variables,[],[3336])). % 181.73/181.62 cnf(11838,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x118381),x118381))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11841,plain, % 181.73/181.62 (P27(a865,a865,a115,x118411)), % 181.73/181.62 inference(rename_variables,[],[3478])). % 181.73/181.62 cnf(11844,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x118441),x118441))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11855,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x118551),x118551))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11858,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(f870(f866(x118581),f866(x118581)),a859)),f152(x118581,x118582)),f300(f866(x118581),f151(x118581,x118582))))), % 181.73/181.62 inference(rename_variables,[],[3972])). % 181.73/181.62 cnf(11865,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x118651),f324(a115,x118651)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(11868,plain, % 181.73/181.62 (P1(f324(f324(f326(f871(x118681,a859)),x118682),f324(f301(x118681),x118682)))), % 181.73/181.62 inference(rename_variables,[],[3630])). % 181.73/181.62 cnf(11869,plain, % 181.73/181.62 (~E(f324(a115,x118691),x118691)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11874,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x118741),x118741))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11879,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x118791),x118791))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11890,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x118901,a859)),x118902),f324(f324(f302(x118901),x118903),x118902)))), % 181.73/181.62 inference(rename_variables,[],[3712])). % 181.73/181.62 cnf(11893,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x118931),x118931))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11894,plain, % 181.73/181.62 (~E(f324(a115,x118941),x118941)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11905,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119051),x119051))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11906,plain, % 181.73/181.62 (~E(f324(a115,x119061),x119061)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11909,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x119091),x119091))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11912,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x119121),x119121))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11915,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x119151),x119151))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11918,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x119181),x119181))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(11921,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x119211),x119211))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11924,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119241),x119241))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11927,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119271),x119271))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11928,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x119281),f324(a115,x119281)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(11937,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119371),x119371))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11938,plain, % 181.73/181.62 (~E(f324(a115,x119381),x119381)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(11941,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x119411),x119411))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11958,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x119581),x119581))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(11963,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x119631))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(11980,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119801),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(11983,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119831),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(11986,plain, % 181.73/181.62 (~P1(f324(f324(f326(x119861),x119862),f191(f871(x119861,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11989,plain, % 181.73/181.62 (~P1(f324(f324(f326(x119891),x119892),f191(f871(x119891,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(11992,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119921),x119921))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11995,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119951),x119951))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(11998,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x119981),x119981))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12001,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x120011),x120011))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12004,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x120041),f324(a115,x120041)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12011,plain, % 181.73/181.62 (P1(f324(f324(f326(f871(x120111,a859)),x120112),f324(f301(x120111),x120112)))), % 181.73/181.62 inference(rename_variables,[],[3630])). % 181.73/181.62 cnf(12015,plain, % 181.73/181.62 (~P1(f324(f324(f326(a865),f324(a115,f324(f136(a865,a865,f81(a865),f2(a865)),x120151))),f324(f167(a865),f324(f130(a865,x120152),x120151))))), % 181.73/181.62 inference(scs_inference,[],[3509,4490,4491,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,11605,11699,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,11556,11869,11894,11906,4467,10375,10468,10916,3478,2870,2871,2875,2878,2879,2882,2883,2885,2886,2889,2891,2893,2896,2897,2901,2902,2913,2920,2923,2931,2932,2933,2961,2965,3006,3021,3022,3029,3031,3038,3045,3060,4445,3310,3198,11582,3210,3321,3725,3336,10166,3964,3103,3817,11350,3162,3128,3122,3109,3110,3326,10759,3197,3220,10416,3373,4543,3901,4482,10207,10372,3259,11680,4532,10942,11025,11258,11261,3374,3159,3160,10274,10579,3431,3080,3181,11340,4051,3903,10948,11091,11143,4555,10862,11096,11206,11228,11266,11272,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,3629,4338,4339,4480,3570,3781,3337,10293,10411,10482,10543,10546,10582,10680,10932,11777,11865,11928,3718,11573,3252,3349,4526,10184,10187,10213,10688,10701,10820,11250,11343,11749,11754,11776,11980,4538,11454,11487,11524,11553,3705,3479,3852,3296,3298,3271,4523,4477,3463,4539,4045,11223,3591,3309,11705,4015,3972,3913,10756,3967,3630,11868,4004,3648,10954,11030,11117,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,11434,11651,11698,11838,11893,11909,11912,11915,11918,3269,10331,10386,10594,10683,10807,11427,11496,11733,11737,11746,11844,11855,11874,11879,11921,11941,3270,3345,4522,10250,10340,10453,10477,10725,10770,10780,11503,11604,11626,11629,11632,11648,11808,11811,11814,11817,11905,11924,11927,11937,11992,11995,11998,3426,10549,10815,10859,11165,11247,11414,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,11285,11677,11714,11986,3330,10576,10606,10615,11198,3369,3363,3785,3723,10253,11576,11608,4531,10204,10564,10567,11049,11067,11539,11594,11636,11661,11767,11796,11799,11802,11805,3290,10609,10764,10835,11609,11766,3746,4095,4529,3757,3793,4512,4515,3242,3247,4514,4513,4517,3764,3581,4546,10178,10181,10434,10485,10488,10493,10919,11408,11664,11770,4553,11131,11255,3981,3869,11288,11635,11639,3712,10875,10881,10903,3567,11005,3714,10612,10970,11140,11170,3535,10532,10535,10618,10791,4550,11570,4540,4551,10671,10773,11411,4155,4056,3745,3692,4548,10226,10229,10570,10573,11451,4549,11550,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997,10068,10069,10122,10136,2,12,13,4583,4584,4602,4633,4634,4636,4663,4671,4672,4683,4732,4734,4764,4778,4807,4901,4902,4916,4935,4991,4992,4995,4996,4998,5000,5001,5012,5013,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5086,5094,5097,5104,5160,5166,5167,5173,5201,5212,5218,5233,5253,5260,5261,5262,5271,5280,5287,5289,5290,5296,5303,5304,5317,5318,5319,5320,5322,5323,5328,5329,5330,5331,5362,5363,5364,5372,5373,5374,5375,5418,5423,5425,5461,5463,5464,5466,5467,5469,5470,5472,5481,5486,5488,5489,5490,5491,5492,5493,5500,5510,5513,5524,5540,5541,5544,5553,5555,5556,5557,5582,5592,5608,5609,5619,5620,5622,5624,5629,5664,5669,5671,5729,5763,5764,5768,5774,5777,5778,5779,5780,5786,5797,5798,5800,5801,5809,5830,5859,5875,5878,5879,5881,5890,5907,5911,5914,5915,5916,5931,5941,5942,5970,5971,5975,5995,5998,6002,6021,6025,6026,6051,6054,6062,6070,6076,6080,6087,6088,6089,6090,6123,6138,6191,6226,6228,6249,6250,6255,6259,6260,6263,6269,6278,6293,6313,6314,6317,6320,6330,6345,6366,6372,6374,6389,6390,6393,6394,6396,6398,6399,6400,6402,6404,6406,6411,6412,6413,6415,6421,6423,6428,6465,6470,6485,6487,6488,6489,6523,6528,6530,6535,6536,6544,6548,6560,6584,6585,6587,6588,6599,6605,6622,6625,6644,6677,6678,6679,6684,6698,6717,6719,6721,6723,6728,6734,6736,6751,6758,6794,6795,6796,6810,6811,6813,6814,6833,6835,6849,6875,6897,6908,6910,6912,6914,6915,6916,6948,6949,6954,6955,6962,6963,6965,6967,6986,6995,6996,7008,7018,7057])). % 181.73/181.62 cnf(12016,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x120161,a859)),f324(f167(x120161),f324(f130(x120161,x120162),x120163))),f324(f167(x120161),x120163)))), % 181.73/181.62 inference(rename_variables,[],[3913])). % 181.73/181.62 cnf(12023,plain, % 181.73/181.62 (~P1(f324(f324(f326(x120231),x120232),f191(f871(x120231,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12028,plain, % 181.73/181.62 (E(f324(f192(f866(x120281)),f165(x120281,x120282,x120283)),x120282)), % 181.73/181.62 inference(rename_variables,[],[3336])). % 181.73/181.62 cnf(12035,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x120351,a859)),x120352),f247(f871(x120351,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12036,plain, % 181.73/181.62 (~E(f324(a115,x120361),x120361)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(12039,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x120391,a859)),f324(f167(x120391),f324(f130(x120391,x120392),x120393))),f324(f167(x120391),x120393)))), % 181.73/181.62 inference(rename_variables,[],[3913])). % 181.73/181.62 cnf(12045,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x120451),f324(a115,x120451)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12054,plain, % 181.73/181.62 (E(f76(x120541,x120542,x120543,x120543,x120544),x120544)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12065,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x120651)),x120651))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(12066,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x120661),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12069,plain, % 181.73/181.62 (P1(f324(f61(x120691),f191(f871(x120691,a859))))), % 181.73/181.62 inference(rename_variables,[],[3345])). % 181.73/181.62 cnf(12070,plain, % 181.73/181.62 (~P1(f324(f324(f326(x120701),x120702),f191(f871(x120701,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12075,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x120751),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12076,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x120761),x120761))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12081,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x120811,a859)),f324(f167(x120811),f171(x120811,x120812,x120813))),f324(f167(x120811),x120812)))), % 181.73/181.62 inference(rename_variables,[],[3967])). % 181.73/181.62 cnf(12084,plain, % 181.73/181.62 (P27(x120841,x120841,f5(x120841),x120842)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12089,plain, % 181.73/181.62 (P1(f324(f324(f326(f871(x120891,a859)),x120892),f324(f301(x120891),x120892)))), % 181.73/181.62 inference(rename_variables,[],[3630])). % 181.73/181.62 cnf(12096,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x120961),x120961))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12099,plain, % 181.73/181.62 (~P1(f324(f324(f326(x120991),x120992),f191(f871(x120991,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12102,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x121021,a859)),x121022),f324(f324(f302(x121021),x121023),x121022)))), % 181.73/181.62 inference(rename_variables,[],[3712])). % 181.73/181.62 cnf(12103,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x121031,a859)),x121032),f247(f871(x121031,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12110,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x121101),x121101))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12113,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x121131),x121131))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12116,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x121161),x121161))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12119,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x121191),x121191))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12122,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x121221),f324(a115,x121221)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12125,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x121251),f324(a115,x121251)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12128,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x121281,a859)),x121282),x121282))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(12135,plain, % 181.73/181.62 (P1(f324(f324(f326(f871(x121351,a859)),x121352),f324(f301(x121351),x121352)))), % 181.73/181.62 inference(rename_variables,[],[3630])). % 181.73/181.62 cnf(12144,plain, % 181.73/181.62 (~E(f324(a115,x121441),x121441)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(12145,plain, % 181.73/181.62 (E(f324(f303(x121451,x121451,f5(x121451)),x121452),x121452)), % 181.73/181.62 inference(rename_variables,[],[3326])). % 181.73/181.62 cnf(12148,plain, % 181.73/181.62 (P34(x121481,x121482,f116(x121481),f116(x121481))), % 181.73/181.62 inference(rename_variables,[],[3518])). % 181.73/181.62 cnf(12151,plain, % 181.73/181.62 (~E(f324(a115,x121511),x121511)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(12154,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x121541,a859)),f324(f167(x121541),f171(x121541,x121542,x121543))),f324(f167(x121541),x121542)))), % 181.73/181.62 inference(rename_variables,[],[3967])). % 181.73/181.62 cnf(12155,plain, % 181.73/181.62 (P1(f324(f61(x121551),f324(f167(x121551),x121552)))), % 181.73/181.62 inference(rename_variables,[],[3309])). % 181.73/181.62 cnf(12166,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x121661),x121661))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12169,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x121691),x121691))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12174,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x121741))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(12181,plain, % 181.73/181.62 (P16(a865,f324(f163(a865),f324(f324(f148(f866(x121811),a865),f192(f866(x121811))),f175(x121811,x121812))))), % 181.73/181.62 inference(rename_variables,[],[3827])). % 181.73/181.62 cnf(12184,plain, % 181.73/181.62 (P27(x121841,x121841,f5(x121841),x121842)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12187,plain, % 181.73/181.62 (P27(x121871,x121871,f5(x121871),x121872)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12190,plain, % 181.73/181.62 (P1(f324(f324(f326(f866(x121901)),f116(x121901)),f155(x121901,x121902)))), % 181.73/181.62 inference(rename_variables,[],[3471])). % 181.73/181.62 cnf(12193,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x121931,f871(x121932,a859))),x121933),x121934))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(12198,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x121981),x121981))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12199,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x121991))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(12202,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x122021,f871(x122022,a859))),x122023),x122024))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(12205,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(f870(f866(x122051),f866(x122051)),a859)),f152(x122051,x122052)),f300(f866(x122051),f151(x122051,x122052))))), % 181.73/181.62 inference(rename_variables,[],[3972])). % 181.73/181.62 cnf(12211,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x122111,a859)),f324(f167(x122111),f171(x122111,x122112,x122113))),f324(f167(x122111),x122112)))), % 181.73/181.62 inference(rename_variables,[],[3967])). % 181.73/181.62 cnf(12212,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x122121,a859)),f324(f167(x122121),f324(f130(x122121,x122122),x122123))),f324(f167(x122121),x122123)))), % 181.73/181.62 inference(rename_variables,[],[3913])). % 181.73/181.62 cnf(12215,plain, % 181.73/181.62 (~P1(f324(f324(f239(f871(x122151,a859)),x122152),f191(f871(x122151,a859))))), % 181.73/181.62 inference(rename_variables,[],[4544])). % 181.73/181.62 cnf(12218,plain, % 181.73/181.62 (P27(x122181,f869(x122181),f233(x122181),x122182)), % 181.73/181.62 inference(rename_variables,[],[3519])). % 181.73/181.62 cnf(12223,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x122231,a859)),f324(f303(x122232,x122231,x122233),f324(f304(x122232,x122231,x122233),x122234))),x122234))), % 181.73/181.62 inference(rename_variables,[],[4155])). % 181.73/181.62 cnf(12226,plain, % 181.73/181.62 (P1(f324(f61(f869(x122261)),f324(f303(x122262,f869(x122261),f324(f173(x122262,x122261),x122263)),f247(f871(x122262,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3981])). % 181.73/181.62 cnf(12231,plain, % 181.73/181.62 (P1(f324(f324(f326(f866(x122311)),f116(x122311)),f155(x122311,x122312)))), % 181.73/181.62 inference(rename_variables,[],[3471])). % 181.73/181.62 cnf(12234,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(f866(x122341),f866(x122341))),f324(f324(f259(f866(x122341),f866(x122341)),x122342),f116(x122341))),f139(x122341,x122343)))), % 181.73/181.62 inference(rename_variables,[],[4555])). % 181.73/181.62 cnf(12237,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x122371),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12239,plain, % 181.73/181.62 (~P1(f324(f61(x122391),f247(f871(x122391,a859))))), % 181.73/181.62 inference(scs_inference,[],[3509,11020,12084,12184,3518,3519,3236,4490,4491,3137,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,11605,11699,11734,4471,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,11556,11869,11894,11906,11938,12036,12144,4467,10375,10468,10916,3478,2870,2871,2874,2875,2878,2879,2881,2882,2883,2885,2886,2889,2891,2893,2896,2897,2901,2902,2913,2920,2923,2931,2932,2933,2942,2961,2965,3006,3021,3022,3029,3031,3038,3045,3060,4445,3310,3198,11582,3210,3321,3725,3336,10166,11835,3964,3103,3817,11350,3162,3128,3122,3109,3110,3143,3326,10759,10884,3197,3220,10416,3373,4543,3901,4482,10207,10372,3259,11680,4532,10942,11025,11258,11261,3374,3159,3160,10274,10579,3431,3080,3181,11340,4051,3903,10948,11091,11143,4555,10862,11096,11206,11228,11266,11272,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,12190,12231,3629,4338,4339,4480,3570,3781,3827,3457,3707,3337,10293,10411,10482,10543,10546,10582,10680,10932,11777,11865,11928,12004,12045,12122,3718,11573,3252,3349,3534,4526,10184,10187,10213,10688,10701,10820,11250,11343,11749,11754,11776,11980,11983,12066,12075,4538,11454,11487,11524,11553,3705,3479,3852,3296,3298,3271,4523,4477,3463,4539,4045,11223,3591,3309,11705,11708,4015,3972,11858,12205,3913,10756,12016,12039,3967,10951,12081,12154,3630,11868,12011,12089,12135,4004,3648,10954,11030,11117,11176,12035,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,11434,11651,11698,11838,11893,11909,11912,11915,11918,12096,12110,12113,12116,12119,3269,10331,10386,10594,10683,10807,11427,11496,11733,11737,11746,11844,11855,11874,11879,11921,11941,3270,3345,12069,4522,10250,10340,10453,10477,10725,10770,10780,11503,11604,11626,11629,11632,11648,11808,11811,11814,11817,11905,11924,11927,11937,11992,11995,11998,12001,12076,12166,3426,10549,10815,10859,11165,11247,11414,11660,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,11285,11677,11714,11986,11989,12023,12070,3330,10576,10606,10615,11198,3369,3363,3785,3723,10253,11576,11608,4531,10204,10564,10567,11049,11067,11539,11594,11636,11661,11767,11796,11799,11802,11805,12065,3290,10609,10764,10835,11609,11766,11963,12174,3746,4095,4529,3757,3793,4512,4515,3242,3247,4514,4513,4517,3764,3581,4546,10178,10181,10434,10485,10488,10493,10919,11408,11664,11770,4553,11131,11255,3981,3869,11288,11635,11639,3712,10875,10881,10903,11890,3567,11005,11134,12128,3714,10612,10970,11140,11170,3535,10532,10535,10618,10791,4550,11570,4540,4551,10671,10773,11411,11440,12193,4155,10749,4056,3745,3692,4548,10226,10229,10570,10573,11451,4549,11550,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997,10068,10069,10122,10136,2,12,13,4583,4584,4602,4633,4634,4636,4663,4671,4672,4683,4732,4734,4764,4778,4807,4901,4902,4916,4935,4991,4992,4995,4996,4998,5000,5001,5012,5013,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5086,5094,5097,5104,5160,5166,5167,5173,5201,5212,5218,5233,5253,5260,5261,5262,5271,5280,5287,5289,5290,5296,5303,5304,5317,5318,5319,5320,5322,5323,5328,5329,5330,5331,5362,5363,5364,5372,5373,5374,5375,5418,5423,5425,5461,5463,5464,5466,5467,5469,5470,5472,5481,5486,5488,5489,5490,5491,5492,5493,5500,5510,5513,5524,5540,5541,5544,5553,5555,5556,5557,5582,5592,5608,5609,5619,5620,5622,5624,5629,5664,5669,5671,5729,5763,5764,5768,5774,5777,5778,5779,5780,5786,5797,5798,5800,5801,5809,5830,5859,5875,5878,5879,5881,5890,5907,5911,5914,5915,5916,5931,5941,5942,5970,5971,5975,5995,5998,6002,6021,6025,6026,6051,6054,6062,6070,6076,6080,6087,6088,6089,6090,6123,6138,6191,6226,6228,6249,6250,6255,6259,6260,6263,6269,6278,6293,6313,6314,6317,6320,6330,6345,6366,6372,6374,6389,6390,6393,6394,6396,6398,6399,6400,6402,6404,6406,6411,6412,6413,6415,6421,6423,6428,6465,6470,6485,6487,6488,6489,6523,6528,6530,6535,6536,6544,6548,6560,6584,6585,6587,6588,6599,6605,6622,6625,6644,6677,6678,6679,6684,6698,6717,6719,6721,6723,6728,6734,6736,6751,6758,6794,6795,6796,6810,6811,6813,6814,6833,6835,6849,6875,6897,6908,6910,6912,6914,6915,6916,6948,6949,6954,6955,6962,6963,6965,6967,6986,6995,6996,7008,7018,7057,7067,7071,7078,7089,7090,7095,7097,7103,7111,7124,7141,7159,7161,7178,7227,7228,7229,7231,7233,7237,7242,7265,7308,7340,7355,7372,7404,7407,7433,7457,7474,7477,7478,7488,7507,7509,7511,7513,7514,7515,7540,7566,7567,7599,7601,7602,7603,7608,7628,7637,7647,7652,7658,7660,7666,7677,7678,7680,7702,7706,7727,7793,7794,7795,7843,7851,7852,7878,7879,7896,7897,7954,7955,7984,8012,8023,8025,8034,8046,8076,8082,8089])). % 181.73/181.62 cnf(12240,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x122401,a859)),x122402),x122402))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(12243,plain, % 181.73/181.62 (~P1(f324(f324(f326(x122431),x122432),f191(f871(x122431,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12246,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x122461,f871(x122462,a859))),x122463),x122464))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(12249,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x122491,a859)),f324(f303(x122492,x122491,x122493),f324(f304(x122492,x122491,x122493),x122494))),x122494))), % 181.73/181.62 inference(rename_variables,[],[4155])). % 181.73/181.62 cnf(12250,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x122501,a859)),x122502),x122502))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(12255,plain, % 181.73/181.62 (E(f76(x122551,x122552,x122553,x122553,x122554),x122554)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12258,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x122581,a859)),f324(f167(x122581),f171(x122581,x122582,x122583))),f324(f167(x122581),x122582)))), % 181.73/181.62 inference(rename_variables,[],[3967])). % 181.73/181.62 cnf(12259,plain, % 181.73/181.62 (P1(f324(f61(x122591),f324(f167(x122591),x122592)))), % 181.73/181.62 inference(rename_variables,[],[3309])). % 181.73/181.62 cnf(12262,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x122621),x122621))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12265,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x122651),x122651))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12268,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x122681),x122681))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12279,plain, % 181.73/181.62 (P27(x122791,x122791,f5(x122791),x122792)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12287,plain, % 181.73/181.62 (~P1(f324(f324(f326(x122871),x122872),f191(f871(x122871,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12290,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x122901,x122901)),f324(f324(f259(x122901,x122901),x122902),x122902)),f300(x122901,x122903)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(12293,plain, % 181.73/181.62 (~P1(f324(f324(f326(x122931),x122932),f191(f871(x122931,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12296,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x122961,x122961)),f324(f324(f259(x122961,x122961),x122962),x122962)),f300(x122961,x122963)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(12306,plain, % 181.73/181.62 (~E(f324(f324(f145(x123061),x123062),x123063),x123063)), % 181.73/181.62 inference(rename_variables,[],[4482])). % 181.73/181.62 cnf(12313,plain, % 181.73/181.62 (P1(f324(f324(f326(x123131),x123132),f247(f871(x123131,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(12314,plain, % 181.73/181.62 (~E(f324(a115,x123141),x123141)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(12317,plain, % 181.73/181.62 (P1(f324(f324(f326(f866(x123171)),f116(x123171)),f155(x123171,x123172)))), % 181.73/181.62 inference(rename_variables,[],[3471])). % 181.73/181.62 cnf(12318,plain, % 181.73/181.62 (~E(f324(f324(f145(x123181),x123182),x123183),f116(x123181))), % 181.73/181.62 inference(rename_variables,[],[4489])). % 181.73/181.62 cnf(12321,plain, % 181.73/181.62 (P27(x123211,x123211,f5(x123211),x123212)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12324,plain, % 181.73/181.62 (P1(f324(f324(f326(x123241),f324(x123242,x123243)),f324(f303(x123244,x123241,x123242),f247(f871(x123244,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(12325,plain, % 181.73/181.62 (P27(x123251,x123251,f5(x123251),x123252)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12328,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x123281,a859)),f191(f871(x123281,a859))),x123282))), % 181.73/181.62 inference(rename_variables,[],[3714])). % 181.73/181.62 cnf(12329,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x123291,a859)),x123292),x123292))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(12332,plain, % 181.73/181.62 (P1(f324(f324(f326(x123321),f324(x123322,x123323)),f324(f303(x123324,x123321,x123322),f247(f871(x123324,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(12333,plain, % 181.73/181.62 (P27(x123331,x123331,f5(x123331),x123332)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12336,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(f866(x123361),f866(x123361))),f324(f324(f259(f866(x123361),f866(x123361)),f116(x123361)),f116(x123361))),f152(x123361,x123362)))), % 181.73/181.62 inference(rename_variables,[],[4051])). % 181.73/181.62 cnf(12339,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x123391),x123391))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12340,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x123401),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12346,plain, % 181.73/181.62 (E(f324(f324(f124(x123461),x123462),f116(x123461)),x123462)), % 181.73/181.62 inference(rename_variables,[],[3198])). % 181.73/181.62 cnf(12347,plain, % 181.73/181.62 (~E(f324(f324(f145(x123471),x123472),x123473),x123473)), % 181.73/181.62 inference(rename_variables,[],[4482])). % 181.73/181.62 cnf(12350,plain, % 181.73/181.62 (E(f324(f324(f124(x123501),x123502),f116(x123501)),x123502)), % 181.73/181.62 inference(rename_variables,[],[3198])). % 181.73/181.62 cnf(12351,plain, % 181.73/181.62 (~E(f324(f324(f145(x123511),x123512),x123513),x123513)), % 181.73/181.62 inference(rename_variables,[],[4482])). % 181.73/181.62 cnf(12354,plain, % 181.73/181.62 (E(f324(f324(f124(x123541),x123542),f116(x123541)),x123542)), % 181.73/181.62 inference(rename_variables,[],[3198])). % 181.73/181.62 cnf(12361,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x123611,a859)),f324(f167(x123611),f324(f130(x123611,x123612),x123613))),f324(f167(x123611),x123613)))), % 181.73/181.62 inference(rename_variables,[],[3913])). % 181.73/181.62 cnf(12362,plain, % 181.73/181.62 (E(f324(f303(x123621,x123621,f5(x123621)),x123622),x123622)), % 181.73/181.62 inference(rename_variables,[],[3326])). % 181.73/181.62 cnf(12367,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x123671,a859)),x123672),f247(f871(x123671,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12371,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x123711),x123711))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12372,plain, % 181.73/181.62 (~E(f324(a115,x123721),x123721)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(12375,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x123751,a859)),f191(f871(x123751,a859))),x123752))), % 181.73/181.62 inference(rename_variables,[],[3714])). % 181.73/181.62 cnf(12378,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x123781),x123781))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12381,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x123811,a859)),x123812),x123812))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(12386,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x123861,a859)),x123862),f324(f324(f302(x123861),x123863),x123862)))), % 181.73/181.62 inference(rename_variables,[],[3712])). % 181.73/181.62 cnf(12389,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x123891,a859)),x123892),x123892))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(12390,plain, % 181.73/181.62 (~P1(f324(f324(f326(x123901),x123902),f191(f871(x123901,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12393,plain, % 181.73/181.62 (~P1(f324(f324(f326(x123931),x123932),f191(f871(x123931,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12402,plain, % 181.73/181.62 (P27(x124021,x124021,f5(x124021),x124022)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12405,plain, % 181.73/181.62 (E(f324(f192(f866(x124051)),f165(x124051,x124052,x124053)),x124052)), % 181.73/181.62 inference(rename_variables,[],[3336])). % 181.73/181.62 cnf(12408,plain, % 181.73/181.62 (P28(x124081,x124081,f34(x124081),x124082,x124082)), % 181.73/181.62 inference(rename_variables,[],[3929])). % 181.73/181.62 cnf(12411,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x124111),x124111))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12412,plain, % 181.73/181.62 (P1(f324(f247(f871(x124121,a859)),x124122))), % 181.73/181.62 inference(rename_variables,[],[3330])). % 181.73/181.62 cnf(12415,plain, % 181.73/181.62 (~P1(f324(f324(f326(x124151),x124152),f191(f871(x124151,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12418,plain, % 181.73/181.62 (P1(f324(f324(f326(x124181),f324(x124182,x124183)),f324(f303(x124184,x124181,x124182),f247(f871(x124184,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(12419,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x124191,x124191)),f324(f324(f259(x124191,x124191),x124192),x124192)),f300(x124191,x124193)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(12422,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x124221,x124221)),f324(f324(f259(x124221,x124221),x124222),x124222)),f300(x124221,x124223)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(12425,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x124251),x124251))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12426,plain, % 181.73/181.62 (P1(f324(f247(f871(x124261,a859)),x124262))), % 181.73/181.62 inference(rename_variables,[],[3330])). % 181.73/181.62 cnf(12429,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x124291,a859)),x124292),f247(f871(x124291,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12430,plain, % 181.73/181.62 (P28(x124301,x124301,f34(x124301),x124302,x124302)), % 181.73/181.62 inference(rename_variables,[],[3929])). % 181.73/181.62 cnf(12433,plain, % 181.73/181.62 (P1(f324(f61(x124331),f324(f167(x124331),x124332)))), % 181.73/181.62 inference(rename_variables,[],[3309])). % 181.73/181.62 cnf(12442,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x124421,x124421)),f324(f324(f259(x124421,x124421),x124422),x124422)),f324(f324(f281(x124421,x124421,x124421),f300(x124421,x124423)),f300(x124421,f300(x124421,x124423)))))), % 181.73/181.62 inference(scs_inference,[],[3929,12408,3509,11020,12084,12184,12187,12279,12321,12325,12333,3518,3519,3236,4490,4491,3137,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,11605,11699,11734,12054,4471,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,11556,11869,11894,11906,11938,12036,12144,12151,12314,4467,10375,10468,10916,3325,3478,11841,2870,2871,2874,2875,2878,2879,2881,2882,2883,2885,2886,2889,2891,2893,2896,2897,2901,2902,2910,2913,2920,2923,2931,2932,2933,2942,2961,2965,3006,3021,3022,3029,3031,3038,3045,3060,4445,3310,3198,11582,12346,12350,12354,3210,3321,3725,3336,10166,11835,12028,3964,3103,4463,3817,11350,3162,3128,3586,3122,3109,3110,3143,3326,10759,10884,12145,12362,3196,3197,3220,10416,3373,4543,3901,4482,10207,10372,11212,12306,12347,4489,12318,3259,11680,4532,10942,11025,11258,11261,3374,3159,3160,10274,10579,3431,3080,3181,11340,4051,12336,3903,10948,11091,11143,12290,12296,12419,12422,4555,10862,11096,11206,11228,11266,11272,12234,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,12190,12231,12317,3629,4338,4339,4480,11331,3570,3781,3827,3457,3707,3337,10293,10411,10482,10543,10546,10582,10680,10932,11777,11865,11928,12004,12045,12122,12125,3718,11573,3252,3349,3534,4526,10184,10187,10213,10688,10701,10820,11250,11343,11749,11754,11776,11980,11983,12066,12075,12237,4538,11454,11487,11524,11553,3705,3479,3852,3296,3298,3271,4523,4477,3657,3463,4539,4045,11223,3591,3309,11705,11708,12155,12259,4015,3972,11858,12205,3913,10756,12016,12039,12212,3967,10951,12081,12154,12211,12258,3630,11868,12011,12089,12135,4004,3648,10954,11030,11117,11176,12035,12103,12367,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,11434,11651,11698,11838,11893,11909,11912,11915,11918,12096,12110,12113,12116,12119,12198,12262,12378,3269,10331,10386,10594,10683,10807,11427,11496,11733,11737,11746,11844,11855,11874,11879,11921,11941,3270,3345,12069,4522,10250,10340,10453,10477,10725,10770,10780,11503,11604,11626,11629,11632,11648,11808,11811,11814,11817,11905,11924,11927,11937,11992,11995,11998,12001,12076,12166,12169,12265,12268,12339,12371,3426,10549,10815,10859,11165,11247,11414,11660,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,11285,11677,11714,11986,11989,12023,12070,12099,12243,12287,12293,12390,12393,3330,10576,10606,10615,11198,11761,12412,3369,3363,3785,3723,10253,11576,11608,4531,10204,10564,10567,11049,11067,11539,11594,11636,11661,11767,11796,11799,11802,11805,12065,3290,10609,10764,10835,11609,11766,11963,12174,3746,4095,4529,3757,3793,4512,4515,3242,3247,4514,4513,4517,3764,3581,4546,10178,10181,10434,10485,10488,10493,10919,11408,11664,11770,4553,11131,11255,11291,3981,3869,11288,11635,11639,11702,12324,12332,3712,10875,10881,10903,11890,12102,3567,11005,11134,12128,12240,12250,12329,12381,3714,10612,10970,11140,11170,11183,12328,3535,10532,10535,10618,10791,4550,11570,4540,4551,10671,10773,11411,11440,12193,12202,4155,10749,12223,4056,3745,3692,4548,10226,10229,10570,10573,11451,4549,11550,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,5713,5715,5720,5727,5742,5756,5761,5762,5775,5776,5781,5785,5787,5792,5833,5845,5854,5858,5867,5871,5872,5880,5893,5899,5917,5920,5929,5954,5968,5993,6013,6014,6017,6030,6032,6034,6036,6049,6050,6053,6055,6058,6059,6071,6077,6078,6079,6081,6083,6120,6121,6128,6137,6173,6175,6177,6179,6188,6190,6192,6198,6200,6205,6208,6216,6223,6224,6225,6230,6252,6253,6254,6256,6262,6267,6301,6302,6304,6305,6306,6308,6309,6310,6311,6319,6352,6353,6354,6363,6384,6385,6405,6407,6418,6419,6425,6455,6457,6471,6475,6509,6511,6512,6565,6589,6631,6651,6660,6661,6662,6663,6682,6683,6689,6702,6705,6707,6708,6709,6711,6713,6727,6738,6740,6741,6754,6757,6808,6819,6821,6825,6842,6843,6877,6889,6920,6951,7005,7033,7088,7109,7117,7120,7175,7183,7241,7243,7258,7268,7269,7270,7286,7292,7294,7344,7354,7357,7373,7424,7426,7429,7472,7473,7491,7558,7577,7600,7621,7636,7650,7661,7669,7670,7696,7699,7701,7708,7744,7754,7779,7840,7876,7908,7947,7963,7965,7981,7982,8055,8107,8126,8150,8156,8171,8196,8197,8235,8236,8253,8297,8299,8301,8308,8322,8326,8341,8362,8370,8372,8383,8388,8392,8412,8426,8427,8444,8445,8450,8451,8452,8453,8454,8472,8473,8474,8483,8496,8499,8511,8516,8518,8520,8521,8529,8535,8543,8546,8563,8564,8573,8574,8582,8602,8615,8619,8640,8662,8663,8666,8667,8673,8682,8683,8706,8718,8728,8729,8730,8731,8733,8756,8757,8768,8812,8818,8823,8825,8836,8841,8843,8845,8846,8852,8861,8933,8964,8965,8966,8981,8999,9007,9008,9037,9038,9081,9107,9144,9157,9158,9159,9168,9194,9210,9213,9217,9237,9238,9266,9329,9368,9369,9370,9393,9394,9415,9435,9441,9454,9475,9478,9501,9510,9511,9512,9513,9519,9529,9531,9536,9568,9569,9575,9576,9621,9622,9656,9665,9675,9677,9678,9687,9701,9704,9732,9764,9766,9770,9826,9867,9868,9870,9880,9881,9901,9906,9947,9997,10068,10069,10122,10136,2,12,13,4583,4584,4602,4633,4634,4636,4663,4671,4672,4683,4732,4734,4764,4778,4807,4901,4902,4916,4935,4991,4992,4995,4996,4998,5000,5001,5012,5013,5021,5032,5033,5039,5058,5059,5076,5081,5082,5083,5084,5086,5094,5097,5104,5160,5166,5167,5173,5201,5212,5218,5233,5253,5260,5261,5262,5271,5280,5287,5289,5290,5296,5303,5304,5317,5318,5319,5320,5322,5323,5328,5329,5330,5331,5362,5363,5364,5372,5373,5374,5375,5418,5423,5425,5461,5463,5464,5466,5467,5469,5470,5472,5481,5486,5488,5489,5490,5491,5492,5493,5500,5510,5513,5524,5540,5541,5544,5553,5555,5556,5557,5582,5592,5608,5609,5619,5620,5622,5624,5629,5664,5669,5671,5729,5763,5764,5768,5774,5777,5778,5779,5780,5786,5797,5798,5800,5801,5809,5830,5859,5875,5878,5879,5881,5890,5907,5911,5914,5915,5916,5931,5941,5942,5970,5971,5975,5995,5998,6002,6021,6025,6026,6051,6054,6062,6070,6076,6080,6087,6088,6089,6090,6123,6138,6191,6226,6228,6249,6250,6255,6259,6260,6263,6269,6278,6293,6313,6314,6317,6320,6330,6345,6366,6372,6374,6389,6390,6393,6394,6396,6398,6399,6400,6402,6404,6406,6411,6412,6413,6415,6421,6423,6428,6465,6470,6485,6487,6488,6489,6523,6528,6530,6535,6536,6544,6548,6560,6584,6585,6587,6588,6599,6605,6622,6625,6644,6677,6678,6679,6684,6698,6717,6719,6721,6723,6728,6734,6736,6751,6758,6794,6795,6796,6810,6811,6813,6814,6833,6835,6849,6875,6897,6908,6910,6912,6914,6915,6916,6948,6949,6954,6955,6962,6963,6965,6967,6986,6995,6996,7008,7018,7057,7067,7071,7078,7089,7090,7095,7097,7103,7111,7124,7141,7159,7161,7178,7227,7228,7229,7231,7233,7237,7242,7265,7308,7340,7355,7372,7404,7407,7433,7457,7474,7477,7478,7488,7507,7509,7511,7513,7514,7515,7540,7566,7567,7599,7601,7602,7603,7608,7628,7637,7647,7652,7658,7660,7666,7677,7678,7680,7702,7706,7727,7793,7794,7795,7843,7851,7852,7878,7879,7896,7897,7954,7955,7984,8012,8023,8025,8034,8046,8076,8082,8089,8102,8121,8127,8149,8193,8223,8237,8256,8259,8290,8316,8373,8374,8377,8378,8442,8476,8477,8478,8479,8506,8538,8567,8575,8576,8618,8639,8685,8700,8747,8750,8765,8772,8809,8857,8858,8873,8874,9004,9010,9014,9035,9045,9068,9070,9073,9077,9079,9080,9093,9094,9114,9121,9134,9143,9180,9198,9250,9251,9258,9298,9321,9326,9361,9366,9372])). % 181.73/181.62 cnf(12445,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x124451,f871(x124452,a859))),x124453),x124454))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(12448,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x124481,a859)),x124482),f247(f871(x124481,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12451,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x124511,x124511)),f324(f324(f259(x124511,x124511),x124512),x124512)),f300(x124511,x124513)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(12454,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),f324(f324(f81(a865),x124541),x124542)),x124542))), % 181.73/181.62 inference(rename_variables,[],[4548])). % 181.73/181.62 cnf(12455,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x124551),f324(a115,x124551)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12458,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x124581,a859)),f324(f167(x124581),f324(f130(x124581,x124582),x124583))),f324(f167(x124581),x124583)))), % 181.73/181.62 inference(rename_variables,[],[3913])). % 181.73/181.62 cnf(12461,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x124611,a859)),x124612),f247(f871(x124611,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12464,plain, % 181.73/181.62 (E(f76(x124641,x124642,x124643,x124643,x124644),x124644)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12472,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(x124721,x124721)),f324(f324(f259(x124721,x124721),x124722),x124722)),f300(x124721,x124723)))), % 181.73/181.62 inference(rename_variables,[],[3903])). % 181.73/181.62 cnf(12475,plain, % 181.73/181.62 (~P1(f324(f324(f326(x124751),x124752),f191(f871(x124751,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12476,plain, % 181.73/181.62 (P1(f324(f324(f326(f870(f866(x124761),f866(x124761))),f324(f324(f259(f866(x124761),f866(x124761)),f116(x124761)),f116(x124761))),f152(x124761,x124762)))), % 181.73/181.62 inference(rename_variables,[],[4051])). % 181.73/181.62 cnf(12481,plain, % 181.73/181.62 (~P1(f324(f324(f326(x124811),x124812),f191(f871(x124811,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12484,plain, % 181.73/181.62 (P33(x124841,x124842,f116(x124841))), % 181.73/181.62 inference(rename_variables,[],[3202])). % 181.73/181.62 cnf(12487,plain, % 181.73/181.62 (E(f324(f192(f866(x124871)),f165(x124871,x124872,x124873)),x124872)), % 181.73/181.62 inference(rename_variables,[],[3336])). % 181.73/181.62 cnf(12490,plain, % 181.73/181.62 (~P1(f324(f324(f326(x124901),x124902),f191(f871(x124901,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12496,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x124961),x124961))), % 181.73/181.62 inference(rename_variables,[],[4522])). % 181.73/181.62 cnf(12499,plain, % 181.73/181.62 (P1(f324(f324(f326(x124991),x124992),f247(f871(x124991,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(12503,plain, % 181.73/181.62 (~P1(f324(f324(f191(f871(x125031,f871(x125032,a859))),x125033),x125034))), % 181.73/181.62 inference(rename_variables,[],[4551])). % 181.73/181.62 cnf(12506,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x125061,a859)),x125062),x125062))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(12509,plain, % 181.73/181.62 (~P1(f324(f324(f326(x125091),x125092),f191(f871(x125091,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12512,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),f2(a1)),f324(f324(f249(a1),f324(f75(a1),x125121)),x125122)))), % 181.73/181.62 inference(rename_variables,[],[3745])). % 181.73/181.62 cnf(12515,plain, % 181.73/181.62 (~E(f324(a115,x125151),x125151)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(12517,plain, % 181.73/181.62 (E(f76(x125171,x125172,x125173,x125173,x125174),x125174)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12519,plain, % 181.73/181.62 (P27(x125191,x125191,f5(x125191),x125192)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12521,plain, % 181.73/181.62 (P27(x125211,x125211,f5(x125211),x125212)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12533,plain, % 181.73/181.62 (E(f76(x125331,x125332,x125333,x125333,x125334),x125334)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12535,plain, % 181.73/181.62 (E(f76(x125351,x125352,x125353,x125353,x125354),x125354)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12537,plain, % 181.73/181.62 (E(f76(x125371,x125372,x125373,x125373,x125374),x125374)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12541,plain, % 181.73/181.62 (P52(x125411,x125411,f256(x125411,x125412))), % 181.73/181.62 inference(rename_variables,[],[3236])). % 181.73/181.62 cnf(12547,plain, % 181.73/181.62 (P39(x125471,f147(x125471,x125472))), % 181.73/181.62 inference(rename_variables,[],[3137])). % 181.73/181.62 cnf(12551,plain, % 181.73/181.62 (E(f76(x125511,x125512,x125513,x125513,x125514),x125514)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12553,plain, % 181.73/181.62 (E(f76(x125531,x125532,x125533,x125533,x125534),x125534)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12555,plain, % 181.73/181.62 (E(f76(x125551,x125552,x125553,x125553,x125554),x125554)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12572,plain, % 181.73/181.62 (E(f191(f871(f870(x125721,x125721),a859)),f256(x125721,f191(f871(x125721,a859))))), % 181.73/181.62 inference(rename_variables,[],[3340])). % 181.73/181.62 cnf(12574,plain, % 181.73/181.62 (P26(x125741,x125742,f191(f871(f864(x125741),a859)))), % 181.73/181.62 inference(rename_variables,[],[3324])). % 181.73/181.62 cnf(12580,plain, % 181.73/181.62 (E(f76(x125801,x125802,x125803,x125803,x125804),x125804)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12582,plain, % 181.73/181.62 (P17(x125821,f871(x125821,a859),f302(x125821))), % 181.73/181.62 inference(rename_variables,[],[3239])). % 181.73/181.62 cnf(12586,plain, % 181.73/181.62 (P53(x125861,f191(f871(x125861,a859)),x125862)), % 181.73/181.62 inference(rename_variables,[],[3288])). % 181.73/181.62 cnf(12590,plain, % 181.73/181.62 (P28(x125901,x125901,f34(x125901),x125902,x125902)), % 181.73/181.62 inference(rename_variables,[],[3929])). % 181.73/181.62 cnf(12592,plain, % 181.73/181.62 (P28(x125921,x125921,f34(x125921),x125922,x125922)), % 181.73/181.62 inference(rename_variables,[],[3929])). % 181.73/181.62 cnf(12594,plain, % 181.73/181.62 (P28(x125941,x125941,f34(x125941),x125942,x125942)), % 181.73/181.62 inference(rename_variables,[],[3929])). % 181.73/181.62 cnf(12599,plain, % 181.73/181.62 (P41(x125991,x125992,f256(x125991,x125992))), % 181.73/181.62 inference(rename_variables,[],[3235])). % 181.73/181.62 cnf(12601,plain, % 181.73/181.62 (P41(x126011,x126012,f256(x126011,x126012))), % 181.73/181.62 inference(rename_variables,[],[3235])). % 181.73/181.62 cnf(12609,plain, % 181.73/181.62 (E(f76(x126091,x126092,x126093,x126093,x126094),x126094)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12611,plain, % 181.73/181.62 (E(f76(x126111,x126112,x126113,x126113,x126114),x126114)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12614,plain, % 181.73/181.62 (P30(x126141,f2(a865),f324(f324(f324(f93(x126141),x126142),f324(a25,x126143)),x126144))), % 181.73/181.62 inference(rename_variables,[],[3641])). % 181.73/181.62 cnf(12622,plain, % 181.73/181.62 (P34(x126221,x126222,f116(x126221),f116(x126221))), % 181.73/181.62 inference(rename_variables,[],[3518])). % 181.73/181.62 cnf(12624,plain, % 181.73/181.62 (P34(x126241,x126242,f116(x126241),f116(x126241))), % 181.73/181.62 inference(rename_variables,[],[3518])). % 181.73/181.62 cnf(12631,plain, % 181.73/181.62 (P44(x126311,x126312,x126313,x126314,f191(f871(x126311,a859)),x126314)), % 181.73/181.62 inference(rename_variables,[],[4222])). % 181.73/181.62 cnf(12634,plain, % 181.73/181.62 (P44(x126341,x126342,x126343,x126344,f191(f871(x126341,a859)),x126344)), % 181.73/181.62 inference(rename_variables,[],[4222])). % 181.73/181.62 cnf(12643,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),f2(a865)),f324(a115,x126431)))), % 181.73/181.62 inference(rename_variables,[],[3349])). % 181.73/181.62 cnf(12644,plain, % 181.73/181.62 (~E(f324(a115,x126441),x126441)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(12650,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x126501),f324(a115,x126501)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12655,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x126551),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12664,plain, % 181.73/181.62 (~P1(f324(f324(f239(a1),f324(f103(a1),x126641)),f324(f80(a1),f324(f103(a1),x126642))))), % 181.73/181.62 inference(rename_variables,[],[4545])). % 181.73/181.62 cnf(12674,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x126741),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12677,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x126771),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12680,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x126801,x126802)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(12683,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x126831,x126832)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(12686,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x126861,x126862)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(12689,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x126891,x126892)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(12696,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),f324(f80(a1),f324(f103(a1),x126961))),f324(f103(a1),x126962)))), % 181.73/181.62 inference(rename_variables,[],[3746])). % 181.73/181.62 cnf(12701,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x127011),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12702,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x127021),x127021))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12709,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x127091),f324(a115,x127091)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12714,plain, % 181.73/181.62 (P1(f324(f324(f326(x127141),f324(x127142,x127143)),f324(f303(x127144,x127141,x127142),f247(f871(x127144,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(12715,plain, % 181.73/181.62 (~E(f324(a115,x127151),f2(a865))), % 181.73/181.62 inference(rename_variables,[],[4461])). % 181.73/181.62 cnf(12720,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x127201),x127201))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(12723,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x127231,x127232)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(12726,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x127261,x127262)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(12729,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x127291),x127291))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12730,plain, % 181.73/181.62 (~E(f324(a115,x127301),f2(a865))), % 181.73/181.62 inference(rename_variables,[],[4461])). % 181.73/181.62 cnf(12747,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f44(a865,x127471,x127472)),x127471))), % 181.73/181.62 inference(rename_variables,[],[3723])). % 181.73/181.62 cnf(12752,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x127521),f324(a115,x127521)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12755,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x127551),f324(a115,x127551)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12756,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x127561),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12765,plain, % 181.73/181.62 (~P1(f324(f324(f239(a1),f324(f103(a1),x127651)),f2(a1)))), % 181.73/181.62 inference(rename_variables,[],[4538])). % 181.73/181.62 cnf(12766,plain, % 181.73/181.62 (P1(f324(f247(f871(x127661,a859)),x127662))), % 181.73/181.62 inference(rename_variables,[],[3330])). % 181.73/181.62 cnf(12769,plain, % 181.73/181.62 (~P1(f324(f324(f239(a1),f324(f103(a1),x127691)),f2(a1)))), % 181.73/181.62 inference(rename_variables,[],[4538])). % 181.73/181.62 cnf(12770,plain, % 181.73/181.62 (P1(f324(f247(f871(x127701,a859)),x127702))), % 181.73/181.62 inference(rename_variables,[],[3330])). % 181.73/181.62 cnf(12773,plain, % 181.73/181.62 (P1(f324(f247(f871(x127731,a859)),x127732))), % 181.73/181.62 inference(rename_variables,[],[3330])). % 181.73/181.62 cnf(12781,plain, % 181.73/181.62 (E(f76(x127811,x127812,x127813,x127814,x127815),f76(x127811,x127812,x127814,x127813,x127815))), % 181.73/181.62 inference(rename_variables,[],[4118])). % 181.73/181.62 cnf(12784,plain, % 181.73/181.62 (~P1(f324(f324(f326(x127841),x127842),f191(f871(x127841,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12785,plain, % 181.73/181.62 (P1(f324(f61(x127851),f191(f871(x127851,a859))))), % 181.73/181.62 inference(rename_variables,[],[3345])). % 181.73/181.62 cnf(12794,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x127941))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(12797,plain, % 181.73/181.62 (~P1(f324(f324(f326(x127971),x127972),f191(f871(x127971,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12800,plain, % 181.73/181.62 (~P1(f324(f324(f326(x128001),x128002),f191(f871(x128001,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12803,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x128031),x128031))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12811,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x128111),f324(a115,x128111)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(12814,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x128141),x128141))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12819,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x128191),x128191))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12822,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x128221),x128221))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12825,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x128251),x128251))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12828,plain, % 181.73/181.62 (E(f324(f324(f22(f871(x128281,a859)),f191(f871(x128281,a859))),x128282),f191(f871(x128281,a859)))), % 181.73/181.62 inference(rename_variables,[],[3539])). % 181.73/181.62 cnf(12829,plain, % 181.73/181.62 (P1(f324(f61(x128291),f191(f871(x128291,a859))))), % 181.73/181.62 inference(rename_variables,[],[3345])). % 181.73/181.62 cnf(12832,plain, % 181.73/181.62 (E(f324(f324(f22(f871(x128321,a859)),f191(f871(x128321,a859))),x128322),f191(f871(x128321,a859)))), % 181.73/181.62 inference(rename_variables,[],[3539])). % 181.73/181.62 cnf(12833,plain, % 181.73/181.62 (P1(f324(f61(x128331),f191(f871(x128331,a859))))), % 181.73/181.62 inference(rename_variables,[],[3345])). % 181.73/181.62 cnf(12836,plain, % 181.73/181.62 (E(f324(f324(f22(f871(x128361,a859)),f191(f871(x128361,a859))),x128362),f191(f871(x128361,a859)))), % 181.73/181.62 inference(rename_variables,[],[3539])). % 181.73/181.62 cnf(12837,plain, % 181.73/181.62 (P1(f324(f61(x128371),f191(f871(x128371,a859))))), % 181.73/181.62 inference(rename_variables,[],[3345])). % 181.73/181.62 cnf(12840,plain, % 181.73/181.62 (E(f324(f324(f22(f871(x128401,a859)),f191(f871(x128401,a859))),x128402),f191(f871(x128401,a859)))), % 181.73/181.62 inference(rename_variables,[],[3539])). % 181.73/181.62 cnf(12841,plain, % 181.73/181.62 (P1(f324(f61(x128411),f191(f871(x128411,a859))))), % 181.73/181.62 inference(rename_variables,[],[3345])). % 181.73/181.62 cnf(12845,plain, % 181.73/181.62 (E(f76(x128451,x128452,x128453,x128453,x128454),x128454)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(12850,plain, % 181.73/181.62 (E(f324(f324(f22(f871(x128501,a859)),f191(f871(x128501,a859))),x128502),f191(f871(x128501,a859)))), % 181.73/181.62 inference(rename_variables,[],[3539])). % 181.73/181.62 cnf(12851,plain, % 181.73/181.62 (P1(f324(f61(x128511),f191(f871(x128511,a859))))), % 181.73/181.62 inference(rename_variables,[],[3345])). % 181.73/181.62 cnf(12855,plain, % 181.73/181.62 (P1(f324(f61(x128551),f191(f871(x128551,a859))))), % 181.73/181.62 inference(rename_variables,[],[3345])). % 181.73/181.62 cnf(12858,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x128581),x128581))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12862,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x128621),x128621))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(12869,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x128691),x128691))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12882,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x128821),x128821))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(12891,plain, % 181.73/181.62 (~P1(f324(f324(f326(x128911),x128912),f191(f871(x128911,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(12902,plain, % 181.73/181.62 (P1(f324(f324(f326(x129021),x129022),f247(f871(x129021,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(12906,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x129061,a859)),x129062),f247(f871(x129061,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12909,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x129091,a859)),f324(f167(x129091),f324(f130(x129091,x129092),x129093))),f324(f167(x129091),x129093)))), % 181.73/181.62 inference(rename_variables,[],[3913])). % 181.73/181.62 cnf(12915,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x129151),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12916,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x129161),x129161))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(12920,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x129201),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12921,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x129211),x129211))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(12926,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x129261),x129261))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12933,plain, % 181.73/181.62 (E(f324(f324(f16(x129331,x129332),x129333),x129334),x129333)), % 181.73/181.62 inference(rename_variables,[],[3259])). % 181.73/181.62 cnf(12936,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x129361,a859)),f324(f167(x129361),f171(x129361,x129362,x129363))),f324(f167(x129361),x129362)))), % 181.73/181.62 inference(rename_variables,[],[3967])). % 181.73/181.62 cnf(12940,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x129401),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12941,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x129411),x129411))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(12945,plain, % 181.73/181.62 (~P1(f324(f324(f239(a865),x129451),f2(a865)))), % 181.73/181.62 inference(rename_variables,[],[4526])). % 181.73/181.62 cnf(12946,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x129461),x129461))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(12951,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x129511),x129511))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12953,plain, % 181.73/181.62 (~P1(f324(f324(f239(f871(a865,a859)),f295(a865,f324(a115,x129531),f324(a115,x129531))),f295(a865,x129532,x129531)))), % 181.73/181.62 inference(scs_inference,[],[4562,3929,12408,12430,12590,12592,3509,11020,12084,12184,12187,12279,12321,12325,12333,12402,12519,3518,12148,12622,12624,3519,12218,3235,12599,12601,3236,12541,3202,12484,4490,4491,11657,4222,12631,12634,3239,12582,3079,4118,3137,12547,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,11605,11699,11734,12054,12255,12464,12517,12533,12535,12537,12551,12553,12555,12580,12609,12611,4471,3569,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,11556,11869,11894,11906,11938,12036,12144,12151,12314,12372,12515,4467,10375,10468,10916,3325,3288,12586,3478,11841,4461,12715,2870,2871,2874,2875,2878,2879,2881,2882,2883,2885,2886,2889,2890,2891,2892,2893,2896,2897,2901,2902,2906,2910,2913,2920,2923,2931,2932,2933,2942,2948,2961,2965,2981,2985,2993,2999,3006,3018,3021,3022,3028,3029,3030,3031,3038,3045,4444,3060,3136,4445,3604,3250,3310,3222,3843,3198,11582,12346,12350,12354,3210,3321,3725,3336,10166,11835,12028,12405,12487,3964,3103,4463,3817,11350,3324,12574,3162,3128,3586,3641,12614,3122,3322,3936,3646,3109,3110,3083,3089,3143,3326,10759,10884,12145,12362,3196,3197,3220,10416,3373,4543,10345,3901,4482,10207,10372,11212,12306,12347,4489,12318,3259,11680,11683,4532,10942,11025,11258,11261,3666,3374,3592,3340,12572,3159,3160,10274,10579,3431,3151,3080,3181,11340,4051,12336,12476,3903,10948,11091,11143,12290,12296,12419,12422,12451,4555,10862,11096,11206,11228,11266,11272,12234,4556,10981,11099,11209,4557,11102,4558,11157,4559,3180,3471,12190,12231,12317,3629,4338,4339,4480,11331,3570,3607,3781,3539,12828,12832,12836,12840,12850,3827,12181,3457,3707,3337,10293,10411,10482,10543,10546,10582,10680,10932,11777,11865,11928,12004,12045,12122,12125,12455,12650,12709,12752,12755,12811,3718,11573,3252,3349,11695,3534,4526,10184,10187,10213,10688,10701,10820,11250,11343,11749,11754,11776,11980,11983,12066,12075,12237,12340,12655,12674,12677,12701,12756,12915,12920,12940,4538,11454,11487,11524,11553,12765,12769,3705,3479,3480,12680,12683,12686,12689,12723,3852,3296,3298,3271,4523,3158,4477,3657,4191,3973,3463,4539,4045,11223,3591,3309,11705,11708,12155,12259,12433,4015,3972,11858,12205,3913,10756,12016,12039,12212,12361,12458,3967,10951,12081,12154,12211,12258,3630,11868,12011,12089,12135,4004,3648,10954,11030,11117,11176,12035,12103,12367,12429,12448,12461,4544,10704,11107,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,11434,11651,11698,11838,11893,11909,11912,11915,11918,12096,12110,12113,12116,12119,12198,12262,12378,12425,12702,12729,12803,12814,12819,12822,12825,12858,12869,12926,12951,3269,10331,10386,10594,10683,10807,11427,11496,11733,11737,11746,11844,11855,11874,11879,11921,11941,11958,12720,12862,12882,12916,12921,12941,3270,3345,12069,12785,12829,12833,12837,12841,12851,12855,4522,10250,10340,10453,10477,10725,10770,10780,11503,11604,11626,11629,11632,11648,11808,11811,11814,11817,11905,11924,11927,11937,11992,11995,11998,12001,12076,12166,12169,12265,12268,12339,12371,12411,12496,3426,10549,10815,10859,11165,11247,11414,11660,12313,12499,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,11285,11677,11714,11986,11989,12023,12070,12099,12243,12287,12293,12390,12393,12415,12475,12481,12490,12509,12784,12797,12800,3330,10576,10606,10615,11198,11761,12412,12426,12766,12770,12773,3369,3363,3785,3723,10253,11576,11608,12747,4531,10204,10564,10567,11049,11067,11539,11594,11636,11661,11767,11796,11799,11802,11805,12065,3290,10609,10764,10835,11609,11766,11963,12174,12199,3746,11711,12696,4095,3485,4529,3757,3793,4512,4515,4516,3242,3247,4514,4513,4517,3764,3581,4197,4546,10178,10181,10434,10485,10488,10493,10919,11408,11664,11770,4553,11131,11255,11291,3981,12226,3869,11288,11635,11639,11702,12324,12332,12418,3712,10875,10881,10903,11890,12102,3567,11005,11134,12128,12240,12250,12329,12381,12389,4049,3714,10612,10970,11140,11170,11183,12328,3535,10532,10535,10618,10791,3537,4550,11570,4540,4545,12664,4551,10671,10773,11411,11440,12193,12202,12246,12445,4155,10749,12223,4056,3745,12512,3692,3693,4548,10226,10229,10570,10573,11451,11640,12454,4549,11550,11645,3716,10538,3988,4570,4596,4645,4647,4679,4696,4703,4704,4705,4743,4773,4779,4862,4886,4887,4947,4948,4970,4971,4984,4988,5010,5016,5031,5034,5035,5036,5041,5042,5063,5087,5088,5098,5103,5109,5145,5146,5154,5164,5168,5170,5179,5181,5187,5191,5204,5211,5214,5215,5216,5220,5254,5267,5274,5276,5277,5281,5282,5283,5291,5294,5298,5299,5300,5307,5311,5312,5313,5321,5325,5326,5327,5332,5345,5354,5366,5368,5376,5377,5381,5385,5410,5416,5426,5427,5442,5454,5476,5482,5498,5499,5502,5521,5529,5530,5535,5536,5546,5547,5559,5563,5572,5573,5575,5590,5595,5605,5606,5618,5625,5639,5643,5646,5652,5653,5654,5657,5662,5698,5699,5702,5704,5707,5708,5709,5711,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% 181.73/181.62 cnf(12954,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x129541),x129541))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(12957,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x129571)),x129571))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(12963,plain, % 181.73/181.62 (P1(f324(f324(f326(x129631),f324(x129632,x129633)),f324(f303(x129634,x129631,x129632),f247(f871(x129634,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(12964,plain, % 181.73/181.62 (P27(x129641,x129641,f5(x129641),x129642)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12969,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x129691,a859)),x129692),f247(f871(x129691,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12970,plain, % 181.73/181.62 (P27(x129701,x129701,f5(x129701),x129702)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12974,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x129741,a859)),x129742),f247(f871(x129741,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(12975,plain, % 181.73/181.62 (P27(x129751,x129751,f5(x129751),x129752)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12979,plain, % 181.73/181.62 (P27(x129791,x129791,f5(x129791),x129792)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12982,plain, % 181.73/181.62 (~P1(f324(f324(f239(f871(x129821,a859)),x129822),f191(f871(x129821,a859))))), % 181.73/181.62 inference(rename_variables,[],[4544])). % 181.73/181.62 cnf(12985,plain, % 181.73/181.62 (P27(x129851,x129851,f5(x129851),x129852)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12988,plain, % 181.73/181.62 (P27(x129881,x129881,f5(x129881),x129882)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12994,plain, % 181.73/181.62 (P27(x129941,x129941,f5(x129941),x129942)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(12997,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x129971,a859)),x129972),f247(f871(x129971,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(13002,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x130021,a859)),f191(f871(x130021,a859))),x130022))), % 181.73/181.62 inference(rename_variables,[],[3714])). % 181.73/181.62 cnf(13006,plain, % 181.73/181.62 (E(f76(x130061,x130062,x130063,x130063,x130064),x130064)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(13010,plain, % 181.73/181.62 (~P1(f324(f324(f326(x130101),x130102),f191(f871(x130101,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(13014,plain, % 181.73/181.62 (P1(f324(f324(f326(x130141),x130142),f247(f871(x130141,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(13017,plain, % 181.73/181.62 (P28(x130171,x130171,f34(x130171),x130172,x130172)), % 181.73/181.62 inference(rename_variables,[],[3929])). % 181.73/181.62 cnf(13021,plain, % 181.73/181.62 (P1(f324(f324(f326(x130211),f324(x130212,x130213)),f324(f303(x130214,x130211,x130212),f247(f871(x130214,a859)))))), % 181.73/181.62 inference(rename_variables,[],[3869])). % 181.73/181.62 cnf(13022,plain, % 181.73/181.62 (P27(x130221,x130221,f5(x130221),x130222)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(13025,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x130251,a859)),x130252),f247(f871(x130251,a859))))), % 181.73/181.62 inference(rename_variables,[],[3648])). % 181.73/181.62 cnf(13029,plain, % 181.73/181.62 (P1(f324(f324(f326(x130291),x130292),f247(f871(x130291,a859))))), % 181.73/181.62 inference(rename_variables,[],[3426])). % 181.73/181.62 cnf(13036,plain, % 181.73/181.62 (~P1(f324(f324(f326(x130361),x130362),f191(f871(x130361,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(13039,plain, % 181.73/181.62 (~P1(f324(f324(f326(x130391),x130392),f191(f871(x130391,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(13043,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),x130431),x130431))), % 181.73/181.62 inference(rename_variables,[],[3268])). % 181.73/181.62 cnf(13046,plain, % 181.73/181.62 (E(f76(x130461,x130462,x130463,x130463,x130464),x130464)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(13048,plain, % 181.73/181.62 (~E(f324(a115,x130481),x130481)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(13052,plain, % 181.73/181.62 (E(f324(f324(f16(x130521,x130522),x130523),x130524),x130523)), % 181.73/181.62 inference(rename_variables,[],[3259])). % 181.73/181.62 cnf(13055,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x130551),f324(a115,x130551)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(13056,plain, % 181.73/181.62 (~E(f324(a115,x130561),x130561)), % 181.73/181.62 inference(rename_variables,[],[4449])). % 181.73/181.62 cnf(13059,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x130591),f324(a115,f324(f324(f81(a865),x130592),x130591))))), % 181.73/181.62 inference(rename_variables,[],[3716])). % 181.73/181.62 cnf(13060,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),x130601),f324(a115,x130601)))), % 181.73/181.62 inference(rename_variables,[],[3337])). % 181.73/181.62 cnf(13069,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),f2(a1)),f324(f103(a1),x130691)))), % 181.73/181.62 inference(rename_variables,[],[3369])). % 181.73/181.62 cnf(13072,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x130721))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(13076,plain, % 181.73/181.62 (~E(f324(a115,x130761),f2(a865))), % 181.73/181.62 inference(rename_variables,[],[4461])). % 181.73/181.62 cnf(13085,plain, % 181.73/181.62 (~P1(f324(f324(f326(x130851),x130852),f191(f871(x130851,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(13088,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x130881,x130882)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(13089,plain, % 181.73/181.62 (E(f324(f324(f190(a865),f324(a115,x130891)),f324(a115,x130892)),f324(a115,f324(f324(f190(a865),x130891),x130892)))), % 181.73/181.62 inference(rename_variables,[],[3444])). % 181.73/181.62 cnf(13092,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x130921,x130922)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(13093,plain, % 181.73/181.62 (E(f324(f324(f189(a865),f324(a115,x130931)),f324(a115,x130932)),f324(a115,f324(f324(f189(a865),x130931),x130932)))), % 181.73/181.62 inference(rename_variables,[],[3443])). % 181.73/181.62 cnf(13096,plain, % 181.73/181.62 (P1(f324(f61(a865),f297(a865,x130961,x130962)))), % 181.73/181.62 inference(rename_variables,[],[3480])). % 181.73/181.62 cnf(13104,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x131041,a859)),f324(f167(x131041),f324(f130(x131041,x131042),x131043))),f324(f167(x131041),x131043)))), % 181.73/181.62 inference(rename_variables,[],[3913])). % 181.73/181.62 cnf(13105,plain, % 181.73/181.62 (E(f324(f324(f16(x131051,x131052),x131053),x131054),x131053)), % 181.73/181.62 inference(rename_variables,[],[3259])). % 181.73/181.62 cnf(13108,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x131081,a859)),f324(f167(x131081),f324(f324(f170(x131081),x131082),x131083))),f324(f167(x131081),x131083)))), % 181.73/181.62 inference(rename_variables,[],[3961])). % 181.73/181.62 cnf(13109,plain, % 181.73/181.62 (E(f324(f324(f16(x131091,x131092),x131093),x131094),x131093)), % 181.73/181.62 inference(rename_variables,[],[3259])). % 181.73/181.62 cnf(13113,plain, % 181.73/181.62 (E(f324(f324(f16(x131131,x131132),x131133),x131134),x131133)), % 181.73/181.62 inference(rename_variables,[],[3259])). % 181.73/181.62 cnf(13126,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),f2(a1)),f324(f103(a1),x131261)))), % 181.73/181.62 inference(rename_variables,[],[3369])). % 181.73/181.62 cnf(13131,plain, % 181.73/181.62 (P27(x131311,x131311,f5(x131311),x131312)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(13134,plain, % 181.73/181.62 (~P1(f324(f324(f326(x131341),x131342),f191(f871(x131341,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(13137,plain, % 181.73/181.62 (~P1(f324(f324(f326(x131371),x131372),f191(f871(x131371,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(13138,plain, % 181.73/181.62 (E(f76(x131381,x131382,x131383,x131383,x131384),x131384)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(13139,plain, % 181.73/181.62 (P27(x131391,x131391,f5(x131391),x131392)), % 181.73/181.62 inference(rename_variables,[],[3509])). % 181.73/181.62 cnf(13143,plain, % 181.73/181.62 (E(f76(x131431,x131432,x131433,x131433,x131434),x131434)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(13149,plain, % 181.73/181.62 (E(f76(x131491,x131492,x131493,x131493,x131494),x131494)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(13150,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x131501),x131501))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(13153,plain, % 181.73/181.62 (E(f76(x131531,x131532,x131533,x131533,x131534),x131534)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(13154,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x131541),x131541))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(13157,plain, % 181.73/181.62 (E(f76(x131571,x131572,x131573,x131573,x131574),x131574)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(13158,plain, % 181.73/181.62 (P1(f324(f324(f238(a1),x131581),x131581))), % 181.73/181.62 inference(rename_variables,[],[3269])). % 181.73/181.62 cnf(13169,plain, % 181.73/181.62 (P1(f324(f324(f238(a865),f2(a865)),x131691))), % 181.73/181.62 inference(rename_variables,[],[3290])). % 181.73/181.62 cnf(13170,plain, % 181.73/181.62 (P1(f324(f324(f239(a865),f2(a865)),f324(a115,x131701)))), % 181.73/181.62 inference(rename_variables,[],[3349])). % 181.73/181.62 cnf(13171,plain, % 181.73/181.62 (E(f76(x131711,x131712,x131713,x131713,x131714),x131714)), % 181.73/181.62 inference(rename_variables,[],[3926])). % 181.73/181.62 cnf(13240,plain, % 181.73/181.62 (P1(f324(f324(f239(a1),f2(a1)),f324(f75(a1),f79(a1))))), % 181.73/181.62 inference(scs_inference,[],[4562,3929,12408,12430,12590,12592,12594,13017,3509,11020,12084,12184,12187,12279,12321,12325,12333,12402,12519,12521,12964,12970,12975,12979,12985,12988,12994,13022,13131,13139,3518,12148,12622,12624,3519,12218,3235,12599,12601,3236,12541,3202,12484,4490,4491,11657,4222,12631,12634,3239,12582,3079,4118,12781,3137,12547,3926,10146,10152,10216,10219,10309,10312,10603,10623,10887,10890,11297,11300,11315,11318,11366,11369,11372,11375,11385,11422,11435,11465,11468,11479,11484,11490,11585,11588,11591,11595,11605,11699,11734,12054,12255,12464,12517,12533,12535,12537,12551,12553,12555,12580,12609,12611,12845,13006,13046,13138,13143,13149,13153,13157,13171,4471,3569,4449,10149,10159,10173,10282,10285,10288,10391,10504,10810,10992,10995,11012,11015,11215,11303,11310,11324,11378,11381,11493,11540,11556,11869,11894,11906,11938,12036,12144,12151,12314,12372,12515,12644,13048,13056,4467,10375,10468,10916,3325,3288,12586,3478,11841,4461,12715,12730,13076,2870,2871,2874,2875,2878,2879,2881,2882,2883,2885,2886,2889,2890,2891,2892,2893,2896,2897,2901,2902,2906,2910,2913,2920,2923,2928,2931,2932,2933,2942,2946,2948,2961,2965,2966,2971,2981,2982,2985,2993,2999,3006,3018,3021,3022,3028,3029,3030,3031,3038,3045,4444,3060,3136,4445,3604,3250,3310,3222,3843,3198,11582,12346,12350,12354,3210,3321,3725,3336,10166,11835,12028,12405,12487,3964,3100,3103,4463,3817,11350,3324,12574,3162,3128,3586,3641,12614,3122,3322,3936,3144,3646,3109,3110,3083,3089,3143,3326,10759,10884,12145,12362,3196,3197,3220,10416,3373,4543,10345,3901,4482,10207,10372,11212,12306,12347,12351,4489,12318,3259,11680,11683,12933,13052,13105,13109,13113,4532,10942,11025,11258,11261,3666,3256,3374,3592,3366,3340,12572,3159,3160,10274,10579,4520,3431,3151,3080,3209,3264,3181,11340,4051,12336,12476,3903,10948,11091,11143,12290,12296,12419,12422,12451,12472,4555,10862,11096,11206,11228,11266,11272,12234,4556,10981,11099,11209,4557,11102,11154,4558,11157,4559,3180,3471,12190,12231,12317,3629,4338,4339,3454,4480,11331,3570,3607,3781,3539,12828,12832,12836,12840,12850,3827,12181,3457,3707,3337,10293,10411,10482,10543,10546,10582,10680,10932,11777,11865,11928,12004,12045,12122,12125,12455,12650,12709,12752,12755,12811,13055,13060,3718,11573,3252,3349,11695,12643,13170,3534,4526,10184,10187,10213,10688,10701,10820,11250,11343,11749,11754,11776,11980,11983,12066,12075,12237,12340,12655,12674,12677,12701,12756,12915,12920,12940,12945,4538,11454,11487,11524,11553,12765,12769,3705,3479,3480,12680,12683,12686,12689,12723,12726,13088,13092,13096,3852,3443,13093,3444,13089,3296,3298,3271,4523,3158,4477,3657,4191,3973,3463,4539,4045,11223,3591,3309,11705,11708,12155,12259,12433,4015,3972,11858,12205,3913,10756,12016,12039,12212,12361,12458,12909,13104,3961,13108,3967,10951,12081,12154,12211,12258,12936,3968,3630,11868,12011,12089,12135,4004,3648,10954,11030,11117,11176,12035,12103,12367,12429,12448,12461,12906,12969,12974,12997,13025,4544,10704,11107,12215,12982,3268,10302,10398,10529,10589,10660,10707,10710,10743,10767,10804,10842,10878,11434,11651,11698,11838,11893,11909,11912,11915,11918,12096,12110,12113,12116,12119,12198,12262,12378,12425,12702,12729,12803,12814,12819,12822,12825,12858,12869,12926,12951,12954,13043,3269,10331,10386,10594,10683,10807,11427,11496,11733,11737,11746,11844,11855,11874,11879,11921,11941,11958,12720,12862,12882,12916,12921,12941,12946,13150,13154,13158,3270,3345,12069,12785,12829,12833,12837,12841,12851,12855,4522,10250,10340,10453,10477,10725,10770,10780,11503,11604,11626,11629,11632,11648,11808,11811,11814,11817,11905,11924,11927,11937,11992,11995,11998,12001,12076,12166,12169,12265,12268,12339,12371,12411,12496,3426,10549,10815,10859,11165,11247,11414,11660,12313,12499,12902,13014,13029,4534,10734,10746,10851,10869,10872,10945,11046,11054,11070,11110,11128,11137,11173,11218,11238,11241,11244,11275,11282,11285,11677,11714,11986,11989,12023,12070,12099,12243,12287,12293,12390,12393,12415,12475,12481,12490,12509,12784,12797,12800,12891,13010,13036,13039,13085,13134,13137,3330,10576,10606,10615,11198,11761,12412,12426,12766,12770,12773,3369,13069,13126,3363,3785,3723,10253,11576,11608,12747,4531,10204,10564,10567,11049,11067,11539,11594,11636,11661,11767,11796,11799,11802,11805,12065,12957,3290,10609,10764,10835,11609,11766,11963,12174,12199,12794,13072,13169,3746,11711,12696,4095,3485,4529,3757,3793,4512,4515,4516,3242,3247,4514,4513,4517,4275,3764,3581,11569,4197,4546,10178,10181,10434,10485,10488,10493,10919,11408,11664,11770,4553,11131,11255,11291,3981,12226,3869,11288,11635,11639,11702,12324,12332,12418,12714,12963,13021,3712,10875,10881,10903,11890,12102,12386,3567,11005,11134,12128,12240,12250,12329,12381,12389,12506,4049,3714,10612,10970,11140,11170,11183,12328,12375,13002,3535,10532,10535,10618,10791,3537,4550,11570,4540,4545,12664,4551,10671,10773,11411,11440,12193,12202,12246,12445,12503,4155,10749,12223,12249,4056,3745,12512,3692,3693,4548,10226,10229,10570,10573,11451,11640,12454,4549,11550,11645,3716,10538,10797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% 181.73/181.62 cnf(13403,plain, % 181.73/181.62 (E(f324(x134031,f661(f324(x134031,x134032),f324(f233(x134033),x134032),x134031,x134034,x134033)),f324(x134031,x134032))), % 181.73/181.62 inference(rename_variables,[],[11082])). % 181.73/181.62 cnf(13421,plain, % 181.73/181.62 (~P1(f324(f324(f238(a865),f324(a115,x134211)),x134211))), % 181.73/181.62 inference(rename_variables,[],[4531])). % 181.73/181.62 cnf(13435,plain, % 181.73/181.62 (~E(f324(f324(f145(x134351),x134352),x134353),x134353)), % 181.73/181.62 inference(rename_variables,[],[4482])). % 181.73/181.62 cnf(13438,plain, % 181.73/181.62 (~P1(f324(f324(f326(f870(x134381,x134381)),x134382),f256(x134381,f191(f871(x134381,a859)))))), % 181.73/181.62 inference(rename_variables,[],[10868])). % 181.73/181.62 cnf(13446,plain, % 181.73/181.62 (~P1(f324(f324(f326(x134461),x134462),f191(f871(x134461,a859))))), % 181.73/181.62 inference(rename_variables,[],[4534])). % 181.73/181.62 cnf(13486,plain, % 181.73/181.62 (~P1(f324(f324(f326(a865),x134861),f324(f245(a865),f2(a865))))), % 181.73/181.62 inference(rename_variables,[],[11730])). % 181.73/181.62 cnf(13491,plain, % 181.73/181.62 (~P1(f324(f324(f326(a865),x134911),f324(f245(a865),f2(a865))))), % 181.73/181.62 inference(rename_variables,[],[11730])). % 181.73/181.62 cnf(13512,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x135121,a859)),x135122),x135122))), % 181.73/181.62 inference(rename_variables,[],[3567])). % 181.73/181.62 cnf(13526,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x135261,a859)),f324(f167(x135261),f171(x135261,x135262,x135263))),f324(f167(x135261),x135262)))), % 181.73/181.62 inference(rename_variables,[],[3967])). % 181.73/181.62 cnf(13529,plain, % 181.73/181.62 (P1(f324(f324(f238(f871(x135291,a859)),f324(f167(x135291),f171(x135291,x135292,x135293))),f324(f167(x135291),x135292)))), % 181.73/181.62 inference(rename_variables,[],[3967])). % 181.73/181.62 cnf(13571,plain, % 181.73/181.62 ($false), % 181.73/181.62 inference(scs_inference,[],[3298,4051,3852,3271,4550,4523,4555,3363,3718,4534,13446,3967,13526,13529,4482,13435,3349,4045,3723,3567,13512,3716,3926,3198,3629,4559,4531,13421,4551,4549,3478,11470,10236,11793,11279,13240,12442,10682,11082,13403,10855,10349,12953,10627,11611,12239,11728,11730,13486,13491,10868,13438,10871,12015,2911,12,5196,5376,9329,9665,5993,8451,5781,6512,7175,7241,8452,9081,7577,9159,8573,9435,5041,5702,8966,4886,5454,6319,6354,5529,8861,5661,8444,6661,8615,4970,5427,5654,8197,5294,5291,5727,7840,9370,8748,4696,5028,6713,8729,9881,5854,6017,7908,5715,4840,8383,6128,6078,8427,8563,9157,5146,5410,6036,9107,9415,6363,8499,9868,5368,8602,5742,8619,4971,5088,6884,4679]), % 181.73/181.62 ['proof']). % 181.73/181.62 % SZS output end Proof % 181.73/181.62 % Total time :157.560000s %------------------------------------------------------------------------------